|\^/| Maple 18 (X86 64 WINDOWS)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2014
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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#BEGIN OUTFILE1
# before write maple top matter
# before write_ats library and user def block
#BEGIN ATS LIBRARY BLOCK
# Begin Function number 2
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s\n",str);
> fi;# end if 1;
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
# End Function number 2
# Begin Function number 3
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s",str);
> fi;# end if 1;
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
# End Function number 3
# Begin Function number 4
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> print(label,str);
> fi;# end if 1;
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
# End Function number 4
# Begin Function number 5
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 5
# Begin Function number 6
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> if vallen = 5 then # if number 1
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 6
# Begin Function number 7
> omniout_float_arr := proc(iolevel,prelabel,elemnt,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> print(prelabel,"[",elemnt,"]",value, postlabel);
> fi;# end if 0;
> end;
omniout_float_arr := proc(
iolevel, prelabel, elemnt, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
print(prelabel, "[", elemnt, "]", value, postlabel)
end if
end proc
# End Function number 7
# Begin Function number 8
> logitem_time := proc(fd,secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> fprintf(fd,"
");
> if (secs_in >= 0) then # if number 0
> years_int := int_trunc(secs_in / glob_sec_in_year);
> sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
> days_int := int_trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := sec_temp mod int_trunc(glob_sec_in_day) ;
> hours_int := int_trunc(sec_temp / glob_sec_in_hour);
> sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
> minutes_int := int_trunc(sec_temp / glob_sec_in_minute);
> sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
> if (years_int > 0) then # if number 1
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 2
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 3
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 4
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 4
> else
> fprintf(fd," 0.0 Seconds");
> fi;# end if 3
> fprintf(fd," | \n");
> end;
logitem_time := proc(fd, secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
fprintf(fd, "");
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, " 0.0 Seconds")
end if;
fprintf(fd, " | \n")
end proc
# End Function number 8
# Begin Function number 9
> omniout_timestr := proc(secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> if (secs_in >= 0) then # if number 3
> years_int := int_trunc(secs_in / glob_sec_in_year);
> sec_temp := (int_trunc(secs_in) mod int_trunc(glob_sec_in_year));
> days_int := int_trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_day)) ;
> hours_int := int_trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_hour));
> minutes_int := int_trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod int_trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 4
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 5
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 6
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 7
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 7
> else
> printf(" 0.0 Seconds\n");
> fi;# end if 6
> end;
omniout_timestr := proc(secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" 0.0 Seconds\n")
end if
end proc
# End Function number 9
# Begin Function number 10
> zero_ats_ar := proc(arr_a)
> global ATS_MAX_TERMS;
> local iii;
> iii := 1;
> while (iii <= ATS_MAX_TERMS) do # do number 1
> arr_a [iii] := glob__0;
> iii := iii + 1;
> od;# end do number 1
> end;
zero_ats_ar := proc(arr_a)
local iii;
global ATS_MAX_TERMS;
iii := 1;
while iii <= ATS_MAX_TERMS do arr_a[iii] := glob__0; iii := iii + 1
end do
end proc
# End Function number 10
# Begin Function number 11
> ats := proc(mmm_ats,arr_a,arr_b,jjj_ats)
> global ATS_MAX_TERMS;
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := glob__0;
> if (jjj_ats <= mmm_ats) then # if number 6
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> if ((lll_ats <= ATS_MAX_TERMS and (iii_ats <= ATS_MAX_TERMS) )) then # if number 7
> ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]);
> fi;# end if 7;
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 6;
> ret_ats;
> end;
ats := proc(mmm_ats, arr_a, arr_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
global ATS_MAX_TERMS;
ret_ats := glob__0;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
if lll_ats <= ATS_MAX_TERMS and iii_ats <= ATS_MAX_TERMS then
ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats])
end if;
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
# End Function number 11
# Begin Function number 12
> att := proc(mmm_att,arr_aa,arr_bb,jjj_att)
> global ATS_MAX_TERMS;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := glob__0;
> if (jjj_att < mmm_att) then # if number 6
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while ((iii_att < mmm_att) and (iii_att <= ATS_MAX_TERMS) ) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if ((lll_att <= ATS_MAX_TERMS and (iii_att <= ATS_MAX_TERMS) )) then # if number 7
> ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att);
> fi;# end if 7;
> iii_att := iii_att + 1;
> od;# end do number 1;
> ret_att := ret_att / c(mmm_att) ;
> fi;# end if 6;
> ret_att;
> end;
att := proc(mmm_att, arr_aa, arr_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global ATS_MAX_TERMS;
ret_att := glob__0;
if jjj_att < mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att < mmm_att and iii_att <= ATS_MAX_TERMS do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= ATS_MAX_TERMS and iii_att <= ATS_MAX_TERMS then
ret_att :=
ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])*c(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/c(mmm_att)
end if;
ret_att
end proc
# End Function number 12
# Begin Function number 13
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
# End Function number 13
# Begin Function number 14
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
# End Function number 14
# Begin Function number 15
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
# End Function number 15
# Begin Function number 16
> logitem_good_digits := proc(file,rel_error)
> global glob_small_float,glob_prec;
> local good_digits;
> fprintf(file,"");
> fprintf(file,"%d",glob_min_good_digits);
> fprintf(file," | ");
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float, glob_prec;
fprintf(file, "");
fprintf(file, "%d", glob_min_good_digits);
fprintf(file, " | ")
end proc
# End Function number 16
# Begin Function number 17
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
# End Function number 17
# Begin Function number 18
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
# End Function number 18
# Begin Function number 19
> logitem_h_reason := proc(file)
> global glob_h_reason;
> fprintf(file,"");
> if (glob_h_reason = 1) then # if number 6
> fprintf(file,"Max H");
> elif
> (glob_h_reason = 2) then # if number 7
> fprintf(file,"Display Interval");
> elif
> (glob_h_reason = 3) then # if number 8
> fprintf(file,"Optimal");
> elif
> (glob_h_reason = 4) then # if number 9
> fprintf(file,"Pole Accuracy");
> elif
> (glob_h_reason = 5) then # if number 10
> fprintf(file,"Min H (Pole)");
> elif
> (glob_h_reason = 6) then # if number 11
> fprintf(file,"Pole");
> elif
> (glob_h_reason = 7) then # if number 12
> fprintf(file,"Opt Iter");
> else
> fprintf(file,"Impossible");
> fi;# end if 12
> fprintf(file," | ");
> end;
logitem_h_reason := proc(file)
global glob_h_reason;
fprintf(file, "");
if glob_h_reason = 1 then fprintf(file, "Max H")
elif glob_h_reason = 2 then fprintf(file, "Display Interval")
elif glob_h_reason = 3 then fprintf(file, "Optimal")
elif glob_h_reason = 4 then fprintf(file, "Pole Accuracy")
elif glob_h_reason = 5 then fprintf(file, "Min H (Pole)")
elif glob_h_reason = 6 then fprintf(file, "Pole")
elif glob_h_reason = 7 then fprintf(file, "Opt Iter")
else fprintf(file, "Impossible")
end if;
fprintf(file, " | ")
end proc
# End Function number 19
# Begin Function number 20
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
# End Function number 20
# Begin Function number 21
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file) fprintf(file, "\n") end proc
# End Function number 21
# Begin Function number 22
> chk_data := proc()
> global glob_max_iter,ALWAYS, ATS_MAX_TERMS;
> local errflag;
> errflag := false;
> if (glob_max_iter < 2) then # if number 12
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 12;
> if (errflag) then # if number 12
> quit;
> fi;# end if 12
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, ATS_MAX_TERMS;
errflag := false;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
# End Function number 22
# Begin Function number 23
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := c(clock_sec2);
> sub1 := c(t_end2-t_start2);
> sub2 := c(t2-t_start2);
> if (sub1 = glob__0) then # if number 12
> sec_left := glob__0;
> else
> if (sub2 > glob__0) then # if number 13
> rrr := (sub1/sub2);
> sec_left := rrr * c(ms2) - c(ms2);
> else
> sec_left := glob__0;
> fi;# end if 13
> fi;# end if 12;
> sec_left;
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := c(clock_sec2);
sub1 := c(t_end2 - t_start2);
sub2 := c(t2 - t_start2);
if sub1 = glob__0 then sec_left := glob__0
else
if glob__0 < sub2 then
rrr := sub1/sub2; sec_left := rrr*c(ms2) - c(ms2)
else sec_left := glob__0
end if
end if;
sec_left
end proc
# End Function number 23
# Begin Function number 24
> comp_percent := proc(t_end2,t_start2, t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub2 > glob_small_float) then # if number 12
> rrr := (glob__100*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 12;
> rrr;
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < sub2 then rrr := glob__100*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
# End Function number 24
# Begin Function number 25
> comp_rad_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 12
> ret := float_abs(term1 * glob_h / term2);
> else
> ret := glob_larger_float;
> fi;# end if 12;
> ret;
> #BOTTOM TWO TERM RADIUS ANALYSIS
> end;
comp_rad_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := float_abs(term1*glob_h/term2)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 25
# Begin Function number 26
> comp_ord_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM ORDER ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 12
> ret := glob__1 + float_abs(term2) * c(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(c(last_no));
> else
> ret := glob_larger_float;
> fi;# end if 12;
> ret;
> #BOTTOM TWO TERM ORDER ANALYSIS
> end;
comp_ord_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := glob__1 + float_abs(term2)*
c(last_no)*ln(float_abs(term1*glob_h/term2))/ln(c(last_no))
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 26
# Begin Function number 27
> c := proc(in_val)
> #To Force Conversion when needed
> local ret;
> ret := evalf(in_val);
> ret;
> #End Conversion
> end;
c := proc(in_val) local ret; ret := evalf(in_val); ret end proc
# End Function number 27
# Begin Function number 28
> comp_rad_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret,temp;
> temp := float_abs(term2*term2*c(last_no)+glob__m2*term2*term2-term1*term3*c(last_no)+term1*term3);
> if (float_abs(temp) > glob__0) then # if number 12
> ret := float_abs((term2*glob_h*term1)/(temp));
> else
> ret := glob_larger_float;
> fi;# end if 12;
> ret;
> #BOTTOM THREE TERM RADIUS ANALYSIS
> end;
comp_rad_from_three_terms := proc(term1, term2, term3, last_no)
local ret, temp;
global glob_h, glob_larger_float;
temp := float_abs(term2*term2*c(last_no) + glob__m2*term2*term2
- term1*term3*c(last_no) + term1*term3);
if glob__0 < float_abs(temp) then
ret := float_abs(term2*glob_h*term1/temp)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 28
# Begin Function number 29
> comp_ord_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM ORDER ANALYSIS
> local ret;
> ret := float_abs((glob__4*term1*term3*c(last_no)-glob__3*term1*term3-glob__4*term2*term2*c(last_no)+glob__4*term2*term2+term2*term2*c(last_no*last_no)-term1*term3*c(last_no*last_no))/(term2*term2*c(last_no)-glob__2*term2*term2-term1*term3*c(last_no)+term1*term3));
> ret;
> #TOP THREE TERM ORDER ANALYSIS
> end;
comp_ord_from_three_terms := proc(term1, term2, term3, last_no)
local ret;
ret := float_abs((glob__4*term1*term3*c(last_no) - glob__3*term1*term3
- glob__4*term2*term2*c(last_no) + glob__4*term2*term2
+ term2*term2*c(last_no*last_no) - term1*term3*c(last_no*last_no))
/(term2*term2*c(last_no) - glob__2*term2*term2
- term1*term3*c(last_no) + term1*term3));
ret
end proc
# End Function number 29
# Begin Function number 30
> comp_rad_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> #TOP SIX TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float,glob_six_term_ord_save;
> local ret,rm0,rm1,rm2,rm3,rm4,nr1,nr2,dr1,dr2,ds2,rad_c,ord_no,ds1,rcs;
> if ((term5 <> glob__0) and (term4 <> glob__0) and (term3 <> glob__0) and (term2 <> glob__0) and (term1 <> glob__0)) then # if number 12
> rm0 := term6/term5;
> rm1 := term5/term4;
> rm2 := term4/term3;
> rm3 := term3/term2;
> rm4 := term2/term1;
> nr1 := c(last_no-1)*rm0 - glob__2*c(last_no-2)*rm1 + c(last_no-3)*rm2;
> nr2 := c(last_no-2)*rm1 - glob__2*c(last_no-3)*rm2 + c(last_no-4)*rm3;
> dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
> dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
> ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
> ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
> if ((float_abs(nr1 * dr2 - nr2 * dr1) = glob__0) or (float_abs(dr1) = glob__0)) then # if number 13
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> else
> if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0) then # if number 14
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) -c(last_no)/glob__2;
> if (float_abs(rcs) <> glob__0) then # if number 15
> if (rcs > glob__0) then # if number 16
> rad_c := sqrt(rcs) * float_abs(glob_h);
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 16
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 15
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 14
> fi;# end if 13
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 12;
> glob_six_term_ord_save := ord_no;
> rad_c;
> #BOTTOM SIX TERM RADIUS ANALYSIS
> end;
comp_rad_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
local ret, rm0, rm1, rm2, rm3, rm4, nr1, nr2, dr1, dr2, ds2, rad_c, ord_no,
ds1, rcs;
global glob_h, glob_larger_float, glob_six_term_ord_save;
if term5 <> glob__0 and term4 <> glob__0 and term3 <> glob__0 and
term2 <> glob__0 and term1 <> glob__0 then
rm0 := term6/term5;
rm1 := term5/term4;
rm2 := term4/term3;
rm3 := term3/term2;
rm4 := term2/term1;
nr1 := c(last_no - 1)*rm0 - glob__2*c(last_no - 2)*rm1
+ c(last_no - 3)*rm2;
nr2 := c(last_no - 2)*rm1 - glob__2*c(last_no - 3)*rm2
+ c(last_no - 4)*rm3;
dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
if
float_abs(nr1*dr2 - nr2*dr1) = glob__0 or float_abs(dr1) = glob__0
then rad_c := glob_larger_float; ord_no := glob_larger_float
else
if glob__0 < float_abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no :=
(rcs*nr1 - ds1)/(glob__2*dr1) - c(last_no)/glob__2;
if float_abs(rcs) <> glob__0 then
if glob__0 < rcs then
rad_c := sqrt(rcs)*float_abs(glob_h)
else
rad_c := glob_larger_float;
ord_no := glob_larger_float
end if
else
rad_c := glob_larger_float; ord_no := glob_larger_float
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if;
glob_six_term_ord_save := ord_no;
rad_c
end proc
# End Function number 30
# Begin Function number 31
> comp_ord_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> global glob_six_term_ord_save;
> #TOP SIX TERM ORDER ANALYSIS
> #TOP SAVED FROM SIX TERM RADIUS ANALYSIS
> glob_six_term_ord_save;
> #BOTTOM SIX TERM ORDER ANALYSIS
> end;
comp_ord_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
global glob_six_term_ord_save;
glob_six_term_ord_save
end proc
# End Function number 31
# Begin Function number 32
> factorial_2 := proc(nnn)
> ret := nnn!;
> ret;;
> end;
Warning, `ret` is implicitly declared local to procedure `factorial_2`
factorial_2 := proc(nnn) local ret; ret := nnn!; ret end proc
# End Function number 32
# Begin Function number 33
> factorial_1 := proc(nnn)
> global ATS_MAX_TERMS,array_fact_1;
> local ret;
> if (nnn <= ATS_MAX_TERMS) then # if number 12
> if (array_fact_1[nnn] = 0) then # if number 13
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 13;
> else
> ret := factorial_2(nnn);
> fi;# end if 12;
> ret;
> end;
factorial_1 := proc(nnn)
local ret;
global ATS_MAX_TERMS, array_fact_1;
if nnn <= ATS_MAX_TERMS then
if array_fact_1[nnn] = 0 then
ret := factorial_2(nnn); array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := factorial_2(nnn)
end if;
ret
end proc
# End Function number 33
# Begin Function number 34
> factorial_3 := proc(mmm,nnn)
> global ATS_MAX_TERMS,array_fact_2;
> local ret;
> if ((nnn <= ATS_MAX_TERMS) and (mmm <= ATS_MAX_TERMS)) then # if number 12
> if (array_fact_2[mmm,nnn] = 0) then # if number 13
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 13;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 12;
> ret;
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global ATS_MAX_TERMS, array_fact_2;
if nnn <= ATS_MAX_TERMS and mmm <= ATS_MAX_TERMS then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := factorial_2(mmm)/factorial_2(nnn)
end if;
ret
end proc
# End Function number 34
# Begin Function number 35
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
# End Function number 35
# Begin Function number 36
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
# End Function number 36
# Begin Function number 37
> float_abs := proc(x)
> abs(x);
> end;
float_abs := proc(x) abs(x) end proc
# End Function number 37
# Begin Function number 38
> expt := proc(x,y)
> x^y;
> end;
expt := proc(x, y) x^y end proc
# End Function number 38
# Begin Function number 39
> neg := proc(x)
> -x;
> end;
neg := proc(x) -x end proc
# End Function number 39
# Begin Function number 40
> int_trunc := proc(x)
> trunc(x);
> end;
int_trunc := proc(x) trunc(x) end proc
# End Function number 40
# Begin Function number 41
> estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer)
> local desired_abs_gbl_error,range,estimated_steps,step_error;
> global glob_desired_digits_correct,ALWAYS,ATS_MAX_TERMS;
> omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
> desired_abs_gbl_error := expt(glob__10,c( -glob_desired_digits_correct)) * c(float_abs(c(estimated_answer)));
> omniout_float(ALWAYS,"estimated_h",32,estimated_h,32,"");
> omniout_float(ALWAYS,"estimated_answer",32,estimated_answer,32,"");
> omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,"");
> range := (x_end - x_start);
> omniout_float(ALWAYS,"range",32,range,32,"");
> estimated_steps := range / estimated_h;
> omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,"");
> step_error := (c(float_abs(desired_abs_gbl_error) /sqrt(c( estimated_steps))/c(ATS_MAX_TERMS)));
> omniout_float(ALWAYS,"step_error",32,step_error,32,"");
> (step_error);;
> end;
estimated_needed_step_error := proc(
x_start, x_end, estimated_h, estimated_answer)
local desired_abs_gbl_error, range, estimated_steps, step_error;
global glob_desired_digits_correct, ALWAYS, ATS_MAX_TERMS;
omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, "");
desired_abs_gbl_error :=
expt(glob__10, c(-glob_desired_digits_correct))*
c(float_abs(c(estimated_answer)));
omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, "");
omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, "")
;
omniout_float(ALWAYS, "desired_abs_gbl_error", 32,
desired_abs_gbl_error, 32, "");
range := x_end - x_start;
omniout_float(ALWAYS, "range", 32, range, 32, "");
estimated_steps := range/estimated_h;
omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, "");
step_error := c(float_abs(desired_abs_gbl_error)/(
sqrt(c(estimated_steps))*c(ATS_MAX_TERMS)));
omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
step_error
end proc
# End Function number 41
#END ATS LIBRARY BLOCK
#BEGIN USER FUNCTION BLOCK
#BEGIN BLOCK 3
#BEGIN USER DEF BLOCK
> exact_soln_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]);
> array_tmp4_a1[1] := sin(array_tmp3[1]);
> array_tmp4_a2[1] := cos(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 tan $eq_no = 1
> array_tmp4_a1[2] := att(1,array_tmp4_a2,array_tmp3,1);
> array_tmp4_a2[2] := neg(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 tan $eq_no = 1
> array_tmp4_a1[3] := att(2,array_tmp4_a2,array_tmp3,1);
> array_tmp4_a2[3] := neg(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 tan $eq_no = 1
> array_tmp4_a1[4] := att(3,array_tmp4_a2,array_tmp3,1);
> array_tmp4_a2[4] := neg(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 tan $eq_no = 1
> array_tmp4_a1[5] := att(4,array_tmp4_a2,array_tmp3,1);
> array_tmp4_a2[5] := neg(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] := neg(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] := sin(array_tmp3[1]);
array_tmp4_a2[1] := cos(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] := neg(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] := neg(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] := neg(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] := neg(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] :=
neg(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 := 40;
> # before first input block
> #BEGIN FIRST INPUT BLOCK
> #BEGIN BLOCK 1
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=40;
> #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..(40),[]);
> array_norms:= Array(0..(40),[]);
> array_fact_1:= Array(0..(40),[]);
> 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..(40),[]);
> array_x:= Array(0..(40),[]);
> array_tmp0:= Array(0..(40),[]);
> array_tmp1:= Array(0..(40),[]);
> array_tmp2:= Array(0..(40),[]);
> array_tmp3:= Array(0..(40),[]);
> array_tmp4_g:= Array(0..(40),[]);
> array_tmp4_a1:= Array(0..(40),[]);
> array_tmp4_a2:= Array(0..(40),[]);
> array_tmp4:= Array(0..(40),[]);
> array_tmp5:= Array(0..(40),[]);
> array_m1:= Array(0..(40),[]);
> array_y_higher := Array(0..(2) ,(0..40+ 1),[]);
> array_y_higher_work := Array(0..(2) ,(0..40+ 1),[]);
> array_y_higher_work2 := Array(0..(2) ,(0..40+ 1),[]);
> array_y_set_initial := Array(0..(2) ,(0..40+ 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..(40) ,(0..40+ 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 <= 40) do # do number 1
> array_y_init[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_norms[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) 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 <= 40) do # do number 1
> array_y[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_x[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp0[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp3[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp4_g[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp4_a1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp4_a2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp4[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp5[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) 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 <= 40) 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 <= 40) 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 <= 40) 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 <= 40) 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 <=40) do # do number 1
> term := 1;
> while (term <= 40) 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;
> array_y_set_initial[1,31] := false;
> array_y_set_initial[1,32] := false;
> array_y_set_initial[1,33] := false;
> array_y_set_initial[1,34] := false;
> array_y_set_initial[1,35] := false;
> array_y_set_initial[1,36] := false;
> array_y_set_initial[1,37] := false;
> array_y_set_initial[1,38] := false;
> array_y_set_initial[1,39] := false;
> array_y_set_initial[1,40] := false;
> # before generate init omniout const
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> ATS_MAX_TERMS := 40;
> 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/tan_sqrt_linpostode.ode#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = tan ( 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:=40;");
> 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_min_h := c(0.001);");
> 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(0.005);");
> omniout_str(ALWAYS,"glob_display_interval:=c(0.01);");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"return(c(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_min_h := c(0.001);
> 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(0.005);
> glob_display_interval:=c(0.01);
> #END OVERRIDE BLOCK
> #END BLOCK 2
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_sec := (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours);
> # after second input block
> glob_check_sign := c(my_check_sign(x_start,x_end));
> glob__pi := arccos(glob__m1);
> glob_prec = expt(10.0,c(-Digits));
> if (glob_optimize) then # if number 9
> #BEGIN OPTIMIZE CODE
> omniout_str(ALWAYS,"START of Optimize");
> #Start Series -- INITIALIZE FOR OPTIMIZE
> found_h := false;
> glob_min_pole_est := glob_larger_float;
> last_min_pole_est := glob_larger_float;
> glob_least_given_sing := glob_larger_float;
> glob_least_ratio_sing := glob_larger_float;
> glob_least_3_sing := glob_larger_float;
> glob_least_6_sing := glob_larger_float;
> glob_min_h := float_abs(glob_min_h) * glob_check_sign;
> glob_max_h := float_abs(glob_max_h) * glob_check_sign;
> glob_h := float_abs(glob_min_h) * glob_check_sign;
> glob_display_interval := c((float_abs(c(glob_display_interval))) * (glob_check_sign));
> display_max := c(x_end) - c(x_start)/glob__10;
> if ((glob_display_interval) > (display_max)) then # if number 10
> glob_display_interval := c(display_max);
> fi;# end if 10;
> chk_data();
> min_value := glob_larger_float;
> est_answer := est_size_answer();
> opt_iter := 1;
> est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
> omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
> estimated_step_error := glob_small_float;
> while ((opt_iter <= 100) and ( not found_h)) do # do number 1
> omniout_int(ALWAYS,"opt_iter",32,opt_iter,4,"");
> array_x[1] := c(x_start);
> array_x[2] := c(glob_h);
> glob_next_display := c(x_start);
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1));
> term_no := term_no + 1;
> od;# end do number 2;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 2
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 3
> it := term_no + r_order - 1;
> if (term_no < ATS_MAX_TERMS) then # if number 10
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 10;
> term_no := term_no + 1;
> od;# end do number 3;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> atomall();
> if (glob_check_sign * glob_min_h >= glob_check_sign * glob_h) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> glob_h := glob_check_sign * float_abs(glob_min_h);
> glob_h_reason := 1;
> found_h := true;
> fi;# end if 10;
> if (glob_check_sign * glob_display_interval <= glob_check_sign * glob_h) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR DISPLAY INTERVAL");
> glob_h_reason := 2;
> glob_h := glob_display_interval;
> found_h := true;
> fi;# end if 10;
> if (glob_look_poles) then # if number 10
> check_for_pole();
> fi;# end if 10;
> if ( not found_h) then # if number 10
> est_answer := est_size_answer();
> est_needed_step_err := estimated_needed_step_error(x_start,x_end,glob_h,est_answer);
> omniout_float(ALWAYS,"est_needed_step_err",32,est_needed_step_err,16,"");
> estimated_step_error := test_suggested_h();
> omniout_float(ALWAYS,"estimated_step_error",32,estimated_step_error,32,"");
> if (estimated_step_error < est_needed_step_err) then # if number 11
> omniout_str(ALWAYS,"Double H and LOOP");
> glob_h := glob_h*glob__2;
> else
> omniout_str(ALWAYS,"Found H for OPTIMAL");
> found_h := true;
> glob_h_reason := 3;
> glob_h := glob_h/glob__2;
> fi;# end if 11;
> fi;# end if 10;
> opt_iter := opt_iter + 1;
> od;# end do number 1;
> if (( not found_h) and (opt_iter = 1)) then # if number 10
> omniout_str(ALWAYS,"Beginning glob_h too large.");
> found_h := false;
> fi;# end if 10;
> if (glob_check_sign * glob_max_h <= glob_check_sign * glob_h) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR MAX H");
> glob_h := glob_check_sign * float_abs(glob_max_h);
> glob_h_reason := 1;
> found_h := true;
> fi;# end if 10;
> else
> found_h := true;
> glob_h := glob_h * glob_check_sign;
> fi;# end if 9;
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 9
> html_log_file := fopen("entry.html",WRITE,TEXT);
> fi;# end if 9;
> #BEGIN SOLUTION CODE
> if (found_h) then # if number 9
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := c(x_start);
> array_x[2] := c(glob_h);
> glob_next_display := c(x_start);
> glob_min_pole_est := glob_larger_float;
> glob_least_given_sing := glob_larger_float;
> glob_least_ratio_sing := glob_larger_float;
> glob_least_3_sing := glob_larger_float;
> glob_least_6_sing := glob_larger_float;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 1
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1));
> term_no := term_no + 1;
> od;# end do number 1;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 1
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 2
> it := term_no + r_order - 1;
> if (term_no < ATS_MAX_TERMS) then # if number 10
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 10;
> term_no := term_no + 1;
> od;# end do number 2;
> r_order := r_order + 1;
> od;# end do number 1
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> glob_clock_sec := elapsed_time_seconds();
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_iter < glob_max_iter) and (glob_check_sign * array_x[1] < glob_check_sign * x_end ) and (((glob_clock_sec) - (glob_orig_start_sec)) < (glob_max_sec))) do # do number 1
> #left paren 0001C
> if (reached_interval()) then # if number 10
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> fi;# end if 10;
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> track_estimated_error();
> atomall();
> track_estimated_error();
> display_alot(current_iter);
> if (glob_look_poles) then # if number 10
> check_for_pole();
> fi;# end if 10;
> if (reached_interval()) then # if number 10
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 10;
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y;
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := ATS_MAX_TERMS;
> while (term_no >= 1) do # do number 2
> array_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 3
> array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 3;
> term_no := term_no - 1;
> od;# end do number 2;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> ;
> od;# end do number 1;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 10
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 10;
> if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec )) then # if number 10
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 10;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 1 ) = tan ( 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,"2015-05-02T22:11:40-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"tan_sqrt_lin")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = tan ( 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,"tan_sqrt_lin diffeq.mxt")
> ;
> logitem_str(html_log_file,"tan_sqrt_lin maple results")
> ;
> logitem_str(html_log_file,"PROBLEM - Singularity not accurate")
> ;
> 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 := 40;
Digits := 32;
max_terms := 40;
glob_html_log := true;
array_y_init := Array(0 .. 40, []);
array_norms := Array(0 .. 40, []);
array_fact_1 := Array(0 .. 40, []);
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 .. 40, []);
array_x := Array(0 .. 40, []);
array_tmp0 := Array(0 .. 40, []);
array_tmp1 := Array(0 .. 40, []);
array_tmp2 := Array(0 .. 40, []);
array_tmp3 := Array(0 .. 40, []);
array_tmp4_g := Array(0 .. 40, []);
array_tmp4_a1 := Array(0 .. 40, []);
array_tmp4_a2 := Array(0 .. 40, []);
array_tmp4 := Array(0 .. 40, []);
array_tmp5 := Array(0 .. 40, []);
array_m1 := Array(0 .. 40, []);
array_y_higher := Array(0 .. 2, 0 .. 41, []);
array_y_higher_work := Array(0 .. 2, 0 .. 41, []);
array_y_higher_work2 := Array(0 .. 2, 0 .. 41, []);
array_y_set_initial := Array(0 .. 2, 0 .. 41, []);
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 .. 40, 0 .. 41, []);
term := 1;
while term <= 40 do array_y_init[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 40 do array_norms[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 40 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 <= 40 do array_y[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_x[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp0[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp1[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp3[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp4_g[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 40 do array_tmp4_a1[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 40 do array_tmp4_a2[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 40 do array_tmp4[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp5[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_m1[term] := c(0.); term := term + 1 end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 40 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 <= 40 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 <= 40 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 <= 40 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 <= 40 do
term := 1;
while term <= 40 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;
array_y_set_initial[1, 31] := false;
array_y_set_initial[1, 32] := false;
array_y_set_initial[1, 33] := false;
array_y_set_initial[1, 34] := false;
array_y_set_initial[1, 35] := false;
array_y_set_initial[1, 36] := false;
array_y_set_initial[1, 37] := false;
array_y_set_initial[1, 38] := false;
array_y_set_initial[1, 39] := false;
array_y_set_initial[1, 40] := false;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
ATS_MAX_TERMS := 40;
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/tan_sqrt_linpostode.ode#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = tan ( 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:=40;");
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_min_h := c(0.001);");
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(0.005);");
omniout_str(ALWAYS, "glob_display_interval:=c(0.01);");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "return(c(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_min_h := c(0.001);
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(0.005);
glob_display_interval := c(0.01);
glob_last_good_h := glob_h;
glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours;
glob_check_sign := c(my_check_sign(x_start, x_end));
glob__pi := arccos(glob__m1);
glob_prec = expt(10.0, c(-Digits));
if glob_optimize then
omniout_str(ALWAYS, "START of Optimize");
found_h := false;
glob_min_pole_est := glob_larger_float;
last_min_pole_est := glob_larger_float;
glob_least_given_sing := glob_larger_float;
glob_least_ratio_sing := glob_larger_float;
glob_least_3_sing := glob_larger_float;
glob_least_6_sing := glob_larger_float;
glob_min_h := float_abs(glob_min_h)*glob_check_sign;
glob_max_h := float_abs(glob_max_h)*glob_check_sign;
glob_h := float_abs(glob_min_h)*glob_check_sign;
glob_display_interval :=
c(float_abs(c(glob_display_interval))*glob_check_sign);
display_max := c(x_end) - c(x_start)/glob__10;
if display_max < glob_display_interval then
glob_display_interval := c(display_max)
end if;
chk_data();
min_value := glob_larger_float;
est_answer := est_size_answer();
opt_iter := 1;
est_needed_step_err :=
estimated_needed_step_error(x_start, x_end, glob_h, est_answer)
;
omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, "");
estimated_step_error := glob_small_float;
while opt_iter <= 100 and not found_h do
omniout_int(ALWAYS, "opt_iter", 32, opt_iter, 4, "");
array_x[1] := c(x_start);
array_x[2] := c(glob_h);
glob_next_display := c(x_start);
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, c(term_no - 1))/
c(factorial_1(term_no - 1));
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
if term_no < ATS_MAX_TERMS then
array_y_higher[r_order, term_no] :=
array_y_init[it]*expt(glob_h, c(term_no - 1))/
c(factorial_1(term_no - 1))
end if;
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
atomall();
if glob_check_sign*glob_h <= glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
glob_h := float_abs(glob_min_h)*glob_check_sign;
glob_h_reason := 1;
found_h := true
end if;
if
glob_check_sign*glob_display_interval <= glob_check_sign*glob_h
then
omniout_str(ALWAYS, "SETTING H FOR DISPLAY INTERVAL");
glob_h_reason := 2;
glob_h := glob_display_interval;
found_h := true
end if;
if glob_look_poles then check_for_pole() end if;
if not found_h then
est_answer := est_size_answer();
est_needed_step_err := estimated_needed_step_error(x_start,
x_end, glob_h, est_answer);
omniout_float(ALWAYS, "est_needed_step_err", 32,
est_needed_step_err, 16, "");
estimated_step_error := test_suggested_h();
omniout_float(ALWAYS, "estimated_step_error", 32,
estimated_step_error, 32, "");
if estimated_step_error < est_needed_step_err then
omniout_str(ALWAYS, "Double H and LOOP");
glob_h := glob_h*glob__2
else
omniout_str(ALWAYS, "Found H for OPTIMAL");
found_h := true;
glob_h_reason := 3;
glob_h := glob_h/glob__2
end if
end if;
opt_iter := opt_iter + 1
end do;
if not found_h and opt_iter = 1 then
omniout_str(ALWAYS, "Beginning glob_h too large.");
found_h := false
end if;
if glob_check_sign*glob_max_h <= glob_check_sign*glob_h then
omniout_str(ALWAYS, "SETTING H FOR MAX H");
glob_h := float_abs(glob_max_h)*glob_check_sign;
glob_h_reason := 1;
found_h := true
end if
else found_h := true; glob_h := glob_check_sign*glob_h
end if;
if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT)
end if;
if found_h then
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := c(x_start);
array_x[2] := c(glob_h);
glob_next_display := c(x_start);
glob_min_pole_est := glob_larger_float;
glob_least_given_sing := glob_larger_float;
glob_least_ratio_sing := glob_larger_float;
glob_least_3_sing := glob_larger_float;
glob_least_6_sing := glob_larger_float;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1));
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
if term_no < ATS_MAX_TERMS then
array_y_higher[r_order, term_no] := array_y_init[it]*
expt(glob_h, c(term_no - 1))/
c(factorial_1(term_no - 1))
end if;
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
glob_clock_sec := elapsed_time_seconds();
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_iter < glob_max_iter and
glob_check_sign*array_x[1] < glob_check_sign*x_end and
glob_clock_sec - glob_orig_start_sec < glob_max_sec do
if reached_interval() then
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop")
end if;
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
track_estimated_error();
atomall();
track_estimated_error();
display_alot(current_iter);
if glob_look_poles then check_for_pole() end if;
if reached_interval() then glob_next_display :=
glob_next_display + glob_display_interval
end if;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
term_no := ATS_MAX_TERMS;
while 1 <= term_no do
array_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if glob_max_sec <= elapsed_time_seconds() - glob_orig_start_sec
then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff ( y , x , 1 ) = tan ( 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, "2015-05-02T22:11:40-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"tan_sqrt_lin");
logitem_str(html_log_file, "diff ( y , x , 1 ) = ta\
n ( 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, "tan_sqrt_lin diffeq.mxt");
logitem_str(html_log_file, "tan_sqrt_lin maple results");
logitem_str(html_log_file, "PROBLEM - Singularity not accurate")
;
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/tan_sqrt_linpostode.ode#################
diff ( y , x , 1 ) = tan ( sqrt ( 2.0 * x + 3.0 ) ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=40;
!
#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_min_h := c(0.001);
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(0.005);
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
memory used=3.9MB, alloc=40.3MB, time=0.11
x[1] = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 0
absolute error = 0
relative error = -1 %
Desired digits = 8
Estimated correct digits = -16
Correct digits = -16
h = 0.005
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) = -0.044835654091227186696021046065236
absolute error = 0.044835654091227186696021046065236
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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) = -0.088523045624558613678763922026379
absolute error = 0.088523045624558613678763922026379
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 0.13
y[1] (closed_form) = 0
y[1] (numeric) = -0.13112011011839056579468950270955
absolute error = 0.13112011011839056579468950270955
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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) = -0.17268042908874564151342270416347
absolute error = 0.17268042908874564151342270416347
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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) = -0.21325365607654129834769401501985
absolute error = 0.21325365607654129834769401501985
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 0.16
y[1] (closed_form) = 0
y[1] (numeric) = -0.25288589180180111872986857836264
absolute error = 0.25288589180180111872986857836264
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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
memory used=35.4MB, alloc=44.3MB, time=0.45
TOP MAIN SOLVE Loop
x[1] = 0.17
y[1] (closed_form) = 0
y[1] (numeric) = -0.29162001556505884687975790171297
absolute error = 0.29162001556505884687975790171297
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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) = -0.32949597888001458176409701616131
absolute error = 0.32949597888001458176409701616131
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 0.19
y[1] (closed_form) = 0
y[1] (numeric) = -0.36655106638790463367382277192777
absolute error = 0.36655106638790463367382277192777
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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) = -0.40282012833328674301167383470402
absolute error = 0.40282012833328674301167383470402
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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) = -0.43833578824174902630873238821902
absolute error = 0.43833578824174902630873238821902
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 0.22
y[1] (closed_form) = 0
y[1] (numeric) = -0.4731286289076860335908052016303
absolute error = 0.4731286289076860335908052016303
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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) = -0.50722735935507319323748807916558
absolute error = 0.50722735935507319323748807916558
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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) = -0.540658965060382002510878232789
absolute error = 0.540658965060382002510878232789
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 0.25
y[1] (closed_form) = 0
y[1] (numeric) = -0.5734488434117753643447500511803
absolute error = 0.5734488434117753643447500511803
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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
memory used=79.7MB, alloc=52.3MB, time=0.94
TOP MAIN SOLVE Loop
x[1] = 0.26
y[1] (closed_form) = 0
y[1] (numeric) = -0.60562092611230480337199470792958
absolute error = 0.60562092611230480337199470792958
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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) = -0.63719779000872780227474402386786
absolute error = 0.63719779000872780227474402386786
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 0.28
y[1] (closed_form) = 0
y[1] (numeric) = -0.66820075763503857668192446246792
absolute error = 0.66820075763503857668192446246792
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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) = -0.6986499885953512941084542274147
absolute error = 0.6986499885953512941084542274147
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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) = -0.728564562769869000165387575506
absolute error = 0.728564562769869000165387575506
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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) = -0.75796255620658750667114820718218
absolute error = 0.75796255620658750667114820718218
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 0.32
y[1] (closed_form) = 0
y[1] (numeric) = -0.78686111045703842231196750229484
absolute error = 0.78686111045703842231196750229484
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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) = -0.81527649602421025702116445311705
absolute error = 0.81527649602421025702116445311705
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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) = -0.84322417051266946046380502488114
absolute error = 0.84322417051266946046380502488114
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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=124.0MB, alloc=52.3MB, time=1.41
TOP MAIN SOLVE Loop
x[1] = 0.35
y[1] (closed_form) = 0
y[1] (numeric) = -0.87071883200305292823949983097782
absolute error = 0.87071883200305292823949983097782
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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) = -0.89777446811402643471630673528889
absolute error = 0.89777446811402643471630673528889
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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) = -0.92440440116324369725503379271387
absolute error = 0.92440440116324369725503379271387
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 0.38
y[1] (closed_form) = 0
y[1] (numeric) = -0.95062132979373905606709766163202
absolute error = 0.95062132979373905606709766163202
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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) = -0.97643736739264707828881727353932
absolute error = 0.97643736739264707828881727353932
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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) = -1.001864077594404802221354747181
absolute error = 1.001864077594404802221354747181
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 0.41
y[1] (closed_form) = 0
y[1] (numeric) = -1.0269125071300105161761123466129
absolute error = 1.0269125071300105161761123466129
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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) = -1.051593216256935833627548966112
absolute error = 1.051593216256935833627548966112
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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) = -1.0759163069804443189677921597782
absolute error = 1.0759163069804443189677921597782
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
memory used=168.2MB, alloc=52.3MB, time=1.87
x[1] = 0.44
y[1] (closed_form) = 0
y[1] (numeric) = -1.0998914492559563934127331691624
absolute error = 1.0998914492559563934127331691624
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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) = -1.1235279053433700217486572906054
absolute error = 1.1235279053433700217486572906054
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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) = -1.1468345524676012992213780037444
absolute error = 1.1468345524676012992213780037444
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 0.47
y[1] (closed_form) = 0
y[1] (numeric) = -1.1698199039247910320147462849739
absolute error = 1.1698199039247910320147462849739
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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) = -1.1924921287604101000324468199076
absolute error = 1.1924921287604101000324468199076
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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) = -1.2148590701336949088218098411456
absolute error = 1.2148590701336949088218098411456
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 0.5
y[1] (closed_form) = 0
y[1] (numeric) = -1.2369282624722871050013510870526
absolute error = 1.2369282624722871050013510870526
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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) = -1.2587069475114932595277939588658
absolute error = 1.2587069475114932595277939588658
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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) = -1.2802020893040934375194186909774
absolute error = 1.2802020893040934375194186909774
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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
memory used=212.5MB, alloc=52.3MB, time=2.36
x[1] = 0.53
y[1] (closed_form) = 0
y[1] (numeric) = -1.3014203882790015936541781635986
absolute error = 1.3014203882790015936541781635986
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 0.54
y[1] (closed_form) = 0
y[1] (numeric) = -1.3223682944202185621533771494797
absolute error = 1.3223682944202185621533771494797
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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) = -1.343052019631335047792696626954
absolute error = 1.343052019631335047792696626954
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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) = -1.3634775493452628494737477124679
absolute error = 1.3634775493452628494737477124679
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 0.57
y[1] (closed_form) = 0
y[1] (numeric) = -1.3836506534338319451894310028204
absolute error = 1.3836506534338319451894310028204
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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) = -1.403576896467331244637395108754
absolute error = 1.403576896467331244637395108754
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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) = -1.4232616473699407905720712763411
absolute error = 1.4232616473699407905720712763411
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 0.6
y[1] (closed_form) = 0
y[1] (numeric) = -1.4427100885132579166320924532062
absolute error = 1.4427100885132579166320924532062
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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) = -1.4619272242867194875459404500685
absolute error = 1.4619272242867194875459404500685
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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
memory used=256.8MB, alloc=52.3MB, time=2.83
x[1] = 0.62
y[1] (closed_form) = 0
y[1] (numeric) = -1.4809178891806315332104958003613
absolute error = 1.4809178891806315332104958003613
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 0.63
y[1] (closed_form) = 0
y[1] (numeric) = -1.4996867554147049917889689267426
absolute error = 1.4996867554147049917889689267426
relative error = -1 %
Desired digits = 8
Estimated correct digits = 13
Correct digits = -16
h = 0.005
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) = -1.5182383401424340375509531829236
absolute error = 1.5182383401424340375509531829236
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -1.5365770122593167915202578564473
absolute error = 1.5365770122593167915202578564473
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 0.66
y[1] (closed_form) = 0
y[1] (numeric) = -1.5547069988407850008272337741051
absolute error = 1.5547069988407850008272337741051
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -1.5726323912337598089174539764664
absolute error = 1.5726323912337598089174539764664
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -1.5903571508239674067980356852872
absolute error = 1.5903571508239674067980356852872
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 0.69
y[1] (closed_form) = 0
y[1] (numeric) = -1.6078851144995153955356196126041
absolute error = 1.6078851144995153955356196126041
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -1.6252199998297339863115364258595
absolute error = 1.6252199998297339863115364258595
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -1.6423654099769130577116393351379
absolute error = 1.6423654099769130577116393351379
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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=301.0MB, alloc=52.3MB, time=3.30
TOP MAIN SOLVE Loop
x[1] = 0.72
y[1] (closed_form) = 0
y[1] (numeric) = -1.6593248383573052151947140095508
absolute error = 1.6593248383573052151947140095508
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -1.6761016730666061389542143443077
absolute error = 1.6761016730666061389542143443077
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -1.692699201084057470662448417464
absolute error = 1.692699201084057470662448417464
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -1.7091206122683359952075102533021
absolute error = 1.7091206122683359952075102533021
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -1.7253690031574884517830365829068
absolute error = 1.7253690031574884517830365829068
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -1.7414473805843372168631301101492
absolute error = 1.7414473805843372168631301101492
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -1.7573586651180122461113246358877
absolute error = 1.7573586651180122461113246358877
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 0.79
y[1] (closed_form) = 0
y[1] (numeric) = -1.7731056943415535305963818106919
absolute error = 1.7731056943415535305963818106919
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -1.788691225974870922954077671504
absolute error = 1.788691225974870922954077671504
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
memory used=345.2MB, alloc=52.3MB, time=3.77
TOP MAIN SOLVE Loop
x[1] = 0.81
y[1] (closed_form) = 0
y[1] (numeric) = -1.8041179408517399965591616062186
absolute error = 1.8041179408517399965591616062186
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 0.82
y[1] (closed_form) = 0
y[1] (numeric) = -1.8193884457589495100234555736869
absolute error = 1.8193884457589495100234555736869
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -1.834505276145194332155138949233
absolute error = 1.834505276145194332155138949233
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -1.849470898706823949962716914608
absolute error = 1.849470898706823949962716914608
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 0.85
y[1] (closed_form) = 0
y[1] (numeric) = -1.8642877138571078510836378639406
absolute error = 1.8642877138571078510836378639406
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -1.8789580580852623344832951140784
absolute error = 1.8789580580852623344832951140784
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -1.8934842062110961004704212688154
absolute error = 1.8934842062110961004704212688154
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 0.88
y[1] (closed_form) = 0
y[1] (numeric) = -1.9078683735407719687904447450752
absolute error = 1.9078683735407719687904447450752
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -1.9221127179288471407673539138658
absolute error = 1.9221127179288471407673539138658
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
memory used=389.5MB, alloc=52.3MB, time=4.25
TOP MAIN SOLVE Loop
x[1] = 0.9
y[1] (closed_form) = 0
y[1] (numeric) = -1.9362193417514426110527052399991
absolute error = 1.9362193417514426110527052399991
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 0.91
y[1] (closed_form) = 0
y[1] (numeric) = -1.9501902937951018659917172602702
absolute error = 1.9501902937951018659917172602702
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -1.9640275710656282494663930495928
absolute error = 1.9640275710656282494663930495928
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -1.9777331205209378409335985559517
absolute error = 1.9777331205209378409335985559517
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 0.94
y[1] (closed_form) = 0
y[1] (numeric) = -1.9913088407317290063467555737891
absolute error = 1.9913088407317290063467555737891
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.0047565834735496960039389892594
absolute error = 2.0047565834735496960039389892594
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.0180781552536379223252036540493
absolute error = 2.0180781552536379223252036540493
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
x[1] = 0.97
y[1] (closed_form) = 0
y[1] (numeric) = -2.0312753187757185970857480582334
absolute error = 2.0312753187757185970857480582334
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.0443497943457600690885445360405
absolute error = 2.0443497943457600690885445360405
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
memory used=433.3MB, alloc=52.3MB, time=4.72
TOP MAIN SOLVE Loop
x[1] = 0.99
y[1] (closed_form) = 0
y[1] (numeric) = -2.0573032612215253849076794460518
absolute error = 2.0573032612215253849076794460518
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.0701373589085956735105334456035
absolute error = 2.0701373589085956735105334456035
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 1.01
y[1] (closed_form) = 0
y[1] (numeric) = -2.0828536884053953715303585827089
absolute error = 2.0828536884053953715303585827089
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.0954538133996105603022104489724
absolute error = 2.0954538133996105603022104489724
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.1079392614182618333557464493173
absolute error = 2.1079392614182618333557464493173
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 1.04
y[1] (closed_form) = 0
y[1] (numeric) = -2.1203115249335712584125369421416
absolute error = 2.1203115249335712584125369421416
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.1325720624266485910959137823147
absolute error = 2.1325720624266485910959137823147
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.1447222994109144302637711329347
absolute error = 2.1447222994109144302637711329347
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 1.07
y[1] (closed_form) = 0
y[1] (numeric) = -2.1567636294170770071056433539418
absolute error = 2.1567636294170770071056433539418
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
memory used=477.3MB, alloc=52.3MB, time=5.19
x[1] = 1.08
y[1] (closed_form) = 0
y[1] (numeric) = -2.1686974149413843369991423214365
absolute error = 2.1686974149413843369991423214365
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.1805249883587841319363062556126
absolute error = 2.1805249883587841319363062556126
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 1.1
y[1] (closed_form) = 0
y[1] (numeric) = -2.1922476528025397990805877145688
absolute error = 2.1922476528025397990805877145688
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.2038666830117716919256642057004
absolute error = 2.2038666830117716919256642057004
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.215383326148318213901877572025
absolute error = 2.215383326148318213901877572025
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 1.13
y[1] (closed_form) = 0
y[1] (numeric) = -2.2267988025842411025107051151632
absolute error = 2.2267988025842411025107051151632
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.2381143066612329688339872048991
absolute error = 2.2381143066612329688339872048991
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.2493310074231226758490896120504
absolute error = 2.2493310074231226758490896120504
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 1.16
y[1] (closed_form) = 0
y[1] (numeric) = -2.2604500493226151707640533150479
absolute error = 2.2604500493226151707640533150479
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
memory used=521.3MB, alloc=52.3MB, time=5.66
x[1] = 1.17
y[1] (closed_form) = 0
y[1] (numeric) = -2.2714725529033467196492080988071
absolute error = 2.2714725529033467196492080988071
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.2823996154582839204888097689182
absolute error = 2.2823996154582839204888097689182
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
x[1] = 1.19
y[1] (closed_form) = 0
y[1] (numeric) = -2.2932323116654452011660042727349
absolute error = 2.2932323116654452011660042727349
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.3039716942018765627629577389334
absolute error = 2.3039716942018765627629577389334
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.3146187943367689390326370079723
absolute error = 2.3146187943367689390326370079723
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.3251746225045625543911268876223
absolute error = 2.3251746225045625543911268876223
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 1.23
y[1] (closed_form) = 0
y[1] (numeric) = -2.3356401688588439301517431005392
absolute error = 2.3356401688588439301517431005392
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.3460164038078035765203237234632
absolute error = 2.3460164038078035765203237234632
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.3563042785319867896183025728993
absolute error = 2.3563042785319867896183025728993
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 1.26
y[1] (closed_form) = 0
y[1] (numeric) = -2.3665047254850362303471800210069
absolute error = 2.3665047254850362303471800210069
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
memory used=565.3MB, alloc=52.3MB, time=6.12
TOP MAIN SOLVE Loop
x[1] = 1.27
y[1] (closed_form) = 0
y[1] (numeric) = -2.3766186588780929848336755558277
absolute error = 2.3766186588780929848336755558277
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.3866469751484924912537573064504
absolute error = 2.3866469751484924912537573064504
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 1.29
y[1] (closed_form) = 0
y[1] (numeric) = -2.3965905534133629684465555410589
absolute error = 2.3965905534133629684465555410589
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.4064502559087067075122006183563
absolute error = 2.4064502559087067075122006183563
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.4162269284145187039184357539896
absolute error = 2.4162269284145187039184357539896
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 1.32
y[1] (closed_form) = 0
y[1] (numeric) = -2.4259214006664725352568222537174
absolute error = 2.4259214006664725352568222537174
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.4355344867546800544165977268045
absolute error = 2.4355344867546800544165977268045
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.4450669855100092999543856564148
absolute error = 2.4450669855100092999543856564148
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 1.35
y[1] (closed_form) = 0
y[1] (numeric) = -2.4545196808784239595304748254553
absolute error = 2.4545196808784239595304748254553
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
memory used=609.4MB, alloc=52.3MB, time=6.61
TOP MAIN SOLVE Loop
x[1] = 1.36
y[1] (closed_form) = 0
y[1] (numeric) = -2.463893342283787697190557470893
absolute error = 2.463893342283787697190557470893
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.4731887249795576134902642918487
absolute error = 2.4731887249795576134902642918487
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 1.38
y[1] (closed_form) = 0
y[1] (numeric) = -2.482406570389772994992079884245
absolute error = 2.482406570389772994992079884245
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.4915476064397282757885731970946
absolute error = 2.4915476064397282757885731970946
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.5006125478767027307582742102761
absolute error = 2.5006125478767027307582742102761
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
x[1] = 1.41
y[1] (closed_form) = 0
y[1] (numeric) = -2.509602096581103803432995326045
absolute error = 2.509602096581103803432995326045
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.5185169418683660985089052538021
absolute error = 2.5185169418683660985089052538021
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.5273577607819339005242906796031
absolute error = 2.5273577607819339005242906796031
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.5361252183776415787443066174185
absolute error = 2.5361252183776415787443066174185
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
memory used=653.4MB, alloc=52.3MB, time=7.08
x[1] = 1.45
y[1] (closed_form) = 0
y[1] (numeric) = -2.5448199679997933687100680131806
absolute error = 2.5448199679997933687100680131806
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.5534426515492317501427210671771
absolute error = 2.5534426515492317501427210671771
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.5619938997436719377727722082594
absolute error = 2.5619938997436719377727722082594
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 1.48
y[1] (closed_form) = 0
y[1] (numeric) = -2.5704743323705688368135810745434
absolute error = 2.5704743323705688368135810745434
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.5788845585327721605179441678626
absolute error = 2.5788845585327721605179441678626
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.5872251768872152374252227906998
absolute error = 2.5872251768872152374252227906998
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 1.51
y[1] (closed_form) = 0
y[1] (numeric) = -2.5954967758768733258774005369314
absolute error = 2.5954967758768733258774005369314
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.6036999339562179798951514122598
absolute error = 2.6036999339562179798951514122598
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.6118352198103851515990846216421
absolute error = 2.6118352198103851515990846216421
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
memory used=697.4MB, alloc=52.3MB, time=7.55
x[1] = 1.54
y[1] (closed_form) = 0
y[1] (numeric) = -2.6199031925682662502971845882196
absolute error = 2.6199031925682662502971845882196
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.6279044020097232875439795103455
absolute error = 2.6279044020097232875439795103455
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.6358393887671215023942204585973
absolute error = 2.6358393887671215023942204585973
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 1.57
y[1] (closed_form) = 0
y[1] (numeric) = -2.6437086845213654642202951626464
absolute error = 2.6437086845213654642202951626464
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.6515128121926175752865223247823
absolute error = 2.6515128121926175752865223247823
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.659252286125871126118355864058
absolute error = 2.659252286125871126118355864058
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 1.6
y[1] (closed_form) = 0
y[1] (numeric) = -2.6669276122715435787560781323656
absolute error = 2.6669276122715435787560781323656
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.6745392883612495522191300868958
absolute error = 2.6745392883612495522191300868958
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.6820878040789070476534103637334
absolute error = 2.6820878040789070476534103637334
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.6895736412273247651170541008118
absolute error = 2.6895736412273247651170541008118
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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=741.4MB, alloc=52.3MB, time=8.03
TOP MAIN SOLVE Loop
x[1] = 1.64
y[1] (closed_form) = 0
y[1] (numeric) = -2.6969972738904129178698285374089
absolute error = 2.6969972738904129178698285374089
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.704359168591154732080728204098
absolute error = 2.704359168591154732080728204098
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.7116597844454708193591438364702
absolute error = 2.7116597844454708193591438364702
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 1.67
y[1] (closed_form) = 0
y[1] (numeric) = -2.71889957331210381630325429102
absolute error = 2.71889957331210381630325429102
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.7260789799386460897243351278583
absolute error = 2.7260789799386460897243351278583
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.7331984421038288992203959391457
absolute error = 2.7331984421038288992203959391457
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 1.7
y[1] (closed_form) = 0
y[1] (numeric) = -2.7402583907561871816757562583727
absolute error = 2.7402583907561871816757562583727
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.7472592501492100668335234456663
absolute error = 2.7472592501492100668335234456663
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.7542014379730833415195420104357
absolute error = 2.7542014379730833415195420104357
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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=785.6MB, alloc=52.3MB, time=8.50
TOP MAIN SOLVE Loop
x[1] = 1.73
y[1] (closed_form) = 0
y[1] (numeric) = -2.7610853654831263449757837334666
absolute error = 2.7610853654831263449757837334666
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.7679114376250221920457313682026
absolute error = 2.7679114376250221920457313682026
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.7746800531569367779520074750133
absolute error = 2.7746800531569367779520074750133
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 1.76
y[1] (closed_form) = 0
y[1] (numeric) = -2.7813916047686187117566888760859
absolute error = 2.7813916047686187117566888760859
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.7880464791975691492502745465433
absolute error = 2.7880464791975691492502745465433
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.7946450573423674442255502423891
absolute error = 2.7946450573423674442255502423891
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.8011877143732356043876667188796
absolute error = 2.8011877143732356043876667188796
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 1.8
y[1] (closed_form) = 0
y[1] (numeric) = -2.807674819839921719327316669308
absolute error = 2.807674819839921719327316669308
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.8141067377769798180871781746155
absolute error = 2.8141067377769798180871781746155
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
memory used=829.5MB, alloc=52.3MB, time=8.97
TOP MAIN SOLVE Loop
x[1] = 1.82
y[1] (closed_form) = 0
y[1] (numeric) = -2.8204838268065210081682237048013
absolute error = 2.8204838268065210081682237048013
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 1.83
y[1] (closed_form) = 0
y[1] (numeric) = -2.8268064402385082418631783846107
absolute error = 2.8268064402385082418631783846107
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.8330749261686646452942980471475
absolute error = 2.8330749261686646452942980471475
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.8392896275740630263993653917739
absolute error = 2.8392896275740630263993653917739
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 1.86
y[1] (closed_form) = 0
y[1] (numeric) = -2.8454508824064619464731782193408
absolute error = 2.8454508824064619464731782193408
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.8515590236834515920338731858276
absolute error = 2.8515590236834515920338731858276
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.8576143795774706162191048891636
absolute error = 2.8576143795774706162191048891636
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 1.89
y[1] (closed_form) = 0
y[1] (numeric) = -2.8636172735027531282653150628248
absolute error = 2.8636172735027531282653150628248
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.8695680242002630926786737376239
absolute error = 2.8695680242002630926786737376239
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
memory used=873.5MB, alloc=52.3MB, time=9.44
x[1] = 1.91
y[1] (closed_form) = 0
y[1] (numeric) = -2.8754669458206715534111144972446
absolute error = 2.8754669458206715534111144972446
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 1.92
y[1] (closed_form) = 0
y[1] (numeric) = -2.8813143480054303197918883563676
absolute error = 2.8813143480054303197918883563676
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.8871105359659940373501515740684
absolute error = 2.8871105359659940373501515740684
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.8928558105612409153397995351076
absolute error = 2.8928558105612409153397995351076
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.8985504683731407912068670202995
absolute error = 2.8985504683731407912068670202995
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 1.96
y[1] (closed_form) = 0
y[1] (numeric) = -2.9041948017807176779994649269414
absolute error = 2.9041948017807176779994649269414
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.9097890990323524614962280233698
absolute error = 2.9097890990323524614962280233698
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.9153336443164699874107644946427
absolute error = 2.9153336443164699874107644946427
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 1.99
y[1] (closed_form) = 0
y[1] (numeric) = -2.9208287178306534033040718507844
absolute error = 2.9208287178306534033040718507844
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.9262745958492272927852643410047
absolute error = 2.9262745958492272927852643410047
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
memory used=917.6MB, alloc=52.3MB, time=9.92
TOP MAIN SOLVE Loop
x[1] = 2.01
y[1] (closed_form) = 0
y[1] (numeric) = -2.9316715507893498592731637104407
absolute error = 2.9316715507893498592731637104407
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 2.02
y[1] (closed_form) = 0
y[1] (numeric) = -2.9370198512756531811819333686347
absolute error = 2.9370198512756531811819333686347
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.9423197622034693681181882190403
absolute error = 2.9423197622034693681181882190403
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.9475715448006792968468412550489
absolute error = 2.9475715448006792968468412550489
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 2.05
y[1] (closed_form) = 0
y[1] (numeric) = -2.9527754566882194947834003788733
absolute error = 2.9527754566882194947834003788733
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.9579317519392816660561786231517
absolute error = 2.9579317519392816660561786231517
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.9630406811372383192739405978993
absolute error = 2.9630406811372383192739405978993
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 2.08
y[1] (closed_form) = 0
y[1] (numeric) = -2.9681024914323269556171090816657
absolute error = 2.9681024914323269556171090816657
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.973117426597124309388288439185
absolute error = 2.973117426597124309388288439185
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
memory used=961.6MB, alloc=52.3MB, time=10.39
TOP MAIN SOLVE Loop
x[1] = 2.1
y[1] (closed_form) = 0
y[1] (numeric) = -2.9780857270808411994124651530861
absolute error = 2.9780857270808411994124651530861
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.9830076300624676474255409467736
absolute error = 2.9830076300624676474255409467736
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.9878833695027970476408102140971
absolute error = 2.9878833695027970476408102140971
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.9927131761953573288954233262364
absolute error = 2.9927131761953573288954233262364
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.9974972778162762360591512388681
absolute error = 2.9974972778162762360591512388681
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 2.15
y[1] (closed_form) = 0
y[1] (numeric) = -3.0022358989731070696876414176845
absolute error = 3.0022358989731070696876414176845
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.0069292612526404612169098134586
absolute error = 3.0069292612526404612169098134586
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.0115775832677270243614886780791
absolute error = 3.0115775832677270243614886780791
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 2.18
y[1] (closed_form) = 0
y[1] (numeric) = -3.0161810807031350108713812441591
absolute error = 3.0161810807031350108713812441591
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
memory used=1005.7MB, alloc=52.3MB, time=10.88
TOP MAIN SOLVE Loop
x[1] = 2.19
y[1] (closed_form) = 0
y[1] (numeric) = -3.0207399663604664095364192489456
absolute error = 3.0207399663604664095364192489456
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.0252544502021542604504699576206
absolute error = 3.0252544502021542604504699576206
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 2.21
y[1] (closed_form) = 0
y[1] (numeric) = -3.0297247393945633112463168611088
absolute error = 3.0297247393945633112463168611088
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.0341510383502155175019652708468
absolute error = 3.0341510383502155175019652708468
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.0385335487691612850490709000964
absolute error = 3.0385335487691612850490709000964
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 2.24
y[1] (closed_form) = 0
y[1] (numeric) = -3.0428724696795167667626899854651
absolute error = 3.0428724696795167667626899854651
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.0471679974771869598858828968504
absolute error = 3.0471679974771869598858828968504
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.0514203259647938013776392519566
absolute error = 3.0514203259647938013776392519566
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
x[1] = 2.27
y[1] (closed_form) = 0
y[1] (numeric) = -3.0556296463898279275291958522569
absolute error = 3.0556296463898279275291958522569
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
memory used=1049.8MB, alloc=52.3MB, time=11.34
x[1] = 2.28
y[1] (closed_form) = 0
y[1] (numeric) = -3.0597961474820422495583095785929
absolute error = 3.0597961474820422495583095785929
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.0639200154901049984737162775711
absolute error = 3.0639200154901049984737162775711
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.068001434217529409636179882416
absolute error = 3.068001434217529409636179882416
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 2.31
y[1] (closed_form) = 0
y[1] (numeric) = -3.0720405850578967495835892453906
absolute error = 3.0720405850578967495835892453906
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.076037647029388934311978212156
absolute error = 3.076037647029388934311978212156
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.0799927968086465488088244647322
absolute error = 3.0799927968086465488088244647322
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 2.34
y[1] (closed_form) = 0
y[1] (numeric) = -3.0839062087639676517355786766501
absolute error = 3.0839062087639676517355786766501
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.0877780549878623362876825634034
absolute error = 3.0877780549878623362876825634034
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.091608505328977617974709756959
absolute error = 3.091608505328977617974709756959
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
memory used=1093.8MB, alloc=52.3MB, time=11.81
x[1] = 2.37
y[1] (closed_form) = 0
y[1] (numeric) = -3.0953977274234068319300835457061
absolute error = 3.0953977274234068319300835457061
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.099145886725397345964776722464
absolute error = 3.099145886725397345964776722464
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.1028531465374700305238000686737
absolute error = 3.1028531465374700305238000686737
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 2.4
y[1] (closed_form) = 0
y[1] (numeric) = -3.1065196680399635726044424142477
absolute error = 3.1065196680399635726044424142477
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.110145610320016377181810279649
absolute error = 3.110145610320016377181810279649
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.1137311303999984664046809498221
absolute error = 3.1137311303999984664046809498221
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
x[1] = 2.43
y[1] (closed_form) = 0
y[1] (numeric) = -3.1172763832654054634306965836944
absolute error = 3.1172763832654054634306965836944
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.1207815218922264339348322572095
absolute error = 3.1207815218922264339348322572095
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.1242466972737970537313731268637
absolute error = 3.1242466972737970537313731268637
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.1276720584471492752915105080243
absolute error = 3.1276720584471492752915105080243
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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=1137.9MB, alloc=52.3MB, time=12.30
TOP MAIN SOLVE Loop
x[1] = 2.47
y[1] (closed_form) = 0
y[1] (numeric) = -3.1310577525188683789214884536996
absolute error = 3.1310577525188683789214884536996
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.1344039246904680157061260797554
absolute error = 3.1344039246904680157061260797554
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.1377107182832935787459508215207
absolute error = 3.1377107182832935787459508215207
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 2.5
y[1] (closed_form) = 0
y[1] (numeric) = -3.1409782747629639764594567688378
absolute error = 3.1409782747629639764594567688378
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.1442067337633616265310177273258
absolute error = 3.1442067337633616265310177273258
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.1473962331101802412147424074848
absolute error = 3.1473962331101802412147424074848
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 2.53
y[1] (closed_form) = 0
y[1] (numeric) = -3.1505469088440397339188426922742
absolute error = 3.1505469088440397339188426922742
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.1536588952431773430661117235308
absolute error = 3.1536588952431773430661117235308
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.1567323248457238419341957361221
absolute error = 3.1567323248457238419341957361221
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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=1182.0MB, alloc=52.3MB, time=12.77
TOP MAIN SOLVE Loop
x[1] = 2.56
y[1] (closed_form) = 0
y[1] (numeric) = -3.1597673284715734823125978889762
absolute error = 3.1597673284715734823125978889762
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.1627640352438561051673633718772
absolute error = 3.1627640352438561051673633718772
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.165722572610019642881946292518
absolute error = 3.165722572610019642881946292518
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
x[1] = 2.59
y[1] (closed_form) = 0
y[1] (numeric) = -3.1686430663625310348535499383465
absolute error = 3.1686430663625310348535499383465
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.1715256406592033810846127414742
absolute error = 3.1715256406592033810846127414742
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.174370418043156966741827597343
absolute error = 3.174370418043156966741827597343
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.1771775194624216042890278890929
absolute error = 3.1771775194624216042890278890929
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 2.63
y[1] (closed_form) = 0
y[1] (numeric) = -3.1799470642891875585702621104522
absolute error = 3.1799470642891875585702621104522
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.1826791703387121439659150087873
absolute error = 3.1826791703387121439659150087873
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
memory used=1226.1MB, alloc=52.3MB, time=13.23
x[1] = 2.65
y[1] (closed_form) = 0
y[1] (numeric) = -3.1853739538878889113137982974054
absolute error = 3.1853739538878889113137982974054
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 2.66
y[1] (closed_form) = 0
y[1] (numeric) = -3.1880315296934861755299804062138
absolute error = 3.1880315296934861755299804062138
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.1906520110100614726370773034926
absolute error = 3.1906520110100614726370773034926
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.1932355096075583770719927904731
absolute error = 3.1932355096075583770719927904731
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 2.69
y[1] (closed_form) = 0
y[1] (numeric) = -3.1957821357885919565665851932974
absolute error = 3.1957821357885919565665851932974
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.1982919984054289924438823498912
absolute error = 3.1982919984054289924438823498912
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2007652048766689477240607768544
absolute error = 3.2007652048766689477240607768544
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 2.72
y[1] (closed_form) = 0
y[1] (numeric) = -3.203201861203631523867437810044
absolute error = 3.203201861203631523867437810044
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2056020719864565091792301226013
absolute error = 3.2056020719864565091792301226013
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
memory used=1270.2MB, alloc=52.3MB, time=13.72
x[1] = 2.74
y[1] (closed_form) = 0
y[1] (numeric) = -3.2079659404399214877497357013866
absolute error = 3.2079659404399214877497357013866
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
x[1] = 2.75
y[1] (closed_form) = 0
y[1] (numeric) = -3.2102935684089828471945786808518
absolute error = 3.2102935684089828471945786808518
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2125850563840453962870124543567
absolute error = 3.2125850563840453962870124543567
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2148405035159657797357854519477
absolute error = 3.2148405035159657797357854519477
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2170600076307947567588731965516
absolute error = 3.2170600076307947567588731965516
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 2.79
y[1] (closed_form) = 0
y[1] (numeric) = -3.219243665244263292639843933589
absolute error = 3.219243665244263292639843933589
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2213915715760172980372479693349
absolute error = 3.2213915715760172980372479693349
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2235038205636057393587061794557
absolute error = 3.2235038205636057393587061794557
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 2.82
y[1] (closed_form) = 0
y[1] (numeric) = -3.2255805048762267349237254190623
absolute error = 3.2255805048762267349237254190623
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2276217159282361458388900392733
absolute error = 3.2276217159282361458388900392733
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
memory used=1314.2MB, alloc=52.3MB, time=14.20
TOP MAIN SOLVE Loop
x[1] = 2.84
y[1] (closed_form) = 0
y[1] (numeric) = -3.2296275438924230674148701262122
absolute error = 3.2296275438924230674148701262122
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 2.85
y[1] (closed_form) = 0
y[1] (numeric) = -3.2315980777130565264881521372436
absolute error = 3.2315980777130565264881521372436
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2335334051187075920955511798173
absolute error = 3.2335334051187075920955511798173
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2354336126348510115128439728257
absolute error = 3.2354336126348510115128439728257
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 2.88
y[1] (closed_form) = 0
y[1] (numeric) = -3.2372987855962503906390431792206
absolute error = 3.2372987855962503906390431792206
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.239129008159130847015949154195
absolute error = 3.239129008159130847015949154195
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2409243633131429753518736956221
absolute error = 3.2409243633131429753518736956221
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
x[1] = 2.91
y[1] (closed_form) = 0
y[1] (numeric) = -3.2426849328931218792041436002669
absolute error = 3.2426849328931218792041436002669
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2444107975906449384045004481727
absolute error = 3.2444107975906449384045004481727
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
memory used=1358.3MB, alloc=52.3MB, time=14.67
TOP MAIN SOLVE Loop
x[1] = 2.93
y[1] (closed_form) = 0
y[1] (numeric) = -3.246102036965391899824116994982
absolute error = 3.246102036965391899824116994982
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2477587294563107991118415869545
absolute error = 3.2477587294563107991118415869545
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 2.95
y[1] (closed_form) = 0
y[1] (numeric) = -3.2493809523925931430434787807177
absolute error = 3.2493809523925931430434787807177
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2509687820044617060361999491765
absolute error = 3.2509687820044617060361999491765
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2525222934337742201570394810568
absolute error = 3.2525222934337742201570394810568
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 2.98
y[1] (closed_form) = 0
y[1] (numeric) = -3.2540415607444461655360039995967
absolute error = 3.2540415607444461655360039995967
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2555266569326957974323281856183
absolute error = 3.2555266569326957974323281856183
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2569776539371144772481124914976
absolute error = 3.2569776539371144772481124914976
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 3.01
y[1] (closed_form) = 0
y[1] (numeric) = -3.2583946226485653074897215618859
absolute error = 3.2583946226485653074897215618859
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
memory used=1402.2MB, alloc=52.3MB, time=15.14
TOP MAIN SOLVE Loop
x[1] = 3.02
y[1] (closed_form) = 0
y[1] (numeric) = -3.259777632919913004998089036366
absolute error = 3.259777632919913004998089036366
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2611267535755878826600332625111
absolute error = 3.2611267535755878826600332625111
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 3.04
y[1] (closed_form) = 0
y[1] (numeric) = -3.2624420524209867472307488134996
absolute error = 3.2624420524209867472307488134996
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2637235962517134598010063254032
absolute error = 3.2637235962517134598010063254032
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.26497145086266184579072699439
absolute error = 3.26497145086266184579072699439
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
x[1] = 3.07
y[1] (closed_form) = 0
y[1] (numeric) = -3.2661856810569435831041687885484
absolute error = 3.2661856810569435831041687885484
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2673663506546636402028114730166
absolute error = 3.2673663506546636402028114730166
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2685135225015457803031325650947
absolute error = 3.2685135225015457803031325650947
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2696272584774105936518980013269
absolute error = 3.2696272584774105936518980013269
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
memory used=1446.2MB, alloc=52.3MB, time=15.61
x[1] = 3.11
y[1] (closed_form) = 0
y[1] (numeric) = -3.270707619504508466836481459977
absolute error = 3.270707619504508466836481459977
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2717546655557098463182323820383
absolute error = 3.2717546655557098463182323820383
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2727684556625551028001844478283
absolute error = 3.2727684556625551028001844478283
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 3.14
y[1] (closed_form) = 0
y[1] (numeric) = -3.2737490479231662536245433199442
absolute error = 3.2737490479231662536245433199442
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2746964995100227521094535791343
absolute error = 3.2746964995100227521094535791343
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2756108666776035055484577109283
absolute error = 3.2756108666776035055484577109283
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 3.17
y[1] (closed_form) = 0
y[1] (numeric) = -3.2764922047698972374806326135162
absolute error = 3.2764922047698972374806326135162
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2773405682277832647662714577226
absolute error = 3.2773405682277832647662714577226
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2781560105962847159446361619136
absolute error = 3.2781560105962847159446361619136
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
memory used=1490.2MB, alloc=52.3MB, time=16.08
x[1] = 3.2
y[1] (closed_form) = 0
y[1] (numeric) = -3.2789385845316961742799928193675
absolute error = 3.2789385845316961742799928193675
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2796883418085876867938778383734
absolute error = 3.2796883418085876867938778383734
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.280405333326687039410084916793
absolute error = 3.280405333326687039410084916793
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 3.23
y[1] (closed_form) = 0
y[1] (numeric) = -3.2810896091176421580796873319099
absolute error = 3.2810896091176421580796873319099
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2817412183516654563826852938188
absolute error = 3.2817412183516654563826852938188
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2823602093440619115974352036819
absolute error = 3.2823602093440619115974352036819
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2829466295616426135663683981399
absolute error = 3.2829466295616426135663683981399
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 3.27
y[1] (closed_form) = 0
y[1] (numeric) = -3.2835005256290254938447636857268
absolute error = 3.2835005256290254938447636857268
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2840219433348249065772338459133
absolute error = 3.2840219433348249065772338459133
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2845109276377316972834462049698
absolute error = 3.2845109276377316972834462049698
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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=1534.2MB, alloc=52.3MB, time=16.56
TOP MAIN SOLVE Loop
x[1] = 3.3
y[1] (closed_form) = 0
y[1] (numeric) = -3.2849675226724853612303197510983
absolute error = 3.2849675226724853612303197510983
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2853917717557398593029799378994
absolute error = 3.2853917717557398593029799378994
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2857837173918246262420997056063
absolute error = 3.2857837173918246262420997056063
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 3.33
y[1] (closed_form) = 0
y[1] (numeric) = -3.2861434012784022737724254868249
absolute error = 3.2861434012784022737724254868249
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2864708643120244594882999661671
absolute error = 3.2864708643120244594882999661671
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2867661465935873613693592535771
absolute error = 3.2867661465935873613693592535771
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 3.36
y[1] (closed_form) = 0
y[1] (numeric) = -3.2870292874336881674562862269735
absolute error = 3.2870292874336881674562862269735
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2872603253578839605059900889669
absolute error = 3.2872603253578839605059900889669
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2874592981118543483517472743283
absolute error = 3.2874592981118543483517472743283
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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=1578.3MB, alloc=52.3MB, time=17.03
TOP MAIN SOLVE Loop
x[1] = 3.39
y[1] (closed_form) = 0
y[1] (numeric) = -3.287626242666469162201006381102
absolute error = 3.287626242666469162201006381102
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2877611952227625171964753056938
absolute error = 3.2877611952227625171964753056938
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.28786419121681450222992493367
absolute error = 3.28786419121681450222992493367
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2879352653245417392184081243544
absolute error = 3.2879352653245417392184081243544
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 3.43
y[1] (closed_form) = 0
y[1] (numeric) = -3.2879744514663980258152358276075
absolute error = 3.2879744514663980258152358276075
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2879817828119862498193759055785
absolute error = 3.2879817828119862498193759055785
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2879572917845827383536067850935
absolute error = 3.2879572917845827383536067850935
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 3.46
y[1] (closed_form) = 0
y[1] (numeric) = -3.287901010065575180190779086159
absolute error = 3.287901010065575180190779086159
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2878129685988152354062645157082
absolute error = 3.2878129685988152354062645157082
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
memory used=1622.3MB, alloc=52.3MB, time=17.50
TOP MAIN SOLVE Loop
x[1] = 3.48
y[1] (closed_form) = 0
y[1] (numeric) = -3.2876931975948869228107821251673
absolute error = 3.2876931975948869228107821251673
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 3.49
y[1] (closed_form) = 0
y[1] (numeric) = -3.2875417265352918523592861301698
absolute error = 3.2875417265352918523592861301698
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2873585841765523469267850948378
absolute error = 3.2873585841765523469267850948378
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2871437985542334754794480010327
absolute error = 3.2871437985542334754794480010327
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 3.52
y[1] (closed_form) = 0
y[1] (numeric) = -3.2868973969868849977380386543234
absolute error = 3.2868973969868849977380386543234
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2866194060799041989197889855503
absolute error = 3.2866194060799041989197889855503
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2863098517293205720437315571137
absolute error = 3.2863098517293205720437315571137
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 3.55
y[1] (closed_form) = 0
y[1] (numeric) = -3.2859687591255032845829858504245
absolute error = 3.2859687591255032845829858504245
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2855961527567923459355141283273
absolute error = 3.2855961527567923459355141283273
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
memory used=1666.4MB, alloc=52.3MB, time=17.97
x[1] = 3.57
y[1] (closed_form) = 0
y[1] (numeric) = -3.2851920564130543722526642205399
absolute error = 3.2851920564130543722526642205399
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2847564931891638256028754404342
absolute error = 3.2847564931891638256028754404342
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 3.59
y[1] (closed_form) = 0
y[1] (numeric) = -3.2842894854884105852469534140118
absolute error = 3.2842894854884105852469534140118
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2837910550258346899522628027352
absolute error = 3.2837910550258346899522628027352
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2832612228314890717672094406031
absolute error = 3.2832612228314890717672094406031
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 3.62
y[1] (closed_form) = 0
y[1] (numeric) = -3.2827000092536310835058672731066
absolute error = 3.2827000092536310835058672731066
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2821074339618436043471426373434
absolute error = 3.2821074339618436043471426373434
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2814835159500864904252546541118
absolute error = 3.2814835159500864904252546541118
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 3.65
y[1] (closed_form) = 0
y[1] (numeric) = -3.2808282735396791200705395075878
absolute error = 3.2808282735396791200705395075878
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
memory used=1710.4MB, alloc=52.3MB, time=18.44
x[1] = 3.66
y[1] (closed_form) = 0
y[1] (numeric) = -3.2801417243822147664438439931134
absolute error = 3.2801417243822147664438439931134
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2794238854624075136864322865181
absolute error = 3.2794238854624075136864322865181
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 3.68
y[1] (closed_form) = 0
y[1] (numeric) = -3.2786747731008724163729429112073
absolute error = 3.2786747731008724163729429112073
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2778944029568395860002296815623
absolute error = 3.2778944029568395860002296815623
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2770827900308028724628010486606
absolute error = 3.2770827900308028724628010486606
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 3.71
y[1] (closed_form) = 0
y[1] (numeric) = -3.2762399486671037929491026068729
absolute error = 3.2762399486671037929491026068729
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2753658925564513454352943346981
absolute error = 3.2753658925564513454352943346981
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2744606347383783289478405176339
absolute error = 3.2744606347383783289478405176339
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2735241876036347780066910506869
absolute error = 3.2735241876036347780066910506869
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 3.75
y[1] (closed_form) = 0
y[1] (numeric) = -3.2725565628965191041407700864836
absolute error = 3.2725565628965191041407700864836
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
memory used=1754.5MB, alloc=52.3MB, time=18.92
TOP MAIN SOLVE Loop
x[1] = 3.76
y[1] (closed_form) = 0
y[1] (numeric) = -3.2715577717171475230807269679032
absolute error = 3.2715577717171475230807269679032
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.270527824523662332174409128403
absolute error = 3.270527824523662332174409128403
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 3.78
y[1] (closed_form) = 0
y[1] (numeric) = -3.2694667311343795887323860620196
absolute error = 3.2694667311343795887323860620196
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2683745007298767263883173685109
absolute error = 3.2683745007298767263883173685109
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2672511418550206331463731649864
absolute error = 3.2672511418550206331463731649864
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 3.81
y[1] (closed_form) = 0
y[1] (numeric) = -3.2660966624209367015797620966339
absolute error = 3.2660966624209367015797620966339
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.264911069706919348635300815012
absolute error = 3.264911069706919348635300815012
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2636943703622844896835854191885
absolute error = 3.2636943703622844896835854191885
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 3.84
y[1] (closed_form) = 0
y[1] (numeric) = -3.2624465704081644388275291137525
absolute error = 3.2624465704081644388275291137525
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
memory used=1798.5MB, alloc=52.3MB, time=19.39
TOP MAIN SOLVE Loop
x[1] = 3.85
y[1] (closed_form) = 0
y[1] (numeric) = -3.2611676752392456950387498950113
absolute error = 3.2611676752392456950387498950113
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2598576896254500614265723959654
absolute error = 3.2598576896254500614265723959654
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 3.87
y[1] (closed_form) = 0
y[1] (numeric) = -3.2585166177135595328533972209242
absolute error = 3.2585166177135595328533972209242
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2571444630287853751881373995347
absolute error = 3.2571444630287853751881373995347
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2557412284762818077316703285966
absolute error = 3.2557412284762818077316703285966
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2543069163426046887502443166203
absolute error = 3.2543069163426046887502443166203
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 3.91
y[1] (closed_form) = 0
y[1] (numeric) = -3.2528415282971155926100425762343
absolute error = 3.2528415282971155926100425762343
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2513450653933316557142638601371
absolute error = 3.2513450653933316557142638601371
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2498175280702215572988335307886
absolute error = 3.2498175280702215572988335307886
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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=1842.6MB, alloc=52.3MB, time=19.86
TOP MAIN SOLVE Loop
x[1] = 3.94
y[1] (closed_form) = 0
y[1] (numeric) = -3.2482589161534479901400006968128
absolute error = 3.2482589161534479901400006968128
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2466692288565569653624759864701
absolute error = 3.2466692288565569653624759864701
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2450484647821142848063687743004
absolute error = 3.2450484647821142848063687743004
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 3.97
y[1] (closed_form) = 0
y[1] (numeric) = -3.2433966219227895038110164001302
absolute error = 3.2433966219227895038110164001302
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2417136976623876967999588923687
absolute error = 3.2417136976623876967999588923687
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.239999688776829327699970011673
absolute error = 3.239999688776829327699970011673
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 4
y[1] (closed_form) = 0
y[1] (numeric) = -3.2382545914350785169944472204346
absolute error = 3.2382545914350785169944472204346
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2364784012000199870938945006959
absolute error = 3.2364784012000199870938945006959
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2346711130292849577000725886907
absolute error = 3.2346711130292849577000725886907
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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=1886.7MB, alloc=52.3MB, time=20.34
x[1] = 4.03
y[1] (closed_form) = 0
y[1] (numeric) = -3.2328327212760262529420736469051
absolute error = 3.2328327212760262529420736469051
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2309632196896428722685947800346
absolute error = 3.2309632196896428722685947800346
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2290626014164542673875889082955
absolute error = 3.2290626014164542673875889082955
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2271308590003245579488708540323
absolute error = 3.2271308590003245579488708540323
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 4.07
y[1] (closed_form) = 0
y[1] (numeric) = -3.2251679843832369091638144201017
absolute error = 3.2251679843832369091638144201017
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2231739689058182851457090649231
absolute error = 3.2231739689058182851457090649231
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2211488033078147824314200017263
absolute error = 3.2211488033078147824314200017263
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 4.1
y[1] (closed_form) = 0
y[1] (numeric) = -3.2190924777285177389065300581372
absolute error = 3.2190924777285177389065300581372
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2170049817071408041989999809536
absolute error = 3.2170049817071408041989999809536
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
memory used=1930.7MB, alloc=52.3MB, time=20.81
x[1] = 4.12
y[1] (closed_form) = 0
y[1] (numeric) = -3.214886304183148148527476582
absolute error = 3.214886304183148148527476582
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 4.13
y[1] (closed_form) = 0
y[1] (numeric) = -3.2127364334965339779866600237662
absolute error = 3.2127364334965339779866600237662
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2105553573880535153206101480164
absolute error = 3.2105553573880535153206101480164
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2083430629994055963725656530355
absolute error = 3.2083430629994055963725656530355
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 4.16
y[1] (closed_form) = 0
y[1] (numeric) = -3.2060995368733670236038472460858
absolute error = 3.2060995368733670236038472460858
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2038247649538788093418327494584
absolute error = 3.2038247649538788093418327494584
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.2015187325860844327449811229792
absolute error = 3.2015187325860844327449811229792
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
x[1] = 4.19
y[1] (closed_form) = 0
y[1] (numeric) = -3.199181424516320225858631099245
absolute error = 3.199181424516320225858631099245
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.1968128248920579955760297932513
absolute error = 3.1968128248920579955760297932513
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.1944129172617999798120105732503
absolute error = 3.1944129172617999798120105732503
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
memory used=1974.8MB, alloc=52.3MB, time=21.30
TOP MAIN SOLVE Loop
x[1] = 4.22
y[1] (closed_form) = 0
y[1] (numeric) = -3.1919816845749262277392217401363
absolute error = 3.1919816845749262277392217401363
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 4.23
y[1] (closed_form) = 0
y[1] (numeric) = -3.1895191091814944855261216081759
absolute error = 3.1895191091814944855261216081759
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.1870251728319926606494428839064
absolute error = 3.1870251728319926606494428839064
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.1844998566770439295288579707141
absolute error = 3.1844998566770439295288579707141
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 4.26
y[1] (closed_form) = 0
y[1] (numeric) = -3.1819431412670645449455405388394
absolute error = 3.1819431412670645449455405388394
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.1793550065518743914566350476303
absolute error = 3.1793550065518743914566350476303
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.176735431880260328801755371121
absolute error = 3.176735431880260328801755371121
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 4.29
y[1] (closed_form) = 0
y[1] (numeric) = -3.1740843959994923551129983195392
absolute error = 3.1740843959994923551129983195392
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.1714018770547926135840600717011
absolute error = 3.1714018770547926135840600717011
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
memory used=2018.8MB, alloc=52.3MB, time=21.77
TOP MAIN SOLVE Loop
x[1] = 4.31
y[1] (closed_form) = 0
y[1] (numeric) = -3.1686878525887572581243848655106
absolute error = 3.1686878525887572581243848655106
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 4.32
y[1] (closed_form) = 0
y[1] (numeric) = -3.1659422995407311854183751878824
absolute error = 3.1659422995407311854183751878824
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.1631651942461356327250873481257
absolute error = 3.1631651942461356327250873481257
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.16035651243574863268807745737
absolute error = 3.16035651243574863268807745737
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
x[1] = 4.35
y[1] (closed_form) = 0
y[1] (numeric) = -3.1575162292349383083757166172155
absolute error = 3.1575162292349383083757166172155
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.1546443191628489837369399393254
absolute error = 3.1546443191628489837369399393254
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.1517407561315400766336233816536
absolute error = 3.1517407561315400766336233816536
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.1488055134450777335961977880626
absolute error = 3.1488055134450777335961977880626
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 4.39
y[1] (closed_form) = 0
y[1] (numeric) = -3.1458385637985791574413233143136
absolute error = 3.1458385637985791574413233143136
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
memory used=2062.8MB, alloc=52.3MB, time=22.23
x[1] = 4.4
y[1] (closed_form) = 0
y[1] (numeric) = -3.1428398792772095708870807306406
absolute error = 3.1428398792772095708870807306406
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.13980943135513175129981768255
absolute error = 3.13980943135513175129981768255
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 4.42
y[1] (closed_form) = 0
y[1] (numeric) = -3.1367471908944080637051532048257
absolute error = 3.1367471908944080637051532048257
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.133653128143854911191333435191
absolute error = 3.133653128143854911191333435191
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.1305272127378495138237907784683
absolute error = 3.1305272127378495138237907784683
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 4.45
y[1] (closed_form) = 0
y[1] (numeric) = -3.1273694136950889191730362682439
absolute error = 3.1273694136950889191730362682439
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.1241796994173011395315613540779
absolute error = 3.1241796994173011395315613540779
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.1209580376879083028568927896717
absolute error = 3.1209580376879083028568927896717
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 4.48
y[1] (closed_form) = 0
y[1] (numeric) = -3.1177043956706416964249848184282
absolute error = 3.1177043956706416964249848184282
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
memory used=2106.9MB, alloc=52.3MB, time=22.72
x[1] = 4.49
y[1] (closed_form) = 0
y[1] (numeric) = -3.1144187399081085741083976207426
absolute error = 3.1144187399081085741083976207426
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.1111010363203105901048491832268
absolute error = 3.1111010363203105901048491832268
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.1077512502031137138313855061102
absolute error = 3.1077512502031137138313855061102
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.1043693462266694725652334083341
absolute error = 3.1043693462266694725652334083341
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.100955288433787360252017985973
absolute error = 3.100955288433787360252017985973
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.0975090402382582427130736755564
absolute error = 3.0975090402382582427130736755564
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 4.55
y[1] (closed_form) = 0
y[1] (numeric) = -3.0940305644231285812636772394049
absolute error = 3.0940305644231285812636772394049
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.0905198231389252885007978570051
absolute error = 3.0905198231389252885007978570051
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.0869767779018310217299995049684
absolute error = 3.0869767779018310217299995049684
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 4.58
y[1] (closed_form) = 0
y[1] (numeric) = -3.0834013895918097111740390998151
absolute error = 3.0834013895918097111740390998151
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
memory used=2151.0MB, alloc=52.3MB, time=23.19
TOP MAIN SOLVE Loop
x[1] = 4.59
y[1] (closed_form) = 0
y[1] (numeric) = -3.0797936184506821117380640844063
absolute error = 3.0797936184506821117380640844063
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.0761534240801511586956962659932
absolute error = 3.0761534240801511586956962659932
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 4.61
y[1] (closed_form) = 0
y[1] (numeric) = -3.0724807654397768992042520696236
absolute error = 3.0724807654397768992042520696236
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.0687756008449007630534354775737
absolute error = 3.0687756008449007630534354775737
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.0650378879645189274975754258265
absolute error = 3.0650378879645189274975754258265
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 4.64
y[1] (closed_form) = 0
y[1] (numeric) = -3.0612675838191045224143739819721
absolute error = 3.0612675838191045224143739819721
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.0574646447783784133706768015125
absolute error = 3.0574646447783784133706768015125
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.0536290265590282914554455046115
absolute error = 3.0536290265590282914554455046115
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.049760684222375789959354743593
absolute error = 3.049760684222375789959354743593
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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=2195.0MB, alloc=52.3MB, time=23.66
TOP MAIN SOLVE Loop
x[1] = 4.68
y[1] (closed_form) = 0
y[1] (numeric) = -3.0458595721719913391366853714425
absolute error = 3.0458595721719913391366853714425
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.0419256441512564613758471684002
absolute error = 3.0419256441512564613758471684002
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.0379588532408732001273241364909
absolute error = 3.0379588532408732001273241364909
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 4.71
y[1] (closed_form) = 0
y[1] (numeric) = -3.0339591518563203668894515578873
absolute error = 3.0339591518563203668894515578873
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.0299264917452562814305397991495
absolute error = 3.0299264917452562814305397991495
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.0258608239848676712277608328418
absolute error = 3.0258608239848676712277608328418
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 4.74
y[1] (closed_form) = 0
y[1] (numeric) = -3.0217620989791643868261866624807
absolute error = 3.0217620989791643868261866624807
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.0176302664562195804626614827367
absolute error = 3.0176302664562195804626614827367
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.0134652754653549858560176255547
absolute error = 3.0134652754653549858560176255547
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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=2239.1MB, alloc=52.3MB, time=24.14
TOP MAIN SOLVE Loop
x[1] = 4.77
y[1] (closed_form) = 0
y[1] (numeric) = -3.0092670743742709275346929429643
absolute error = 3.0092670743742709275346929429643
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.0050356108661206784522244492146
absolute error = 3.0050356108661206784522244492146
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -3.0007708319365287749274950562924
absolute error = 3.0007708319365287749274950562924
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 4.8
y[1] (closed_form) = 0
y[1] (numeric) = -2.9964726838905528881370761087643
absolute error = 2.9964726838905528881370761087643
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.9921411123395888414785795854028
absolute error = 2.9921411123395888414785795854028
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.9877760621982183531136127571983
absolute error = 2.9877760621982183531136127571983
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.9833774776809990728836768980944
absolute error = 2.9833774776809990728836768980944
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 4.84
y[1] (closed_form) = 0
y[1] (numeric) = -2.9789453022991964725690907008834
absolute error = 2.9789453022991964725690907008834
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.974479478857457138126625525243
absolute error = 2.974479478857457138126625525243
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
memory used=2283.2MB, alloc=52.3MB, time=24.61
x[1] = 4.86
y[1] (closed_form) = 0
y[1] (numeric) = -2.9699799494504230020928460096275
absolute error = 2.9699799494504230020928460096275
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 4.87
y[1] (closed_form) = 0
y[1] (numeric) = -2.9654466554592860437739422801267
absolute error = 2.9654466554592860437739422801267
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.9608795375482829741558576936451
absolute error = 2.9608795375482829741558576936451
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.9562785356611294116574482623836
absolute error = 2.9562785356611294116574482623836
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 4.9
y[1] (closed_form) = 0
y[1] (numeric) = -2.9516435890173930439108953480551
absolute error = 2.9516435890173930439108953480551
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.9469746361088052596842182349795
absolute error = 2.9469746361088052596842182349795
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.9422716146955107238570301254323
absolute error = 2.9422716146955107238570301254323
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
TOP MAIN SOLVE Loop
x[1] = 4.93
y[1] (closed_form) = 0
y[1] (numeric) = -2.9375344618022543570191266026691
absolute error = 2.9375344618022543570191266026691
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.9327631137145051697785089509008
absolute error = 2.9327631137145051697785089509008
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.9279575059745163902373860656074
absolute error = 2.9279575059745163902373860656074
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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=2327.4MB, alloc=52.3MB, time=25.09
TOP MAIN SOLVE Loop
x[1] = 4.96
y[1] (closed_form) = 0
y[1] (numeric) = -2.9231175733773213113178673036774
absolute error = 2.9231175733773213113178673036774
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.9182432499666642726896910874907
absolute error = 2.9182432499666642726896910874907
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.9133344690308661799666024246461
absolute error = 2.9133344690308661799666024246461
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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) = -2.9083911630986239515920023411366
absolute error = 2.9083911630986239515920023411366
relative error = -1 %
Desired digits = 8
Estimated correct digits = 12
Correct digits = -16
h = 0.005
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
Finished!
diff ( y , x , 1 ) = tan ( sqrt ( 2.0 * x + 3.0 ) ) ;
Iterations = 980
Total Elapsed Time = 25 Seconds
Elapsed Time(since restart) = 25 Seconds
Time to Timeout = 2 Minutes 34 Seconds
Percent Done = 100.1 %
> quit
memory used=2348.8MB, alloc=52.3MB, time=25.31