|\^/| Maple 18 (X86 64 WINDOWS)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2014
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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#BEGIN OUTFILE1
# before write maple top matter
# before write_ats library and user def block
#BEGIN ATS LIBRARY BLOCK
# Begin Function number 2
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s\n",str);
> fi;# end if 1;
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
# End Function number 2
# Begin Function number 3
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s",str);
> fi;# end if 1;
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
# End Function number 3
# Begin Function number 4
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> print(label,str);
> fi;# end if 1;
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
# End Function number 4
# Begin Function number 5
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 5
# Begin Function number 6
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> if vallen = 5 then # if number 1
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 6
# Begin Function number 7
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;# end if 0;
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
print(prelabel, "[", elemnt, "]", value, postlabel)
end if
end proc
# End Function number 7
# Begin Function number 8
> logitem_time := proc(fd,secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> fprintf(fd,"
");
> if (secs_in >= 0) then # if number 0
> years_int := int_trunc(secs_in / glob_sec_in_year);
> sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
> days_int := int_trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := sec_temp mod int_trunc(glob_sec_in_day) ;
> hours_int := int_trunc(sec_temp / glob_sec_in_hour);
> sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
> minutes_int := int_trunc(sec_temp / glob_sec_in_minute);
> sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
> if (years_int > 0) then # if number 1
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 2
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 3
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 4
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 4
> else
> fprintf(fd," 0.0 Seconds");
> fi;# end if 3
> fprintf(fd," | \n");
> end;
logitem_time := proc(fd, secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
fprintf(fd, "");
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, " 0.0 Seconds")
end if;
fprintf(fd, " | \n")
end proc
# End Function number 8
# Begin Function number 9
> omniout_timestr := proc(secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> if (secs_in >= 0) then # if number 3
> years_int := int_trunc(secs_in / glob_sec_in_year);
> sec_temp := (int_trunc(secs_in) mod int_trunc(glob_sec_in_year));
> days_int := int_trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_day)) ;
> hours_int := int_trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_hour));
> minutes_int := int_trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod int_trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 4
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 5
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 6
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 7
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 7
> else
> printf(" 0.0 Seconds\n");
> fi;# end if 6
> end;
omniout_timestr := proc(secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" 0.0 Seconds\n")
end if
end proc
# End Function number 9
# Begin Function number 10
> zero_ats_ar := proc(arr_a)
> global ATS_MAX_TERMS;
> local iii;
> iii := 1;
> while (iii <= ATS_MAX_TERMS) do # do number 1
> arr_a [iii] := glob__0;
> iii := iii + 1;
> od;# end do number 1
> end;
zero_ats_ar := proc(arr_a)
local iii;
global ATS_MAX_TERMS;
iii := 1;
while iii <= ATS_MAX_TERMS do arr_a[iii] := glob__0; iii := iii + 1
end do
end proc
# End Function number 10
# Begin Function number 11
> ats := proc(mmm_ats,arr_a,arr_b,jjj_ats)
> global ATS_MAX_TERMS;
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := glob__0;
> if (jjj_ats <= mmm_ats) then # if number 6
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> if ((lll_ats <= ATS_MAX_TERMS and (iii_ats <= ATS_MAX_TERMS) )) then # if number 7
> ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]);
> fi;# end if 7;
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 6;
> ret_ats;
> end;
ats := proc(mmm_ats, arr_a, arr_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
global ATS_MAX_TERMS;
ret_ats := glob__0;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
if lll_ats <= ATS_MAX_TERMS and iii_ats <= ATS_MAX_TERMS then
ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats])
end if;
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
# End Function number 11
# Begin Function number 12
> att := proc(mmm_att,arr_aa,arr_bb,jjj_att)
> global ATS_MAX_TERMS;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := glob__0;
> if (jjj_att < mmm_att) then # if number 6
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while ((iii_att < mmm_att) and (iii_att <= ATS_MAX_TERMS) ) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if ((lll_att <= ATS_MAX_TERMS and (iii_att <= ATS_MAX_TERMS) )) then # if number 7
> ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att);
> fi;# end if 7;
> iii_att := iii_att + 1;
> od;# end do number 1;
> ret_att := ret_att / c(mmm_att) ;
> fi;# end if 6;
> ret_att;
> end;
att := proc(mmm_att, arr_aa, arr_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global ATS_MAX_TERMS;
ret_att := glob__0;
if jjj_att < mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att < mmm_att and iii_att <= ATS_MAX_TERMS do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= ATS_MAX_TERMS and iii_att <= ATS_MAX_TERMS then
ret_att :=
ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])*c(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/c(mmm_att)
end if;
ret_att
end proc
# End Function number 12
# Begin Function number 13
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
# End Function number 13
# Begin Function number 14
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
# End Function number 14
# Begin Function number 15
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
# End Function number 15
# Begin Function number 16
> logitem_good_digits := proc(file,rel_error)
> global glob_small_float,glob_prec;
> local good_digits;
> fprintf(file,"");
> fprintf(file,"%d",glob_min_good_digits);
> fprintf(file," | ");
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float, glob_prec;
fprintf(file, "");
fprintf(file, "%d", glob_min_good_digits);
fprintf(file, " | ")
end proc
# End Function number 16
# Begin Function number 17
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
# End Function number 17
# Begin Function number 18
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
# End Function number 18
# Begin Function number 19
> logitem_h_reason := proc(file)
> global glob_h_reason;
> fprintf(file,"");
> if (glob_h_reason = 1) then # if number 6
> fprintf(file,"Max H");
> elif
> (glob_h_reason = 2) then # if number 7
> fprintf(file,"Display Interval");
> elif
> (glob_h_reason = 3) then # if number 8
> fprintf(file,"Optimal");
> elif
> (glob_h_reason = 4) then # if number 9
> fprintf(file,"Pole Accuracy");
> elif
> (glob_h_reason = 5) then # if number 10
> fprintf(file,"Min H (Pole)");
> elif
> (glob_h_reason = 6) then # if number 11
> fprintf(file,"Pole");
> elif
> (glob_h_reason = 7) then # if number 12
> fprintf(file,"Opt Iter");
> else
> fprintf(file,"Impossible");
> fi;# end if 12
> fprintf(file," | ");
> end;
logitem_h_reason := proc(file)
global glob_h_reason;
fprintf(file, "");
if glob_h_reason = 1 then fprintf(file, "Max H")
elif glob_h_reason = 2 then fprintf(file, "Display Interval")
elif glob_h_reason = 3 then fprintf(file, "Optimal")
elif glob_h_reason = 4 then fprintf(file, "Pole Accuracy")
elif glob_h_reason = 5 then fprintf(file, "Min H (Pole)")
elif glob_h_reason = 6 then fprintf(file, "Pole")
elif glob_h_reason = 7 then fprintf(file, "Opt Iter")
else fprintf(file, "Impossible")
end if;
fprintf(file, " | ")
end proc
# End Function number 19
# Begin Function number 20
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
# End Function number 20
# Begin Function number 21
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file) fprintf(file, "\n") end proc
# End Function number 21
# Begin Function number 22
> chk_data := proc()
> global glob_max_iter,ALWAYS, ATS_MAX_TERMS;
> local errflag;
> errflag := false;
> if (glob_max_iter < 2) then # if number 12
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 12;
> if (errflag) then # if number 12
> quit;
> fi;# end if 12
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, ATS_MAX_TERMS;
errflag := false;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
# End Function number 22
# Begin Function number 23
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := c(clock_sec2);
> sub1 := c(t_end2-t_start2);
> sub2 := c(t2-t_start2);
> if (sub1 = glob__0) then # if number 12
> sec_left := glob__0;
> else
> if (sub2 > glob__0) then # if number 13
> rrr := (sub1/sub2);
> sec_left := rrr * c(ms2) - c(ms2);
> else
> sec_left := glob__0;
> fi;# end if 13
> fi;# end if 12;
> sec_left;
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := c(clock_sec2);
sub1 := c(t_end2 - t_start2);
sub2 := c(t2 - t_start2);
if sub1 = glob__0 then sec_left := glob__0
else
if glob__0 < sub2 then
rrr := sub1/sub2; sec_left := rrr*c(ms2) - c(ms2)
else sec_left := glob__0
end if
end if;
sec_left
end proc
# End Function number 23
# Begin Function number 24
> comp_percent := proc(t_end2,t_start2, t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub2 > glob_small_float) then # if number 12
> rrr := (glob__100*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 12;
> rrr;
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < sub2 then rrr := glob__100*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
# End Function number 24
# Begin Function number 25
> comp_rad_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 12
> ret := float_abs(term1 * glob_h / term2);
> else
> ret := glob_larger_float;
> fi;# end if 12;
> ret;
> #BOTTOM TWO TERM RADIUS ANALYSIS
> end;
comp_rad_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := float_abs(term1*glob_h/term2)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 25
# Begin Function number 26
> comp_ord_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM ORDER ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 12
> ret := glob__1 + float_abs(term2) * c(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(c(last_no));
> else
> ret := glob_larger_float;
> fi;# end if 12;
> ret;
> #BOTTOM TWO TERM ORDER ANALYSIS
> end;
comp_ord_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := glob__1 + float_abs(term2)*
c(last_no)*ln(float_abs(term1*glob_h/term2))/ln(c(last_no))
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 26
# Begin Function number 27
> c := proc(in_val)
> #To Force Conversion when needed
> local ret;
> ret := evalf(in_val);
> ret;
> #End Conversion
> end;
c := proc(in_val) local ret; ret := evalf(in_val); ret end proc
# End Function number 27
# Begin Function number 28
> comp_rad_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret,temp;
> temp := float_abs(term2*term2*c(last_no)+glob__m2*term2*term2-term1*term3*c(last_no)+term1*term3);
> if (float_abs(temp) > glob__0) then # if number 12
> ret := float_abs((term2*glob_h*term1)/(temp));
> else
> ret := glob_larger_float;
> fi;# end if 12;
> ret;
> #BOTTOM THREE TERM RADIUS ANALYSIS
> end;
comp_rad_from_three_terms := proc(term1, term2, term3, last_no)
local ret, temp;
global glob_h, glob_larger_float;
temp := float_abs(term2*term2*c(last_no) + glob__m2*term2*term2
- term1*term3*c(last_no) + term1*term3);
if glob__0 < float_abs(temp) then
ret := float_abs(term2*glob_h*term1/temp)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 28
# Begin Function number 29
> comp_ord_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM ORDER ANALYSIS
> local ret;
> ret := float_abs((glob__4*term1*term3*c(last_no)-glob__3*term1*term3-glob__4*term2*term2*c(last_no)+glob__4*term2*term2+term2*term2*c(last_no*last_no)-term1*term3*c(last_no*last_no))/(term2*term2*c(last_no)-glob__2*term2*term2-term1*term3*c(last_no)+term1*term3));
> ret;
> #TOP THREE TERM ORDER ANALYSIS
> end;
comp_ord_from_three_terms := proc(term1, term2, term3, last_no)
local ret;
ret := float_abs((glob__4*term1*term3*c(last_no) - glob__3*term1*term3
- glob__4*term2*term2*c(last_no) + glob__4*term2*term2
+ term2*term2*c(last_no*last_no) - term1*term3*c(last_no*last_no))
/(term2*term2*c(last_no) - glob__2*term2*term2
- term1*term3*c(last_no) + term1*term3));
ret
end proc
# End Function number 29
# Begin Function number 30
> comp_rad_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> #TOP SIX TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float,glob_six_term_ord_save;
> local ret,rm0,rm1,rm2,rm3,rm4,nr1,nr2,dr1,dr2,ds2,rad_c,ord_no,ds1,rcs;
> if ((term5 <> glob__0) and (term4 <> glob__0) and (term3 <> glob__0) and (term2 <> glob__0) and (term1 <> glob__0)) then # if number 12
> rm0 := term6/term5;
> rm1 := term5/term4;
> rm2 := term4/term3;
> rm3 := term3/term2;
> rm4 := term2/term1;
> nr1 := c(last_no-1)*rm0 - glob__2*c(last_no-2)*rm1 + c(last_no-3)*rm2;
> nr2 := c(last_no-2)*rm1 - glob__2*c(last_no-3)*rm2 + c(last_no-4)*rm3;
> dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
> dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
> ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
> ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
> if ((float_abs(nr1 * dr2 - nr2 * dr1) = glob__0) or (float_abs(dr1) = glob__0)) then # if number 13
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> else
> if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0) then # if number 14
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) -c(last_no)/glob__2;
> if (float_abs(rcs) <> glob__0) then # if number 15
> if (rcs > glob__0) then # if number 16
> rad_c := sqrt(rcs) * float_abs(glob_h);
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 16
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 15
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 14
> fi;# end if 13
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 12;
> glob_six_term_ord_save := ord_no;
> rad_c;
> #BOTTOM SIX TERM RADIUS ANALYSIS
> end;
comp_rad_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
local ret, rm0, rm1, rm2, rm3, rm4, nr1, nr2, dr1, dr2, ds2, rad_c, ord_no,
ds1, rcs;
global glob_h, glob_larger_float, glob_six_term_ord_save;
if term5 <> glob__0 and term4 <> glob__0 and term3 <> glob__0 and
term2 <> glob__0 and term1 <> glob__0 then
rm0 := term6/term5;
rm1 := term5/term4;
rm2 := term4/term3;
rm3 := term3/term2;
rm4 := term2/term1;
nr1 := c(last_no - 1)*rm0 - glob__2*c(last_no - 2)*rm1
+ c(last_no - 3)*rm2;
nr2 := c(last_no - 2)*rm1 - glob__2*c(last_no - 3)*rm2
+ c(last_no - 4)*rm3;
dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
if
float_abs(nr1*dr2 - nr2*dr1) = glob__0 or float_abs(dr1) = glob__0
then rad_c := glob_larger_float; ord_no := glob_larger_float
else
if glob__0 < float_abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no :=
(rcs*nr1 - ds1)/(glob__2*dr1) - c(last_no)/glob__2;
if float_abs(rcs) <> glob__0 then
if glob__0 < rcs then
rad_c := sqrt(rcs)*float_abs(glob_h)
else
rad_c := glob_larger_float;
ord_no := glob_larger_float
end if
else
rad_c := glob_larger_float; ord_no := glob_larger_float
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if;
glob_six_term_ord_save := ord_no;
rad_c
end proc
# End Function number 30
# Begin Function number 31
> comp_ord_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> global glob_six_term_ord_save;
> #TOP SIX TERM ORDER ANALYSIS
> #TOP SAVED FROM SIX TERM RADIUS ANALYSIS
> glob_six_term_ord_save;
> #BOTTOM SIX TERM ORDER ANALYSIS
> end;
comp_ord_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
global glob_six_term_ord_save;
glob_six_term_ord_save
end proc
# End Function number 31
# Begin Function number 32
> factorial_2 := proc(nnn)
> ret := nnn!;
> ret;;
> end;
Warning, `ret` is implicitly declared local to procedure `factorial_2`
factorial_2 := proc(nnn) local ret; ret := nnn!; ret end proc
# End Function number 32
# Begin Function number 33
> factorial_1 := proc(nnn)
> global ATS_MAX_TERMS,array_fact_1;
> local ret;
> if (nnn <= ATS_MAX_TERMS) then # if number 12
> if (array_fact_1[nnn] = 0) then # if number 13
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 13;
> else
> ret := factorial_2(nnn);
> fi;# end if 12;
> ret;
> end;
factorial_1 := proc(nnn)
local ret;
global ATS_MAX_TERMS, array_fact_1;
if nnn <= ATS_MAX_TERMS then
if array_fact_1[nnn] = 0 then
ret := factorial_2(nnn); array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := factorial_2(nnn)
end if;
ret
end proc
# End Function number 33
# Begin Function number 34
> factorial_3 := proc(mmm,nnn)
> global ATS_MAX_TERMS,array_fact_2;
> local ret;
> if ((nnn <= ATS_MAX_TERMS) and (mmm <= ATS_MAX_TERMS)) then # if number 12
> if (array_fact_2[mmm,nnn] = 0) then # if number 13
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 13;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 12;
> ret;
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global ATS_MAX_TERMS, array_fact_2;
if nnn <= ATS_MAX_TERMS and mmm <= ATS_MAX_TERMS then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := factorial_2(mmm)/factorial_2(nnn)
end if;
ret
end proc
# End Function number 34
# Begin Function number 35
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
# End Function number 35
# Begin Function number 36
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
# End Function number 36
# Begin Function number 37
> float_abs := proc(x)
> abs(x);
> end;
float_abs := proc(x) abs(x) end proc
# End Function number 37
# Begin Function number 38
> expt := proc(x,y)
> x^y;
> end;
expt := proc(x, y) x^y end proc
# End Function number 38
# Begin Function number 39
> neg := proc(x)
> -x;
> end;
neg := proc(x) -x end proc
# End Function number 39
# Begin Function number 40
> int_trunc := proc(x)
> trunc(x);
> end;
int_trunc := proc(x) trunc(x) end proc
# End Function number 40
# Begin Function number 41
> estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer)
> local desired_abs_gbl_error,range,estimated_steps,step_error;
> global glob_desired_digits_correct,ALWAYS,ATS_MAX_TERMS;
> omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
> desired_abs_gbl_error := expt(glob__10,c( -glob_desired_digits_correct)) * c(float_abs(c(estimated_answer)));
> omniout_float(ALWAYS,"estimated_h",32,estimated_h,32,"");
> omniout_float(ALWAYS,"estimated_answer",32,estimated_answer,32,"");
> omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,"");
> range := (x_end - x_start);
> omniout_float(ALWAYS,"range",32,range,32,"");
> estimated_steps := range / estimated_h;
> omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,"");
> step_error := (c(float_abs(desired_abs_gbl_error) /sqrt(c( estimated_steps))/c(ATS_MAX_TERMS)));
> omniout_float(ALWAYS,"step_error",32,step_error,32,"");
> (step_error);;
> end;
estimated_needed_step_error := proc(
x_start, x_end, estimated_h, estimated_answer)
local desired_abs_gbl_error, range, estimated_steps, step_error;
global glob_desired_digits_correct, ALWAYS, ATS_MAX_TERMS;
omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, "");
desired_abs_gbl_error :=
expt(glob__10, c(-glob_desired_digits_correct))*
c(float_abs(c(estimated_answer)));
omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, "");
omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, "")
;
omniout_float(ALWAYS, "desired_abs_gbl_error", 32,
desired_abs_gbl_error, 32, "");
range := x_end - x_start;
omniout_float(ALWAYS, "range", 32, range, 32, "");
estimated_steps := range/estimated_h;
omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, "");
step_error := c(float_abs(desired_abs_gbl_error)/(
sqrt(c(estimated_steps))*c(ATS_MAX_TERMS)));
omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
step_error
end proc
# End Function number 41
#END ATS LIBRARY BLOCK
#BEGIN USER FUNCTION BLOCK
#BEGIN BLOCK 3
#BEGIN USER DEF BLOCK
> exact_soln_y1 := proc(x)
> return(neg(cos(c(x))));
> end;
exact_soln_y1 := proc(x) return neg(cos(c(x))) end proc
> exact_soln_y2 := proc(x)
> return(neg(sin(c(x))));
> end;
exact_soln_y2 := proc(x) return neg(sin(c(x))) end proc
> exact_soln_y2p := proc(x)
> return(neg(cos(c(x))));
> end;
exact_soln_y2p := proc(x) return neg(cos(c(x))) end proc
#END USER DEF BLOCK
#END BLOCK 3
#END USER FUNCTION BLOCK
# before write_aux functions
# Begin Function number 2
> display_poles := proc()
> local rad_given;
> global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ;
> if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1
> rad_given := sqrt((array_x[1] - array_given_rad_poles[1,1]) * (array_x[1] - array_given_rad_poles[1,1]) + array_given_rad_poles[1,2] * array_given_rad_poles[1,2]);
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," ");
> omniout_float(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," ");
> if (rad_given < glob_least_given_sing) then # if number 2
> glob_least_given_sing := rad_given;
> fi;# end if 2;
> elif
> (glob_type_given_pole = 3) then # if number 2
> omniout_str(ALWAYS,"NO POLE (given) for Equation 1");
> elif
> (glob_type_given_pole = 5) then # if number 3
> omniout_str(ALWAYS,"SOME POLE (given) for Equation 1");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 1");
> fi;# end if 3;
> if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," ");
> if (array_rad_test_poles[1,1]< glob_least_ratio_sing) then # if number 4
> glob_least_ratio_sing := array_rad_test_poles[1,1];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," ");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," ");
> if (array_rad_test_poles[1,2]< glob_least_3_sing) then # if number 4
> glob_least_3_sing := array_rad_test_poles[1,2];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," ");
> if (array_rad_test_poles[1,3]< glob_least_6_sing) then # if number 4
> glob_least_6_sing := array_rad_test_poles[1,3];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1");
> fi;# end if 3
> ;
> if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 3
> rad_given := sqrt((array_x[1] - array_given_rad_poles[2,1]) * (array_x[1] - array_given_rad_poles[2,1]) + array_given_rad_poles[2,2] * array_given_rad_poles[2,2]);
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 2 ",4,rad_given,4," ");
> omniout_float(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[2,1],4," ");
> if (rad_given < glob_least_given_sing) then # if number 4
> glob_least_given_sing := rad_given;
> fi;# end if 4;
> elif
> (glob_type_given_pole = 3) then # if number 4
> omniout_str(ALWAYS,"NO POLE (given) for Equation 2");
> elif
> (glob_type_given_pole = 5) then # if number 5
> omniout_str(ALWAYS,"SOME POLE (given) for Equation 2");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 2");
> fi;# end if 5;
> if (array_rad_test_poles[2,1] < glob_large_float) then # if number 5
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 2 ",4,array_rad_test_poles[2,1],4," ");
> if (array_rad_test_poles[2,1]< glob_least_ratio_sing) then # if number 6
> glob_least_ratio_sing := array_rad_test_poles[2,1];
> fi;# end if 6;
> omniout_float(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[2,1],4," ");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 2");
> fi;# end if 5;
> if ((array_rad_test_poles[2,2] > glob__small) and (array_rad_test_poles[2,2] < glob_large_float)) then # if number 5
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 2 ",4,array_rad_test_poles[2,2],4," ");
> if (array_rad_test_poles[2,2]< glob_least_3_sing) then # if number 6
> glob_least_3_sing := array_rad_test_poles[2,2];
> fi;# end if 6;
> omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[2,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 2");
> fi;# end if 5;
> if ((array_rad_test_poles[2,3] > glob__small) and (array_rad_test_poles[2,3] < glob_large_float)) then # if number 5
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 2 ",4,array_rad_test_poles[2,3],4," ");
> if (array_rad_test_poles[2,3]< glob_least_6_sing) then # if number 6
> glob_least_6_sing := array_rad_test_poles[2,3];
> fi;# end if 6;
> omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[2,3],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 2");
> fi;# end if 5
> ;
> 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;
if glob_type_given_pole = 1 or glob_type_given_pole = 2 then
rad_given := sqrt((array_x[1] - array_given_rad_poles[2, 1])*
(array_x[1] - array_given_rad_poles[2, 1])
+ array_given_rad_poles[2, 2]*array_given_rad_poles[2, 2]);
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 2 ", 4,
rad_given, 4, " ");
omniout_float(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles[2, 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 2")
elif glob_type_given_pole = 5 then
omniout_str(ALWAYS, "SOME POLE (given) for Equation 2")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 2")
end if;
if array_rad_test_poles[2, 1] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (ratio test) for eq 2 ", 4,
array_rad_test_poles[2, 1], 4, " ");
if array_rad_test_poles[2, 1] < glob_least_ratio_sing then
glob_least_ratio_sing := array_rad_test_poles[2, 1]
end if;
omniout_float(ALWAYS,
"Order of pole (ratio test) ", 4,
array_ord_test_poles[2, 1], 4, " ")
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 2")
end if;
if glob__small < array_rad_test_poles[2, 2] and
array_rad_test_poles[2, 2] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 2 ", 4,
array_rad_test_poles[2, 2], 4, " ");
if array_rad_test_poles[2, 2] < glob_least_3_sing then
glob_least_3_sing := array_rad_test_poles[2, 2]
end if;
omniout_float(ALWAYS,
"Order of pole (three term test) ", 4,
array_ord_test_poles[2, 2], 4, " ")
else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 2")
end if;
if glob__small < array_rad_test_poles[2, 3] and
array_rad_test_poles[2, 3] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 2 ", 4,
array_rad_test_poles[2, 3], 4, " ");
if array_rad_test_poles[2, 3] < glob_least_6_sing then
glob_least_6_sing := array_rad_test_poles[2, 3]
end if;
omniout_float(ALWAYS,
"Order of pole (six term test) ", 4,
array_ord_test_poles[2, 3], 4, " ")
else omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 2")
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 5
> ret := glob__1;
> else
> ret := glob__m1;
> fi;# end if 5;
> 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_2,
#END CONST
> array_y1_init,
> array_y2_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_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_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_y1[1]) < min_size) then # if number 5
> min_size := float_abs(array_y1[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 5;
> if (float_abs(array_y2[1]) < min_size) then # if number 5
> min_size := float_abs(array_y2[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 5;
> if (min_size < glob__1) then # if number 5
> min_size := glob__1;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 5;
> 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_2,
array_y1_init, array_y2_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_y1, array_x, array_y2,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_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_y1[1]) < min_size then
min_size := float_abs(array_y1[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if float_abs(array_y2[1]) < min_size then
min_size := float_abs(array_y2[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_2,
#END CONST
> array_y1_init,
> array_y2_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_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_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_y1[no_terms-3] + array_y1[no_terms - 2] * hn_div_ho + array_y1[no_terms - 1] * hn_div_ho_2 + array_y1[no_terms] * hn_div_ho_3);
> if (est_tmp >= max_estimated_step_error) then # if number 5
> max_estimated_step_error := est_tmp;
> fi;# end if 5;
> est_tmp := float_abs(array_y2[no_terms-3] + array_y2[no_terms - 2] * hn_div_ho + array_y2[no_terms - 1] * hn_div_ho_2 + array_y2[no_terms] * hn_div_ho_3);
> if (est_tmp >= max_estimated_step_error) then # if number 5
> max_estimated_step_error := est_tmp;
> fi;# end if 5;
> 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_2,
array_y1_init, array_y2_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_y1, array_x, array_y2,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_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_y1[no_terms - 3]
+ array_y1[no_terms - 2]*hn_div_ho
+ array_y1[no_terms - 1]*hn_div_ho_2
+ array_y1[no_terms]*hn_div_ho_3);
if max_estimated_step_error <= est_tmp then
max_estimated_step_error := est_tmp
end if;
est_tmp := float_abs(array_y2[no_terms - 3]
+ array_y2[no_terms - 2]*hn_div_ho
+ array_y2[no_terms - 1]*hn_div_ho_2
+ array_y2[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_2,
#END CONST
> array_y1_init,
> array_y2_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_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_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_y1[no_terms-3])) + c(float_abs(array_y1[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y1[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y1[no_terms])) * c(hn_div_ho_3);
> if (glob_prec * c(float_abs(array_y1[1])) > c(est_tmp)) then # if number 5
> est_tmp := c(glob_prec) * c(float_abs(array_y1[1]));
> fi;# end if 5;
> if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 5
> array_max_est_error[1] := c(est_tmp);
> fi;# end if 5
> ;
> est_tmp := c(float_abs(array_y2[no_terms-3])) + c(float_abs(array_y2[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y2[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y2[no_terms])) * c(hn_div_ho_3);
> if (glob_prec * c(float_abs(array_y2[1])) > c(est_tmp)) then # if number 5
> est_tmp := c(glob_prec) * c(float_abs(array_y2[1]));
> fi;# end if 5;
> if (c(est_tmp) >= c(array_max_est_error[2])) then # if number 5
> array_max_est_error[2] := c(est_tmp);
> fi;# end if 5
> ;
> 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_2,
array_y1_init, array_y2_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_y1, array_x, array_y2,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_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_y1[no_terms - 3]))
+ c(float_abs(array_y1[no_terms - 2]))*c(hn_div_ho)
+ c(float_abs(array_y1[no_terms - 1]))*c(hn_div_ho_2)
+ c(float_abs(array_y1[no_terms]))*c(hn_div_ho_3);
if c(est_tmp) < glob_prec*c(float_abs(array_y1[1])) then
est_tmp := c(glob_prec)*c(float_abs(array_y1[1]))
end if;
if c(array_max_est_error[1]) <= c(est_tmp) then
array_max_est_error[1] := c(est_tmp)
end if;
est_tmp := c(float_abs(array_y2[no_terms - 3]))
+ c(float_abs(array_y2[no_terms - 2]))*c(hn_div_ho)
+ c(float_abs(array_y2[no_terms - 1]))*c(hn_div_ho_2)
+ c(float_abs(array_y2[no_terms]))*c(hn_div_ho_3);
if c(est_tmp) < glob_prec*c(float_abs(array_y2[1])) then
est_tmp := c(glob_prec)*c(float_abs(array_y2[1]))
end if;
if c(array_max_est_error[2]) <= c(est_tmp) then
array_max_est_error[2] := 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_2,
#END CONST
> array_y1_init,
> array_y2_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_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_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 5
> ret := true;
> else
> ret := false;
> fi;# end if 5;
> 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_2,
array_y1_init, array_y2_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_y1, array_x, array_y2,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_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_2,
#END CONST
> array_y1_init,
> array_y2_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_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_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 5
> if (iter >= 0) then # if number 6
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> closed_form_val_y := evalf(exact_soln_y1(ind_var));
> omniout_float(ALWAYS,"y1[1] (closed_form) ",33,closed_form_val_y,20," ");
> term_no := 1;
> numeric_val := array_y1[term_no];
> abserr := float_abs(numeric_val - closed_form_val_y);
> omniout_float(ALWAYS,"y1[1] (numeric) ",33,numeric_val,20," ");
> if (c(float_abs(closed_form_val_y)) > c(glob_prec)) then # if number 7
> relerr := abserr*glob__100/float_abs(closed_form_val_y);
> if (c(relerr) > c(glob_prec)) then # if number 8
> glob_good_digits := -int_trunc(log10(c(relerr))) + 3;
> else
> glob_good_digits := Digits;
> fi;# end if 8;
> else
> relerr := glob__m1 ;
> glob_good_digits := -16;
> fi;# end if 7;
> if (glob_good_digits < glob_min_good_digits) then # if number 7
> glob_min_good_digits := glob_good_digits;
> fi;# end if 7;
> if (glob_apfp_est_good_digits < glob_min_apfp_est_good_digits) then # if number 7
> glob_min_apfp_est_good_digits := glob_apfp_est_good_digits;
> fi;# end if 7;
> if (evalf(float_abs(numeric_val)) > glob_prec) then # if number 7
> est_rel_err := evalf(array_max_est_error[1]*100.0 * sqrt(glob_iter)*36*ATS_MAX_TERMS/float_abs(numeric_val));
> if (evalf(est_rel_err) > glob_prec) then # if number 8
> glob_est_digits := -int_trunc(log10(est_rel_err)) + 3;
> else
> glob_est_digits := Digits;
> fi;# end if 8;
> else
> relerr := glob__m1 ;
> glob_est_digits := -16;
> fi;# end if 7;
> array_est_digits[1] := glob_est_digits;
> if (glob_iter = 1) then # if number 7
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 7;
> array_est_rel_error[1] := est_rel_err;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_int(INFO,"Desired digits ",32,glob_desired_digits_correct,4," ");
> omniout_int(INFO,"Estimated correct digits ",32,glob_est_digits,4," ");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> ;
> closed_form_val_y := evalf(exact_soln_y2(ind_var));
> omniout_float(ALWAYS,"y2[1] (closed_form) ",33,closed_form_val_y,20," ");
> term_no := 1;
> numeric_val := array_y2[term_no];
> abserr := float_abs(numeric_val - closed_form_val_y);
> omniout_float(ALWAYS,"y2[1] (numeric) ",33,numeric_val,20," ");
> if (c(float_abs(closed_form_val_y)) > c(glob_prec)) then # if number 7
> relerr := abserr*glob__100/float_abs(closed_form_val_y);
> if (c(relerr) > c(glob_prec)) then # if number 8
> glob_good_digits := -int_trunc(log10(c(relerr))) + 3;
> else
> glob_good_digits := Digits;
> fi;# end if 8;
> else
> relerr := glob__m1 ;
> glob_good_digits := -16;
> fi;# end if 7;
> if (glob_good_digits < glob_min_good_digits) then # if number 7
> glob_min_good_digits := glob_good_digits;
> fi;# end if 7;
> if (glob_apfp_est_good_digits < glob_min_apfp_est_good_digits) then # if number 7
> glob_min_apfp_est_good_digits := glob_apfp_est_good_digits;
> fi;# end if 7;
> if (evalf(float_abs(numeric_val)) > glob_prec) then # if number 7
> est_rel_err := evalf(array_max_est_error[2]*100.0 * sqrt(glob_iter)*36*ATS_MAX_TERMS/float_abs(numeric_val));
> if (evalf(est_rel_err) > glob_prec) then # if number 8
> glob_est_digits := -int_trunc(log10(est_rel_err)) + 3;
> else
> glob_est_digits := Digits;
> fi;# end if 8;
> else
> relerr := glob__m1 ;
> glob_est_digits := -16;
> fi;# end if 7;
> array_est_digits[2] := glob_est_digits;
> if (glob_iter = 1) then # if number 7
> array_1st_rel_error[2] := relerr;
> else
> array_last_rel_error[2] := relerr;
> fi;# end if 7;
> array_est_rel_error[2] := est_rel_err;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_int(INFO,"Desired digits ",32,glob_desired_digits_correct,4," ");
> omniout_int(INFO,"Estimated correct digits ",32,glob_est_digits,4," ");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> fi;# end if 6;
> #BOTTOM DISPLAY ALOT
> fi;# end if 5;
> 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_2,
array_y1_init, array_y2_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_y1, array_x, array_y2,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_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_y1(ind_var));
omniout_float(ALWAYS, "y1[1] (closed_form) ", 33,
closed_form_val_y, 20, " ");
term_no := 1;
numeric_val := array_y1[term_no];
abserr := float_abs(numeric_val - closed_form_val_y);
omniout_float(ALWAYS, "y1[1] (numeric) ", 33,
numeric_val, 20, " ");
if c(glob_prec) < c(float_abs(closed_form_val_y)) then
relerr := abserr*glob__100/float_abs(closed_form_val_y);
if c(glob_prec) < c(relerr) then
glob_good_digits := -int_trunc(log10(c(relerr))) + 3
else glob_good_digits := Digits
end if
else relerr := glob__m1; glob_good_digits := -16
end if;
if glob_good_digits < glob_min_good_digits then
glob_min_good_digits := glob_good_digits
end if;
if glob_apfp_est_good_digits < glob_min_apfp_est_good_digits
then glob_min_apfp_est_good_digits := glob_apfp_est_good_digits
end if;
if glob_prec < evalf(float_abs(numeric_val)) then
est_rel_err := evalf(array_max_est_error[1]*100.0*
sqrt(glob_iter)*36*ATS_MAX_TERMS/float_abs(numeric_val))
;
if glob_prec < evalf(est_rel_err) then
glob_est_digits := -int_trunc(log10(est_rel_err)) + 3
else glob_est_digits := Digits
end if
else relerr := glob__m1; glob_est_digits := -16
end if;
array_est_digits[1] := glob_est_digits;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
array_est_rel_error[1] := est_rel_err;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_int(INFO, "Desired digits ", 32,
glob_desired_digits_correct, 4, " ");
omniout_int(INFO, "Estimated correct digits ", 32,
glob_est_digits, 4, " ");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ");
closed_form_val_y := evalf(exact_soln_y2(ind_var));
omniout_float(ALWAYS, "y2[1] (closed_form) ", 33,
closed_form_val_y, 20, " ");
term_no := 1;
numeric_val := array_y2[term_no];
abserr := float_abs(numeric_val - closed_form_val_y);
omniout_float(ALWAYS, "y2[1] (numeric) ", 33,
numeric_val, 20, " ");
if c(glob_prec) < c(float_abs(closed_form_val_y)) then
relerr := abserr*glob__100/float_abs(closed_form_val_y);
if c(glob_prec) < c(relerr) then
glob_good_digits := -int_trunc(log10(c(relerr))) + 3
else glob_good_digits := Digits
end if
else relerr := glob__m1; glob_good_digits := -16
end if;
if glob_good_digits < glob_min_good_digits then
glob_min_good_digits := glob_good_digits
end if;
if glob_apfp_est_good_digits < glob_min_apfp_est_good_digits
then glob_min_apfp_est_good_digits := glob_apfp_est_good_digits
end if;
if glob_prec < evalf(float_abs(numeric_val)) then
est_rel_err := evalf(array_max_est_error[2]*100.0*
sqrt(glob_iter)*36*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[2] := glob_est_digits;
if glob_iter = 1 then array_1st_rel_error[2] := relerr
else array_last_rel_error[2] := relerr
end if;
array_est_rel_error[2] := est_rel_err;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_int(INFO, "Desired digits ", 32,
glob_desired_digits_correct, 4, " ");
omniout_int(INFO, "Estimated correct digits ", 32,
glob_est_digits, 4, " ");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end if
end proc
# End Function number 8
# Begin Function number 9
> prog_report := proc(x_start,x_end)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2,
#END CONST
> array_y1_init,
> array_y2_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_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_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 5
> 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 5;
> 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_2,
array_y1_init, array_y2_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_y1, array_x, array_y2,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_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_2,
#END CONST
> array_y1_init,
> array_y2_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_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_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_y1_higher[1,last_no-1],array_y1_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[1,1]) then # if number 8
> array_rad_test_poles[1,1] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_ratio(array_y1_higher[1,last_no-1],array_y1_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 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[2,1] := glob_larger_float;
> array_ord_test_poles[2,1] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 2 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_ratio(array_y2_higher[1,last_no-1],array_y2_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[2,1]) then # if number 10
> array_rad_test_poles[2,1] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_ratio(array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
> array_rad_test_poles[2,1] := rad_c;
> array_ord_test_poles[2,1] := tmp_ord;
> fi;# end if 10;
> fi;# end if 9;
> #BOTTOM general radius test2
> 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_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 9
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 9;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 9
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 10
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 11
> found_sing := 0;
> fi;# end if 11;
> 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 11
> if (rad_c < array_rad_test_poles[1,2]) then # if number 12
> array_rad_test_poles[1,2] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_three_terms(array_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
> array_rad_test_poles[1,2] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 13
> glob_min_pole_est := rad_c;
> fi;# end if 13;
> array_ord_test_poles[1,2] := tmp_ord;
> fi;# end if 12;
> fi;# end if 11;
> #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[2,2] := glob_larger_float;
> array_ord_test_poles[2,2] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 2 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_three_terms(array_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 11
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 11;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 11
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 12
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 13
> found_sing := 0;
> fi;# end if 13;
> 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 13
> if (rad_c < array_rad_test_poles[2,2]) then # if number 14
> array_rad_test_poles[2,2] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_three_terms(array_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
> array_rad_test_poles[2,2] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 15
> glob_min_pole_est := rad_c;
> fi;# end if 15;
> array_ord_test_poles[2,2] := tmp_ord;
> fi;# end if 14;
> fi;# end if 13;
> #BOTTOM general radius test2
> 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_y1_higher[1,last_no-5],array_y1_higher[1,last_no-4],array_y1_higher[1,last_no-3],array_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 13
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 13;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 13
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 14
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 15
> found_sing := 0;
> fi;# end if 15;
> 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 15
> if (rad_c < array_rad_test_poles[1,3]) then # if number 16
> array_rad_test_poles[1,3] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_six_terms(array_y1_higher[1,last_no-5],array_y1_higher[1,last_no-4],array_y1_higher[1,last_no-3],array_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
> array_rad_test_poles[1,3] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 17
> glob_min_pole_est := rad_c;
> fi;# end if 17;
> array_ord_test_poles[1,3] := tmp_ord;
> fi;# end if 16;
> fi;# end if 15;
> #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[2,3] := glob_larger_float;
> array_ord_test_poles[2,3] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 2 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_six_terms(array_y2_higher[1,last_no-5],array_y2_higher[1,last_no-4],array_y2_higher[1,last_no-3],array_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 15
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 15;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 15
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 16
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 17
> found_sing := 0;
> fi;# end if 17;
> 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 17
> if (rad_c < array_rad_test_poles[2,3]) then # if number 18
> array_rad_test_poles[2,3] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_six_terms(array_y2_higher[1,last_no-5],array_y2_higher[1,last_no-4],array_y2_higher[1,last_no-3],array_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
> array_rad_test_poles[2,3] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 19
> glob_min_pole_est := rad_c;
> fi;# end if 19;
> array_ord_test_poles[2,3] := tmp_ord;
> fi;# end if 18;
> fi;# end if 17;
> #BOTTOM general radius test2
> #START ADJUST ALL SERIES
> if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 17
> 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 18
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> h_new := glob_min_h;
> glob_h_reason := 5;
> fi;# end if 18;
> term := 1;
> ratio := c(1.0);
> while (term <= ATS_MAX_TERMS) do # do number 1
> array_y1[term] := array_y1[term]* ratio;
> array_y1_higher[1,term] := array_y1_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> array_y2[term] := array_y2[term]* ratio;
> array_y2_higher[1,term] := array_y2_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 17;
> #BOTTOM ADJUST ALL SERIES
> ;
> if (reached_interval()) then # if number 17
> display_poles();
> fi;# end if 17
> 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_2,
array_y1_init, array_y2_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_y1, array_x, array_y2,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_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_y1_higher[1, last_no - 1],
array_y1_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_y1_higher[1, last_no - 1],
array_y1_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[2, 1] := glob_larger_float;
array_ord_test_poles[2, 1] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 12;
cnt := 0;
while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do
tmp_rad := comp_rad_from_ratio(array_y2_higher[1, last_no - 1],
array_y2_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[2, 1] then
array_rad_test_poles[2, 1] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_ratio(array_y2_higher[1, last_no - 1],
array_y2_higher[1, last_no], last_no);
array_rad_test_poles[2, 1] := rad_c;
array_ord_test_poles[2, 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_y1_higher[1, last_no - 2],
array_y1_higher[1, last_no - 1], array_y1_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_y1_higher[1, last_no - 2],
array_y1_higher[1, last_no - 1],
array_y1_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[2, 2] := glob_larger_float;
array_ord_test_poles[2, 2] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 12;
cnt := 0;
while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do
tmp_rad := comp_rad_from_three_terms(
array_y2_higher[1, last_no - 2],
array_y2_higher[1, last_no - 1], array_y2_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[2, 2] then
array_rad_test_poles[2, 2] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_three_terms(
array_y2_higher[1, last_no - 2],
array_y2_higher[1, last_no - 1],
array_y2_higher[1, last_no], last_no);
array_rad_test_poles[2, 2] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[2, 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_y1_higher[1, last_no - 5],
array_y1_higher[1, last_no - 4],
array_y1_higher[1, last_no - 3],
array_y1_higher[1, last_no - 2],
array_y1_higher[1, last_no - 1], array_y1_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_y1_higher[1, last_no - 5],
array_y1_higher[1, last_no - 4],
array_y1_higher[1, last_no - 3],
array_y1_higher[1, last_no - 2],
array_y1_higher[1, last_no - 1],
array_y1_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;
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[2, 3] := glob_larger_float;
array_ord_test_poles[2, 3] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 12;
cnt := 0;
while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do
tmp_rad := comp_rad_from_six_terms(array_y2_higher[1, last_no - 5],
array_y2_higher[1, last_no - 4],
array_y2_higher[1, last_no - 3],
array_y2_higher[1, last_no - 2],
array_y2_higher[1, last_no - 1], array_y2_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[2, 3] then
array_rad_test_poles[2, 3] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_six_terms(
array_y2_higher[1, last_no - 5],
array_y2_higher[1, last_no - 4],
array_y2_higher[1, last_no - 3],
array_y2_higher[1, last_no - 2],
array_y2_higher[1, last_no - 1],
array_y2_higher[1, last_no], last_no);
array_rad_test_poles[2, 3] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[2, 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_y1[term] := array_y1[term]*ratio;
array_y1_higher[1, term] := array_y1_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
array_y2[term] := array_y2[term]*ratio;
array_y2_higher[1, term] := array_y2_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_2,
#END CONST
> array_y1_init,
> array_y2_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_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_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 neg FULL $eq_no = 1
> array_tmp1[1] := neg(array_y2[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y1_set_initial[1,2]) then # if number 1
> if (1 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
> if (2 <= ATS_MAX_TERMS) then # if number 3
> array_y1[2] := temporary;
> array_y1_higher[1,2] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(1);
> array_y1_higher[2,1] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #emit pre diff $eq_no = 2 i = 1 order_d = 1
> array_tmp4[1] := array_y1_higher[2,1];
> #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5
> if ( not array_y2_set_initial[2,3]) then # if number 1
> if (1 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp4[1]) * (expt((glob_h) , c(2))) * c(factorial_3(0,2));
> if (3 <= ATS_MAX_TERMS) then # if number 3
> array_y2[3] := temporary;
> array_y2_higher[1,3] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y2_higher[2,2] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(1);
> array_y2_higher[3,1] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre neg FULL $eq_no = 1
> array_tmp1[2] := neg(array_y2[2]);
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y1_set_initial[1,3]) then # if number 1
> if (2 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2));
> if (3 <= ATS_MAX_TERMS) then # if number 3
> array_y1[3] := temporary;
> array_y1_higher[1,3] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y1_higher[2,2] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #emit pre diff $eq_no = 2 i = 2 order_d = 1
> array_tmp4[2] := array_y1_higher[2,2];
> #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5
> if ( not array_y2_set_initial[2,4]) then # if number 1
> if (2 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp4[2]) * (expt((glob_h) , c(2))) * c(factorial_3(1,3));
> if (4 <= ATS_MAX_TERMS) then # if number 3
> array_y2[4] := temporary;
> array_y2_higher[1,4] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y2_higher[2,3] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y2_higher[3,2] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre neg FULL $eq_no = 1
> array_tmp1[3] := neg(array_y2[3]);
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp2[3] := array_tmp1[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y1_set_initial[1,4]) then # if number 1
> if (3 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3));
> if (4 <= ATS_MAX_TERMS) then # if number 3
> array_y1[4] := temporary;
> array_y1_higher[1,4] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y1_higher[2,3] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #emit pre diff $eq_no = 2 i = 3 order_d = 1
> array_tmp4[3] := array_y1_higher[2,3];
> #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5
> if ( not array_y2_set_initial[2,5]) then # if number 1
> if (3 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp4[3]) * (expt((glob_h) , c(2))) * c(factorial_3(2,4));
> if (5 <= ATS_MAX_TERMS) then # if number 3
> array_y2[5] := temporary;
> array_y2_higher[1,5] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y2_higher[2,4] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y2_higher[3,3] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre neg FULL $eq_no = 1
> array_tmp1[4] := neg(array_y2[4]);
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp2[4] := array_tmp1[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y1_set_initial[1,5]) then # if number 1
> if (4 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4));
> if (5 <= ATS_MAX_TERMS) then # if number 3
> array_y1[5] := temporary;
> array_y1_higher[1,5] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y1_higher[2,4] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #emit pre diff $eq_no = 2 i = 4 order_d = 1
> array_tmp4[4] := array_y1_higher[2,4];
> #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5
> if ( not array_y2_set_initial[2,6]) then # if number 1
> if (4 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp4[4]) * (expt((glob_h) , c(2))) * c(factorial_3(3,5));
> if (6 <= ATS_MAX_TERMS) then # if number 3
> array_y2[6] := temporary;
> array_y2_higher[1,6] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y2_higher[2,5] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y2_higher[3,4] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre neg FULL $eq_no = 1
> array_tmp1[5] := neg(array_y2[5]);
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp2[5] := array_tmp1[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y1_set_initial[1,6]) then # if number 1
> if (5 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5));
> if (6 <= ATS_MAX_TERMS) then # if number 3
> array_y1[6] := temporary;
> array_y1_higher[1,6] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y1_higher[2,5] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #emit pre diff $eq_no = 2 i = 5 order_d = 1
> array_tmp4[5] := array_y1_higher[2,5];
> #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5
> if ( not array_y2_set_initial[2,7]) then # if number 1
> if (5 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp4[5]) * (expt((glob_h) , c(2))) * c(factorial_3(4,6));
> if (7 <= ATS_MAX_TERMS) then # if number 3
> array_y2[7] := temporary;
> array_y2_higher[1,7] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(6);
> array_y2_higher[2,6] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y2_higher[3,5] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= ATS_MAX_TERMS) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit neg FULL $eq_no = 1
> array_tmp1[kkk] := neg(array_y2[kkk]);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp2[kkk] := array_tmp1[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1
> if ( not array_y1_set_initial[1,kkk + order_d]) then # if number 2
> temporary := c(array_tmp2[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
> array_y1[kkk + order_d] := c(temporary);
> array_y1_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_y1_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;
> #emit diff $eq_no = 2
> if (kkk <= ATS_MAX_TERMS) then # if number 1
> array_tmp4[kkk] := array_y1_higher[2,kkk];
> fi;# end if 1;
> #emit assign $eq_no = 2
> order_d := 2;
> if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1
> if ( not array_y2_set_initial[2,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_y2[kkk + order_d] := c(temporary);
> array_y2_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_y2_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_2,
array_y1_init, array_y2_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_y1, array_x, array_y2,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_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] := neg(array_y2[1]);
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
if not array_y1_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
if 2 <= ATS_MAX_TERMS then
array_y1[2] := temporary;
array_y1_higher[1, 2] := temporary
end if;
temporary := c(temporary)*c(1)/c(glob_h);
array_y1_higher[2, 1] := c(temporary)
end if
end if;
kkk := 2;
array_tmp4[1] := array_y1_higher[2, 1];
if not array_y2_set_initial[2, 3] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[1])*expt(glob_h, c(2))*c(factorial_3(0, 2));
if 3 <= ATS_MAX_TERMS then
array_y2[3] := temporary;
array_y2_higher[1, 3] := temporary
end if;
temporary := c(temporary)*c(2)/c(glob_h);
array_y2_higher[2, 2] := c(temporary);
temporary := c(temporary)*c(1)/c(glob_h);
array_y2_higher[3, 1] := c(temporary)
end if
end if;
kkk := 2;
array_tmp1[2] := neg(array_y2[2]);
array_tmp2[2] := array_tmp1[2];
if not array_y1_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
if 3 <= ATS_MAX_TERMS then
array_y1[3] := temporary;
array_y1_higher[1, 3] := temporary
end if;
temporary := c(temporary)*c(2)/c(glob_h);
array_y1_higher[2, 2] := c(temporary)
end if
end if;
kkk := 3;
array_tmp4[2] := array_y1_higher[2, 2];
if not array_y2_set_initial[2, 4] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[2])*expt(glob_h, c(2))*c(factorial_3(1, 3));
if 4 <= ATS_MAX_TERMS then
array_y2[4] := temporary;
array_y2_higher[1, 4] := temporary
end if;
temporary := c(temporary)*c(3)/c(glob_h);
array_y2_higher[2, 3] := c(temporary);
temporary := c(temporary)*c(2)/c(glob_h);
array_y2_higher[3, 2] := c(temporary)
end if
end if;
kkk := 3;
array_tmp1[3] := neg(array_y2[3]);
array_tmp2[3] := array_tmp1[3];
if not array_y1_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[3])*expt(glob_h, c(1))*c(factorial_3(2, 3));
if 4 <= ATS_MAX_TERMS then
array_y1[4] := temporary;
array_y1_higher[1, 4] := temporary
end if;
temporary := c(temporary)*c(3)/c(glob_h);
array_y1_higher[2, 3] := c(temporary)
end if
end if;
kkk := 4;
array_tmp4[3] := array_y1_higher[2, 3];
if not array_y2_set_initial[2, 5] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[3])*expt(glob_h, c(2))*c(factorial_3(2, 4));
if 5 <= ATS_MAX_TERMS then
array_y2[5] := temporary;
array_y2_higher[1, 5] := temporary
end if;
temporary := c(temporary)*c(4)/c(glob_h);
array_y2_higher[2, 4] := c(temporary);
temporary := c(temporary)*c(3)/c(glob_h);
array_y2_higher[3, 3] := c(temporary)
end if
end if;
kkk := 4;
array_tmp1[4] := neg(array_y2[4]);
array_tmp2[4] := array_tmp1[4];
if not array_y1_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[4])*expt(glob_h, c(1))*c(factorial_3(3, 4));
if 5 <= ATS_MAX_TERMS then
array_y1[5] := temporary;
array_y1_higher[1, 5] := temporary
end if;
temporary := c(temporary)*c(4)/c(glob_h);
array_y1_higher[2, 4] := c(temporary)
end if
end if;
kkk := 5;
array_tmp4[4] := array_y1_higher[2, 4];
if not array_y2_set_initial[2, 6] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[4])*expt(glob_h, c(2))*c(factorial_3(3, 5));
if 6 <= ATS_MAX_TERMS then
array_y2[6] := temporary;
array_y2_higher[1, 6] := temporary
end if;
temporary := c(temporary)*c(5)/c(glob_h);
array_y2_higher[2, 5] := c(temporary);
temporary := c(temporary)*c(4)/c(glob_h);
array_y2_higher[3, 4] := c(temporary)
end if
end if;
kkk := 5;
array_tmp1[5] := neg(array_y2[5]);
array_tmp2[5] := array_tmp1[5];
if not array_y1_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[5])*expt(glob_h, c(1))*c(factorial_3(4, 5));
if 6 <= ATS_MAX_TERMS then
array_y1[6] := temporary;
array_y1_higher[1, 6] := temporary
end if;
temporary := c(temporary)*c(5)/c(glob_h);
array_y1_higher[2, 5] := c(temporary)
end if
end if;
kkk := 6;
array_tmp4[5] := array_y1_higher[2, 5];
if not array_y2_set_initial[2, 7] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[5])*expt(glob_h, c(2))*c(factorial_3(4, 6));
if 7 <= ATS_MAX_TERMS then
array_y2[7] := temporary;
array_y2_higher[1, 7] := temporary
end if;
temporary := c(temporary)*c(6)/c(glob_h);
array_y2_higher[2, 6] := c(temporary);
temporary := c(temporary)*c(5)/c(glob_h);
array_y2_higher[3, 5] := c(temporary)
end if
end if;
kkk := 6;
while kkk <= ATS_MAX_TERMS do
array_tmp1[kkk] := neg(array_y2[kkk]);
array_tmp2[kkk] := array_tmp1[kkk];
order_d := 1;
if kkk + order_d <= ATS_MAX_TERMS then
if not array_y1_set_initial[1, kkk + order_d] then
temporary := c(array_tmp2[kkk])*expt(glob_h, c(order_d))*
c(factorial_3(kkk - 1, kkk + order_d - 1));
array_y1[kkk + order_d] := c(temporary);
array_y1_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_y1_higher[adj3, term] := c(temporary)
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
if kkk <= ATS_MAX_TERMS then
array_tmp4[kkk] := array_y1_higher[2, kkk]
end if;
order_d := 2;
if kkk + order_d <= ATS_MAX_TERMS then
if not array_y2_set_initial[2, 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_y2[kkk + order_d] := c(temporary);
array_y2_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_y2_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_2,
> #END CONST
> array_y1_init,
> array_y2_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_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_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_y1_init:= Array(0..(30),[]);
> array_y2_init:= Array(0..(30),[]);
> array_norms:= Array(0..(30),[]);
> array_fact_1:= Array(0..(30),[]);
> array_1st_rel_error:= Array(0..(3),[]);
> array_last_rel_error:= Array(0..(3),[]);
> array_est_rel_error:= Array(0..(3),[]);
> array_max_est_error:= Array(0..(3),[]);
> array_type_pole:= Array(0..(3),[]);
> array_type_real_pole:= Array(0..(3),[]);
> array_type_complex_pole:= Array(0..(3),[]);
> array_est_digits:= Array(0..(3),[]);
> array_y1:= Array(0..(30),[]);
> array_x:= Array(0..(30),[]);
> array_y2:= 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_y1_higher := Array(0..(2) ,(0..30+ 1),[]);
> array_y1_higher_work := Array(0..(2) ,(0..30+ 1),[]);
> array_y1_higher_work2 := Array(0..(2) ,(0..30+ 1),[]);
> array_y1_set_initial := Array(0..(3) ,(0..30+ 1),[]);
> array_y2_higher := Array(0..(3) ,(0..30+ 1),[]);
> array_y2_higher_work := Array(0..(3) ,(0..30+ 1),[]);
> array_y2_higher_work2 := Array(0..(3) ,(0..30+ 1),[]);
> array_y2_set_initial := Array(0..(3) ,(0..30+ 1),[]);
> array_given_rad_poles := Array(0..(3) ,(0..3+ 1),[]);
> array_given_ord_poles := Array(0..(3) ,(0..3+ 1),[]);
> array_rad_test_poles := Array(0..(3) ,(0..4+ 1),[]);
> array_ord_test_poles := Array(0..(3) ,(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_y1_init[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_y2_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 <= 3) do # do number 1
> array_1st_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_last_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_est_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_max_est_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_type_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_type_real_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_type_complex_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) 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_y1[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_y2[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_y1_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_y1_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_y1_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 <=3) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y1_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 <=3) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y2_higher[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y2_higher_work[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y2_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 <=3) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y2_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 <=3) 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 <=3) 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 <=3) 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 <=3) 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_y1);
> zero_ats_ar(array_x);
> zero_ats_ar(array_y2);
> 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_2);
> array_const_2[1] := c(2);
> zero_ats_ar(array_m1);
> array_m1[1] := glob__m1;
> #END SYMBOLS INITIALIZATED
> # before generate factorials init
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= ATS_MAX_TERMS) do # do number 1
> jjjf := 0;
> while (jjjf <= ATS_MAX_TERMS) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Table
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> glob_yes_pole := 4;
> glob_no_pole := 3;
> glob_not_given := 0;
> glob_no_sing_tests := 4;
> glob_ratio_test := 1;
> glob_three_term_test := 2;
> glob_six_term_test := 3;
> glob_log_10 := log(c(10.0));
> MAX_UNCHANGED := 10;
> glob__small := c(0.1e-50);
> glob_small_float := c(0.1e-50);
> glob_smallish_float := c(0.1e-60);
> glob_large_float := c(1.0e100);
> glob_larger_float := c(1.1e100);
> glob__m2 := c(-2);
> glob__m1 := c(-1);
> glob__0 := c(0);
> glob__1 := c(1);
> glob__2 := c(2);
> glob__3 := c(3);
> glob__4 := c(4);
> glob__5 := c(5);
> glob__8 := c(8);
> glob__10 := c(10);
> glob__100 := c(100);
> glob__pi := c(0.0);
> glob__0_5 := c(0.5);
> glob__0_8 := c(0.8);
> glob__m0_8 := c(-0.8);
> glob__0_25 := c(0.25);
> glob__0_125 := c(0.125);
> glob_prec := c(1.0e-16);
> glob_check_sign := c(1.0);
> glob_desired_digits_correct := c(8.0);
> glob_max_estimated_step_error := c(0.0);
> glob_ratio_of_radius := c(0.1);
> glob_percent_done := c(0.0);
> glob_total_exp_sec := c(0.1);
> glob_optimal_expect_sec := c(0.1);
> glob_estimated_size_answer := c(100.0);
> glob_almost_1 := c(0.9990);
> glob_clock_sec := c(0.0);
> glob_clock_start_sec := c(0.0);
> glob_disp_incr := c(0.1);
> glob_h := c(0.1);
> glob_diff_rc_fm := c(0.1);
> glob_diff_rc_fmm1 := c(0.1);
> glob_diff_rc_fmm2 := c(0.1);
> glob_diff_ord_fm := c(0.1);
> glob_diff_ord_fmm1 := c(0.1);
> glob_diff_ord_fmm2 := c(0.1);
> glob_six_term_ord_save := c(0.1);
> glob_guess_error_rc := c(0.1);
> glob_guess_error_ord := c(0.1);
> glob_least_given_sing := c(9.9e200);
> glob_least_ratio_sing := c(9.9e200);
> glob_least_3_sing := c(9.9e100);
> glob_least_6_sing := c(9.9e100);
> glob_last_good_h := c(0.1);
> glob_max_h := c(0.1);
> glob_min_h := c(0.000001);
> glob_display_interval := c(0.1);
> glob_abserr := c(0.1e-10);
> glob_relerr := c(0.1e-10);
> glob_min_pole_est := c(0.1e+10);
> glob_max_rel_trunc_err := c(0.1e-10);
> glob_max_trunc_err := c(0.1e-10);
> glob_max_hours := c(0.0);
> glob_optimal_clock_start_sec := c(0.0);
> glob_optimal_start := c(0.0);
> glob_upper_ratio_limit := c(1.0001);
> glob_lower_ratio_limit := c(0.9999);
> glob_max_sec := c(10000.0);
> glob_orig_start_sec := c(0.0);
> glob_normmax := c(0.0);
> glob_max_minutes := c(0.0);
> glob_next_display := c(0.0);
> glob_est_digits := 1;
> glob_subiter_method := 3;
> glob_html_log := true;
> glob_min_good_digits := 99999;
> glob_good_digits := 0;
> glob_min_apfp_est_good_digits := 99999;
> glob_apfp_est_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> glob_h_reason := 0;
> glob_sec_in_minute := 60 ;
> glob_min_in_hour := 60;
> glob_hours_in_day := 24;
> glob_days_in_year := 365;
> glob_sec_in_hour := 3600;
> glob_sec_in_day := 86400;
> glob_sec_in_year := 31536000;
> glob_not_yet_finished := true;
> glob_initial_pass := true;
> glob_not_yet_start_msg := true;
> glob_reached_optimal_h := false;
> glob_optimal_done := false;
> glob_type_given_pole := 0;
> glob_optimize := false;
> glob_look_poles := false;
> glob_dump_closed_form := false;
> glob_max_iter := 1000;
> glob_no_eqs := 0;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_start := 0;
> glob_iter := 0;
> # before generate set diff initial
> array_y1_set_initial[1,1] := true;
> array_y1_set_initial[1,2] := false;
> array_y1_set_initial[1,3] := false;
> array_y1_set_initial[1,4] := false;
> array_y1_set_initial[1,5] := false;
> array_y1_set_initial[1,6] := false;
> array_y1_set_initial[1,7] := false;
> array_y1_set_initial[1,8] := false;
> array_y1_set_initial[1,9] := false;
> array_y1_set_initial[1,10] := false;
> array_y1_set_initial[1,11] := false;
> array_y1_set_initial[1,12] := false;
> array_y1_set_initial[1,13] := false;
> array_y1_set_initial[1,14] := false;
> array_y1_set_initial[1,15] := false;
> array_y1_set_initial[1,16] := false;
> array_y1_set_initial[1,17] := false;
> array_y1_set_initial[1,18] := false;
> array_y1_set_initial[1,19] := false;
> array_y1_set_initial[1,20] := false;
> array_y1_set_initial[1,21] := false;
> array_y1_set_initial[1,22] := false;
> array_y1_set_initial[1,23] := false;
> array_y1_set_initial[1,24] := false;
> array_y1_set_initial[1,25] := false;
> array_y1_set_initial[1,26] := false;
> array_y1_set_initial[1,27] := false;
> array_y1_set_initial[1,28] := false;
> array_y1_set_initial[1,29] := false;
> array_y1_set_initial[1,30] := false;
> array_y2_set_initial[2,1] := true;
> array_y2_set_initial[2,2] := true;
> array_y2_set_initial[2,3] := false;
> array_y2_set_initial[2,4] := false;
> array_y2_set_initial[2,5] := false;
> array_y2_set_initial[2,6] := false;
> array_y2_set_initial[2,7] := false;
> array_y2_set_initial[2,8] := false;
> array_y2_set_initial[2,9] := false;
> array_y2_set_initial[2,10] := false;
> array_y2_set_initial[2,11] := false;
> array_y2_set_initial[2,12] := false;
> array_y2_set_initial[2,13] := false;
> array_y2_set_initial[2,14] := false;
> array_y2_set_initial[2,15] := false;
> array_y2_set_initial[2,16] := false;
> array_y2_set_initial[2,17] := false;
> array_y2_set_initial[2,18] := false;
> array_y2_set_initial[2,19] := false;
> array_y2_set_initial[2,20] := false;
> array_y2_set_initial[2,21] := false;
> array_y2_set_initial[2,22] := false;
> array_y2_set_initial[2,23] := false;
> array_y2_set_initial[2,24] := false;
> array_y2_set_initial[2,25] := false;
> array_y2_set_initial[2,26] := false;
> array_y2_set_initial[2,27] := false;
> array_y2_set_initial[2,28] := false;
> array_y2_set_initial[2,29] := false;
> array_y2_set_initial[2,30] := 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 := 2;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := (0.0);
> glob_max_minutes := (15.0);
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/mtest5postode.ode#################");
> omniout_str(ALWAYS,"diff ( y1 , x , 1 ) = neg ( y2 ) ; ");
> omniout_str(ALWAYS,"diff ( y2 , x , 2 ) = diff ( y1 , x , 1 ) ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := c(0.5);");
> omniout_str(ALWAYS,"x_end := c(5.0);");
> omniout_str(ALWAYS,"array_y1_init[0 + 1] := exact_soln_y1(x_start);");
> omniout_str(ALWAYS,"array_y2_init[0 + 1] := exact_soln_y2(x_start);");
> omniout_str(ALWAYS,"array_y2_init[1 + 1] := exact_soln_y2p(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_type_given_pole := 3;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=8;");
> omniout_str(ALWAYS,"glob_max_minutes:=(3.0);");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"glob_max_iter:=100000;");
> omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.0000001);");
> omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.9999999);");
> omniout_str(ALWAYS,"glob_look_poles:=true;");
> omniout_str(ALWAYS,"glob_h:=c(0.005);");
> omniout_str(ALWAYS,"glob_display_interval:=c(0.01);");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y1 := proc(x)");
> omniout_str(ALWAYS,"return(neg(cos(c(x))));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2 := proc(x)");
> omniout_str(ALWAYS,"return(neg(sin(c(x))));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2p := proc(x)");
> omniout_str(ALWAYS,"return(neg(cos(c(x))));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := glob__0;
> glob_smallish_float := glob__0;
> glob_large_float := c(1.0e100);
> glob_larger_float := c( 1.1e100);
> glob_almost_1 := c( 0.99);
> # before second block
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #BEGIN BLOCK 2
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := c(0.5);
> x_end := c(5.0);
> array_y1_init[0 + 1] := exact_soln_y1(x_start);
> array_y2_init[0 + 1] := exact_soln_y2(x_start);
> array_y2_init[1 + 1] := exact_soln_y2p(x_start);
> glob_look_poles := true;
> glob_type_given_pole := 3;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=8;
> glob_max_minutes:=(3.0);
> glob_subiter_method:=3;
> glob_max_iter:=100000;
> glob_upper_ratio_limit:=c(1.0000001);
> glob_lower_ratio_limit:=c(0.9999999);
> glob_look_poles:=true;
> glob_h:=c(0.005);
> glob_display_interval:=c(0.01);
> #END OVERRIDE BLOCK
> #END BLOCK 2
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_sec := (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours);
> # after second input block
> glob_check_sign := c(my_check_sign(x_start,x_end));
> glob__pi := arccos(glob__m1);
> glob_prec = expt(10.0,c(-Digits));
> if (glob_optimize) then # if number 17
> #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 18
> glob_display_interval := c(display_max);
> fi;# end if 18;
> 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_y1
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y1[term_no] := array_y1_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 18
> array_y1_higher[r_order,term_no] := array_y1_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 18;
> term_no := term_no + 1;
> od;# end do number 3;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> order_diff := 2;
> #Start Series array_y2
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y2[term_no] := array_y2_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 18
> array_y2_higher[r_order,term_no] := array_y2_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 18;
> term_no := term_no + 1;
> od;# end do number 3;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> if (glob_subiter_method = 1 ) then # if number 18
> atomall();
> elif
> (glob_subiter_method = 2 ) then # if number 19
> subiter := 1;
> while (subiter <= 3) do # do number 2
> atomall();
> subiter := subiter + 1;
> od;# end do number 2;
> else
> subiter := 1;
> while (subiter <= 3 + ATS_MAX_TERMS) do # do number 2
> atomall();
> subiter := subiter + 1;
> od;# end do number 2;
> fi;# end if 19;
> if (glob_check_sign * glob_min_h >= glob_check_sign * glob_h) then # if number 19
> 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 19;
> if (glob_check_sign * glob_display_interval <= glob_check_sign * glob_h) then # if number 19
> omniout_str(ALWAYS,"SETTING H FOR DISPLAY INTERVAL");
> glob_h_reason := 2;
> glob_h := glob_display_interval;
> found_h := true;
> fi;# end if 19;
> if (glob_look_poles) then # if number 19
> check_for_pole();
> fi;# end if 19;
> if ( not found_h) then # if number 19
> 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 20
> 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 20;
> fi;# end if 19;
> opt_iter := opt_iter + 1;
> od;# end do number 1;
> if (( not found_h) and (opt_iter = 1)) then # if number 19
> omniout_str(ALWAYS,"Beginning glob_h too large.");
> found_h := false;
> fi;# end if 19;
> if (glob_check_sign * glob_max_h <= glob_check_sign * glob_h) then # if number 19
> 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 19;
> else
> found_h := true;
> glob_h := glob_h * glob_check_sign;
> fi;# end if 18;
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 18
> html_log_file := fopen("entry.html",WRITE,TEXT);
> fi;# end if 18;
> #BEGIN SOLUTION CODE
> if (found_h) then # if number 18
> 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_y1
> term_no := 1;
> while (term_no <= order_diff) do # do number 1
> array_y1[term_no] := array_y1_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 19
> array_y1_higher[r_order,term_no] := array_y1_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 19;
> term_no := term_no + 1;
> od;# end do number 2;
> r_order := r_order + 1;
> od;# end do number 1
> ;
> order_diff := 2;
> #Start Series array_y2
> term_no := 1;
> while (term_no <= order_diff) do # do number 1
> array_y2[term_no] := array_y2_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 19
> array_y2_higher[r_order,term_no] := array_y2_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 19;
> 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 19
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> fi;# end if 19;
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> track_estimated_error();
> if (glob_subiter_method = 1 ) then # if number 19
> atomall();
> elif
> (glob_subiter_method = 2 ) then # if number 20
> subiter := 1;
> while (subiter <= 3) do # do number 2
> atomall();
> subiter := subiter + 1;
> od;# end do number 2;
> else
> subiter := 1;
> while (subiter <= 3 + ATS_MAX_TERMS) do # do number 2
> atomall();
> subiter := subiter + 1;
> od;# end do number 2;
> fi;# end if 20;
> track_estimated_error();
> display_alot(current_iter);
> if (glob_look_poles) then # if number 20
> check_for_pole();
> fi;# end if 20;
> if (reached_interval()) then # if number 20
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 20;
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y1;
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y1
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y1_higher_work[2,iii] := array_y1_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_y1
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y1_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_y1
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y1_higher_work[1,iii] := array_y1_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_y1
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y1_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_y1
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y1_higher_work[1,iii] := array_y1_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_y1
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y1_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_y1[term_no] := array_y1_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 3
> array_y1_higher[ord,term_no] := array_y1_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
> #Jump Series array_y2;
> order_diff := 3;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =2
> #sum_and_adjust array_y2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 3;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := glob__0;
> ord := 3;
> calc_term := 1;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 2;
> calc_term := 2;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[2,iii] := array_y2_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 =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := glob__0;
> ord := 2;
> calc_term := 2;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[2,iii] := array_y2_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 =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := glob__0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 1;
> calc_term := 3;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[1,iii] := array_y2_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 =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := glob__0;
> ord := 1;
> calc_term := 3;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[1,iii] := array_y2_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 =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := glob__0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[1,iii] := array_y2_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 =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := glob__0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #END SUM AND ADJUST EQ =2
> #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_y2[term_no] := array_y2_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 3
> array_y2_higher[ord,term_no] := array_y2_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 20
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 20;
> if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec )) then # if number 20
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 20;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y1 , x , 1 ) = neg ( y2 ) ; ");
> omniout_str(INFO,"diff ( y2 , x , 2 ) = diff ( y1 , x , 1 ) ; ");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 20
> logstart(html_log_file);
> logitem_str(html_log_file,"2015-05-02T21:41:05-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"mtest5")
> ;
> logitem_str(html_log_file,"diff ( y1 , x , 1 ) = neg ( y2 ) ; ")
> ;
> 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 21
> logitem_integer(html_log_file,array_est_digits[1])
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 21;
> if (glob_min_good_digits <> -16) then # if number 21
> logitem_integer(html_log_file,glob_min_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 21;
> if (glob_good_digits <> -16) then # if number 21
> logitem_integer(html_log_file,glob_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 21;
> 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 21
> logitem_str(html_log_file,"Not Given")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 4) then # if number 22
> logitem_str(html_log_file,"No Solution")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 5) then # if number 23
> logitem_str(html_log_file,"Some Pole")
> ;
> logitem_str(html_log_file,"????")
> ;
> elif
> (glob_type_given_pole = 3) then # if number 24
> logitem_str(html_log_file,"No Pole")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 1) then # if number 25
> 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 26
> logitem_str(html_log_file,"Complex Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> fi;# end if 26;
> if (glob_least_ratio_sing < glob_large_float) then # if number 26
> logitem_float(html_log_file,glob_least_ratio_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 26;
> if (glob_least_3_sing < glob_large_float) then # if number 26
> logitem_float(html_log_file,glob_least_3_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 26;
> if (glob_least_6_sing < glob_large_float) then # if number 26
> logitem_float(html_log_file,glob_least_6_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 26;
> 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 26
> logitem_time(html_log_file,(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 26;
> log_revs(html_log_file," 308.maple.seems.ok | ")
> ;
> logitem_str(html_log_file,"mtest5 diffeq.mxt")
> ;
> logitem_str(html_log_file,"mtest5 maple results")
> ;
> logitem_str(html_log_file,"OK")
> ;
> logend(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logitem_str(html_log_file,"diff ( y2 , x , 2 ) = diff ( y1 , x , 1 ) ; ")
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> ;
> logditto(html_log_file)
> ;
> if (array_est_digits[2] <> -16) then # if number 26
> logitem_integer(html_log_file,array_est_digits[2])
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 26;
> if (glob_min_good_digits <> -16) then # if number 26
> logitem_integer(html_log_file,glob_min_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 26;
> if (glob_good_digits <> -16) then # if number 26
> logitem_integer(html_log_file,glob_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 26;
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> logditto(html_log_file)
> ;
> if (glob_type_given_pole = 0) then # if number 26
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> elif
> (glob_type_given_pole = 4) then # if number 27
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> elif
> (glob_type_given_pole = 5) then # if number 28
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> elif
> (glob_type_given_pole = 3) then # if number 29
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> elif
> (glob_type_given_pole = 1) then # if number 30
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> elif
> (glob_type_given_pole = 2) then # if number 31
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> fi;# end if 31;
> if (glob_least_ratio_sing < glob_large_float) then # if number 31
> logditto(html_log_file)
> ;
> else
> logditto(html_log_file)
> ;
> fi;# end if 31;
> if (glob_least_3_sing < glob_large_float) then # if number 31
> logditto(html_log_file)
> ;
> else
> logditto(html_log_file)
> ;
> fi;# end if 31;
> if (glob_least_6_sing < glob_large_float) then # if number 31
> logditto(html_log_file)
> ;
> else
> logditto(html_log_file)
> ;
> fi;# end if 31;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> if (c(glob_percent_done) < glob__100) then # if number 31
> logditto(html_log_file)
> ;
> 0;
> else
> logditto(html_log_file)
> ;
> 0;
> fi;# end if 31;
> logditto(html_log_file);
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 30;
> if (glob_html_log) then # if number 30
> fclose(html_log_file);
> fi;# end if 30
> ;
> ;;
> fi;# end if 29
> #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_2,
array_y1_init, array_y2_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_y1, array_x, array_y2,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_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_y1_init := Array(0 .. 30, []);
array_y2_init := Array(0 .. 30, []);
array_norms := Array(0 .. 30, []);
array_fact_1 := Array(0 .. 30, []);
array_1st_rel_error := Array(0 .. 3, []);
array_last_rel_error := Array(0 .. 3, []);
array_est_rel_error := Array(0 .. 3, []);
array_max_est_error := Array(0 .. 3, []);
array_type_pole := Array(0 .. 3, []);
array_type_real_pole := Array(0 .. 3, []);
array_type_complex_pole := Array(0 .. 3, []);
array_est_digits := Array(0 .. 3, []);
array_y1 := Array(0 .. 30, []);
array_x := Array(0 .. 30, []);
array_y2 := 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_y1_higher := Array(0 .. 2, 0 .. 31, []);
array_y1_higher_work := Array(0 .. 2, 0 .. 31, []);
array_y1_higher_work2 := Array(0 .. 2, 0 .. 31, []);
array_y1_set_initial := Array(0 .. 3, 0 .. 31, []);
array_y2_higher := Array(0 .. 3, 0 .. 31, []);
array_y2_higher_work := Array(0 .. 3, 0 .. 31, []);
array_y2_higher_work2 := Array(0 .. 3, 0 .. 31, []);
array_y2_set_initial := Array(0 .. 3, 0 .. 31, []);
array_given_rad_poles := Array(0 .. 3, 0 .. 4, []);
array_given_ord_poles := Array(0 .. 3, 0 .. 4, []);
array_rad_test_poles := Array(0 .. 3, 0 .. 5, []);
array_ord_test_poles := Array(0 .. 3, 0 .. 5, []);
array_fact_2 := Array(0 .. 30, 0 .. 31, []);
term := 1;
while term <= 30 do array_y1_init[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 30 do array_y2_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 <= 3 do array_1st_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 3 do
array_last_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 3 do array_est_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 3 do array_max_est_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 3 do array_type_pole[term] := 0; term := term + 1 end do;
term := 1;
while term <= 3 do array_type_real_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 3 do array_type_complex_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 3 do array_est_digits[term] := 0; term := term + 1 end do
;
term := 1;
while term <= 30 do array_y1[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_y2[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_y1_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_y1_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_y1_higher_work2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 30 do
array_y1_set_initial[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 30 do
array_y2_higher[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 30 do
array_y2_higher_work[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 30 do
array_y2_higher_work2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 30 do
array_y2_set_initial[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 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 <= 3 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 <= 3 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 <= 3 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_y1);
zero_ats_ar(array_x);
zero_ats_ar(array_y2);
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_2);
array_const_2[1] := c(2);
zero_ats_ar(array_m1);
array_m1[1] := glob__m1;
iiif := 0;
while iiif <= ATS_MAX_TERMS do
jjjf := 0;
while jjjf <= ATS_MAX_TERMS do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
glob_yes_pole := 4;
glob_no_pole := 3;
glob_not_given := 0;
glob_no_sing_tests := 4;
glob_ratio_test := 1;
glob_three_term_test := 2;
glob_six_term_test := 3;
glob_log_10 := log(c(10.0));
MAX_UNCHANGED := 10;
glob__small := c(0.1*10^(-50));
glob_small_float := c(0.1*10^(-50));
glob_smallish_float := c(0.1*10^(-60));
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob__m2 := c(-2);
glob__m1 := c(-1);
glob__0 := c(0);
glob__1 := c(1);
glob__2 := c(2);
glob__3 := c(3);
glob__4 := c(4);
glob__5 := c(5);
glob__8 := c(8);
glob__10 := c(10);
glob__100 := c(100);
glob__pi := c(0.);
glob__0_5 := c(0.5);
glob__0_8 := c(0.8);
glob__m0_8 := c(-0.8);
glob__0_25 := c(0.25);
glob__0_125 := c(0.125);
glob_prec := c(0.10*10^(-15));
glob_check_sign := c(1.0);
glob_desired_digits_correct := c(8.0);
glob_max_estimated_step_error := c(0.);
glob_ratio_of_radius := c(0.1);
glob_percent_done := c(0.);
glob_total_exp_sec := c(0.1);
glob_optimal_expect_sec := c(0.1);
glob_estimated_size_answer := c(100.0);
glob_almost_1 := c(0.9990);
glob_clock_sec := c(0.);
glob_clock_start_sec := c(0.);
glob_disp_incr := c(0.1);
glob_h := c(0.1);
glob_diff_rc_fm := c(0.1);
glob_diff_rc_fmm1 := c(0.1);
glob_diff_rc_fmm2 := c(0.1);
glob_diff_ord_fm := c(0.1);
glob_diff_ord_fmm1 := c(0.1);
glob_diff_ord_fmm2 := c(0.1);
glob_six_term_ord_save := c(0.1);
glob_guess_error_rc := c(0.1);
glob_guess_error_ord := c(0.1);
glob_least_given_sing := c(0.99*10^201);
glob_least_ratio_sing := c(0.99*10^201);
glob_least_3_sing := c(0.99*10^101);
glob_least_6_sing := c(0.99*10^101);
glob_last_good_h := c(0.1);
glob_max_h := c(0.1);
glob_min_h := c(0.1*10^(-5));
glob_display_interval := c(0.1);
glob_abserr := c(0.1*10^(-10));
glob_relerr := c(0.1*10^(-10));
glob_min_pole_est := c(0.1*10^10);
glob_max_rel_trunc_err := c(0.1*10^(-10));
glob_max_trunc_err := c(0.1*10^(-10));
glob_max_hours := c(0.);
glob_optimal_clock_start_sec := c(0.);
glob_optimal_start := c(0.);
glob_upper_ratio_limit := c(1.0001);
glob_lower_ratio_limit := c(0.9999);
glob_max_sec := c(10000.0);
glob_orig_start_sec := c(0.);
glob_normmax := c(0.);
glob_max_minutes := c(0.);
glob_next_display := c(0.);
glob_est_digits := 1;
glob_subiter_method := 3;
glob_html_log := true;
glob_min_good_digits := 99999;
glob_good_digits := 0;
glob_min_apfp_est_good_digits := 99999;
glob_apfp_est_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
glob_h_reason := 0;
glob_sec_in_minute := 60;
glob_min_in_hour := 60;
glob_hours_in_day := 24;
glob_days_in_year := 365;
glob_sec_in_hour := 3600;
glob_sec_in_day := 86400;
glob_sec_in_year := 31536000;
glob_not_yet_finished := true;
glob_initial_pass := true;
glob_not_yet_start_msg := true;
glob_reached_optimal_h := false;
glob_optimal_done := false;
glob_type_given_pole := 0;
glob_optimize := false;
glob_look_poles := false;
glob_dump_closed_form := false;
glob_max_iter := 1000;
glob_no_eqs := 0;
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_start := 0;
glob_iter := 0;
array_y1_set_initial[1, 1] := true;
array_y1_set_initial[1, 2] := false;
array_y1_set_initial[1, 3] := false;
array_y1_set_initial[1, 4] := false;
array_y1_set_initial[1, 5] := false;
array_y1_set_initial[1, 6] := false;
array_y1_set_initial[1, 7] := false;
array_y1_set_initial[1, 8] := false;
array_y1_set_initial[1, 9] := false;
array_y1_set_initial[1, 10] := false;
array_y1_set_initial[1, 11] := false;
array_y1_set_initial[1, 12] := false;
array_y1_set_initial[1, 13] := false;
array_y1_set_initial[1, 14] := false;
array_y1_set_initial[1, 15] := false;
array_y1_set_initial[1, 16] := false;
array_y1_set_initial[1, 17] := false;
array_y1_set_initial[1, 18] := false;
array_y1_set_initial[1, 19] := false;
array_y1_set_initial[1, 20] := false;
array_y1_set_initial[1, 21] := false;
array_y1_set_initial[1, 22] := false;
array_y1_set_initial[1, 23] := false;
array_y1_set_initial[1, 24] := false;
array_y1_set_initial[1, 25] := false;
array_y1_set_initial[1, 26] := false;
array_y1_set_initial[1, 27] := false;
array_y1_set_initial[1, 28] := false;
array_y1_set_initial[1, 29] := false;
array_y1_set_initial[1, 30] := false;
array_y2_set_initial[2, 1] := true;
array_y2_set_initial[2, 2] := true;
array_y2_set_initial[2, 3] := false;
array_y2_set_initial[2, 4] := false;
array_y2_set_initial[2, 5] := false;
array_y2_set_initial[2, 6] := false;
array_y2_set_initial[2, 7] := false;
array_y2_set_initial[2, 8] := false;
array_y2_set_initial[2, 9] := false;
array_y2_set_initial[2, 10] := false;
array_y2_set_initial[2, 11] := false;
array_y2_set_initial[2, 12] := false;
array_y2_set_initial[2, 13] := false;
array_y2_set_initial[2, 14] := false;
array_y2_set_initial[2, 15] := false;
array_y2_set_initial[2, 16] := false;
array_y2_set_initial[2, 17] := false;
array_y2_set_initial[2, 18] := false;
array_y2_set_initial[2, 19] := false;
array_y2_set_initial[2, 20] := false;
array_y2_set_initial[2, 21] := false;
array_y2_set_initial[2, 22] := false;
array_y2_set_initial[2, 23] := false;
array_y2_set_initial[2, 24] := false;
array_y2_set_initial[2, 25] := false;
array_y2_set_initial[2, 26] := false;
array_y2_set_initial[2, 27] := false;
array_y2_set_initial[2, 28] := false;
array_y2_set_initial[2, 29] := false;
array_y2_set_initial[2, 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 := 2;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/mtest5postode.ode#################");
omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = neg ( y2 ) ; ")
;
omniout_str(ALWAYS,
"diff ( y2 , x , 2 ) = diff ( y1 , x , 1 ) ; ");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := c(0.5);");
omniout_str(ALWAYS, "x_end := c(5.0);");
omniout_str(ALWAYS, "array_y1_init[0 + 1] := exact_soln_y1(x_start);");
omniout_str(ALWAYS, "array_y2_init[0 + 1] := exact_soln_y2(x_start);");
omniout_str(ALWAYS, "array_y2_init[1 + 1] := exact_soln_y2p(x_start);")
;
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_type_given_pole := 3;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=8;");
omniout_str(ALWAYS, "glob_max_minutes:=(3.0);");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "glob_max_iter:=100000;");
omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.0000001);");
omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.9999999);");
omniout_str(ALWAYS, "glob_look_poles:=true;");
omniout_str(ALWAYS, "glob_h:=c(0.005);");
omniout_str(ALWAYS, "glob_display_interval:=c(0.01);");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y1 := proc(x)");
omniout_str(ALWAYS, "return(neg(cos(c(x))));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2 := proc(x)");
omniout_str(ALWAYS, "return(neg(sin(c(x))));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2p := proc(x)");
omniout_str(ALWAYS, "return(neg(cos(c(x))));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := glob__0;
glob_smallish_float := glob__0;
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob_almost_1 := c(0.99);
x_start := c(0.5);
x_end := c(5.0);
array_y1_init[1] := exact_soln_y1(x_start);
array_y2_init[1] := exact_soln_y2(x_start);
array_y2_init[2] := exact_soln_y2p(x_start);
glob_look_poles := true;
glob_type_given_pole := 3;
glob_desired_digits_correct := 8;
glob_max_minutes := 3.0;
glob_subiter_method := 3;
glob_max_iter := 100000;
glob_upper_ratio_limit := c(1.0000001);
glob_lower_ratio_limit := c(0.9999999);
glob_look_poles := true;
glob_h := c(0.005);
glob_display_interval := c(0.01);
glob_last_good_h := glob_h;
glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours;
glob_check_sign := c(my_check_sign(x_start, x_end));
glob__pi := arccos(glob__m1);
glob_prec = expt(10.0, c(-Digits));
if glob_optimize then
omniout_str(ALWAYS, "START of Optimize");
found_h := false;
glob_min_pole_est := glob_larger_float;
last_min_pole_est := glob_larger_float;
glob_least_given_sing := glob_larger_float;
glob_least_ratio_sing := glob_larger_float;
glob_least_3_sing := glob_larger_float;
glob_least_6_sing := glob_larger_float;
glob_min_h := float_abs(glob_min_h)*glob_check_sign;
glob_max_h := float_abs(glob_max_h)*glob_check_sign;
glob_h := float_abs(glob_min_h)*glob_check_sign;
glob_display_interval :=
c(float_abs(c(glob_display_interval))*glob_check_sign);
display_max := c(x_end) - c(x_start)/glob__10;
if display_max < glob_display_interval then
glob_display_interval := c(display_max)
end if;
chk_data();
min_value := glob_larger_float;
est_answer := est_size_answer();
opt_iter := 1;
est_needed_step_err :=
estimated_needed_step_error(x_start, x_end, glob_h, est_answer)
;
omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, "");
estimated_step_error := glob_small_float;
while opt_iter <= 100 and not found_h do
omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, "");
array_x[1] := c(x_start);
array_x[2] := c(glob_h);
glob_next_display := c(x_start);
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y1[term_no] := array_y1_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_y1_higher[r_order, term_no] :=
array_y1_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;
order_diff := 2;
term_no := 1;
while term_no <= order_diff do
array_y2[term_no] := array_y2_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_y2_higher[r_order, term_no] :=
array_y2_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;
if glob_subiter_method = 1 then atomall()
elif glob_subiter_method = 2 then
subiter := 1;
while subiter <= 3 do atomall(); subiter := subiter + 1
end do
else
subiter := 1;
while subiter <= 3 + ATS_MAX_TERMS do
atomall(); subiter := subiter + 1
end do
end if;
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_y1[term_no] := array_y1_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_y1_higher[r_order, term_no] := array_y1_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;
order_diff := 2;
term_no := 1;
while term_no <= order_diff do
array_y2[term_no] := array_y2_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_y2_higher[r_order, term_no] := array_y2_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();
if glob_subiter_method = 1 then atomall()
elif glob_subiter_method = 2 then
subiter := 1;
while subiter <= 3 do atomall(); subiter := subiter + 1
end do
else
subiter := 1;
while subiter <= 3 + ATS_MAX_TERMS do
atomall(); subiter := subiter + 1
end do
end if;
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_y1_higher_work[2, iii] := array_y1_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_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_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_y1_higher_work[1, iii] := array_y1_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_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_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_y1_higher_work[1, iii] := array_y1_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_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_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_y1[term_no] := array_y1_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y1_higher[ord, term_no] :=
array_y1_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
order_diff := 3;
ord := 3;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 3;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 2;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 2;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[2, iii] := array_y2_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_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 3;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 3;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_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_y2_higher_work[1, iii] := array_y2_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_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_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_y2_higher_work[1, iii] := array_y2_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_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_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_y2[term_no] := array_y2_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y2_higher[ord, term_no] :=
array_y2_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 ( y1 , x , 1 ) = neg ( y2 ) ; ");
omniout_str(INFO,
"diff ( y2 , x , 2 ) = diff ( y1 , x , 1 ) ; ")
;
omniout_int(INFO, "Iterations ", 32, glob_iter,
4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2015-05-02T21:41:05-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"mtest5");
logitem_str(html_log_file,
"diff ( y1 , x , 1 ) = neg ( y2 ) ; ");
logitem_float(html_log_file, x_start);
logitem_float(html_log_file, x_end);
logitem_float(html_log_file, array_x[1]);
logitem_float(html_log_file, glob_h);
logitem_h_reason(html_log_file);
logitem_integer(html_log_file, Digits);
logitem_float(html_log_file, glob_desired_digits_correct);
if array_est_digits[1] <> -16 then
logitem_integer(html_log_file, array_est_digits[1])
else logitem_str(html_log_file, "Unknown")
end if;
if glob_min_good_digits <> -16 then
logitem_integer(html_log_file, glob_min_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
if glob_good_digits <> -16 then
logitem_integer(html_log_file, glob_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
logitem_integer(html_log_file, ATS_MAX_TERMS);
if glob_type_given_pole = 0 then
logitem_str(html_log_file, "Not Given");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 4 then
logitem_str(html_log_file, "No Solution");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 5 then
logitem_str(html_log_file, "Some Pole");
logitem_str(html_log_file, "????")
elif glob_type_given_pole = 3 then
logitem_str(html_log_file, "No Pole");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 1 then
logitem_str(html_log_file, "Real Sing");
logitem_float(html_log_file, glob_least_given_sing)
elif glob_type_given_pole = 2 then
logitem_str(html_log_file, "Complex Sing");
logitem_float(html_log_file, glob_least_given_sing)
end if;
if glob_least_ratio_sing < glob_large_float then
logitem_float(html_log_file, glob_least_ratio_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_3_sing < glob_large_float then
logitem_float(html_log_file, glob_least_3_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_6_sing < glob_large_float then
logitem_float(html_log_file, glob_least_6_sing)
else logitem_str(html_log_file, "NONE")
end if;
logitem_integer(html_log_file, glob_iter);
logitem_time(html_log_file, glob_clock_sec);
if c(glob_percent_done) < glob__100 then
logitem_time(html_log_file, glob_total_exp_sec); 0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 308.maple.seems.ok | ");
logitem_str(html_log_file,
"mtest5 diffeq.mxt");
logitem_str(html_log_file, "mtest5 maple results");
logitem_str(html_log_file, "OK");
logend(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logitem_str(html_log_file, "diff ( y2 , x , 2 ) = d\
iff ( y1 , x , 1 ) ; ");
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
if array_est_digits[2] <> -16 then
logitem_integer(html_log_file, array_est_digits[2])
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");
logditto(html_log_file);
if glob_type_given_pole = 0 then
logditto(html_log_file); logditto(html_log_file)
elif glob_type_given_pole = 4 then
logditto(html_log_file); logditto(html_log_file)
elif glob_type_given_pole = 5 then
logditto(html_log_file); logditto(html_log_file)
elif glob_type_given_pole = 3 then
logditto(html_log_file); logditto(html_log_file)
elif glob_type_given_pole = 1 then
logditto(html_log_file); logditto(html_log_file)
elif glob_type_given_pole = 2 then
logditto(html_log_file); logditto(html_log_file)
end if;
if glob_least_ratio_sing < glob_large_float then
logditto(html_log_file)
else logditto(html_log_file)
end if;
if glob_least_3_sing < glob_large_float then
logditto(html_log_file)
else logditto(html_log_file)
end if;
if glob_least_6_sing < glob_large_float then
logditto(html_log_file)
else logditto(html_log_file)
end if;
logditto(html_log_file);
logditto(html_log_file);
if c(glob_percent_done) < glob__100 then
logditto(html_log_file); 0
else logditto(html_log_file); 0
end if;
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end if
end proc
# End Function number 12
> main();
##############ECHO OF PROBLEM#################
##############temp/mtest5postode.ode#################
diff ( y1 , x , 1 ) = neg ( y2 ) ;
diff ( y2 , x , 2 ) = diff ( y1 , x , 1 ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := c(0.5);
x_end := c(5.0);
array_y1_init[0 + 1] := exact_soln_y1(x_start);
array_y2_init[0 + 1] := exact_soln_y2(x_start);
array_y2_init[1 + 1] := exact_soln_y2p(x_start);
glob_look_poles := true;
glob_type_given_pole := 3;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=8;
glob_max_minutes:=(3.0);
glob_subiter_method:=3;
glob_max_iter:=100000;
glob_upper_ratio_limit:=c(1.0000001);
glob_lower_ratio_limit:=c(0.9999999);
glob_look_poles:=true;
glob_h:=c(0.005);
glob_display_interval:=c(0.01);
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y1 := proc(x)
return(neg(cos(c(x))));
end;
exact_soln_y2 := proc(x)
return(neg(sin(c(x))));
end;
exact_soln_y2p := proc(x)
return(neg(cos(c(x))));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
TOP MAIN SOLVE Loop
memory used=3.8MB, alloc=40.3MB, time=0.13
x[1] = 0.5
y1[1] (closed_form) = -0.87758256189037271611628158260383
y1[1] (numeric) = -0.87758256189037271611628158260383
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
y2[1] (closed_form) = -0.47942553860420300027328793521557
y2[1] (numeric) = -0.47942553860420300027328793521557
absolute error = 0
relative error = 0 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.51
y1[1] (closed_form) = -0.87274450764575126310580847357551
y1[1] (numeric) = -0.87274450764575126310548553836393
absolute error = 3.2293521158e-22
relative error = 3.7002262260134445518481841751712e-20 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
y2[1] (closed_form) = -0.48817724688290749450013023767457
y2[1] (numeric) = -0.48817724688290749462247640457479
absolute error = 1.2234616690022e-19
relative error = 2.5061833111112924997505687286828e-17 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.52
y1[1] (closed_form) = -0.86781917967764990038784757198851
y1[1] (numeric) = -0.86781917967764990038407895948097
absolute error = 3.76861250754e-21
relative error = 4.3426241269982593838454058926118e-19 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
y2[1] (closed_form) = -0.49688013784373671433445894254775
y2[1] (numeric) = -0.49688013784373671495868242948029
absolute error = 6.2422348693254e-19
relative error = 1.2562858512345111183515164508660e-16 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 18
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.53
y1[1] (closed_form) = -0.8628070705147610118066950185642
y1[1] (numeric) = -0.86280707051476101179257348677463
absolute error = 1.412153178957e-20
relative error = 1.6366963452379829633349852656947e-18 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
y2[1] (closed_form) = -0.50553334120484696181366102246608
y2[1] (numeric) = -0.50553334120484696331711860517896
absolute error = 1.50345758271288e-18
relative error = 2.9740028207232815486042843945565e-16 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 18
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.54
y1[1] (closed_form) = -0.8577086813638241425379687789178
y1[1] (numeric) = -0.8577086813638241425028247074642
absolute error = 3.514407145360e-20
relative error = 4.0974368357468607183549193653684e-18 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
y2[1] (closed_form) = -0.51413599165311310467728068295824
y2[1] (numeric) = -0.51413599165311310743507928284706
absolute error = 2.75779859988882e-18
relative error = 5.3639477582995262944940503474303e-16 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 18
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=46.1MB, alloc=40.3MB, time=0.64
TOP MAIN SOLVE Loop
x[1] = 0.55
y1[1] (closed_form) = -0.85252452205950574280498179761777
y1[1] (numeric) = -0.85252452205950574273440606180094
absolute error = 7.057573581683e-20
relative error = 8.2784405598486529461017856040074e-18 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
y2[1] (closed_form) = -0.52268722893065916778837810775729
y2[1] (numeric) = -0.52268722893065917217329975607178
absolute error = 4.38492164831449e-18
relative error = 8.3891884201674330685330582586950e-16 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 18
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.56
y1[1] (closed_form) = -0.84725511101341612609452550386632
y1[1] (numeric) = -0.84725511101341612597039309685337
absolute error = 1.2413240701295e-19
relative error = 1.4651125192325264895325116571847e-17 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
y2[1] (closed_form) = -0.53118619792088340385186944111203
y2[1] (numeric) = -0.53118619792088341023429669559359
absolute error = 6.38242725448156e-18
relative error = 1.2015423743054745989141686205183e-15 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.57
y1[1] (closed_form) = -0.84190097516226874013375636391601
y1[1] (numeric) = -0.8419009751622687399342507624485
absolute error = 1.9950560146751e-19
relative error = 2.3697038886201208348803131838359e-17 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
y2[1] (closed_form) = -0.53963204873396924099446349307883
y2[1] (numeric) = -0.53963204873396924974230531821778
absolute error = 8.74784182513895e-18
relative error = 1.6210752948536436743308378172095e-15 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.58
y1[1] (closed_form) = -0.83646264991518693465788732805002
y1[1] (numeric) = -0.8364626499151869343575255969847
absolute error = 3.0036173106532e-19
relative error = 3.5908564607848916429713824811201e-17 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
y2[1] (closed_form) = -0.54802393679187355618269605957646
y2[1] (numeric) = -0.54802393679187356766131418160915
absolute error = 1.147861812203269e-17
relative error = 2.0945468530495951455747038594004e-15 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.59
y1[1] (closed_form) = -0.83094067910016349524799652249068
y1[1] (numeric) = -0.83094067910016349481765515337029
absolute error = 4.3034136912039e-19
relative error = 5.1789661999267178056210022099925e-17 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
y2[1] (closed_form) = -0.55636102291278377572254337887577
y2[1] (numeric) = -0.55636102291278379029467912657126
absolute error = 1.457213574769549e-17
relative error = 2.6191870292070848452730852741073e-15 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=88.4MB, alloc=40.3MB, time=1.14
TOP MAIN SOLVE Loop
x[1] = 0.6
y1[1] (closed_form) = -0.82533561490967829724095249895538
y1[1] (numeric) = -0.82533561490967829664789397769655
absolute error = 5.9305852125883e-19
relative error = 7.1856649652000313776752486800948e-17 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
y2[1] (closed_form) = -0.56464247339503535720094544565866
y2[1] (numeric) = -0.56464247339503537522664708787329
absolute error = 1.802570164221463e-17
relative error = 3.1924097976248914864458895037051e-15 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.61
y1[1] (closed_form) = -0.81964801784547951790074657865482
y1[1] (numeric) = -0.81964801784547951710864667733086
absolute error = 7.9209990132396e-19
relative error = 9.6639030910617915562278994840295e-17 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 32
h = 0.005
y2[1] (closed_form) = -0.57286746010048126119097603216272
y2[1] (numeric) = -0.5728674601004812830275266230675
absolute error = 2.183655059090478e-17
relative error = 3.8117980356354395237845522524697e-15 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.62
y1[1] (closed_form) = -0.8138784566625339286839996543607
y1[1] (numeric) = -0.81387845666253392765297544194832
absolute error = 1.03102421241238e-18
relative error = 1.2668036657958661955649213716780e-16 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 18
h = 0.005
y2[1] (closed_form) = -0.58103516053730507584296322758221
y2[1] (numeric) = -0.58103516053730510184480897039341
absolute error = 2.600184574281120e-17
relative error = 4.4750898927986242446081180708582e-15 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.63
y1[1] (closed_form) = -0.80802750831215187252370896577706
y1[1] (numeric) = -0.80802750831215187121034753262817
absolute error = 1.31336143314889e-18
relative error = 1.6253919818798060638192977266428e-16 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 18
h = 0.005
y2[1] (closed_form) = -0.58914475794226951311811209079462
y2[1] (numeric) = -0.58914475794226954363679123076202
absolute error = 3.051867913996740e-17
relative error = 5.1801664579960389493091884246155e-15 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.64
y1[1] (closed_form) = -0.80209575788429261358611077926032
y1[1] (numeric) = -0.80209575788429261194349866995287
absolute error = 1.64261210930745e-18
relative error = 2.0479002577450449332260516025654e-16 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 18
h = 0.005
y2[1] (closed_form) = -0.59719544136239205188354623920793
y2[1] (numeric) = -0.59719544136239208726761849653756
absolute error = 3.538407225732963e-17
relative error = 5.9250405824611366814312749022424e-15 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=130.7MB, alloc=40.3MB, time=1.63
TOP MAIN SOLVE Loop
x[1] = 0.65
y1[1] (closed_form) = -0.79608379854905582891760457067991
y1[1] (numeric) = -0.79608379854905582689535791979533
absolute error = 2.02224665088458e-18
relative error = 2.5402434449367408551225738505177e-16 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 18
h = 0.005
y2[1] (closed_form) = -0.60518640573603956037252167860594
y2[1] (numeric) = -0.60518640573603960096749823191523
absolute error = 4.059497655330929e-17
relative error = 6.7078467342532065614957338451980e-15 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.66
y1[1] (closed_form) = -0.78999223149736509278381709123024
y1[1] (numeric) = -0.78999223149736509032811245649967
absolute error = 2.45570463473057e-18
relative error = 3.1085174471601885050348787569082e-16 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 18
h = 0.005
y2[1] (closed_form) = -0.6131168519734337886151454793963
y2[1] (numeric) = -0.61311685197343383476341951021939
absolute error = 4.614827403082309e-17
relative error = 7.5268317747727938882144015083094e-15 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.67
y1[1] (closed_form) = -0.78382166588084928530294214483812
y1[1] (numeric) = -0.78382166588084928235654803199439
absolute error = 2.94639411284373e-18
relative error = 3.7590108070470443262965629400686e-16 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 18
h = 0.005
y2[1] (closed_form) = -0.62098598703655968035744391412659
y2[1] (numeric) = -0.62098598703655973239822172290571
absolute error = 5.204077780877912e-17
relative error = 8.3803465609788859993164508631898e-15 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.68
y1[1] (closed_form) = -0.77757271875092793718239408404432
y1[1] (numeric) = -0.77757271875092793368470315761333
absolute error = 3.49769092643099e-18
relative error = 4.4982171340187800757597783471374e-16 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 18
h = 0.005
y2[1] (closed_form) = -0.62879302401846851370417818742025
y2[1] (numeric) = -0.62879302401846857197341089133588
absolute error = 5.826923270391563e-17
relative error = 9.2668382883020315920013940750138e-15 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=172.9MB, alloc=40.3MB, time=2.13
x[1] = 0.69
y1[1] (closed_form) = -0.77124601499710660197353931549777
y1[1] (numeric) = -0.77124601499710659786060128965914
absolute error = 4.11293802583863e-18
relative error = 5.3328483335554868997847899362401e-16 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 18
h = 0.005
y2[1] (closed_form) = -0.63653718222196794023742920700872
y2[1] (numeric) = -0.63653718222196800506774502991699
absolute error = 6.483031582290827e-17
relative error = 1.0184843499103118012143884050072e-14 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.7
y1[1] (closed_form) = -0.76484218728448842625585999019186
y1[1] (numeric) = -0.76484218728448842146041519373708
absolute error = 4.79544479645478e-18
relative error = 6.2698487036660813918096448404091e-16 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 18
h = 0.005
y2[1] (closed_form) = -0.64421768723769105367261435139872
y2[1] (numeric) = -0.64421768723769112539325151605839
absolute error = 7.172063716465967e-17
relative error = 1.1132981690115808403066168144647e-14 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.71
y1[1] (closed_form) = -0.75836187599050816654145794413955
y1[1] (numeric) = -0.75836187599050816099297155345398
absolute error = 5.54848639068557e-18
relative error = 7.3164099704229015659981182788196e-16 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 18
h = 0.005
y2[1] (closed_form) = -0.65183377102153668121012797285284
y2[1] (numeric) = -0.65183377102153676014686820553713
absolute error = 7.893674023268429e-17
relative error = 1.2109949459810392178979787980049e-14 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.72
y1[1] (closed_form) = -0.75180572914089497944548696225195
y1[1] (numeric) = -0.75180572914089497307018389614683
absolute error = 6.37530306610512e-18
relative error = 8.4799873411317571349250139083549e-16 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 18
h = 0.005
y2[1] (closed_form) = -0.65938467197147315361800383264817
y2[1] (numeric) = -0.65938467197147324009310649014807
absolute error = 8.647510265749990e-17
relative error = 1.3114515143178981507874403967467e-14 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.73
y1[1] (closed_form) = -0.74517440234487038879013215855033
y1[1] (numeric) = -0.74517440234487038151103262867123
absolute error = 7.27909952987910e-18
relative error = 9.7683166611382026985518248986490e-16 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 18
h = 0.005
y2[1] (closed_form) = -0.66686963500369787373259413076153
y2[1] (numeric) = -0.66686963500369796806473095969727
absolute error = 9.433213682893574e-17
relative error = 1.4145513887195157230037165407874e-14 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=215.1MB, alloc=40.3MB, time=2.61
x[1] = 0.74
y1[1] (closed_form) = -0.73846855872958790979142456069883
y1[1] (numeric) = -0.73846855872958790152838027113811
absolute error = 8.26304428956072e-18
relative error = 1.1189432768506638483955018518998e-15 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 0.005
y2[1] (closed_form) = -0.67428791162814506748388115760817
y2[1] (numeric) = -0.6742879116281451699880716958744
absolute error = 1.0250419053826623e-16
relative error = 1.5201843125254636552734446815992e-14 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.75
y1[1] (closed_form) = -0.73168886887382088631183875300008
y1[1] (numeric) = -0.73168886887382087698156974264352
absolute error = 9.33026901035656e-18
relative error = 1.2751689149948728870122353755656e-15 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 0.005
y2[1] (closed_form) = -0.68163876002333416673324195277989
y2[1] (numeric) = -0.6816387600233342777207895828575
absolute error = 1.1098754763007761e-16
relative error = 1.6282458413350531006417241428943e-14 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.76
y1[1] (closed_form) = -0.72483601074090517233968836666701
y1[1] (numeric) = -0.72483601074090516185582048770746
absolute error = 1.048386787895955e-17
relative error = 1.4463779011535673177681934720507e-15 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 0.005
y2[1] (closed_form) = -0.68892144511055133914775563876973
y2[1] (numeric) = -0.68892144511055145892618430254335
absolute error = 1.1977842866377362e-16
relative error = 1.7386369594657160887759604395207e-14 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.77
y1[1] (closed_form) = -0.71791066961094336337129056532434
y1[1] (numeric) = -0.71791066961094335164439359127968
absolute error = 1.172689697404466e-17
relative error = 1.6334757889027900873028496458726e-15 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 17
h = 0.005
y2[1] (closed_form) = -0.69613523862735674701988373445221
y2[1] (numeric) = -0.69613523862735687589287531907742
absolute error = 1.2887299158462521e-16
relative error = 1.8512637262658571391180507539572e-14 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.78
y1[1] (closed_form) = -0.71091353801227735721626502376456
y1[1] (numeric) = -0.71091353801227734415389138024204
absolute error = 1.306237364352252e-17
relative error = 1.8374067935244377079851141703368e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = 0.005
y2[1] (closed_form) = -0.70327941920041018436789732511792
y2[1] (numeric) = -0.70327941920041032263522972938561
absolute error = 1.3826733240426769e-16
relative error = 1.9660369496020515175294137162186e-14 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=257.3MB, alloc=40.3MB, time=3.11
x[1] = 0.79
y1[1] (closed_form) = -0.70384531565223609691278086108495
y1[1] (numeric) = -0.70384531565223608241950497244022
absolute error = 1.449327588864473e-17
relative error = 2.0591564035933333794902439746357e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = 0.005
y2[1] (closed_form) = -0.7103532724176078098140288749692
y2[1] (numeric) = -0.710353272417607957771514765517
absolute error = 1.4795748589054780e-16
relative error = 2.0828718841118457385705296415401e-14 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.8
y1[1] (closed_form) = -0.69670670934716542092074998164232
y1[1] (numeric) = -0.69670670934716540489820822658826
absolute error = 1.602254175505406e-17
relative error = 2.2997541921288013144069570993652e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = 0.005
y2[1] (closed_form) = -0.71735609089952276162717461058139
y2[1] (numeric) = -0.7173560908995229195666008772031
absolute error = 1.5793942626662171e-16
relative error = 2.2016879520542561688252720978024e-14 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.81
y1[1] (closed_form) = -0.6894984329517470175496392406801
y1[1] (numeric) = -0.68949843295174699989657050980866
absolute error = 1.765306873087144e-17
relative error = 2.5602768457788286136792870962349e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = 0.005
y2[1] (closed_form) = -0.72428717437014251092817685251454
y2[1] (numeric) = -0.72428717437014267913724477171828
absolute error = 1.6820906791920374e-16
relative error = 2.3224084848041438492098598719268e-14 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.82
y1[1] (closed_form) = -0.68222120728761355166655797843693
y1[1] (numeric) = -0.68222120728761353227884482652619
absolute error = 1.938771315191074e-17
relative error = 2.8418514324690569406454688088216e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = 0.005
y2[1] (closed_form) = -0.73114582972689587938131336468772
y2[1] (numeric) = -0.73114582972689605814357948055216
absolute error = 1.7876226611586444e-16
relative error = 2.4449604832272286675275319837675e-14 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.83
y1[1] (closed_form) = -0.67487576007126710211246291786445
y1[1] (numeric) = -0.6748757600712670808831733037531
absolute error = 2.122928961411135e-17
relative error = 3.1456589301517556413848587084164e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = 0.005
y2[1] (closed_form) = -0.73793137110996271872858022613808
y2[1] (numeric) = -0.7379313711099629083233979574136
absolute error = 1.8959481773127552e-16
relative error = 2.5692743953424237906920723923232e-14 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=299.7MB, alloc=40.3MB, time=3.59
TOP MAIN SOLVE Loop
x[1] = 0.84
y1[1] (closed_form) = -0.66746282584130811792267103687086
y1[1] (numeric) = -0.66746282584130809474210064359324
absolute error = 2.318057039327762e-17
relative error = 3.4729380417642750851648569734907e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = 0.005
y2[1] (closed_form) = -0.74464311997085932125657267062965
y2[1] (numeric) = -0.74464311997085952195903465292729
absolute error = 2.0070246198229764e-16
relative error = 2.6952839098298777037497925448154e-14 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.85
y1[1] (closed_form) = -0.65998314588498217039541602946147
y1[1] (numeric) = -0.65998314588498214515113115724875
absolute error = 2.524428487221272e-17
relative error = 3.8249893242898265925422890335556e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = 0.005
y2[1] (closed_form) = -0.75128040514029270271207152423547
y2[1] (numeric) = -0.75128040514029291479295269604176
absolute error = 2.1208088117180629e-16
relative error = 2.8229257640787623297613503446970e-14 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.86
y1[1] (closed_form) = -0.65243746816405184627203066422386
y1[1] (numeric) = -0.65243746816405181884891168888959
absolute error = 2.742311897533427e-17
relative error = 4.2031796629495343699054348702919e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = 0.005
y2[1] (closed_form) = -0.75784256289527697229458872952865
y2[1] (numeric) = -0.75784256289527719602029017067798
absolute error = 2.2372570144114933e-16
relative error = 2.9521395655902877726300950701850e-14 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.87
y1[1] (closed_form) = -0.64482654724000119477766380548283
y1[1] (numeric) = -0.64482654724000116505794919462574
absolute error = 2.971971461085709e-17
relative error = 4.6089471250934031152884661403963e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = 0.005
y2[1] (closed_form) = -0.76432893702550507814480282372285
y2[1] (numeric) = -0.76432893702550531377729635485208
absolute error = 2.3563249353112923e-16
relative error = 3.0828676256603163518555243350441e-14 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.88
y1[1] (closed_form) = -0.63715114419858020801549860572209
y1[1] (numeric) = -0.63715114419858017587882948509413
absolute error = 3.213666912062796e-17
relative error = 5.0438062323579472521334600948066e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = 0.005
y2[1] (closed_form) = -0.77073887889896929120964513075599
y2[1] (numeric) = -0.77073887889896953900641868215717
absolute error = 2.4779677355140118e-16
relative error = 3.2150548043636852341591799058724e-14 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=342.0MB, alloc=40.3MB, time=4.09
TOP MAIN SOLVE Loop
x[1] = 0.89
y1[1] (closed_form) = -0.62941202657369688020355305738025
y1[1] (numeric) = -0.62941202657369684552701831968423
absolute error = 3.467653473769602e-17
relative error = 5.5093536941871253246548649142518e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = 0.005
y2[1] (closed_form) = -0.77707174752682386549033371297318
y2[1] (numeric) = -0.777071747526824125704337471151
absolute error = 2.6021400375817782e-16
relative error = 3.3486483659502168513176134997002e-14 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.9
y1[1] (closed_form) = -0.62160996827066445648471615140713
y1[1] (numeric) = -0.62160996827066441914289809970584
absolute error = 3.734181805170129e-17
relative error = 6.0072746509498915751721578961118e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = 0.005
y2[1] (closed_form) = -0.78332690962748338846138231571355
y2[1] (numeric) = -0.78332690962748366134097565584318
absolute error = 2.7287959334012963e-16
relative error = 3.4835978438414612422175765248176e-14 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.91
y1[1] (closed_form) = -0.61374574948881154652117822617468
y1[1] (numeric) = -0.61374574948881150638619874401201
absolute error = 4.013497948216267e-17
relative error = 6.5393494807240733606853901621824e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = 0.005
y2[1] (closed_form) = -0.78950373968995041187895751787155
y2[1] (numeric) = -0.78950373968995069766785673024088
absolute error = 2.8578889921236933e-16
relative error = 3.6198549144884707263009061910640e-14 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.92
y1[1] (closed_form) = -0.60582015664346284179740470667438
y1[1] (numeric) = -0.60582015664346279873897194692865
absolute error = 4.305843275974573e-17
relative error = 7.1074612304599284390322854696983e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = 0.005
y2[1] (closed_form) = -0.79560162003636603026827610248162
y2[1] (numeric) = -0.79560162003636632920550292088893
absolute error = 2.9893722681840731e-16
relative error = 3.7573732794151831284501100047096e-14 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.93
y1[1] (closed_form) = -0.59783398228729823849490708443298
y1[1] (numeric) = -0.5978339822872981923803626688435
absolute error = 4.611454441558948e-17
relative error = 7.7136037398135779325836842010606e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = 0.005
y2[1] (closed_form) = -0.80161994088377715208431921591065
y2[1] (numeric) = -0.80161994088377746440415015587486
absolute error = 3.1231983093996421e-16
relative error = 3.8961085548300487350663293960176e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=384.4MB, alloc=40.3MB, time=4.59
TOP MAIN SOLVE Loop
x[1] = 0.94
y1[1] (closed_form) = -0.58978802503109822996098981522402
y1[1] (numeric) = -0.58978802503109818065535653645395
absolute error = 4.930563327877007e-17
relative error = 8.3598905345984757857814331120507e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = 0.005
y2[1] (closed_form) = -0.80755810040511428687021979863415
y2[1] (numeric) = -0.80755810040511461280213631315971
absolute error = 3.2593191651452556e-16
relative error = 4.0360181682410305561640507508809e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.95
y1[1] (closed_form) = -0.58168308946388349416618097376046
y1[1] (numeric) = -0.58168308946388344153221099178233
absolute error = 5.263396998197813e-17
relative error = 9.0485645767163316088161156322470e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = 0.005
y2[1] (closed_form) = -0.81341550478937375068542210210256
y2[1] (numeric) = -0.81341550478937409045406156262509
absolute error = 3.3976863946052253e-16
relative error = 4.1770612615566309455570215964709e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.96
y1[1] (closed_form) = -0.57351998607245666212505080035186
y1[1] (numeric) = -0.57351998607245660602327432486609
absolute error = 5.610177647548577e-17
relative error = 9.7820089688030597790592429370456e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = 0.005
y2[1] (closed_form) = -0.81919156830099827163322214643043
y2[1] (numeric) = -0.81919156830099862545832965645197
absolute error = 3.5382510751002154e-16
relative error = 4.3191986001986584003750040509333e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.97
y1[1] (closed_form) = -0.56529953116035431303652775484986
y1[1] (numeric) = -0.56529953116035425332530220537251
absolute error = 5.971122554947735e-17
relative error = 1.0562758724903224943410670389312e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = -0.82488571333845005747662003785634
y2[1] (numeric) = -0.82488571333845042557300108666113
absolute error = 3.6809638104880479e-16
relative error = 4.4623924877915189519396160642904e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=426.7MB, alloc=40.3MB, time=5.09
x[1] = 0.98
y1[1] (closed_form) = -0.55702254676621730087665826735994
y1[1] (numeric) = -0.55702254676621723741221790254233
absolute error = 6.346444036481761e-17
relative error = 1.1393513733556942342461057641466e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = -0.83049737049197046808453328771915
y2[1] (numeric) = -0.83049737049197085066200725144165
absolute error = 3.8257747396372250e-16
relative error = 4.6066066860282899539986761447451e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 0.99
y1[1] (closed_form) = -0.54868986058158757534312640865361
y1[1] (numeric) = -0.54868986058158750797963241632449
absolute error = 6.736349399232912e-17
relative error = 1.2277153057088885005841411709393e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = -0.83602597860052051678925941154711
y2[1] (numeric) = -0.83602597860052091405261390874406
absolute error = 3.9726335449719695e-16
relative error = 4.7518063393460870439762923618054e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1
y1[1] (closed_form) = -0.54030230586813971740093660744298
y1[1] (numeric) = -0.54030230586813964599052764679291
absolute error = 7.141040896065007e-17
relative error = 1.3216750731039396094001183947532e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = -0.8414709848078965066525023216303
y2[1] (numeric) = -0.84147098480789691880144843038729
absolute error = 4.1214894610875699e-16
relative error = 4.8979579040725744377761634590610e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.01
y1[1] (closed_form) = -0.53186072137435546620673135577918
y1[1] (numeric) = -0.53186072137435539059957454303717
absolute error = 7.560715681274201e-17
relative error = 1.4215593251061899645515388035885e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = -0.84683184461801519012309878478201
y2[1] (numeric) = -0.84683184461801561735222712826342
absolute error = 4.2722912834348141e-16
relative error = 5.0450290817322045495453866364557e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.02
y1[1] (closed_form) = -0.52336595125164956988961380803381
y1[1] (numeric) = -0.52336595125164948993395613691772
absolute error = 7.995565767111609e-17
relative error = 1.5277198961816124053016428996346e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = -0.85210802194936292361654998545538
y2[1] (numeric) = -0.85210802194936336611528769268327
absolute error = 4.4249873770722789e-16
relative error = 5.1929887562251311234661384890864e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=469.0MB, alloc=40.3MB, time=5.59
x[1] = 1.03
y1[1] (closed_form) = -0.51481884496995534753350229983735
y1[1] (numeric) = -0.51481884496995526307572248799238
absolute error = 8.445777981184497e-17
relative error = 1.6405339594119538741244400210185e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = -0.85729898918860337214627438529442
y2[1] (numeric) = -0.85729898918860383009884293381836
absolute error = 4.5795256854852394e-16
relative error = 5.3418069346139828455781017971686e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.04
y1[1] (closed_form) = -0.50622025723277840373447342099217
y1[1] (numeric) = -0.50622025723277831461913417356576
absolute error = 8.911533924742641e-17
relative error = 1.7604064233732936191908478098756e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = -0.86240422724333840328079169211617
y2[1] (numeric) = -0.86240422724333887686616563911114
absolute error = 4.7358537394699497e-16
relative error = 5.4914546912739887158931732549270e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.05
y1[1] (closed_form) = -0.4975710478917269902908495728121
y1[1] (numeric) = -0.49757104789172689636075025424872
absolute error = 9.393009931856338e-17
relative error = 1.8877726048683375596555563771219e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = -0.86742322559401689438140948500027
y2[1] (numeric) = -0.86742322559401738377327609320416
absolute error = 4.8939186660820389e-16
relative error = 5.6419041151805135712186831706148e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.06
y1[1] (closed_form) = -0.48887208186052756191863753995641
y1[1] (numeric) = -0.48887208186052746301486724503245
absolute error = 9.890377029492396e-17
relative error = 2.0231012153224295982325836801306e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = -0.87235548234498626228294592199742
y2[1] (numeric) = -0.87235548234498676764966568677314
absolute error = 5.0536671976477572e-16
relative error = 5.7931282601250478925903672582800e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.07
y1[1] (closed_form) = -0.48012422902853412436509306817592
y1[1] (numeric) = -0.48012422902853402032708408323237
absolute error = 1.0403800898494355e-16
relative error = 2.1668977046930180468102448328813e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = -0.87720050427468161030706325777682
y2[1] (numeric) = -0.87720050427468213181163134145674
absolute error = 5.2150456808367992e-16
relative error = 5.9451010976662517479068213307339e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=511.4MB, alloc=40.3MB, time=6.08
x[1] = 1.08
y1[1] (closed_form) = -0.47132836417374002391352478852603
y1[1] (numeric) = -0.47132836417373991457910643379604
absolute error = 1.0933441835472999e-16
relative error = 2.3197080138895985775946767566853e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = -0.88195780688494747373533498762476
y2[1] (numeric) = -0.8819578068849480115353435671669
absolute error = 5.3780000857954214e-16
relative error = 6.0977974726369063184415641737374e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.09
y1[1] (closed_form) = -0.46248536687530087702789707387514
y1[1] (numeric) = -0.46248536687530076223334991774361
absolute error = 1.1479454715613153e-16
relative error = 2.4821227951863692925635956593462e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = -0.88662691444948723160860062863605
y2[1] (numeric) = -0.88662691444948778585620216249263
absolute error = 5.5424760153385658e-16
relative error = 6.2511930610407054897297188121003e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.1
y1[1] (closed_form) = -0.45359612142557738777137005178472
y1[1] (numeric) = -0.45359612142557726735148048775891
absolute error = 1.2041988956402581e-16
relative error = 2.6547821702171100332160768836356e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = -0.8912073600614353399518025778717
y2[1] (numeric) = -0.89120736006143591079367399784053
absolute error = 5.7084187141996883e-16
relative error = 6.4052643301848165935186405535349e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.11
y1[1] (closed_form) = -0.44466151674170684864373751193357
y1[1] (numeric) = -0.44466151674170672243185268904661
absolute error = 1.2621188482288696e-16
relative error = 2.8383811072231915246552710216202e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = -0.89569868568004762924062595933937
y2[1] (numeric) = -0.89569868568004821681793379303834
absolute error = 5.8757730783369897e-16
relative error = 6.5599885009051733419857247961272e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.12
y1[1] (closed_form) = -0.43568244627671216761398879396113
y1[1] (numeric) = -0.43568244627671203544207189127442
absolute error = 1.3217191690268671e-16
relative error = 3.0336755137190268454408353246556e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = -0.90010044217650499711910324733915
y2[1] (numeric) = -0.9001004421765056015674696768124
absolute error = 6.0444836642947325e-16
relative error = 6.7153435117515927325858333938494e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=553.7MB, alloc=40.3MB, time=6.58
TOP MAIN SOLVE Loop
x[1] = 1.13
y1[1] (closed_form) = -0.42665980793015731037121583565354
y1[1] (numeric) = -0.42665980793015717206990167146994
absolute error = 1.3830131416418360e-16
relative error = 3.2414891581918827498526988527455e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = -0.9044121893788259160370815224114
y2[1] (numeric) = -0.9044121893788265374865513842438
absolute error = 6.2144946986183240e-16
relative error = 6.8713079850091388564932312552855e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.14
y1[1] (closed_form) = -0.41759450395835809217518674082258
y1[1] (numeric) = -0.41759450395835794757383770716876
absolute error = 1.4460134903365382e-16
relative error = 3.4627215555517285539736870339470e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = -0.9086334961158832645942155781022
y2[1] (numeric) = -0.90863349611588390316922431028586
absolute error = 6.3857500873218366e-16
relative error = 7.0278611944407397255727009028837e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.15
y1[1] (closed_form) = -0.40848744088415729815257671880992
y1[1] (numeric) = -0.40848744088415714707933903169487
absolute error = 1.5107323768711505e-16
relative error = 3.6983569766581346734044292890777e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = -0.91276394026052108094403304975368
y2[1] (numeric) = -0.91276394026052173676337559041657
absolute error = 6.5581934254066289e-16
relative error = 7.1849830346439730663001578202719e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.16
y1[1] (closed_form) = -0.39933952940627315445163962339401
y1[1] (numeric) = -0.39933952940627299673349987929998
absolute error = 1.5771813974409403e-16
relative error = 3.9494747734737142071243823540473e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = -0.91680310877176692661866166687433
y2[1] (numeric) = -0.91680310877176759979546230984707
absolute error = 6.7317680064297274e-16
relative error = 7.3426539919222327673761889430043e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.17
y1[1] (closed_form) = -0.3901516843082302153326619350505
y1[1] (numeric) = -0.39015168430823005079550396406376
absolute error = 1.6453715797098674e-16
relative error = 4.2172612496271579771351958049070e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = -0.92075059773613563957301300896203
y2[1] (numeric) = -0.92075059773613633021469622102345
absolute error = 6.9064168321206142e-16
relative error = 7.5008551165772064347778327730607e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=596.1MB, alloc=40.3MB, time=7.08
TOP MAIN SOLVE Loop
x[1] = 1.18
y1[1] (closed_form) = -0.38092482436688177302959946671276
y1[1] (numeric) = -0.38092482436688160149826147265367
absolute error = 1.7153133799405909e-16
relative error = 4.5030233532076494657158002309811e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = -0.92460601240802034610753802587476
y2[1] (numeric) = -0.92460601240802105431580023038186
absolute error = 7.0820826220450710e-16
relative error = 7.6595679965358168307251222955859e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.19
y1[1] (closed_form) = -0.37165987226053293806567955835047
y1[1] (numeric) = -0.37165987226053275936401153621613
absolute error = 1.7870166802213434e-16
relative error = 4.8082045267686250180387236641280e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = -0.92836896724916669260202111160267
y2[1] (numeric) = -0.92836896724916741847280344307365
absolute error = 7.2587078233147098e-16
relative error = 7.8187747322305007204854930252152e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.2
y1[1] (closed_form) = -0.36235775447667357763837335562308
y1[1] (numeric) = -0.36235775447667339158929477661077
absolute error = 1.8604907857901231e-16
relative error = 5.1344031217907614994720519227901e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = -0.93203908596722634967013443549483
y2[1] (numeric) = -0.93203908596722709329359646957751
absolute error = 7.4362346203408268e-16
relative error = 7.9784579126570127444215038305492e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.21
y1[1] (closed_form) = -0.35301940121933033870301071366479
y1[1] (numeric) = -0.35301940121933014512856846800064
absolute error = 1.9357444224566415e-16
relative error = 5.4833938751540934831523274630999e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = -0.93561600155338593341646488854361
y2[1] (numeric) = -0.93561600155338669487695935166377
absolute error = 7.6146049446312016e-16
relative error = 8.1386005925388342245699825255889e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.22
y1[1] (closed_form) = -0.3436457463160470204755229744352
y1[1] (numeric) = -0.34364574631604681919694956219054
absolute error = 2.0127857341224466e-16
relative error = 5.8571530586364681125685989010690e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = -0.93909935631906758093524527188837
y2[1] (numeric) = -0.93909935631906836031129373473432
absolute error = 7.7937604846284595e-16
relative error = 8.2991862705318032535530963592919e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=638.4MB, alloc=40.3MB, time=7.56
TOP MAIN SOLVE Loop
x[1] = 1.23
y1[1] (closed_form) = -0.33423772712450259823954724549766
y1[1] (numeric) = -0.33423772712450238907731920553442
absolute error = 2.0916222803996324e-16
relative error = 6.2578880558881645265308259847481e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = -0.94248880193169751002382356538924
y2[1] (numeric) = -0.94248880193169830738809312425052
absolute error = 7.9736426955886128e-16
relative error = 8.4601988684067839443739232621093e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.24
y1[1] (closed_form) = -0.32479628443877623657769341569738
y1[1] (numeric) = -0.32479628443877601935158998284447
absolute error = 2.1722610343285291e-16
relative error = 6.6880723037889248282901897108805e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = -0.94578399944953898628470596308179
y2[1] (numeric) = -0.94578399944953980170398691292043
absolute error = 8.1541928094983864e-16
relative error = 8.6216227111520744455938910049427e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.25
y1[1] (closed_form) = -0.31532236239526866544753855243804
y1[1] (numeric) = -0.31532236239526843997670053296266
absolute error = 2.2547083801947538e-16
relative error = 7.1504867687385598031909555303326e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = -0.94898461935558621434849084703605
y2[1] (numeric) = -0.94898461935558704788367535002912
absolute error = 8.3353518450299307e-16
relative error = 8.7834425079408580273877927189512e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.26
y1[1] (closed_form) = -0.30581690837828932688634248917648
y1[1] (numeric) = -0.30581690837828909298933134457746
absolute error = 2.3389701114459902e-16
relative error = 7.6482694297358192686319567607654e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = -0.95209034159051576385681622142542
y2[1] (numeric) = -0.95209034159051661556287797457715
absolute error = 8.5170606175315173e-16
relative error = 8.9456433339123370998300256496336e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=680.7MB, alloc=40.3MB, time=8.06
x[1] = 1.27
y1[1] (closed_form) = -0.29628087292531873355113701608796
y1[1] (numeric) = -0.29628087292531849104599414520301
absolute error = 2.4250514287088495e-16
relative error = 8.1849746315554894808764102704864e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = -0.95510085558469223509018174218289
y2[1] (numeric) = -0.95510085558469310501615664746397
absolute error = 8.6992597490528108e-16
relative error = 9.1082106127182880379450926577764e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.28
y1[1] (closed_form) = -0.28671520963195551277938689359259
y1[1] (numeric) = -0.28671520963195526148369310297764
absolute error = 2.5129569379061495e-16
relative error = 8.7646446839423993529065060680643e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = -0.95801586028922496370075385916029
y2[1] (numeric) = -0.95801586028922585188972169949055
absolute error = 8.8818896784033026e-16
relative error = 9.2711300997896426614726128826799e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.29
y1[1] (closed_form) = -0.27712087505655764138660609006118
y1[1] (numeric) = -0.27712087505655738111754124256722
absolute error = 2.6026906484749396e-16
relative error = 9.3918967596495791633441953132261e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = -0.96083506420607265890556129128537
y2[1] (numeric) = -0.96083506420607356539462841553423
absolute error = 9.0648906712424886e-16
relative error = 9.4343878662803663119118224459539e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.3
y1[1] (closed_form) = -0.26749882862458740699798410929287
y1[1] (numeric) = -0.26749882862458713757238694073491
absolute error = 2.6942559716855796e-16
relative error = 1.0072029046029005760475196381169e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.96355818541719296470134863003955
y2[1] (numeric) = -0.96355818541719388952163165007642
absolute error = 9.2482028302003687e-16
relative error = 9.5979702836483746150205662473617e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.31
y1[1] (closed_form) = -0.2578500325326696613381769786162
y1[1] (numeric) = -0.25785003253266938257260507239934
absolute error = 2.7876557190621686e-16
relative error = 1.0811151318000985506042633978600e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.9661849516127340291692578059375
y2[1] (numeric) = -0.96618495161273497234586830862169
absolute error = 9.4317661050268419e-16
relative error = 9.7618640088355253565358474166116e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=723.1MB, alloc=40.3MB, time=8.56
x[1] = 1.32
y1[1] (closed_form) = -0.24817545165237295957398272942735
y1[1] (numeric) = -0.2481754516523726712847726389666
absolute error = 2.8828921009046075e-16
relative error = 1.1616346748681508358072985353728e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.96871510011826526273589984597277
y2[1] (numeric) = -0.96871510011826622428793012282929
absolute error = 9.6155203027685652e-16
relative error = 9.9260559700108500247135815468722e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.33
y1[1] (closed_form) = -0.23847605343372320751578498601058
y1[1] (numeric) = -0.2384760534337229095191124947545
absolute error = 2.9799667249125608e-16
relative error = 1.2495874038525831485886553982209e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.9711483779210445623376830377638
y2[1] (numeric) = -0.97114837792104554227819283494793
absolute error = 9.7994050979718413e-16
relative error = 1.0090533352843167470254415518034e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.34
y1[1] (closed_form) = -0.22875280780845946523263949230014
y1[1] (numeric) = -0.22875280780845915734458000114307
absolute error = 3.0788805949115707e-16
relative error = 1.3459422091507596291744715231051e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.97348454169531937478787034808955
y2[1] (numeric) = -0.97348454169532037312387463909938
absolute error = 9.9833600429100983e-16
relative error = 1.0255283587271059631368484770977e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.35
y1[1] (closed_form) = -0.21900668709304158142002217301063
y1[1] (numeric) = -0.21900668709304126345661120485418
absolute error = 3.1796341096815645e-16
relative error = 1.4518433897549194241863339944963e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.97572335782665906926111353926522
y2[1] (numeric) = -0.97572335782666008599357132271681
absolute error = 1.01673245778345159e-15
relative error = 1.0420294334739887838738157856905e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.36
y1[1] (closed_form) = -0.20923866589141935767597525239186
y1[1] (numeric) = -0.20923866589141902945326906359423
absolute error = 3.2822270618879763e-16
relative error = 1.5686522602811991737911665884099e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.97786460243531618567849243942663
y2[1] (numeric) = -0.97786460243531722080229656406227
absolute error = 1.03512380412463564e-15
relative error = 1.0585553475877117021959105427024e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=765.5MB, alloc=40.3MB, time=9.06
x[1] = 1.37
y1[1] (closed_form) = -0.19944972099757296568819838964531
y1[1] (numeric) = -0.19944972099757262702233467807572
absolute error = 3.3866586371156959e-16
relative error = 1.6980011905641657786574653324711e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.97990806139861422288768850489193
y2[1] (numeric) = -0.97990806139861527639165652384675
absolute error = 1.05350396801895482e-15
relative error = 1.0751049098578674839927332246483e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.38
y1[1] (closed_form) = -0.1896408312978343632091500735982
y1[1] (numeric) = -0.18964083129783401391640877299446
absolute error = 3.4929274130060374e-16
relative error = 1.8418646391189519628848068909641e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.98185353037235972787813108520605
y2[1] (numeric) = -0.98185353037236079974499714141322
absolute error = 1.07186686605620717e-15
relative error = 1.0916769486480439078022012996134e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.39
y1[1] (closed_form) = -0.17981297767299947659616321780405
y1[1] (numeric) = -0.17981297767299911649302736811297
absolute error = 3.6010313584969108e-16
relative error = 2.0026537600893296352940251497733e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.98370081481127654484003822444291
y2[1] (numeric) = -0.98370081481127763504644596891219
absolute error = 1.09020640774446928e-15
relative error = 1.1082703107790206337293940355464e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.4
y1[1] (closed_form) = -0.16996714290024093861674803520365
y1[1] (numeric) = -0.16996714290024056751996471856759
absolute error = 3.7109678331663606e-16
relative error = 2.1833442451547498952380615176967e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.9854497299884601806594745788061
y2[1] (numeric) = -0.98544972998846128917597112336468
absolute error = 1.10851649654455858e-15
relative error = 1.1248838604456663015460116862853e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.41
y1[1] (closed_form) = -0.16010431155483119016356254936092
y1[1] (numeric) = -0.16010431155483080789020388139849
absolute error = 3.8227335866796243e-16
relative error = 2.3876518686821537366525157708097e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.98710010101385034142908886194224
y2[1] (numeric) = -0.98710010101385146822011976788094
absolute error = 1.12679103090593870e-15
relative error = 1.1415164781652963350577953034665e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=807.9MB, alloc=40.3MB, time=9.56
TOP MAIN SOLVE Loop
x[1] = 1.42
y1[1] (closed_form) = -0.15022546991168577348698210297591
y1[1] (numeric) = -0.15022546991168537985450626899114
absolute error = 3.9363247583398477e-16
relative error = 2.6202778800784752693954015276730e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.9886517628517197927362734733357
y2[1] (numeric) = -0.9886517628517209377601787772572
absolute error = 1.14502390530392150e-15
relative error = 1.1581670597553516441426143364067e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.43
y1[1] (closed_form) = -0.14033160584673666253389762457492
y1[1] (numeric) = -0.140331605846736257360209950317
absolute error = 4.0517368767425792e-16
relative error = 2.8872589694211072150233790819996e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.99010456033717779485729149548183
y2[1] (numeric) = -0.99010456033717895806630277350144
absolute error = 1.16320901127801961e-15
relative error = 1.1748345153383512331222673381290e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.44
y1[1] (closed_form) = -0.13042370873814549297752015612917
y1[1] (numeric) = -0.13042370873814507608103420271418
absolute error = 4.1689648595341499e-16
relative error = 3.1964777722310220548617344683725e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.99145834819168646252760446395798
y2[1] (numeric) = -0.99145834819168764386784293526057
absolute error = 1.18134023847130259e-15
relative error = 1.1915177683721563298007106601630e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.45
y1[1] (closed_form) = -0.12050276936736657053286662724802
y1[1] (numeric) = -0.1205027693673661417325652998446
absolute error = 4.2880030132740342e-16
relative error = 3.5584269438667946056899834801837e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.99271299103758849766535413432301
y2[1] (numeric) = -0.99271299103758969707682980493312
absolute error = 1.19941147567061011e-15
relative error = 1.2082157547036624757186010267455e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.46
y1[1] (closed_form) = -0.11056977982006955117464810912337
y1[1] (numeric) = -0.11056977982006911029014476899657
absolute error = 4.4088450334012680e-16
relative error = 3.9873870062649951340921252305353e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.99386836341164484228683230125003
y2[1] (numeric) = -0.9938683634116460597034441487252
absolute error = 1.21741661184747517e-15
relative error = 1.2249274216441077264721174583670e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=850.3MB, alloc=40.3MB, time=10.05
TOP MAIN SOLVE Loop
x[1] = 1.47
y1[1] (closed_form) = -0.10062573338693170090697460146241
y1[1] (numeric) = -0.1006257333869312477585741709635
absolute error = 4.5314840043049891e-16
relative error = 4.5033053194059945189051393372464e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.99492434977758089785992846273557
y2[1] (numeric) = -0.9949243497775821332094656623458
absolute error = 1.23534953719961023e-15
relative error = 1.2416517270642509576776363554337e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.48
y1[1] (closed_form) = -0.090671624464309655776226540647838
y1[1] (numeric) = -0.090671624464309190184986590733144
absolute error = 4.65591239949914694e-16
relative error = 5.1349167140286721021976507079574e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.99588084453764005648407513256269
y2[1] (numeric) = -0.99588084453764130968821932537183
absolute error = 1.25320414419280914e-15
relative error = 1.2583876385077345045848072378386e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.49
y1[1] (closed_form) = -0.080708448454800614868318484563714
y1[1] (numeric) = -0.080708448454800136656110294421809
absolute error = 4.78212208190141905e-16
relative error = 5.9251815311250403605571362910167e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.9967377520431433885532007170437
y2[1] (numeric) = -0.99673775204314465952752932016119
absolute error = 1.27097432860311749e-15
relative error = 1.2751341323209997996261574817625e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.5
y1[1] (closed_form) = -0.070737201667702910088189851434269
y1[1] (numeric) = -0.070737201667702419077759429799275
absolute error = 4.91010430421634994e-16
relative error = 6.9413324084859838455361672885849e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.99749498660405443094172337114149
y2[1] (numeric) = -0.9974949866040557195957139302657
absolute error = 1.28865399055912421e-15
relative error = 1.2918901927981743406478691874976e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.51
y1[1] (closed_form) = -0.060758881219385906581595514916193
y1[1] (numeric) = -0.06075888121938540259662457264418
absolute error = 5.03984970942272013e-16
relative error = 8.2948362581348698729851877625525e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.99815247249754811924273786483671
y2[1] (numeric) = -0.99815247249754942547977344906345
absolute error = 1.30623703558422674e-15
relative error = 1.3086548113393922445549235121322e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=892.7MB, alloc=40.3MB, time=10.55
TOP MAIN SOLVE Loop
x[1] = 1.52
y1[1] (closed_form) = -0.050774484933579196726129270152727
y1[1] (numeric) = -0.050774484933578679591296133639337
absolute error = 5.17134833136513390e-16
relative error = 1.0184935087239288784251858388878e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = -0.99871014397558300717231239411685
y2[1] (numeric) = -0.99871014397558433088968803283938
absolute error = 1.32371737563872253e-15
relative error = 1.3254269856210506971695811656900e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.53
y1[1] (closed_form) = -0.040785011241591058688989007076121
y1[1] (numeric) = -0.040785011241590528230029462095993
absolute error = 5.30458959544980128e-16
relative error = 1.3006223202999574888971811692732e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = -0.99916794527147601592426506870898
y2[1] (numeric) = -0.99916794527147735701319523028833
absolute error = 1.34108893016157935e-15
relative error = 1.3422057187765393023249765822175e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.54
y1[1] (closed_form) = -0.030791459082466157622476807076397
y1[1] (numeric) = -0.030791459082465613666244862628908
absolute error = 5.43956231944447489e-16
relative error = 1.7665815396653194379974655803084e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = -0.99952583060547905600596353844003
y2[1] (numeric) = -0.99952583060548041435159065017688
absolute error = 1.35834562711173685e-15
relative error = 1.3589900185860097846846198577449e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.55
y1[1] (closed_form) = -0.020794827803092473643912774695556
y1[1] (numeric) = -0.020794827803091916018441336446821
absolute error = 5.57625471438248735e-16
relative error = 2.6815584948259213057845291582525e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = -0.99978376418935696389761134763447
y2[1] (numeric) = -0.99978376418935833937901535642645
absolute error = 1.37548140400879198e-15
relative error = 1.3757788966737798165838663316307e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=934.9MB, alloc=40.3MB, time=11.05
x[1] = 1.56
y1[1] (closed_form) = -0.010796117058267445823920663760906
y1[1] (numeric) = -0.010796117058266874358482106678886
absolute error = 5.71465438557082020e-16
relative error = 5.2932497440778067989133939573696e-12 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 14
h = 0.005
y2[1] (closed_form) = -0.99994172022996629574517002341348
y2[1] (numeric) = -0.99994172022996768823537899633439
absolute error = 1.39249020897292091e-15
relative error = 1.3925713677119866855905255719729e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.57
y1[1] (closed_form) = -0.00079632671073332548540853364535419
y1[1] (numeric) = -0.0007963267107327400105751634332882
absolute error = 5.8547483337021206599e-16
relative error = 7.3521938355057430469211841592773e-11 %
Desired digits = 8
Estimated correct digits = 9
Correct digits = 13
h = 0.005
y2[1] (closed_form) = -0.99999968293183462021052992382333
y2[1] (numeric) = -0.9999996829318360295765316877133
absolute error = 1.40936600176388997e-15
relative error = 1.4093664486291241846657074570751e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.58
y1[1] (closed_form) = 0.0092035432688082648053890569827275
y1[1] (numeric) = 0.0092035432688088644576846640395094
absolute error = 5.996522956070567819e-16
relative error = 6.5154503878885299928609214286101e-12 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 14
h = 0.005
y2[1] (closed_form) = -0.99995764649874005255179423225172
y2[1] (numeric) = -0.99995764649874147865454905126018
absolute error = 1.42610275481900846e-15
relative error = 1.4261631578221101693744816494361e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.59
y1[1] (closed_form) = 0.019202492901692568095027346243403
y1[1] (numeric) = 0.019202492901693182091432135390902
absolute error = 6.13996404789147499e-16
relative error = 3.1974827848264843026711132602877e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = -0.99981561513429087198158434374551
y2[1] (numeric) = -0.99981561513429231467603863362147
absolute error = 1.44269445428987596e-15
relative error = 1.4429605143705417466301368803428e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.6
y1[1] (closed_form) = 0.029199522301288726205770462946499
y1[1] (numeric) = 0.029199522301289354711450835396533
absolute error = 6.28505680372450034e-16
relative error = 2.1524519267382357894036955155617e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = -0.99957360304150516434211382554623
y2[1] (numeric) = -0.99957360304150662347721490332352
absolute error = 1.45913510107777729e-15
relative error = 1.4597575372518013698654311496551e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=977.2MB, alloc=40.3MB, time=11.55
x[1] = 1.61
y1[1] (closed_form) = 0.039193631772987609585327609601018
y1[1] (numeric) = 0.039193631772988252763909509633355
absolute error = 6.43178581900032337e-16
relative error = 1.6410282813936964708262986939996e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = -0.9992316344213905321324131478443
y2[1] (numeric) = -0.99923163442139200755112501542231
absolute error = 1.47541871186757801e-15
relative error = 1.4765532445556787211911281193334e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.62
y1[1] (closed_form) = 0.049183821914170445143744274712327
y1[1] (numeric) = 0.049183821914171103157253439775287
absolute error = 6.58013509165062960e-16
relative error = 1.3378657525097321227972055325818e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = -0.9987897434705240139155188912468
y2[1] (numeric) = -0.99878974347052550545483905122054
absolute error = 1.49153932015997374e-15
relative error = 1.4933466526971715996142568250978e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.63
y1[1] (closed_form) = 0.059169093714148245297971697419802
y1[1] (numeric) = 0.059169093714148918306774081542996
absolute error = 6.73008802384123194e-16
relative error = 1.1374330079069579900312479703400e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = -0.9982479743776324551116699849331
y2[1] (numeric) = -0.99824797437763396260264728687983
absolute error = 1.50749097730194673e-15
relative error = 1.5101367756261232060020048491517e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.64
y1[1] (closed_form) = 0.069148448654062044364492707456605
y1[1] (numeric) = 0.069148448654062732527235088270792
absolute error = 6.88162742380814187e-16
relative error = 9.9519621303953704146128034148765e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.99760638131917367213758197436794
y2[1] (numeric) = -0.99760638131917519540533548965101
absolute error = 1.52326775351528307e-15
relative error = 1.5269226240323432424172159853415e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.65
y1[1] (closed_form) = 0.079120888806733952359614597341276
y1[1] (numeric) = 0.079120888806734655833165376980197
absolute error = 7.03473550779638921e-16
relative error = 8.8911229561385630262268642443368e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.99686502845391885177170304020219
y2[1] (numeric) = -0.99686502845392039063544196320683
absolute error = 1.53886373892300464e-15
relative error = 1.5437032045448470220751937198581e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=1019.7MB, alloc=40.3MB, time=12.03
x[1] = 1.66
y1[1] (closed_form) = 0.089085416936459041185257931650621
y1[1] (numeric) = 0.089085416936459760124648141788099
absolute error = 7.18939390210137478e-16
relative error = 8.0702253515064910644776044589581e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.99602398991653672750100059061296
y2[1] (numeric) = -0.99602398991653828177404516418237
absolute error = 1.55427304457356941e-15
relative error = 1.5604775189238283009533756200677e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.67
y1[1] (closed_form) = 0.099041036598728084094782342448611
y1[1] (numeric) = 0.099041036598728818653146863701143
absolute error = 7.34558364521252532e-16
relative error = 7.4167071523833986183405718279687e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.99508334981018017442629724653424
y2[1] (numeric) = -0.99508334981018174391610070922899
absolute error = 1.56948980346269475e-15
relative error = 1.5772445632439604560583186874726e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.68
y1[1] (closed_form) = 0.10898675223987117624800473417282
y1[1] (numeric) = 0.10898675223987192657652374007341
absolute error = 7.5032851900590059e-16
relative error = 6.8845846268956356967827893050854e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.99404320219807596406048786919357
y2[1] (numeric) = -0.99404320219807754856865942185161
absolute error = 1.58450817155265804e-15
relative error = 1.5940033270675938833848201133277e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.69
y1[1] (closed_form) = 0.11892156929661227207639046983309
y1[1] (numeric) = 0.11892156929661303832423110555608
absolute error = 7.6624784063572299e-16
relative error = 6.4433041471607215948473484024900e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.99290365109411852003714929394559
y2[1] (numeric) = -0.99290365109412011935947808287494
absolute error = 1.59932232878892935e-15
relative error = 1.6107527926063872243875771214457e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.7
y1[1] (closed_form) = 0.12884449429552468408764285733487
y1[1] (numeric) = 0.12884449429552546640190116332424
absolute error = 7.8231425830598937e-16
relative error = 6.0717709560148621979235107554312e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.99166481045246861534613339864788
y2[1] (numeric) = -0.99166481045247022927261351263938
absolute error = 1.61392648011399150e-15
relative error = 1.6274919338698753242992424097909e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1062.1MB, alloc=40.3MB, time=12.53
TOP MAIN SOLVE Loop
x[1] = 1.71
y1[1] (closed_form) = 0.13875453495237759764268978305111
y1[1] (numeric) = 0.13875453495237839616833287367558
absolute error = 7.9852564309062447e-16
relative error = 5.7549516732169445425968455525203e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.99032680415615805121775222386113
y2[1] (numeric) = -0.99032680415615967953260870206399
absolute error = 1.62831485647820286e-15
relative error = 1.6442197157994369638478991599590e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.72
y1[1] (closed_form) = 0.14865070027136366713637828033119
y1[1] (numeric) = 0.14865070027136448201618678765963
absolute error = 8.1487980850732844e-16
relative error = 5.4818430523351414197999658450081e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.98888976600470145717817065708548
y2[1] (numeric) = -0.98888976600470309965988650464395
absolute error = 1.64248171584755847e-15
relative error = 1.6609350933860808655418165784185e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.73
y1[1] (closed_form) = 0.15853200064419777090494835134257
y1[1] (numeric) = 0.158532000644198602279459144101
absolute error = 8.3137451079275843e-16
relative error = 5.2442062638107917940057553795526e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.98735383970071645108567767622206
y2[1] (numeric) = -0.98735383970071810750702188442807
absolute error = 1.65642134420820601e-15
relative error = 1.6776370107704196181314151438421e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.74
y1[1] (closed_form) = 0.16839744794907701506737731534509
y1[1] (numeric) = 0.16839744794907786307482650308369
absolute error = 8.4800744918773860e-16
relative error = 5.0357500040272226784549186518922e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.98571917883555349712068269566555
y2[1] (numeric) = -0.98571917883555516724873926323827
absolute error = 1.67012805656757272e-15
relative error = 1.6943244003231456272357238292061e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.75
y1[1] (closed_form) = 0.17824605564949209038267694394263
y1[1] (numeric) = 0.17824605564949295515894317640649
absolute error = 8.6477626623246386e-16
relative error = 4.8515871113186567040487514422913e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.98398594687393689873166293696799
y2[1] (numeric) = -0.98398594687393858232786088892858
absolute error = 1.68359619795196059e-15
relative error = 1.7109961817042637855110776780037e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1104.2MB, alloc=40.3MB, time=13.03
TOP MAIN SOLVE Loop
x[1] = 1.76
y1[1] (closed_form) = 0.1880768388928801010698001765041
y1[1] (numeric) = 0.18807683889288098274834824816538
absolute error = 8.8167854807166128e-16
relative error = 4.6878634990979657214567870290703e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.98215431713761846242496809945596
y2[1] (numeric) = -0.98215431713762015924511249992271
absolute error = 1.69682014440046675e-15
relative error = 1.7276512608992686837301609436934e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.77
y1[1] (closed_form) = 0.19788881460910900038948584173039
y1[1] (numeric) = 0.19788881460910989910131061140216
absolute error = 8.9871182476967177e-16
relative error = 4.5414988540150831504850861020245e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.98022447278804546701848144889842
y2[1] (numeric) = -0.98022447278804717681278540398556
absolute error = 1.70979430395508714e-15
relative error = 1.7442885292303827233642692781706e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.78
y1[1] (closed_form) = 0.20768100160878378462655329031263
y1[1] (numeric) = 0.20768100160878470050012392572567
absolute error = 9.1587357063541304e-16
relative error = 4.4100017023255560745718155323298e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.9781966068080446715477686473056
y2[1] (numeric) = -0.97819660680804639406088629416708
absolute error = 1.72251311764686148e-15
relative error = 1.7609068623408923101431634014362e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.79
y1[1] (closed_form) = 0.21745242068136461493517026446461
y1[1] (numeric) = 0.21745242068136554809637482164836
absolute error = 9.3316120455718375e-16
relative error = 4.2913350958946323284329136568420e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.97607092198252419340866043310862
y2[1] (numeric) = -0.9760709219825259283797209110271
absolute error = 1.73497106047791848e-15
relative error = 1.7775051191505342433276490215313e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.8
y1[1] (closed_form) = 0.22720209469308705531667430653058
y1[1] (numeric) = 0.22720209469308800588876465379747
absolute error = 9.5057209034726689e-16
relative error = 4.1838174583352086879091770845113e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.97384763087819518653237317884336
y2[1] (numeric) = -0.97384763087819693369501557812343
absolute error = 1.74716264239928007e-15
relative error = 1.7940821407797909512019781659016e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1146.3MB, alloc=40.3MB, time=13.51
TOP MAIN SOLVE Loop
x[1] = 1.81
y1[1] (closed_form) = 0.23692904868467463478774985084198
y1[1] (numeric) = 0.23692904868467560289128694713147
absolute error = 9.6810353709628949e-16
relative error = 4.0860483021004493338202645402024e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.97152695582231534740845126909038
y2[1] (numeric) = -0.97152695582231710649086055337514
absolute error = 1.75908240928428476e-15
relative error = 1.8106367494408535194507656290462e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.82
y1[1] (closed_form) = 0.24663230996883396256417104483087
y1[1] (numeric) = 0.24663230996883494831697058212497
absolute error = 9.8575279953729410e-16
relative error = 3.9968518304104605506554834438456e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.96910912888045637458721531849805
y2[1] (numeric) = -0.96910912888045814531215921598812
absolute error = 1.77072494389749007e-15
relative error = 1.8271677472929019604238031006471e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.83
y1[1] (closed_form) = 0.25631090822752264682983758361853
y1[1] (numeric) = 0.2563109082275236503469160030945
absolute error = 1.00351707841947597e-15
relative error = 3.9152335940718982577193468845820e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.96659439183329760489723892974281
y2[1] (numeric) = -0.96659439183329938698210578865769
absolute error = 1.78208486685891488e-15
relative error = 1.8436739152592349588783869317649e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.84
y1[1] (closed_form) = 0.2659638756089802903802829832816
y1[1] (numeric) = 0.26596387560898131177380387482054
absolute error = 1.02139352089153894e-15
relative error = 3.8403468085763279894767466169304e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.96398299615244814699489367172712
y2[1] (numeric) = -0.96398299615244994015173127521027
absolute error = 1.79315683760348315e-15
relative error = 1.8601540118036543849736280184394e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=1188.2MB, alloc=40.3MB, time=14.00
x[1] = 1.85
y1[1] (closed_form) = 0.2755902468245128601219498354748
y1[1] (numeric) = 0.27559024682451389950117073009588
absolute error = 1.03937922089462108e-15
relative error = 3.7714659095191596007716718885857e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.96127520297529993001245916863613
y2[1] (numeric) = -0.96127520297530173394801450416673
absolute error = 1.80393555533553060e-15
relative error = 1.8766067716633723658002008750864e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.86
y1[1] (closed_form) = 0.28518905924502075207093548828912
y1[1] (numeric) = 0.2851890592450218095421550530293
absolute error = 1.05747121956474018e-15
relative error = 3.7079655943470526385794199191822e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.9584712830789141819789777659032
y2[1] (numeric) = -0.95847128307891599639473774414038
absolute error = 1.81441575997823718e-15
relative error = 1.8930309045355615466130264953029e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.87
y1[1] (closed_form) = 0.29475935299726089912514806480989
y1[1] (numeric) = 0.2947593529972619747916537095175
absolute error = 1.07566650564470761e-15
relative error = 3.6493040668830054799387484247865e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.95557151685294394934425049217263
y2[1] (numeric) = -0.95557151685294577393648361002094
absolute error = 1.82459223311784831e-15
relative error = 1.9094250937145093068995694351545e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.88
y1[1] (closed_form) = 0.30430017105983329547931375952224
y1[1] (numeric) = 0.30430017105983438944132966498004
absolute error = 1.09396201590545780e-15
relative error = 3.5950095331703133757058283732834e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.95257619427159536533145742581513
y2[1] (numeric) = -0.9525761942715971997912563683637
absolute error = 1.83445979894254857e-15
relative error = 1.9257879946761649557190090671846e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.89
y1[1] (closed_form) = 0.31381055935888233911038241555123
y1[1] (numeric) = 0.31381055935888345146501799229029
absolute error = 1.11235463557673906e-15
relative error = 3.5446692356346743365726478694684e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.94948561486463047096820167213832
y2[1] (numeric) = -0.94948561486463231498152684799082
absolute error = 1.84401332517585250e-15
relative error = 1.9421182336066841103299968495105e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=1230.3MB, alloc=40.3MB, time=14.50
x[1] = 1.9
y1[1] (closed_form) = 0.32328956686350342227883369508031
y1[1] (numeric) = 0.32328956686350455312003248219075
absolute error = 1.13084119878711044e-15
relative error = 3.4979204858304772187610357816051e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.94630008768741448848970961163496
y2[1] (numeric) = -0.94630008768741634173743361601219
absolute error = 1.85324772400437723e-15
relative error = 1.9584144058713742810181636352718e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.91
y1[1] (closed_form) = 0.33273624568084522946633893939753
y1[1] (numeric) = 0.33273624568084637888482795258509
absolute error = 1.14941848901318756e-15
relative error = 3.4544432833316560691535282658795e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.94301993129001054236188657694821
y2[1] (numeric) = -0.94301993129001240451983957681128
absolute error = 1.86215795299986307e-15
relative error = 1.9746750744202314008980261440447e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.92
y1[1] (closed_form) = 0.34214965115089823259923660315905
y1[1] (numeric) = 0.3421496511508994006824761412385
absolute error = 1.16808323953807945e-15
relative error = 3.4139542028143696531801398076119e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.93964547368532491842637133968703
y2[1] (numeric) = -0.9396454736853267891653873749953
absolute error = 1.87073901603530827e-15
relative error = 1.9908987681260246268848559481827e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.93
y1[1] (closed_form) = 0.35152884194095990478728906471187
y1[1] (numeric) = 0.35152884194096109161942298366845
absolute error = 1.18683213391895658e-15
relative error = 3.3762013021915505480448394879190e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.93617705231630604661512937274878
y2[1] (numeric) = -0.93617705231630792560109356783412
absolute error = 1.87898596419508534e-15
relative error = 2.0070839800506374098193807162640e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.94
y1[1] (closed_form) = 0.36087288013976720613506768584073
y1[1] (numeric) = 0.36087288013976841179687414953031
absolute error = 1.20566180646368958e-15
relative error = 3.3409598582102732541401787527981e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.9326150140222004873089793388657
y2[1] (numeric) = -0.93261501402220237420287601777236
absolute error = 1.88689389667890666e-15
relative error = 2.0232291656351030893709813652528e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1272.3MB, alloc=40.3MB, time=14.98
TOP MAIN SOLVE Loop
x[1] = 1.95
y1[1] (closed_form) = 0.37018083135128692845582845913069
y1[1] (numeric) = 0.3701808313512881530246711756269
absolute error = 1.22456884271649621e-15
relative error = 3.3080287767640484381728182549753e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.92895971500386929571329703509148
y2[1] (numeric) = -0.9289597150038711901712587345998
absolute error = 1.89445796169950832e-15
relative error = 2.0393327408084833243473894257426e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.96
y1[1] (closed_form) = 0.37945176478815451993156521544745
y1[1] (numeric) = 0.37945176478815576348134516798068
absolute error = 1.24354977995253323e-15
relative error = 3.2772275565691441045606780819252e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.92521152078816823258555628949003
y2[1] (numeric) = -0.92521152078817013425891366341147
absolute error = 1.90167335737392144e-15
relative error = 2.0553930800104238962130533251216e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.97
y1[1] (closed_form) = 0.38868475336475204591463981387931
y1[1] (numeric) = 0.38868475336475330851574749524773
absolute error = 1.26260110768136842e-15
relative error = 3.2483937091726110713765112267252e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.92137080619139538326395099715317
y2[1] (numeric) = -0.92137080619139729179928360535458
absolute error = 1.90853533260820141e-15
relative error = 2.0714085141218848033952473707510e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.98
y1[1] (closed_form) = 0.39787887378991597815247385990719
y1[1] (numeric) = 0.39787887378991725987174201917375
absolute error = 1.28171926815926656e-15
relative error = 3.2213805572296536240932221076548e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.917437955281809840204735217402
y2[1] (numeric) = -0.91743795528181175524392319288796
absolute error = 1.91503918797548596e-15
relative error = 2.0873773282981762932026327768526e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 1.99
y1[1] (closed_form) = 0.40703320665926554173363571613029
y1[1] (numeric) = 0.40703320665926684263429262635246
absolute error = 1.30090065691022217e-15
relative error = 3.1960553478852361978195857519149e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.91341336134122519712879327105761
y2[1] (numeric) = -0.91341336134122711830906985831175
absolute error = 1.92118027658725414e-15
relative error = 2.1032977596980387801952542910466e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1314.5MB, alloc=40.3MB, time=15.48
TOP MAIN SOLVE Loop
x[1] = 2
y1[1] (closed_form) = 0.41614683654714238699756822950076
y1[1] (numeric) = 0.41614683654714370713919148517106
absolute error = 1.32014162325567030e-15
relative error = 3.1722976298682511250119342100120e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.90929742682568169539601986591174
y2[1] (numeric) = -0.90929742682568362235002482357049
absolute error = 1.92695400495765875e-15
relative error = 2.1191679951020784336577804802999e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.01
y1[1] (closed_form) = 0.42521885209815239251738234016543
y1[1] (numeric) = 0.42521885209815373195585319297088
absolute error = 1.33943847085280545e-15
relative error = 3.1499978522674380965012695786928e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.90509056332520095536009971027372
y2[1] (numeric) = -0.90509056332520288771593357107976
absolute error = 1.93235583386080604e-15
relative error = 2.1349861684134104692365024470079e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.02
y1[1] (closed_form) = 0.4342483461183004450517028740902
y1[1] (numeric) = 0.43424834611830180383916111552769
absolute error = 1.35878745824143749e-15
relative error = 3.1290561504436190870621110400787e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.90079319152262731719701352455371
y2[1] (numeric) = -0.90079319152262925457829270541074
absolute error = 1.93738127918085703e-15
relative error = 2.1507503580328641054534435599104e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.03
y1[1] (closed_form) = 0.4432344156657090830635167316961
y1[1] (numeric) = 0.44323441566571046124831613100836
absolute error = 1.37818479939931226e-15
relative error = 3.1093812905511159194900565639443e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.89640574115155990703888883196757
y2[1] (numeric) = -0.89640574115156184906480158679328
absolute error = 1.94202591275482571e-15
relative error = 2.1664585841005646218748566709808e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.04
y1[1] (closed_form) = 0.45217616214091193201727020529136
y1[1] (numeric) = 0.45217616214091332964393451111438
absolute error = 1.39762666430582302e-15
relative error = 3.0908897490051228614199099668630e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.8919286509533796351715256485842
y2[1] (numeric) = -0.89192865095338158145688885653495
absolute error = 1.94628536320795075e-15
relative error = 2.1821088055951254094339785488599e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1356.6MB, alloc=40.3MB, time=15.97
TOP MAIN SOLVE Loop
x[1] = 2.05
y1[1] (closed_form) = 0.4610726913767129021859299941674
y1[1] (numeric) = 0.4610726913767143192951095082054
absolute error = 1.41710917951403800e-15
relative error = 3.0735049071822148896966236429060e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.88736236863337542355996660468034
y2[1] (numeric) = -0.88736236863337737371528338619786
absolute error = 1.95015531678151752e-15
relative error = 2.1976989172810504371195451334325e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.06
y1[1] (closed_form) = 0.4699231137276021631231096264879
y1[1] (numeric) = 0.46992311372760359975153835745586
absolute error = 1.43662842873096796e-15
relative error = 3.0571563448648127900676868720549e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.8827073508159740500427975851999
y2[1] (numeric) = -0.88270735081597600367431573820884
absolute error = 1.95363151815300894e-15
relative error = 2.2132267464942637534399498804305e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.07
y1[1] (closed_form) = 0.47872654415871995327732713901173
y1[1] (numeric) = 0.47872654415872140945778054500808
absolute error = 1.45618045340599635e-15
relative error = 3.0417792185828853779759907735727e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.87796406299907808617345112044384
y2[1] (numeric) = -0.87796406299908004288322236890775
absolute error = 1.95670977124846391e-15
relative error = 2.2286900497549391952412532729841e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.08
y1[1] (closed_form) = 0.48748210233435932844156884977235
y1[1] (numeric) = 0.48748210233436080420282217716589
absolute error = 1.47576125332739354e-15
relative error = 3.0273137131815825309595753912257e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.87313297950751649487667680502462
y2[1] (numeric) = -0.87313297950751845426261685194835
absolute error = 1.95938594004692373e-15
relative error = 2.2440865091959982084845859880398e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=1398.7MB, alloc=40.3MB, time=16.47
x[1] = 2.09
y1[1] (closed_form) = 0.49618891270599899883706631187045
y1[1] (numeric) = 0.49618891270600049420385353870605
absolute error = 1.49536678722683560e-15
relative error = 3.0137045567418144969542855525747e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.86821458344561254282162205872751
y2[1] (numeric) = -0.86821458344561450447757143557486
absolute error = 1.96165594937684735e-15
relative error = 2.2594137287947676099166383728851e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.1
y1[1] (closed_form) = 0.50484610459985745162093852371917
y1[1] (numeric) = 0.5048461045998589666139119155656
absolute error = 1.51499297339184643e-15
relative error = 3.0009005904732778708953449114337e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.86320936664887377068075931326902
y2[1] (numeric) = -0.8632093666488757341965450176467
absolute error = 1.96351578570437768e-15
relative error = 2.2746692303943380514971439949288e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.11
y1[1] (closed_form) = 0.51345281230395960347841015707169
y1[1] (numeric) = 0.51345281230396113811410044315309
absolute error = 1.53463569028608140e-15
relative error = 2.9888543864428001337777065142377e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.85811782963480885223737550831068
y2[1] (numeric) = -0.85811782963481081719887342165258
absolute error = 1.96496149791334190e-15
relative error = 2.2898504495001286872896157012068e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.12
y1[1] (closed_form) = 0.52200817515470727670690188298389
y1[1] (numeric) = 0.52200817515470883099767906035303
absolute error = 1.55429077717736914e-15
relative error = 2.9775219070404880812960927757875e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.85294048155287626061472733365415
y2[1] (numeric) = -0.85294048155287822660392541052429
absolute error = 1.96598919807687014e-15
relative error = 2.3049547308360375353425700736085e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.13
y1[1] (closed_form) = 0.53051133762294484181652620960972
y1[1] (numeric) = 0.53051133762294641577056098303692
absolute error = 1.57395403477342720e-15
relative error = 2.9668622009584607529932972407692e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.8476778401335697467185299963159
y2[1] (numeric) = -0.8476778401335717133135922168333
absolute error = 1.96659506222051740e-15
relative error = 2.3199793236433293447292829666985e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=1440.8MB, alloc=40.3MB, time=16.95
x[1] = 2.14
y1[1] (closed_form) = 0.5389614493995114201544499120086
y1[1] (numeric) = 0.53896144939951301377567577717444
absolute error = 1.59362122586516584e-15
relative error = 2.9568371311913176160255335309045e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.84233043163664572130250663706891
y2[1] (numeric) = -0.84233043163664768807783771384423
absolute error = 1.96677533107677532e-15
relative error = 2.3349213767040759043212007364455e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.15
y1[1] (closed_form) = 0.54735766548027109140415388226403
y1[1] (numeric) = 0.54735766548027270469222985975757
absolute error = 1.61328807597749354e-15
relative error = 2.9474111311877530375092236472821e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.83689879079849771787564813704379
y2[1] (numeric) = -0.8368987907984996844019589679046
absolute error = 1.96652631083086081e-15
relative error = 2.3497779330695035333118882353362e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.16
y1[1] (closed_form) = 0.55569914625061260300969874398337
y1[1] (numeric) = 0.55569914625061423595997277151963
absolute error = 1.63295027402753626e-15
relative error = 2.9385509858082422685059877571625e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.83138346077868319896103812034632
y2[1] (numeric) = -0.83138346077868516480541197801655
absolute error = 1.96584437385767023e-15
relative error = 2.3645459244720096373361220144855e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.17
y1[1] (closed_form) = 0.56398505756941013162446999441651
y1[1] (numeric) = 0.56398505756941178422794298459807
absolute error = 1.65260347299018156e-15
relative error = 2.9302256341903069179123681525473e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.82578499310560805298105642394338
y2[1] (numeric) = -0.82578499310561001770701587373187
absolute error = 1.96472595944978849e-15
relative error = 2.3792221653978682432933945803990e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.18
y1[1] (closed_form) = 0.57221457085243670057822486766249
y1[1] (numeric) = 0.57221457085243837282151543852022
absolute error = 1.67224329057085773e-15
relative error = 2.9224059920034745155589519110647e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.82010394762137421327400974608394
y2[1] (numeric) = -0.82010394762137617644158428252784
absolute error = 1.96316757453644390e-15
relative error = 2.3938033467957400632435994107209e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=1483.0MB, alloc=40.3MB, time=17.45
x[1] = 2.19
y1[1] (closed_form) = 0.58038686315522191209020516379695
y1[1] (numeric) = 0.58038686315522360395551504925361
absolute error = 1.69186530988545666e-15
relative error = 2.9150647909013314956604405860851e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.814340892425795914434327645905
y2[1] (numeric) = -0.81434089242579787560012203920544
absolute error = 1.96116579439330044e-15
relative error = 2.4082860293940170793913151910544e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.2
y1[1] (closed_form) = 0.58850111725534570852414261265493
y1[1] (numeric) = 0.58850111725534741998922275996332
absolute error = 1.71146508014730839e-15
relative error = 2.9081764332568259477693087178038e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.80849640381959018430403691041612
y2[1] (numeric) = -0.80849640381959214302130025339661
absolute error = 1.95871726334298049e-15
relative error = 2.4226666365977471081013717689061e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.21
y1[1] (closed_form) = 0.59655652173415993337760917751863
y1[1] (numeric) = 0.59655652173416166441572653863276
absolute error = 1.73103811736111413e-15
relative error = 2.9017168605064831283771602310876e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.80257106624674725251897404255597
y2[1] (numeric) = -0.80257106624674920833766948876819
absolute error = 1.95581869544621222e-15
relative error = 2.4369414469333780012193659083826e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.22
y1[1] (closed_form) = 0.60455227105792951991771443750015
y1[1] (numeric) = 0.6045522710579312704976194612435
absolute error = 1.75057990502374335e-15
relative error = 2.8956634336354994148160514616384e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.79656547223608663852085674960916
y2[1] (numeric) = -0.796565472236088590987731933106
absolute error = 1.95246687518349684e-15
relative error = 2.4511065860068101538969529127784e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.23
y1[1] (closed_form) = 0.61248756565838519341190391068563
y1[1] (numeric) = 0.6124875656583869634977987424855
absolute error = 1.77008589483179987e-15
relative error = 2.8899948245138169760280264775541e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.79048022234200476337771012718854
y2[1] (numeric) = -0.79048022234200671203636825438086
absolute error = 1.94865865812719232e-15
relative error = 2.4651580179372236531260296695187e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1525.2MB, alloc=40.3MB, time=17.95
TOP MAIN SOLVE Loop
x[1] = 2.24
y1[1] (closed_form) = 0.62036161201267963175076226631044
y1[1] (numeric) = 0.62036161201268142130226966217069
absolute error = 1.78955150739586025e-15
relative error = 2.8846909169474584308391046773805e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.7843159250844200106020886706045
y2[1] (numeric) = -0.78431592508442195499306027451588
absolute error = 1.94439097160391138e-15
relative error = 2.4790915362258218156519872176653e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.25
y1[1] (closed_form) = 0.6281736227227390889133890573964
y1[1] (numeric) = 0.62817362272274089788552201868382
absolute error = 1.80897213296128742e-15
relative error = 2.8797327164431492480016923684608e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.77807319688792124141096667558776
y2[1] (numeric) = -0.77807319688792318107178202272029
absolute error = 1.93966081534713253e-15
relative error = 2.4929027540149721619997924050780e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.26
y1[1] (closed_form) = 0.63592281659400254617912656874484
y1[1] (numeric) = 0.63592281659400437452225870426591
absolute error = 1.82834313213552107e-15
relative error = 2.8751022678005360361234476769525e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.77175266202012584952506163774032
y2[1] (numeric) = -0.77175266202012778399032377766488
absolute error = 1.93446526213992456e-15
relative error = 2.5065870936891920501479912528187e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.27
y1[1] (closed_form) = 0.6436084187135405172361343481243
y1[1] (numeric) = 0.6436084187135423648959709698697
absolute error = 1.84765983662174540e-15
relative error = 2.8707825797476218112088114892156e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.76535495252925351965074260193472
y2[1] (numeric) = -0.76535495252925544845220104962051
absolute error = 1.92880145844768579e-15
relative error = 2.5201397757649746593193192401125e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.28
y1[1] (closed_form) = 0.6512296605275456953713983504607
y1[1] (numeric) = 0.65122966052754756228894830929457
absolute error = 1.86691754995883387e-15
relative error = 2.8667575559234944269877538106071e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.75888070818092193221665357630092
y2[1] (numeric) = -0.75888070818092385488327861710183
absolute error = 1.92266662504080091e-15
relative error = 2.5335558070115350699055456849483e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1567.3MB, alloc=40.3MB, time=18.44
TOP MAIN SOLVE Loop
x[1] = 2.29
y1[1] (closed_form) = 0.65878577991818769374203101818895
y1[1] (numeric) = 0.65878577991818957985357928565886
absolute error = 1.88611154826746991e-15
relative error = 2.8630119315898098452693451617127e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.75233057639417073474190827797365
y2[1] (numeric) = -0.75233057639417265079996588509307
absolute error = 1.91605805760711942e-15
relative error = 2.5468299677391200173068075683356e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.3
y1[1] (closed_form) = 0.66627602127982419331788057116602
y1[1] (numeric) = 0.66627602127982609855496157350688
absolute error = 1.90523708100234086e-15
relative error = 2.8595312155203238874324232614758e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.7457052121767201773854062116435
y2[1] (numeric) = -0.74570521217672208635853356580425
absolute error = 1.90897312735416075e-15
relative error = 2.5599567981855070238206685195543e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.31
y1[1] (closed_form) = 0.67369963559456087744416432347103
y1[1] (numeric) = 0.67369963559456280173353603377342
absolute error = 1.92428937171030239e-15
relative error = 2.8563016365773408541498967256961e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.73900527805947088675876419209826
y2[1] (numeric) = -0.73900527805947278816804579305133
absolute error = 1.90140928160095307e-15
relative error = 2.5729305839246504090668430748285e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.32
y1[1] (closed_form) = 0.68105588050715259709363616600823
y1[1] (numeric) = 0.68105588050715454035725496041724
absolute error = 1.94326361879440901e-15
relative error = 2.8533100945363622515708921792116e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.73223144403025132797089867772467
y2[1] (numeric) = -0.73223144403025322133494303713794
absolute error = 1.89336404435941327e-15
relative error = 2.5857453402140307971586677348707e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.33
y1[1] (closed_form) = 0.688344020399238276754180427816
y1[1] (numeric) = 0.68834402039924023890917671152176
absolute error = 1.96215499628370576e-15
relative error = 2.8505441147664207786811069349391e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.72538438746681958010284419247542
y2[1] (numeric) = -0.7253843874668214649378610976531
absolute error = 1.88483501690517768e-15
relative error = 2.5983947951890452155105925618038e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1609.5MB, alloc=40.3MB, time=18.92
TOP MAIN SOLVE Loop
x[1] = 2.34
y1[1] (closed_form) = 0.69556332646290213752310557206135
y1[1] (numeric) = 0.69556332646290411848176018073634
absolute error = 1.98095865460867499e-15
relative error = 2.8479918064143788615481048728284e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.71846479306912612487942868679401
y2[1] (numeric) = -0.71846479306912800069930702458799
absolute error = 1.87581987833779398e-15
relative error = 2.6108723718036305926300999229083e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.35
y1[1] (closed_form) = 0.70271307677355388134712911225892
y1[1] (numeric) = 0.70271307677355588101685049449053
absolute error = 1.99966972138223161e-15
relative error = 2.8456418237775531763310329231308e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.71147335279084442220249118201321
y2[1] (numeric) = -0.71147335279084628851887731219945
absolute error = 1.86631638613018624e-15
relative error = 2.6231711684061302031500686025968e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.36
y1[1] (closed_form) = 0.7097925563621205484503630346451
y1[1] (numeric) = 0.709792556362122566733665220804
absolute error = 2.01828330218615890e-15
relative error = 2.8434833305809918311126191889941e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.7044107657701761194310307129327
y2[1] (numeric) = -0.70441076577017797575340738023922
absolute error = 1.85632237666730652e-15
relative error = 2.6352839378280565646447237234192e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.37
y1[1] (closed_form) = 0.71680105728654282882471660882235
y1[1] (numeric) = 0.71680105728654486561919797169881
absolute error = 2.03679448136287646e-15
relative error = 2.8415059669040963790333649770184e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.69727773825993781382969642028923
y2[1] (numeric) = -0.69727773825993965966546219417682
absolute error = 1.84583576577388759e-15
relative error = 2.6472030648507229590620186928544e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=1651.5MB, alloc=40.3MB, time=19.42
x[1] = 2.38
y1[1] (closed_form) = 0.72373787870256867821114760736753
y1[1] (numeric) = 0.72373787870257073340947041979839
absolute error = 2.05519832281243086e-15
relative error = 2.8396998185264896581541203106218e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.6900749835569363594511131070202
y2[1] (numeric) = -0.69007498355693819430566233823317
absolute error = 1.83485454923121297e-15
relative error = 2.6589205419005363991352435547458e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.39
y1[1] (closed_form) = 0.73060232693383715926915829261806
y1[1] (numeric) = 0.73060232693383923275902908721667
absolute error = 2.07348987079459861e-15
relative error = 2.8380553884854686709116807285556e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.68280322193063978086250031101305
y2[1] (numeric) = -0.6828032219306416042393035938347
absolute error = 1.82337680328282165e-15
relative error = 2.6704279428078667111269960023779e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.4
y1[1] (closed_form) = 0.73739371554124549960882222733478
y1[1] (numeric) = 0.73739371554124759127297296332548
absolute error = 2.09166415073599070e-15
relative error = 2.8365635706573840719911200339647e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.67546318055115092656577152534128
y2[1] (numeric) = -0.67546318055115273796645665440781
absolute error = 1.81140068512906653e-15
relative error = 2.6817163944466018923698184917322e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.41
y1[1] (closed_form) = 0.74411136539159243003734439556795
y1[1] (numeric) = 0.74411136539159453975351443761442
absolute error = 2.10971617004204647e-15
relative error = 2.8352156251931422840864267404533e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.66805559341649106468574980065472
y2[1] (numeric) = -0.66805559341649286361018321110154
absolute error = 1.79892443341044682e-15
relative error = 2.6927765460515042037440034361327e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.42
y1[1] (closed_form) = 0.75075460472549093874353256891074
y1[1] (numeric) = 0.75075460472549306638445148271524
absolute error = 2.12764091891380450e-15
relative error = 2.8340031556539890232926947903541e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.66058120127920069250633410656023
y2[1] (numeric) = -0.66058120127920247845270278619646
absolute error = 1.78594636867963623e-15
relative error = 2.7035985359879922566749541954172e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=1693.6MB, alloc=40.3MB, time=19.91
x[1] = 2.43
y1[1] (closed_form) = 0.7573227692245436502013552441779
y1[1] (numeric) = 0.75732276922454579563472641351472
absolute error = 2.14543337116933682e-15
relative error = 2.8329180877080206363960489860062e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.6530407515722648997124970471899
y2[1] (numeric) = -0.65304075157226667217739090931989
absolute error = 1.77246489386212999e-15
relative error = 2.7141719557236400519136043161885e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.44
y1[1] (closed_form) = 0.7638152020777741113106750925374
y1[1] (numeric) = 0.76381520207777627439916016226986
absolute error = 2.16308848506973246e-15
relative error = 2.8319526492606779243310200780833e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.64543499833437069274006107298253
y2[1] (numeric) = -0.64543499833437245121855577841821
absolute error = 1.75847849470543568e-15
relative error = 2.7244858107221007437659652013549e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.45
y1[1] (closed_form) = 0.77023125404730734170190306733649
y1[1] (numeric) = 0.7702312540473095223031072168517
absolute error = 2.18060120414951521e-15
relative error = 2.8310993519039717201185431142557e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.63776470213450375443853285563378
y2[1] (numeric) = -0.63776470213450549842427307236739
absolute error = 1.74398574021673361e-15
relative error = 2.7345284779478580536069340088445e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.46
y1[1] (closed_form) = 0.7765702835332930802042763146862
y1[1] (numeric) = 0.77657028353329527817073436606637
absolute error = 2.19796645805138017e-15
relative error = 2.8303509735795202727846403345477e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.63003062999589217930819371861593
y2[1] (numeric) = -0.63003062999589390829347680755063
absolute error = 1.72898528308893470e-15
relative error = 2.7442876596336399416525379086481e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.47
y1[1] (closed_form) = 0.78283165663806523520721558406155
y1[1] (numeric) = 0.78283165663806745038637894919396
absolute error = 2.21517916336513241e-15
relative error = 2.8297005423597725177751706087048e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.62223355531930478987454240485577
y2[1] (numeric) = -0.62223355531930650335040251992058
absolute error = 1.71347586011506481e-15
relative error = 2.7537503329208582114793763839362e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1735.9MB, alloc=40.3MB, time=20.41
TOP MAIN SOLVE Loop
x[1] = 2.48
y1[1] (closed_form) = 0.78901474722953112302319203359033
y1[1] (numeric) = 0.78901474722953335525741650430128
absolute error = 2.23223422447071095e-15
relative error = 2.8291413212601651985851120806095e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.6143742578057117043045348806656
y2[1] (numeric) = -0.61437425780571340176082747157164
absolute error = 1.69745629259090604e-15
relative error = 2.7629026949363260850873513992165e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.49
y1[1] (closed_form) = 0.79511893700378415538109133257157
y1[1] (numeric) = 0.79511893700378640450762571775165
absolute error = 2.24912653438518008e-15
relative error = 2.8286667940025128156772362512460e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.6064535233783148891434102397918
y2[1] (numeric) = -0.60645352337831657006889694561911
absolute error = 1.68092548670582731e-15
relative error = 2.7717301028148871738323348689678e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.5
y1[1] (closed_form) = 0.80114361554693371483350279046735
y1[1] (numeric) = 0.80114361554693598068447840403699
absolute error = 2.26585097561356964e-15
relative error = 2.8282706516567482921708149955699e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.59847214410395649405185470218616
y2[1] (numeric) = -0.59847214410395815793428862392379
absolute error = 1.66388243392173763e-15
relative error = 2.7802170081164479680993760680935e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.51
y1[1] (closed_form) = 0.80708818039614603514191750787841
y1[1] (numeric) = 0.80708818039614831754433851132363
absolute error = 2.28240242100344522e-15
relative error = 2.8279467800942956635460733513961e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.59043091811391282764453715502405
y2[1] (numeric) = -0.5904309181139144739707484951214
absolute error = 1.64632621134009735e-15
relative error = 2.7883468850160534307825394821687e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.52
y1[1] (closed_form) = 0.81295203709988998260266426045185
y1[1] (numeric) = 0.81295203709989228137839886354035
absolute error = 2.29877573460308850e-15
relative error = 2.8276892481919332101905625824019e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.58233064952408189496642758229713
y2[1] (numeric) = -0.58233064952408352322240963922115
absolute error = 1.62825598205692402e-15
relative error = 2.7961021515656777767981679479633e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1778.0MB, alloc=40.3MB, time=20.91
TOP MAIN SOLVE Loop
x[1] = 2.53
y1[1] (closed_form) = 0.81873459927738171378565517255499
y1[1] (numeric) = 0.8187345992773840287514276957223
absolute error = 2.31496577252316731e-15
relative error = 2.8274922967300575152770335036721e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.5741721483545724777866405874022
y2[1] (numeric) = -0.57417214835457408745763609313333
absolute error = 1.60967099550573113e-15
relative error = 2.8034640832346676690796765695885e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.54
y1[1] (closed_form) = 0.82443528867722226526970435580657
y1[1] (numeric) = 0.82443528867722459623708815758109
absolute error = 2.33096738380177452e-15
relative error = 2.8273503279338401223379018237361e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.56595623044870279873476574798203
y2[1] (numeric) = -0.5659562304487043893053535363214
absolute error = 1.59057058778833937e-15
relative error = 2.8104127178303158141924823447802e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.55
y1[1] (closed_form) = 0.83005353523522221166431047583229
y1[1] (numeric) = 0.83005353523522455843972174854645
absolute error = 2.34677541127271416e-15
relative error = 2.8272578956099262981263598915634e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.55768371739141686934577028176624
y2[1] (numeric) = -0.55768371739141844029995227526821
absolute error = 1.57095418199350197e-15
relative error = 2.8169267507785408768424032385121e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.56
y1[1] (closed_form) = 0.83558877713140760950028812338244
y1[1] (numeric) = 0.83558877713140997188498056029506
absolute error = 2.36238469243691262e-15
relative error = 2.8272096958351030513114136962859e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.54935543642712668031068338313728
y2[1] (numeric) = -0.54935543642712823113197188642414
absolute error = 1.55082128850328686e-15
relative error = 2.8229834196043439595859311959569e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.57
y1[1] (closed_form) = 0.84104046084620152644236372156713
y1[1] (numeric) = 0.84104046084620390423242405839933
absolute error = 2.37779006033683220e-15
relative error = 2.8272005581567987491695871452545e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.54097222037698844964557254874584
y2[1] (numeric) = -0.54097222037698997981707783590608
absolute error = 1.53017150528716024e-15
relative error = 2.8285583762893155640980842046965e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1820.0MB, alloc=40.3MB, time=21.39
TOP MAIN SOLVE Loop
x[1] = 2.58
y1[1] (closed_form) = 0.84640804121577553771763249456923
y1[1] (numeric) = 0.84640804121577793070397692833309
absolute error = 2.39298634443376386e-15
relative error = 2.8272254372684034685635052765071e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.53253490755562120108505876447165
y2[1] (numeric) = -0.53253490755562271008957694818925
absolute error = 1.50900451818371760e-15
relative error = 2.8336255459950443599914625403807e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.59
y1[1] (closed_form) = 0.85169098148656565465635974540831
y1[1] (numeric) = 0.85169098148656806262473123328344
absolute error = 2.40796837148787513e-15
relative error = 2.8272794051252470352844922679991e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.52404434168727600077313024887591
y2[1] (numeric) = -0.52404434168727748809323141888579
absolute error = 1.48732010117000988e-15
relative error = 2.8381569704221130169630184962962e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.6
y1[1] (closed_form) = 0.8568887533689472337977021516452
y1[1] (numeric) = 0.85688875336894965652866859253443
absolute error = 2.42273096644088923e-15
relative error = 2.8273576434696692167753026248195e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.51550137182146423525772693520937
y2[1] (numeric) = -0.51550137182146570037584355362334
absolute error = 1.46511811661841397e-15
relative error = 2.8421226338187796480203337653240e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.61
y1[1] (closed_form) = 0.86200083709006349911416744872265
y1[1] (numeric) = 0.86200083709006593638312074999296
absolute error = 2.43726895330127031e-15
relative error = 2.8274554367359851876549635661183e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.5069068522480533678909866995555
y2[1] (numeric) = -0.50690685224805481028950224055414
absolute error = 1.44239851554099864e-15
relative error = 2.8454902693545858705132754335288e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=1862.1MB, alloc=40.3MB, time=21.89
x[1] = 2.62
y1[1] (closed_form) = 0.86702672144580239454661367674835
y1[1] (numeric) = 0.86702672144580484612376970853796
absolute error = 2.45157715603178961e-15
relative error = 2.8275681653083134345080682832821e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.49826164241183866398876000999763
y2[1] (numeric) = -0.49826164241184008315009783133577
absolute error = 1.41916133782133814e-15
relative error = 2.8482251432237059546228411230050e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.63
y1[1] (closed_form) = 0.87196590385191656920784839019493
y1[1] (numeric) = 0.87196590385191903485824782954179
absolute error = 2.46565039943934686e-15
relative error = 2.8276912991062103373170010735536e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.48956660682659942750568705361163
y2[1] (numeric) = -0.4895666068266008229123994873394
absolute error = 1.39540671243372777e-15
relative error = 2.8502898134307793084907148706647e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.64
y1[1] (closed_form) = 0.87681789039428138329890731626599
y1[1] (numeric) = 0.87681789039428386278241738318662
absolute error = 2.47948351006692063e-15
relative error = 2.8278203914748633770787150041514e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.48082261498864834353055026953286
y2[1] (numeric) = -0.48082261498864971466540791929004
absolute error = 1.37113485764975718e-15
relative error = 2.8516438597259574853167519272790e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.65
y1[1] (closed_form) = 0.88158219587828590897930236605381
y1[1] (numeric) = 0.88158219587828840205061945357483
absolute error = 2.49307131708752102e-15
relative error = 2.8279510733582493019684412130240e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.47203054128988257159561077839739
y2[1] (numeric) = -0.47203054128988391794169201059605
absolute error = 1.34634608123219866e-15
relative error = 2.8522435805809077003009722269524e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.66
y1[1] (closed_form) = 0.88625834387735198713231100388259
y1[1] (numeric) = 0.88625834387735449354096420390022
absolute error = 2.50640865320001763e-15
relative error = 2.8280790477351781135247238563203e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.46319126493034528461814059379635
y2[1] (numeric) = -0.46319126493034660565892120996602
absolute error = 1.32104078061616967e-15
relative error = 2.8520416524150726796546560114102e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=1904.2MB, alloc=40.3MB, time=22.37
x[1] = 2.67
y1[1] (closed_form) = 0.89084586678057648816006285842974
y1[1] (numeric) = 0.89084586678057900765041838514513
absolute error = 2.51949035552671539e-15
relative error = 2.8282000842995312282040473476676e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.4543056698303063972473913211913
y2[1] (numeric) = -0.45430566983030769246683439872132
absolute error = 1.29521944307753002e-15
relative error = 2.8509867454688034869530371701934e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.68
y1[1] (closed_form) = 0.89534430583949201262204581862066
y1[1] (numeric) = 0.895344305839494544933312331171
absolute error = 2.53231126651255034e-15
relative error = 2.8283100143672736866514497879542e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.44537464454187127547089883192945
y2[1] (numeric) = -0.44537464454187254435354472040585
absolute error = 1.26888264588847640e-15
relative error = 2.8490230897488466463118888126032e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.69
y1[1] (closed_form) = 0.89975321121394135568593488432887
y1[1] (numeric) = 0.89975321121394390055216971010607
absolute error = 2.54486623482577720e-15
relative error = 2.8284047259939864315664457822303e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.43639908216012626653550411876099
y2[1] (numeric) = -0.43639908216012750856656057905888
absolute error = 1.24203105646029789e-15
relative error = 2.8460899833069862570172800008897e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.7
y1[1] (closed_form) = 0.90407214201706114798252728194333
y1[1] (numeric) = 0.90407214201706370513264354196349
absolute error = 2.55715011626002016e-15
relative error = 2.8284801592877341877400195667023e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.42737988023382993455605308585788
y2[1] (numeric) = -0.4273798802338311492214855591163
absolute error = 1.21466543247325842e-15
relative error = 2.8421212337105934840008918252031e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.71
y1[1] (closed_form) = 0.90830066635937017453818459371608
y1[1] (numeric) = 0.90830066635937274369595923127411
absolute error = 2.56915777463755803e-15
relative error = 2.8285323019030659644789935070896e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.41831794067565893261379068110859
y2[1] (numeric) = -0.41831794067566011940041267468204
absolute error = 1.18678662199357345e-15
relative error = 2.8370445218694158241836541157057e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1946.3MB, alloc=40.3MB, time=22.88
TOP MAIN SOLVE Loop
x[1] = 2.72
y1[1] (closed_form) = 0.91243836139195796298962879998706
y1[1] (numeric) = 0.91243836139196054387371151370146
absolute error = 2.58088408271371440e-15
relative error = 2.8285571847028457933107366743663e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.40921416967201748668244467400742
y2[1] (numeric) = -0.40921416967201864507800825145718
absolute error = 1.15839556357744976e-15
relative error = 2.8307806753268009280921302036371e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.73
y1[1] (closed_form) = 0.91648481334876932225826112489279
y1[1] (numeric) = 0.91648481334877191458218420711626
absolute error = 2.59232392308222347e-15
relative error = 2.8285508775754385549812755706487e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.40006947759241951035844795789445
y2[1] (numeric) = -0.40006947759242063985173432005369
absolute error = 1.12949328636215924e-15
relative error = 2.8232428356178122074039142849941e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.74
y1[1] (closed_form) = 0.92043961758798060326537325177928
y1[1] (numeric) = 0.92043961758798320673756233322094
absolute error = 2.60347218908144166e-15
relative error = 2.8285094853955345844650916646615e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.39088477889845241210831170164027
y2[1] (numeric) = -0.3908847788984535121892218457593
absolute error = 1.10008091014411903e-15
relative error = 2.8143355012293993971757878971979e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.75
y1[1] (closed_form) = 0.92430237863246354409665948952671
y1[1] (numeric) = 0.92430237863246615842044519080164
absolute error = 2.61432378570127493e-15
relative error = 2.8284291441175937440735496957016e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.38166099205233169857656137237778
y2[1] (numeric) = -0.3816609920523327687362068163298
absolute error = 1.07015964544395202e-15
relative error = 2.8039534239255353992173548425351e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.76
y1[1] (closed_form) = 0.9280727102093326532652331971401
y1[1] (numeric) = 0.92807271020933527813886368783158
absolute error = 2.62487363049069148e-15
relative error = 2.8283060169915293352577293629784e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.37239903942505551841770059244975
y2[1] (numeric) = -0.3723990394250565581484941509534
absolute error = 1.03973079355850365e-15
relative error = 2.7919803315382803733979900535256e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1988.5MB, alloc=40.3MB, time=23.36
TOP MAIN SOLVE Loop
x[1] = 2.77
y1[1] (closed_form) = 0.93175023528857217636777720782907
y1[1] (numeric) = 0.93175023528857481148443167351841
absolute error = 2.63511665446568934e-15
relative error = 2.8281362908908393196948723609663e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.36309984720416833112128200917246
y2[1] (numeric) = -0.3630998472041693399170286089648
absolute error = 1.00879574659979234e-15
relative error = 2.7782874445346544832726085923049e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.78
y1[1] (closed_form) = 0.93533458612073878346935166911759
y1[1] (numeric) = 0.93533458612074142851715468670565
absolute error = 2.64504780301758806e-15
relative error = 2.8279161727439306959933082826549e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.35376434530114292438633931722734
y2[1] (numeric) = -0.35376434530114390174232683810017
absolute error = 9.7735598752087283e-16
relative error = 2.7627317464367295482620352433723e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.79
y1[1] (closed_form) = 0.93882540427373620697953961962409
y1[1] (numeric) = 0.93882540427373886164157644113753
absolute error = 2.65466203682151344e-15
relative error = 2.8276418860598764489904002155872e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.34439346725839004176626159556229
y2[1] (numeric) = -0.34439346725839098717935172415571
absolute error = 9.4541309012859342e-16
relative error = 2.7451539590885240975151769736046e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.8
y1[1] (closed_form) = 0.94222234066865815258678811736615
y1[1] (numeric) = 0.94222234066866081654112086231049
absolute error = 2.66395433274494434e-15
relative error = 2.8273096675402969971097680695560e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.33498815015590491954385375271242
y2[1] (numeric) = -0.33498815015590583251257283594195
absolute error = 9.1296871908322953e-16
relative error = 2.7253761622861285651210176175454e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.81
y1[1] (closed_form) = 0.94552505561469589898972047835884
y1[1] (numeric) = 0.94552505561469857190940523454882
absolute error = 2.67291968475618998e-15
relative error = 2.8269157637694714004395287975985e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.32554933451756006810510128120633
y2[1] (numeric) = -0.32554933451756094812973116618438
absolute error = 8.8002462988497805e-16
relative error = 2.7031989826952316861892747376445e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2030.6MB, alloc=40.3MB, time=23.86
TOP MAIN SOLVE Loop
x[1] = 2.82
y1[1] (closed_form) = 0.94873321884310709569453606376004
y1[1] (numeric) = 0.94873321884310977724764089642668
absolute error = 2.68155310483266664e-15
relative error = 2.8264564279751625286748503691803e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.31607796421705366845541285602457
y2[1] (numeric) = -0.31607796421705451503808170332316
absolute error = 8.4658266884729859e-16
relative error = 2.6783982583042151665165801873515e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.83
y1[1] (closed_form) = 0.95184650954024236202702511272453
y1[1] (numeric) = 0.95184650954024505187664898156628
absolute error = 2.68984962386884175e-15
relative error = 2.8259279168529847255879707224877e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.3065749863835229889603130778681
y2[1] (numeric) = -0.30657498638352380160508613495731
absolute error = 8.1264477305708921e-16
relative error = 2.6507210605906273969208676264040e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.84
y1[1] (closed_form) = 0.95486461637962638472681949358624
y1[1] (numeric) = 0.95486461637962908253111207730022
absolute error = 2.69780429258371398e-15
relative error = 2.8253264874474576822075873039662e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.29704135130683226089025606809731
y2[1] (numeric) = -0.29704135130683303910322638978365
absolute error = 7.7821297032168634e-16
relative error = 2.6198809253255192487294969304640e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.85
y1[1] (closed_form) = 0.95778723755309030604085410717493
y1[1] (numeric) = 0.95778723755309301145303653487234
absolute error = 2.70541218242769741e-15
relative error = 2.8246483940831754529411519095631e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.28747801234254448390307892669172
y2[1] (numeric) = -0.28747801234254522719245802937169
absolute error = 7.4328937910267997e-16
relative error = 2.5855521020404626966810555350173e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=2072.8MB, alloc=40.3MB, time=24.34
x[1] = 2.86
y1[1] (closed_form) = 0.96061408080095228910317316639277
y1[1] (numeric) = 0.96061408080095500177155965517059
absolute error = 2.71266838648877782e-15
relative error = 2.8238898853397784385606832411482e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.27788592581658666420435690975324
y2[1] (numeric) = -0.27788592581658737208056534629041
absolute error = 7.0787620843653717e-16
relative error = 2.5473625782104468218033029032690e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.87
y1[1] (closed_form) = 0.96334486344124324256969375873794
y1[1] (numeric) = 0.96334486344124596213771415654727
absolute error = 2.71956802039780933e-15
relative error = 2.8230472010646501252739181898345e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.26826605092961801878239892098714
y2[1] (numeric) = -0.26826605092961869075815676301573
absolute error = 6.7197575784202859e-16
relative error = 2.5048855623491747697941091144039e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.88
y1[1] (closed_form) = 0.96597931239797478195981790476552
y1[1] (numeric) = 0.96597931239797750806604113758476
absolute error = 2.72610622323281924e-15
relative error = 2.8221165694174701058410379542285e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.25861934966111070881776692011768
y2[1] (numeric) = -0.25861934966111134440818413457195
absolute error = 6.3559041721445427e-16
relative error = 2.4576290136345885349240741113916e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.89
y1[1] (closed_form) = 0.96851716422844660093231550720928
y1[1] (numeric) = 0.9685171642284493332104739293984
absolute error = 2.73227815842218912e-15
relative error = 2.8210942039409430003656962522765e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.24894678667315269411404584058049
y2[1] (numeric) = -0.24894678667315329283671254724765
absolute error = 5.9872266670666716e-16
relative error = 2.4050226745555159214531348574193e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.9
y1[1] (closed_form) = 0.97095816514959052178110666934553
y1[1] (numeric) = 0.97095816514959325986012131592569
absolute error = 2.73807901464658016e-15
relative error = 2.8199763006521897200123797343594e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.23924932921398232818425691873958
y2[1] (numeric) = -0.23924932921398288955933351563357
absolute error = 5.6137507659689399e-16
relative error = 2.3464018830949592849199421831766e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=2114.9MB, alloc=40.3MB, time=24.84
x[1] = 2.91
y1[1] (closed_form) = 0.97330207106334859076784710660275
y1[1] (numeric) = 0.97330207106335133427185384607344
absolute error = 2.74350400673947069e-15
relative error = 2.8187590351494343809005898265705e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.22952794702126434045301822382699
y2[1] (numeric) = -0.22952794702126486400332536718229
absolute error = 5.2355030714335530e-16
relative error = 2.2809871910493392414674154155738e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.92
y1[1] (closed_form) = 0.97554864758108268050293173515827
y1[1] (numeric) = 0.97554864758108542905130832133216
absolute error = 2.74854837658617389e-15
relative error = 2.8174385597287483497073617204866e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.21978361222511687789562909306458
y2[1] (numeric) = -0.21978361222511736314673751875241
absolute error = 4.8525110842568783e-16
relative error = 2.2078584636631671419828497478793e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.93
y1[1] (closed_form) = 0.97769767004701315843501960467633
y1[1] (numeric) = 0.97769767004701591164241362588015
absolute error = 2.75320739402120382e-15
relative error = 2.8160110005057230510516265934156e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.21001729925089930332910403425911
y2[1] (numeric) = -0.21001729925089974980942420743378
absolute error = 4.4648032017317467e-16
relative error = 2.1259216348639090577027910972922e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.94
y1[1] (closed_form) = 0.97974892356068427760176338132832
y1[1] (numeric) = 0.97974892356068703507812110518606
absolute error = 2.75747635772385774e-15
relative error = 2.8144724545370357962596507533527e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.20022998472177047149431709442312
y2[1] (numeric) = -0.20022998472177087873518867421279
absolute error = 4.0724087157978967e-16
relative error = 2.0338655678652282173975364601344e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.95
y1[1] (closed_form) = 0.98170220299845404312138940470197
y1[1] (numeric) = 0.98170220299845680447198551658499
absolute error = 2.76135059611188302e-15
relative error = 2.8128189869369494700636234216877e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.19042264736102722702044731405738
y2[1] (numeric) = -0.19042264736102759455622842012235
absolute error = 3.6753578110606497e-16
relative error = 1.9301054060510164392170593186675e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=2157.0MB, alloc=40.3MB, time=25.34
x[1] = 2.96
y1[1] (closed_form) = 0.98355731303400640545638732297616
y1[1] (numeric) = 0.98355731303400917028185555607306
absolute error = 2.76482546823309690e-15
relative error = 2.8110466279838471483277669606521e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.18059626789423289034054450880135
y2[1] (numeric) = -0.18059626789423321770870077659321
absolute error = 3.2736815626779186e-16
relative error = 1.8127072064385996164875156150275e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.97
y1[1] (closed_form) = 0.98531406815788372924707637480614
y1[1] (numeric) = 0.98531406815788649714344102963359
absolute error = 2.76789636465482745e-15
relative error = 2.8091513702119476443437964276834e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.17075182895114551862806449866797
y2[1] (numeric) = -0.17075182895114580536925791023509
absolute error = 2.8674119341156712e-16
relative error = 1.6792862200826427303286774740494e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.98
y1[1] (closed_form) = 0.9869722926960375844844419643954
y1[1] (numeric) = 0.98697229269604035504315031543966
absolute error = 2.77055870835104426e-15
relative error = 2.8071291654833779835443670478812e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.16089031496745574884655395454133
y2[1] (numeric) = -0.16089031496745599450473143173985
absolute error = 2.4565817747719852e-16
relative error = 1.5268674035903856379450532893094e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 2.99
y1[1] (closed_form) = 0.98853182082739600495858418721084
y1[1] (numeric) = 0.98853182082739877776653977425842
absolute error = 2.77280795558704758e-15
relative error = 2.8049759220357941619952737596529e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.15101271208634404904629503561052
y2[1] (numeric) = -0.15101271208634425316877678259577
absolute error = 2.0412248174698525e-16
relative error = 1.3516907214425418705965842395908e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3
y1[1] (closed_form) = 0.98999249660044545727157279473126
y1[1] (numeric) = 0.98999249660044823191116959631597
absolute error = 2.77463959680158471e-15
relative error = 2.8026875015007424173163276743204e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.14112000805986722210074480280811
y2[1] (numeric) = -0.14112000805986738423831238469849
absolute error = 1.6213756758189038e-16
relative error = 1.1489339450229261348555731534831e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2199.2MB, alloc=40.3MB, time=25.83
TOP MAIN SOLVE Loop
x[1] = 3.01
y1[1] (closed_form) = 0.99135417394882586223162557418242
y1[1] (numeric) = 0.99135417394882863828078306044502
absolute error = 2.77604915748626260e-15
relative error = 2.8002597158879400415860643480494e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.13121319215018402315021812468485
y2[1] (numeric) = -0.1312131921501841428572022693093
absolute error = 1.1970698414462445e-16
relative error = 9.1230906117740207734584555364356e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.02
y1[1] (closed_form) = 0.99261671670593710913946653326304
y1[1] (numeric) = 0.99261671670593988617166559538903
absolute error = 2.77703219906212599e-15
relative error = 2.7976883245306277734573341155355e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.12129325503062976810875799633911
y2[1] (numeric) = -0.12129325503062984494312610600013
absolute error = 7.683436810966102e-17
relative error = 6.3345952823393437288752248736823e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.03
y1[1] (closed_form) = 0.99377999861855560232760730870843
y1[1] (numeric) = 0.99377999861855837991192706197886
absolute error = 2.77758431975327043e-15
relative error = 2.7949690309871045296997038385045e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.11136118868664982569090503291726
y2[1] (numeric) = -0.11136118868664985921434839312381
absolute error = 3.352344336020655e-17
relative error = 3.0103345479308267382347646844039e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.04
y1[1] (closed_form) = 0.99484390335945947830924495484319
y1[1] (numeric) = 0.99484390335946225601040041220306
absolute error = 2.77770115545735987e-15
relative error = 2.7920974798935004042427395667626e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.10141798631660189952660831260879
y2[1] (numeric) = -0.10141798631660188930462898475784
absolute error = 1.022197932785095e-17
relative error = 1.0079059641295239013363486811150e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.05
y1[1] (closed_form) = 0.99580832453906123102558220156492
y1[1] (numeric) = 0.99580832453906400840396281448364
absolute error = 2.77737838061291872e-15
relative error = 2.7890692537627749480943650182583e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.091464642232437020053401588696418
y2[1] (numeric) = -0.091464642232436965655398973707628
absolute error = 5.4398002614988790e-17
relative error = 5.9474351276363581237357577978756e-14 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 16
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2241.3MB, alloc=40.3MB, time=26.33
TOP MAIN SOLVE Loop
x[1] = 3.06
y1[1] (closed_form) = 0.99667316571604658193873927179315
y1[1] (numeric) = 0.99667316571604935855044833506178
absolute error = 2.77661170906326863e-15
relative error = 2.7858798697248449260611772764344e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.081502151760269178003890088835723
y2[1] (numeric) = -0.08150215176026907900324714877169
absolute error = 9.9000642940064033e-17
relative error = 1.2146997447535495907915822995988e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.07
y1[1] (closed_form) = 0.99743834040701853109211366272677
y1[1] (numeric) = 0.99743834040702130648900857970712
absolute error = 2.77539689491698035e-15
relative error = 2.7825247762026484793662390287253e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.071531511140843542442340790318903
y2[1] (numeric) = -0.071531511140843398416509915052694
absolute error = 1.44025830875266209e-16
relative error = 2.0134599224624708536452527826981e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.08
y1[1] (closed_form) = 0.99810377209514562474111853735979
y1[1] (numeric) = 0.99810377209514839847085194207135
absolute error = 2.77372973340471156e-15
relative error = 2.7789993495188413442193341468587e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.061553717429913216445629637135705
y2[1] (numeric) = -0.061553717429913026976218143158561
absolute error = 1.89469411493977144e-16
relative error = 3.0781148467549878367624300062193e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.09
y1[1] (closed_form) = 0.99866939423781357473474351808576
y1[1] (numeric) = 0.99866939423781634634080525038738
absolute error = 2.77160606173230162e-15
relative error = 2.7752988904276943025151151862045e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.051569768398534492669958510574615
y2[1] (numeric) = -0.051569768398534257342813759069639
absolute error = 2.35327144751504976e-16
relative error = 4.5632771303699027681413396819542e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.1
y1[1] (closed_form) = 0.99913515027327946449237605454147
y1[1] (numeric) = 0.99913515027328223351413598453632
absolute error = 2.76902175992999485e-15
relative error = 2.7714186205666200948764083800907e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.041580662433290579194698271596673
y2[1] (numeric) = -0.04158066243329029759999239293888
absolute error = 2.81594705878657793e-16
relative error = 6.7722515563678373780865473625298e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2283.4MB, alloc=40.3MB, time=26.81
TOP MAIN SOLVE Loop
x[1] = 3.11
y1[1] (closed_form) = 0.99950099362632787616083083671683
y1[1] (numeric) = 0.9995009936263306421335825343808
absolute error = 2.76597275169766397e-15
relative error = 2.7673536788216009483822540708810e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.031587398436453773187626872703365
y2[1] (numeric) = -0.031587398436453444919941084582788
absolute error = 3.28267685788120577e-16
relative error = 1.0392362208888965105575034080109e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.12
y1[1] (closed_form) = 0.99976688771292837334358497397559
y1[1] (numeric) = 0.99976688771293113579859021988146
absolute error = 2.76245500524590587e-15
relative error = 2.7630991176006153429463385511603e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.021590975726096066090998104201892
y2[1] (numeric) = -0.021590975726095690749406610604474
absolute error = 3.75341591493597418e-16
relative error = 1.7384188480187048076881069633882e-12 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 14
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.13
y1[1] (closed_form) = 0.99993280594389387365782723913921
y1[1] (numeric) = 0.99993280594389663212236137202161
absolute error = 2.75846453413288240e-15
relative error = 2.7586498990089735687375973524870e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.011592393936158169184681483118307
y2[1] (numeric) = -0.011592393936157746372834941439044
absolute error = 4.22811846541679263e-16
relative error = 3.6473212424473833437203029294827e-12 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 14
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.14
y1[1] (closed_form) = 0.99999873172753954528511430634505
y1[1] (numeric) = 0.99999873172754229928251240312401
absolute error = 2.75399739809677896e-15
relative error = 2.7540008909202649819213327882564e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = -0.0015926529164869525405414363244433
y2[1] (numeric) = -0.0015926529164864818667499799286864
absolute error = 4.706737914563957569e-16
relative error = 2.9552816347117250177826419204673e-11 %
Desired digits = 8
Estimated correct digits = 9
Correct digits = 13
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=2325.5MB, alloc=40.3MB, time=27.31
x[1] = 3.15
y1[1] (closed_form) = 0.99996465847134196162819465679473
y1[1] (numeric) = 0.99996465847134471067789854054905
absolute error = 2.74904970388375432e-15
relative error = 2.7491468629363959429249764024647e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.008407247367148706459141516571067
y2[1] (numeric) = 0.0084072473671492253818257129791045
absolute error = 5.189226841964080375e-16
relative error = 6.1723256320980497040943408140752e-12 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 14
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.16
y1[1] (closed_form) = 0.99983058958259834815991709427395
y1[1] (numeric) = 0.9998305895826010917775231655295
absolute error = 2.74361760607125555e-15
relative error = 2.7440824822299546874918260236846e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.01840630693305366670737927118737
y2[1] (numeric) = 0.018406306933054234261079895984994
absolute error = 5.67553700624797624e-16
relative error = 3.0834740651075223759899420342484e-12 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 14
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.17
y1[1] (closed_form) = 0.99959653846808585554008835013528
y1[1] (numeric) = 0.99959653846808859323739623670747
absolute error = 2.73769730788657219e-15
relative error = 2.7388023092618769833254311178890e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.028403525883603859571285274896733
y2[1] (numeric) = 0.028403525883604476133220266301609
absolute error = 6.16561934991404876e-16
relative error = 2.1707232317496177662802135215625e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.18
y1[1] (closed_form) = 0.99926252853272089307268415386031
y1[1] (numeric) = 0.99926252853272362435774617436491
absolute error = 2.73128506202050460e-15
relative error = 2.7333007933671041853789999479789e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.03839790450523521805369524672612
y2[1] (numeric) = 0.038397904505235883996095674394908
absolute error = 6.65942400427668788e-16
relative error = 1.7343196432421810229988002184675e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.19
y1[1] (closed_form) = 0.99882859317721865656895082969948
y1[1] (numeric) = 0.99882859317722138094612226572098
absolute error = 2.72437717143602150e-15
relative error = 2.7275722682006208916515868325347e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.048388443368414200108007148451169
y2[1] (numeric) = 0.048388443368414915798036602369387
absolute error = 7.15690029453918218e-16
relative error = 1.4790515661040844433714982520869e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=2367.6MB, alloc=40.3MB, time=27.80
x[1] = 3.2
y1[1] (closed_form) = 0.99829477579475308466166072228358
y1[1] (numeric) = 0.99829477579475580163165089406619
absolute error = 2.71696999017178261e-15
relative error = 2.7216109470359332638941722545941e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.058374143427579909137217414619095
y2[1] (numeric) = 0.058374143427580674936891913682042
absolute error = 7.65799674499062947e-16
relative error = 1.3118816474782689156131797880336e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.21
y1[1] (closed_form) = 0.99766112976661757757210666520424
y1[1] (numeric) = 0.99766112976662028663203080560686
absolute error = 2.70905992414040262e-15
relative error = 2.7154109179076985768789529760694e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.068354006121047817548388360676863
y2[1] (numeric) = 0.068354006121048633814496793308186
absolute error = 8.16266108432631323e-16
relative error = 1.1941744964985799914477778220986e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.22
y1[1] (closed_form) = 0.99692771845688691225434273747586
y1[1] (numeric) = 0.99692771845688961289777465880912
absolute error = 2.70064343192133326e-15
relative error = 2.7089661385898411599165884305936e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.078327033470865103073444147916042
y2[1] (numeric) = 0.078327033470865970157469257015584
absolute error = 8.67084025109099542e-16
relative error = 1.1070048062417993287982335729058e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.23
y1[1] (closed_form) = 0.99609461520608088772070849458495
y1[1] (numeric) = 0.99609461520608357943773404282573
absolute error = 2.69171702554824078e-15
relative error = 2.7022704314000879230088478837651e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.088292228182607612405875728529723
y2[1] (numeric) = 0.088292228182608530653915652985704
absolute error = 9.18248039924455981e-16
relative error = 1.0400100425887072115197165963836e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.24
y1[1] (closed_form) = 0.99516190332383033417882384374247
y1[1] (numeric) = 0.99516190332383301645609513449949
absolute error = 2.68227727129075702e-15
relative error = 2.6953174778214268723257814583843e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.098248593745108472540154959437637
y2[1] (numeric) = 0.098248593745109442292845344379967
absolute error = 9.69752690384942330e-16
relative error = 9.8703976659536020201062922602461e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2409.7MB, alloc=40.3MB, time=28.30
TOP MAIN SOLVE Loop
x[1] = 3.25
y1[1] (closed_form) = 0.9941296760805462193730292251716
y1[1] (numeric) = 0.99412967608054889169381965565386
absolute error = 2.67232079043048226e-15
relative error = 2.6881008129305315116907134896176e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.10819513453010837703583084256083
y2[1] (numeric) = 0.10819513453010939862826753047245
absolute error = 1.02159243668791162e-15
relative error = 9.4421291782175697991410674427316e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.26
y1[1] (closed_form) = 0.99299803669809268521269456717166
y1[1] (numeric) = 0.99299803669809534705695459829096
absolute error = 2.66184426003111930e-15
relative error = 2.6806138196227030610575442638938e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.11813085589181758226072311033608
y2[1] (numeric) = 0.11813085589181865602238542507768
absolute error = 1.07376166231474160e-15
relative error = 9.0895952137862777062985044453801e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.27
y1[1] (closed_form) = 0.99176709833946494737596174049474
y1[1] (numeric) = 0.99176709833946759822037544311302
absolute error = 2.65084441370261828e-15
relative error = 2.6728497226223565339189622969325e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.12805476426637965749655689075362
y2[1] (numeric) = 0.12805476426638078375123152649389
absolute error = 1.12625467463574027e-15
relative error = 8.7951016979962111526001745069938e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.28
y1[1] (closed_form) = 0.99043698409747309009035841613171
y1[1] (numeric) = 0.99043698409747572940840077534453
absolute error = 2.63931804235921282e-15
relative error = 2.6648015822675159465760708747766e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.13796586727122704261491407058525
y2[1] (numeric) = 0.13796586727122822168061959756401
absolute error = 1.17906570552697876e-15
relative error = 8.5460681605331698950807131620559e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.29
y1[1] (closed_form) = 0.98900782698243288770137512553948
y1[1] (numeric) = 0.98900782698243551496337009676794
absolute error = 2.62726199497122846e-15
relative error = 2.6564622880561842422419423058378e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.14786317380431847785052978374264
y2[1] (numeric) = 0.14786317380431971003944178272781
absolute error = 1.23218891199898517e-15
relative error = 8.3333049081555557502338631573142e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2451.8MB, alloc=40.3MB, time=28.78
TOP MAIN SOLVE Loop
x[1] = 3.3
y1[1] (closed_form) = 0.98747976990886488393659105110285
y1[1] (numeric) = 0.98747976990886749860977036164798
absolute error = 2.61467317931054513e-15
relative error = 2.6478245519418133779659718590022e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.15774569414324838201165427760248
y2[1] (numeric) = 0.15774569414324966763003111483365
absolute error = 1.28561837683723117e-15
relative error = 8.1499427532377844628271147556314e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.31
y1[1] (closed_form) = 0.98585296568120305894633807058553
y1[1] (numeric) = 0.98585296568120566049490076018163
absolute error = 2.60154856268959610e-15
relative error = 2.6388809013644163029884378156909e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.16761244004421826827224999431698
y2[1] (numeric) = 0.16761244004421960762035924865884
absolute error = 1.33934810925434186e-15
relative error = 7.9907440575473097078503577204865e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.32
y1[1] (closed_form) = 0.98412757697851451324228958473119
y1[1] (numeric) = 0.98412757697851710112746227851769
absolute error = 2.58788517269378650e-15
relative error = 2.6296236720031322164469588211802e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.17746242484086030048692055230841
y2[1] (numeric) = 0.17746242484086169385896610626594
absolute error = 1.39337204555395753e-15
relative error = 7.8516454782101959447787302963620e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.33
y1[1] (closed_form) = 0.98230377633823169655284671485927
y1[1] (numeric) = 0.98230377633823427023294462207447
absolute error = 2.57368009790721520e-15
relative error = 2.6200450002352764390937440311875e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.18729466354290310775529282413595
y2[1] (numeric) = 0.18729466354290455543934263031036
absolute error = 1.44768404980617441e-15
relative error = 7.7294463302984451620665268845733e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.34
y1[1] (closed_form) = 0.98038174613889880835887990106991
y1[1] (numeric) = 0.98038174613890136728936853265478
absolute error = 2.55893048863158487e-15
relative error = 2.6101368152860732442718518397640e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.19710817293466999073661691059272
y2[1] (numeric) = 0.19710817293467149301453144508283
absolute error = 1.50227791453449011e-15
relative error = 7.6215911911091009560363411189113e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2493.9MB, alloc=40.3MB, time=29.28
TOP MAIN SOLVE Loop
x[1] = 3.35
y1[1] (closed_form) = 0.97836167858193409545539437527153
y1[1] (numeric) = 0.97836167858193663908895197345668
absolute error = 2.54363355759818515e-15
relative error = 2.5998908310523790067631412933582e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.20690197167339966997603411602551
y2[1] (numeric) = 0.20690197167340122712339553020306
absolute error = 1.55714736141417755e-15
relative error = 7.5260150921721353282643793240649e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.36
y1[1] (closed_form) = 0.97624377567240987029416530777832
y1[1] (numeric) = 0.9762437756724123980807459806138
absolute error = 2.52778658067283548e-15
relative error = 2.5892985375827524085273778442295e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.21667508038737974424961398190553
y2[1] (numeric) = 0.21667508038738135653565596391547
absolute error = 1.61228604198200994e-15
relative error = 7.4410312394923549191354327608650e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.37
y1[1] (closed_form) = 0.97402824919885217208949176597085
y1[1] (numeric) = 0.97402824919885468347638931964497
absolute error = 2.51138689755367412e-15
relative error = 2.5783511921952105364681797184133e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.22642652177388304566410348430857
y2[1] (numeric) = 0.22642652177388471335164184156603
absolute error = 1.66768753835725746e-15
relative error = 7.3652482283973118543642059538328e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.38
y1[1] (closed_form) = 0.97171532071206209070412534999057
y1[1] (numeric) = 0.97171532071206458513603781167177
absolute error = 2.49443191246168120e-15
relative error = 2.5670398102129227167264020294683e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.23615532069689709795749177758963
y2[1] (numeric) = 0.23615532069689882130285575146477
absolute error = 1.72334536397387514e-15
relative error = 7.2975080929291066901071520429336e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=2535.9MB, alloc=40.3MB, time=29.78
x[1] = 3.39
y1[1] (closed_form) = 0.96930522150296087116533607467248
y1[1] (numeric) = 0.96930522150296334808443089849679
absolute error = 2.47691909482382431e-15
relative error = 2.5553551552969306197052075108090e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.24586050428463690513600137155794
y2[1] (numeric) = 0.24586050428463868438896569535746
absolute error = 1.77925296432379952e-15
relative error = 7.2368393187054069219558920853775e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.4
y1[1] (closed_form) = 0.96679819257946101428220153976569
y1[1] (numeric) = 0.96679819257946347312818148848162
absolute error = 2.45884597994871593e-15
relative error = 2.5432877293537386370466085143394e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.25554110202683131924990242936374
y2[1] (numeric) = 0.25554110202683315465362014063406
absolute error = 1.83540371771127032e-15
relative error = 7.1824207657935062651716425140340e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.41
y1[1] (closed_form) = 0.96419448464236568623478364095296
y1[1] (numeric) = 0.96419448464236812644495333562578
absolute error = 2.44021016969467282e-15
relative error = 2.5308277619942865260412529502016e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.26519614587177325875244430757411
y2[1] (numeric) = 0.26519614587177515054338032566604
absolute error = 1.89179093601809193e-15
relative error = 7.1335536562918386787600164955478e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.42
y1[1] (closed_form) = 0.96149435806029884717415014560141
y1[1] (numeric) = 0.96149435806030126818348327566994
absolute error = 2.42100933313006853e-15
relative error = 2.5179651995193903480444050632218e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.2748246703231240725009433576662
y2[1] (numeric) = 0.27482467032312602090880883741388
absolute error = 1.94840786547974768e-15
relative error = 7.0896395989083311197527697514957e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.43
y1[1] (closed_form) = 0.95869808284366860579948964122556
y1[1] (numeric) = 0.95869808284367100704069682709639
absolute error = 2.40124120718587083e-15
relative error = 2.5046896934052098879702102186140e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.28442571253646236904429691459137
y2[1] (numeric) = 0.28442571253646437429198438687012
absolute error = 2.00524768747227875e-15
relative error = 7.0501631852823893272860050396223e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=2578.1MB, alloc=40.3MB, time=30.27
x[1] = 3.44
y1[1] (closed_form) = 0.95580593861766640355516501297249
y1[1] (numeric) = 0.95580593861766878445876231322939
absolute error = 2.38090359730025690e-15
relative error = 2.4909905882606639571423868314093e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.29399831241556765639445181056032
y2[1] (numeric) = 0.29399831241556971869797112039799
absolute error = 2.06230351930983767e-15
relative error = 7.0146780856169144862255503753961e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.45
y1[1] (closed_form) = 0.95281821459430472850678513994775
y1[1] (numeric) = 0.95281821459430708850116319514776
absolute error = 2.35999437805520001e-15
relative error = 2.4768569092269600935774266338138e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.30354151270842916399808636621989
y2[1] (numeric) = 0.30354151270843128356650141904523
absolute error = 2.11956841505282534e-15
relative error = 6.9827958493730146341873919128394e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.46
y1[1] (closed_form) = 0.94973520954349615510160537578203
y1[1] (numeric) = 0.94973520954349849361309918070432
absolute error = 2.33851149380492229e-15
relative error = 2.4622773487875229632980856900822e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.31305435910297024610631577597493
y2[1] (numeric) = 0.31305435910297242314168210249342
absolute error = 2.17703536632651849e-15
relative error = 6.9541768163350991440919029599039e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.47
y1[1] (closed_form) = 0.94655723176317660188518005352668
y1[1] (numeric) = 0.94655723176317891833813934963583
absolute error = 2.31645295929610915e-15
relative error = 2.4472402529545861656974552916372e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.32253590032247879418185398715726
y2[1] (numeric) = 0.32253590032248102887915713725092
absolute error = 2.23469730315009366e-15
relative error = 6.9285226882210383961626040903207e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.48
y1[1] (closed_form) = 0.94328459904847579482359814738228
y1[1] (numeric) = 0.94328459904847808864045842716422
absolute error = 2.29381686027978194e-15
relative error = 2.4317336067965440413294423326588e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.33198518822073411538191643544275
y2[1] (numeric) = 0.33198518822073640792901121139422
absolute error = 2.29254709477595147e-15
relative error = 6.9055704173514406694505848295860e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2620.2MB, alloc=40.3MB, time=30.77
TOP MAIN SOLVE Loop
x[1] = 3.49
y1[1] (closed_form) = 0.93991763865993801915927867276677
y1[1] (numeric) = 0.93991763865994028976063278749294
absolute error = 2.27060135411472617e-15
relative error = 2.4157450192678309832829141249220e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.3414012778768207645082874807375
y2[1] (numeric) = 0.34140127787682311508583801998214
absolute error = 2.35057755053924464e-15
relative error = 6.8850871477620666995720703917230e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.5
y1[1] (closed_form) = 0.93645668729079633769865762667176
y1[1] (numeric) = 0.9364566872907985845033279890457
absolute error = 2.24680467036237394e-15
relative error = 2.3992617073005934147772910151363e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.35078322768961984812036880004364
y2[1] (numeric) = 0.35078322768962225690178951755427
absolute error = 2.40878142071751063e-15
relative error = 6.8668660032082535685339374589183e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.51
y1[1] (closed_form) = 0.93290209103330354808266630575758
y1[1] (numeric) = 0.93290209103330577050777767879747
absolute error = 2.22242511137303989e-15
relative error = 2.3822704791147282684704435395893e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.36013009947196835175953992341737
y2[1] (numeric) = 0.36013009947197081891093732372657
absolute error = 2.46715139740030920e-15
relative error = 6.8507225611458401438811807488950e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.52
y1[1] (closed_form) = 0.92925420534412324591621651227224
y1[1] (numeric) = 0.9292542053441254433772693756834
absolute error = 2.19746105286341116e-15
relative error = 2.3647577166999670006591862522447e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.36944095854447707443057432143296
y2[1] (numeric) = 0.36944095854447960011068969019625
absolute error = 2.52568011536876329e-15
relative error = 6.8364918857926147664853042266846e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.53
y1[1] (closed_form) = 0.92551339500878445462153901468401
y1[1] (numeric) = 0.9255133950087866265324834998769
absolute error = 2.17191094448519289e-15
relative error = 2.3467093574205679952798500987991e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.37871487382899778862484425400664
y2[1] (numeric) = 0.37871487382900037298499723890712
absolute error = 2.58436015298490048e-15
relative error = 6.8240260195109844558626447102970e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2662.5MB, alloc=40.3MB, time=31.26
TOP MAIN SOLVE Loop
x[1] = 3.54
y1[1] (closed_form) = 0.92168003410520337652276888612977
y1[1] (numeric) = 0.92168003410520552229607927094145
absolute error = 2.14577331038481168e-15
relative error = 2.3281108746898238169530030774900e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.38795091794173027924720110048451
y2[1] (numeric) = 0.38795091794173292243123419117534
absolute error = 2.64318403309069083e-15
relative error = 6.8131918519849812976867595214291e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.55
y1[1] (closed_form) = 0.91775450596627591295627082271047
y1[1] (numeric) = 0.91775450596627803200302057679123
absolute error = 2.11904674975408076e-15
relative error = 2.3089472576579731860195707586657e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.39714816728595995082022742343695
y2[1] (numeric) = 0.39714816728596265296445134011233
absolute error = 2.70214422391667538e-15
relative error = 6.8038693024385562602569317319896e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.56
y1[1] (closed_form) = 0.91373720314154469412352061310366
y1[1] (numeric) = 0.91373720314154678585345798483483
absolute error = 2.09172993737173117e-15
relative error = 2.2892029898532068777050538575380e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.40630570214441672928242142268591
y2[1] (numeric) = 0.40630570214441949051556142276443
absolute error = 2.76123314000007852e-15
relative error = 6.7959497625229726235266659041866e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.57
y1[1] (closed_form) = 0.90962852735794445195161343603674
y1[1] (numeric) = 0.90962852735794651577323757175177
absolute error = 2.06382162413571503e-15
relative error = 2.2688620267112494101617097868607e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.41542260677124602256709945606629
y2[1] (numeric) = 0.41542260677124884301024256836208
absolute error = 2.82044314311229579e-15
relative error = 6.7893347572809948685615561410095e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.58
y1[1] (closed_form) = 0.90542888947962966139140085454902
y1[1] (numeric) = 0.90542888947963169671203844073643
absolute error = 2.03532063758618741e-15
relative error = 2.2479077719244544300295410402311e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.42449796948358254294260094834376
y2[1] (numeric) = 0.42449796948358542270914414399138
absolute error = 2.87976654319564762e-15
relative error = 6.7839347893677559229989217026392e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2704.6MB, alloc=40.3MB, time=31.75
TOP MAIN SOLVE Loop
x[1] = 3.59
y1[1] (closed_form) = 0.90113870946688846735564983934783
y1[1] (numeric) = 0.90113870946689047358153225842266
absolute error = 2.00622588241907483e-15
relative error = 2.2263230525364439451271067181037e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.43353088275271783380787293204403
y2[1] (numeric) = 0.43353088275272077300347224133183
absolute error = 2.93919559930928780e-15
relative error = 6.7796683379204126333605104923280e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.6
y1[1] (closed_form) = 0.89675841633414700587029172526594
y1[1] (numeric) = 0.89675841633414898240663271540531
absolute error = 1.97653634099013937e-15
relative error = 2.2040900927030154182070298787329e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.44252044329485238426672734749269
y2[1] (numeric) = 0.44252044329485538298924793164741
absolute error = 2.99872252058415472e-15
relative error = 6.7764609884612698913476650750545e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.61
y1[1] (closed_form) = 0.89228844810706831897164969353841
y1[1] (numeric) = 0.89228844810707026522272350298694
absolute error = 1.94625107380944853e-15
relative error = 2.1811904860343010193306367138471e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.45146575216142325634494018639253
y2[1] (numeric) = 0.45146575216142631468440737324401
absolute error = 3.05833946718685148e-15
relative error = 6.7742446742523469319657664132079e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.62
y1[1] (closed_form) = 0.887729251778750153422404272068
y1[1] (numeric) = 0.88772925177875206879162429823007
absolute error = 1.91536922002616207e-15
relative error = 2.1576051664269500517112514795029e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.46036591482899819216274354079485
y2[1] (numeric) = 0.4603659148290013102012948331351
absolute error = 3.11803855129234025e-15
relative error = 6.7729570127938949250658145654308e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=2746.7MB, alloc=40.3MB, time=32.25
x[1] = 3.63
y1[1] (closed_form) = 0.88308128326502602342992354439801
y1[1] (numeric) = 0.88308128326502790731992144794647
absolute error = 1.88388999790354846e-15
relative error = 2.1333143772883754279065365014785e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.46922004128872721172690481453191
y2[1] (numeric) = 0.46922004128873038953874287986648
absolute error = 3.17781183806533457e-15
relative error = 6.7725407238305018828074854029539e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.64
y1[1] (closed_form) = 0.87834500735887400722343724413409
y1[1] (numeric) = 0.87834500735887585903614252827832
absolute error = 1.85181270528414423e-15
relative error = 2.1082976390478087021848363648684e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.47802724613534275625715663887291
y2[1] (numeric) = 0.47802724613534599390850328914522
absolute error = 3.23765134665027231e-15
relative error = 6.7729431174172099816164368001419e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.65
y1[1] (closed_form) = 0.87352089768393783657240447452827
y1[1] (numeric) = 0.87352089768393965570912451949955
absolute error = 1.81913672004497128e-15
relative error = 2.0825337148409944410094147538144e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.48678664865569947710681138829532
y2[1] (numeric) = 0.4867866486557027746558625580459
absolute error = 3.29754905116975058e-15
relative error = 6.7741156423993915614087410873857e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.66
y1[1] (closed_form) = 0.86860943664716492709839092015993
y1[1] (numeric) = 0.86860943664716671295989146288798
absolute error = 1.78586150054272805e-15
relative error = 2.0560005742467626016594920027569e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.49549737291684481637245114641035
y2[1] (numeric) = 0.49549737291684817386933287771305
absolute error = 3.35749688173130270e-15
relative error = 6.7760134871487267113858139741751e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.67
y1[1] (closed_form) = 0.86361111539056608553795618647981
y1[1] (numeric) = 0.8636111153905678375245422353515
absolute error = 1.75198658604887169e-15
relative error = 2.0286753549443836162206507042503e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.50415854785361157220802405891391
y2[1] (numeric) = 0.5041585478536149896947495013101
absolute error = 3.41748672544239619e-15
relative error = 6.7785952256326795191392100876648e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=2788.9MB, alloc=40.3MB, time=32.75
x[1] = 3.68
y1[1] (closed_form) = 0.85852643374210171794562486853616
y1[1] (numeric) = 0.85852643374210343545722204304576
absolute error = 1.71751159717450960e-15
relative error = 2.0005343221504627135026784697491e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.51276930735572368965980922504404
y2[1] (numeric) = 0.5127693073557271671702366585735
absolute error = 3.47751042743352946e-15
relative error = 6.7818225029234726341413800335996e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.69
y1[1] (closed_form) = 0.85335590016569945017519302837216
y1[1] (numeric) = 0.85335590016570113261142931339227
absolute error = 1.68243623628502011e-15
relative error = 1.9715528256830882528531930136929e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.52132879035440656651575454812466
y2[1] (numeric) = 0.52132879035441010407554643742832
absolute error = 3.53755979188930366e-15
relative error = 6.7856597551123568001040069196691e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.7
y1[1] (closed_form) = 0.8481000317104081588356701063544
y1[1] (numeric) = 0.84810003171040980559595801067745
absolute error = 1.64676028790432305e-15
relative error = 1.9417052544889245442758117840139e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.52983614090849321321077762570121
y2[1] (numeric) = 0.5298361409084968108373607130463
absolute error = 3.59762658308734509e-15
relative error = 6.7900739593161934570224002760926e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.71
y1[1] (closed_form) = 0.84275935395869349727638917260975
y1[1] (numeric) = 0.8427593539586951077600082813321
absolute error = 1.61048361910872235e-15
relative error = 1.9109649884558357930731148129251e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.53829050829001765624379404325037
y2[1] (numeric) = 0.53829050829002131394632048820267
absolute error = 3.65770252644495230e-15
relative error = 6.7950344100703933391585140414974e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.72
y1[1] (closed_form) = 0.83733440097388008700560008948967
y1[1] (numeric) = 0.83733440097388166061177999973382
absolute error = 1.57360617991024415e-15
relative error = 1.8793043473193351052132140258772e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.54669104706928702583745896705622
y2[1] (numeric) = 0.54669104706929074361676854039718
absolute error = 3.71777930957334096e-15
relative error = 6.8005125189148262627282156137457e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=2831.1MB, alloc=40.3MB, time=33.25
x[1] = 3.73
y1[1] (closed_form) = 0.83182571524674563027960569792163
y1[1] (numeric) = 0.83182571524674716640760932731651
absolute error = 1.53612800362939488e-15
relative error = 1.8466945364555495530315159153589e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.55503691719942382070274923216573
y2[1] (numeric) = 0.55503691719942759855133257152407
absolute error = 3.77784858333935834e-15
relative error = 6.8064816344134885120121999363768e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.74
y1[1] (closed_form) = 0.82623384764127228440667735620253
y1[1] (numeric) = 0.82623384764127378245588461346804
absolute error = 1.49804920725726551e-15
relative error = 1.8131055893363457753090167375659e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.56332728410036989575236111967948
y2[1] (numeric) = 0.56332728410037373365432405421765
absolute error = 3.83790196293453817e-15
relative error = 6.8129168802175866435808202024645e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.75
y1[1] (closed_form) = 0.82055935733956072258311240229071
y1[1] (numeric) = 0.82055935733956218195310420919972
absolute error = 1.45936999180690901e-15
relative error = 1.7785063064036184325407247983131e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.57156131874234377243415557335029
y2[1] (numeric) = 0.57156131874234767036518452471597
absolute error = 3.89793102895136568e-15
relative error = 6.8197950090960027594450452105747e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.76
y1[1] (closed_form) = 0.81480281178591238980944513756309
y1[1] (numeric) = 0.81480281178591380990008779148282
absolute error = 1.42009064265391973e-15
relative error = 1.7428641900993406971023864831838e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.57973819772874292602316503775395
y2[1] (numeric) = 0.57973819772874688395049350437522
absolute error = 3.95792732846662127e-15
relative error = 6.8270942711256691865412701567281e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.77
y1[1] (closed_form) = 0.80896478663008554561462174619622
y1[1] (numeric) = 0.80896478663008692582615161234064
absolute error = 1.38021152986614442e-15
relative error = 1.7061453757656231034175738825063e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.58785710337848275971251772647441
y2[1] (numeric) = 0.58785710337848677759489385814481
absolute error = 4.01788237613167040e-15
relative error = 6.8347942944644807555616331551250e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2873.2MB, alloc=40.3MB, time=33.73
TOP MAIN SOLVE Loop
x[1] = 3.78
y1[1] (closed_form) = 0.80304586566973076793658025923771
y1[1] (numeric) = 0.80304586566973210766968878169401
absolute error = 1.33973310852245630e-15
relative error = 1.6683145581045171185096447794253e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.59591722380776403167448581090021
y2[1] (numeric) = 0.59591722380776810946214108046638
absolute error = 4.07778765526956617e-15
relative error = 6.8428759773270340305398886478566e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.79
y1[1] (closed_form) = 0.79704664079201167456087725184016
y1[1] (numeric) = 0.79704664079201297321679627236455
absolute error = 1.29865591902052439e-15
relative error = 1.6293349128603968736947891223884e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.60391775301126055841709072023268
y2[1] (numeric) = 0.60391775301126469605170969906274
absolute error = 4.13763461897883006e-15
relative error = 6.8513213899537084071349746793832e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.8
y1[1] (closed_form) = 0.79096771191441669999656817435073
y1[1] (numeric) = 0.79096771191441795697715554786321
absolute error = 1.25698058737351248e-15
relative error = 1.5891680133581972595653719314826e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.61185789094271907573358608611888
y2[1] (numeric) = 0.61185789094272327314827732989403
absolute error = 4.19741469124377515e-15
relative error = 6.8601136855105604946406093723440e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.81
y1[1] (closed_form) = 0.78480968692476784656233037436496
y1[1] (numeric) = 0.7848096869247690612701558700075
absolute error = 1.21470782549564254e-15
relative error = 1.5477737414982810878673502994730e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.61973684359496319732588971051781
y2[1] (numeric) = 0.61973684359496745444515776175312
absolute error = 4.25711926805123531e-15
relative error = 6.8692370189846726443461032151775e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.82
y1[1] (closed_form) = 0.7785731816204324087577276566562
y1[1] (numeric) = 0.7785731816204335805961591332156
absolute error = 1.17183843147655940e-15
relative error = 1.5051101927729260657028535182370e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.62755382307929347077277195688991
y2[1] (numeric) = 0.62755382307929778751249047045265
absolute error = 4.31673971851356274e-15
relative error = 6.8786764732498946279433396086093e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2915.4MB, alloc=40.3MB, time=34.23
TOP MAIN SOLVE Loop
x[1] = 3.83
y1[1] (closed_form) = 0.77225881964674374969652252702348
y1[1] (numeric) = 0.77225881964674487806981237145826
absolute error = 1.12837328984443478e-15
relative error = 1.4611335748299894429654524154637e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.63530804770427559090337023862228
y2[1] (numeric) = 0.63530804770427996717075623637755
absolute error = 4.37626738599775527e-15
relative error = 6.8884179915737957252648464915030e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.84
y1[1] (closed_form) = 0.76586723243463728747307694024768
y1[1] (numeric) = 0.76586723243463837178644875799754
absolute error = 1.08431337181774986e-15
relative error = 1.4157980990658067671610463672904e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.64299874205390889182034887886274
y2[1] (numeric) = 0.64299874205391332751393813943675
absolute error = 4.43569358926057401e-15
relative error = 6.8984483159201675483352528566493e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.85
y1[1] (closed_form) = 0.75939905913750792781123507395279
y1[1] (numeric) = 0.75939905913750896747097061965024
absolute error = 1.03965973554569745e-15
relative error = 1.3690558646813406375182908907499e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.650625137065167300788642218662
y2[1] (numeric) = 0.65062513706517179579826580817274
absolute error = 4.49500962358951074e-15
relative error = 6.9087549304743290749474446424791e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.86
y1[1] (closed_form) = 0.75285494656729525719980460936484
y1[1] (numeric) = 0.75285494656729625161333094651054
absolute error = 9.9441352633714570e-16
relative error = 1.3208567345824808316141918327142e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.6581864701049049999590093452957
y2[1] (numeric) = 0.6581864701049095541657712947595
absolute error = 4.55420676194946380e-15
relative error = 6.9193260098822631604945159179676e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.87
y1[1] (closed_form) = 0.74623554912980288794206080932728
y1[1] (numeric) = 0.74623554912980383651803768743445
absolute error = 9.4857597687810717e-16
relative error = 1.2711482024466090697055103374874e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.66568198504611910542431592310351
y2[1] (numeric) = 0.66568198504612371870057205808356
absolute error = 4.61327625613498005e-15
relative error = 6.9301503717505104399045379348564e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2957.6MB, alloc=40.3MB, time=34.72
TOP MAIN SOLVE Loop
x[1] = 3.88
y1[1] (closed_form) = 0.73954152875925842313086807704128
y1[1] (numeric) = 0.7395415287592593252792755146995
absolute error = 9.0214840743765822e-16
relative error = 1.2198752502123959982776830229210e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.67311093234356173740418951936854
y2[1] (numeric) = 0.6731109323435664096135274472885
absolute error = 4.67220933792791996e-15
relative error = 6.9412174330028311574314155746875e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.89
y1[1] (closed_form) = 0.73277355485212058549838830263169
y1[1] (numeric) = 0.73277355485212144063061436488697
absolute error = 8.5513222606225528e-16
relative error = 1.1669801951775233318809228763558e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.68047256910869392041403980815868
y2[1] (numeric) = 0.68047256910869865141126006856014
absolute error = 4.73099722026040146e-15
relative error = 6.9525171697328259415491808319451e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.9
y1[1] (closed_form) = 0.72593230420014012937233048461435
y1[1] (numeric) = 0.72593230420014093690125924301021
absolute error = 8.0752892875839586e-16
relative error = 1.1124025258087419051825680900522e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.68776615918397381809088812537869
y2[1] (numeric) = 0.68776615918397860772198650825655
absolute error = 4.78963109838287786e-15
relative error = 6.9640400802297642811212457459803e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.91
y1[1] (closed_form) = 0.71901846092268122959176361387439
y1[1] (numeric) = 0.71901846092268198893186327744806
absolute error = 7.5934009966357367e-16
relative error = 1.0560787252793894237618191820926e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.69499097321647187391443044807649
y2[1] (numeric) = 0.69499097321647672201658148528061
absolute error = 4.84810215103720412e-15
relative error = 6.9757771508884685443787865922800e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=2999.7MB, alloc=40.3MB, time=35.22
x[1] = 3.92
y1[1] (closed_form) = 0.71203271639831011518720258429259
y1[1] (numeric) = 0.71203271639831082575461378977146
absolute error = 7.1056741120547887e-16
relative error = 9.9794208165006345650528577428858e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = 0.70214628873080549637060743782065
y2[1] (numeric) = 0.70214628873081040277214907236539
absolute error = 4.90640154163454474e-15
relative error = 6.9877198247438156149297506734691e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.93
y1[1] (closed_form) = 0.70497576919565778890458983952695
y1[1] (numeric) = 0.70497576919565845011721408892246
absolute error = 6.6121262424939551e-16
relative error = 9.3792248349727843016831525949601e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = 0.70923139020138599514994389285155
y2[1] (numeric) = 0.70923139020139095967036333082754
absolute error = 4.96452041943797599e-15
relative error = 6.9998599723967409614352003413825e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.94
y1[1] (closed_form) = 0.69784832500356374624360614943559
y1[1] (numeric) = 0.69784832500356435752119438318583
absolute error = 6.1127758823375024e-16
relative error = 8.7594619967115144973848128372447e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = 0.71624556912397054374724335454079
y2[1] (numeric) = 0.71624556912397556619716410417519
absolute error = 5.02244992074963440e-15
relative error = 7.0121898651219850123246186243333e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.95
y1[1] (closed_form) = 0.69065109656050767958019331164023
y1[1] (numeric) = 0.69065109656050824034443460540751
absolute error = 5.6076424129376728e-16
relative error = 8.1193564172476332027481170567404e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = 0.72318812408651201332600433544282
y2[1] (numeric) = 0.72318812408651709350717443770527
absolute error = 5.08018117010226245e-15
relative error = 7.0247021499685762594059235753857e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.96
y1[1] (closed_form) = 0.68338480358333622414406980875151
y1[1] (numeric) = 0.68338480358333673381868018193822
absolute error = 5.0967461037318671e-16
relative error = 7.4580910740288914700278990960843e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = 0.73005836083929959292321305873169
y2[1] (numeric) = 0.73005836083930473062849451373351
absolute error = 5.13770528145500182e-15
relative error = 7.0373898266825180979002852039402e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=3041.9MB, alloc=40.3MB, time=35.70
x[1] = 3.97
y1[1] (closed_form) = 0.67605017269529187311724748931934
y1[1] (numeric) = 0.67605017269529233112805881332343
absolute error = 4.5801081132400409e-16
relative error = 6.7748050340405416210408037252933e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = 0.73685559236438318199094255175134
y2[1] (numeric) = 0.73685559236438837700430194503536
absolute error = 5.19501335939328402e-15
relative error = 7.0502462262976120105797355432413e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.98
y1[1] (closed_form) = 0.66864793735335125890206371667484
y1[1] (numeric) = 0.66864793735335166467711271086624
absolute error = 4.0577504899419140e-16
relative error = 6.0685904543478310667324276254697e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = 0.7435791389442746128933574013766
y2[1] (numeric) = 0.74357913894427986498985773404338
absolute error = 5.25209650033266678e-15
relative error = 7.0632649912550464327570168850601e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 3.99
y1[1] (closed_form) = 0.66117883777488006667005095201013
y1[1] (numeric) = 0.66117883777488041963966825537065
absolute error = 3.5296961730336052e-16
relative error = 5.3384893335551758280149088914375e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = 0.75022832822991883329412529862008
y2[1] (numeric) = 0.75022832822992414223991902508507
absolute error = 5.30894579372646499e-15
relative error = 7.0764400569255206106211850325895e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4
y1[1] (closed_form) = 0.65364362086361191463916818309775
y1[1] (numeric) = 0.65364362086361221423606748942979
absolute error = 2.9959689930633204e-16
relative error = 4.5834899897056500517221330688597e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = 0.75680249530792825137263909451183
y2[1] (numeric) = 0.75680249530793361692496237153505
absolute error = 5.36555232327702322e-15
relative error = 7.0897656344194320944348829458289e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.01
y1[1] (closed_form) = 0.64604304013495860312968241468503
y1[1] (numeric) = 0.64604304013495884878904965925879
absolute error = 2.4565936724457376e-16
relative error = 3.8025232373566850523119697680090e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = 0.7633009827670735204905561792977
y2[1] (numeric) = 0.7633009827670789423977243297747
absolute error = 5.42190716815047700e-15
relative error = 7.1032361945811994322138288791653e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3084.1MB, alloc=40.3MB, time=36.20
TOP MAIN SOLVE Loop
x[1] = 4.02
y1[1] (closed_form) = 0.63837785564065920131155338076535
y1[1] (numeric) = 0.6383778556406593924711359662402
absolute error = 1.9115958258547485e-16
relative error = 2.9944582334177636531858869893931e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = 0.76972314076402411428559733354449
y2[1] (numeric) = 0.76972314076402959228700152839331
absolute error = 5.47800140419484882e-15
relative error = 7.1168464530732524322759912909578e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.03
y1[1] (closed_form) = 0.63064883389277550667185452185245
y1[1] (numeric) = 0.63064883389277564277205057127535
absolute error = 1.3610019604942290e-16
relative error = 2.1580979577703143110456102876015e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = 0.7760683270883321181898793012325
y2[1] (numeric) = 0.77606832708833765201598446255707
absolute error = 5.53382610516132457e-15
relative error = 7.1305913564637258177102676736484e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.04
y1[1] (closed_form) = 0.62285674778704147759294657917268
y1[1] (numeric) = 0.62285674778704155807689420382579
absolute error = 8.048394762465311e-17
relative error = 1.2921742906471820509659249583207e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = 0.78233590722665273904778223066649
y2[1] (numeric) = 0.78233590722665832842012615922198
absolute error = 5.58937234392855549e-15
relative error = 7.1444660692395430168756339626982e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.05
y1[1] (closed_form) = 0.61500237652557430403427072848237
y1[1] (numeric) = 0.6150023765255743283479372983222
absolute error = 2.431366656983983e-17
relative error = 3.9534264415690056609174569719666e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = 0.005
y2[1] (closed_form) = 0.78852525442619511083590710941938
y2[1] (numeric) = 0.78852525442620075546710083924917
absolute error = 5.64463119372982979e-15
relative error = 7.1584659616734692381196803166414e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.06
y1[1] (closed_form) = 0.60708650553895484514628584778934
y1[1] (numeric) = 0.60708650553895481273855725219213
absolute error = 3.240772859559721e-17
relative error = 5.3382389988765295104140653660619e-15 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 17
h = 0.005
y2[1] (closed_form) = 0.79463574975739705145742669274634
y2[1] (numeric) = 0.79463574975740275105115607570434
absolute error = 5.69959372938295800e-15
relative error = 7.1725865984799307827116733157580e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3126.2MB, alloc=40.3MB, time=36.69
TOP MAIN SOLVE Loop
x[1] = 4.07
y1[1] (closed_form) = 0.59910992640768522570785577303961
y1[1] (numeric) = 0.59910992640768513603062565954112
absolute error = 8.967723011349849e-17
relative error = 1.4968409996344225804318721463446e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = 0.80066678217581750318737928027569
y2[1] (numeric) = 0.80066678217582325743840780299096
absolute error = 5.75425102852271527e-15
relative error = 7.1868237282000115077336397283941e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.08
y1[1] (closed_form) = 0.59107343678303144556199101824792
y1[1] (numeric) = 0.59107343678303129807024999694112
absolute error = 1.4749174102130680e-16
relative error = 2.4953200709550309036392428130931e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = 0.80661774858324046757643767338011
y2[1] (numeric) = 0.80661774858324627617061050906344
absolute error = 5.80859417283568333e-15
relative error = 7.2011732732611130979035217268654e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.09
y1[1] (closed_form) = 0.58297784030725891772303711364428
y1[1] (numeric) = 0.58297784030725871187496191487515
absolute error = 2.0584807519876913e-16
relative error = 3.5309759816990083900223792039040e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = 0.81248805388798432447058271235272
y2[1] (numeric) = 0.81248805388799018708483200968713
absolute error = 5.86261424929733441e-15
relative error = 7.2156313206613598121346700172178e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.1
y1[1] (closed_form) = 0.57482394653326891153502867965979
y1[1] (numeric) = 0.57482394653326864679207125263982
absolute error = 2.6474295742701997e-16
relative error = 4.6056354997677105645695998089714e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = 0.81827711106441050426503702435845
y2[1] (numeric) = 0.81827711106441642056738843555739
absolute error = 5.91630235141119894e-15
relative error = 7.2301941132329906894249677563834e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.11
y1[1] (closed_form) = 0.56661257084364393716992399387447
y1[1] (numeric) = 0.56661257084364361299690053380854
absolute error = 3.2417302346006593e-16
relative error = 5.7212465826057553003642467908629e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = 0.82398434121162556257482398369604
y2[1] (numeric) = 0.82398434121163153222440443365424
absolute error = 5.96964958044995820e-15
relative error = 7.2448580414427572734721897348259e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3168.4MB, alloc=40.3MB, time=37.19
TOP MAIN SOLVE Loop
x[1] = 4.12
y1[1] (closed_form) = 0.5583445343691101668598082727593
y1[1] (numeric) = 0.5583445343691097827249881640689
absolute error = 3.8413482010869040e-16
relative error = 6.8798886075375588222287811838221e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = 0.82960917361137078716340306097222
y2[1] (numeric) = 0.82960917361137680981044975927513
absolute error = 6.02264704669830291e-15
relative error = 7.2596196356907730802306771303444e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.13
y1[1] (closed_form) = 0.55002066390642504655299469207052
y1[1] (numeric) = 0.55002066390642460192818935527568
absolute error = 4.4462480533679484e-16
relative error = 8.0837836560343996081010536580717e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = 0.83515104578509354821692987595635
y2[1] (numeric) = 0.83515104578509962350280057335445
absolute error = 6.07528587069739810e-15
relative error = 7.2744755590723762692657990331486e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.14
y1[1] (closed_form) = 0.54164179183569830916443077359731
y1[1] (numeric) = 0.54164179183569780352508240340516
absolute error = 5.0563934837019215e-16
relative error = 9.3353089808028117409713769448443e-14 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 16
h = 0.005
y2[1] (closed_form) = 0.84060940355019468487667282814088
y2[1] (numeric) = 0.84060940355020081243385731893503
absolute error = 6.12755718449079415e-15
relative error = 7.2894226005704013988364475335971e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.15
y1[1] (closed_form) = 0.53320875603715465725018617166272
y1[1] (numeric) = 0.53320875603715409007545635379706
absolute error = 5.6717472981786566e-16
relative error = 1.0637010802919826975705151810187e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.84598370107544630333780572921222
y2[1] (numeric) = 0.84598370107545248278993860083617
absolute error = 6.17945213287162395e-15
relative error = 7.3044576686478379575932680621457e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=3210.5MB, alloc=40.3MB, time=37.67
x[1] = 4.16
y1[1] (closed_form) = 0.52472239980734643876839021070922
y1[1] (numeric) = 0.52472239980734580954124840500332
absolute error = 6.2922714180570590e-16
relative error = 1.1991619607562564934014113282365e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.85127340093557444478094790264673
y2[1] (numeric) = 0.85127340093558067574282253357174
absolute error = 6.23096187463092501e-15
relative error = 7.3195777852132054021283820389831e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.17
y1[1] (closed_form) = 0.51618357177482469458922054275779
y1[1] (numeric) = 0.51618357177482400279653242002231
absolute error = 6.9179268812273548e-16
relative error = 1.3402067131739654355999624320680e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.85647797416500116491514400141294
y2[1] (numeric) = 0.85647797416500744699272780833865
absolute error = 6.28207758380692571e-15
relative error = 7.3347800799331220774798837071177e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.18
y1[1] (closed_form) = 0.50759312581527701057891803304672
y1[1] (numeric) = 0.50759312581527625571153365321564
absolute error = 7.5486738437983108e-16
relative error = 1.4871505266494526385722239184306e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.86159690031074065096911416280091
y2[1] (numeric) = 0.86159690031074698375956509793504
absolute error = 6.33279045093513413e-15
relative error = 7.3500617848685053837899735936083e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.19
y1[1] (closed_form) = 0.49895192096614066040190125149245
y1[1] (numeric) = 0.49895192096613984195474307054292
absolute error = 8.1844715818094953e-16
relative error = 1.6403327130120220789444454497550e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.86662966748444408656315532592254
y2[1] (numeric) = 0.86662966748445046965483962499021
absolute error = 6.38309168429906767e-15
relative error = 7.3654202294126325989350319043530e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.2
y1[1] (closed_form) = 0.49026082134069957765554488137713
y1[1] (numeric) = 0.49026082134069869512769557451336
absolute error = 8.8252784930686377e-16
relative error = 1.8001190608979214478621005007723e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.87157577241358806001857709790882
y2[1] (numeric) = 0.87157577241359449299108827937027
absolute error = 6.43297251118146145e-15
relative error = 7.3808528355109311648906413669143e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=3252.6MB, alloc=40.3MB, time=38.17
x[1] = 4.21
y1[1] (closed_form) = 0.48152069604167374756882294948685
y1[1] (numeric) = 0.48152069604167280046361303807413
absolute error = 9.4710520991141272e-16
relative error = 1.9669044709751051688640070859082e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.8764347204918013973064980899522
y2[1] (numeric) = 0.87643472049180787973067720574546
absolute error = 6.48242417911579326e-15
relative error = 7.3963571131438682584117493665086e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.22
y1[1] (closed_form) = 0.47273241907430965925363841315521
y1[1] (numeric) = 0.47273241907430864707873368288811
absolute error = 1.01217490473026710e-15
relative error = 2.1411159122792496829712577865549e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.88120602582832538699464673122123
y2[1] (numeric) = 0.88120602582833191843260386918349
absolute error = 6.53143795713796226e-15
relative error = 7.4119306560556845159396059358036e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.23
y1[1] (closed_form) = 0.46389686925898050939118958954484
y1[1] (numeric) = 0.46389686925897943165867828733257
absolute error = 1.07773251130221227e-15
relative error = 2.3232157462579137877485713915608e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.88588921129660245121088859729926
y2[1] (numeric) = 0.88588921129660903121602563525809
absolute error = 6.58000513703795883e-15
relative error = 7.4275711377129786763043465166714e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.24
y1[1] (closed_form) = 0.45501493014330489726017186970594
y1[1] (numeric) = 0.45501493014330375348665166675892
absolute error = 1.14377352020294702e-15
relative error = 2.5137054730110080463685570916226e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.89048380858198840379687432458221
y2[1] (numeric) = 0.89048380858199503191390893594466
absolute error = 6.62811703461136245e-15
relative error = 7.4432763074783072897734342667362e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.25
y1[1] (closed_form) = 0.44608748991379279916407772054484
y1[1] (numeric) = 0.44608748991379158887074242914913
absolute error = 1.21029333529139571e-15
relative error = 2.7131299636429774116053527212437e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.89498935822858352446575282843828
y2[1] (numeric) = 0.89498935822859020023074373894272
absolute error = 6.67576499091050444e-15
relative error = 7.4590439869850272301337034513837e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=3294.8MB, alloc=40.3MB, time=38.66
x[1] = 4.26
y1[1] (closed_form) = 0.43711544130702765758652413548598
y1[1] (numeric) = 0.43711544130702638029925016695618
absolute error = 1.27728727396852980e-15
relative error = 2.9220822539448331460250728230533e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.89940540968517776589555981885312
y2[1] (numeric) = 0.89940540968518448883593331398515
absolute error = 6.72294037349513203e-15
relative error = 7.4748720667005860612774749771814e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.27
y1[1] (closed_form) = 0.42809968152039346679167732209429
y1[1] (numeric) = 0.42809968152039212204110987340152
absolute error = 1.34475056744869277e-15
relative error = 3.1412089882263381894454594493584e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.90373152135030549927585981966133
y2[1] (numeric) = 0.90373152135031226891043750207179
absolute error = 6.76963457768241046e-15
relative error = 7.4907585026663649621318972471163e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.28
y1[1] (closed_form) = 0.41904111212235578208682073683604
y1[1] (numeric) = 0.41904111212235436940845969341495
absolute error = 1.41267836104342109e-15
relative error = 3.3712166185520556848201949409672e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.90796726061640529287063252329942
y2[1] (numeric) = 0.90796726061641210870966031939865
absolute error = 6.81583902779609923e-15
relative error = 7.5067013134030061925574917184301e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.29
y1[1] (closed_form) = 0.40994063896230562457137463377925
y1[1] (numeric) = 0.40994063896230414350566017602716
absolute error = 1.48106571445775209e-15
relative error = 3.6128784845699020534906785986578e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.91211220391308030765634688524802
y2[1] (numeric) = 0.91211220391308716920152529998678
absolute error = 6.86154517841473876e-15
relative error = 7.5226985769709199131649261970902e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.3
y1[1] (closed_form) = 0.40079917207997529690676239633603
y1[1] (numeric) = 0.40079917207997374699916029732787
absolute error = 1.54990760209900816e-15
relative error = 3.8670429234063893077338482596977e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.91616593674945498403170936028464
y2[1] (numeric) = 0.91616593674946189077622497896834
absolute error = 6.90674451561868370e-15
relative error = 7.5387484281763681695561380862155e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3337.0MB, alloc=40.3MB, time=39.16
TOP MAIN SOLVE Loop
x[1] = 4.31
y1[1] (closed_form) = 0.39161762561443516845006009684425
y1[1] (numeric) = 0.39161762561443354925114669879949
absolute error = 1.61919891339804476e-15
relative error = 4.1346425888200893523562322637273e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.92012805375562378396571242699099
y2[1] (numeric) = 0.92012805375563073539427066280976
absolute error = 6.95142855823581877e-15
relative error = 7.5548490559141719148088437611002e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.32
y1[1] (closed_form) = 0.38239691771268052999708015943008
y1[1] (numeric) = 0.38239691771267884106262701648179
absolute error = 1.68893445314294829e-15
relative error = 4.4167051953382994731242649563773e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.92399815872318784374430909898398
y2[1] (numeric) = 0.92399815872319483933316818477711
absolute error = 6.99558885908579313e-15
relative error = 7.5709987006386855856634110602498e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.33
y1[1] (closed_form) = 0.37313797043781765937323745066286
y1[1] (numeric) = 0.37313797043781590026429562549457
absolute error = 1.75910894182516829e-15
relative error = 4.7143659482339350913961541515498e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.92777586464487548368421918677298
y2[1] (numeric) = 0.92777586464488252290122540938249
absolute error = 7.03921700622260951e-15
relative error = 7.5871956519552367274544253310465e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.34
y1[1] (closed_form) = 0.36384170967685827918912735442367
y1[1] (numeric) = 0.36384170967685644947211135635711
absolute error = 1.82971701599806656e-15
relative error = 5.0288819762393600655536957971275e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.93146079375324261279591291098884
y2[1] (numeric) = 0.9314607937532496951005370863925
absolute error = 7.08230462417540366e-15
relative error = 7.6034382463247381890672666649691e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.35
y1[1] (closed_form) = 0.35450906504813162723820257743587
y1[1] (numeric) = 0.3545090650481297264849739295715
absolute error = 1.90075322864786437e-15
relative error = 5.3616491538511137128321780247994e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.93505257755844915838755579834142
y2[1] (numeric) = 0.9350525775584562832309309855918
absolute error = 7.12484337518725038e-15
relative error = 7.6197248648746533983040586615343e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3379.1MB, alloc=40.3MB, time=39.66
TOP MAIN SOLVE Loop
x[1] = 4.36
y1[1] (closed_form) = 0.34514096980832339825235256696343
y1[1] (numeric) = 0.34514096980832142604030298999628
absolute error = 1.97221204957696715e-15
relative error = 5.7142217879037941045879468337218e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.93855085688510774299843471888496
y2[1] (numeric) = 0.93855085688511490982339517071699
absolute error = 7.16682496045183203e-15
relative error = 7.6360539313099316692157403112404e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.37
y1[1] (closed_form) = 0.33573836075915085304374269242283
y1[1] (numeric) = 0.33573836075914880895587689277834
absolute error = 2.04408786579964449e-15
relative error = 6.0883357540010596606636703576234e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.94195528190820092382487885040826
y2[1] (numeric) = 0.94195528190820813206600019821378
absolute error = 7.20824112134780552e-15
relative error = 7.6524239099179348998341037296727e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.38
y1[1] (closed_form) = 0.32630217815368342744422852384408
y1[1] (numeric) = 0.32630217815368131106924657380242
absolute error = 2.11637498195004166e-15
relative error = 6.4859358093321118274564038701642e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.94526551218806340294466391093816
y2[1] (numeric) = 0.94526551218807065202830458164214
absolute error = 7.24908364067070398e-15
relative error = 7.6688333036617515908038353118130e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.39
y1[1] (closed_form) = 0.31683336560231820890338536675574
y1[1] (numeric) = 0.31683336560231601983576466425862
absolute error = 2.18906762070249712e-15
relative error = 6.9092079886881715860713685461385e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.94848121670442571014802896361413
y2[1] (numeric) = 0.94848121670443299949237282582335
absolute error = 7.28934434386220922e-15
relative error = 7.6852806523566408075041583068176e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.4
y1[1] (closed_form) = 0.30733286997841968311913974221771
y1[1] (numeric) = 0.30733286997841742095921653807887
absolute error = 2.26215992320413884e-15
relative error = 7.3606182227204767055516786475818e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.95160207388951595403539233338039
y2[1] (numeric) = 0.95160207388952328305049257001182
absolute error = 7.32901510023663143e-15
relative error = 7.7017645309246704483782643526035e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3421.2MB, alloc=40.3MB, time=40.14
TOP MAIN SOLVE Loop
x[1] = 4.41
y1[1] (closed_form) = 0.29780164132363318664770646649064
y1[1] (numeric) = 0.2978016413236308510017569467597
absolute error = 2.33564594951973094e-15
relative error = 7.8429586188260435053923458626715e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.95462777166021633123424156453615
y2[1] (numeric) = 0.95462777166022369932206576896857
absolute error = 7.36808782420443242e-15
relative error = 7.7182835477229119628207137559989e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.42
y1[1] (closed_form) = 0.28824063275288153406866514349322
y1[1] (numeric) = 0.28824063275287912454898605475335
absolute error = 2.40951967908873987e-15
relative error = 8.3594032391488079148087526393351e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.95755800744927117811107273183889
y2[1] (numeric) = 0.95755800744927858466554922446793
absolute error = 7.40655447649262904e-15
relative error = 7.7348363429408303237243274111383e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.43
y1[1] (closed_form) = 0.27865080035905431996329034893364
y1[1] (numeric) = 0.27865080035905183618827915434505
absolute error = 2.48377501119458859e-15
relative error = 8.9135757298889173038923461792053e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.96039248823554344419921453430048
y2[1] (numeric) = 0.96039248823555088860627989621426
absolute error = 7.44440706536191378e-15
relative error = 7.7514215870627647411826639642215e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.44
y1[1] (closed_form) = 0.26903310311739942669651235616339
y1[1] (numeric) = 0.26903310311739686829074691009873
absolute error = 2.55840576544606466e-15
relative error = 9.5096318475337933897474209932779e-13 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 15
h = 0.005
y2[1] (closed_form) = 0.96313093057331656172040803307784
y2[1] (numeric) = 0.96313093057332404335805585340694
absolute error = 7.48163764782032910e-15
relative error = 7.7680379793916329468742564057373e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=3463.2MB, alloc=40.3MB, time=40.64
x[1] = 4.45
y1[1] (closed_form) = 0.25938850278962629877205672974446
y1[1] (numeric) = 0.25938850278962366536637445889721
absolute error = 2.63340568227084725e-15
relative error = 1.0152360856204320588262133070411e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = 0.96577306062063878103760801869169
y2[1] (numeric) = 0.96577306062064629927593885202471
absolute error = 7.51823833083333302e-15
relative error = 7.7846842466302136015357006561325e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.46
y1[1] (closed_form) = 0.24971796382773057335341360111266
y1[1] (numeric) = 0.2497179638277278645849901799966
absolute error = 2.70876842342111606e-15
relative error = 1.0847311030013748277227107955813e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = 0.96831861416670713762908092824644
y2[1] (numeric) = 0.96831861416671469183035345833972
absolute error = 7.55420127253009328e-15
relative error = 7.8013591415165659801116961664179e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.47
y1[1] (closed_form) = 0.24002245327754968440743865533016
y1[1] (numeric) = 0.24002245327754689991986616412646
absolute error = 2.78448757249120370e-15
relative error = 1.1600946221774363489730927651868e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = 0.97076733665828831220992179927159
y2[1] (numeric) = 0.97076733665829590172860520511928
absolute error = 7.58951868340584769e-15
relative error = 7.8180614415103365395008431806593e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.48
y1[1] (closed_form) = 0.23030294068205908482980140684885
y1[1] (numeric) = 0.23030294068205622427316595959765
absolute error = 2.86055663544725120e-15
relative error = 1.2420842855829380592962624517346e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = 0.97311898322517374193699541853268
y2[1] (numeric) = 0.97311898322518136611982293870137
absolute error = 7.62418282752016869e-15
relative error = 7.8347899475268788587849556967434e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.49
y1[1] (closed_form) = 0.2205603979844187568494820065161
y1[1] (numeric) = 0.22056039798441581988044083769092
absolute error = 2.93696904116882518e-15
relative error = 1.3315940069061283068566865815730e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = 0.97537331870466643720739369365918
y2[1] (numeric) = 0.97537331870467409539341738462945
absolute error = 7.65818602369097027e-15
relative error = 7.8515434827162773561285681486593e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=3505.4MB, alloc=40.3MB, time=41.12
x[1] = 4.5
y1[1] (closed_form) = 0.21079579943077970598048182479383
y1[1] (numeric) = 0.2107957994307766922623398223409
absolute error = 3.01371814200245293e-15
relative error = 1.4296860516862841085850415373690e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = 0.97753011766509705538913501449863
y2[1] (numeric) = 0.97753011766510474690978169859462
absolute error = 7.69152064668409599e-15
relative error = 7.8683208912845177683153192313239e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.51
y1[1] (closed_form) = 0.20101012147286015779035832174077
y1[1] (numeric) = 0.20101012147285706699314399470997
absolute error = 3.09079721432703080e-15
relative error = 1.5376326284864923426929025864847e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = 0.97958916442836687989632919704766
y2[1] (numeric) = 0.97958916442837460407545759537445
absolute error = 7.72417912839832679e-15
relative error = 7.8851210373541883050307809756054e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.52
y1[1] (closed_form) = 0.19120434267030119978472111819888
y1[1] (numeric) = 0.19120434267029803158526198713996
absolute error = 3.16819945913105892e-15
relative error = 1.6569704510289657055353575532077e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = 0.98155025309151545032968624674211
y2[1] (numeric) = 0.98155025309152320648364529239001
absolute error = 7.75615395904564790e-15
relative error = 7.9019428038622267522609713145157e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.53
y1[1] (closed_form) = 0.1813794435928116327621307913814
y1[1] (numeric) = 0.18137944359280838684412818972705
absolute error = 3.24591800260165435e-15
relative error = 1.7895732494849793701559517041110e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = 0.98341318754731068693732785543696
y2[1] (numeric) = 0.98341318754731847437501618205158
absolute error = 7.78743768832661462e-15
relative error = 7.9187850914923504191999929739000e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.54
y1[1] (closed_form) = 0.1715364067221118170727192195978
y1[1] (numeric) = 0.17153640672210849312682249430517
absolute error = 3.32394589672529263e-15
relative error = 1.9377495193251130408337596599278e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = 0.98517778150385945040061393078254
y2[1] (numeric) = 0.9851777815038672684235405314393
absolute error = 7.81802292660065676e-15
relative error = 7.9356468176399180442850141087833e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3547.5MB, alloc=40.3MB, time=41.63
TOP MAIN SOLVE Loop
x[1] = 4.55
y1[1] (closed_form) = 0.16167621635368631931419242500794
y1[1] (numeric) = 0.16167621635368291703807252478154
absolute error = 3.40227611990022640e-15
relative error = 2.1043763867267496001200099526309e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = 0.98684385850323657590534765402509
y2[1] (numeric) = 0.98684385850324442380769370518747
absolute error = 7.84790234605116238e-15
relative error = 7.9525269154070774642197003162695e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.56
y1[1] (closed_form) = 0.1517998584983551841186737926099
y1[1] (numeric) = 0.15179985849835170321709623208174
absolute error = 3.48090157756052816e-15
relative error = 2.2930861807082944057373983660549e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = 0.98841125193913051861047608903809
y2[1] (numeric) = 0.98841125193913839567915793421972
absolute error = 7.87706868184518163e-15
relative error = 7.9694243326261489747791806697108e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.57
y1[1] (closed_form) = 0.14190832078367367382118531437459
y1[1] (numeric) = 0.14190832078367011400608250267219
absolute error = 3.55981510281170240e-15
relative error = 2.5085316232008105440864880559636e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = 0.98987980507350384596444412806507
y2[1] (numeric) = 0.98987980507351175147917741565706
absolute error = 7.90551473328759199e-15
relative error = 7.9863380309092834049241584486009e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.58
y1[1] (closed_form) = 0.1320025923551703359536334006823
y1[1] (numeric) = 0.13200259235516669694417632287118
absolute error = 3.63900945707781112e-15
relative error = 2.7567712058916067091786725781514e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = 0.99124937105226691083385383609731
y2[1] (numeric) = 0.99124937105227484406721880566412
absolute error = 7.93323336496956681e-15
relative error = 8.0032669847225161751249998983146e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.59
y1[1] (closed_form) = 0.1220836637774332746752485243965
y1[1] (numeric) = 0.12208366377742955619791776434166
absolute error = 3.71847733076005484e-15
relative error = 3.0458434942934617065276983345118e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = 0.99251981291996313809017767868781
y2[1] (numeric) = 0.99251981291997109830768558987722
absolute error = 7.96021750791118941e-15
relative error = 8.0202101804824140721743175235306e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3589.7MB, alloc=40.3MB, time=42.13
TOP MAIN SOLVE Loop
x[1] = 4.6
y1[1] (closed_form) = 0.11215252693505451742990782122919
y1[1] (numeric) = 0.11215252693505071921856391447934
absolute error = 3.79821134390674985e-15
relative error = 3.3866480298800799699824307118221e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = 0.99369100363346445613810465990883
y2[1] (numeric) = 0.99369100363347244259826535796441
absolute error = 7.98646016069805558e-15
relative error = 8.0371666156735809762695454244817e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.61
y1[1] (closed_form) = 0.10221017493344238231112882817269
y1[1] (numeric) = 0.10221017493343850410708193353198
absolute error = 3.87820404689464071e-15
relative error = 3.7943424413665906020915786298978e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = 0.99476282607467550385377935740314
y2[1] (numeric) = 0.99476282607468351580816996911101
absolute error = 8.01195439061170787e-15
relative error = 8.0541352979853523984785841442968e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.62
y1[1] (closed_form) = 0.09225760199951176481534177561582
y1[1] (numeric) = 0.092257601999507806367420654130139
absolute error = 3.958447921121485681e-15
relative error = 4.2906468793134620263750714258321e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = 0.99573517306224534252282683445147
y2[1] (numeric) = 0.99573517306225337921616158819702
absolute error = 8.03669333475374555e-15
relative error = 8.0711152444660666989083054487766e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.63
y1[1] (closed_form) = 0.082295803382262274872007287402623
y1[1] (numeric) = 0.082295803382258235936627577551669
absolute error = 4.038935379709850954e-15
relative error = 4.9078266615237731028450329901855e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = 0.9966079473622855016167293539807
y2[1] (numeric) = 0.99660794736229356228693051743554
absolute error = 8.06067020116345484e-15
relative error = 8.0881054806933538217089798254399e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.64
y1[1] (closed_form) = 0.072325775253254166254025200760118
y1[1] (numeric) = 0.072325775253250046595256978712032
absolute error = 4.119658768222048086e-15
relative error = 5.6959759557318973343616986518154e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = 0.99738106169809328661190893188283
y2[1] (numeric) = 0.9973810616981013704901788606872
absolute error = 8.08387826992880437e-15
relative error = 8.1051050399589299543761069223936e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3631.9MB, alloc=40.3MB, time=42.61
TOP MAIN SOLVE Loop
x[1] = 4.65
y1[1] (closed_form) = 0.062348514606992010692557016177074
y1[1] (numeric) = 0.062348514606987810082191630029435
absolute error = 4.200610365386147639e-15
relative error = 6.7373062403560043534445278846874e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = 0.99805443875887937652883655089603
y2[1] (numeric) = 0.99805443875888748283973084154777
absolute error = 8.10631089429065174e-15
relative error = 8.1221129624664298311017520907683e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.66
y1[1] (closed_form) = 0.052365019161226078245837166795957
y1[1] (numeric) = 0.052365019161221796463453333795709
absolute error = 4.281782383833000248e-15
relative error = 8.1767990395455940357767436709940e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = 0.99862801120749883843868709783252
y2[1] (numeric) = 0.99862801120750696640018883784
absolute error = 8.12796150174000748e-15
relative error = 8.1391282945408466145852201751616e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.67
y1[1] (closed_form) = 0.042376287257181393700854320105276
y1[1] (numeric) = 0.042376287257177030533883475910276
absolute error = 4.363166970844195000e-15
relative error = 1.0296246446424541371948603654938e-11 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 0.005
y2[1] (closed_form) = 0.99910172168718478584253184927338
y2[1] (numeric) = 0.9991017216871929346661269574767
absolute error = 8.14882359510820332e-15
relative error = 8.1561500878481832467812342667900e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.68
y1[1] (closed_form) = 0.032383317759724446019120367944567
y1[1] (numeric) = 0.032383317759720001262911257061192
absolute error = 4.444756209110883375e-15
relative error = 1.3725450375683508717495456283142e-11 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 0.005
y2[1] (closed_form) = 0.99947552282728400756284194975967
y2[1] (numeric) = 0.99947552282729217645359559957237
absolute error = 8.16889075364981270e-15
relative error = 8.1731773986239492387931996645671e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=3674.0MB, alloc=40.3MB, time=43.11
x[1] = 4.69
y1[1] (closed_form) = 0.022387109957477534072388396442007
y1[1] (numeric) = 0.022387109957473007530270893046502
absolute error = 4.526542117503395505e-15
relative error = 2.0219412537398477570255814187328e-11 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 13
h = 0.005
y2[1] (closed_form) = 0.99974937724799399358919340694292
y2[1] (numeric) = 0.99974937724800218174582752511456
absolute error = 8.18815663411817164e-15
relative error = 8.1902092869091619655073783382418e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.7
y1[1] (closed_form) = 0.012388663462890737150508296327111
y1[1] (numeric) = 0.012388663462886128633856444753077
absolute error = 4.608516651851574034e-15
relative error = 3.7199465992889561072577893566061e-11 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 13
h = 0.005
y2[1] (closed_form) = 0.99992325756410088417953654157497
y2[1] (numeric) = 0.99992325756410909079450837492429
absolute error = 8.20661497183334932e-15
relative error = 8.2072448157925336291418154994618e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.71
y1[1] (closed_form) = 0.0023889781122815029610961477246958
y1[1] (numeric) = 0.0023889781122768122893904119754212
absolute error = 4.6906717057357492746e-15
relative error = 1.9634636590521547819740515948700e-10 %
Desired digits = 8
Estimated correct digits = 9
Correct digits = 12
h = 0.005
y2[1] (closed_form) = 0.99999714638771796842523471259357
y2[1] (numeric) = 0.99999714638772619268481645501154
absolute error = 8.22425958174241797e-15
relative error = 8.2242830506575422304704917859768e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.72
y1[1] (closed_form) = -0.0076109461341481509210826531746326
y1[1] (numeric) = -0.0076109461341529239201939414525969
absolute error = 4.7729991112882779643e-15
relative error = 6.2712296568138727012336221842126e-11 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 13
h = 0.005
y2[1] (closed_form) = 0.99997103633002445843229788796164
y2[1] (numeric) = 0.99997103633003269951665735983452
absolute error = 8.24108435947187288e-15
relative error = 8.2413230584330991571589955223745e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.73
y1[1] (closed_form) = -0.017610109292306823958480184942845
y1[1] (numeric) = -0.017610109292311679449120190509171
absolute error = 4.855490640005566326e-15
relative error = 2.7572177772495384230913698639738e-11 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 13
h = 0.005
y2[1] (closed_form) = 0.99984493000200436524284191155768
y2[1] (numeric) = 0.99984493000201262232612428361145
absolute error = 8.25708328237205377e-15
relative error = 8.2583639068465356847110048015393e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=3716.2MB, alloc=40.3MB, time=43.59
x[1] = 4.74
y1[1] (closed_form) = -0.027607511454211308473521317218995
y1[1] (numeric) = -0.027607511454216246611524887715737
absolute error = 4.938138003570496742e-15
relative error = 1.7886936357015339300144156263543e-11 %
Desired digits = 8
Estimated correct digits = 10
Correct digits = 13
h = 0.005
y2[1] (closed_form) = 0.99961884001418540260979704807277
y2[1] (numeric) = 0.99961884001419367486020760149246
absolute error = 8.27225041055341969e-15
relative error = 8.2754046636776371112480638956830e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.75
y1[1] (closed_form) = -0.037602152887976554715496312373334
y1[1] (numeric) = -0.037602152887981575648350997549156
absolute error = 5.020932854685175822e-15
relative error = 1.3352780277351194039230983930977e-11 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 0.005
y2[1] (closed_form) = 0.99929278897537794473427075559708
y2[1] (numeric) = 0.99929278897538623131415867012757
absolute error = 8.28657988791453049e-15
relative error = 8.2924443960124558791413488854335e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.76
y1[1] (closed_form) = -0.047593034137788026258408716410526
y1[1] (numeric) = -0.047593034137793130125196630330737
absolute error = 5.103866787913920211e-15
relative error = 1.0723978582953046837010913933494e-11 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 13
h = 0.005
y2[1] (closed_form) = 0.99886680949041416406874008456944
y2[1] (numeric) = 0.99886680949042246413468324615802
absolute error = 8.30006594316158858e-15
relative error = 8.3094821694956337547128347554022e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.77
y1[1] (closed_form) = -0.057579156123846448577548772787261
y1[1] (numeric) = -0.057579156123851635508889309182265
absolute error = 5.186931340536395004e-15
relative error = 9.0083490098046499324966836353911e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = 0.99834094415688757527040933829949
y2[1] (numeric) = 0.99834094415689588797330015769518
absolute error = 8.31270289081939569e-15
relative error = 8.3265170475799584354795857569088e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.78
y1[1] (closed_form) = -0.067559520242274956413221714659554
y1[1] (numeric) = -0.067559520242280226531215125477755
absolute error = 5.270117993410818201e-15
relative error = 7.8007036972904288225627399431939e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = 0.99771524556089331134762062164767
y2[1] (numeric) = 0.99771524556090163583275285522782
absolute error = 8.32448513223358015e-15
relative error = 8.3435480907718713198361995317510e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3758.4MB, alloc=40.3MB, time=44.09
TOP MAIN SOLVE Loop
x[1] = 4.79
y1[1] (closed_form) = -0.077533128464978649290150241347593
y1[1] (numeric) = -0.077533128464984002708322088490769
absolute error = 5.353418171847143176e-15
relative error = 6.9046848461238824786631627180644e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = 0.99698977627176955796815287876274
y2[1] (numeric) = 0.99698977627177789337530944271372
absolute error = 8.33540715656395098e-15
relative error = 8.3605743558716307066170881608399e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.8
y1[1] (closed_form) = -0.087498983439446569320215257649488
y1[1] (numeric) = -0.087498983439452006143461747779224
absolute error = 5.436823246490129736e-15
relative error = 6.2135844701014935800171644562489e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = 0.99616460883584067178159646650363
y2[1] (numeric) = 0.99616460883584901724513823534005
absolute error = 8.34546354176883642e-15
relative error = 8.3775948952068189466095338331854e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.81
y1[1] (closed_form) = -0.097456088588486121173922639538394
y1[1] (numeric) = -0.097456088588491641498456851751281
absolute error = 5.520324534212212887e-15
relative error = 5.6644224226175311748940211214710e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = 0.99523982576916260843875697540403
y2[1] (numeric) = 0.99523982576917096308771255566873
absolute error = 8.35464895558026470e-15
relative error = 8.3946087558578612270881935757046e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.82
y1[1] (closed_form) = -0.10740344820987996086171061916977
y1[1] (numeric) = -0.10740344820988556477500963524679
absolute error = 5.60391329901607702e-15
relative error = 5.2176288493692675797842719978369e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = 0.99421551954927138575924090129834
y2[1] (numeric) = 0.99421551954927974871739737114497
absolute error = 8.36295815646984663e-15
relative error = 8.4116149788742004278456450570599e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.83
y1[1] (closed_form) = -0.11734006757595538771926678895382
y1[1] (numeric) = -0.1173400675759610753000197357957
absolute error = 5.68758075294684188e-15
relative error = 4.8470917653641323638313230094912e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = 0.9930917926059354071940301512694
y2[1] (numeric) = 0.9930917926059437775800247564893
absolute error = 8.37038599460521990e-15
relative error = 8.4286125984797436459523612447297e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3800.5MB, alloc=40.3MB, time=44.59
TOP MAIN SOLVE Loop
x[1] = 4.84
y1[1] (closed_form) = -0.12726495303305628274063040973268
y1[1] (numeric) = -0.12726495303306205405868742349781
absolute error = 5.77131805701376513e-15
relative error = 4.5348840505325146635588032840131e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = 0.99186875731091257034299275504052
y2[1] (numeric) = 0.99186875731092094727040555195688
absolute error = 8.37692741279691636e-15
relative error = 8.4456006412661639633977391992586e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.85
y1[1] (closed_form) = -0.13717711210090764614813971846528
y1[1] (numeric) = -0.13717711210091350126446183983051
absolute error = 5.85511632212136523e-15
relative error = 4.2682895363873345927010003810800e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = 0.99054653596671318480794231629118
y2[1] (numeric) = 0.99054653596672156738538975180554
absolute error = 8.38257744743551436e-15
relative error = 8.4625781253726040329190831973956e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.86
y1[1] (closed_form) = -0.1470755535718627978282707459854
y1[1] (numeric) = -0.147075553571868736794880755852
absolute error = 5.93896661000986660e-15
relative error = 4.0380379102962339559000120103866e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = 0.98912526079436982308009669404291
y2[1] (numeric) = 0.98912526079437821041132611298214
absolute error = 8.38733122941893923e-15
relative error = 8.4795440596502866740413816614827e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.87
y1[1] (closed_form) = -0.15695928761002331599602978562804
y1[1] (numeric) = -0.15695928761002933885596399049601
absolute error = 6.02285993420486797e-15
relative error = 3.8372115635291989752578828342101e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = 0.98760507392021532746665541129251
y2[1] (numeric) = 0.98760507392022371865064048106872
absolute error = 8.39118398506977621e-15
relative error = 8.4964974428104917534628166327128e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.88
y1[1] (closed_form) = -0.16682732585022180217663274703162
y1[1] (numeric) = -0.16682732585022790896389372316508
absolute error = 6.10678726097613346e-15
relative error = 3.6605437567577088236776512909736e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = 0.98598612736167029524478484231842
y2[1] (numeric) = 0.98598612736167868937582188477935
absolute error = 8.39413103704246093e-15
relative error = 8.5134372625543072795222308790075e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3842.7MB, alloc=40.3MB, time=45.08
TOP MAIN SOLVE Loop
x[1] = 4.89
y1[1] (closed_form) = -0.17667868149685757431045858971384
y1[1] (numeric) = -0.17667868149686376504996889511806
absolute error = 6.19073951030540422e-15
relative error = 3.5039538770927002683022870907534e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = 0.9842685830120414632826520572489
y2[1] (numeric) = 0.98426858301204985945045727746271
absolute error = 8.39616780522021381e-15
relative error = 8.5303624946825065564777539916176e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.9
y1[1] (closed_form) = -0.18651236942257540449432914412192
y1[1] (numeric) = -0.18651236942258167920188600724965
absolute error = 6.27470755686312773e-15
relative error = 3.3642313248654911465012395057826e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = 0.98245261262433251227637724991833
y2[1] (numeric) = 0.98245261262434090956618485150412
absolute error = 8.39728980760158579e-15
relative error = 8.5472721021838414383835645307023e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.91
y1[1] (closed_form) = -0.1963274062667774335675731995194
y1[1] (numeric) = -0.19632740626678379224980419351936
absolute error = 6.35868223099399996e-15
relative error = 3.2388153808508891565419940743678e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = 0.98053839779406890950899010226969
y2[1] (numeric) = 0.98053839779407730700165127875344
absolute error = 8.39749266117648375e-15
relative error = 8.5641650342999740379961854775354e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.92
y1[1] (closed_form) = -0.20612281053395841143350924081177
y1[1] (numeric) = -0.20612281053396485408782895202649
absolute error = 6.44265431971121472e-15
relative error = 3.1256386923027121604975821319256e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = 0.97852612994113850763280160634113
y2[1] (numeric) = 0.97852612994114690440488439788655
absolute error = 8.39677208279154542e-15
relative error = 8.5810402255651959480527394434775e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=3884.8MB, alloc=40.3MB, time=45.58
x[1] = 4.93
y1[1] (closed_form) = -0.21589760269185442967426044648577
y1[1] (numeric) = -0.21589760269186095628882814579863
absolute error = 6.52661456769931286e-15
relative error = 3.0230139132274647458412165239471e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = 0.97641601029064971540018032274914
y2[1] (numeric) = 0.97641601029065811052407032748358
absolute error = 8.39512389000473444e-15
relative error = 8.5978965948190036761847822125065e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.94
y1[1] (closed_form) = -0.22565080526939533166743080403972
y1[1] (numeric) = -0.22565080526940194222110912956284
absolute error = 6.61055367832552312e-15
relative error = 2.9295502271456339671454072084408e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = 0.97420824985280915450970852682316
y2[1] (numeric) = 0.97420824985281754705371045585056
absolute error = 8.39254400192902740e-15
relative error = 8.6147330441895120888654009856298e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.95
y1[1] (closed_form) = -0.23538144295445100504525741163474
y1[1] (numeric) = -0.23538144295445769950757207111939
absolute error = 6.69446231465948465e-15
relative error = 2.8440909489857021111310750428466e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = 0.97190306940182081478526506337735
y2[1] (numeric) = 0.97190306940182920381370512844349
absolute error = 8.38902844006506614e-15
relative error = 8.6315484580455937481247126549236e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.96
y1[1] (closed_form) = -0.24508854269136178194844802293532
y1[1] (numeric) = -0.24508854269136856027954852417574
absolute error = 6.77833110050124042e-15
relative error = 2.7656662470090017394333348733971e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = 0.96950069945380881775493302309673
y2[1] (numeric) = 0.96950069945381720232826214574614
absolute error = 8.38457332912264941e-15
relative error = 8.6483417019155297037212637279649e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.97
y1[1] (closed_form) = -0.25477113377824319411595351401254
y1[1] (numeric) = -0.25477113377825005626657493140172
absolute error = 6.86215062141738918e-15
relative error = 2.6934568762371301909766885133707e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = 0.96700138024376599633497671407791
y2[1] (numeric) = 0.96700138024377437550987454501741
absolute error = 8.37917489783093950e-15
relative error = 8.6651116213698474062808407208221e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=3927.0MB, alloc=40.3MB, time=46.06
x[1] = 4.98
y1[1] (closed_form) = -0.26442824796405535241625332068078
y1[1] (numeric) = -0.26442824796406229832767910596339
absolute error = 6.94591142578528261e-15
relative error = 2.6267660430626399669026258778703e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = 0.96440536170153059574171007792892
y2[1] (numeric) = 0.96440536170153896857118981518946
absolute error = 8.37282947973726054e-15
relative error = 8.6818570408659022354573819371369e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
x[1] = 4.99
y1[1] (closed_form) = -0.27405891954542724396309159769695
y1[1] (numeric) = -0.27405891954543427356711744284981
absolute error = 7.02960402584515286e-15
relative error = 2.5649973507539663403752708045537e-12 %
Desired digits = 8
Estimated correct digits = 11
Correct digits = 14
h = 0.005
y2[1] (closed_form) = 0.96171290342679349794114601441111
y2[1] (numeric) = 0.96171290342680186347466000877733
absolute error = 8.36553351399436622e-15
relative error = 8.6985767625516304593045687171124e-13 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = 15
h = 0.005
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
Finished!
diff ( y1 , x , 1 ) = neg ( y2 ) ;
diff ( y2 , x , 2 ) = diff ( y1 , x , 1 ) ;
Iterations = 900
Total Elapsed Time = 46 Seconds
Elapsed Time(since restart) = 46 Seconds
Time to Timeout = 2 Minutes 13 Seconds
Percent Done = 100.1 %
> quit
memory used=3942.9MB, alloc=40.3MB, time=46.25