|\^/| Maple 18 (X86 64 WINDOWS)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2014
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
| Type ? for help.
#BEGIN OUTFILE1
# before write maple top matter
# before write_ats library and user def block
#BEGIN ATS LIBRARY BLOCK
# Begin Function number 2
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s\n",str);
> fi;# end if 1;
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
# End Function number 2
# Begin Function number 3
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s",str);
> fi;# end if 1;
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
# End Function number 3
# Begin Function number 4
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> print(label,str);
> fi;# end if 1;
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
# End Function number 4
# Begin Function number 5
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 5
# Begin Function number 6
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> if vallen = 5 then # if number 1
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 6
# Begin Function number 7
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;# end if 0;
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
print(prelabel, "[", elemnt, "]", value, postlabel)
end if
end proc
# End Function number 7
# Begin Function number 8
> logitem_time := proc(fd,secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> fprintf(fd,"
");
> if (secs_in >= 0) then # if number 0
> years_int := int_trunc(secs_in / glob_sec_in_year);
> sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
> days_int := int_trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := sec_temp mod int_trunc(glob_sec_in_day) ;
> hours_int := int_trunc(sec_temp / glob_sec_in_hour);
> sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
> minutes_int := int_trunc(sec_temp / glob_sec_in_minute);
> sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
> if (years_int > 0) then # if number 1
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 2
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 3
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 4
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 4
> else
> fprintf(fd," 0.0 Seconds");
> fi;# end if 3
> fprintf(fd," | \n");
> end;
logitem_time := proc(fd, secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
fprintf(fd, "");
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, " 0.0 Seconds")
end if;
fprintf(fd, " | \n")
end proc
# End Function number 8
# Begin Function number 9
> omniout_timestr := proc(secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> if (secs_in >= 0) then # if number 3
> years_int := int_trunc(secs_in / glob_sec_in_year);
> sec_temp := (int_trunc(secs_in) mod int_trunc(glob_sec_in_year));
> days_int := int_trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_day)) ;
> hours_int := int_trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_hour));
> minutes_int := int_trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod int_trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 4
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 5
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 6
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 7
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 7
> else
> printf(" 0.0 Seconds\n");
> fi;# end if 6
> end;
omniout_timestr := proc(secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" 0.0 Seconds\n")
end if
end proc
# End Function number 9
# Begin Function number 10
> zero_ats_ar := proc(arr_a)
> global ATS_MAX_TERMS;
> local iii;
> iii := 1;
> while (iii <= ATS_MAX_TERMS) do # do number 1
> arr_a [iii] := glob__0;
> iii := iii + 1;
> od;# end do number 1
> end;
zero_ats_ar := proc(arr_a)
local iii;
global ATS_MAX_TERMS;
iii := 1;
while iii <= ATS_MAX_TERMS do arr_a[iii] := glob__0; iii := iii + 1
end do
end proc
# End Function number 10
# Begin Function number 11
> ats := proc(mmm_ats,arr_a,arr_b,jjj_ats)
> global ATS_MAX_TERMS;
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := glob__0;
> if (jjj_ats <= mmm_ats) then # if number 6
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> if ((lll_ats <= ATS_MAX_TERMS and (iii_ats <= ATS_MAX_TERMS) )) then # if number 7
> ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]);
> fi;# end if 7;
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 6;
> ret_ats;
> end;
ats := proc(mmm_ats, arr_a, arr_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
global ATS_MAX_TERMS;
ret_ats := glob__0;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
if lll_ats <= ATS_MAX_TERMS and iii_ats <= ATS_MAX_TERMS then
ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats])
end if;
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
# End Function number 11
# Begin Function number 12
> att := proc(mmm_att,arr_aa,arr_bb,jjj_att)
> global ATS_MAX_TERMS;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := glob__0;
> if (jjj_att < mmm_att) then # if number 6
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while ((iii_att < mmm_att) and (iii_att <= ATS_MAX_TERMS) ) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if ((lll_att <= ATS_MAX_TERMS and (iii_att <= ATS_MAX_TERMS) )) then # if number 7
> ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att);
> fi;# end if 7;
> iii_att := iii_att + 1;
> od;# end do number 1;
> ret_att := ret_att / c(mmm_att) ;
> fi;# end if 6;
> ret_att;
> end;
att := proc(mmm_att, arr_aa, arr_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global ATS_MAX_TERMS;
ret_att := glob__0;
if jjj_att < mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att < mmm_att and iii_att <= ATS_MAX_TERMS do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= ATS_MAX_TERMS and iii_att <= ATS_MAX_TERMS then
ret_att :=
ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])*c(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/c(mmm_att)
end if;
ret_att
end proc
# End Function number 12
# Begin Function number 13
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
# End Function number 13
# Begin Function number 14
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
# End Function number 14
# Begin Function number 15
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
# End Function number 15
# Begin Function number 16
> logitem_good_digits := proc(file,rel_error)
> global glob_small_float,glob_prec;
> local good_digits;
> fprintf(file,"");
> fprintf(file,"%d",glob_min_good_digits);
> fprintf(file," | ");
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float, glob_prec;
fprintf(file, "");
fprintf(file, "%d", glob_min_good_digits);
fprintf(file, " | ")
end proc
# End Function number 16
# Begin Function number 17
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
# End Function number 17
# Begin Function number 18
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
# End Function number 18
# Begin Function number 19
> logitem_h_reason := proc(file)
> global glob_h_reason;
> fprintf(file,"");
> if (glob_h_reason = 1) then # if number 6
> fprintf(file,"Max H");
> elif
> (glob_h_reason = 2) then # if number 7
> fprintf(file,"Display Interval");
> elif
> (glob_h_reason = 3) then # if number 8
> fprintf(file,"Optimal");
> elif
> (glob_h_reason = 4) then # if number 9
> fprintf(file,"Pole Accuracy");
> elif
> (glob_h_reason = 5) then # if number 10
> fprintf(file,"Min H (Pole)");
> elif
> (glob_h_reason = 6) then # if number 11
> fprintf(file,"Pole");
> elif
> (glob_h_reason = 7) then # if number 12
> fprintf(file,"Opt Iter");
> else
> fprintf(file,"Impossible");
> fi;# end if 12
> fprintf(file," | ");
> end;
logitem_h_reason := proc(file)
global glob_h_reason;
fprintf(file, "");
if glob_h_reason = 1 then fprintf(file, "Max H")
elif glob_h_reason = 2 then fprintf(file, "Display Interval")
elif glob_h_reason = 3 then fprintf(file, "Optimal")
elif glob_h_reason = 4 then fprintf(file, "Pole Accuracy")
elif glob_h_reason = 5 then fprintf(file, "Min H (Pole)")
elif glob_h_reason = 6 then fprintf(file, "Pole")
elif glob_h_reason = 7 then fprintf(file, "Opt Iter")
else fprintf(file, "Impossible")
end if;
fprintf(file, " | ")
end proc
# End Function number 19
# Begin Function number 20
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
# End Function number 20
# Begin Function number 21
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file) fprintf(file, "\n") end proc
# End Function number 21
# Begin Function number 22
> chk_data := proc()
> global glob_max_iter,ALWAYS, ATS_MAX_TERMS;
> local errflag;
> errflag := false;
> if (glob_max_iter < 2) then # if number 12
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 12;
> if (errflag) then # if number 12
> quit;
> fi;# end if 12
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, ATS_MAX_TERMS;
errflag := false;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
# End Function number 22
# Begin Function number 23
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := c(clock_sec2);
> sub1 := c(t_end2-t_start2);
> sub2 := c(t2-t_start2);
> if (sub1 = glob__0) then # if number 12
> sec_left := glob__0;
> else
> if (sub2 > glob__0) then # if number 13
> rrr := (sub1/sub2);
> sec_left := rrr * c(ms2) - c(ms2);
> else
> sec_left := glob__0;
> fi;# end if 13
> fi;# end if 12;
> sec_left;
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := c(clock_sec2);
sub1 := c(t_end2 - t_start2);
sub2 := c(t2 - t_start2);
if sub1 = glob__0 then sec_left := glob__0
else
if glob__0 < sub2 then
rrr := sub1/sub2; sec_left := rrr*c(ms2) - c(ms2)
else sec_left := glob__0
end if
end if;
sec_left
end proc
# End Function number 23
# Begin Function number 24
> comp_percent := proc(t_end2,t_start2, t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub2 > glob_small_float) then # if number 12
> rrr := (glob__100*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 12;
> rrr;
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < sub2 then rrr := glob__100*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
# End Function number 24
# Begin Function number 25
> comp_rad_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 12
> ret := float_abs(term1 * glob_h / term2);
> else
> ret := glob_larger_float;
> fi;# end if 12;
> ret;
> #BOTTOM TWO TERM RADIUS ANALYSIS
> end;
comp_rad_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := float_abs(term1*glob_h/term2)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 25
# Begin Function number 26
> comp_ord_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM ORDER ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 12
> ret := glob__1 + float_abs(term2) * c(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(c(last_no));
> else
> ret := glob_larger_float;
> fi;# end if 12;
> ret;
> #BOTTOM TWO TERM ORDER ANALYSIS
> end;
comp_ord_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := glob__1 + float_abs(term2)*
c(last_no)*ln(float_abs(term1*glob_h/term2))/ln(c(last_no))
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 26
# Begin Function number 27
> c := proc(in_val)
> #To Force Conversion when needed
> local ret;
> ret := evalf(in_val);
> ret;
> #End Conversion
> end;
c := proc(in_val) local ret; ret := evalf(in_val); ret end proc
# End Function number 27
# Begin Function number 28
> comp_rad_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret,temp;
> temp := float_abs(term2*term2*c(last_no)+glob__m2*term2*term2-term1*term3*c(last_no)+term1*term3);
> if (float_abs(temp) > glob__0) then # if number 12
> ret := float_abs((term2*glob_h*term1)/(temp));
> else
> ret := glob_larger_float;
> fi;# end if 12;
> ret;
> #BOTTOM THREE TERM RADIUS ANALYSIS
> end;
comp_rad_from_three_terms := proc(term1, term2, term3, last_no)
local ret, temp;
global glob_h, glob_larger_float;
temp := float_abs(term2*term2*c(last_no) + glob__m2*term2*term2
- term1*term3*c(last_no) + term1*term3);
if glob__0 < float_abs(temp) then
ret := float_abs(term2*glob_h*term1/temp)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 28
# Begin Function number 29
> comp_ord_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM ORDER ANALYSIS
> local ret;
> ret := float_abs((glob__4*term1*term3*c(last_no)-glob__3*term1*term3-glob__4*term2*term2*c(last_no)+glob__4*term2*term2+term2*term2*c(last_no*last_no)-term1*term3*c(last_no*last_no))/(term2*term2*c(last_no)-glob__2*term2*term2-term1*term3*c(last_no)+term1*term3));
> ret;
> #TOP THREE TERM ORDER ANALYSIS
> end;
comp_ord_from_three_terms := proc(term1, term2, term3, last_no)
local ret;
ret := float_abs((glob__4*term1*term3*c(last_no) - glob__3*term1*term3
- glob__4*term2*term2*c(last_no) + glob__4*term2*term2
+ term2*term2*c(last_no*last_no) - term1*term3*c(last_no*last_no))
/(term2*term2*c(last_no) - glob__2*term2*term2
- term1*term3*c(last_no) + term1*term3));
ret
end proc
# End Function number 29
# Begin Function number 30
> comp_rad_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> #TOP SIX TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float,glob_six_term_ord_save;
> local ret,rm0,rm1,rm2,rm3,rm4,nr1,nr2,dr1,dr2,ds2,rad_c,ord_no,ds1,rcs;
> if ((term5 <> glob__0) and (term4 <> glob__0) and (term3 <> glob__0) and (term2 <> glob__0) and (term1 <> glob__0)) then # if number 12
> rm0 := term6/term5;
> rm1 := term5/term4;
> rm2 := term4/term3;
> rm3 := term3/term2;
> rm4 := term2/term1;
> nr1 := c(last_no-1)*rm0 - glob__2*c(last_no-2)*rm1 + c(last_no-3)*rm2;
> nr2 := c(last_no-2)*rm1 - glob__2*c(last_no-3)*rm2 + c(last_no-4)*rm3;
> dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
> dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
> ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
> ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
> if ((float_abs(nr1 * dr2 - nr2 * dr1) = glob__0) or (float_abs(dr1) = glob__0)) then # if number 13
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> else
> if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0) then # if number 14
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) -c(last_no)/glob__2;
> if (float_abs(rcs) <> glob__0) then # if number 15
> if (rcs > glob__0) then # if number 16
> rad_c := sqrt(rcs) * float_abs(glob_h);
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 16
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 15
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 14
> fi;# end if 13
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 12;
> glob_six_term_ord_save := ord_no;
> rad_c;
> #BOTTOM SIX TERM RADIUS ANALYSIS
> end;
comp_rad_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
local ret, rm0, rm1, rm2, rm3, rm4, nr1, nr2, dr1, dr2, ds2, rad_c, ord_no,
ds1, rcs;
global glob_h, glob_larger_float, glob_six_term_ord_save;
if term5 <> glob__0 and term4 <> glob__0 and term3 <> glob__0 and
term2 <> glob__0 and term1 <> glob__0 then
rm0 := term6/term5;
rm1 := term5/term4;
rm2 := term4/term3;
rm3 := term3/term2;
rm4 := term2/term1;
nr1 := c(last_no - 1)*rm0 - glob__2*c(last_no - 2)*rm1
+ c(last_no - 3)*rm2;
nr2 := c(last_no - 2)*rm1 - glob__2*c(last_no - 3)*rm2
+ c(last_no - 4)*rm3;
dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
if
float_abs(nr1*dr2 - nr2*dr1) = glob__0 or float_abs(dr1) = glob__0
then rad_c := glob_larger_float; ord_no := glob_larger_float
else
if glob__0 < float_abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no :=
(rcs*nr1 - ds1)/(glob__2*dr1) - c(last_no)/glob__2;
if float_abs(rcs) <> glob__0 then
if glob__0 < rcs then
rad_c := sqrt(rcs)*float_abs(glob_h)
else
rad_c := glob_larger_float;
ord_no := glob_larger_float
end if
else
rad_c := glob_larger_float; ord_no := glob_larger_float
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if;
glob_six_term_ord_save := ord_no;
rad_c
end proc
# End Function number 30
# Begin Function number 31
> comp_ord_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> global glob_six_term_ord_save;
> #TOP SIX TERM ORDER ANALYSIS
> #TOP SAVED FROM SIX TERM RADIUS ANALYSIS
> glob_six_term_ord_save;
> #BOTTOM SIX TERM ORDER ANALYSIS
> end;
comp_ord_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
global glob_six_term_ord_save;
glob_six_term_ord_save
end proc
# End Function number 31
# Begin Function number 32
> factorial_2 := proc(nnn)
> ret := nnn!;
> ret;;
> end;
Warning, `ret` is implicitly declared local to procedure `factorial_2`
factorial_2 := proc(nnn) local ret; ret := nnn!; ret end proc
# End Function number 32
# Begin Function number 33
> factorial_1 := proc(nnn)
> global ATS_MAX_TERMS,array_fact_1;
> local ret;
> if (nnn <= ATS_MAX_TERMS) then # if number 12
> if (array_fact_1[nnn] = 0) then # if number 13
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 13;
> else
> ret := factorial_2(nnn);
> fi;# end if 12;
> ret;
> end;
factorial_1 := proc(nnn)
local ret;
global ATS_MAX_TERMS, array_fact_1;
if nnn <= ATS_MAX_TERMS then
if array_fact_1[nnn] = 0 then
ret := factorial_2(nnn); array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := factorial_2(nnn)
end if;
ret
end proc
# End Function number 33
# Begin Function number 34
> factorial_3 := proc(mmm,nnn)
> global ATS_MAX_TERMS,array_fact_2;
> local ret;
> if ((nnn <= ATS_MAX_TERMS) and (mmm <= ATS_MAX_TERMS)) then # if number 12
> if (array_fact_2[mmm,nnn] = 0) then # if number 13
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 13;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 12;
> ret;
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global ATS_MAX_TERMS, array_fact_2;
if nnn <= ATS_MAX_TERMS and mmm <= ATS_MAX_TERMS then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := factorial_2(mmm)/factorial_2(nnn)
end if;
ret
end proc
# End Function number 34
# Begin Function number 35
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
# End Function number 35
# Begin Function number 36
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
# End Function number 36
# Begin Function number 37
> float_abs := proc(x)
> abs(x);
> end;
float_abs := proc(x) abs(x) end proc
# End Function number 37
# Begin Function number 38
> expt := proc(x,y)
> x^y;
> end;
expt := proc(x, y) x^y end proc
# End Function number 38
# Begin Function number 39
> neg := proc(x)
> -x;
> end;
neg := proc(x) -x end proc
# End Function number 39
# Begin Function number 40
> int_trunc := proc(x)
> trunc(x);
> end;
int_trunc := proc(x) trunc(x) end proc
# End Function number 40
# Begin Function number 41
> estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer)
> local desired_abs_gbl_error,range,estimated_steps,step_error;
> global glob_desired_digits_correct,ALWAYS,ATS_MAX_TERMS;
> omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
> desired_abs_gbl_error := expt(glob__10,c( -glob_desired_digits_correct)) * c(float_abs(c(estimated_answer)));
> omniout_float(ALWAYS,"estimated_h",32,estimated_h,32,"");
> omniout_float(ALWAYS,"estimated_answer",32,estimated_answer,32,"");
> omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,"");
> range := (x_end - x_start);
> omniout_float(ALWAYS,"range",32,range,32,"");
> estimated_steps := range / estimated_h;
> omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,"");
> step_error := (c(float_abs(desired_abs_gbl_error) /sqrt(c( estimated_steps))/c(ATS_MAX_TERMS)));
> omniout_float(ALWAYS,"step_error",32,step_error,32,"");
> (step_error);;
> end;
estimated_needed_step_error := proc(
x_start, x_end, estimated_h, estimated_answer)
local desired_abs_gbl_error, range, estimated_steps, step_error;
global glob_desired_digits_correct, ALWAYS, ATS_MAX_TERMS;
omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, "");
desired_abs_gbl_error :=
expt(glob__10, c(-glob_desired_digits_correct))*
c(float_abs(c(estimated_answer)));
omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, "");
omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, "")
;
omniout_float(ALWAYS, "desired_abs_gbl_error", 32,
desired_abs_gbl_error, 32, "");
range := x_end - x_start;
omniout_float(ALWAYS, "range", 32, range, 32, "");
estimated_steps := range/estimated_h;
omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, "");
step_error := c(float_abs(desired_abs_gbl_error)/(
sqrt(c(estimated_steps))*c(ATS_MAX_TERMS)));
omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
step_error
end proc
# End Function number 41
#END ATS LIBRARY BLOCK
#BEGIN USER FUNCTION BLOCK
#BEGIN BLOCK 3
#BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return(c(0.0));
> end;
exact_soln_y := proc(x) return c(0.) end proc
#END USER DEF BLOCK
#END BLOCK 3
#END USER FUNCTION BLOCK
# before write_aux functions
# Begin Function number 2
> display_poles := proc()
> local rad_given;
> global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ;
> if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1
> rad_given := sqrt((array_x[1] - array_given_rad_poles[1,1]) * (array_x[1] - array_given_rad_poles[1,1]) + array_given_rad_poles[1,2] * array_given_rad_poles[1,2]);
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," ");
> omniout_float(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," ");
> if (rad_given < glob_least_given_sing) then # if number 2
> glob_least_given_sing := rad_given;
> fi;# end if 2;
> elif
> (glob_type_given_pole = 3) then # if number 2
> omniout_str(ALWAYS,"NO POLE (given) for Equation 1");
> elif
> (glob_type_given_pole = 5) then # if number 3
> omniout_str(ALWAYS,"SOME POLE (given) for Equation 1");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 1");
> fi;# end if 3;
> if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," ");
> if (array_rad_test_poles[1,1]< glob_least_ratio_sing) then # if number 4
> glob_least_ratio_sing := array_rad_test_poles[1,1];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," ");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," ");
> if (array_rad_test_poles[1,2]< glob_least_3_sing) then # if number 4
> glob_least_3_sing := array_rad_test_poles[1,2];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," ");
> if (array_rad_test_poles[1,3]< glob_least_6_sing) then # if number 4
> glob_least_6_sing := array_rad_test_poles[1,3];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1");
> fi;# end if 3
> ;
> end;
display_poles := proc()
local rad_given;
global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float,
glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord,
glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
glob_least_3_sing, glob_least_6_sing, glob_least_given_sing,
glob_least_ratio_sing, array_x;
if glob_type_given_pole = 1 or glob_type_given_pole = 2 then
rad_given := sqrt((array_x[1] - array_given_rad_poles[1, 1])*
(array_x[1] - array_given_rad_poles[1, 1])
+ array_given_rad_poles[1, 2]*array_given_rad_poles[1, 2]);
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 1 ", 4,
rad_given, 4, " ");
omniout_float(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles[1, 1], 4, " ");
if rad_given < glob_least_given_sing then
glob_least_given_sing := rad_given
end if
elif glob_type_given_pole = 3 then
omniout_str(ALWAYS, "NO POLE (given) for Equation 1")
elif glob_type_given_pole = 5 then
omniout_str(ALWAYS, "SOME POLE (given) for Equation 1")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 1")
end if;
if array_rad_test_poles[1, 1] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (ratio test) for eq 1 ", 4,
array_rad_test_poles[1, 1], 4, " ");
if array_rad_test_poles[1, 1] < glob_least_ratio_sing then
glob_least_ratio_sing := array_rad_test_poles[1, 1]
end if;
omniout_float(ALWAYS,
"Order of pole (ratio test) ", 4,
array_ord_test_poles[1, 1], 4, " ")
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 2] and
array_rad_test_poles[1, 2] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 1 ", 4,
array_rad_test_poles[1, 2], 4, " ");
if array_rad_test_poles[1, 2] < glob_least_3_sing then
glob_least_3_sing := array_rad_test_poles[1, 2]
end if;
omniout_float(ALWAYS,
"Order of pole (three term test) ", 4,
array_ord_test_poles[1, 2], 4, " ")
else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 3] and
array_rad_test_poles[1, 3] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 1 ", 4,
array_rad_test_poles[1, 3], 4, " ");
if array_rad_test_poles[1, 3] < glob_least_6_sing then
glob_least_6_sing := array_rad_test_poles[1, 3]
end if;
omniout_float(ALWAYS,
"Order of pole (six term test) ", 4,
array_ord_test_poles[1, 3], 4, " ")
else omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 1")
end if
end proc
# End Function number 2
# Begin Function number 3
> my_check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 3
> ret := glob__1;
> else
> ret := glob__m1;
> fi;# end if 3;
> ret;;
> end;
my_check_sign := proc(x0, xf)
local ret;
if x0 < xf then ret := glob__1 else ret := glob__m1 end if; ret
end proc
# End Function number 3
# Begin Function number 4
> est_size_answer := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_3D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local min_size;
> min_size := glob_estimated_size_answer;
> if (float_abs(array_y[1]) < min_size) then # if number 3
> min_size := float_abs(array_y[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> if (min_size < glob__1) then # if number 3
> min_size := glob__1;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> min_size;
> end;
est_size_answer := proc()
local min_size;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_3D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1,
array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
min_size := glob_estimated_size_answer;
if float_abs(array_y[1]) < min_size then
min_size := float_abs(array_y[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if min_size < glob__1 then
min_size := glob__1;
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
min_size
end proc
# End Function number 4
# Begin Function number 5
> test_suggested_h := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_3D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> max_estimated_step_error := glob__small;
> no_terms := ATS_MAX_TERMS;
> hn_div_ho := glob__0_5;
> hn_div_ho_2 := glob__0_25;
> hn_div_ho_3 := glob__0_125;
> omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,"");
> omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,"");
> omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,"");
> est_tmp := float_abs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3);
> if (est_tmp >= max_estimated_step_error) then # if number 3
> max_estimated_step_error := est_tmp;
> fi;# end if 3;
> omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,"");
> max_estimated_step_error;
> end;
test_suggested_h := proc()
local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3,
no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_3D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1,
array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
max_estimated_step_error := glob__small;
no_terms := ATS_MAX_TERMS;
hn_div_ho := glob__0_5;
hn_div_ho_2 := glob__0_25;
hn_div_ho_3 := glob__0_125;
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, "");
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, "");
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, "");
est_tmp := float_abs(array_y[no_terms - 3]
+ array_y[no_terms - 2]*hn_div_ho
+ array_y[no_terms - 1]*hn_div_ho_2
+ array_y[no_terms]*hn_div_ho_3);
if max_estimated_step_error <= est_tmp then
max_estimated_step_error := est_tmp
end if;
omniout_float(ALWAYS, "max_estimated_step_error", 32,
max_estimated_step_error, 32, "");
max_estimated_step_error
end proc
# End Function number 5
# Begin Function number 6
> track_estimated_error := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_3D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> no_terms := ATS_MAX_TERMS;
> hn_div_ho := glob__0_5;
> hn_div_ho_2 := glob__0_25;
> hn_div_ho_3 := glob__0_125;
> est_tmp := c(float_abs(array_y[no_terms-3])) + c(float_abs(array_y[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y[no_terms])) * c(hn_div_ho_3);
> if (glob_prec * c(float_abs(array_y[1])) > c(est_tmp)) then # if number 3
> est_tmp := c(glob_prec) * c(float_abs(array_y[1]));
> fi;# end if 3;
> if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 3
> array_max_est_error[1] := c(est_tmp);
> fi;# end if 3
> ;
> end;
track_estimated_error := proc()
local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_3D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1,
array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
no_terms := ATS_MAX_TERMS;
hn_div_ho := glob__0_5;
hn_div_ho_2 := glob__0_25;
hn_div_ho_3 := glob__0_125;
est_tmp := c(float_abs(array_y[no_terms - 3]))
+ c(float_abs(array_y[no_terms - 2]))*c(hn_div_ho)
+ c(float_abs(array_y[no_terms - 1]))*c(hn_div_ho_2)
+ c(float_abs(array_y[no_terms]))*c(hn_div_ho_3);
if c(est_tmp) < glob_prec*c(float_abs(array_y[1])) then
est_tmp := c(glob_prec)*c(float_abs(array_y[1]))
end if;
if c(array_max_est_error[1]) <= c(est_tmp) then
array_max_est_error[1] := c(est_tmp)
end if
end proc
# End Function number 6
# Begin Function number 7
> reached_interval := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_3D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local ret;
> if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 3
> ret := true;
> else
> ret := false;
> fi;# end if 3;
> return(ret);
> end;
reached_interval := proc()
local ret;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_3D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1,
array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
if glob_check_sign*glob_next_display - glob_h/glob__10 <=
glob_check_sign*array_x[1] then ret := true
else ret := false
end if;
return ret
end proc
# End Function number 7
# Begin Function number 8
> display_alot := proc(iter)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_3D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err;
> #TOP DISPLAY ALOT
> if (reached_interval()) then # if number 3
> if (iter >= 0) then # if number 4
> ind_var := array_x[1];
> omniout_float(ALWAYS,"x[1] ",33,ind_var,20," ");
> closed_form_val_y := evalf(exact_soln_y(ind_var));
> omniout_float(ALWAYS,"y[1] (closed_form) ",33,closed_form_val_y,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> abserr := float_abs(numeric_val - closed_form_val_y);
> omniout_float(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> if (c(float_abs(closed_form_val_y)) > c(glob_prec)) then # if number 5
> relerr := abserr*glob__100/float_abs(closed_form_val_y);
> if (c(relerr) > c(glob_prec)) then # if number 6
> glob_good_digits := -int_trunc(log10(c(relerr))) + 3;
> else
> glob_good_digits := Digits;
> fi;# end if 6;
> else
> relerr := glob__m1 ;
> glob_good_digits := -16;
> fi;# end if 5;
> if (glob_good_digits < glob_min_good_digits) then # if number 5
> glob_min_good_digits := glob_good_digits;
> fi;# end if 5;
> if (glob_apfp_est_good_digits < glob_min_apfp_est_good_digits) then # if number 5
> glob_min_apfp_est_good_digits := glob_apfp_est_good_digits;
> fi;# end if 5;
> if (evalf(float_abs(numeric_val)) > glob_prec) then # if number 5
> est_rel_err := evalf(array_max_est_error[1]*100.0 * sqrt(glob_iter)*24*ATS_MAX_TERMS/float_abs(numeric_val));
> if (evalf(est_rel_err) > glob_prec) then # if number 6
> glob_est_digits := -int_trunc(log10(est_rel_err)) + 3;
> else
> glob_est_digits := Digits;
> fi;# end if 6;
> else
> relerr := glob__m1 ;
> glob_est_digits := -16;
> fi;# end if 5;
> array_est_digits[1] := glob_est_digits;
> if (glob_iter = 1) then # if number 5
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 5;
> array_est_rel_error[1] := est_rel_err;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_int(INFO,"Desired digits ",32,glob_desired_digits_correct,4," ");
> omniout_int(INFO,"Estimated correct digits ",32,glob_est_digits,4," ");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> fi;# end if 4;
> #BOTTOM DISPLAY ALOT
> fi;# end if 3;
> end;
display_alot := proc(iter)
local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no,
est_rel_err;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_3D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1,
array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
if reached_interval() then
if 0 <= iter then
ind_var := array_x[1];
omniout_float(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
closed_form_val_y := evalf(exact_soln_y(ind_var));
omniout_float(ALWAYS, "y[1] (closed_form) ", 33,
closed_form_val_y, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
abserr := float_abs(numeric_val - closed_form_val_y);
omniout_float(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
if c(glob_prec) < c(float_abs(closed_form_val_y)) then
relerr := abserr*glob__100/float_abs(closed_form_val_y);
if c(glob_prec) < c(relerr) then
glob_good_digits := -int_trunc(log10(c(relerr))) + 3
else glob_good_digits := Digits
end if
else relerr := glob__m1; glob_good_digits := -16
end if;
if glob_good_digits < glob_min_good_digits then
glob_min_good_digits := glob_good_digits
end if;
if glob_apfp_est_good_digits < glob_min_apfp_est_good_digits
then glob_min_apfp_est_good_digits := glob_apfp_est_good_digits
end if;
if glob_prec < evalf(float_abs(numeric_val)) then
est_rel_err := evalf(array_max_est_error[1]*100.0*
sqrt(glob_iter)*24*ATS_MAX_TERMS/float_abs(numeric_val))
;
if glob_prec < evalf(est_rel_err) then
glob_est_digits := -int_trunc(log10(est_rel_err)) + 3
else glob_est_digits := Digits
end if
else relerr := glob__m1; glob_est_digits := -16
end if;
array_est_digits[1] := glob_est_digits;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
array_est_rel_error[1] := est_rel_err;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_int(INFO, "Desired digits ", 32,
glob_desired_digits_correct, 4, " ");
omniout_int(INFO, "Estimated correct digits ", 32,
glob_est_digits, 4, " ");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end if
end proc
# End Function number 8
# Begin Function number 9
> prog_report := proc(x_start,x_end)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_3D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := (clock_sec1) - (glob_orig_start_sec);
> glob_clock_sec := (clock_sec1) - (glob_clock_start_sec);
> left_sec := (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1);
> expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h) ,( clock_sec1) - (glob_orig_start_sec));
> opt_clock_sec := ( clock_sec1) - (glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec));
> glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
> percent_done := comp_percent((x_end),(x_start),(array_x[1]) + (glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr((total_clock_sec));
> omniout_str_noeol(INFO,"Elapsed Time(since restart) ");
> omniout_timestr((glob_clock_sec));
> if (c(percent_done) < glob__100) then # if number 3
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr((expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr((glob_optimal_expect_sec));
> omniout_str_noeol(INFO,"Expected Total Time ");
> omniout_timestr((glob_total_exp_sec));
> fi;# end if 3;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr((left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_3D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1,
array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec := clock_sec1 - glob_orig_start_sec;
glob_clock_sec := clock_sec1 - glob_clock_start_sec;
left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1;
expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h,
clock_sec1 - glob_orig_start_sec);
opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec;
glob_optimal_expect_sec :=
comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec)
;
glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h);
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(total_clock_sec);
omniout_str_noeol(INFO, "Elapsed Time(since restart) ");
omniout_timestr(glob_clock_sec);
if c(percent_done) < glob__100 then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(expect_sec);
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(glob_optimal_expect_sec);
omniout_str_noeol(INFO, "Expected Total Time ");
omniout_timestr(glob_total_exp_sec)
end if;
omniout_str_noeol(INFO, "Time to Timeout ");
omniout_timestr(left_sec);
omniout_float(INFO, "Percent Done ", 33,
percent_done, 4, "%")
end proc
# End Function number 9
# Begin Function number 10
> check_for_pole := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_3D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad, last_no;
> #TOP CHECK FOR POLE
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,1] := glob_larger_float;
> array_ord_test_poles[1,1] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 3
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 3;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 3
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 4
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 5
> found_sing := 0;
> fi;# end if 5;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 5
> if (rad_c < array_rad_test_poles[1,1]) then # if number 6
> array_rad_test_poles[1,1] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,1] := rad_c;
> array_ord_test_poles[1,1] := tmp_ord;
> fi;# end if 6;
> fi;# end if 5;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,2] := glob_larger_float;
> array_ord_test_poles[1,2] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 5
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 5;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 6
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 7
> found_sing := 0;
> fi;# end if 7;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 7
> if (rad_c < array_rad_test_poles[1,2]) then # if number 8
> array_rad_test_poles[1,2] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,2] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 9
> glob_min_pole_est := rad_c;
> fi;# end if 9;
> array_ord_test_poles[1,2] := tmp_ord;
> fi;# end if 8;
> fi;# end if 7;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,3] := glob_larger_float;
> array_ord_test_poles[1,3] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 7
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 7;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 8
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 9
> found_sing := 0;
> fi;# end if 9;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 9
> if (rad_c < array_rad_test_poles[1,3]) then # if number 10
> array_rad_test_poles[1,3] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,3] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 11
> glob_min_pole_est := rad_c;
> fi;# end if 11;
> array_ord_test_poles[1,3] := tmp_ord;
> fi;# end if 10;
> fi;# end if 9;
> #BOTTOM general radius test1
> #START ADJUST ALL SERIES
> if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 9
> h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius;
> omniout_str(ALWAYS,"SETTING H FOR POLE");
> glob_h_reason := 6;
> if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> h_new := glob_min_h;
> glob_h_reason := 5;
> fi;# end if 10;
> term := 1;
> ratio := c(1.0);
> while (term <= ATS_MAX_TERMS) do # do number 1
> array_y[term] := array_y[term]* ratio;
> array_y_higher[1,term] := array_y_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / float_abs(glob_h);
> term := term + 1;
> od;# end do number 1;
> glob_h := h_new;
> fi;# end if 9;
> #BOTTOM ADJUST ALL SERIES
> ;
> if (reached_interval()) then # if number 9
> display_poles();
> fi;# end if 9
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2,
term3, part1, part2, part3, part4, part5, part6, part7, part8, part9,
part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4,
found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio,
prev_tmp_rad, last_no;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_3D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1,
array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 1] := glob_larger_float;
array_ord_test_poles[1, 1] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do
tmp_rad := comp_rad_from_ratio(array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 1] then
array_rad_test_poles[1, 1] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_ratio(array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
array_rad_test_poles[1, 1] := rad_c;
array_ord_test_poles[1, 1] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 2] := glob_larger_float;
array_ord_test_poles[1, 2] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do
tmp_rad := comp_rad_from_three_terms(
array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 2] then
array_rad_test_poles[1, 2] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_three_terms(
array_y_higher[1, last_no - 2],
array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
last_no);
array_rad_test_poles[1, 2] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 2] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 3] := glob_larger_float;
array_ord_test_poles[1, 3] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do
tmp_rad := comp_rad_from_six_terms(array_y_higher[1, last_no - 5],
array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3],
array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 3] then
array_rad_test_poles[1, 3] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_six_terms(
array_y_higher[1, last_no - 5],
array_y_higher[1, last_no - 4],
array_y_higher[1, last_no - 3],
array_y_higher[1, last_no - 2],
array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
last_no);
array_rad_test_poles[1, 3] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 3] := tmp_ord
end if
end if;
if
float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h)
then
h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius;
omniout_str(ALWAYS, "SETTING H FOR POLE");
glob_h_reason := 6;
if glob_check_sign*h_new < glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
h_new := glob_min_h;
glob_h_reason := 5
end if;
term := 1;
ratio := c(1.0);
while term <= ATS_MAX_TERMS do
array_y[term] := array_y[term]*ratio;
array_y_higher[1, term] := array_y_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/float_abs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
if reached_interval() then display_poles() end if
end proc
# End Function number 10
# Begin Function number 11
> atomall := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_3D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> # before write maple main top matter
> # before generate constants assign
> # before generate globals assign
> #END OUTFILE1
> #BEGIN OUTFILE2
> #END OUTFILE2
> #BEGIN ATOMHDR1
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 1
> array_tmp1[1] := array_const_2D0[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp2[1] := array_tmp1[1] + array_const_3D0[1];
> #emit pre sqrt 1 $eq_no = 1
> array_tmp3[1] := sqrt(array_tmp2[1]);
> #emit pre tanh $eq_no = 1
> array_tmp4_a1[1] := sinh(array_tmp3[1]);
> array_tmp4_a2[1] := cosh(array_tmp3[1]);
> array_tmp4[1] := (array_tmp4_a1[1] / array_tmp4_a2[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp5[1] := array_const_0D0[1] + array_tmp4[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y_set_initial[1,2]) then # if number 1
> if (1 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp5[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
> if (2 <= ATS_MAX_TERMS) then # if number 3
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(1);
> array_y_higher[2,1] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
> array_tmp1[2] := array_const_2D0[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre sqrt 2 $eq_no = 1
> array_tmp3[2] := array_tmp2[2] / array_tmp3[1]/glob__2;
> #emit pre tanh $eq_no = 1
> array_tmp4_a1[2] := att(1,array_tmp4_a2,array_tmp3,1);
> array_tmp4_a2[2] := att(1,array_tmp4_a1,array_tmp3,1);
> array_tmp4[2] := (array_tmp4_a1[2] - ats(2,array_tmp4_a2,array_tmp4,2)) / array_tmp4_a2[1];
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp5[2] := array_tmp4[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y_set_initial[1,3]) then # if number 1
> if (2 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp5[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2));
> if (3 <= ATS_MAX_TERMS) then # if number 3
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y_higher[2,2] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre sqrt ID_LINEAR iii = 3 $eq_no = 1
> array_tmp3[3] := 0;
> array_tmp3[3] := neg(ats(3,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2;
> #emit pre tanh $eq_no = 1
> array_tmp4_a1[3] := att(2,array_tmp4_a2,array_tmp3,1);
> array_tmp4_a2[3] := att(2,array_tmp4_a1,array_tmp3,1);
> array_tmp4[3] := (array_tmp4_a1[3] - ats(3,array_tmp4_a2,array_tmp4,2)) / array_tmp4_a2[1];
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp5[3] := array_tmp4[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y_set_initial[1,4]) then # if number 1
> if (3 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp5[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3));
> if (4 <= ATS_MAX_TERMS) then # if number 3
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y_higher[2,3] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre sqrt ID_LINEAR iii = 4 $eq_no = 1
> array_tmp3[4] := 0;
> array_tmp3[4] := neg(ats(4,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2;
> #emit pre tanh $eq_no = 1
> array_tmp4_a1[4] := att(3,array_tmp4_a2,array_tmp3,1);
> array_tmp4_a2[4] := att(3,array_tmp4_a1,array_tmp3,1);
> array_tmp4[4] := (array_tmp4_a1[4] - ats(4,array_tmp4_a2,array_tmp4,2)) / array_tmp4_a2[1];
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp5[4] := array_tmp4[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y_set_initial[1,5]) then # if number 1
> if (4 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp5[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4));
> if (5 <= ATS_MAX_TERMS) then # if number 3
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y_higher[2,4] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre sqrt ID_LINEAR iii = 5 $eq_no = 1
> array_tmp3[5] := 0;
> array_tmp3[5] := neg(ats(5,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2;
> #emit pre tanh $eq_no = 1
> array_tmp4_a1[5] := att(4,array_tmp4_a2,array_tmp3,1);
> array_tmp4_a2[5] := att(4,array_tmp4_a1,array_tmp3,1);
> array_tmp4[5] := (array_tmp4_a1[5] - ats(5,array_tmp4_a2,array_tmp4,2)) / array_tmp4_a2[1];
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp5[5] := array_tmp4[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y_set_initial[1,6]) then # if number 1
> if (5 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp5[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5));
> if (6 <= ATS_MAX_TERMS) then # if number 3
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y_higher[2,5] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= ATS_MAX_TERMS) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit sqrt LINEAR $eq_no = 1
> array_tmp3[kkk] := 0;
> array_tmp3[kkk] := neg(ats(kkk,array_tmp3,array_tmp3,2)) /array_tmp3[1] / glob__2;
> array_tmp4_a1[kkk] := att(kkk-1 ,array_tmp4_a2,array_tmp3,1);
> array_tmp4_a2[kkk] := att(kkk-1,array_tmp4_a1,array_tmp3,1);
> array_tmp4[kkk] := (array_tmp4_a1[kkk] - ats(kkk ,array_tmp4_a2,array_tmp4,2)) / array_tmp4_a2[1];
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp5[kkk] := array_tmp4[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1
> if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2
> temporary := c(array_tmp5[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
> array_y[kkk + order_d] := c(temporary);
> array_y_higher[1,kkk + order_d] := c(temporary);
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := c(temporary) / c(glob_h) * c(adj2);
> else
> temporary := c(temporary);
> fi;# end if 4;
> array_y_higher[adj3,term] := c(temporary);
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 1
> fi;# end if 2
> fi;# end if 1;
> kkk := kkk + 1;
> od;# end do number 1;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_3D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1,
array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
array_tmp1[1] := array_const_2D0[1]*array_x[1];
array_tmp2[1] := array_tmp1[1] + array_const_3D0[1];
array_tmp3[1] := sqrt(array_tmp2[1]);
array_tmp4_a1[1] := sinh(array_tmp3[1]);
array_tmp4_a2[1] := cosh(array_tmp3[1]);
array_tmp4[1] := array_tmp4_a1[1]/array_tmp4_a2[1];
array_tmp5[1] := array_const_0D0[1] + array_tmp4[1];
if not array_y_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
if 2 <= ATS_MAX_TERMS then
array_y[2] := temporary; array_y_higher[1, 2] := temporary
end if;
temporary := c(temporary)*c(1)/c(glob_h);
array_y_higher[2, 1] := c(temporary)
end if
end if;
kkk := 2;
array_tmp1[2] := array_const_2D0[1]*array_x[2];
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := array_tmp2[2]/(array_tmp3[1]*glob__2);
array_tmp4_a1[2] := att(1, array_tmp4_a2, array_tmp3, 1);
array_tmp4_a2[2] := att(1, array_tmp4_a1, array_tmp3, 1);
array_tmp4[2] := (
array_tmp4_a1[2] - ats(2, array_tmp4_a2, array_tmp4, 2))/
array_tmp4_a2[1];
array_tmp5[2] := array_tmp4[2];
if not array_y_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
if 3 <= ATS_MAX_TERMS then
array_y[3] := temporary; array_y_higher[1, 3] := temporary
end if;
temporary := c(temporary)*c(2)/c(glob_h);
array_y_higher[2, 2] := c(temporary)
end if
end if;
kkk := 3;
array_tmp3[3] := 0;
array_tmp3[3] :=
neg(ats(3, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2);
array_tmp4_a1[3] := att(2, array_tmp4_a2, array_tmp3, 1);
array_tmp4_a2[3] := att(2, array_tmp4_a1, array_tmp3, 1);
array_tmp4[3] := (
array_tmp4_a1[3] - ats(3, array_tmp4_a2, array_tmp4, 2))/
array_tmp4_a2[1];
array_tmp5[3] := array_tmp4[3];
if not array_y_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[3])*expt(glob_h, c(1))*c(factorial_3(2, 3));
if 4 <= ATS_MAX_TERMS then
array_y[4] := temporary; array_y_higher[1, 4] := temporary
end if;
temporary := c(temporary)*c(3)/c(glob_h);
array_y_higher[2, 3] := c(temporary)
end if
end if;
kkk := 4;
array_tmp3[4] := 0;
array_tmp3[4] :=
neg(ats(4, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2);
array_tmp4_a1[4] := att(3, array_tmp4_a2, array_tmp3, 1);
array_tmp4_a2[4] := att(3, array_tmp4_a1, array_tmp3, 1);
array_tmp4[4] := (
array_tmp4_a1[4] - ats(4, array_tmp4_a2, array_tmp4, 2))/
array_tmp4_a2[1];
array_tmp5[4] := array_tmp4[4];
if not array_y_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[4])*expt(glob_h, c(1))*c(factorial_3(3, 4));
if 5 <= ATS_MAX_TERMS then
array_y[5] := temporary; array_y_higher[1, 5] := temporary
end if;
temporary := c(temporary)*c(4)/c(glob_h);
array_y_higher[2, 4] := c(temporary)
end if
end if;
kkk := 5;
array_tmp3[5] := 0;
array_tmp3[5] :=
neg(ats(5, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2);
array_tmp4_a1[5] := att(4, array_tmp4_a2, array_tmp3, 1);
array_tmp4_a2[5] := att(4, array_tmp4_a1, array_tmp3, 1);
array_tmp4[5] := (
array_tmp4_a1[5] - ats(5, array_tmp4_a2, array_tmp4, 2))/
array_tmp4_a2[1];
array_tmp5[5] := array_tmp4[5];
if not array_y_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[5])*expt(glob_h, c(1))*c(factorial_3(4, 5));
if 6 <= ATS_MAX_TERMS then
array_y[6] := temporary; array_y_higher[1, 6] := temporary
end if;
temporary := c(temporary)*c(5)/c(glob_h);
array_y_higher[2, 5] := c(temporary)
end if
end if;
kkk := 6;
while kkk <= ATS_MAX_TERMS do
array_tmp3[kkk] := 0;
array_tmp3[kkk] := neg(ats(kkk, array_tmp3, array_tmp3, 2))/(
array_tmp3[1]*glob__2);
array_tmp4_a1[kkk] := att(kkk - 1, array_tmp4_a2, array_tmp3, 1);
array_tmp4_a2[kkk] := att(kkk - 1, array_tmp4_a1, array_tmp3, 1);
array_tmp4[kkk] := (
array_tmp4_a1[kkk] - ats(kkk, array_tmp4_a2, array_tmp4, 2))/
array_tmp4_a2[1];
array_tmp5[kkk] := array_tmp4[kkk];
order_d := 1;
if kkk + order_d <= ATS_MAX_TERMS then
if not array_y_set_initial[1, kkk + order_d] then
temporary := c(array_tmp5[kkk])*expt(glob_h, c(order_d))*
c(factorial_3(kkk - 1, kkk + order_d - 1));
array_y[kkk + order_d] := c(temporary);
array_y_higher[1, kkk + order_d] := c(temporary);
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while
1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1
do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := c(temporary)*c(adj2)/c(glob_h)
else temporary := c(temporary)
end if;
array_y_higher[adj3, term] := c(temporary)
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
# End Function number 12
#END OUTFILE5
# Begin Function number 12
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it;
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_h,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_3D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4_a1,
> array_tmp4_a2,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> ATS_MAX_TERMS := 30;
> # before first input block
> #BEGIN FIRST INPUT BLOCK
> #BEGIN BLOCK 1
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=30;
> #END BLOCK 1
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> # before generate arrays
> array_y_init:= Array(0..(30),[]);
> array_norms:= Array(0..(30),[]);
> array_fact_1:= Array(0..(30),[]);
> array_1st_rel_error:= Array(0..(2),[]);
> array_last_rel_error:= Array(0..(2),[]);
> array_est_rel_error:= Array(0..(2),[]);
> array_max_est_error:= Array(0..(2),[]);
> array_type_pole:= Array(0..(2),[]);
> array_type_real_pole:= Array(0..(2),[]);
> array_type_complex_pole:= Array(0..(2),[]);
> array_est_digits:= Array(0..(2),[]);
> array_y:= Array(0..(30),[]);
> array_x:= Array(0..(30),[]);
> array_tmp0:= Array(0..(30),[]);
> array_tmp1:= Array(0..(30),[]);
> array_tmp2:= Array(0..(30),[]);
> array_tmp3:= Array(0..(30),[]);
> array_tmp4_g:= Array(0..(30),[]);
> array_tmp4_a1:= Array(0..(30),[]);
> array_tmp4_a2:= Array(0..(30),[]);
> array_tmp4:= Array(0..(30),[]);
> array_tmp5:= Array(0..(30),[]);
> array_m1:= Array(0..(30),[]);
> array_y_higher := Array(0..(2) ,(0..30+ 1),[]);
> array_y_higher_work := Array(0..(2) ,(0..30+ 1),[]);
> array_y_higher_work2 := Array(0..(2) ,(0..30+ 1),[]);
> array_y_set_initial := Array(0..(2) ,(0..30+ 1),[]);
> array_given_rad_poles := Array(0..(2) ,(0..3+ 1),[]);
> array_given_ord_poles := Array(0..(2) ,(0..3+ 1),[]);
> array_rad_test_poles := Array(0..(2) ,(0..4+ 1),[]);
> array_ord_test_poles := Array(0..(2) ,(0..4+ 1),[]);
> array_fact_2 := Array(0..(30) ,(0..30+ 1),[]);
> # before generate constants
> # before generate globals definition
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> # before generate const definition
> # before arrays initialized
> term := 1;
> while (term <= 30) do # do number 1
> array_y_init[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_norms[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_fact_1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_1st_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_last_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_est_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_max_est_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_real_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_complex_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_est_digits[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_y[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_x[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp0[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp3[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp4_g[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp4_a1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp4_a2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp4[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp5[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_m1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y_higher[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y_higher_work[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y_higher_work2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y_set_initial[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_rad_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_ord_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_rad_test_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_ord_test_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=30) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_fact_2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> # before symbols initialized
> #BEGIN SYMBOLS INITIALIZATED
> zero_ats_ar(array_y);
> zero_ats_ar(array_x);
> zero_ats_ar(array_tmp0);
> zero_ats_ar(array_tmp1);
> zero_ats_ar(array_tmp2);
> zero_ats_ar(array_tmp3);
> zero_ats_ar(array_tmp4_g);
> zero_ats_ar(array_tmp4_a1);
> zero_ats_ar(array_tmp4_a2);
> zero_ats_ar(array_tmp4);
> zero_ats_ar(array_tmp5);
> zero_ats_ar(array_m1);
> zero_ats_ar(array_const_1);
> array_const_1[1] := c(1);
> zero_ats_ar(array_const_0D0);
> array_const_0D0[1] := c(0.0);
> zero_ats_ar(array_const_2D0);
> array_const_2D0[1] := c(2.0);
> zero_ats_ar(array_const_3D0);
> array_const_3D0[1] := c(3.0);
> zero_ats_ar(array_m1);
> array_m1[1] := glob__m1;
> #END SYMBOLS INITIALIZATED
> # before generate factorials init
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= ATS_MAX_TERMS) do # do number 1
> jjjf := 0;
> while (jjjf <= ATS_MAX_TERMS) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Table
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> glob_yes_pole := 4;
> glob_no_pole := 3;
> glob_not_given := 0;
> glob_no_sing_tests := 4;
> glob_ratio_test := 1;
> glob_three_term_test := 2;
> glob_six_term_test := 3;
> glob_log_10 := log(c(10.0));
> MAX_UNCHANGED := 10;
> glob__small := c(0.1e-50);
> glob_small_float := c(0.1e-50);
> glob_smallish_float := c(0.1e-60);
> glob_large_float := c(1.0e100);
> glob_larger_float := c(1.1e100);
> glob__m2 := c(-2);
> glob__m1 := c(-1);
> glob__0 := c(0);
> glob__1 := c(1);
> glob__2 := c(2);
> glob__3 := c(3);
> glob__4 := c(4);
> glob__5 := c(5);
> glob__8 := c(8);
> glob__10 := c(10);
> glob__100 := c(100);
> glob__pi := c(0.0);
> glob__0_5 := c(0.5);
> glob__0_8 := c(0.8);
> glob__m0_8 := c(-0.8);
> glob__0_25 := c(0.25);
> glob__0_125 := c(0.125);
> glob_prec := c(1.0e-16);
> glob_check_sign := c(1.0);
> glob_desired_digits_correct := c(8.0);
> glob_max_estimated_step_error := c(0.0);
> glob_ratio_of_radius := c(0.1);
> glob_percent_done := c(0.0);
> glob_total_exp_sec := c(0.1);
> glob_optimal_expect_sec := c(0.1);
> glob_estimated_size_answer := c(100.0);
> glob_almost_1 := c(0.9990);
> glob_clock_sec := c(0.0);
> glob_clock_start_sec := c(0.0);
> glob_disp_incr := c(0.1);
> glob_h := c(0.1);
> glob_diff_rc_fm := c(0.1);
> glob_diff_rc_fmm1 := c(0.1);
> glob_diff_rc_fmm2 := c(0.1);
> glob_diff_ord_fm := c(0.1);
> glob_diff_ord_fmm1 := c(0.1);
> glob_diff_ord_fmm2 := c(0.1);
> glob_six_term_ord_save := c(0.1);
> glob_guess_error_rc := c(0.1);
> glob_guess_error_ord := c(0.1);
> glob_least_given_sing := c(9.9e200);
> glob_least_ratio_sing := c(9.9e200);
> glob_least_3_sing := c(9.9e100);
> glob_least_6_sing := c(9.9e100);
> glob_last_good_h := c(0.1);
> glob_max_h := c(0.1);
> glob_min_h := c(0.000001);
> glob_display_interval := c(0.1);
> glob_abserr := c(0.1e-10);
> glob_relerr := c(0.1e-10);
> glob_min_pole_est := c(0.1e+10);
> glob_max_rel_trunc_err := c(0.1e-10);
> glob_max_trunc_err := c(0.1e-10);
> glob_max_hours := c(0.0);
> glob_optimal_clock_start_sec := c(0.0);
> glob_optimal_start := c(0.0);
> glob_upper_ratio_limit := c(1.0001);
> glob_lower_ratio_limit := c(0.9999);
> glob_max_sec := c(10000.0);
> glob_orig_start_sec := c(0.0);
> glob_normmax := c(0.0);
> glob_max_minutes := c(0.0);
> glob_next_display := c(0.0);
> glob_est_digits := 1;
> glob_subiter_method := 3;
> glob_html_log := true;
> glob_min_good_digits := 99999;
> glob_good_digits := 0;
> glob_min_apfp_est_good_digits := 99999;
> glob_apfp_est_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> glob_h_reason := 0;
> glob_sec_in_minute := 60 ;
> glob_min_in_hour := 60;
> glob_hours_in_day := 24;
> glob_days_in_year := 365;
> glob_sec_in_hour := 3600;
> glob_sec_in_day := 86400;
> glob_sec_in_year := 31536000;
> glob_not_yet_finished := true;
> glob_initial_pass := true;
> glob_not_yet_start_msg := true;
> glob_reached_optimal_h := false;
> glob_optimal_done := false;
> glob_type_given_pole := 0;
> glob_optimize := false;
> glob_look_poles := false;
> glob_dump_closed_form := false;
> glob_max_iter := 1000;
> glob_no_eqs := 0;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_start := 0;
> glob_iter := 0;
> # before generate set diff initial
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> # before generate init omniout const
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> ATS_MAX_TERMS := 30;
> glob_iolevel := INFO;
> # set default block
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> glob_display_flag := true;
> glob_no_eqs := 1;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := (0.0);
> glob_max_minutes := (15.0);
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/tanh_sqrtpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = tanh ( sqrt ( 2.0 * x + 3.0 ) ) ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := c(0.1);");
> omniout_str(ALWAYS,"x_end := c(5.0) ;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_h := 0.1;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_type_given_pole := 1;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_rad_poles[1,1] := c(-1.5);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_rad_poles[1,2] := c(0.0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_ord_poles[1,1] := c(0.5);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_ord_poles[1,2] := c(0.0);");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=8;");
> omniout_str(ALWAYS,"glob_max_minutes:=(3.0);");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"glob_max_iter:=100000;");
> omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.0000001);");
> omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.9999999);");
> omniout_str(ALWAYS,"glob_look_poles:=true;");
> omniout_str(ALWAYS,"glob_h:=c(0.001);");
> omniout_str(ALWAYS,"glob_display_interval:=c(0.01);");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"return(c(0.0));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := glob__0;
> glob_smallish_float := glob__0;
> glob_large_float := c(1.0e100);
> glob_larger_float := c( 1.1e100);
> glob_almost_1 := c( 0.99);
> # before second block
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #BEGIN BLOCK 2
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := c(0.1);
> x_end := c(5.0) ;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_max_h := 0.1;
> glob_type_given_pole := 1;
> array_given_rad_poles[1,1] := c(-1.5);
> array_given_rad_poles[1,2] := c(0.0);
> array_given_ord_poles[1,1] := c(0.5);
> array_given_ord_poles[1,2] := c(0.0);
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=8;
> glob_max_minutes:=(3.0);
> glob_subiter_method:=3;
> glob_max_iter:=100000;
> glob_upper_ratio_limit:=c(1.0000001);
> glob_lower_ratio_limit:=c(0.9999999);
> glob_look_poles:=true;
> glob_h:=c(0.001);
> glob_display_interval:=c(0.01);
> #END OVERRIDE BLOCK
> #END BLOCK 2
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_sec := (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours);
> # after second input block
> glob_check_sign := c(my_check_sign(x_start,x_end));
> glob__pi := arccos(glob__m1);
> glob_prec = expt(10.0,c(-Digits));
> if (glob_optimize) then # if number 9
> #BEGIN OPTIMIZE CODE
> omniout_str(ALWAYS,"START of Optimize");
> #Start Series -- INITIALIZE FOR OPTIMIZE
> found_h := false;
> glob_min_pole_est := glob_larger_float;
> last_min_pole_est := glob_larger_float;
> glob_least_given_sing := glob_larger_float;
> glob_least_ratio_sing := glob_larger_float;
> glob_least_3_sing := glob_larger_float;
> glob_least_6_sing := glob_larger_float;
> glob_min_h := float_abs(glob_min_h) * glob_check_sign;
> glob_max_h := float_abs(glob_max_h) * glob_check_sign;
> glob_h := float_abs(glob_min_h) * glob_check_sign;
> glob_display_interval := c((float_abs(c(glob_display_interval))) * (glob_check_sign));
> display_max := c(x_end) - c(x_start)/glob__10;
> if ((glob_display_interval) > (display_max)) then # if number 10
> glob_display_interval := c(display_max);
> fi;# end if 10;
> chk_data();
> min_value := glob_larger_float;
> est_answer := est_size_answer();
> opt_iter := 1;
> est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
> omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
> estimated_step_error := glob_small_float;
> while ((opt_iter <= 100) and ( not found_h)) do # do number 1
> omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,"");
> array_x[1] := c(x_start);
> array_x[2] := c(glob_h);
> glob_next_display := c(x_start);
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1));
> term_no := term_no + 1;
> od;# end do number 2;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> if (term_no < ATS_MAX_TERMS) then # if number 10
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 10;
> term_no := term_no + 1;
> od;# end do number 3;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> atomall();
> if (glob_check_sign * glob_min_h >= glob_check_sign * glob_h) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> glob_h := glob_check_sign * float_abs(glob_min_h);
> glob_h_reason := 1;
> found_h := true;
> fi;# end if 10;
> if (glob_check_sign * glob_display_interval <= glob_check_sign * glob_h) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR DISPLAY INTERVAL");
> glob_h_reason := 2;
> glob_h := glob_display_interval;
> found_h := true;
> fi;# end if 10;
> if (glob_look_poles) then # if number 10
> check_for_pole();
> fi;# end if 10;
> if ( not found_h) then # if number 10
> est_answer := est_size_answer();
> est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
> omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
> estimated_step_error := test_suggested_h();
> omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,"");
> if (estimated_step_error < est_needed_step_err) then # if number 11
> omniout_str(ALWAYS,"Double H and LOOP");
> glob_h := glob_h*glob__2;
> else
> omniout_str(ALWAYS,"Found H for OPTIMAL");
> found_h := true;
> glob_h_reason := 3;
> glob_h := glob_h/glob__2;
> fi;# end if 11;
> fi;# end if 10;
> opt_iter := opt_iter + 1;
> od;# end do number 1;
> if (( not found_h) and (opt_iter = 1)) then # if number 10
> omniout_str(ALWAYS,"Beginning glob_h too large.");
> found_h := false;
> fi;# end if 10;
> if (glob_check_sign * glob_max_h <= glob_check_sign * glob_h) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR MAX H");
> glob_h := glob_check_sign * float_abs(glob_max_h);
> glob_h_reason := 1;
> found_h := true;
> fi;# end if 10;
> else
> found_h := true;
> glob_h := glob_h * glob_check_sign;
> fi;# end if 9;
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 9
> html_log_file := fopen("entry.html",WRITE,TEXT);
> fi;# end if 9;
> #BEGIN SOLUTION CODE
> if (found_h) then # if number 9
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := c(x_start);
> array_x[2] := c(glob_h);
> glob_next_display := c(x_start);
> glob_min_pole_est := glob_larger_float;
> glob_least_given_sing := glob_larger_float;
> glob_least_ratio_sing := glob_larger_float;
> glob_least_3_sing := glob_larger_float;
> glob_least_6_sing := glob_larger_float;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 1
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1));
> term_no := term_no + 1;
> od;# end do number 1;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 1
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 2
> it := term_no + r_order - 1;
> if (term_no < ATS_MAX_TERMS) then # if number 10
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 10;
> term_no := term_no + 1;
> od;# end do number 2;
> r_order := r_order + 1;
> od;# end do number 1
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> glob_clock_sec := elapsed_time_seconds();
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_iter < glob_max_iter) and (glob_check_sign * array_x[1] < glob_check_sign * x_end ) and (((glob_clock_sec) - (glob_orig_start_sec)) < (glob_max_sec))) do # do number 1
> #left paren 0001C
> if (reached_interval()) then # if number 10
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> fi;# end if 10;
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> track_estimated_error();
> atomall();
> track_estimated_error();
> display_alot(current_iter);
> if (glob_look_poles) then # if number 10
> check_for_pole();
> fi;# end if 10;
> if (reached_interval()) then # if number 10
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 10;
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y;
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := ATS_MAX_TERMS;
> while (term_no >= 1) do # do number 2
> array_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 3
> array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 3;
> term_no := term_no - 1;
> od;# end do number 2;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> ;
> od;# end do number 1;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 10
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 10;
> if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec )) then # if number 10
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 10;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 1 ) = tanh ( sqrt ( 2.0 * x + 3.0 ) ) ; ");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 10
> logstart(html_log_file);
> logitem_str(html_log_file,"2015-05-02T18:39:08-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"tanh_sqrt")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = tanh ( sqrt ( 2.0 * x + 3.0 ) ) ; ")
> ;
> logitem_float(html_log_file,x_start)
> ;
> logitem_float(html_log_file,x_end)
> ;
> logitem_float(html_log_file,array_x[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_h_reason(html_log_file)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_float(html_log_file,glob_desired_digits_correct)
> ;
> if (array_est_digits[1] <> -16) then # if number 11
> logitem_integer(html_log_file,array_est_digits[1])
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_min_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_min_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> logitem_integer(html_log_file,ATS_MAX_TERMS)
> ;
> if (glob_type_given_pole = 0) then # if number 11
> logitem_str(html_log_file,"Not Given")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 4) then # if number 12
> logitem_str(html_log_file,"No Solution")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 5) then # if number 13
> logitem_str(html_log_file,"Some Pole")
> ;
> logitem_str(html_log_file,"????")
> ;
> elif
> (glob_type_given_pole = 3) then # if number 14
> logitem_str(html_log_file,"No Pole")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 1) then # if number 15
> logitem_str(html_log_file,"Real Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> elif
> (glob_type_given_pole = 2) then # if number 16
> logitem_str(html_log_file,"Complex Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> fi;# end if 16;
> if (glob_least_ratio_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_ratio_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_3_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_3_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_6_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_6_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_time(html_log_file,(glob_clock_sec))
> ;
> if (c(glob_percent_done) < glob__100) then # if number 16
> logitem_time(html_log_file,(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 16;
> log_revs(html_log_file," 308.maple.seems.ok | ")
> ;
> logitem_str(html_log_file,"tanh_sqrt diffeq.mxt")
> ;
> logitem_str(html_log_file,"tanh_sqrt maple results")
> ;
> logitem_str(html_log_file,"??")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 15;
> if (glob_html_log) then # if number 15
> fclose(html_log_file);
> fi;# end if 15
> ;
> ;;
> fi;# end if 14
> #END OUTFILEMAIN
> end;
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max,
term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order,
sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it,
last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err,
estimated_step_error, min_value, est_answer, found_h, repeat_it;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_prec, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_h,
glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm,
glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_six_term_ord_save,
glob_guess_error_rc, glob_guess_error_ord, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_max_h, glob_min_h, glob_display_interval,
glob_abserr, glob_relerr, glob_min_pole_est, glob_max_rel_trunc_err,
glob_max_trunc_err, glob_max_hours, glob_optimal_clock_start_sec,
glob_optimal_start, glob_upper_ratio_limit, glob_lower_ratio_limit,
glob_max_sec, glob_orig_start_sec, glob_normmax, glob_max_minutes,
glob_next_display, glob_est_digits, glob_subiter_method, glob_html_log,
glob_min_good_digits, glob_good_digits, glob_min_apfp_est_good_digits,
glob_apfp_est_good_digits, glob_max_opt_iter, glob_dump, glob_djd_debug,
glob_display_flag, glob_djd_debug2, glob_h_reason, glob_sec_in_minute,
glob_min_in_hour, glob_hours_in_day, glob_days_in_year, glob_sec_in_hour,
glob_sec_in_day, glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_3D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4_a1,
array_tmp4_a2, array_tmp4, array_tmp5, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
ATS_MAX_TERMS := 30;
Digits := 32;
max_terms := 30;
glob_html_log := true;
array_y_init := Array(0 .. 30, []);
array_norms := Array(0 .. 30, []);
array_fact_1 := Array(0 .. 30, []);
array_1st_rel_error := Array(0 .. 2, []);
array_last_rel_error := Array(0 .. 2, []);
array_est_rel_error := Array(0 .. 2, []);
array_max_est_error := Array(0 .. 2, []);
array_type_pole := Array(0 .. 2, []);
array_type_real_pole := Array(0 .. 2, []);
array_type_complex_pole := Array(0 .. 2, []);
array_est_digits := Array(0 .. 2, []);
array_y := Array(0 .. 30, []);
array_x := Array(0 .. 30, []);
array_tmp0 := Array(0 .. 30, []);
array_tmp1 := Array(0 .. 30, []);
array_tmp2 := Array(0 .. 30, []);
array_tmp3 := Array(0 .. 30, []);
array_tmp4_g := Array(0 .. 30, []);
array_tmp4_a1 := Array(0 .. 30, []);
array_tmp4_a2 := Array(0 .. 30, []);
array_tmp4 := Array(0 .. 30, []);
array_tmp5 := Array(0 .. 30, []);
array_m1 := Array(0 .. 30, []);
array_y_higher := Array(0 .. 2, 0 .. 31, []);
array_y_higher_work := Array(0 .. 2, 0 .. 31, []);
array_y_higher_work2 := Array(0 .. 2, 0 .. 31, []);
array_y_set_initial := Array(0 .. 2, 0 .. 31, []);
array_given_rad_poles := Array(0 .. 2, 0 .. 4, []);
array_given_ord_poles := Array(0 .. 2, 0 .. 4, []);
array_rad_test_poles := Array(0 .. 2, 0 .. 5, []);
array_ord_test_poles := Array(0 .. 2, 0 .. 5, []);
array_fact_2 := Array(0 .. 30, 0 .. 31, []);
term := 1;
while term <= 30 do array_y_init[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 30 do array_norms[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 30 do array_fact_1[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_1st_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do
array_last_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_est_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_max_est_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_type_pole[term] := 0; term := term + 1 end do;
term := 1;
while term <= 2 do array_type_real_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 2 do array_type_complex_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 2 do array_est_digits[term] := 0; term := term + 1 end do
;
term := 1;
while term <= 30 do array_y[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_x[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp0[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp1[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp3[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp4_g[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 30 do array_tmp4_a1[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 30 do array_tmp4_a2[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 30 do array_tmp4[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp5[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_m1[term] := c(0.); term := term + 1 end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 do
array_y_higher[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 do
array_y_higher_work[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 do
array_y_higher_work2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 do
array_y_set_initial[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_rad_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_ord_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 4 do
array_rad_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 4 do
array_ord_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 30 do
term := 1;
while term <= 30 do
array_fact_2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
zero_ats_ar(array_y);
zero_ats_ar(array_x);
zero_ats_ar(array_tmp0);
zero_ats_ar(array_tmp1);
zero_ats_ar(array_tmp2);
zero_ats_ar(array_tmp3);
zero_ats_ar(array_tmp4_g);
zero_ats_ar(array_tmp4_a1);
zero_ats_ar(array_tmp4_a2);
zero_ats_ar(array_tmp4);
zero_ats_ar(array_tmp5);
zero_ats_ar(array_m1);
zero_ats_ar(array_const_1);
array_const_1[1] := c(1);
zero_ats_ar(array_const_0D0);
array_const_0D0[1] := c(0.);
zero_ats_ar(array_const_2D0);
array_const_2D0[1] := c(2.0);
zero_ats_ar(array_const_3D0);
array_const_3D0[1] := c(3.0);
zero_ats_ar(array_m1);
array_m1[1] := glob__m1;
iiif := 0;
while iiif <= ATS_MAX_TERMS do
jjjf := 0;
while jjjf <= ATS_MAX_TERMS do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
glob_yes_pole := 4;
glob_no_pole := 3;
glob_not_given := 0;
glob_no_sing_tests := 4;
glob_ratio_test := 1;
glob_three_term_test := 2;
glob_six_term_test := 3;
glob_log_10 := log(c(10.0));
MAX_UNCHANGED := 10;
glob__small := c(0.1*10^(-50));
glob_small_float := c(0.1*10^(-50));
glob_smallish_float := c(0.1*10^(-60));
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob__m2 := c(-2);
glob__m1 := c(-1);
glob__0 := c(0);
glob__1 := c(1);
glob__2 := c(2);
glob__3 := c(3);
glob__4 := c(4);
glob__5 := c(5);
glob__8 := c(8);
glob__10 := c(10);
glob__100 := c(100);
glob__pi := c(0.);
glob__0_5 := c(0.5);
glob__0_8 := c(0.8);
glob__m0_8 := c(-0.8);
glob__0_25 := c(0.25);
glob__0_125 := c(0.125);
glob_prec := c(0.10*10^(-15));
glob_check_sign := c(1.0);
glob_desired_digits_correct := c(8.0);
glob_max_estimated_step_error := c(0.);
glob_ratio_of_radius := c(0.1);
glob_percent_done := c(0.);
glob_total_exp_sec := c(0.1);
glob_optimal_expect_sec := c(0.1);
glob_estimated_size_answer := c(100.0);
glob_almost_1 := c(0.9990);
glob_clock_sec := c(0.);
glob_clock_start_sec := c(0.);
glob_disp_incr := c(0.1);
glob_h := c(0.1);
glob_diff_rc_fm := c(0.1);
glob_diff_rc_fmm1 := c(0.1);
glob_diff_rc_fmm2 := c(0.1);
glob_diff_ord_fm := c(0.1);
glob_diff_ord_fmm1 := c(0.1);
glob_diff_ord_fmm2 := c(0.1);
glob_six_term_ord_save := c(0.1);
glob_guess_error_rc := c(0.1);
glob_guess_error_ord := c(0.1);
glob_least_given_sing := c(0.99*10^201);
glob_least_ratio_sing := c(0.99*10^201);
glob_least_3_sing := c(0.99*10^101);
glob_least_6_sing := c(0.99*10^101);
glob_last_good_h := c(0.1);
glob_max_h := c(0.1);
glob_min_h := c(0.1*10^(-5));
glob_display_interval := c(0.1);
glob_abserr := c(0.1*10^(-10));
glob_relerr := c(0.1*10^(-10));
glob_min_pole_est := c(0.1*10^10);
glob_max_rel_trunc_err := c(0.1*10^(-10));
glob_max_trunc_err := c(0.1*10^(-10));
glob_max_hours := c(0.);
glob_optimal_clock_start_sec := c(0.);
glob_optimal_start := c(0.);
glob_upper_ratio_limit := c(1.0001);
glob_lower_ratio_limit := c(0.9999);
glob_max_sec := c(10000.0);
glob_orig_start_sec := c(0.);
glob_normmax := c(0.);
glob_max_minutes := c(0.);
glob_next_display := c(0.);
glob_est_digits := 1;
glob_subiter_method := 3;
glob_html_log := true;
glob_min_good_digits := 99999;
glob_good_digits := 0;
glob_min_apfp_est_good_digits := 99999;
glob_apfp_est_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
glob_h_reason := 0;
glob_sec_in_minute := 60;
glob_min_in_hour := 60;
glob_hours_in_day := 24;
glob_days_in_year := 365;
glob_sec_in_hour := 3600;
glob_sec_in_day := 86400;
glob_sec_in_year := 31536000;
glob_not_yet_finished := true;
glob_initial_pass := true;
glob_not_yet_start_msg := true;
glob_reached_optimal_h := false;
glob_optimal_done := false;
glob_type_given_pole := 0;
glob_optimize := false;
glob_look_poles := false;
glob_dump_closed_form := false;
glob_max_iter := 1000;
glob_no_eqs := 0;
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_start := 0;
glob_iter := 0;
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
ATS_MAX_TERMS := 30;
glob_iolevel := INFO;
glob_orig_start_sec := elapsed_time_seconds();
glob_display_flag := true;
glob_no_eqs := 1;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/tanh_sqrtpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = tanh ( sqrt ( 2.0\
* x + 3.0 ) ) ; ");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := c(0.1);");
omniout_str(ALWAYS, "x_end := c(5.0) ;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_h := 0.1;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_type_given_pole := 1;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_rad_poles[1,1] := c(-1.5);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_rad_poles[1,2] := c(0.0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_ord_poles[1,1] := c(0.5);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_ord_poles[1,2] := c(0.0);");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=8;");
omniout_str(ALWAYS, "glob_max_minutes:=(3.0);");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "glob_max_iter:=100000;");
omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.0000001);");
omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.9999999);");
omniout_str(ALWAYS, "glob_look_poles:=true;");
omniout_str(ALWAYS, "glob_h:=c(0.001);");
omniout_str(ALWAYS, "glob_display_interval:=c(0.01);");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "return(c(0.0));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := glob__0;
glob_smallish_float := glob__0;
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob_almost_1 := c(0.99);
x_start := c(0.1);
x_end := c(5.0);
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_h := 0.1;
glob_type_given_pole := 1;
array_given_rad_poles[1, 1] := c(-1.5);
array_given_rad_poles[1, 2] := c(0.);
array_given_ord_poles[1, 1] := c(0.5);
array_given_ord_poles[1, 2] := c(0.);
glob_desired_digits_correct := 8;
glob_max_minutes := 3.0;
glob_subiter_method := 3;
glob_max_iter := 100000;
glob_upper_ratio_limit := c(1.0000001);
glob_lower_ratio_limit := c(0.9999999);
glob_look_poles := true;
glob_h := c(0.001);
glob_display_interval := c(0.01);
glob_last_good_h := glob_h;
glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours;
glob_check_sign := c(my_check_sign(x_start, x_end));
glob__pi := arccos(glob__m1);
glob_prec = expt(10.0, c(-Digits));
if glob_optimize then
omniout_str(ALWAYS, "START of Optimize");
found_h := false;
glob_min_pole_est := glob_larger_float;
last_min_pole_est := glob_larger_float;
glob_least_given_sing := glob_larger_float;
glob_least_ratio_sing := glob_larger_float;
glob_least_3_sing := glob_larger_float;
glob_least_6_sing := glob_larger_float;
glob_min_h := float_abs(glob_min_h)*glob_check_sign;
glob_max_h := float_abs(glob_max_h)*glob_check_sign;
glob_h := float_abs(glob_min_h)*glob_check_sign;
glob_display_interval :=
c(float_abs(c(glob_display_interval))*glob_check_sign);
display_max := c(x_end) - c(x_start)/glob__10;
if display_max < glob_display_interval then
glob_display_interval := c(display_max)
end if;
chk_data();
min_value := glob_larger_float;
est_answer := est_size_answer();
opt_iter := 1;
est_needed_step_err :=
estimated_needed_step_error(x_start, x_end, glob_h, est_answer)
;
omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, "");
estimated_step_error := glob_small_float;
while opt_iter <= 100 and not found_h do
omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, "");
array_x[1] := c(x_start);
array_x[2] := c(glob_h);
glob_next_display := c(x_start);
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, c(term_no - 1))/
c(factorial_1(term_no - 1));
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
if term_no < ATS_MAX_TERMS then
array_y_higher[r_order, term_no] :=
array_y_init[it]*expt(glob_h, c(term_no - 1))/
c(factorial_1(term_no - 1))
end if;
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
atomall();
if glob_check_sign*glob_h <= glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
glob_h := float_abs(glob_min_h)*glob_check_sign;
glob_h_reason := 1;
found_h := true
end if;
if
glob_check_sign*glob_display_interval <= glob_check_sign*glob_h
then
omniout_str(ALWAYS, "SETTING H FOR DISPLAY INTERVAL");
glob_h_reason := 2;
glob_h := glob_display_interval;
found_h := true
end if;
if glob_look_poles then check_for_pole() end if;
if not found_h then
est_answer := est_size_answer();
est_needed_step_err := estimated_needed_step_error(x_start,
x_end, glob_h, est_answer);
omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, "");
estimated_step_error := test_suggested_h();
omniout_float(ALWAYS, "estimated_step_error", 32,
estimated_step_error, 32, "");
if estimated_step_error < est_needed_step_err then
omniout_str(ALWAYS, "Double H and LOOP");
glob_h := glob_h*glob__2
else
omniout_str(ALWAYS, "Found H for OPTIMAL");
found_h := true;
glob_h_reason := 3;
glob_h := glob_h/glob__2
end if
end if;
opt_iter := opt_iter + 1
end do;
if not found_h and opt_iter = 1 then
omniout_str(ALWAYS, "Beginning glob_h too large.");
found_h := false
end if;
if glob_check_sign*glob_max_h <= glob_check_sign*glob_h then
omniout_str(ALWAYS, "SETTING H FOR MAX H");
glob_h := float_abs(glob_max_h)*glob_check_sign;
glob_h_reason := 1;
found_h := true
end if
else found_h := true; glob_h := glob_check_sign*glob_h
end if;
if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT)
end if;
if found_h then
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := c(x_start);
array_x[2] := c(glob_h);
glob_next_display := c(x_start);
glob_min_pole_est := glob_larger_float;
glob_least_given_sing := glob_larger_float;
glob_least_ratio_sing := glob_larger_float;
glob_least_3_sing := glob_larger_float;
glob_least_6_sing := glob_larger_float;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1));
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
if term_no < ATS_MAX_TERMS then
array_y_higher[r_order, term_no] := array_y_init[it]*
expt(glob_h, c(term_no - 1))/
c(factorial_1(term_no - 1))
end if;
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
glob_clock_sec := elapsed_time_seconds();
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_iter < glob_max_iter and
glob_check_sign*array_x[1] < glob_check_sign*x_end and
glob_clock_sec - glob_orig_start_sec < glob_max_sec do
if reached_interval() then
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop")
end if;
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
track_estimated_error();
atomall();
track_estimated_error();
display_alot(current_iter);
if glob_look_poles then check_for_pole() end if;
if reached_interval() then glob_next_display :=
glob_next_display + glob_display_interval
end if;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
term_no := ATS_MAX_TERMS;
while 1 <= term_no do
array_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if glob_max_sec <= elapsed_time_seconds() - glob_orig_start_sec
then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff ( y , x , 1 ) = tanh ( sqrt ( 2\
.0 * x + 3.0 ) ) ; ");
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, "2015-05-02T18:39:08-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"tanh_sqrt");
logitem_str(html_log_file, "diff ( y , x , 1 ) = ta\
nh ( sqrt ( 2.0 * x + 3.0 ) ) ; ");
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, "tanh_sqrt diffeq.mxt");
logitem_str(html_log_file, "tanh_sqrt maple results");
logitem_str(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/tanh_sqrtpostode.ode#################
diff ( y , x , 1 ) = tanh ( sqrt ( 2.0 * x + 3.0 ) ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := c(0.1);
x_end := c(5.0) ;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_h := 0.1;
glob_type_given_pole := 1;
array_given_rad_poles[1,1] := c(-1.5);
array_given_rad_poles[1,2] := c(0.0);
array_given_ord_poles[1,1] := c(0.5);
array_given_ord_poles[1,2] := c(0.0);
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=8;
glob_max_minutes:=(3.0);
glob_subiter_method:=3;
glob_max_iter:=100000;
glob_upper_ratio_limit:=c(1.0000001);
glob_lower_ratio_limit:=c(0.9999999);
glob_look_poles:=true;
glob_h:=c(0.001);
glob_display_interval:=c(0.01);
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return(c(0.0));
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
TOP MAIN SOLVE Loop
x[1] = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 0
memory used=4.3MB, alloc=40.3MB, time=0.08
absolute error = 0
relative error = -1 %
Desired digits = 8
Estimated correct digits = -16
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 1.6
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.11
y[1] (closed_form) = 0
y[1] (numeric) = 0.0094590443916663969645925910802989
absolute error = 0.0094590443916663969645925910802989
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 1.61
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.12
y[1] (closed_form) = 0
y[1] (numeric) = 0.018923925070309697281451477238366
absolute error = 0.018923925070309697281451477238366
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 1.62
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=35.6MB, alloc=44.3MB, time=0.42
TOP MAIN SOLVE Loop
x[1] = 0.13
y[1] (closed_form) = 0
y[1] (numeric) = 0.028394563018230195767219458177815
absolute error = 0.028394563018230195767219458177815
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 1.63
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.14
y[1] (closed_form) = 0
y[1] (numeric) = 0.037870880543987960601016329501099
absolute error = 0.037870880543987960601016329501099
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 1.64
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.15
y[1] (closed_form) = 0
y[1] (numeric) = 0.047352801255258205072623974894738
absolute error = 0.047352801255258205072623974894738
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 1.65
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=79.6MB, alloc=52.3MB, time=0.89
TOP MAIN SOLVE Loop
x[1] = 0.16
y[1] (closed_form) = 0
y[1] (numeric) = 0.056840250032352381573685999439139
absolute error = 0.056840250032352381573685999439139
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 1.66
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.17
y[1] (closed_form) = 0
y[1] (numeric) = 0.066333153002385754410140866943441
absolute error = 0.066333153002385754410140866943441
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 1.67
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.18
y[1] (closed_form) = 0
y[1] (numeric) = 0.075831437514072853977189514601243
absolute error = 0.075831437514072853977189514601243
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 1.68
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=123.8MB, alloc=52.3MB, time=1.36
TOP MAIN SOLVE Loop
x[1] = 0.19
y[1] (closed_form) = 0
y[1] (numeric) = 0.085335032113132835949885035836124
absolute error = 0.085335032113132835949885035836124
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 1.69
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.2
y[1] (closed_form) = 0
y[1] (numeric) = 0.094843866518287366485838594619938
absolute error = 0.094843866518287366485838594619938
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 1.7
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.21
y[1] (closed_form) = 0
y[1] (numeric) = 0.10435787159783422904159333608539
absolute error = 0.10435787159783422904159333608539
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 1.71
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=167.8MB, alloc=52.3MB, time=1.81
TOP MAIN SOLVE Loop
x[1] = 0.22
y[1] (closed_form) = 0
y[1] (numeric) = 0.11387697934678040125093994777782
absolute error = 0.11387697934678040125093994777782
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 1.72
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.23
y[1] (closed_form) = 0
y[1] (numeric) = 0.12340112286451888233452467005861
absolute error = 0.12340112286451888233452467005861
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 1.73
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.24
y[1] (closed_form) = 0
y[1] (numeric) = 0.13293023633303406359343734141664
absolute error = 0.13293023633303406359343734141664
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 1.74
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=211.9MB, alloc=52.3MB, time=2.28
TOP MAIN SOLVE Loop
x[1] = 0.25
y[1] (closed_form) = 0
y[1] (numeric) = 0.14246425499562092753056755049755
absolute error = 0.14246425499562092753056755049755
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 1.75
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.26
y[1] (closed_form) = 0
y[1] (numeric) = 0.1520031151361038358477312673416
absolute error = 0.1520031151361038358477312673416
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 1.76
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.27
y[1] (closed_form) = 0
y[1] (numeric) = 0.16154675405854112375121010292233
absolute error = 0.16154675405854112375121010292233
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 1.77
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=256.0MB, alloc=52.3MB, time=2.73
TOP MAIN SOLVE Loop
x[1] = 0.28
y[1] (closed_form) = 0
y[1] (numeric) = 0.17109511006740215839467670868918
absolute error = 0.17109511006740215839467670868918
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 1.78
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.29
y[1] (closed_form) = 0
y[1] (numeric) = 0.1806481224482039435936014081363
absolute error = 0.1806481224482039435936014081363
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 1.79
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.3
y[1] (closed_form) = 0
y[1] (numeric) = 0.19020573144859476182384856645736
absolute error = 0.19020573144859476182384856645736
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 1.8
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.31
y[1] (closed_form) = 0
y[1] (numeric) = 0.19976787825987273860325063341742
absolute error = 0.19976787825987273860325063341742
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 1.81
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=300.2MB, alloc=52.3MB, time=3.20
TOP MAIN SOLVE Loop
x[1] = 0.32
y[1] (closed_form) = 0
y[1] (numeric) = 0.2093345049989275942533149571217
absolute error = 0.2093345049989275942533149571217
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 1.82
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.33
y[1] (closed_form) = 0
y[1] (numeric) = 0.21890555469059421432602883049816
absolute error = 0.21890555469059421432602883049816
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 1.83
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.34
y[1] (closed_form) = 0
y[1] (numeric) = 0.2284809712504070232088739270448
absolute error = 0.2284809712504070232088739270448
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 1.84
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=344.3MB, alloc=52.3MB, time=3.67
TOP MAIN SOLVE Loop
x[1] = 0.35
y[1] (closed_form) = 0
y[1] (numeric) = 0.23806069946774448611559580178966
absolute error = 0.23806069946774448611559580178966
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 1.85
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.36
y[1] (closed_form) = 0
y[1] (numeric) = 0.24764468498935339333326359041076
absolute error = 0.24764468498935339333326359041076
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 1.86
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.37
y[1] (closed_form) = 0
y[1] (numeric) = 0.25723287430324289770746041251347
absolute error = 0.25723287430324289770746041251347
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 1.87
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=388.3MB, alloc=52.3MB, time=4.13
TOP MAIN SOLVE Loop
x[1] = 0.38
y[1] (closed_form) = 0
y[1] (numeric) = 0.26682521472293858236543950956343
absolute error = 0.26682521472293858236543950956343
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 1.88
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.39
y[1] (closed_form) = 0
y[1] (numeric) = 0.27642165437208713103980673378394
absolute error = 0.27642165437208713103980673378394
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 1.89
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.4
y[1] (closed_form) = 0
y[1] (numeric) = 0.28602214216940245848145630894161
absolute error = 0.28602214216940245848145630894161
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 1.9
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=432.4MB, alloc=52.3MB, time=4.59
TOP MAIN SOLVE Loop
x[1] = 0.41
y[1] (closed_form) = 0
y[1] (numeric) = 0.29562662781394443374041633682606
absolute error = 0.29562662781394443374041633682606
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 1.91
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.42
y[1] (closed_form) = 0
y[1] (numeric) = 0.30523506177072159492978307895621
absolute error = 0.30523506177072159492978307895621
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 1.92
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.43
y[1] (closed_form) = 0
y[1] (numeric) = 0.3148473952566095108372221381185
absolute error = 0.3148473952566095108372221381185
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 1.93
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=476.5MB, alloc=52.3MB, time=5.05
TOP MAIN SOLVE Loop
x[1] = 0.44
y[1] (closed_form) = 0
y[1] (numeric) = 0.32446358022657669276092916366517
absolute error = 0.32446358022657669276092916366517
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 1.94
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.45
y[1] (closed_form) = 0
y[1] (numeric) = 0.33408356936021019955772594759338
absolute error = 0.33408356936021019955772594759338
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 1.95
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.46
y[1] (closed_form) = 0
y[1] (numeric) = 0.34370731604853331042100677143895
absolute error = 0.34370731604853331042100677143895
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 1.96
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=520.4MB, alloc=52.3MB, time=5.51
TOP MAIN SOLVE Loop
x[1] = 0.47
y[1] (closed_form) = 0
y[1] (numeric) = 0.35333477438110786366274681077105
absolute error = 0.35333477438110786366274681077105
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 1.97
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.48
y[1] (closed_form) = 0
y[1] (numeric) = 0.36296589913341407605090272669618
absolute error = 0.36296589913341407605090272669618
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 1.98
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.49
y[1] (closed_form) = 0
y[1] (numeric) = 0.37260064575450086633301244054403
absolute error = 0.37260064575450086633301244054403
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 1.99
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=564.6MB, alloc=52.3MB, time=5.98
TOP MAIN SOLVE Loop
x[1] = 0.5
y[1] (closed_form) = 0
y[1] (numeric) = 0.38223897035489990872852834161645
absolute error = 0.38223897035489990872852834161645
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.51
y[1] (closed_form) = 0
y[1] (numeric) = 0.39188082969479683765499344224117
absolute error = 0.39188082969479683765499344224117
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.01
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.52
y[1] (closed_form) = 0
y[1] (numeric) = 0.40152618117245321401441962750352
absolute error = 0.40152618117245321401441962750352
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.02
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.53
y[1] (closed_form) = 0
y[1] (numeric) = 0.4111749828128730462437026100089
absolute error = 0.4111749828128730462437026100089
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.03
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=608.6MB, alloc=52.3MB, time=6.44
TOP MAIN SOLVE Loop
x[1] = 0.54
y[1] (closed_form) = 0
y[1] (numeric) = 0.4208271932567078362543573138409
absolute error = 0.4208271932567078362543573138409
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.04
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.55
y[1] (closed_form) = 0
y[1] (numeric) = 0.43048277174939429157067188765739
absolute error = 0.43048277174939429157067188765739
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.05
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.56
y[1] (closed_form) = 0
y[1] (numeric) = 0.44014167813051901063101909159334
absolute error = 0.44014167813051901063101909159334
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.06
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=652.8MB, alloc=52.3MB, time=6.91
TOP MAIN SOLVE Loop
x[1] = 0.57
y[1] (closed_form) = 0
y[1] (numeric) = 0.44980387282340460854546402508332
absolute error = 0.44980387282340460854546402508332
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.07
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.58
y[1] (closed_form) = 0
y[1] (numeric) = 0.45946931682491190579675743191222
absolute error = 0.45946931682491190579675743191222
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.08
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.59
y[1] (closed_form) = 0
y[1] (numeric) = 0.46913797169545295261631615954322
absolute error = 0.46913797169545295261631615954322
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.09
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=696.8MB, alloc=52.3MB, time=7.36
TOP MAIN SOLVE Loop
x[1] = 0.6
y[1] (closed_form) = 0
y[1] (numeric) = 0.47880979954920980723944739608592
absolute error = 0.47880979954920980723944739608592
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.1
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.61
y[1] (closed_form) = 0
y[1] (numeric) = 0.48848476304455412711535027625671
absolute error = 0.48848476304455412711535027625671
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.11
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.62
y[1] (closed_form) = 0
y[1] (numeric) = 0.49816282537466276858101903338665
absolute error = 0.49816282537466276858101903338665
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.12
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=740.7MB, alloc=52.3MB, time=7.83
TOP MAIN SOLVE Loop
x[1] = 0.63
y[1] (closed_form) = 0
y[1] (numeric) = 0.50784395025832472266127893010453
absolute error = 0.50784395025832472266127893010453
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.13
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.64
y[1] (closed_form) = 0
y[1] (numeric) = 0.51752810193093484268080799281962
absolute error = 0.51752810193093484268080799281962
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.14
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.65
y[1] (closed_form) = 0
y[1] (numeric) = 0.52721524513566994341319838614271
absolute error = 0.52721524513566994341319838614271
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.15
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=784.8MB, alloc=52.3MB, time=8.30
TOP MAIN SOLVE Loop
x[1] = 0.66
y[1] (closed_form) = 0
y[1] (numeric) = 0.53690534511484297168627904460778
absolute error = 0.53690534511484297168627904460778
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.16
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.67
y[1] (closed_form) = 0
y[1] (numeric) = 0.54659836760143106484601293830893
absolute error = 0.54659836760143106484601293830893
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.17
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.68
y[1] (closed_form) = 0
y[1] (numeric) = 0.55629427881077342638205790327931
absolute error = 0.55629427881077342638205790327931
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.18
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=828.9MB, alloc=52.3MB, time=8.75
TOP MAIN SOLVE Loop
x[1] = 0.69
y[1] (closed_form) = 0
y[1] (numeric) = 0.56599304543243505746032466330383
absolute error = 0.56599304543243505746032466330383
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.19
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.7
y[1] (closed_form) = 0
y[1] (numeric) = 0.57569463462223248921060263933209
absolute error = 0.57569463462223248921060263933209
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.2
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.71
y[1] (closed_form) = 0
y[1] (numeric) = 0.58539901399441776349501662885362
absolute error = 0.58539901399441776349501662885362
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.21
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=873.1MB, alloc=52.3MB, time=9.22
TOP MAIN SOLVE Loop
x[1] = 0.72
y[1] (closed_form) = 0
y[1] (numeric) = 0.59510615161401700964582169701906
absolute error = 0.59510615161401700964582169701906
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.22
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.73
y[1] (closed_form) = 0
y[1] (numeric) = 0.60481601598932006141475288038332
absolute error = 0.60481601598932006141475288038332
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.23
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.74
y[1] (closed_form) = 0
y[1] (numeric) = 0.6145285760645176522227262219586
absolute error = 0.6145285760645176522227262219586
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.24
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.75
y[1] (closed_form) = 0
y[1] (numeric) = 0.62424380121248281783620372024484
memory used=917.3MB, alloc=52.3MB, time=9.69
absolute error = 0.62424380121248281783620372024484
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.25
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.76
y[1] (closed_form) = 0
y[1] (numeric) = 0.63396166122769322391937203370401
absolute error = 0.63396166122769322391937203370401
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.26
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.77
y[1] (closed_form) = 0
y[1] (numeric) = 0.64368212631929122161030029733128
absolute error = 0.64368212631929122161030029733128
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.27
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.78
y[1] (closed_form) = 0
y[1] (numeric) = 0.65340516710427851743191078602235
absolute error = 0.65340516710427851743191078602235
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.28
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=961.3MB, alloc=52.3MB, time=10.14
TOP MAIN SOLVE Loop
x[1] = 0.79
y[1] (closed_form) = 0
y[1] (numeric) = 0.66313075460084242455914850590862
absolute error = 0.66313075460084242455914850590862
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.29
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.8
y[1] (closed_form) = 0
y[1] (numeric) = 0.67285886022181074080329241442031
absolute error = 0.67285886022181074080329241442031
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.3
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.81
y[1] (closed_form) = 0
y[1] (numeric) = 0.68258945576823237472104811865592
absolute error = 0.68258945576823237472104811865592
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.31
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1005.4MB, alloc=52.3MB, time=10.61
TOP MAIN SOLVE Loop
x[1] = 0.82
y[1] (closed_form) = 0
y[1] (numeric) = 0.69232251342308091508517288194017
absolute error = 0.69232251342308091508517288194017
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.32
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.83
y[1] (closed_form) = 0
y[1] (numeric) = 0.70205800574507841063743464065346
absolute error = 0.70205800574507841063743464065346
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.33
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.84
y[1] (closed_form) = 0
y[1] (numeric) = 0.71179590566263669665358690575941
absolute error = 0.71179590566263669665358690575941
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.34
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1049.5MB, alloc=52.3MB, time=11.08
TOP MAIN SOLVE Loop
x[1] = 0.85
y[1] (closed_form) = 0
y[1] (numeric) = 0.72153618646791367245110936617181
absolute error = 0.72153618646791367245110936617181
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.35
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.86
y[1] (closed_form) = 0
y[1] (numeric) = 0.73127882181098199962864832890006
absolute error = 0.73127882181098199962864832890006
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.36
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.87
y[1] (closed_form) = 0
y[1] (numeric) = 0.74102378569410775460398721562756
absolute error = 0.74102378569410775460398721562756
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.37
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1093.7MB, alloc=52.3MB, time=11.53
TOP MAIN SOLVE Loop
x[1] = 0.88
y[1] (closed_form) = 0
y[1] (numeric) = 0.75077105246613663097533980903667
absolute error = 0.75077105246613663097533980903667
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.38
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.89
y[1] (closed_form) = 0
y[1] (numeric) = 0.76052059681698534742699009000688
absolute error = 0.76052059681698534742699009000688
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.39
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.9
y[1] (closed_form) = 0
y[1] (numeric) = 0.77027239377223597539093688932541
absolute error = 0.77027239377223597539093688932541
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.4
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1137.8MB, alloc=52.3MB, time=12.00
TOP MAIN SOLVE Loop
x[1] = 0.91
y[1] (closed_form) = 0
y[1] (numeric) = 0.78002641868783095751538700157011
absolute error = 0.78002641868783095751538700157011
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.41
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.92
y[1] (closed_form) = 0
y[1] (numeric) = 0.78978264724486664323091542755906
absolute error = 0.78978264724486664323091542755906
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.42
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.93
y[1] (closed_form) = 0
y[1] (numeric) = 0.79954105544448322139627951601596
absolute error = 0.79954105544448322139627951601596
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.43
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1181.8MB, alloc=52.3MB, time=12.47
TOP MAIN SOLVE Loop
x[1] = 0.94
y[1] (closed_form) = 0
y[1] (numeric) = 0.80930161960284898219687442919533
absolute error = 0.80930161960284898219687442919533
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.44
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.95
y[1] (closed_form) = 0
y[1] (numeric) = 0.81906431634623689120659402557597
absolute error = 0.81906431634623689120659402557597
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.45
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.96
y[1] (closed_form) = 0
y[1] (numeric) = 0.82882912260619150785372655581346
absolute error = 0.82882912260619150785372655581346
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.46
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=1225.8MB, alloc=52.3MB, time=12.92
x[1] = 0.97
y[1] (closed_form) = 0
y[1] (numeric) = 0.83859601561478432849721269939143
absolute error = 0.83859601561478432849721269939143
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.47
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.98
y[1] (closed_form) = 0
y[1] (numeric) = 0.84836497289995568096335999851797
absolute error = 0.84836497289995568096335999851797
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.48
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 0.99
y[1] (closed_form) = 0
y[1] (numeric) = 0.85813597228094134275572692723828
absolute error = 0.85813597228094134275572692723828
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.49
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1
y[1] (closed_form) = 0
y[1] (numeric) = 0.86790899186378209927174953367205
absolute error = 0.86790899186378209927174953367205
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.5
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1270.0MB, alloc=52.3MB, time=13.39
TOP MAIN SOLVE Loop
x[1] = 1.01
y[1] (closed_form) = 0
y[1] (numeric) = 0.87768401003691450127682794266353
absolute error = 0.87768401003691450127682794266353
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.51
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.02
y[1] (closed_form) = 0
y[1] (numeric) = 0.8874610054668411226367698820163
absolute error = 0.8874610054668411226367698820163
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.52
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.03
y[1] (closed_form) = 0
y[1] (numeric) = 0.8972399570938786599282098282229
absolute error = 0.8972399570938786599282098282229
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.53
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1314.1MB, alloc=52.3MB, time=13.86
TOP MAIN SOLVE Loop
x[1] = 1.04
y[1] (closed_form) = 0
y[1] (numeric) = 0.90702084412798225506819296638869
absolute error = 0.90702084412798225506819296638869
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.54
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.05
y[1] (closed_form) = 0
y[1] (numeric) = 0.91680364604464446056168664407852
absolute error = 0.91680364604464446056168664407852
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.55
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.06
y[1] (closed_form) = 0
y[1] (numeric) = 0.92658834258086730439140092392899
absolute error = 0.92658834258086730439140092392899
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.56
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1358.1MB, alloc=52.3MB, time=14.31
TOP MAIN SOLVE Loop
x[1] = 1.07
y[1] (closed_form) = 0
y[1] (numeric) = 0.93637491373120594799893658565372
absolute error = 0.93637491373120594799893658565372
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.57
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.08
y[1] (closed_form) = 0
y[1] (numeric) = 0.94616333974388246625987504146807
absolute error = 0.94616333974388246625987504146807
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.58
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.09
y[1] (closed_form) = 0
y[1] (numeric) = 0.9559536011169683128669285818956
absolute error = 0.9559536011169683128669285818956
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.59
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1402.1MB, alloc=52.3MB, time=14.78
TOP MAIN SOLVE Loop
x[1] = 1.1
y[1] (closed_form) = 0
y[1] (numeric) = 0.96574567859463406813267280495381
absolute error = 0.96574567859463406813267280495381
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.6
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.11
y[1] (closed_form) = 0
y[1] (numeric) = 0.97553955316346509893375561656632
absolute error = 0.97553955316346509893375561656632
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.61
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.12
y[1] (closed_form) = 0
y[1] (numeric) = 0.98533520604884179236799982859837
absolute error = 0.98533520604884179236799982859837
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.62
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1446.3MB, alloc=52.3MB, time=15.25
TOP MAIN SOLVE Loop
x[1] = 1.13
y[1] (closed_form) = 0
y[1] (numeric) = 0.99513261871138305570981361054384
absolute error = 0.99513261871138305570981361054384
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.63
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.14
y[1] (closed_form) = 0
y[1] (numeric) = 1.0049317728434518054522936680356
absolute error = 1.0049317728434518054522936680356
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.64
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.15
y[1] (closed_form) = 0
y[1] (numeric) = 1.0147326503657211976400527456242
absolute error = 1.0147326503657211976400527456242
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.65
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1490.3MB, alloc=52.3MB, time=15.70
TOP MAIN SOLVE Loop
x[1] = 1.16
y[1] (closed_form) = 0
y[1] (numeric) = 1.0245352334238003803480609789697
absolute error = 1.0245352334238003803480609789697
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.66
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.17
y[1] (closed_form) = 0
y[1] (numeric) = 1.034339504384918577070854567984
absolute error = 1.034339504384918577070854567984
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.67
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.18
y[1] (closed_form) = 0
y[1] (numeric) = 1.0441454458346663369748160199549
absolute error = 1.0441454458346663369748160199549
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.68
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=1534.3MB, alloc=52.3MB, time=16.17
x[1] = 1.19
y[1] (closed_form) = 0
y[1] (numeric) = 1.0539530405737928144546598889351
absolute error = 1.0539530405737928144546598889351
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.69
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.2
y[1] (closed_form) = 0
y[1] (numeric) = 1.0637622716150579662438941225024
absolute error = 1.0637622716150579662438941225024
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.7
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.21
y[1] (closed_form) = 0
y[1] (numeric) = 1.0735731221801385794773563139946
absolute error = 1.0735731221801385794773563139946
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.71
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.22
y[1] (closed_form) = 0
y[1] (numeric) = 1.0833855756965870686108141805787
absolute error = 1.0833855756965870686108141805787
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.72
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1578.5MB, alloc=52.3MB, time=16.64
TOP MAIN SOLVE Loop
x[1] = 1.23
y[1] (closed_form) = 0
y[1] (numeric) = 1.0931996157948420029863412093179
absolute error = 1.0931996157948420029863412093179
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.73
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.24
y[1] (closed_form) = 0
y[1] (numeric) = 1.1030152263052893501104261000608
absolute error = 1.1030152263052893501104261000608
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.74
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.25
y[1] (closed_form) = 0
y[1] (numeric) = 1.1128323912553734424016865325324
absolute error = 1.1128323912553734424016865325324
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.75
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1622.6MB, alloc=52.3MB, time=17.09
TOP MAIN SOLVE Loop
x[1] = 1.26
y[1] (closed_form) = 0
y[1] (numeric) = 1.1226510948667566972832349484374
absolute error = 1.1226510948667566972832349484374
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.76
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.27
y[1] (closed_form) = 0
y[1] (numeric) = 1.1324713215525271420572689254916
absolute error = 1.1324713215525271420572689254916
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.77
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.28
y[1] (closed_form) = 0
y[1] (numeric) = 1.1422930559144528160219129948723
absolute error = 1.1422930559144528160219129948723
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.78
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1666.8MB, alloc=52.3MB, time=17.56
TOP MAIN SOLVE Loop
x[1] = 1.29
y[1] (closed_form) = 0
y[1] (numeric) = 1.1521162827402821427878204262658
absolute error = 1.1521162827402821427878204262658
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.79
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.3
y[1] (closed_form) = 0
y[1] (numeric) = 1.1619409870010893857391834248505
absolute error = 1.1619409870010893857391834248505
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.8
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.31
y[1] (closed_form) = 0
y[1] (numeric) = 1.1717671538486643190747779227017
absolute error = 1.1717671538486643190747779227017
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.81
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1710.9MB, alloc=52.3MB, time=18.03
TOP MAIN SOLVE Loop
x[1] = 1.32
y[1] (closed_form) = 0
y[1] (numeric) = 1.1815947686129452658732282873315
absolute error = 1.1815947686129452658732282873315
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.82
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.33
y[1] (closed_form) = 0
y[1] (numeric) = 1.191423816799494673166140136492
absolute error = 1.191423816799494673166140136492
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.83
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.34
y[1] (closed_form) = 0
y[1] (numeric) = 1.2012542840870164120860312889118
absolute error = 1.2012542840870164120860312889118
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.84
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1755.0MB, alloc=52.3MB, time=18.48
TOP MAIN SOLVE Loop
x[1] = 1.35
y[1] (closed_form) = 0
y[1] (numeric) = 1.2110861563249140087956135295266
absolute error = 1.2110861563249140087956135295266
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.85
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.36
y[1] (closed_form) = 0
y[1] (numeric) = 1.2209194195308890291130829075782
absolute error = 1.2209194195308890291130829075782
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.86
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.37
y[1] (closed_form) = 0
y[1] (numeric) = 1.230754059888578856536437729193
absolute error = 1.230754059888578856536437729193
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.87
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1799.0MB, alloc=52.3MB, time=18.95
TOP MAIN SOLVE Loop
x[1] = 1.38
y[1] (closed_form) = 0
y[1] (numeric) = 1.2405900637452331197498799151954
absolute error = 1.2405900637452331197498799151954
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.88
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.39
y[1] (closed_form) = 0
y[1] (numeric) = 1.2504274176094280416781420591654
absolute error = 1.2504274176094280416781420591654
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.89
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.4
y[1] (closed_form) = 0
y[1] (numeric) = 1.2602661081488179977508622070656
absolute error = 1.2602661081488179977508622070656
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.9
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=1843.1MB, alloc=52.3MB, time=19.41
x[1] = 1.41
y[1] (closed_form) = 0
y[1] (numeric) = 1.2701061221879235862593226745478
absolute error = 1.2701061221879235862593226745478
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.91
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.42
y[1] (closed_form) = 0
y[1] (numeric) = 1.2799474467059555285420889759938
absolute error = 1.2799474467059555285420889759938
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.92
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.43
y[1] (closed_form) = 0
y[1] (numeric) = 1.2897900688346737312341404541552
absolute error = 1.2897900688346737312341404541552
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.93
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.44
y[1] (closed_form) = 0
y[1] (numeric) = 1.2996339758562808569654950115103
absolute error = 1.2996339758562808569654950115103
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.94
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1887.2MB, alloc=52.3MB, time=19.88
TOP MAIN SOLVE Loop
x[1] = 1.45
y[1] (closed_form) = 0
y[1] (numeric) = 1.309479155201349763709334700212
absolute error = 1.309479155201349763709334700212
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.95
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.46
y[1] (closed_form) = 0
y[1] (numeric) = 1.3193255944467841864652029013812
absolute error = 1.3193255944467841864652029013812
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.96
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.47
y[1] (closed_form) = 0
y[1] (numeric) = 1.3291732813138120481286701200956
absolute error = 1.3291732813138120481286701200956
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.97
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1931.4MB, alloc=52.3MB, time=20.34
TOP MAIN SOLVE Loop
x[1] = 1.48
y[1] (closed_form) = 0
y[1] (numeric) = 1.3390222036660107992534018623341
absolute error = 1.3390222036660107992534018623341
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.98
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.49
y[1] (closed_form) = 0
y[1] (numeric) = 1.3488723495073641989630097776376
absolute error = 1.3488723495073641989630097776376
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 2.99
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.5
y[1] (closed_form) = 0
y[1] (numeric) = 1.3587237069803499615263885948298
absolute error = 1.3587237069803499615263885948298
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1975.5MB, alloc=52.3MB, time=20.81
TOP MAIN SOLVE Loop
x[1] = 1.51
y[1] (closed_form) = 0
y[1] (numeric) = 1.3685762643640577050791675399114
absolute error = 1.3685762643640577050791675399114
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.01
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.52
y[1] (closed_form) = 0
y[1] (numeric) = 1.3784300100723366506629433036456
absolute error = 1.3784300100723366506629433036456
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.02
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.53
y[1] (closed_form) = 0
y[1] (numeric) = 1.3882849326519725311704029331636
absolute error = 1.3882849326519725311704029331636
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.03
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2019.5MB, alloc=52.3MB, time=21.27
TOP MAIN SOLVE Loop
x[1] = 1.54
y[1] (closed_form) = 0
y[1] (numeric) = 1.3981410207808931809353701432739
absolute error = 1.3981410207808931809353701432739
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.04
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.55
y[1] (closed_form) = 0
y[1] (numeric) = 1.407998263266402287599095163678
absolute error = 1.407998263266402287599095163678
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.05
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.56
y[1] (closed_form) = 0
y[1] (numeric) = 1.4178566490434407985244372373847
absolute error = 1.4178566490434407985244372373847
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.06
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2063.7MB, alloc=52.3MB, time=21.73
TOP MAIN SOLVE Loop
x[1] = 1.57
y[1] (closed_form) = 0
y[1] (numeric) = 1.4277161671728754844244505141357
absolute error = 1.4277161671728754844244505141357
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.07
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.58
y[1] (closed_form) = 0
y[1] (numeric) = 1.4375768068398141730275839285505
absolute error = 1.4375768068398141730275839285505
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.08
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.59
y[1] (closed_form) = 0
y[1] (numeric) = 1.4474385573519471755243704028864
absolute error = 1.4474385573519471755243704028864
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.09
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2107.9MB, alloc=52.3MB, time=22.19
TOP MAIN SOLVE Loop
x[1] = 1.6
y[1] (closed_form) = 0
y[1] (numeric) = 1.4573014081379144382360637209078
absolute error = 1.4573014081379144382360637209078
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.1
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.61
y[1] (closed_form) = 0
y[1] (numeric) = 1.4671653487456979614199680769783
absolute error = 1.4671653487456979614199680769783
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.11
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.62
y[1] (closed_form) = 0
y[1] (numeric) = 1.4770303688410390363848182459045
absolute error = 1.4770303688410390363848182459045
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.12
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.63
y[1] (closed_form) = 0
y[1] (numeric) = 1.4868964582058798611379724356584
absolute error = 1.4868964582058798611379724356584
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.13
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2152.1MB, alloc=52.3MB, time=22.66
TOP MAIN SOLVE Loop
x[1] = 1.64
y[1] (closed_form) = 0
y[1] (numeric) = 1.4967636067368291036296871786378
absolute error = 1.4967636067368291036296871786378
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.14
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.65
y[1] (closed_form) = 0
y[1] (numeric) = 1.5066318044436509903035178889285
absolute error = 1.5066318044436509903035178889285
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.15
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.66
y[1] (closed_form) = 0
y[1] (numeric) = 1.5165010414477775061109500964569
absolute error = 1.5165010414477775061109500964569
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.16
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2196.3MB, alloc=52.3MB, time=23.13
TOP MAIN SOLVE Loop
x[1] = 1.67
y[1] (closed_form) = 0
y[1] (numeric) = 1.5263713079808433004075957108723
absolute error = 1.5263713079808433004075957108723
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.17
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.68
y[1] (closed_form) = 0
y[1] (numeric) = 1.5362425943832429012224317648332
absolute error = 1.5362425943832429012224317648332
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.18
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.69
y[1] (closed_form) = 0
y[1] (numeric) = 1.54611489110270984828523077953
absolute error = 1.54611489110270984828523077953
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.19
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2240.6MB, alloc=52.3MB, time=23.59
TOP MAIN SOLVE Loop
x[1] = 1.7
y[1] (closed_form) = 0
y[1] (numeric) = 1.5559881886929173629150200315644
absolute error = 1.5559881886929173629150200315644
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.2
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.71
y[1] (closed_form) = 0
y[1] (numeric) = 1.565862477812100180418476261851
absolute error = 1.565862477812100180418476261851
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.21
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.72
y[1] (closed_form) = 0
y[1] (numeric) = 1.5757377492216971780258579754497
absolute error = 1.5757377492216971780258579754497
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.22
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2284.8MB, alloc=52.3MB, time=24.06
TOP MAIN SOLVE Loop
x[1] = 1.73
y[1] (closed_form) = 0
y[1] (numeric) = 1.5856139937850144386075287797988
absolute error = 1.5856139937850144386075287797988
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.23
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.74
y[1] (closed_form) = 0
y[1] (numeric) = 1.5954912024659083974703491291971
absolute error = 1.5954912024659083974703491291971
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.24
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.75
y[1] (closed_form) = 0
y[1] (numeric) = 1.6053693663274887264341182578679
absolute error = 1.6053693663274887264341182578679
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.25
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2328.8MB, alloc=52.3MB, time=24.53
TOP MAIN SOLVE Loop
x[1] = 1.76
y[1] (closed_form) = 0
y[1] (numeric) = 1.6152484765308406161376350496072
absolute error = 1.6152484765308406161376350496072
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.26
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.77
y[1] (closed_form) = 0
y[1] (numeric) = 1.6251285243337661241255154896659
absolute error = 1.6251285243337661241255154896659
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.27
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.78
y[1] (closed_form) = 0
y[1] (numeric) = 1.6350095010895442627242549161829
absolute error = 1.6350095010895442627242549161829
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.28
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.79
y[1] (closed_form) = 0
y[1] (numeric) = 1.6448913982457095070326585772342
absolute error = 1.6448913982457095070326585772342
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.29
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2373.0MB, alloc=52.3MB, time=25.02
TOP MAIN SOLVE Loop
x[1] = 1.8
y[1] (closed_form) = 0
y[1] (numeric) = 1.6547742073428484095310931947137
absolute error = 1.6547742073428484095310931947137
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.3
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.81
y[1] (closed_form) = 0
y[1] (numeric) = 1.6646579200134140138593534275841
absolute error = 1.6646579200134140138593534275841
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.31
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.82
y[1] (closed_form) = 0
y[1] (numeric) = 1.6745425279805577662275199709448
absolute error = 1.6745425279805577662275199709448
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.32
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2417.3MB, alloc=52.3MB, time=25.48
TOP MAIN SOLVE Loop
x[1] = 1.83
y[1] (closed_form) = 0
y[1] (numeric) = 1.6844280230569786287111543281251
absolute error = 1.6844280230569786287111543281251
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.33
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.84
y[1] (closed_form) = 0
y[1] (numeric) = 1.6943143971437891043445895020252
absolute error = 1.6943143971437891043445895020252
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.34
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.85
y[1] (closed_form) = 0
y[1] (numeric) = 1.7042016422293978894669154877553
absolute error = 1.7042016422293978894669154877553
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.35
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2461.4MB, alloc=52.3MB, time=25.95
TOP MAIN SOLVE Loop
x[1] = 1.86
y[1] (closed_form) = 0
y[1] (numeric) = 1.7140897503884088741974244405897
absolute error = 1.7140897503884088741974244405897
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.36
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.87
y[1] (closed_form) = 0
y[1] (numeric) = 1.7239787137805362172235973511566
absolute error = 1.7239787137805362172235973511566
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.37
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.88
y[1] (closed_form) = 0
y[1] (numeric) = 1.733868524649535226277932472328
absolute error = 1.733868524649535226277932472328
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.38
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2505.5MB, alloc=52.3MB, time=26.42
TOP MAIN SOLVE Loop
x[1] = 1.89
y[1] (closed_form) = 0
y[1] (numeric) = 1.743759175322148780762714106507
absolute error = 1.743759175322148780762714106507
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.39
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.9
y[1] (closed_form) = 0
y[1] (numeric) = 1.7536506582070690379568072462641
absolute error = 1.7536506582070690379568072462641
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.4
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.91
y[1] (closed_form) = 0
y[1] (numeric) = 1.7635429657939141691082796037874
absolute error = 1.7635429657939141691082796037874
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.41
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2549.7MB, alloc=52.3MB, time=26.89
TOP MAIN SOLVE Loop
x[1] = 1.92
y[1] (closed_form) = 0
y[1] (numeric) = 1.773436090652219876483572409907
absolute error = 1.773436090652219876483572409907
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.42
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.93
y[1] (closed_form) = 0
y[1] (numeric) = 1.7833300254304454471104755387924
absolute error = 1.7833300254304454471104755387924
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.43
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.94
y[1] (closed_form) = 0
y[1] (numeric) = 1.7932247628549941035206592481242
absolute error = 1.7932247628549941035206592481242
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.44
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.95
y[1] (closed_form) = 0
y[1] (numeric) = 1.8031202957292474162702618082276
absolute error = 1.8031202957292474162702618082276
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.45
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2593.9MB, alloc=52.3MB, time=27.36
TOP MAIN SOLVE Loop
x[1] = 1.96
y[1] (closed_form) = 0
y[1] (numeric) = 1.8130166169326135473962583902714
absolute error = 1.8130166169326135473962583902714
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.46
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.97
y[1] (closed_form) = 0
y[1] (numeric) = 1.8229137194195890982542134830818
absolute error = 1.8229137194195890982542134830818
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.47
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 1.98
y[1] (closed_form) = 0
y[1] (numeric) = 1.8328115962188343393816629320941
absolute error = 1.8328115962188343393816629320941
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.48
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2638.0MB, alloc=52.3MB, time=27.83
TOP MAIN SOLVE Loop
x[1] = 1.99
y[1] (closed_form) = 0
y[1] (numeric) = 1.842710240432261604142844551996
absolute error = 1.842710240432261604142844551996
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.49
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2
y[1] (closed_form) = 0
y[1] (numeric) = 1.8526096452341366319368077624516
absolute error = 1.8526096452341366319368077624516
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.5
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.01
y[1] (closed_form) = 0
y[1] (numeric) = 1.8625098038701926506940413987702
absolute error = 1.8625098038701926506940413987702
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.51
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2682.2MB, alloc=52.3MB, time=28.30
TOP MAIN SOLVE Loop
x[1] = 2.02
y[1] (closed_form) = 0
y[1] (numeric) = 1.8724107096567569922485736986585
absolute error = 1.8724107096567569922485736986585
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.52
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.03
y[1] (closed_form) = 0
y[1] (numeric) = 1.8823123559798900379548801574196
absolute error = 1.8823123559798900379548801574196
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.53
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.04
y[1] (closed_form) = 0
y[1] (numeric) = 1.8922147362945362956236972592369
absolute error = 1.8922147362945362956236972592369
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.54
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2726.3MB, alloc=52.3MB, time=28.76
TOP MAIN SOLVE Loop
x[1] = 2.05
y[1] (closed_form) = 0
y[1] (numeric) = 1.9021178441236874124797511945834
absolute error = 1.9021178441236874124797511945834
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.55
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.06
y[1] (closed_form) = 0
y[1] (numeric) = 1.9120216730575569323991943624664
absolute error = 1.9120216730575569323991943624664
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.56
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.07
y[1] (closed_form) = 0
y[1] (numeric) = 1.9219262167527666091668793840267
absolute error = 1.9219262167527666091668793840267
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.57
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2770.4MB, alloc=52.3MB, time=29.23
TOP MAIN SOLVE Loop
x[1] = 2.08
y[1] (closed_form) = 0
y[1] (numeric) = 1.9318314689315440909051292087401
absolute error = 1.9318314689315440909051292087401
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.58
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.09
y[1] (closed_form) = 0
y[1] (numeric) = 1.941737423380931794167980544996
absolute error = 1.941737423380931794167980544996
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.59
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.1
y[1] (closed_form) = 0
y[1] (numeric) = 1.9516440739520067894695444551303
absolute error = 1.9516440739520067894695444551303
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.6
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.11
y[1] (closed_form) = 0
y[1] (numeric) = 1.9615514145591115232236620553439
absolute error = 1.9615514145591115232236620553439
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=2814.6MB, alloc=52.3MB, time=29.70
Radius of convergence (given) for eq 1 = 3.61
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.12
y[1] (closed_form) = 0
y[1] (numeric) = 1.971459439179095204215916807111
absolute error = 1.971459439179095204215916807111
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.62
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.13
y[1] (closed_form) = 0
y[1] (numeric) = 1.9813681418505656858097432683785
absolute error = 1.9813681418505656858097432683785
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.63
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.14
y[1] (closed_form) = 0
y[1] (numeric) = 1.9912775166731516781072552022003
absolute error = 1.9912775166731516781072552022003
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.64
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2858.8MB, alloc=52.3MB, time=30.17
TOP MAIN SOLVE Loop
x[1] = 2.15
y[1] (closed_form) = 0
y[1] (numeric) = 2.0011875578067751272438788095546
absolute error = 2.0011875578067751272438788095546
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.65
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.16
y[1] (closed_form) = 0
y[1] (numeric) = 2.0110982594709336018952610636639
absolute error = 2.0110982594709336018952610636639
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.66
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.17
y[1] (closed_form) = 0
y[1] (numeric) = 2.0210096159439925299165373888949
absolute error = 2.0210096159439925299165373888949
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.67
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2902.9MB, alloc=52.3MB, time=30.64
TOP MAIN SOLVE Loop
x[1] = 2.18
y[1] (closed_form) = 0
y[1] (numeric) = 2.0309216215624871308191640501276
absolute error = 2.0309216215624871308191640501276
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.68
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.19
y[1] (closed_form) = 0
y[1] (numeric) = 2.0408342707204338925203943391798
absolute error = 2.0408342707204338925203943391798
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.69
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.2
y[1] (closed_form) = 0
y[1] (numeric) = 2.0507475578686514434763194692157
absolute error = 2.0507475578686514434763194692157
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.7
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2947.1MB, alloc=52.3MB, time=31.11
TOP MAIN SOLVE Loop
x[1] = 2.21
y[1] (closed_form) = 0
y[1] (numeric) = 2.060661477514090673932391089045
absolute error = 2.060661477514090673932391089045
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.71
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.22
y[1] (closed_form) = 0
y[1] (numeric) = 2.070576024219173962596649926063
absolute error = 2.070576024219173962596649926063
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.72
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.23
y[1] (closed_form) = 0
y[1] (numeric) = 2.0804911926011433675616337814748
absolute error = 2.0804911926011433675616337814748
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.73
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2991.2MB, alloc=52.3MB, time=31.58
TOP MAIN SOLVE Loop
x[1] = 2.24
y[1] (closed_form) = 0
y[1] (numeric) = 2.0904069773314176427722302944547
absolute error = 2.0904069773314176427722302944547
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.74
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.25
y[1] (closed_form) = 0
y[1] (numeric) = 2.1003233731349579437596514748995
absolute error = 2.1003233731349579437596514748995
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.75
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.26
y[1] (closed_form) = 0
y[1] (numeric) = 2.1102403747896420887372881346625
absolute error = 2.1102403747896420887372881346625
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.76
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=3035.3MB, alloc=52.3MB, time=32.05
x[1] = 2.27
y[1] (closed_form) = 0
y[1] (numeric) = 2.1201579771256472434834781009749
absolute error = 2.1201579771256472434834781009749
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.77
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.28
y[1] (closed_form) = 0
y[1] (numeric) = 2.1300761750248409007201931232523
absolute error = 2.1300761750248409007201931232523
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.78
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.29
y[1] (closed_form) = 0
y[1] (numeric) = 2.1399949634201800269362925455694
absolute error = 2.1399949634201800269362925455694
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.79
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.3
y[1] (closed_form) = 0
y[1] (numeric) = 2.1499143372951182518002607995841
absolute error = 2.1499143372951182518002607995841
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.8
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3079.5MB, alloc=52.3MB, time=32.52
TOP MAIN SOLVE Loop
x[1] = 2.31
y[1] (closed_form) = 0
y[1] (numeric) = 2.1598342916830209774611716928872
absolute error = 2.1598342916830209774611716928872
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.81
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.32
y[1] (closed_form) = 0
y[1] (numeric) = 2.1697548216665882871489144542358
absolute error = 2.1697548216665882871489144542358
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.33
y[1] (closed_form) = 0
y[1] (numeric) = 2.1796759223772855345563622579819
absolute error = 2.1796759223772855345563622579819
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.83
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3123.7MB, alloc=52.3MB, time=32.98
TOP MAIN SOLVE Loop
x[1] = 2.34
y[1] (closed_form) = 0
y[1] (numeric) = 2.189597588994781497518030324346
absolute error = 2.189597588994781497518030324346
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.84
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.35
y[1] (closed_form) = 0
y[1] (numeric) = 2.1995198167463939814927041860841
absolute error = 2.1995198167463939814927041860841
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.85
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.36
y[1] (closed_form) = 0
y[1] (numeric) = 2.2094426009065427603123460196807
absolute error = 2.2094426009065427603123460196807
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.86
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3167.7MB, alloc=52.3MB, time=33.45
TOP MAIN SOLVE Loop
x[1] = 2.37
y[1] (closed_form) = 0
y[1] (numeric) = 2.2193659367962097435771154492173
absolute error = 2.2193659367962097435771154492173
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.87
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.38
y[1] (closed_form) = 0
y[1] (numeric) = 2.2292898197824062619573595192977
absolute error = 2.2292898197824062619573595192977
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.88
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.39
y[1] (closed_form) = 0
y[1] (numeric) = 2.2392142452776473635087048416433
absolute error = 2.2392142452776473635087048416433
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.89
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3211.9MB, alloc=52.3MB, time=33.92
TOP MAIN SOLVE Loop
x[1] = 2.4
y[1] (closed_form) = 0
y[1] (numeric) = 2.2491392087394330159166756214741
absolute error = 2.2491392087394330159166756214741
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.9
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.41
y[1] (closed_form) = 0
y[1] (numeric) = 2.259064705669736111363299322179
absolute error = 2.259064705669736111363299322179
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.91
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.42
y[1] (closed_form) = 0
y[1] (numeric) = 2.2689907316144971724506651122949
absolute error = 2.2689907316144971724506651122949
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.92
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=3256.1MB, alloc=52.3MB, time=34.39
x[1] = 2.43
y[1] (closed_form) = 0
y[1] (numeric) = 2.2789172821631256593260703925594
absolute error = 2.2789172821631256593260703925594
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.93
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.44
y[1] (closed_form) = 0
y[1] (numeric) = 2.2888443529480077798309129272032
absolute error = 2.2888443529480077798309129272032
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.94
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.45
y[1] (closed_form) = 0
y[1] (numeric) = 2.2987719396440207061415299816624
absolute error = 2.2987719396440207061415299816624
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.95
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.46
y[1] (closed_form) = 0
y[1] (numeric) = 2.3087000379680531029854056459474
absolute error = 2.3087000379680531029854056459474
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.96
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3300.3MB, alloc=52.3MB, time=34.86
TOP MAIN SOLVE Loop
x[1] = 2.47
y[1] (closed_form) = 0
y[1] (numeric) = 2.3186286436785318741012024983722
absolute error = 2.3186286436785318741012024983722
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.97
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.48
y[1] (closed_form) = 0
y[1] (numeric) = 2.3285577525749550351665486624099
absolute error = 2.3285577525749550351665486624099
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.98
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.49
y[1] (closed_form) = 0
y[1] (numeric) = 2.338487360497430622944036641962
absolute error = 2.338487360497430622944036641962
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 3.99
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3344.4MB, alloc=52.3MB, time=35.33
TOP MAIN SOLVE Loop
x[1] = 2.5
y[1] (closed_form) = 0
y[1] (numeric) = 2.3484174633262215518940627398856
absolute error = 2.3484174633262215518940627398856
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.51
y[1] (closed_form) = 0
y[1] (numeric) = 2.3583480569812963309735385080416
absolute error = 2.3583480569812963309735385080416
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.01
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.52
y[1] (closed_form) = 0
y[1] (numeric) = 2.3682791374218855547827084997251
absolute error = 2.3682791374218855547827084997251
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.02
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3388.5MB, alloc=52.3MB, time=35.80
TOP MAIN SOLVE Loop
x[1] = 2.53
y[1] (closed_form) = 0
y[1] (numeric) = 2.3782107006460440846388686962689
absolute error = 2.3782107006460440846388686962689
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.03
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.54
y[1] (closed_form) = 0
y[1] (numeric) = 2.3881427426902188365462419184221
absolute error = 2.3881427426902188365462419184221
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.04
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.55
y[1] (closed_form) = 0
y[1] (numeric) = 2.3980752596288220943961626378839
absolute error = 2.3980752596288220943961626378839
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.05
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3432.7MB, alloc=52.3MB, time=36.25
TOP MAIN SOLVE Loop
x[1] = 2.56
y[1] (closed_form) = 0
y[1] (numeric) = 2.4080082475738102680715742716492
absolute error = 2.4080082475738102680715742716492
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.06
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.57
y[1] (closed_form) = 0
y[1] (numeric) = 2.4179417026742680174451560285214
absolute error = 2.4179417026742680174451560285214
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.07
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.58
y[1] (closed_form) = 0
y[1] (numeric) = 2.4278756211159976645516710847228
absolute error = 2.4278756211159976645516710847228
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.08
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=3476.9MB, alloc=52.3MB, time=36.73
x[1] = 2.59
y[1] (closed_form) = 0
y[1] (numeric) = 2.4378099991211138174828496166794
absolute error = 2.4378099991211138174828496166794
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.09
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.6
y[1] (closed_form) = 0
y[1] (numeric) = 2.4477448329476431307977645269887
absolute error = 2.4477448329476431307977645269887
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.1
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.61
y[1] (closed_form) = 0
y[1] (numeric) = 2.4576801188891291284636895303057
absolute error = 2.4576801188891291284636895303057
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.11
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.62
y[1] (closed_form) = 0
y[1] (numeric) = 2.4676158532742420165423032935065
absolute error = 2.4676158532742420165423032935065
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.12
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3521.1MB, alloc=52.3MB, time=37.19
TOP MAIN SOLVE Loop
x[1] = 2.63
y[1] (closed_form) = 0
y[1] (numeric) = 2.4775520324663934140142641798559
absolute error = 2.4775520324663934140142641798559
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.13
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.64
y[1] (closed_form) = 0
y[1] (numeric) = 2.4874886528633559312920626596747
absolute error = 2.4874886528633559312920626596747
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.14
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.65
y[1] (closed_form) = 0
y[1] (numeric) = 2.4974257108968875271070878844687
absolute error = 2.4974257108968875271070878844687
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.15
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3565.1MB, alloc=52.3MB, time=37.66
TOP MAIN SOLVE Loop
x[1] = 2.66
y[1] (closed_form) = 0
y[1] (numeric) = 2.507363203032360575572437206133
absolute error = 2.507363203032360575572437206133
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.16
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.67
y[1] (closed_form) = 0
y[1] (numeric) = 2.5173011257683955763185593740866
absolute error = 2.5173011257683955763185593740866
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.17
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.68
y[1] (closed_form) = 0
y[1] (numeric) = 2.5272394756364994416747516830629
absolute error = 2.5272394756364994416747516830629
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.18
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3609.3MB, alloc=52.3MB, time=38.13
TOP MAIN SOLVE Loop
x[1] = 2.69
y[1] (closed_form) = 0
y[1] (numeric) = 2.5371782492007082959262177127645
absolute error = 2.5371782492007082959262177127645
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.19
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.7
y[1] (closed_form) = 0
y[1] (numeric) = 2.547117443057234722714216262174
absolute error = 2.547117443057234722714216262174
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.2
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.71
y[1] (closed_form) = 0
y[1] (numeric) = 2.5570570538341193976661661264583
absolute error = 2.5570570538341193976661661264583
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.21
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3653.5MB, alloc=52.3MB, time=38.59
TOP MAIN SOLVE Loop
x[1] = 2.72
y[1] (closed_form) = 0
y[1] (numeric) = 2.5669970781908870443437799055762
absolute error = 2.5669970781908870443437799055762
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.22
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.73
y[1] (closed_form) = 0
y[1] (numeric) = 2.5769375128182066525807395966666
absolute error = 2.5769375128182066525807395966666
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.23
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.74
y[1] (closed_form) = 0
y[1] (numeric) = 2.5868783544375558992474461321102
absolute error = 2.5868783544375558992474461321102
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.24
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=3697.6MB, alloc=52.3MB, time=39.06
x[1] = 2.75
y[1] (closed_form) = 0
y[1] (numeric) = 2.5968195998008897124293155878395
absolute error = 2.5968195998008897124293155878395
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.25
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.76
y[1] (closed_form) = 0
y[1] (numeric) = 2.6067612456903129209372904656265
absolute error = 2.6067612456903129209372904656265
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.26
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.77
y[1] (closed_form) = 0
y[1] (numeric) = 2.6167032889177569319850120423118
absolute error = 2.6167032889177569319850120423118
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.27
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.78
y[1] (closed_form) = 0
y[1] (numeric) = 2.6266457263246603807667790697188
absolute error = 2.6266457263246603807667790697188
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.28
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3741.9MB, alloc=52.3MB, time=39.53
TOP MAIN SOLVE Loop
x[1] = 2.79
y[1] (closed_form) = 0
y[1] (numeric) = 2.6365885547816536965543120543067
absolute error = 2.6365885547816536965543120543067
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.29
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.8
y[1] (closed_form) = 0
y[1] (numeric) = 2.646531771188247530798757219499
absolute error = 2.646531771188247530798757219499
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.3
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.81
y[1] (closed_form) = 0
y[1] (numeric) = 2.6564753724725249935775998065618
absolute error = 2.6564753724725249935775998065618
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.31
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3786.0MB, alloc=52.3MB, time=40.00
TOP MAIN SOLVE Loop
x[1] = 2.82
y[1] (closed_form) = 0
y[1] (numeric) = 2.6664193555908376455645059804724
absolute error = 2.6664193555908376455645059804724
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.32
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.83
y[1] (closed_form) = 0
y[1] (numeric) = 2.6763637175275051935238634297123
absolute error = 2.6763637175275051935238634297123
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.33
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.84
y[1] (closed_form) = 0
y[1] (numeric) = 2.6863084552945188381412238574207
absolute error = 2.6863084552945188381412238574207
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.34
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3830.1MB, alloc=52.3MB, time=40.47
TOP MAIN SOLVE Loop
x[1] = 2.85
y[1] (closed_form) = 0
y[1] (numeric) = 2.6962535659312482237962410901294
absolute error = 2.6962535659312482237962410901294
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.35
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.86
y[1] (closed_form) = 0
y[1] (numeric) = 2.7061990465041519406663158106579
absolute error = 2.7061990465041519406663158106579
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.36
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.87
y[1] (closed_form) = 0
y[1] (numeric) = 2.716144894106491530317265615541
absolute error = 2.716144894106491530317265615541
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.37
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3874.3MB, alloc=52.3MB, time=40.94
TOP MAIN SOLVE Loop
x[1] = 2.88
y[1] (closed_form) = 0
y[1] (numeric) = 2.7260911058580489466921953270627
absolute error = 2.7260911058580489466921953270627
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.38
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.89
y[1] (closed_form) = 0
y[1] (numeric) = 2.7360376789048474251515999656415
absolute error = 2.7360376789048474251515999656415
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.39
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.9
y[1] (closed_form) = 0
y[1] (numeric) = 2.7459846104188757129468389312945
absolute error = 2.7459846104188757129468389312945
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.4
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=3918.5MB, alloc=52.3MB, time=41.41
x[1] = 2.91
y[1] (closed_form) = 0
y[1] (numeric) = 2.755931897597815615225717006533
absolute error = 2.755931897597815615225717006533
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.41
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.92
y[1] (closed_form) = 0
y[1] (numeric) = 2.7658795376647728113732329803053
absolute error = 2.7658795376647728113732329803053
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.42
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.93
y[1] (closed_form) = 0
y[1] (numeric) = 2.775827527868010897182842270974
absolute error = 2.775827527868010897182842270974
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.43
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.94
y[1] (closed_form) = 0
y[1] (numeric) = 2.7857758654806886090340533396562
absolute error = 2.7857758654806886090340533396562
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.44
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3962.7MB, alloc=52.3MB, time=41.88
TOP MAIN SOLVE Loop
x[1] = 2.95
y[1] (closed_form) = 0
y[1] (numeric) = 2.7957245478006001869210616631075
absolute error = 2.7957245478006001869210616631075
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.45
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.96
y[1] (closed_form) = 0
y[1] (numeric) = 2.8056735721499188338346376993147
absolute error = 2.8056735721499188338346376993147
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.46
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.97
y[1] (closed_form) = 0
y[1] (numeric) = 2.8156229358749432296458402468522
absolute error = 2.8156229358749432296458402468522
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.47
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4006.9MB, alloc=52.3MB, time=42.34
TOP MAIN SOLVE Loop
x[1] = 2.98
y[1] (closed_form) = 0
y[1] (numeric) = 2.8255726363458470582755330860069
absolute error = 2.8255726363458470582755330860069
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.48
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 2.99
y[1] (closed_form) = 0
y[1] (numeric) = 2.8355226709564315075583457072423
absolute error = 2.8355226709564315075583457072423
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.49
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3
y[1] (closed_form) = 0
y[1] (numeric) = 2.8454730371238807018238389851333
absolute error = 2.8454730371238807018238389851333
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.5
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4051.0MB, alloc=52.3MB, time=42.81
TOP MAIN SOLVE Loop
x[1] = 3.01
y[1] (closed_form) = 0
y[1] (numeric) = 2.8554237322885200278214104348476
absolute error = 2.8554237322885200278214104348476
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.51
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.02
y[1] (closed_form) = 0
y[1] (numeric) = 2.8653747539135773152090937638452
absolute error = 2.8653747539135773152090937638452
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.52
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.03
y[1] (closed_form) = 0
y[1] (numeric) = 2.8753260994849468334100624424716
absolute error = 2.8753260994849468334100624424716
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.53
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4095.1MB, alloc=52.3MB, time=43.28
TOP MAIN SOLVE Loop
x[1] = 3.04
y[1] (closed_form) = 0
y[1] (numeric) = 2.8852777665109560672145217583088
absolute error = 2.8852777665109560672145217583088
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.54
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.05
y[1] (closed_form) = 0
y[1] (numeric) = 2.8952297525221352340689493266436
absolute error = 2.8952297525221352340689493266436
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.55
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.06
y[1] (closed_form) = 0
y[1] (numeric) = 2.9051820550709895065494976640026
absolute error = 2.9051820550709895065494976640026
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.56
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=4139.3MB, alloc=52.3MB, time=43.75
x[1] = 3.07
y[1] (closed_form) = 0
y[1] (numeric) = 2.9151346717317739040619779602
absolute error = 2.9151346717317739040619779602
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.57
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.08
y[1] (closed_form) = 0
y[1] (numeric) = 2.9250876001002708183473718588572
absolute error = 2.9250876001002708183473718588572
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.58
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.09
y[1] (closed_form) = 0
y[1] (numeric) = 2.935040837793570137899434691882
absolute error = 2.935040837793570137899434691882
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.59
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.1
y[1] (closed_form) = 0
y[1] (numeric) = 2.9449943824498519369198226632876
absolute error = 2.9449943824498519369198226632876
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.6
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4183.4MB, alloc=52.3MB, time=44.22
TOP MAIN SOLVE Loop
x[1] = 3.11
y[1] (closed_form) = 0
y[1] (numeric) = 2.9549482317281716949464581076664
absolute error = 2.9549482317281716949464581076664
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.61
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.12
y[1] (closed_form) = 0
y[1] (numeric) = 2.9649023833082480137926981085287
absolute error = 2.9649023833082480137926981085287
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.62
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.13
y[1] (closed_form) = 0
y[1] (numeric) = 2.9748568348902527989284462561672
absolute error = 2.9748568348902527989284462561672
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.63
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4227.5MB, alloc=52.3MB, time=44.69
TOP MAIN SOLVE Loop
x[1] = 3.14
y[1] (closed_form) = 0
y[1] (numeric) = 2.9848115841946038729197958816374
absolute error = 2.9848115841946038729197958816374
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.64
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.15
y[1] (closed_form) = 0
y[1] (numeric) = 2.9947666289617599890212634411398
absolute error = 2.9947666289617599890212634411398
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.65
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.16
y[1] (closed_form) = 0
y[1] (numeric) = 3.0047219669520182134843076177148
absolute error = 3.0047219669520182134843076177148
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.66
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4271.6MB, alloc=52.3MB, time=45.16
TOP MAIN SOLVE Loop
x[1] = 3.17
y[1] (closed_form) = 0
y[1] (numeric) = 3.0146775959453136456077750486308
absolute error = 3.0146775959453136456077750486308
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.67
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.18
y[1] (closed_form) = 0
y[1] (numeric) = 3.0246335137410214450103064533066
absolute error = 3.0246335137410214450103064533066
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.68
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.19
y[1] (closed_form) = 0
y[1] (numeric) = 3.0345897181577611360517136473396
absolute error = 3.0345897181577611360517136473396
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.69
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4315.7MB, alloc=52.3MB, time=45.63
TOP MAIN SOLVE Loop
x[1] = 3.2
y[1] (closed_form) = 0
y[1] (numeric) = 3.0445462070332031597700321052262
absolute error = 3.0445462070332031597700321052262
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.7
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.21
y[1] (closed_form) = 0
y[1] (numeric) = 3.0545029782238776441334963604395
absolute error = 3.0545029782238776441334963604395
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.71
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.22
y[1] (closed_form) = 0
y[1] (numeric) = 3.0644600296049853638322050071433
absolute error = 3.0644600296049853638322050071433
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.72
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4359.9MB, alloc=52.3MB, time=46.09
TOP MAIN SOLVE Loop
x[1] = 3.23
y[1] (closed_form) = 0
y[1] (numeric) = 3.0744173590702108612528642664233
absolute error = 3.0744173590702108612528642664233
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.73
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.24
y[1] (closed_form) = 0
y[1] (numeric) = 3.0843749645315377006918474022697
absolute error = 3.0843749645315377006918474022697
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.74
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.25
y[1] (closed_form) = 0
y[1] (numeric) = 3.0943328439190658282670026995082
absolute error = 3.0943328439190658282670026995082
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.75
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.26
y[1] (closed_form) = 0
y[1] (numeric) = 3.1042909951808310103873038601468
absolute error = 3.1042909951808310103873038601468
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.76
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4404.0MB, alloc=52.3MB, time=46.56
TOP MAIN SOLVE Loop
x[1] = 3.27
y[1] (closed_form) = 0
y[1] (numeric) = 3.1142494162826263240316798312146
absolute error = 3.1142494162826263240316798312146
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.77
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.28
y[1] (closed_form) = 0
y[1] (numeric) = 3.1242081052078256724743002727561
absolute error = 3.1242081052078256724743002727561
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.78
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.29
y[1] (closed_form) = 0
y[1] (numeric) = 3.1341670599572093004733399157081
absolute error = 3.1341670599572093004733399157081
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.79
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4448.1MB, alloc=52.3MB, time=47.03
TOP MAIN SOLVE Loop
x[1] = 3.3
y[1] (closed_form) = 0
y[1] (numeric) = 3.1441262785487912833139095792737
absolute error = 3.1441262785487912833139095792737
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.8
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.31
y[1] (closed_form) = 0
y[1] (numeric) = 3.1540857590176489644635311224356
absolute error = 3.1540857590176489644635311224356
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.81
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.32
y[1] (closed_form) = 0
y[1] (numeric) = 3.1640454994157543169603535184931
absolute error = 3.1640454994157543169603535184931
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.82
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4492.3MB, alloc=52.3MB, time=47.50
TOP MAIN SOLVE Loop
x[1] = 3.33
y[1] (closed_form) = 0
y[1] (numeric) = 3.1740054978118072040103609508583
absolute error = 3.1740054978118072040103609508583
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.83
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.34
y[1] (closed_form) = 0
y[1] (numeric) = 3.1839657522910705146202127233122
absolute error = 3.1839657522910705146202127233122
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.84
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.35
y[1] (closed_form) = 0
y[1] (numeric) = 3.1939262609552071504371782956452
absolute error = 3.1939262609552071504371782956452
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.85
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4536.4MB, alloc=52.3MB, time=47.97
TOP MAIN SOLVE Loop
x[1] = 3.36
y[1] (closed_form) = 0
y[1] (numeric) = 3.2038870219221188403069864207637
absolute error = 3.2038870219221188403069864207637
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.86
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.37
y[1] (closed_form) = 0
y[1] (numeric) = 3.2138480333257867593943908242646
absolute error = 3.2138480333257867593943908242646
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.87
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.38
y[1] (closed_form) = 0
y[1] (numeric) = 3.2238092933161139300399599512377
absolute error = 3.2238092933161139300399599512377
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.88
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4580.6MB, alloc=52.3MB, time=48.44
TOP MAIN SOLVE Loop
x[1] = 3.39
y[1] (closed_form) = 0
y[1] (numeric) = 3.2337708000587693818501170317338
absolute error = 3.2337708000587693818501170317338
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.89
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.4
y[1] (closed_form) = 0
y[1] (numeric) = 3.2437325517350340488358793524416
absolute error = 3.2437325517350340488358793524416
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.9
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.41
y[1] (closed_form) = 0
y[1] (numeric) = 3.2536945465416483817291607130775
absolute error = 3.2536945465416483817291607130775
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.91
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.42
y[1] (closed_form) = 0
y[1] (numeric) = 3.2636567826906616539139954519398
absolute error = 3.2636567826906616539139954519398
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.92
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4624.8MB, alloc=52.3MB, time=48.91
TOP MAIN SOLVE Loop
x[1] = 3.43
y[1] (closed_form) = 0
y[1] (numeric) = 3.2736192584092829397137013557087
absolute error = 3.2736192584092829397137013557087
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.93
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.44
y[1] (closed_form) = 0
y[1] (numeric) = 3.2835819719397337440739058173429
absolute error = 3.2835819719397337440739058173429
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.94
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.45
y[1] (closed_form) = 0
y[1] (numeric) = 3.2935449215391022629755967833625
absolute error = 3.2935449215391022629755967833625
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.95
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4668.9MB, alloc=52.3MB, time=49.38
TOP MAIN SOLVE Loop
x[1] = 3.46
y[1] (closed_form) = 0
y[1] (numeric) = 3.3035081054791992542020077982099
absolute error = 3.3035081054791992542020077982099
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.96
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.47
y[1] (closed_form) = 0
y[1] (numeric) = 3.3134715220464154983682837506409
absolute error = 3.3134715220464154983682837506409
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.97
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.48
y[1] (closed_form) = 0
y[1] (numeric) = 3.3234351695415808304035782099504
absolute error = 3.3234351695415808304035782099504
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.98
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4713.1MB, alloc=52.3MB, time=49.83
TOP MAIN SOLVE Loop
x[1] = 3.49
y[1] (closed_form) = 0
y[1] (numeric) = 3.3333990462798247219515805063304
absolute error = 3.3333990462798247219515805063304
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 4.99
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.5
y[1] (closed_form) = 0
y[1] (numeric) = 3.3433631505904383954275355309446
absolute error = 3.3433631505904383954275355309446
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.51
y[1] (closed_form) = 0
y[1] (numeric) = 3.3533274808167384507376747808828
absolute error = 3.3533274808167384507376747808828
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.01
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4757.2MB, alloc=52.3MB, time=50.30
TOP MAIN SOLVE Loop
x[1] = 3.52
y[1] (closed_form) = 0
y[1] (numeric) = 3.3632920353159319859306952562641
absolute error = 3.3632920353159319859306952562641
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.02
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.53
y[1] (closed_form) = 0
y[1] (numeric) = 3.3732568124589831933105738943647
absolute error = 3.3732568124589831933105738943647
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.03
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.54
y[1] (closed_form) = 0
y[1] (numeric) = 3.3832218106304814127956584476616
absolute error = 3.3832218106304814127956584476616
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.04
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4801.4MB, alloc=52.3MB, time=50.77
TOP MAIN SOLVE Loop
x[1] = 3.55
y[1] (closed_form) = 0
y[1] (numeric) = 3.3931870282285106245606989406294
absolute error = 3.3931870282285106245606989406294
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.05
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.56
y[1] (closed_form) = 0
y[1] (numeric) = 3.4031524636645203632463436742591
absolute error = 3.4031524636645203632463436742591
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.06
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.57
y[1] (closed_form) = 0
y[1] (numeric) = 3.4131181153631980362646855520214
absolute error = 3.4131181153631980362646855520214
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.07
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.58
y[1] (closed_form) = 0
y[1] (numeric) = 3.4230839817623426289697724300176
absolute error = 3.4230839817623426289697724300176
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.08
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4845.6MB, alloc=52.3MB, time=51.25
TOP MAIN SOLVE Loop
x[1] = 3.59
y[1] (closed_form) = 0
y[1] (numeric) = 3.4330500613127397796986522145381
absolute error = 3.4330500613127397796986522145381
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.09
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.6
y[1] (closed_form) = 0
y[1] (numeric) = 3.4430163524780382079215713468452
absolute error = 3.4430163524780382079215713468452
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.1
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.61
y[1] (closed_form) = 0
y[1] (numeric) = 3.4529828537346274789694447931627
absolute error = 3.4529828537346274789694447931627
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.11
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4889.8MB, alloc=52.3MB, time=51.72
TOP MAIN SOLVE Loop
x[1] = 3.62
y[1] (closed_form) = 0
y[1] (numeric) = 3.4629495635715170890327262467211
absolute error = 3.4629495635715170890327262467211
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.12
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.63
y[1] (closed_form) = 0
y[1] (numeric) = 3.4729164804902168543483874033856
absolute error = 3.4729164804902168543483874033856
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.13
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.64
y[1] (closed_form) = 0
y[1] (numeric) = 3.4828836030046185887109222758735
absolute error = 3.4828836030046185887109222758735
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.14
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4934.0MB, alloc=52.3MB, time=52.19
TOP MAIN SOLVE Loop
x[1] = 3.65
y[1] (closed_form) = 0
y[1] (numeric) = 3.4928509296408790536591828961212
absolute error = 3.4928509296408790536591828961212
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.15
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.66
y[1] (closed_form) = 0
y[1] (numeric) = 3.5028184589373041659034817234371
absolute error = 3.5028184589373041659034817234371
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.16
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.67
y[1] (closed_form) = 0
y[1] (numeric) = 3.5127861894442344467668179208228
absolute error = 3.5127861894442344467668179208228
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.17
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4978.2MB, alloc=52.3MB, time=52.66
TOP MAIN SOLVE Loop
x[1] = 3.68
y[1] (closed_form) = 0
y[1] (numeric) = 3.5227541197239316986203526871164
absolute error = 3.5227541197239316986203526871164
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.18
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.69
y[1] (closed_form) = 0
y[1] (numeric) = 3.5327222483504668934964253725957
absolute error = 3.5327222483504668934964253725957
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.19
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.7
y[1] (closed_form) = 0
y[1] (numeric) = 3.5426905739096092592625185441039
absolute error = 3.5426905739096092592625185441039
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.2
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5022.4MB, alloc=52.3MB, time=53.13
TOP MAIN SOLVE Loop
x[1] = 3.71
y[1] (closed_form) = 0
y[1] (numeric) = 3.5526590949987165489366969546077
absolute error = 3.5526590949987165489366969546077
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.21
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.72
y[1] (closed_form) = 0
y[1] (numeric) = 3.5626278102266264789192120500737
absolute error = 3.5626278102266264789192120500737
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.22
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.73
y[1] (closed_form) = 0
y[1] (numeric) = 3.5725967182135493221062288569873
absolute error = 3.5725967182135493221062288569873
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.23
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.74
y[1] (closed_form) = 0
y[1] (numeric) = 3.582565817590961642040043602344
absolute error = 3.582565817590961642040043602344
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.24
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5066.7MB, alloc=52.3MB, time=53.59
TOP MAIN SOLVE Loop
x[1] = 3.75
y[1] (closed_form) = 0
y[1] (numeric) = 3.5925351070015011544357651296181
absolute error = 3.5925351070015011544357651296181
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.25
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.76
y[1] (closed_form) = 0
y[1] (numeric) = 3.6025045850988627026072771504931
absolute error = 3.6025045850988627026072771504931
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.26
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.77
y[1] (closed_form) = 0
y[1] (numeric) = 3.6124742505476953334954268473402
absolute error = 3.6124742505476953334954268473402
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.27
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5110.9MB, alloc=52.3MB, time=54.06
TOP MAIN SOLVE Loop
x[1] = 3.78
y[1] (closed_form) = 0
y[1] (numeric) = 3.6224441020235004611788427388431
absolute error = 3.6224441020235004611788427388431
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.28
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.79
y[1] (closed_form) = 0
y[1] (numeric) = 3.6324141382125311049226146689505
absolute error = 3.6324141382125311049226146689505
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.29
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.8
y[1] (closed_form) = 0
y[1] (numeric) = 3.6423843578116921889923141259143
absolute error = 3.6423843578116921889923141259143
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.3
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5155.0MB, alloc=52.3MB, time=54.53
TOP MAIN SOLVE Loop
x[1] = 3.81
y[1] (closed_form) = 0
y[1] (numeric) = 3.6523547595284418916305359274453
absolute error = 3.6523547595284418916305359274453
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.31
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.82
y[1] (closed_form) = 0
y[1] (numeric) = 3.662325342080694030760343954181
absolute error = 3.662325342080694030760343954181
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.32
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.83
y[1] (closed_form) = 0
y[1] (numeric) = 3.6722961041967214741447446757191
absolute error = 3.6722961041967214741447446757191
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.33
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5199.2MB, alloc=52.3MB, time=55.00
TOP MAIN SOLVE Loop
x[1] = 3.84
y[1] (closed_form) = 0
y[1] (numeric) = 3.6822670446150605618936325694785
absolute error = 3.6822670446150605618936325694785
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.34
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.85
y[1] (closed_form) = 0
y[1] (numeric) = 3.692238162084416529369590353609
absolute error = 3.692238162084416529369590353609
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.35
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.86
y[1] (closed_form) = 0
y[1] (numeric) = 3.7022094553635699187015227186849
absolute error = 3.7022094553635699187015227186849
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.36
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5243.4MB, alloc=52.3MB, time=55.47
TOP MAIN SOLVE Loop
x[1] = 3.87
y[1] (closed_form) = 0
y[1] (numeric) = 3.7121809232212839672703927465246
absolute error = 3.7121809232212839672703927465246
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.37
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.88
y[1] (closed_form) = 0
y[1] (numeric) = 3.7221525644362129616843525787292
absolute error = 3.7221525644362129616843525787292
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.38
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.89
y[1] (closed_form) = 0
y[1] (numeric) = 3.7321243777968115459113506187767
absolute error = 3.7321243777968115459113506187767
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.39
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.9
y[1] (closed_form) = 0
y[1] (numeric) = 3.7420963621012449723858924544466
absolute error = 3.7420963621012449723858924544466
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.4
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5287.7MB, alloc=52.3MB, time=55.94
TOP MAIN SOLVE Loop
x[1] = 3.91
y[1] (closed_form) = 0
y[1] (numeric) = 3.7520685161573002850530669772861
absolute error = 3.7520685161573002850530669772861
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.41
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.92
y[1] (closed_form) = 0
y[1] (numeric) = 3.7620408387822984234572574406947
absolute error = 3.7620408387822984234572574406947
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.42
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.93
y[1] (closed_form) = 0
y[1] (numeric) = 3.7720133288030072371251734203485
absolute error = 3.7720133288030072371251734203485
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.43
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5331.8MB, alloc=52.3MB, time=56.41
TOP MAIN SOLVE Loop
x[1] = 3.94
y[1] (closed_form) = 0
y[1] (numeric) = 3.7819859850555553996329972083653
absolute error = 3.7819859850555553996329972083653
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.44
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.95
y[1] (closed_form) = 0
y[1] (numeric) = 3.7919588063853472118855698913198
absolute error = 3.7919588063853472118855698913198
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.45
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.96
y[1] (closed_form) = 0
y[1] (numeric) = 3.8019317916469782842716804657253
absolute error = 3.8019317916469782842716804657253
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.46
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5376.1MB, alloc=52.3MB, time=56.87
TOP MAIN SOLVE Loop
x[1] = 3.97
y[1] (closed_form) = 0
y[1] (numeric) = 3.8119049397041520874936975057695
absolute error = 3.8119049397041520874936975057695
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.47
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.98
y[1] (closed_form) = 0
y[1] (numeric) = 3.8218782494295973620020282395376
absolute error = 3.8218782494295973620020282395376
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.48
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 3.99
y[1] (closed_form) = 0
y[1] (numeric) = 3.8318517197049863760952349943783
absolute error = 3.8318517197049863760952349943783
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.49
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5420.3MB, alloc=52.3MB, time=57.34
TOP MAIN SOLVE Loop
x[1] = 4
y[1] (closed_form) = 0
y[1] (numeric) = 3.8418253494208540228751138924715
absolute error = 3.8418253494208540228751138924715
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.5
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.01
y[1] (closed_form) = 0
y[1] (numeric) = 3.8517991374765177463726749473212
absolute error = 3.8517991374765177463726749473212
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.51
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.02
y[1] (closed_form) = 0
y[1] (numeric) = 3.8617730827799982872857853541185
absolute error = 3.8617730827799982872857853541185
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.52
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=5464.5MB, alloc=52.3MB, time=57.81
x[1] = 4.03
y[1] (closed_form) = 0
y[1] (numeric) = 3.8717471842479412388922773046248
absolute error = 3.8717471842479412388922773046248
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.53
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.04
y[1] (closed_form) = 0
y[1] (numeric) = 3.8817214408055394038236061223124
absolute error = 3.8817214408055394038236061223124
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.54
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.05
y[1] (closed_form) = 0
y[1] (numeric) = 3.8916958513864559425037014560435
absolute error = 3.8916958513864559425037014560435
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.55
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.06
y[1] (closed_form) = 0
y[1] (numeric) = 3.9016704149327483041755107678256
absolute error = 3.9016704149327483041755107678256
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.56
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5508.7MB, alloc=52.3MB, time=58.28
TOP MAIN SOLVE Loop
x[1] = 4.07
y[1] (closed_form) = 0
y[1] (numeric) = 3.9116451303947929315539170153867
absolute error = 3.9116451303947929315539170153867
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.57
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.08
y[1] (closed_form) = 0
y[1] (numeric) = 3.9216199967312107302582474213535
absolute error = 3.9216199967312107302582474213535
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.58
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.09
y[1] (closed_form) = 0
y[1] (numeric) = 3.9315950129087932942905032486768
absolute error = 3.9315950129087932942905032486768
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.59
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5552.8MB, alloc=52.3MB, time=58.75
TOP MAIN SOLVE Loop
x[1] = 4.1
y[1] (closed_form) = 0
y[1] (numeric) = 3.941570177902429878936756839009
absolute error = 3.941570177902429878936756839009
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.6
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.11
y[1] (closed_form) = 0
y[1] (numeric) = 3.9515454906950351125789066589187
absolute error = 3.9515454906950351125789066589187
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.61
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.12
y[1] (closed_form) = 0
y[1] (numeric) = 3.9615209502774774390121781575556
absolute error = 3.9615209502774774390121781575556
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.62
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5597.1MB, alloc=52.3MB, time=59.22
TOP MAIN SOLVE Loop
x[1] = 4.13
y[1] (closed_form) = 0
y[1] (numeric) = 3.9714965556485082819704318733625
absolute error = 3.9714965556485082819704318733625
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.63
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.14
y[1] (closed_form) = 0
y[1] (numeric) = 3.981472305814691923666514034386
absolute error = 3.981472305814691923666514034386
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.64
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.15
y[1] (closed_form) = 0
y[1] (numeric) = 3.991448199790336089258582074786
absolute error = 3.991448199790336089258582074786
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.65
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5641.2MB, alloc=52.3MB, time=59.69
TOP MAIN SOLVE Loop
x[1] = 4.16
y[1] (closed_form) = 0
y[1] (numeric) = 4.001424236597423229255580845284
absolute error = 4.001424236597423229255580845284
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.66
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.17
y[1] (closed_form) = 0
y[1] (numeric) = 4.0114004152655424919758572484674
absolute error = 4.0114004152655424919758572484674
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.67
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.18
y[1] (closed_form) = 0
y[1] (numeric) = 4.021376734831822378272303624172
absolute error = 4.021376734831822378272303624172
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.68
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=5685.4MB, alloc=52.3MB, time=60.17
x[1] = 4.19
y[1] (closed_form) = 0
y[1] (numeric) = 4.0313531943408640708354351176427
absolute error = 4.0313531943408640708354351176427
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.69
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.2
y[1] (closed_form) = 0
y[1] (numeric) = 4.0413297928446754304824547916651
absolute error = 4.0413297928446754304824547916651
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.7
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.21
y[1] (closed_form) = 0
y[1] (numeric) = 4.0513065294026056519356633436612
absolute error = 4.0513065294026056519356633436612
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.71
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.22
y[1] (closed_form) = 0
y[1] (numeric) = 4.0612834030812805716875485590752
absolute error = 4.0612834030812805716875485590752
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.72
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5729.6MB, alloc=52.3MB, time=60.64
TOP MAIN SOLVE Loop
x[1] = 4.23
y[1] (closed_form) = 0
y[1] (numeric) = 4.0712604129545386206425633278138
absolute error = 4.0712604129545386206425633278138
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.73
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.24
y[1] (closed_form) = 0
y[1] (numeric) = 4.0812375581033674143169900872548
absolute error = 4.0812375581033674143169900872548
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.74
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.25
y[1] (closed_form) = 0
y[1] (numeric) = 4.0912148376158409734684135173218
absolute error = 4.0912148376158409734684135173218
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.75
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5773.8MB, alloc=52.3MB, time=61.11
TOP MAIN SOLVE Loop
x[1] = 4.26
y[1] (closed_form) = 0
y[1] (numeric) = 4.1011922505870575681152014580639
absolute error = 4.1011922505870575681152014580639
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.76
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.27
y[1] (closed_form) = 0
y[1] (numeric) = 4.1111697961190781779940452854558
absolute error = 4.1111697961190781779940452854558
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.77
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.28
y[1] (closed_form) = 0
y[1] (numeric) = 4.1211474733208655625900539896213
absolute error = 4.1211474733208655625900539896213
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.78
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5818.0MB, alloc=52.3MB, time=61.58
TOP MAIN SOLVE Loop
x[1] = 4.29
y[1] (closed_form) = 0
y[1] (numeric) = 4.1311252813082239339591492653467
absolute error = 4.1311252813082239339591492653467
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.79
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.3
y[1] (closed_form) = 0
y[1] (numeric) = 4.1411032192037392256465900583127
absolute error = 4.1411032192037392256465900583127
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.8
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.31
y[1] (closed_form) = 0
y[1] (numeric) = 4.1510812861367199510883819247767
absolute error = 4.1510812861367199510883819247767
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.81
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5862.2MB, alloc=52.3MB, time=62.06
TOP MAIN SOLVE Loop
x[1] = 4.32
y[1] (closed_form) = 0
y[1] (numeric) = 4.1610594812431386449641166778556
absolute error = 4.1610594812431386449641166778556
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.82
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.33
y[1] (closed_form) = 0
y[1] (numeric) = 4.1710378036655738810504582432166
absolute error = 4.1710378036655738810504582432166
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.83
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.34
y[1] (closed_form) = 0
y[1] (numeric) = 4.1810162525531528602040582819014
absolute error = 4.1810162525531528602040582819014
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.84
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
memory used=5906.4MB, alloc=52.3MB, time=62.53
x[1] = 4.35
y[1] (closed_form) = 0
y[1] (numeric) = 4.1909948270614945621811665321628
absolute error = 4.1909948270614945621811665321628
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.85
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.36
y[1] (closed_form) = 0
y[1] (numeric) = 4.2009735263526534550786122774426
absolute error = 4.2009735263526534550786122774426
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.86
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.37
y[1] (closed_form) = 0
y[1] (numeric) = 4.210952349595063756257190898574
absolute error = 4.210952349595063756257190898574
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.87
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.38
y[1] (closed_form) = 0
y[1] (numeric) = 4.2209312959634842386838088870709
absolute error = 4.2209312959634842386838088870709
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.88
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5950.5MB, alloc=52.3MB, time=63.00
TOP MAIN SOLVE Loop
x[1] = 4.39
y[1] (closed_form) = 0
y[1] (numeric) = 4.2309103646389435767030374972388
absolute error = 4.2309103646389435767030374972388
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.89
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.4
y[1] (closed_form) = 0
y[1] (numeric) = 4.2408895548086862253220146588628
absolute error = 4.2408895548086862253220146588628
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.9
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.41
y[1] (closed_form) = 0
y[1] (numeric) = 4.2508688656661188271649318716363
absolute error = 4.2508688656661188271649318716363
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.91
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5994.7MB, alloc=52.3MB, time=63.47
TOP MAIN SOLVE Loop
x[1] = 4.42
y[1] (closed_form) = 0
y[1] (numeric) = 4.260848296410757141324662325237
absolute error = 4.260848296410757141324662325237
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.92
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.43
y[1] (closed_form) = 0
y[1] (numeric) = 4.2708278462481734884094429628649
absolute error = 4.2708278462481734884094429628649
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.93
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.44
y[1] (closed_form) = 0
y[1] (numeric) = 4.2808075143899447061519309232431
absolute error = 4.2808075143899447061519309232431
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.94
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6039.0MB, alloc=52.3MB, time=63.94
TOP MAIN SOLVE Loop
x[1] = 4.45
y[1] (closed_form) = 0
y[1] (numeric) = 4.2907873000536006100164278169306
absolute error = 4.2907873000536006100164278169306
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.95
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.46
y[1] (closed_form) = 0
y[1] (numeric) = 4.3007672024625729533076174501867
absolute error = 4.3007672024625729533076174501867
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.96
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.47
y[1] (closed_form) = 0
y[1] (numeric) = 4.3107472208461448813508075128294
absolute error = 4.3107472208461448813508075128294
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.97
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6083.3MB, alloc=52.3MB, time=64.41
TOP MAIN SOLVE Loop
x[1] = 4.48
y[1] (closed_form) = 0
y[1] (numeric) = 4.3207273544394008743794167851912
absolute error = 4.3207273544394008743794167851912
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.98
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.49
y[1] (closed_form) = 0
y[1] (numeric) = 4.330707602483177173830319767229
absolute error = 4.330707602483177173830319767229
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 5.99
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.5
y[1] (closed_form) = 0
y[1] (numeric) = 4.3406879642240126868116632519126
absolute error = 4.3406879642240126868116632519126
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.51
y[1] (closed_form) = 0
y[1] (numeric) = 4.3506684389141003635709170087004
absolute error = 4.3506684389141003635709170087004
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
memory used=6127.6MB, alloc=52.3MB, time=64.88
Radius of convergence (given) for eq 1 = 6.01
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.52
y[1] (closed_form) = 0
y[1] (numeric) = 4.3606490258112390428532259600486
absolute error = 4.3606490258112390428532259600486
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.02
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.53
y[1] (closed_form) = 0
y[1] (numeric) = 4.3706297241787857601016063721631
absolute error = 4.3706297241787857601016063721631
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.03
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.54
y[1] (closed_form) = 0
y[1] (numeric) = 4.380610533285608513511185790738
absolute error = 4.380610533285608513511185790738
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.04
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6171.8MB, alloc=52.3MB, time=65.34
TOP MAIN SOLVE Loop
x[1] = 4.55
y[1] (closed_form) = 0
y[1] (numeric) = 4.3905914524060394830095376890936
absolute error = 4.3905914524060394830095376890936
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.05
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.56
y[1] (closed_form) = 0
y[1] (numeric) = 4.4005724808198286972942188250604
absolute error = 4.4005724808198286972942188250604
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.06
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.57
y[1] (closed_form) = 0
y[1] (numeric) = 4.4105536178120981441168917017359
absolute error = 4.4105536178120981441168917017359
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.07
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6215.9MB, alloc=52.3MB, time=65.81
TOP MAIN SOLVE Loop
x[1] = 4.58
y[1] (closed_form) = 0
y[1] (numeric) = 4.4205348626732963190609176892017
absolute error = 4.4205348626732963190609176892017
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.08
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.59
y[1] (closed_form) = 0
y[1] (numeric) = 4.4305162146991532081160495016836
absolute error = 4.4305162146991532081160495016836
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.09
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.6
y[1] (closed_form) = 0
y[1] (numeric) = 4.4404976731906356994098458717608
absolute error = 4.4404976731906356994098458717608
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.1
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6260.1MB, alloc=52.3MB, time=66.28
TOP MAIN SOLVE Loop
x[1] = 4.61
y[1] (closed_form) = 0
y[1] (numeric) = 4.4504792374539034195106872795022
absolute error = 4.4504792374539034195106872795022
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.11
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.62
y[1] (closed_form) = 0
y[1] (numeric) = 4.4604609068002649897718001673489
absolute error = 4.4604609068002649897718001673489
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.12
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.63
y[1] (closed_form) = 0
y[1] (numeric) = 4.4704426805461346982395087197807
absolute error = 4.4704426805461346982395087197807
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.13
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6304.3MB, alloc=52.3MB, time=66.75
TOP MAIN SOLVE Loop
x[1] = 4.64
y[1] (closed_form) = 0
y[1] (numeric) = 4.4804245580129895827020383628785
absolute error = 4.4804245580129895827020383628785
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.14
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.65
y[1] (closed_form) = 0
y[1] (numeric) = 4.4904065385273269205076038322158
absolute error = 4.4904065385273269205076038322158
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.15
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.66
y[1] (closed_form) = 0
y[1] (numeric) = 4.5003886214206221208322369970746
absolute error = 4.5003886214206221208322369970746
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.16
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.67
y[1] (closed_form) = 0
y[1] (numeric) = 4.5103708060292870151288554861473
absolute error = 4.5103708060292870151288554861473
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.17
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6348.5MB, alloc=52.3MB, time=67.23
TOP MAIN SOLVE Loop
x[1] = 4.68
y[1] (closed_form) = 0
y[1] (numeric) = 4.520353091694628541539452251023
absolute error = 4.520353091694628541539452251023
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.18
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.69
y[1] (closed_form) = 0
y[1] (numeric) = 4.5303354777628078191020080929565
absolute error = 4.5303354777628078191020080929565
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.19
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.7
y[1] (closed_form) = 0
y[1] (numeric) = 4.5403179635847996076328032799821
absolute error = 4.5403179635847996076328032799821
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.2
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6392.6MB, alloc=52.3MB, time=67.70
TOP MAIN SOLVE Loop
x[1] = 4.71
y[1] (closed_form) = 0
y[1] (numeric) = 4.5503005485163521492132399625497
absolute error = 4.5503005485163521492132399625497
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.21
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.72
y[1] (closed_form) = 0
y[1] (numeric) = 4.5602832319179473872580932789567
absolute error = 4.5602832319179473872580932789567
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.22
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.73
y[1] (closed_form) = 0
y[1] (numeric) = 4.570266013154761559189294807165
absolute error = 4.570266013154761559189294807165
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.23
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6436.8MB, alloc=52.3MB, time=68.17
TOP MAIN SOLVE Loop
x[1] = 4.74
y[1] (closed_form) = 0
y[1] (numeric) = 4.5802488915966261587859262075247
absolute error = 4.5802488915966261587859262075247
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.24
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.75
y[1] (closed_form) = 0
y[1] (numeric) = 4.5902318666179892643270722143866
absolute error = 4.5902318666179892643270722143866
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.25
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.76
y[1] (closed_form) = 0
y[1] (numeric) = 4.600214937597877228689559141369
absolute error = 4.600214937597877228689559141369
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.26
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6481.1MB, alloc=52.3MB, time=68.64
TOP MAIN SOLVE Loop
x[1] = 4.77
y[1] (closed_form) = 0
y[1] (numeric) = 4.6101981039198567276073962000459
absolute error = 4.6101981039198567276073962000459
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.27
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.78
y[1] (closed_form) = 0
y[1] (numeric) = 4.6201813649719971623439504993242
absolute error = 4.6201813649719971623439504993242
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.28
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.79
y[1] (closed_form) = 0
y[1] (numeric) = 4.6301647201468334130715307686094
absolute error = 4.6301647201468334130715307686094
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.29
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6525.2MB, alloc=52.3MB, time=69.11
TOP MAIN SOLVE Loop
x[1] = 4.8
y[1] (closed_form) = 0
y[1] (numeric) = 4.6401481688413289392961376815744
absolute error = 4.6401481688413289392961376815744
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.3
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.81
y[1] (closed_form) = 0
y[1] (numeric) = 4.6501317104568392237076680743231
absolute error = 4.6501317104568392237076680743231
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.31
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.82
y[1] (closed_form) = 0
y[1] (numeric) = 4.6601153443990755558778441552868
absolute error = 4.6601153443990755558778441552868
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.32
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.83
y[1] (closed_form) = 0
y[1] (numeric) = 4.6700990700780691522695846775415
absolute error = 4.6700990700780691522695846775415
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.33
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6569.5MB, alloc=52.3MB, time=69.58
TOP MAIN SOLVE Loop
x[1] = 4.84
y[1] (closed_form) = 0
y[1] (numeric) = 4.6800828869081356090624505525935
absolute error = 4.6800828869081356090624505525935
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.34
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.85
y[1] (closed_form) = 0
y[1] (numeric) = 4.6900667943078396843391899771867
absolute error = 4.6900667943078396843391899771867
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.35
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.86
y[1] (closed_form) = 0
y[1] (numeric) = 4.7000507916999604062182851563009
absolute error = 4.7000507916999604062182851563009
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.36
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6613.7MB, alloc=52.3MB, time=70.05
TOP MAIN SOLVE Loop
x[1] = 4.87
y[1] (closed_form) = 0
y[1] (numeric) = 4.7100348785114565035567713589851
absolute error = 4.7100348785114565035567713589851
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.37
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.88
y[1] (closed_form) = 0
y[1] (numeric) = 4.7200190541734321558864664513521
absolute error = 4.7200190541734321558864664513521
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.38
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.89
y[1] (closed_form) = 0
y[1] (numeric) = 4.7300033181211030592851222167438
absolute error = 4.7300033181211030592851222167438
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.39
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6657.9MB, alloc=52.3MB, time=70.52
TOP MAIN SOLVE Loop
x[1] = 4.9
y[1] (closed_form) = 0
y[1] (numeric) = 4.7399876697937628049218945938114
absolute error = 4.7399876697937628049218945938114
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.4
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.91
y[1] (closed_form) = 0
y[1] (numeric) = 4.7499721086347495670539352310903
absolute error = 4.7499721086347495670539352310903
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.41
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.92
y[1] (closed_form) = 0
y[1] (numeric) = 4.7599566340914130972878381603764
absolute error = 4.7599566340914130972878381603764
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.42
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6702.1MB, alloc=52.3MB, time=70.98
TOP MAIN SOLVE Loop
x[1] = 4.93
y[1] (closed_form) = 0
y[1] (numeric) = 4.7699412456150820219561395180839
absolute error = 4.7699412456150820219561395180839
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.43
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.94
y[1] (closed_form) = 0
y[1] (numeric) = 4.7799259426610314394950715811355
absolute error = 4.7799259426610314394950715811355
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.44
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.95
y[1] (closed_form) = 0
y[1] (numeric) = 4.7899107246884508147453213209227
absolute error = 4.7899107246884508147453213209227
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.45
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6746.2MB, alloc=52.3MB, time=71.45
TOP MAIN SOLVE Loop
x[1] = 4.96
y[1] (closed_form) = 0
y[1] (numeric) = 4.7998955911604121671326445079944
absolute error = 4.7998955911604121671326445079944
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.46
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.97
y[1] (closed_form) = 0
y[1] (numeric) = 4.8098805415438385497198453188144
absolute error = 4.8098805415438385497198453188144
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.47
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.98
y[1] (closed_form) = 0
y[1] (numeric) = 4.8198655753094728161558545081845
absolute error = 4.8198655753094728161558545081845
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.48
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
TOP MAIN SOLVE Loop
x[1] = 4.99
y[1] (closed_form) = 0
y[1] (numeric) = 4.8298506919318466725814325287385
absolute error = 4.8298506919318466725814325287385
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.001
Radius of convergence (given) for eq 1 = 6.49
Order of pole (given) = 0.5
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6790.4MB, alloc=52.3MB, time=71.92
Finished!
diff ( y , x , 1 ) = tanh ( sqrt ( 2.0 * x + 3.0 ) ) ;
Iterations = 4900
Total Elapsed Time = 1 Minutes 12 Seconds
Elapsed Time(since restart) = 1 Minutes 11 Seconds
Time to Timeout = 1 Minutes 48 Seconds
Percent Done = 100 %
> quit
memory used=6802.3MB, alloc=52.3MB, time=72.05