|\^/| 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 MAX_TERMS;
> local iii;
> iii := 1;
> while (iii <= MAX_TERMS) do # do number 1
> arr_a [iii] := 0.0;
> iii := iii + 1;
> od;# end do number 1
> end;
zero_ats_ar := proc(arr_a)
local iii;
global MAX_TERMS;
iii := 1;
while iii <= MAX_TERMS do arr_a[iii] := 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 MAX_TERMS;
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := 0.0;
> 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 <= MAX_TERMS and (iii_ats <= MAX_TERMS) )) then # if number 7
> ret_ats := ret_ats + arr_a[iii_ats]*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 MAX_TERMS;
ret_ats := 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 <= MAX_TERMS and iii_ats <= MAX_TERMS then
ret_ats := ret_ats + arr_a[iii_ats]*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 MAX_TERMS;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := 0.0;
> 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 <= MAX_TERMS) ) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if ((lll_att <= MAX_TERMS and (iii_att <= MAX_TERMS) )) then # if number 7
> ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]* (al_att);
> fi;# end if 7;
> iii_att := iii_att + 1;
> od;# end do number 1;
> ret_att := ret_att / (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 MAX_TERMS;
ret_att := 0.;
if jjj_att < mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att < mmm_att and iii_att <= MAX_TERMS do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= MAX_TERMS and iii_att <= MAX_TERMS then
ret_att := ret_att + arr_aa[iii_att]*arr_bb[lll_att]*al_att
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/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,"");
> if (rel_error <> -1.0) then # if number 6
> if (rel_error > glob_prec) then # if number 7
> good_digits := 3-int_trunc(log10(rel_error));
> fprintf(file,"%d",good_digits);
> else
> good_digits := Digits;
> fprintf(file,"%d",good_digits);
> fi;# end if 7;
> else
> fprintf(file,"Unknown");
> fi;# end if 6;
> fprintf(file," | ");
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float, glob_prec;
fprintf(file, "");
if rel_error <> -1.0 then
if glob_prec < rel_error then
good_digits := 3 - int_trunc(log10(rel_error));
fprintf(file, "%d", good_digits)
else good_digits := Digits; fprintf(file, "%d", good_digits)
end if
else fprintf(file, "Unknown")
end if;
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, 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, 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 := clock_sec2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub1 = 0.0) then # if number 12
> sec_left := 0.0;
> else
> if (sub2 > 0.0) then # if number 13
> rrr := (sub1/sub2);
> sec_left := rrr * ms2 - ms2;
> else
> sec_left := 0.0;
> 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 := clock_sec2;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if sub1 = 0. then sec_left := 0.
else
if 0. < sub2 then rrr := sub1/sub2; sec_left := rrr*ms2 - ms2
else sec_left := 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 := (100.0*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 := 100.0*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 (term2 > 0.0) 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 0. < 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 (term2 > 0.0) then # if number 12
> ret := 1.0 + float_abs(term2) * convfloat(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(convfloat(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 0. < term2 then ret := 1.0 + float_abs(term2)*convfloat(last_no)*
ln(float_abs(term1*glob_h/term2))/ln(convfloat(last_no))
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 26
# Begin Function number 27
> comp_rad_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret,temp;
> temp := float_abs(term2*term2*convfloat(last_no)-2.0*term2*term2-term1*term3*convfloat(last_no)+term1*term3);
> if (temp > 0.0) 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*convfloat(last_no) - 2.0*term2*term2
- term1*term3*convfloat(last_no) + term1*term3);
if 0. < temp then ret := float_abs(term2*glob_h*term1/temp)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 27
# Begin Function number 28
> comp_ord_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM ORDER ANALYSIS
> local ret;
> ret := float_abs((4.0*term1*term3*convfloat(last_no)-3.0*term1*term3-4.0*term2*term2*convfloat(last_no)+4.0*term2*term2+term2*term2*convfloat(last_no*last_no)-term1*term3*convfloat(last_no*last_no))/(term2*term2*convfloat(last_no)-2.0*term2*term2-term1*term3*convfloat(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((4.0*term1*term3*convfloat(last_no) - 3.0*term1*term3
- 4.0*term2*term2*convfloat(last_no) + 4.0*term2*term2
+ term2*term2*convfloat(last_no*last_no)
- term1*term3*convfloat(last_no*last_no))/(
term2*term2*convfloat(last_no) - 2.0*term2*term2
- term1*term3*convfloat(last_no) + term1*term3));
ret
end proc
# End Function number 28
# Begin Function number 29
> comp_rad_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> #TOP SIX TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float,glob_six_term_ord_save;
> local ret,rm0,rm1,rm2,rm3,rm4,nr1,nr2,dr1,dr2,ds2,rad_c,ord_no,ds1,rcs;
> if ((term5 <> 0.0) and (term4 <> 0.0) and (term3 <> 0.0) and (term2 <> 0.0) and (term1 <> 0.0)) then # if number 12
> rm0 := term6/term5;
> rm1 := term5/term4;
> rm2 := term4/term3;
> rm3 := term3/term2;
> rm4 := term2/term1;
> nr1 := convfloat(last_no-1)*rm0 - 2.0*convfloat(last_no-2)*rm1 + convfloat(last_no-3)*rm2;
> nr2 := convfloat(last_no-2)*rm1 - 2.0*convfloat(last_no-3)*rm2 + convfloat(last_no-4)*rm3;
> dr1 := (-1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
> dr2 := (-1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
> ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
> ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
> if ((float_abs(nr1 * dr2 - nr2 * dr1) = 0.0) or (float_abs(dr1) = 0.0)) then # if number 13
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> else
> if (float_abs(nr1*dr2 - nr2 * dr1) <> 0.0) 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)/(2.0*dr1) -convfloat(last_no)/2.0;
> if (float_abs(rcs) <> 0.0) then # if number 15
> if (rcs > 0.0) 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 <> 0. and term4 <> 0. and term3 <> 0. and term2 <> 0. and
term1 <> 0. then
rm0 := term6/term5;
rm1 := term5/term4;
rm2 := term4/term3;
rm3 := term3/term2;
rm4 := term2/term1;
nr1 := convfloat(last_no - 1)*rm0 - 2.0*convfloat(last_no - 2)*rm1
+ convfloat(last_no - 3)*rm2;
nr2 := convfloat(last_no - 2)*rm1 - 2.0*convfloat(last_no - 3)*rm2
+ convfloat(last_no - 4)*rm3;
dr1 := (-1)*(1.0)/rm1 + 2.0/rm2 - 1.0/rm3;
dr2 := (-1)*(1.0)/rm2 + 2.0/rm3 - 1.0/rm4;
ds1 := 3.0/rm1 - 8.0/rm2 + 5.0/rm3;
ds2 := 3.0/rm2 - 8.0/rm3 + 5.0/rm4;
if float_abs(nr1*dr2 - nr2*dr1) = 0. or float_abs(dr1) = 0. then
rad_c := glob_larger_float; ord_no := glob_larger_float
else
if float_abs(nr1*dr2 - nr2*dr1) <> 0. then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no :=
(rcs*nr1 - ds1)/(2.0*dr1) - convfloat(last_no)/2.0;
if float_abs(rcs) <> 0. then
if 0. < rcs then rad_c := sqrt(rcs)*float_abs(glob_h)
else
rad_c := glob_larger_float;
ord_no := glob_larger_float
end if
else
rad_c := glob_larger_float; ord_no := glob_larger_float
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if;
glob_six_term_ord_save := ord_no;
rad_c
end proc
# End Function number 29
# Begin Function number 30
> comp_ord_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> global glob_six_term_ord_save;
> #TOP SIX TERM ORDER ANALYSIS
> #TOP SAVED FROM SIX TERM RADIUS ANALYSIS
> glob_six_term_ord_save;
> #BOTTOM SIX TERM ORDER ANALYSIS
> end;
comp_ord_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
global glob_six_term_ord_save;
glob_six_term_ord_save
end proc
# End Function number 30
# Begin Function number 31
> factorial_2 := proc(nnn)
> ret := nnn!;
> ret;;
> end;
Warning, `ret` is implicitly declared local to procedure `factorial_2`
factorial_2 := proc(nnn) local ret; ret := nnn!; ret end proc
# End Function number 31
# Begin Function number 32
> factorial_1 := proc(nnn)
> global MAX_TERMS,array_fact_1;
> local ret;
> if (nnn <= 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 MAX_TERMS, array_fact_1;
if nnn <= MAX_TERMS then
if array_fact_1[nnn] = 0 then
ret := factorial_2(nnn); array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := factorial_2(nnn)
end if;
ret
end proc
# End Function number 32
# Begin Function number 33
> factorial_3 := proc(mmm,nnn)
> global MAX_TERMS,array_fact_2;
> local ret;
> if ((nnn <= MAX_TERMS) and (mmm <= 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 MAX_TERMS, array_fact_2;
if nnn <= MAX_TERMS and mmm <= MAX_TERMS then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := factorial_2(mmm)/factorial_2(nnn)
end if;
ret
end proc
# End Function number 33
# Begin Function number 34
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
# End Function number 34
# Begin Function number 35
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
# End Function number 35
# Begin Function number 36
> int_trunc := proc(xxx)
> trunc(xxx);
> end;
int_trunc := proc(xxx) trunc(xxx) end proc
# End Function number 36
# Begin Function number 37
> float_abs := proc(xxx)
> abs(xxx);
> end;
float_abs := proc(xxx) abs(xxx) 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
> 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,MAX_TERMS;
> omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
> desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct) * float_abs(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 := (float_abs(desired_abs_gbl_error /sqrt( estimated_steps)/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, MAX_TERMS;
omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, "");
desired_abs_gbl_error := expt(10.0, -glob_desired_digits_correct)*
float_abs(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 :=
float_abs(desired_abs_gbl_error/(sqrt(estimated_steps)*MAX_TERMS));
omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
step_error
end proc
# End Function number 39
#END ATS LIBRARY BLOCK
#BEGIN USER FUNCTION BLOCK
#BEGIN BLOCK 3
#BEGIN USER DEF BLOCK
> exact_soln_x := proc(t)
> return(0);
> end;
exact_soln_x := proc(t) return 0 end proc
> exact_soln_y := proc(t)
> return(0);
> end;
exact_soln_y := proc(t) return 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_t ;
> if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1
> rad_given := sqrt((array_t[1] - array_given_rad_poles[1,1]) * (array_t[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] > 0.0) 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] > 0.0) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," ");
> if (array_rad_test_poles[1,3]< glob_least_6_sing) then # if number 4
> glob_least_6_sing := array_rad_test_poles[1,3];
> fi;# end if 4;
> omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1");
> fi;# end if 3
> ;
> if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 3
> rad_given := sqrt((array_t[1] - array_given_rad_poles[2,1]) * (array_t[1] - array_given_rad_poles[2,1]) + array_given_rad_poles[2,2] * array_given_rad_poles[2,2]);
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 2 ",4,rad_given,4," ");
> omniout_float(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[2,1],4," ");
> if (rad_given < glob_least_given_sing) then # if number 4
> glob_least_given_sing := rad_given;
> fi;# end if 4;
> elif
> (glob_type_given_pole = 3) then # if number 4
> omniout_str(ALWAYS,"NO POLE (given) for Equation 2");
> elif
> (glob_type_given_pole = 5) then # if number 5
> omniout_str(ALWAYS,"SOME POLE (given) for Equation 2");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 2");
> fi;# end if 5;
> if (array_rad_test_poles[2,1] < glob_large_float) then # if number 5
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 2 ",4,array_rad_test_poles[2,1],4," ");
> if (array_rad_test_poles[2,1]< glob_least_ratio_sing) then # if number 6
> glob_least_ratio_sing := array_rad_test_poles[2,1];
> fi;# end if 6;
> omniout_float(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[2,1],4," ");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 2");
> fi;# end if 5;
> if ((array_rad_test_poles[2,2] > 0.0) and (array_rad_test_poles[2,2] < glob_large_float)) then # if number 5
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 2 ",4,array_rad_test_poles[2,2],4," ");
> if (array_rad_test_poles[2,2]< glob_least_3_sing) then # if number 6
> glob_least_3_sing := array_rad_test_poles[2,2];
> fi;# end if 6;
> omniout_float(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[2,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 2");
> fi;# end if 5;
> if ((array_rad_test_poles[2,3] > 0.0) and (array_rad_test_poles[2,3] < glob_large_float)) then # if number 5
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 2 ",4,array_rad_test_poles[2,3],4," ");
> if (array_rad_test_poles[2,3]< glob_least_6_sing) then # if number 6
> glob_least_6_sing := array_rad_test_poles[2,3];
> fi;# end if 6;
> omniout_float(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[2,3],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 2");
> fi;# end if 5
> ;
> end;
display_poles := proc()
local rad_given;
global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float,
glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord,
glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
glob_least_3_sing, glob_least_6_sing, glob_least_given_sing,
glob_least_ratio_sing, array_t;
if glob_type_given_pole = 1 or glob_type_given_pole = 2 then
rad_given := sqrt((array_t[1] - array_given_rad_poles[1, 1])*
(array_t[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 0. < 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 0. < array_rad_test_poles[1, 3] and
array_rad_test_poles[1, 3] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 1 ", 4,
array_rad_test_poles[1, 3], 4, " ");
if array_rad_test_poles[1, 3] < glob_least_6_sing then
glob_least_6_sing := array_rad_test_poles[1, 3]
end if;
omniout_float(ALWAYS,
"Order of pole (six term test) ", 4,
array_ord_test_poles[1, 3], 4, " ")
else omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 1")
end if;
if glob_type_given_pole = 1 or glob_type_given_pole = 2 then
rad_given := sqrt((array_t[1] - array_given_rad_poles[2, 1])*
(array_t[1] - array_given_rad_poles[2, 1])
+ array_given_rad_poles[2, 2]*array_given_rad_poles[2, 2]);
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 2 ", 4,
rad_given, 4, " ");
omniout_float(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles[2, 1], 4, " ");
if rad_given < glob_least_given_sing then
glob_least_given_sing := rad_given
end if
elif glob_type_given_pole = 3 then
omniout_str(ALWAYS, "NO POLE (given) for Equation 2")
elif glob_type_given_pole = 5 then
omniout_str(ALWAYS, "SOME POLE (given) for Equation 2")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 2")
end if;
if array_rad_test_poles[2, 1] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (ratio test) for eq 2 ", 4,
array_rad_test_poles[2, 1], 4, " ");
if array_rad_test_poles[2, 1] < glob_least_ratio_sing then
glob_least_ratio_sing := array_rad_test_poles[2, 1]
end if;
omniout_float(ALWAYS,
"Order of pole (ratio test) ", 4,
array_ord_test_poles[2, 1], 4, " ")
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 2")
end if;
if 0. < array_rad_test_poles[2, 2] and
array_rad_test_poles[2, 2] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 2 ", 4,
array_rad_test_poles[2, 2], 4, " ");
if array_rad_test_poles[2, 2] < glob_least_3_sing then
glob_least_3_sing := array_rad_test_poles[2, 2]
end if;
omniout_float(ALWAYS,
"Order of pole (three term test) ", 4,
array_ord_test_poles[2, 2], 4, " ")
else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 2")
end if;
if 0. < array_rad_test_poles[2, 3] and
array_rad_test_poles[2, 3] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 2 ", 4,
array_rad_test_poles[2, 3], 4, " ");
if array_rad_test_poles[2, 3] < glob_least_6_sing then
glob_least_6_sing := array_rad_test_poles[2, 3]
end if;
omniout_float(ALWAYS,
"Order of pole (six term test) ", 4,
array_ord_test_poles[2, 3], 4, " ")
else omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 2")
end if
end proc
# End Function number 2
# Begin Function number 3
> my_check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 5
> ret := 1.0;
> else
> ret := -1.0;
> fi;# end if 5;
> ret;;
> end;
my_check_sign := proc(x0, xf)
local ret;
if x0 < xf then ret := 1.0 else ret := -1.0 end if; ret
end proc
# End Function number 3
# Begin Function number 4
> est_size_answer := proc()
> global
> 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,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_prec,
> glob_est_digits,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_html_log,
> glob_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_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> 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_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_larger_float,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_look_poles,
> glob_display_interval,
> glob_next_display,
> glob_dump_closed_form,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_2,
> array_const_0D0,
> array_const_0D58,
> array_const_1D5,
#END CONST
> array_x_init,
> 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_good_digits,
> array_x,
> array_t,
> array_y,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7_c1,
> array_tmp7_a1,
> array_tmp7_a2,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17_c1,
> array_tmp17_a1,
> array_tmp17_a2,
> array_tmp17,
> array_tmp18,
> array_m1,
> array_x_higher,
> array_x_higher_work,
> array_x_higher_work2,
> array_x_set_initial,
> 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,
> MAX_TERMS,
> glob_last;
> local min_size;
> min_size := glob_estimated_size_answer;
> if (float_abs(array_x[1]) < min_size) then # if number 5
> min_size := float_abs(array_x[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 5;
> if (float_abs(array_y[1]) < min_size) then # if number 5
> min_size := float_abs(array_y[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 5;
> if (min_size < 1.0) then # if number 5
> min_size := 1.0;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 5;
> min_size;
> end;
est_size_answer := proc()
local min_size;
global 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, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_prec, glob_est_digits, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer,
glob_html_log, glob_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_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished,
glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h,
glob_optimal_done, 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_max_h, glob_min_h, glob_type_given_pole,
glob_large_float, glob_larger_float, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_look_poles, glob_display_interval, glob_next_display,
glob_dump_closed_form, glob_abserr, glob_relerr, glob_min_pole_est,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_iter, glob_normmax,
glob_max_minutes, array_const_2, array_const_0D0, array_const_0D58,
array_const_1D5, array_x_init, 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_good_digits, array_x,
array_t, array_y, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_tmp5, array_tmp6, array_tmp7_c1, array_tmp7_a1,
array_tmp7_a2, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11,
array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16,
array_tmp17_c1, array_tmp17_a1, array_tmp17_a2, array_tmp17, array_tmp18,
array_m1, array_x_higher, array_x_higher_work, array_x_higher_work2,
array_x_set_initial, 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, MAX_TERMS, glob_last;
min_size := glob_estimated_size_answer;
if float_abs(array_x[1]) < min_size then
min_size := float_abs(array_x[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
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 < 1.0 then
min_size := 1.0;
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
> 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,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_prec,
> glob_est_digits,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_html_log,
> glob_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_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> 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_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_larger_float,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_look_poles,
> glob_display_interval,
> glob_next_display,
> glob_dump_closed_form,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_2,
> array_const_0D0,
> array_const_0D58,
> array_const_1D5,
#END CONST
> array_x_init,
> 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_good_digits,
> array_x,
> array_t,
> array_y,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7_c1,
> array_tmp7_a1,
> array_tmp7_a2,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17_c1,
> array_tmp17_a1,
> array_tmp17_a2,
> array_tmp17,
> array_tmp18,
> array_m1,
> array_x_higher,
> array_x_higher_work,
> array_x_higher_work2,
> array_x_set_initial,
> 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,
> 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 := 0.0;
> no_terms := MAX_TERMS;
> hn_div_ho := 0.5;
> hn_div_ho_2 := 0.25;
> hn_div_ho_3 := 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_x[no_terms-3] + array_x[no_terms - 2] * hn_div_ho + array_x[no_terms - 1] * hn_div_ho_2 + array_x[no_terms] * hn_div_ho_3);
> if (est_tmp >= max_estimated_step_error) then # if number 5
> max_estimated_step_error := est_tmp;
> fi;# end if 5;
> est_tmp := float_abs(array_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 5
> max_estimated_step_error := est_tmp;
> fi;# end if 5;
> omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,"");
> max_estimated_step_error;
> end;
test_suggested_h := proc()
local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3,
no_terms, est_tmp;
global 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, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_prec, glob_est_digits, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer,
glob_html_log, glob_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_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished,
glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h,
glob_optimal_done, 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_max_h, glob_min_h, glob_type_given_pole,
glob_large_float, glob_larger_float, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_look_poles, glob_display_interval, glob_next_display,
glob_dump_closed_form, glob_abserr, glob_relerr, glob_min_pole_est,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_iter, glob_normmax,
glob_max_minutes, array_const_2, array_const_0D0, array_const_0D58,
array_const_1D5, array_x_init, 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_good_digits, array_x,
array_t, array_y, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_tmp5, array_tmp6, array_tmp7_c1, array_tmp7_a1,
array_tmp7_a2, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11,
array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16,
array_tmp17_c1, array_tmp17_a1, array_tmp17_a2, array_tmp17, array_tmp18,
array_m1, array_x_higher, array_x_higher_work, array_x_higher_work2,
array_x_set_initial, 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, MAX_TERMS, glob_last;
max_estimated_step_error := 0.;
no_terms := MAX_TERMS;
hn_div_ho := 0.5;
hn_div_ho_2 := 0.25;
hn_div_ho_3 := 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_x[no_terms - 3]
+ array_x[no_terms - 2]*hn_div_ho
+ array_x[no_terms - 1]*hn_div_ho_2
+ array_x[no_terms]*hn_div_ho_3);
if max_estimated_step_error <= est_tmp then
max_estimated_step_error := est_tmp
end if;
est_tmp := float_abs(array_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
> 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,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_prec,
> glob_est_digits,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_html_log,
> glob_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_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> 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_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_larger_float,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_look_poles,
> glob_display_interval,
> glob_next_display,
> glob_dump_closed_form,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_2,
> array_const_0D0,
> array_const_0D58,
> array_const_1D5,
#END CONST
> array_x_init,
> 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_good_digits,
> array_x,
> array_t,
> array_y,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7_c1,
> array_tmp7_a1,
> array_tmp7_a2,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17_c1,
> array_tmp17_a1,
> array_tmp17_a2,
> array_tmp17,
> array_tmp18,
> array_m1,
> array_x_higher,
> array_x_higher_work,
> array_x_higher_work2,
> array_x_set_initial,
> 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,
> MAX_TERMS,
> glob_last;
> local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> no_terms := MAX_TERMS;
> hn_div_ho := 0.5;
> hn_div_ho_2 := 0.25;
> hn_div_ho_3 := 0.125;
> est_tmp := float_abs(array_x[no_terms-3]) + float_abs(array_x[no_terms - 2]) * hn_div_ho + float_abs(array_x[no_terms - 1]) * hn_div_ho_2 + float_abs(array_x[no_terms]) * hn_div_ho_3;
> if (glob_prec * float_abs(array_x[1]) > est_tmp) then # if number 5
> est_tmp := glob_prec * float_abs(array_x[1]);
> fi;# end if 5;
> if (est_tmp >= array_max_est_error[1]) then # if number 5
> array_max_est_error[1] := est_tmp;
> fi;# end if 5
> ;
> est_tmp := float_abs(array_y[no_terms-3]) + float_abs(array_y[no_terms - 2]) * hn_div_ho + float_abs(array_y[no_terms - 1]) * hn_div_ho_2 + float_abs(array_y[no_terms]) * hn_div_ho_3;
> if (glob_prec * float_abs(array_y[1]) > est_tmp) then # if number 5
> est_tmp := glob_prec * float_abs(array_y[1]);
> fi;# end if 5;
> if (est_tmp >= array_max_est_error[2]) then # if number 5
> array_max_est_error[2] := est_tmp;
> fi;# end if 5
> ;
> end;
track_estimated_error := proc()
local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp;
global 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, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_prec, glob_est_digits, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer,
glob_html_log, glob_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_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished,
glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h,
glob_optimal_done, 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_max_h, glob_min_h, glob_type_given_pole,
glob_large_float, glob_larger_float, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_look_poles, glob_display_interval, glob_next_display,
glob_dump_closed_form, glob_abserr, glob_relerr, glob_min_pole_est,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_iter, glob_normmax,
glob_max_minutes, array_const_2, array_const_0D0, array_const_0D58,
array_const_1D5, array_x_init, 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_good_digits, array_x,
array_t, array_y, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_tmp5, array_tmp6, array_tmp7_c1, array_tmp7_a1,
array_tmp7_a2, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11,
array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16,
array_tmp17_c1, array_tmp17_a1, array_tmp17_a2, array_tmp17, array_tmp18,
array_m1, array_x_higher, array_x_higher_work, array_x_higher_work2,
array_x_set_initial, 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, MAX_TERMS, glob_last;
no_terms := MAX_TERMS;
hn_div_ho := 0.5;
hn_div_ho_2 := 0.25;
hn_div_ho_3 := 0.125;
est_tmp := float_abs(array_x[no_terms - 3])
+ float_abs(array_x[no_terms - 2])*hn_div_ho
+ float_abs(array_x[no_terms - 1])*hn_div_ho_2
+ float_abs(array_x[no_terms])*hn_div_ho_3;
if est_tmp < glob_prec*float_abs(array_x[1]) then
est_tmp := glob_prec*float_abs(array_x[1])
end if;
if array_max_est_error[1] <= est_tmp then
array_max_est_error[1] := est_tmp
end if;
est_tmp := float_abs(array_y[no_terms - 3])
+ float_abs(array_y[no_terms - 2])*hn_div_ho
+ float_abs(array_y[no_terms - 1])*hn_div_ho_2
+ float_abs(array_y[no_terms])*hn_div_ho_3;
if est_tmp < glob_prec*float_abs(array_y[1]) then
est_tmp := glob_prec*float_abs(array_y[1])
end if;
if array_max_est_error[2] <= est_tmp then
array_max_est_error[2] := est_tmp
end if
end proc
# End Function number 6
# Begin Function number 7
> reached_interval := proc()
> global
> 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,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_prec,
> glob_est_digits,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_html_log,
> glob_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_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> 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_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_larger_float,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_look_poles,
> glob_display_interval,
> glob_next_display,
> glob_dump_closed_form,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_2,
> array_const_0D0,
> array_const_0D58,
> array_const_1D5,
#END CONST
> array_x_init,
> 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_good_digits,
> array_x,
> array_t,
> array_y,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7_c1,
> array_tmp7_a1,
> array_tmp7_a2,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17_c1,
> array_tmp17_a1,
> array_tmp17_a2,
> array_tmp17,
> array_tmp18,
> array_m1,
> array_x_higher,
> array_x_higher_work,
> array_x_higher_work2,
> array_x_set_initial,
> 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,
> MAX_TERMS,
> glob_last;
> local ret;
> if ((glob_check_sign * array_t[1]) >= (glob_check_sign * glob_next_display - glob_h/10.0)) then # if number 5
> ret := true;
> else
> ret := false;
> fi;# end if 5;
> return(ret);
> end;
reached_interval := proc()
local ret;
global 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, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_prec, glob_est_digits, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer,
glob_html_log, glob_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_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished,
glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h,
glob_optimal_done, 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_max_h, glob_min_h, glob_type_given_pole,
glob_large_float, glob_larger_float, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_look_poles, glob_display_interval, glob_next_display,
glob_dump_closed_form, glob_abserr, glob_relerr, glob_min_pole_est,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_iter, glob_normmax,
glob_max_minutes, array_const_2, array_const_0D0, array_const_0D58,
array_const_1D5, array_x_init, 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_good_digits, array_x,
array_t, array_y, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_tmp5, array_tmp6, array_tmp7_c1, array_tmp7_a1,
array_tmp7_a2, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11,
array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16,
array_tmp17_c1, array_tmp17_a1, array_tmp17_a2, array_tmp17, array_tmp18,
array_m1, array_x_higher, array_x_higher_work, array_x_higher_work2,
array_x_set_initial, 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, MAX_TERMS, glob_last;
if glob_check_sign*glob_next_display - glob_h/10.0 <=
glob_check_sign*array_t[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
> 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,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_prec,
> glob_est_digits,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_html_log,
> glob_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_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> 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_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_larger_float,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_look_poles,
> glob_display_interval,
> glob_next_display,
> glob_dump_closed_form,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_2,
> array_const_0D0,
> array_const_0D58,
> array_const_1D5,
#END CONST
> array_x_init,
> 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_good_digits,
> array_x,
> array_t,
> array_y,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7_c1,
> array_tmp7_a1,
> array_tmp7_a2,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17_c1,
> array_tmp17_a1,
> array_tmp17_a2,
> array_tmp17,
> array_tmp18,
> array_m1,
> array_x_higher,
> array_x_higher_work,
> array_x_higher_work2,
> array_x_set_initial,
> 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,
> MAX_TERMS,
> glob_last;
> local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err;
> #TOP DISPLAY ALOT
> if (reached_interval()) then # if number 5
> if (iter >= 0) then # if number 6
> ind_var := array_t[1];
> omniout_float(ALWAYS,"t[1] ",33,ind_var,20," ");
> closed_form_val_y := evalf(exact_soln_x(ind_var));
> omniout_float(ALWAYS,"x[1] (closed_form) ",33,closed_form_val_y,20," ");
> term_no := 1;
> numeric_val := array_x[term_no];
> abserr := float_abs(numeric_val - closed_form_val_y);
> omniout_float(ALWAYS,"x[1] (numeric) ",33,numeric_val,20," ");
> if (evalf(float_abs(closed_form_val_y)) > glob_prec) then # if number 7
> relerr := abserr*100.0/float_abs(closed_form_val_y);
> if (relerr > glob_prec) then # if number 8
> glob_good_digits := -int_trunc(log10(relerr)) + 3;
> else
> glob_good_digits := Digits;
> fi;# end if 8;
> else
> relerr := -1.0 ;
> glob_good_digits := -16;
> fi;# end if 7;
> if (evalf)(float_abs(numeric_val) > glob_prec) then # if number 7
> est_rel_err := evalf(array_max_est_error[1]*100.0 * sqrt(glob_iter)*72*MAX_TERMS/float_abs(numeric_val));
> if (evalf(est_rel_err) > glob_prec) then # if number 8
> glob_est_digits := -int_trunc(log10(est_rel_err)) + 3;
> else
> glob_est_digits := Digits;
> fi;# end if 8;
> else
> relerr := -1.0 ;
> glob_est_digits := -16;
> fi;# end if 7;
> array_est_digits[1] := glob_est_digits;
> array_good_digits[1] := glob_good_digits;
> if (glob_iter = 1) then # if number 7
> array_1st_rel_error[1] := relerr;
> else
> array_last_rel_error[1] := relerr;
> fi;# end if 7;
> array_est_rel_error[1] := est_rel_err;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_int(INFO,"Desired digits ",32,glob_desired_digits_correct,4," ");
> omniout_int(INFO,"Estimated correct digits ",32,glob_est_digits,4," ");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> ;
> closed_form_val_y := evalf(exact_soln_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 (evalf(float_abs(closed_form_val_y)) > glob_prec) then # if number 7
> relerr := abserr*100.0/float_abs(closed_form_val_y);
> if (relerr > glob_prec) then # if number 8
> glob_good_digits := -int_trunc(log10(relerr)) + 3;
> else
> glob_good_digits := Digits;
> fi;# end if 8;
> else
> relerr := -1.0 ;
> glob_good_digits := -16;
> fi;# end if 7;
> if (evalf)(float_abs(numeric_val) > glob_prec) then # if number 7
> est_rel_err := evalf(array_max_est_error[2]*100.0 * sqrt(glob_iter)*72*MAX_TERMS/float_abs(numeric_val));
> if (evalf(est_rel_err) > glob_prec) then # if number 8
> glob_est_digits := -int_trunc(log10(est_rel_err)) + 3;
> else
> glob_est_digits := Digits;
> fi;# end if 8;
> else
> relerr := -1.0 ;
> glob_est_digits := -16;
> fi;# end if 7;
> array_est_digits[2] := glob_est_digits;
> array_good_digits[2] := glob_good_digits;
> if (glob_iter = 1) then # if number 7
> array_1st_rel_error[2] := relerr;
> else
> array_last_rel_error[2] := relerr;
> fi;# end if 7;
> array_est_rel_error[2] := est_rel_err;
> omniout_float(ALWAYS,"absolute error ",4,abserr,20," ");
> omniout_float(ALWAYS,"relative error ",4,relerr,20,"%");
> omniout_int(INFO,"Desired digits ",32,glob_desired_digits_correct,4," ");
> omniout_int(INFO,"Estimated correct digits ",32,glob_est_digits,4," ");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> omniout_float(ALWAYS,"h ",4,glob_h,20," ");
> fi;# end if 6;
> #BOTTOM DISPLAY ALOT
> fi;# end if 5;
> end;
display_alot := proc(iter)
local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no,
est_rel_err;
global 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, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_prec, glob_est_digits, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer,
glob_html_log, glob_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_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished,
glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h,
glob_optimal_done, 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_max_h, glob_min_h, glob_type_given_pole,
glob_large_float, glob_larger_float, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_look_poles, glob_display_interval, glob_next_display,
glob_dump_closed_form, glob_abserr, glob_relerr, glob_min_pole_est,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_iter, glob_normmax,
glob_max_minutes, array_const_2, array_const_0D0, array_const_0D58,
array_const_1D5, array_x_init, 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_good_digits, array_x,
array_t, array_y, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_tmp5, array_tmp6, array_tmp7_c1, array_tmp7_a1,
array_tmp7_a2, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11,
array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16,
array_tmp17_c1, array_tmp17_a1, array_tmp17_a2, array_tmp17, array_tmp18,
array_m1, array_x_higher, array_x_higher_work, array_x_higher_work2,
array_x_set_initial, 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, MAX_TERMS, glob_last;
if reached_interval() then
if 0 <= iter then
ind_var := array_t[1];
omniout_float(ALWAYS, "t[1] ", 33,
ind_var, 20, " ");
closed_form_val_y := evalf(exact_soln_x(ind_var));
omniout_float(ALWAYS, "x[1] (closed_form) ", 33,
closed_form_val_y, 20, " ");
term_no := 1;
numeric_val := array_x[term_no];
abserr := float_abs(numeric_val - closed_form_val_y);
omniout_float(ALWAYS, "x[1] (numeric) ", 33,
numeric_val, 20, " ");
if glob_prec < evalf(float_abs(closed_form_val_y)) then
relerr := abserr*100.0/float_abs(closed_form_val_y);
if glob_prec < relerr then
glob_good_digits := -int_trunc(log10(relerr)) + 3
else glob_good_digits := Digits
end if
else relerr := -1.0; glob_good_digits := -16
end if;
if evalf(glob_prec < float_abs(numeric_val)) then
est_rel_err := evalf(array_max_est_error[1]*100.0*
sqrt(glob_iter)*72*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 := -1.0; glob_est_digits := -16
end if;
array_est_digits[1] := glob_est_digits;
array_good_digits[1] := glob_good_digits;
if glob_iter = 1 then array_1st_rel_error[1] := relerr
else array_last_rel_error[1] := relerr
end if;
array_est_rel_error[1] := est_rel_err;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_int(INFO, "Desired digits ", 32,
glob_desired_digits_correct, 4, " ");
omniout_int(INFO, "Estimated correct digits ", 32,
glob_est_digits, 4, " ");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ");
closed_form_val_y := evalf(exact_soln_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 glob_prec < evalf(float_abs(closed_form_val_y)) then
relerr := abserr*100.0/float_abs(closed_form_val_y);
if glob_prec < relerr then
glob_good_digits := -int_trunc(log10(relerr)) + 3
else glob_good_digits := Digits
end if
else relerr := -1.0; glob_good_digits := -16
end if;
if evalf(glob_prec < float_abs(numeric_val)) then
est_rel_err := evalf(array_max_est_error[2]*100.0*
sqrt(glob_iter)*72*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 := -1.0; glob_est_digits := -16
end if;
array_est_digits[2] := glob_est_digits;
array_good_digits[2] := glob_good_digits;
if glob_iter = 1 then array_1st_rel_error[2] := relerr
else array_last_rel_error[2] := relerr
end if;
array_est_rel_error[2] := est_rel_err;
omniout_float(ALWAYS, "absolute error ", 4,
abserr, 20, " ");
omniout_float(ALWAYS, "relative error ", 4,
relerr, 20, "%");
omniout_int(INFO, "Desired digits ", 32,
glob_desired_digits_correct, 4, " ");
omniout_int(INFO, "Estimated correct digits ", 32,
glob_est_digits, 4, " ");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ");
omniout_float(ALWAYS, "h ", 4,
glob_h, 20, " ")
end if
end if
end proc
# End Function number 8
# Begin Function number 9
> prog_report := proc(t_start,t_end)
> global
> 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,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_prec,
> glob_est_digits,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_html_log,
> glob_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_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> 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_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_larger_float,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_look_poles,
> glob_display_interval,
> glob_next_display,
> glob_dump_closed_form,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_2,
> array_const_0D0,
> array_const_0D58,
> array_const_1D5,
#END CONST
> array_x_init,
> 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_good_digits,
> array_x,
> array_t,
> array_y,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7_c1,
> array_tmp7_a1,
> array_tmp7_a2,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17_c1,
> array_tmp17_a1,
> array_tmp17_a2,
> array_tmp17,
> array_tmp18,
> array_m1,
> array_x_higher,
> array_x_higher_work,
> array_x_higher_work2,
> array_x_set_initial,
> 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,
> 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((t_end),(t_start),(array_t[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((t_end),(t_start),(array_t[1]) +( glob_h) ,( opt_clock_sec));
> glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec;
> percent_done := comp_percent((t_end),(t_start),(array_t[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 ((percent_done) < (100.0)) then # if number 5
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr((expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr((glob_optimal_expect_sec));
> omniout_str_noeol(INFO,"Expected Total Time ");
> omniout_timestr((glob_total_exp_sec));
> fi;# end if 5;
> omniout_str_noeol(INFO,"Time to Timeout ");
> omniout_timestr((left_sec));
> omniout_float(INFO, "Percent Done ",33,percent_done,4,"%");
> #BOTTOM PROGRESS REPORT
> end;
prog_report := proc(t_start, t_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global 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, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_prec, glob_est_digits, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer,
glob_html_log, glob_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_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished,
glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h,
glob_optimal_done, 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_max_h, glob_min_h, glob_type_given_pole,
glob_large_float, glob_larger_float, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_look_poles, glob_display_interval, glob_next_display,
glob_dump_closed_form, glob_abserr, glob_relerr, glob_min_pole_est,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_iter, glob_normmax,
glob_max_minutes, array_const_2, array_const_0D0, array_const_0D58,
array_const_1D5, array_x_init, 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_good_digits, array_x,
array_t, array_y, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_tmp5, array_tmp6, array_tmp7_c1, array_tmp7_a1,
array_tmp7_a2, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11,
array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16,
array_tmp17_c1, array_tmp17_a1, array_tmp17_a2, array_tmp17, array_tmp18,
array_m1, array_x_higher, array_x_higher_work, array_x_higher_work2,
array_x_set_initial, 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, 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(t_end, t_start, array_t[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(t_end, t_start, array_t[1] + glob_h, opt_clock_sec)
;
glob_total_exp_sec := glob_optimal_expect_sec + total_clock_sec;
percent_done := comp_percent(t_end, t_start, array_t[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 percent_done < 100.0 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
> 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,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_prec,
> glob_est_digits,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_html_log,
> glob_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_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> 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_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_larger_float,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_look_poles,
> glob_display_interval,
> glob_next_display,
> glob_dump_closed_form,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_2,
> array_const_0D0,
> array_const_0D58,
> array_const_1D5,
#END CONST
> array_x_init,
> 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_good_digits,
> array_x,
> array_t,
> array_y,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7_c1,
> array_tmp7_a1,
> array_tmp7_a2,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17_c1,
> array_tmp17_a1,
> array_tmp17_a2,
> array_tmp17,
> array_tmp18,
> array_m1,
> array_x_higher,
> array_x_higher_work,
> array_x_higher_work2,
> array_x_set_initial,
> 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,
> 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 := MAX_TERMS - 2 - 10;
> cnt := 0;
> while (last_no < MAX_TERMS-3 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_ratio(array_x_higher[1,last_no-1],array_x_higher[1,last_no],last_no);
> tmp_ratio := tmp_rad / prev_tmp_rad;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 6
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 7
> found_sing := 0;
> fi;# end if 7;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 7
> if (rad_c < array_rad_test_poles[1,1]) then # if number 8
> array_rad_test_poles[1,1] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_ratio(array_x_higher[1,last_no-1],array_x_higher[1,last_no],last_no);
> array_rad_test_poles[1,1] := rad_c;
> array_ord_test_poles[1,1] := tmp_ord;
> fi;# end if 8;
> fi;# end if 7;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[2,1] := glob_larger_float;
> array_ord_test_poles[2,1] := glob_larger_float;
> found_sing := 1;
> last_no := MAX_TERMS - 2 - 10;
> cnt := 0;
> while (last_no < 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);
> tmp_ratio := tmp_rad / prev_tmp_rad;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 8
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 9
> found_sing := 0;
> fi;# end if 9;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 9
> if (rad_c < array_rad_test_poles[2,1]) then # if number 10
> array_rad_test_poles[2,1] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[2,1] := rad_c;
> array_ord_test_poles[2,1] := tmp_ord;
> fi;# end if 10;
> fi;# end if 9;
> #BOTTOM general radius test2
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,2] := glob_larger_float;
> array_ord_test_poles[1,2] := glob_larger_float;
> found_sing := 1;
> last_no := MAX_TERMS - 2 - 10;
> cnt := 0;
> while (last_no < MAX_TERMS-4 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_three_terms(array_x_higher[1,last_no-2],array_x_higher[1,last_no-1],array_x_higher[1,last_no],last_no);
> tmp_ratio := tmp_rad / prev_tmp_rad;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 9
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 10
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 11
> found_sing := 0;
> fi;# end if 11;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 11
> if (rad_c < array_rad_test_poles[1,2]) then # if number 12
> array_rad_test_poles[1,2] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_three_terms(array_x_higher[1,last_no-2],array_x_higher[1,last_no-1],array_x_higher[1,last_no],last_no);
> array_rad_test_poles[1,2] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 13
> glob_min_pole_est := rad_c;
> fi;# end if 13;
> array_ord_test_poles[1,2] := tmp_ord;
> fi;# end if 12;
> fi;# end if 11;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[2,2] := glob_larger_float;
> array_ord_test_poles[2,2] := glob_larger_float;
> found_sing := 1;
> last_no := MAX_TERMS - 2 - 10;
> cnt := 0;
> while (last_no < 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);
> tmp_ratio := tmp_rad / prev_tmp_rad;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 11
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 12
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 13
> found_sing := 0;
> fi;# end if 13;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 13
> if (rad_c < array_rad_test_poles[2,2]) then # if number 14
> array_rad_test_poles[2,2] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_three_terms(array_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[2,2] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 15
> glob_min_pole_est := rad_c;
> fi;# end if 15;
> array_ord_test_poles[2,2] := tmp_ord;
> fi;# end if 14;
> fi;# end if 13;
> #BOTTOM general radius test2
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,3] := glob_larger_float;
> array_ord_test_poles[1,3] := glob_larger_float;
> found_sing := 1;
> last_no := MAX_TERMS - 2 - 10;
> cnt := 0;
> while (last_no < MAX_TERMS-7 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_six_terms(array_x_higher[1,last_no-5],array_x_higher[1,last_no-4],array_x_higher[1,last_no-3],array_x_higher[1,last_no-2],array_x_higher[1,last_no-1],array_x_higher[1,last_no],last_no);
> tmp_ratio := tmp_rad / prev_tmp_rad;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 13
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 14
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 15
> found_sing := 0;
> fi;# end if 15;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 15
> if (rad_c < array_rad_test_poles[1,3]) then # if number 16
> array_rad_test_poles[1,3] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_six_terms(array_x_higher[1,last_no-5],array_x_higher[1,last_no-4],array_x_higher[1,last_no-3],array_x_higher[1,last_no-2],array_x_higher[1,last_no-1],array_x_higher[1,last_no],last_no);
> array_rad_test_poles[1,3] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 17
> glob_min_pole_est := rad_c;
> fi;# end if 17;
> array_ord_test_poles[1,3] := tmp_ord;
> fi;# end if 16;
> fi;# end if 15;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[2,3] := glob_larger_float;
> array_ord_test_poles[2,3] := glob_larger_float;
> found_sing := 1;
> last_no := MAX_TERMS - 2 - 10;
> cnt := 0;
> while (last_no < 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);
> tmp_ratio := tmp_rad / prev_tmp_rad;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 15
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 16
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 17
> found_sing := 0;
> fi;# end if 17;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 17
> if (rad_c < array_rad_test_poles[2,3]) then # if number 18
> array_rad_test_poles[2,3] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_six_terms(array_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[2,3] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 19
> glob_min_pole_est := rad_c;
> fi;# end if 19;
> array_ord_test_poles[2,3] := tmp_ord;
> fi;# end if 18;
> fi;# end if 17;
> #BOTTOM general radius test2
> #START ADJUST ALL SERIES
> if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 17
> h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius;
> omniout_str(ALWAYS,"SETTING H FOR POLE");
> glob_h_reason := 6;
> if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 18
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> h_new := glob_min_h;
> glob_h_reason := 5;
> fi;# end if 18;
> term := 1;
> ratio := 1.0;
> while (term <= MAX_TERMS) do # do number 1
> array_x[term] := array_x[term]* ratio;
> array_x_higher[1,term] := array_x_higher[1,term]* ratio;
> array_t[term] := array_t[term]* ratio;
> array_y[term] := array_y[term]* ratio;
> array_y_higher[1,term] := array_y_higher[1,term]* ratio;
> array_t[term] := array_t[term]* ratio;
> ratio := ratio * h_new / float_abs(glob_h);
> term := term + 1;
> od;# end do number 1;
> glob_h := h_new;
> fi;# end if 17;
> #BOTTOM ADJUST ALL SERIES
> ;
> if (reached_interval()) then # if number 17
> display_poles();
> fi;# end if 17
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2,
term3, part1, part2, part3, part4, part5, part6, part7, part8, part9,
part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4,
found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio,
prev_tmp_rad, last_no;
global 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, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_prec, glob_est_digits, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer,
glob_html_log, glob_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_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished,
glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h,
glob_optimal_done, 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_max_h, glob_min_h, glob_type_given_pole,
glob_large_float, glob_larger_float, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_look_poles, glob_display_interval, glob_next_display,
glob_dump_closed_form, glob_abserr, glob_relerr, glob_min_pole_est,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_iter, glob_normmax,
glob_max_minutes, array_const_2, array_const_0D0, array_const_0D58,
array_const_1D5, array_x_init, 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_good_digits, array_x,
array_t, array_y, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_tmp5, array_tmp6, array_tmp7_c1, array_tmp7_a1,
array_tmp7_a2, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11,
array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16,
array_tmp17_c1, array_tmp17_a1, array_tmp17_a2, array_tmp17, array_tmp18,
array_m1, array_x_higher, array_x_higher_work, array_x_higher_work2,
array_x_set_initial, 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, 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 := MAX_TERMS - 12;
cnt := 0;
while last_no < MAX_TERMS - 3 and found_sing = 1 do
tmp_rad := comp_rad_from_ratio(array_x_higher[1, last_no - 1],
array_x_higher[1, last_no], last_no);
tmp_ratio := tmp_rad/prev_tmp_rad;
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_x_higher[1, last_no - 1],
array_x_higher[1, last_no], last_no);
array_rad_test_poles[1, 1] := rad_c;
array_ord_test_poles[1, 1] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[2, 1] := glob_larger_float;
array_ord_test_poles[2, 1] := glob_larger_float;
found_sing := 1;
last_no := MAX_TERMS - 12;
cnt := 0;
while last_no < 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);
tmp_ratio := tmp_rad/prev_tmp_rad;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[2, 1] then
array_rad_test_poles[2, 1] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_ratio(array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
array_rad_test_poles[2, 1] := rad_c;
array_ord_test_poles[2, 1] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 2] := glob_larger_float;
array_ord_test_poles[1, 2] := glob_larger_float;
found_sing := 1;
last_no := MAX_TERMS - 12;
cnt := 0;
while last_no < MAX_TERMS - 4 and found_sing = 1 do
tmp_rad := comp_rad_from_three_terms(
array_x_higher[1, last_no - 2], array_x_higher[1, last_no - 1],
array_x_higher[1, last_no], last_no);
tmp_ratio := tmp_rad/prev_tmp_rad;
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_x_higher[1, last_no - 2],
array_x_higher[1, last_no - 1], array_x_higher[1, last_no],
last_no);
array_rad_test_poles[1, 2] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 2] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[2, 2] := glob_larger_float;
array_ord_test_poles[2, 2] := glob_larger_float;
found_sing := 1;
last_no := MAX_TERMS - 12;
cnt := 0;
while last_no < 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);
tmp_ratio := tmp_rad/prev_tmp_rad;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[2, 2] then
array_rad_test_poles[2, 2] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_three_terms(
array_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[2, 2] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[2, 2] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 3] := glob_larger_float;
array_ord_test_poles[1, 3] := glob_larger_float;
found_sing := 1;
last_no := MAX_TERMS - 12;
cnt := 0;
while last_no < MAX_TERMS - 7 and found_sing = 1 do
tmp_rad := comp_rad_from_six_terms(array_x_higher[1, last_no - 5],
array_x_higher[1, last_no - 4], array_x_higher[1, last_no - 3],
array_x_higher[1, last_no - 2], array_x_higher[1, last_no - 1],
array_x_higher[1, last_no], last_no);
tmp_ratio := tmp_rad/prev_tmp_rad;
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_x_higher[1, last_no - 5],
array_x_higher[1, last_no - 4],
array_x_higher[1, last_no - 3],
array_x_higher[1, last_no - 2],
array_x_higher[1, last_no - 1], array_x_higher[1, last_no],
last_no);
array_rad_test_poles[1, 3] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 3] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[2, 3] := glob_larger_float;
array_ord_test_poles[2, 3] := glob_larger_float;
found_sing := 1;
last_no := MAX_TERMS - 12;
cnt := 0;
while last_no < 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);
tmp_ratio := tmp_rad/prev_tmp_rad;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[2, 3] then
array_rad_test_poles[2, 3] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_six_terms(
array_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[2, 3] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[2, 3] := tmp_ord
end if
end if;
if
float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h)
then
h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius;
omniout_str(ALWAYS, "SETTING H FOR POLE");
glob_h_reason := 6;
if glob_check_sign*h_new < glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
h_new := glob_min_h;
glob_h_reason := 5
end if;
term := 1;
ratio := 1.0;
while term <= MAX_TERMS do
array_x[term] := array_x[term]*ratio;
array_x_higher[1, term] := array_x_higher[1, term]*ratio;
array_t[term] := array_t[term]*ratio;
array_y[term] := array_y[term]*ratio;
array_y_higher[1, term] := array_y_higher[1, term]*ratio;
array_t[term] := array_t[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
> 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,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_prec,
> glob_est_digits,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_html_log,
> glob_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_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> 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_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_larger_float,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_look_poles,
> glob_display_interval,
> glob_next_display,
> glob_dump_closed_form,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_2,
> array_const_0D0,
> array_const_0D58,
> array_const_1D5,
#END CONST
> array_x_init,
> 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_good_digits,
> array_x,
> array_t,
> array_y,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7_c1,
> array_tmp7_a1,
> array_tmp7_a2,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17_c1,
> array_tmp17_a1,
> array_tmp17_a2,
> array_tmp17,
> array_tmp18,
> array_m1,
> array_x_higher,
> array_x_higher_work,
> array_x_higher_work2,
> array_x_set_initial,
> 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,
> 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 FULL CONST $eq_no = 1 i = 1
> array_tmp1[1] := array_m1[1] * array_const_0D58[1];
> # emit pre mult FULL FULL $eq_no = 1 i = 1
> array_tmp2[1] := (array_tmp1[1] * (array_x[1]));
> # emit pre mult FULL FULL $eq_no = 1 i = 1
> array_tmp3[1] := (array_x[1] * (array_x[1]));
> # emit pre mult FULL FULL $eq_no = 1 i = 1
> array_tmp4[1] := (array_y[1] * (array_y[1]));
> #emit pre add FULL FULL $eq_no = 1 i = 1
> array_tmp5[1] := array_tmp3[1] + array_tmp4[1];
> #emit pre mult FULL CONST $eq_no = 1 i = 1
> array_tmp6[1] := array_m1[1] * array_const_1D5[1];
> #emit pre expt FULL - FULL $eq_no = 1 i = 1
> array_tmp7[1] := expt(array_tmp5[1] , array_tmp6[1] ) ;
> array_tmp7_a1[1] := ln(array_tmp5[1] ) ;
> # emit pre mult FULL FULL $eq_no = 1 i = 1
> array_tmp8[1] := (array_tmp2[1] * (array_tmp7[1]));
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp9[1] := array_const_0D0[1] + array_tmp8[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_x_set_initial[1,3]) then # if number 1
> if (1 <= MAX_TERMS) then # if number 2
> temporary := array_tmp9[1] * expt(glob_h , (2)) * factorial_3(0,2);
> if (3 <= MAX_TERMS) then # if number 3
> array_x[3] := temporary;
> array_x_higher[1,3] := temporary;
> fi;# end if 3;
> temporary := temporary / glob_h * (2.0);
> array_x_higher[2,2] := temporary;
> temporary := temporary / glob_h * (1.0);
> array_x_higher[3,1] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #emit pre mult FULL CONST $eq_no = 2 i = 1
> array_tmp11[1] := array_m1[1] * array_const_0D58[1];
> # emit pre mult FULL FULL $eq_no = 2 i = 1
> array_tmp12[1] := (array_tmp11[1] * (array_y[1]));
> # emit pre mult FULL FULL $eq_no = 2 i = 1
> array_tmp13[1] := (array_x[1] * (array_x[1]));
> # emit pre mult FULL FULL $eq_no = 2 i = 1
> array_tmp14[1] := (array_y[1] * (array_y[1]));
> #emit pre add FULL FULL $eq_no = 2 i = 1
> array_tmp15[1] := array_tmp13[1] + array_tmp14[1];
> #emit pre mult FULL CONST $eq_no = 2 i = 1
> array_tmp16[1] := array_m1[1] * array_const_1D5[1];
> #emit pre expt FULL - FULL $eq_no = 2 i = 1
> array_tmp17[1] := expt(array_tmp15[1] , array_tmp16[1] ) ;
> array_tmp17_a1[1] := ln(array_tmp15[1] ) ;
> # emit pre mult FULL FULL $eq_no = 2 i = 1
> array_tmp18[1] := (array_tmp12[1] * (array_tmp17[1]));
> #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5
> if ( not array_y_set_initial[2,3]) then # if number 1
> if (1 <= MAX_TERMS) then # if number 2
> temporary := array_tmp18[1] * expt(glob_h , (2)) * factorial_3(0,2);
> if (3 <= MAX_TERMS) then # if number 3
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> fi;# end if 3;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[2,2] := temporary;
> temporary := temporary / glob_h * (1.0);
> array_y_higher[3,1] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre mult FULL CONST $eq_no = 1 i = 2
> array_tmp1[2] := array_m1[2] * array_const_0D58[1];
> # emit pre mult FULL FULL $eq_no = 1 i = 2
> array_tmp2[2] := ats(2,array_tmp1,array_x,1);
> # emit pre mult FULL FULL $eq_no = 1 i = 2
> array_tmp3[2] := ats(2,array_x,array_x,1);
> # emit pre mult FULL FULL $eq_no = 1 i = 2
> array_tmp4[2] := ats(2,array_y,array_y,1);
> #emit pre add FULL FULL $eq_no = 1 i = 2
> array_tmp5[2] := array_tmp3[2] + array_tmp4[2];
> #emit pre mult FULL CONST $eq_no = 1 i = 2
> array_tmp6[2] := array_m1[2] * array_const_1D5[1];
> #emit pre expt FULL - FULL $eq_no = 1 i = 2
> array_tmp7_a1[2] := (array_tmp5[2] -att(1,array_tmp5,array_tmp7_a1,2))/ array_tmp5[1];
> array_tmp7_a2[1] := ats(2,array_tmp5,array_tmp7_a1,1) * 1 / glob_h;
> array_tmp7[2] := ats(1,array_tmp7,array_tmp7_a2,1)*glob_h/1;
> # emit pre mult FULL FULL $eq_no = 1 i = 2
> array_tmp8[2] := ats(2,array_tmp2,array_tmp7,1);
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp9[2] := array_tmp8[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_x_set_initial[1,4]) then # if number 1
> if (2 <= MAX_TERMS) then # if number 2
> temporary := array_tmp9[2] * expt(glob_h , (2)) * factorial_3(1,3);
> if (4 <= MAX_TERMS) then # if number 3
> array_x[4] := temporary;
> array_x_higher[1,4] := temporary;
> fi;# end if 3;
> temporary := temporary / glob_h * (3.0);
> array_x_higher[2,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_x_higher[3,2] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #emit pre mult FULL CONST $eq_no = 2 i = 2
> array_tmp11[2] := array_m1[2] * array_const_0D58[1];
> # emit pre mult FULL FULL $eq_no = 2 i = 2
> array_tmp12[2] := ats(2,array_tmp11,array_y,1);
> # emit pre mult FULL FULL $eq_no = 2 i = 2
> array_tmp13[2] := ats(2,array_x,array_x,1);
> # emit pre mult FULL FULL $eq_no = 2 i = 2
> array_tmp14[2] := ats(2,array_y,array_y,1);
> #emit pre add FULL FULL $eq_no = 2 i = 2
> array_tmp15[2] := array_tmp13[2] + array_tmp14[2];
> #emit pre mult FULL CONST $eq_no = 2 i = 2
> array_tmp16[2] := array_m1[2] * array_const_1D5[1];
> #emit pre expt FULL - FULL $eq_no = 2 i = 2
> array_tmp17_a1[2] := (array_tmp15[2] -att(1,array_tmp15,array_tmp17_a1,2))/ array_tmp15[1];
> array_tmp17_a2[1] := ats(2,array_tmp15,array_tmp17_a1,1) * 1 / glob_h;
> array_tmp17[2] := ats(1,array_tmp17,array_tmp17_a2,1)*glob_h/1;
> # emit pre mult FULL FULL $eq_no = 2 i = 2
> array_tmp18[2] := ats(2,array_tmp12,array_tmp17,1);
> #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5
> if ( not array_y_set_initial[2,4]) then # if number 1
> if (2 <= MAX_TERMS) then # if number 2
> temporary := array_tmp18[2] * expt(glob_h , (2)) * factorial_3(1,3);
> if (4 <= MAX_TERMS) then # if number 3
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> fi;# end if 3;
> temporary := temporary / glob_h * (3.0);
> array_y_higher[2,3] := temporary;
> temporary := temporary / glob_h * (2.0);
> array_y_higher[3,2] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre mult FULL CONST $eq_no = 1 i = 3
> array_tmp1[3] := array_m1[3] * array_const_0D58[1];
> # emit pre mult FULL FULL $eq_no = 1 i = 3
> array_tmp2[3] := ats(3,array_tmp1,array_x,1);
> # emit pre mult FULL FULL $eq_no = 1 i = 3
> array_tmp3[3] := ats(3,array_x,array_x,1);
> # emit pre mult FULL FULL $eq_no = 1 i = 3
> array_tmp4[3] := ats(3,array_y,array_y,1);
> #emit pre add FULL FULL $eq_no = 1 i = 3
> array_tmp5[3] := array_tmp3[3] + array_tmp4[3];
> #emit pre mult FULL CONST $eq_no = 1 i = 3
> array_tmp6[3] := array_m1[3] * array_const_1D5[1];
> #emit pre expt FULL - FULL $eq_no = 1 i = 3
> array_tmp7_a1[3] := (array_tmp5[3] -att(2,array_tmp5,array_tmp7_a1,2))/ array_tmp5[1];
> array_tmp7_a2[2] := ats(3,array_tmp5,array_tmp7_a1,1) * 2 / glob_h;
> array_tmp7[3] := ats(2,array_tmp7,array_tmp7_a2,1)*glob_h/2;
> # emit pre mult FULL FULL $eq_no = 1 i = 3
> array_tmp8[3] := ats(3,array_tmp2,array_tmp7,1);
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp9[3] := array_tmp8[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_x_set_initial[1,5]) then # if number 1
> if (3 <= MAX_TERMS) then # if number 2
> temporary := array_tmp9[3] * expt(glob_h , (2)) * factorial_3(2,4);
> if (5 <= MAX_TERMS) then # if number 3
> array_x[5] := temporary;
> array_x_higher[1,5] := temporary;
> fi;# end if 3;
> temporary := temporary / glob_h * (4.0);
> array_x_higher[2,4] := temporary;
> temporary := temporary / glob_h * (3.0);
> array_x_higher[3,3] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #emit pre mult FULL CONST $eq_no = 2 i = 3
> array_tmp11[3] := array_m1[3] * array_const_0D58[1];
> # emit pre mult FULL FULL $eq_no = 2 i = 3
> array_tmp12[3] := ats(3,array_tmp11,array_y,1);
> # emit pre mult FULL FULL $eq_no = 2 i = 3
> array_tmp13[3] := ats(3,array_x,array_x,1);
> # emit pre mult FULL FULL $eq_no = 2 i = 3
> array_tmp14[3] := ats(3,array_y,array_y,1);
> #emit pre add FULL FULL $eq_no = 2 i = 3
> array_tmp15[3] := array_tmp13[3] + array_tmp14[3];
> #emit pre mult FULL CONST $eq_no = 2 i = 3
> array_tmp16[3] := array_m1[3] * array_const_1D5[1];
> #emit pre expt FULL - FULL $eq_no = 2 i = 3
> array_tmp17_a1[3] := (array_tmp15[3] -att(2,array_tmp15,array_tmp17_a1,2))/ array_tmp15[1];
> array_tmp17_a2[2] := ats(3,array_tmp15,array_tmp17_a1,1) * 2 / glob_h;
> array_tmp17[3] := ats(2,array_tmp17,array_tmp17_a2,1)*glob_h/2;
> # emit pre mult FULL FULL $eq_no = 2 i = 3
> array_tmp18[3] := ats(3,array_tmp12,array_tmp17,1);
> #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5
> if ( not array_y_set_initial[2,5]) then # if number 1
> if (3 <= MAX_TERMS) then # if number 2
> temporary := array_tmp18[3] * expt(glob_h , (2)) * factorial_3(2,4);
> if (5 <= MAX_TERMS) then # if number 3
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> fi;# end if 3;
> temporary := temporary / glob_h * (4.0);
> array_y_higher[2,4] := temporary;
> temporary := temporary / glob_h * (3.0);
> array_y_higher[3,3] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre mult FULL CONST $eq_no = 1 i = 4
> array_tmp1[4] := array_m1[4] * array_const_0D58[1];
> # emit pre mult FULL FULL $eq_no = 1 i = 4
> array_tmp2[4] := ats(4,array_tmp1,array_x,1);
> # emit pre mult FULL FULL $eq_no = 1 i = 4
> array_tmp3[4] := ats(4,array_x,array_x,1);
> # emit pre mult FULL FULL $eq_no = 1 i = 4
> array_tmp4[4] := ats(4,array_y,array_y,1);
> #emit pre add FULL FULL $eq_no = 1 i = 4
> array_tmp5[4] := array_tmp3[4] + array_tmp4[4];
> #emit pre mult FULL CONST $eq_no = 1 i = 4
> array_tmp6[4] := array_m1[4] * array_const_1D5[1];
> #emit pre expt FULL - FULL $eq_no = 1 i = 4
> array_tmp7_a1[4] := (array_tmp5[4] -att(3,array_tmp5,array_tmp7_a1,2))/ array_tmp5[1];
> array_tmp7_a2[3] := ats(4,array_tmp5,array_tmp7_a1,1) * 3 / glob_h;
> array_tmp7[4] := ats(3,array_tmp7,array_tmp7_a2,1)*glob_h/3;
> # emit pre mult FULL FULL $eq_no = 1 i = 4
> array_tmp8[4] := ats(4,array_tmp2,array_tmp7,1);
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp9[4] := array_tmp8[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_x_set_initial[1,6]) then # if number 1
> if (4 <= MAX_TERMS) then # if number 2
> temporary := array_tmp9[4] * expt(glob_h , (2)) * factorial_3(3,5);
> if (6 <= MAX_TERMS) then # if number 3
> array_x[6] := temporary;
> array_x_higher[1,6] := temporary;
> fi;# end if 3;
> temporary := temporary / glob_h * (5.0);
> array_x_higher[2,5] := temporary;
> temporary := temporary / glob_h * (4.0);
> array_x_higher[3,4] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #emit pre mult FULL CONST $eq_no = 2 i = 4
> array_tmp11[4] := array_m1[4] * array_const_0D58[1];
> # emit pre mult FULL FULL $eq_no = 2 i = 4
> array_tmp12[4] := ats(4,array_tmp11,array_y,1);
> # emit pre mult FULL FULL $eq_no = 2 i = 4
> array_tmp13[4] := ats(4,array_x,array_x,1);
> # emit pre mult FULL FULL $eq_no = 2 i = 4
> array_tmp14[4] := ats(4,array_y,array_y,1);
> #emit pre add FULL FULL $eq_no = 2 i = 4
> array_tmp15[4] := array_tmp13[4] + array_tmp14[4];
> #emit pre mult FULL CONST $eq_no = 2 i = 4
> array_tmp16[4] := array_m1[4] * array_const_1D5[1];
> #emit pre expt FULL - FULL $eq_no = 2 i = 4
> array_tmp17_a1[4] := (array_tmp15[4] -att(3,array_tmp15,array_tmp17_a1,2))/ array_tmp15[1];
> array_tmp17_a2[3] := ats(4,array_tmp15,array_tmp17_a1,1) * 3 / glob_h;
> array_tmp17[4] := ats(3,array_tmp17,array_tmp17_a2,1)*glob_h/3;
> # emit pre mult FULL FULL $eq_no = 2 i = 4
> array_tmp18[4] := ats(4,array_tmp12,array_tmp17,1);
> #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5
> if ( not array_y_set_initial[2,6]) then # if number 1
> if (4 <= MAX_TERMS) then # if number 2
> temporary := array_tmp18[4] * expt(glob_h , (2)) * factorial_3(3,5);
> if (6 <= MAX_TERMS) then # if number 3
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> fi;# end if 3;
> temporary := temporary / glob_h * (5.0);
> array_y_higher[2,5] := temporary;
> temporary := temporary / glob_h * (4.0);
> array_y_higher[3,4] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre mult FULL CONST $eq_no = 1 i = 5
> array_tmp1[5] := array_m1[5] * array_const_0D58[1];
> # emit pre mult FULL FULL $eq_no = 1 i = 5
> array_tmp2[5] := ats(5,array_tmp1,array_x,1);
> # emit pre mult FULL FULL $eq_no = 1 i = 5
> array_tmp3[5] := ats(5,array_x,array_x,1);
> # emit pre mult FULL FULL $eq_no = 1 i = 5
> array_tmp4[5] := ats(5,array_y,array_y,1);
> #emit pre add FULL FULL $eq_no = 1 i = 5
> array_tmp5[5] := array_tmp3[5] + array_tmp4[5];
> #emit pre mult FULL CONST $eq_no = 1 i = 5
> array_tmp6[5] := array_m1[5] * array_const_1D5[1];
> #emit pre expt FULL - FULL $eq_no = 1 i = 5
> array_tmp7_a1[5] := (array_tmp5[5] -att(4,array_tmp5,array_tmp7_a1,2))/ array_tmp5[1];
> array_tmp7_a2[4] := ats(5,array_tmp5,array_tmp7_a1,1) * 4 / glob_h;
> array_tmp7[5] := ats(4,array_tmp7,array_tmp7_a2,1)*glob_h/4;
> # emit pre mult FULL FULL $eq_no = 1 i = 5
> array_tmp8[5] := ats(5,array_tmp2,array_tmp7,1);
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp9[5] := array_tmp8[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_x_set_initial[1,7]) then # if number 1
> if (5 <= MAX_TERMS) then # if number 2
> temporary := array_tmp9[5] * expt(glob_h , (2)) * factorial_3(4,6);
> if (7 <= MAX_TERMS) then # if number 3
> array_x[7] := temporary;
> array_x_higher[1,7] := temporary;
> fi;# end if 3;
> temporary := temporary / glob_h * (6.0);
> array_x_higher[2,6] := temporary;
> temporary := temporary / glob_h * (5.0);
> array_x_higher[3,5] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #emit pre mult FULL CONST $eq_no = 2 i = 5
> array_tmp11[5] := array_m1[5] * array_const_0D58[1];
> # emit pre mult FULL FULL $eq_no = 2 i = 5
> array_tmp12[5] := ats(5,array_tmp11,array_y,1);
> # emit pre mult FULL FULL $eq_no = 2 i = 5
> array_tmp13[5] := ats(5,array_x,array_x,1);
> # emit pre mult FULL FULL $eq_no = 2 i = 5
> array_tmp14[5] := ats(5,array_y,array_y,1);
> #emit pre add FULL FULL $eq_no = 2 i = 5
> array_tmp15[5] := array_tmp13[5] + array_tmp14[5];
> #emit pre mult FULL CONST $eq_no = 2 i = 5
> array_tmp16[5] := array_m1[5] * array_const_1D5[1];
> #emit pre expt FULL - FULL $eq_no = 2 i = 5
> array_tmp17_a1[5] := (array_tmp15[5] -att(4,array_tmp15,array_tmp17_a1,2))/ array_tmp15[1];
> array_tmp17_a2[4] := ats(5,array_tmp15,array_tmp17_a1,1) * 4 / glob_h;
> array_tmp17[5] := ats(4,array_tmp17,array_tmp17_a2,1)*glob_h/4;
> # emit pre mult FULL FULL $eq_no = 2 i = 5
> array_tmp18[5] := ats(5,array_tmp12,array_tmp17,1);
> #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5
> if ( not array_y_set_initial[2,7]) then # if number 1
> if (5 <= MAX_TERMS) then # if number 2
> temporary := array_tmp18[5] * expt(glob_h , (2)) * factorial_3(4,6);
> if (7 <= MAX_TERMS) then # if number 3
> array_y[7] := temporary;
> array_y_higher[1,7] := temporary;
> fi;# end if 3;
> temporary := temporary / glob_h * (6.0);
> array_y_higher[2,6] := temporary;
> temporary := temporary / glob_h * (5.0);
> array_y_higher[3,5] := temporary;
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= MAX_TERMS) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit mult FULL CONST $eq_no = 1 i = 1
> array_tmp1[kkk] := array_m1[kkk] * array_const_0D58[1];
> #emit mult FULL FULL $eq_no = 1
> array_tmp2[kkk] := ats(kkk,array_tmp1,array_x,1);
> #emit mult FULL FULL $eq_no = 1
> array_tmp3[kkk] := ats(kkk,array_x,array_x,1);
> #emit mult FULL FULL $eq_no = 1
> array_tmp4[kkk] := ats(kkk,array_y,array_y,1);
> #emit FULL - FULL add $eq_no = 1
> array_tmp5[kkk] := array_tmp3[kkk] + array_tmp4[kkk];
> #emit mult FULL CONST $eq_no = 1 i = 1
> array_tmp6[kkk] := array_m1[kkk] * array_const_1D5[1];
> #emit expt FULL FULL $eq_no = 1 i = 1
> array_tmp7_a1[kkk] := (array_tmp5[kkk] - att(kkk-1,array_tmp5,array_tmp7_a1,2))/array_tmp5[1];
> array_tmp7_a2[kkk-1] := ats(kkk,array_tmp5,array_tmp7_a1,1) * (kkk-1)/glob_h;
> array_tmp7[kkk] := ats(kkk-1,array_tmp7,array_tmp7_a2,1) * glob_h/(kkk-1);
> #emit mult FULL FULL $eq_no = 1
> array_tmp8[kkk] := ats(kkk,array_tmp2,array_tmp7,1);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp9[kkk] := array_tmp8[kkk];
> #emit assign $eq_no = 1
> order_d := 2;
> if (kkk + order_d <= MAX_TERMS) then # if number 1
> if ( not array_x_set_initial[1,kkk + order_d]) then # if number 2
> temporary := array_tmp9[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1));
> array_x[kkk + order_d] := temporary;
> array_x_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while ((term >= 1) and (term <= 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 := temporary / glob_h * (adj2);
> else
> temporary := temporary;
> fi;# end if 4;
> array_x_higher[adj3,term] := temporary;
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 1
> fi;# end if 2
> fi;# end if 1;
> #emit mult FULL CONST $eq_no = 2 i = 1
> array_tmp11[kkk] := array_m1[kkk] * array_const_0D58[1];
> #emit mult FULL FULL $eq_no = 2
> array_tmp12[kkk] := ats(kkk,array_tmp11,array_y,1);
> #emit mult FULL FULL $eq_no = 2
> array_tmp13[kkk] := ats(kkk,array_x,array_x,1);
> #emit mult FULL FULL $eq_no = 2
> array_tmp14[kkk] := ats(kkk,array_y,array_y,1);
> #emit FULL - FULL add $eq_no = 2
> array_tmp15[kkk] := array_tmp13[kkk] + array_tmp14[kkk];
> #emit mult FULL CONST $eq_no = 2 i = 1
> array_tmp16[kkk] := array_m1[kkk] * array_const_1D5[1];
> #emit expt FULL FULL $eq_no = 2 i = 1
> array_tmp17_a1[kkk] := (array_tmp15[kkk] - att(kkk-1,array_tmp15,array_tmp17_a1,2))/array_tmp15[1];
> array_tmp17_a2[kkk-1] := ats(kkk,array_tmp15,array_tmp17_a1,1) * (kkk-1)/glob_h;
> array_tmp17[kkk] := ats(kkk-1,array_tmp17,array_tmp17_a2,1) * glob_h/(kkk-1);
> #emit mult FULL FULL $eq_no = 2
> array_tmp18[kkk] := ats(kkk,array_tmp12,array_tmp17,1);
> #emit assign $eq_no = 2
> order_d := 2;
> if (kkk + order_d <= MAX_TERMS) then # if number 1
> if ( not array_y_set_initial[2,kkk + order_d]) then # if number 2
> temporary := array_tmp18[kkk] * expt(glob_h , (order_d)) * factorial_3((kkk - 1),(kkk + order_d - 1));
> array_y[kkk + order_d] := temporary;
> array_y_higher[1,kkk + order_d] := temporary;
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while ((term >= 1) and (term <= 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 := temporary / glob_h * (adj2);
> else
> temporary := temporary;
> fi;# end if 4;
> array_y_higher[adj3,term] := 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 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, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_prec, glob_est_digits, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer,
glob_html_log, glob_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_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished,
glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h,
glob_optimal_done, 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_max_h, glob_min_h, glob_type_given_pole,
glob_large_float, glob_larger_float, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_look_poles, glob_display_interval, glob_next_display,
glob_dump_closed_form, glob_abserr, glob_relerr, glob_min_pole_est,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_iter, glob_normmax,
glob_max_minutes, array_const_2, array_const_0D0, array_const_0D58,
array_const_1D5, array_x_init, 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_good_digits, array_x,
array_t, array_y, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_tmp5, array_tmp6, array_tmp7_c1, array_tmp7_a1,
array_tmp7_a2, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11,
array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16,
array_tmp17_c1, array_tmp17_a1, array_tmp17_a2, array_tmp17, array_tmp18,
array_m1, array_x_higher, array_x_higher_work, array_x_higher_work2,
array_x_set_initial, 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, MAX_TERMS, glob_last;
array_tmp1[1] := array_m1[1]*array_const_0D58[1];
array_tmp2[1] := array_tmp1[1]*array_x[1];
array_tmp3[1] := array_x[1]*array_x[1];
array_tmp4[1] := array_y[1]*array_y[1];
array_tmp5[1] := array_tmp3[1] + array_tmp4[1];
array_tmp6[1] := array_m1[1]*array_const_1D5[1];
array_tmp7[1] := expt(array_tmp5[1], array_tmp6[1]);
array_tmp7_a1[1] := ln(array_tmp5[1]);
array_tmp8[1] := array_tmp2[1]*array_tmp7[1];
array_tmp9[1] := array_const_0D0[1] + array_tmp8[1];
if not array_x_set_initial[1, 3] then
if 1 <= MAX_TERMS then
temporary := array_tmp9[1]*expt(glob_h, 2)*factorial_3(0, 2);
if 3 <= MAX_TERMS then
array_x[3] := temporary; array_x_higher[1, 3] := temporary
end if;
temporary := temporary*2.0/glob_h;
array_x_higher[2, 2] := temporary;
temporary := temporary*1.0/glob_h;
array_x_higher[3, 1] := temporary
end if
end if;
kkk := 2;
array_tmp11[1] := array_m1[1]*array_const_0D58[1];
array_tmp12[1] := array_tmp11[1]*array_y[1];
array_tmp13[1] := array_x[1]*array_x[1];
array_tmp14[1] := array_y[1]*array_y[1];
array_tmp15[1] := array_tmp13[1] + array_tmp14[1];
array_tmp16[1] := array_m1[1]*array_const_1D5[1];
array_tmp17[1] := expt(array_tmp15[1], array_tmp16[1]);
array_tmp17_a1[1] := ln(array_tmp15[1]);
array_tmp18[1] := array_tmp12[1]*array_tmp17[1];
if not array_y_set_initial[2, 3] then
if 1 <= MAX_TERMS then
temporary := array_tmp18[1]*expt(glob_h, 2)*factorial_3(0, 2);
if 3 <= MAX_TERMS then
array_y[3] := temporary; array_y_higher[1, 3] := temporary
end if;
temporary := temporary*2.0/glob_h;
array_y_higher[2, 2] := temporary;
temporary := temporary*1.0/glob_h;
array_y_higher[3, 1] := temporary
end if
end if;
kkk := 2;
array_tmp1[2] := array_m1[2]*array_const_0D58[1];
array_tmp2[2] := ats(2, array_tmp1, array_x, 1);
array_tmp3[2] := ats(2, array_x, array_x, 1);
array_tmp4[2] := ats(2, array_y, array_y, 1);
array_tmp5[2] := array_tmp3[2] + array_tmp4[2];
array_tmp6[2] := array_m1[2]*array_const_1D5[1];
array_tmp7_a1[2] := (
array_tmp5[2] - att(1, array_tmp5, array_tmp7_a1, 2))/array_tmp5[1]
;
array_tmp7_a2[1] := ats(2, array_tmp5, array_tmp7_a1, 1)/glob_h;
array_tmp7[2] := ats(1, array_tmp7, array_tmp7_a2, 1)*glob_h;
array_tmp8[2] := ats(2, array_tmp2, array_tmp7, 1);
array_tmp9[2] := array_tmp8[2];
if not array_x_set_initial[1, 4] then
if 2 <= MAX_TERMS then
temporary := array_tmp9[2]*expt(glob_h, 2)*factorial_3(1, 3);
if 4 <= MAX_TERMS then
array_x[4] := temporary; array_x_higher[1, 4] := temporary
end if;
temporary := temporary*3.0/glob_h;
array_x_higher[2, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_x_higher[3, 2] := temporary
end if
end if;
kkk := 3;
array_tmp11[2] := array_m1[2]*array_const_0D58[1];
array_tmp12[2] := ats(2, array_tmp11, array_y, 1);
array_tmp13[2] := ats(2, array_x, array_x, 1);
array_tmp14[2] := ats(2, array_y, array_y, 1);
array_tmp15[2] := array_tmp13[2] + array_tmp14[2];
array_tmp16[2] := array_m1[2]*array_const_1D5[1];
array_tmp17_a1[2] := (
array_tmp15[2] - att(1, array_tmp15, array_tmp17_a1, 2))/
array_tmp15[1];
array_tmp17_a2[1] := ats(2, array_tmp15, array_tmp17_a1, 1)/glob_h;
array_tmp17[2] := ats(1, array_tmp17, array_tmp17_a2, 1)*glob_h;
array_tmp18[2] := ats(2, array_tmp12, array_tmp17, 1);
if not array_y_set_initial[2, 4] then
if 2 <= MAX_TERMS then
temporary := array_tmp18[2]*expt(glob_h, 2)*factorial_3(1, 3);
if 4 <= MAX_TERMS then
array_y[4] := temporary; array_y_higher[1, 4] := temporary
end if;
temporary := temporary*3.0/glob_h;
array_y_higher[2, 3] := temporary;
temporary := temporary*2.0/glob_h;
array_y_higher[3, 2] := temporary
end if
end if;
kkk := 3;
array_tmp1[3] := array_m1[3]*array_const_0D58[1];
array_tmp2[3] := ats(3, array_tmp1, array_x, 1);
array_tmp3[3] := ats(3, array_x, array_x, 1);
array_tmp4[3] := ats(3, array_y, array_y, 1);
array_tmp5[3] := array_tmp3[3] + array_tmp4[3];
array_tmp6[3] := array_m1[3]*array_const_1D5[1];
array_tmp7_a1[3] := (
array_tmp5[3] - att(2, array_tmp5, array_tmp7_a1, 2))/array_tmp5[1]
;
array_tmp7_a2[2] := 2*ats(3, array_tmp5, array_tmp7_a1, 1)/glob_h;
array_tmp7[3] := 1/2*ats(2, array_tmp7, array_tmp7_a2, 1)*glob_h;
array_tmp8[3] := ats(3, array_tmp2, array_tmp7, 1);
array_tmp9[3] := array_tmp8[3];
if not array_x_set_initial[1, 5] then
if 3 <= MAX_TERMS then
temporary := array_tmp9[3]*expt(glob_h, 2)*factorial_3(2, 4);
if 5 <= MAX_TERMS then
array_x[5] := temporary; array_x_higher[1, 5] := temporary
end if;
temporary := temporary*4.0/glob_h;
array_x_higher[2, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_x_higher[3, 3] := temporary
end if
end if;
kkk := 4;
array_tmp11[3] := array_m1[3]*array_const_0D58[1];
array_tmp12[3] := ats(3, array_tmp11, array_y, 1);
array_tmp13[3] := ats(3, array_x, array_x, 1);
array_tmp14[3] := ats(3, array_y, array_y, 1);
array_tmp15[3] := array_tmp13[3] + array_tmp14[3];
array_tmp16[3] := array_m1[3]*array_const_1D5[1];
array_tmp17_a1[3] := (
array_tmp15[3] - att(2, array_tmp15, array_tmp17_a1, 2))/
array_tmp15[1];
array_tmp17_a2[2] := 2*ats(3, array_tmp15, array_tmp17_a1, 1)/glob_h;
array_tmp17[3] := 1/2*ats(2, array_tmp17, array_tmp17_a2, 1)*glob_h;
array_tmp18[3] := ats(3, array_tmp12, array_tmp17, 1);
if not array_y_set_initial[2, 5] then
if 3 <= MAX_TERMS then
temporary := array_tmp18[3]*expt(glob_h, 2)*factorial_3(2, 4);
if 5 <= MAX_TERMS then
array_y[5] := temporary; array_y_higher[1, 5] := temporary
end if;
temporary := temporary*4.0/glob_h;
array_y_higher[2, 4] := temporary;
temporary := temporary*3.0/glob_h;
array_y_higher[3, 3] := temporary
end if
end if;
kkk := 4;
array_tmp1[4] := array_m1[4]*array_const_0D58[1];
array_tmp2[4] := ats(4, array_tmp1, array_x, 1);
array_tmp3[4] := ats(4, array_x, array_x, 1);
array_tmp4[4] := ats(4, array_y, array_y, 1);
array_tmp5[4] := array_tmp3[4] + array_tmp4[4];
array_tmp6[4] := array_m1[4]*array_const_1D5[1];
array_tmp7_a1[4] := (
array_tmp5[4] - att(3, array_tmp5, array_tmp7_a1, 2))/array_tmp5[1]
;
array_tmp7_a2[3] := 3*ats(4, array_tmp5, array_tmp7_a1, 1)/glob_h;
array_tmp7[4] := 1/3*ats(3, array_tmp7, array_tmp7_a2, 1)*glob_h;
array_tmp8[4] := ats(4, array_tmp2, array_tmp7, 1);
array_tmp9[4] := array_tmp8[4];
if not array_x_set_initial[1, 6] then
if 4 <= MAX_TERMS then
temporary := array_tmp9[4]*expt(glob_h, 2)*factorial_3(3, 5);
if 6 <= MAX_TERMS then
array_x[6] := temporary; array_x_higher[1, 6] := temporary
end if;
temporary := temporary*5.0/glob_h;
array_x_higher[2, 5] := temporary;
temporary := temporary*4.0/glob_h;
array_x_higher[3, 4] := temporary
end if
end if;
kkk := 5;
array_tmp11[4] := array_m1[4]*array_const_0D58[1];
array_tmp12[4] := ats(4, array_tmp11, array_y, 1);
array_tmp13[4] := ats(4, array_x, array_x, 1);
array_tmp14[4] := ats(4, array_y, array_y, 1);
array_tmp15[4] := array_tmp13[4] + array_tmp14[4];
array_tmp16[4] := array_m1[4]*array_const_1D5[1];
array_tmp17_a1[4] := (
array_tmp15[4] - att(3, array_tmp15, array_tmp17_a1, 2))/
array_tmp15[1];
array_tmp17_a2[3] := 3*ats(4, array_tmp15, array_tmp17_a1, 1)/glob_h;
array_tmp17[4] := 1/3*ats(3, array_tmp17, array_tmp17_a2, 1)*glob_h;
array_tmp18[4] := ats(4, array_tmp12, array_tmp17, 1);
if not array_y_set_initial[2, 6] then
if 4 <= MAX_TERMS then
temporary := array_tmp18[4]*expt(glob_h, 2)*factorial_3(3, 5);
if 6 <= MAX_TERMS then
array_y[6] := temporary; array_y_higher[1, 6] := temporary
end if;
temporary := temporary*5.0/glob_h;
array_y_higher[2, 5] := temporary;
temporary := temporary*4.0/glob_h;
array_y_higher[3, 4] := temporary
end if
end if;
kkk := 5;
array_tmp1[5] := array_m1[5]*array_const_0D58[1];
array_tmp2[5] := ats(5, array_tmp1, array_x, 1);
array_tmp3[5] := ats(5, array_x, array_x, 1);
array_tmp4[5] := ats(5, array_y, array_y, 1);
array_tmp5[5] := array_tmp3[5] + array_tmp4[5];
array_tmp6[5] := array_m1[5]*array_const_1D5[1];
array_tmp7_a1[5] := (
array_tmp5[5] - att(4, array_tmp5, array_tmp7_a1, 2))/array_tmp5[1]
;
array_tmp7_a2[4] := 4*ats(5, array_tmp5, array_tmp7_a1, 1)/glob_h;
array_tmp7[5] := 1/4*ats(4, array_tmp7, array_tmp7_a2, 1)*glob_h;
array_tmp8[5] := ats(5, array_tmp2, array_tmp7, 1);
array_tmp9[5] := array_tmp8[5];
if not array_x_set_initial[1, 7] then
if 5 <= MAX_TERMS then
temporary := array_tmp9[5]*expt(glob_h, 2)*factorial_3(4, 6);
if 7 <= MAX_TERMS then
array_x[7] := temporary; array_x_higher[1, 7] := temporary
end if;
temporary := temporary*6.0/glob_h;
array_x_higher[2, 6] := temporary;
temporary := temporary*5.0/glob_h;
array_x_higher[3, 5] := temporary
end if
end if;
kkk := 6;
array_tmp11[5] := array_m1[5]*array_const_0D58[1];
array_tmp12[5] := ats(5, array_tmp11, array_y, 1);
array_tmp13[5] := ats(5, array_x, array_x, 1);
array_tmp14[5] := ats(5, array_y, array_y, 1);
array_tmp15[5] := array_tmp13[5] + array_tmp14[5];
array_tmp16[5] := array_m1[5]*array_const_1D5[1];
array_tmp17_a1[5] := (
array_tmp15[5] - att(4, array_tmp15, array_tmp17_a1, 2))/
array_tmp15[1];
array_tmp17_a2[4] := 4*ats(5, array_tmp15, array_tmp17_a1, 1)/glob_h;
array_tmp17[5] := 1/4*ats(4, array_tmp17, array_tmp17_a2, 1)*glob_h;
array_tmp18[5] := ats(5, array_tmp12, array_tmp17, 1);
if not array_y_set_initial[2, 7] then
if 5 <= MAX_TERMS then
temporary := array_tmp18[5]*expt(glob_h, 2)*factorial_3(4, 6);
if 7 <= MAX_TERMS then
array_y[7] := temporary; array_y_higher[1, 7] := temporary
end if;
temporary := temporary*6.0/glob_h;
array_y_higher[2, 6] := temporary;
temporary := temporary*5.0/glob_h;
array_y_higher[3, 5] := temporary
end if
end if;
kkk := 6;
while kkk <= MAX_TERMS do
array_tmp1[kkk] := array_m1[kkk]*array_const_0D58[1];
array_tmp2[kkk] := ats(kkk, array_tmp1, array_x, 1);
array_tmp3[kkk] := ats(kkk, array_x, array_x, 1);
array_tmp4[kkk] := ats(kkk, array_y, array_y, 1);
array_tmp5[kkk] := array_tmp3[kkk] + array_tmp4[kkk];
array_tmp6[kkk] := array_m1[kkk]*array_const_1D5[1];
array_tmp7_a1[kkk] := (
array_tmp5[kkk] - att(kkk - 1, array_tmp5, array_tmp7_a1, 2))/
array_tmp5[1];
array_tmp7_a2[kkk - 1] :=
ats(kkk, array_tmp5, array_tmp7_a1, 1)*(kkk - 1)/glob_h;
array_tmp7[kkk] :=
ats(kkk - 1, array_tmp7, array_tmp7_a2, 1)*glob_h/(kkk - 1);
array_tmp8[kkk] := ats(kkk, array_tmp2, array_tmp7, 1);
array_tmp9[kkk] := array_tmp8[kkk];
order_d := 2;
if kkk + order_d <= MAX_TERMS then
if not array_x_set_initial[1, kkk + order_d] then
temporary := array_tmp9[kkk]*expt(glob_h, order_d)*
factorial_3(kkk - 1, kkk + order_d - 1);
array_x[kkk + order_d] := temporary;
array_x_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while
1 <= term and term <= MAX_TERMS and adj3 < order_d + 1 do
if adj3 <= order_d + 1 then
if 0 < adj2 then temporary := temporary*adj2/glob_h
else temporary := temporary
end if;
array_x_higher[adj3, term] := temporary
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
array_tmp11[kkk] := array_m1[kkk]*array_const_0D58[1];
array_tmp12[kkk] := ats(kkk, array_tmp11, array_y, 1);
array_tmp13[kkk] := ats(kkk, array_x, array_x, 1);
array_tmp14[kkk] := ats(kkk, array_y, array_y, 1);
array_tmp15[kkk] := array_tmp13[kkk] + array_tmp14[kkk];
array_tmp16[kkk] := array_m1[kkk]*array_const_1D5[1];
array_tmp17_a1[kkk] := (
array_tmp15[kkk] - att(kkk - 1, array_tmp15, array_tmp17_a1, 2)
)/array_tmp15[1];
array_tmp17_a2[kkk - 1] :=
ats(kkk, array_tmp15, array_tmp17_a1, 1)*(kkk - 1)/glob_h;
array_tmp17[kkk] :=
ats(kkk - 1, array_tmp17, array_tmp17_a2, 1)*glob_h/(kkk - 1);
array_tmp18[kkk] := ats(kkk, array_tmp12, array_tmp17, 1);
order_d := 2;
if kkk + order_d <= MAX_TERMS then
if not array_y_set_initial[2, kkk + order_d] then
temporary := array_tmp18[kkk]*expt(glob_h, order_d)*
factorial_3(kkk - 1, kkk + order_d - 1);
array_y[kkk + order_d] := temporary;
array_y_higher[1, kkk + order_d] := temporary;
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while
1 <= term and term <= MAX_TERMS and adj3 < order_d + 1 do
if adj3 <= order_d + 1 then
if 0 < adj2 then temporary := temporary*adj2/glob_h
else temporary := temporary
end if;
array_y_higher[adj3, term] := 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,
> t_start,t_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
> 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,
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob_prec,
> glob_est_digits,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_subiter_method,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_html_log,
> glob_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_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> 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_max_h,
> glob_min_h,
> glob_type_given_pole,
> glob_large_float,
> glob_larger_float,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_look_poles,
> glob_display_interval,
> glob_next_display,
> glob_dump_closed_form,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_hours,
> glob_max_iter,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_no_eqs,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_small_float,
> glob_smallish_float,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_max_sec,
> glob_orig_start_sec,
> glob_start,
> glob_iter,
> glob_normmax,
> glob_max_minutes,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_2,
> array_const_0D0,
> array_const_0D58,
> array_const_1D5,
> #END CONST
> array_x_init,
> 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_good_digits,
> array_x,
> array_t,
> array_y,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7_c1,
> array_tmp7_a1,
> array_tmp7_a2,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17_c1,
> array_tmp17_a1,
> array_tmp17_a2,
> array_tmp17,
> array_tmp18,
> array_m1,
> array_x_higher,
> array_x_higher_work,
> array_x_higher_work2,
> array_x_set_initial,
> 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,
> MAX_TERMS,
> glob_last;
> MAX_TERMS := 30;
> # before first input block
> #BEGIN FIRST INPUT BLOCK
> #BEGIN BLOCK 1
> #BEGIN FIRST INPUT BLOCK
> max_terms:=30;
> Digits:=16;
> #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_x_init:= Array(0..(MAX_TERMS),[]);
> array_y_init:= Array(0..(MAX_TERMS),[]);
> array_norms:= Array(0..(MAX_TERMS),[]);
> array_fact_1:= Array(0..(MAX_TERMS),[]);
> array_1st_rel_error:= Array(0..(3),[]);
> array_last_rel_error:= Array(0..(3),[]);
> array_est_rel_error:= Array(0..(3),[]);
> array_max_est_error:= Array(0..(3),[]);
> array_type_pole:= Array(0..(3),[]);
> array_type_real_pole:= Array(0..(3),[]);
> array_type_complex_pole:= Array(0..(3),[]);
> array_est_digits:= Array(0..(3),[]);
> array_good_digits:= Array(0..(3),[]);
> array_x:= Array(0..(MAX_TERMS),[]);
> array_t:= Array(0..(MAX_TERMS),[]);
> array_y:= Array(0..(MAX_TERMS),[]);
> array_tmp0:= Array(0..(MAX_TERMS),[]);
> array_tmp1:= Array(0..(MAX_TERMS),[]);
> array_tmp2:= Array(0..(MAX_TERMS),[]);
> array_tmp3:= Array(0..(MAX_TERMS),[]);
> array_tmp4:= Array(0..(MAX_TERMS),[]);
> array_tmp5:= Array(0..(MAX_TERMS),[]);
> array_tmp6:= Array(0..(MAX_TERMS),[]);
> array_tmp7_c1:= Array(0..(MAX_TERMS),[]);
> array_tmp7_a1:= Array(0..(MAX_TERMS),[]);
> array_tmp7_a2:= Array(0..(MAX_TERMS),[]);
> array_tmp7:= Array(0..(MAX_TERMS),[]);
> array_tmp8:= Array(0..(MAX_TERMS),[]);
> array_tmp9:= Array(0..(MAX_TERMS),[]);
> array_tmp10:= Array(0..(MAX_TERMS),[]);
> array_tmp11:= Array(0..(MAX_TERMS),[]);
> array_tmp12:= Array(0..(MAX_TERMS),[]);
> array_tmp13:= Array(0..(MAX_TERMS),[]);
> array_tmp14:= Array(0..(MAX_TERMS),[]);
> array_tmp15:= Array(0..(MAX_TERMS),[]);
> array_tmp16:= Array(0..(MAX_TERMS),[]);
> array_tmp17_c1:= Array(0..(MAX_TERMS),[]);
> array_tmp17_a1:= Array(0..(MAX_TERMS),[]);
> array_tmp17_a2:= Array(0..(MAX_TERMS),[]);
> array_tmp17:= Array(0..(MAX_TERMS),[]);
> array_tmp18:= Array(0..(MAX_TERMS),[]);
> array_m1:= Array(0..(MAX_TERMS),[]);
> array_x_higher := Array(0..(3) ,(0..MAX_TERMS+ 1),[]);
> array_x_higher_work := Array(0..(3) ,(0..MAX_TERMS+ 1),[]);
> array_x_higher_work2 := Array(0..(3) ,(0..MAX_TERMS+ 1),[]);
> array_x_set_initial := Array(0..(3) ,(0..MAX_TERMS+ 1),[]);
> array_y_higher := Array(0..(3) ,(0..MAX_TERMS+ 1),[]);
> array_y_higher_work := Array(0..(3) ,(0..MAX_TERMS+ 1),[]);
> array_y_higher_work2 := Array(0..(3) ,(0..MAX_TERMS+ 1),[]);
> array_y_set_initial := Array(0..(3) ,(0..MAX_TERMS+ 1),[]);
> array_given_rad_poles := Array(0..(3) ,(0..3+ 1),[]);
> array_given_ord_poles := Array(0..(3) ,(0..3+ 1),[]);
> array_rad_test_poles := Array(0..(3) ,(0..4+ 1),[]);
> array_ord_test_poles := Array(0..(3) ,(0..4+ 1),[]);
> array_fact_2 := Array(0..(MAX_TERMS) ,(0..MAX_TERMS+ 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 <= MAX_TERMS) do # do number 1
> array_x_init[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= MAX_TERMS) do # do number 1
> array_y_init[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= MAX_TERMS) do # do number 1
> array_norms[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= MAX_TERMS) do # do number 1
> array_fact_1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_1st_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_last_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_est_rel_error[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_max_est_error[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_type_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_type_real_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_type_complex_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_est_digits[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_good_digits[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= MAX_TERMS) do # do number 1
> array_x[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= MAX_TERMS) do # do number 1
> array_t[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= MAX_TERMS) do # do number 1
> array_y[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= MAX_TERMS) do # do number 1
> array_tmp0[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= MAX_TERMS) do # do number 1
> array_tmp1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= MAX_TERMS) do # do number 1
> array_tmp2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= MAX_TERMS) do # do number 1
> array_tmp3[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= MAX_TERMS) do # do number 1
> array_tmp4[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= MAX_TERMS) do # do number 1
> array_tmp5[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= MAX_TERMS) do # do number 1
> array_tmp6[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= MAX_TERMS) do # do number 1
> array_tmp7_c1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= MAX_TERMS) do # do number 1
> array_tmp7_a1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= MAX_TERMS) do # do number 1
> array_tmp7_a2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= MAX_TERMS) do # do number 1
> array_tmp7[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= MAX_TERMS) do # do number 1
> array_tmp8[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= MAX_TERMS) do # do number 1
> array_tmp9[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= MAX_TERMS) do # do number 1
> array_tmp10[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= MAX_TERMS) do # do number 1
> array_tmp11[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= MAX_TERMS) do # do number 1
> array_tmp12[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= MAX_TERMS) do # do number 1
> array_tmp13[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= MAX_TERMS) do # do number 1
> array_tmp14[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= MAX_TERMS) do # do number 1
> array_tmp15[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= MAX_TERMS) do # do number 1
> array_tmp16[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= MAX_TERMS) do # do number 1
> array_tmp17_c1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= MAX_TERMS) do # do number 1
> array_tmp17_a1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= MAX_TERMS) do # do number 1
> array_tmp17_a2[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= MAX_TERMS) do # do number 1
> array_tmp17[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= MAX_TERMS) do # do number 1
> array_tmp18[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= MAX_TERMS) do # do number 1
> array_m1[term] := 0.0;
> term := term + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= MAX_TERMS) do # do number 2
> array_x_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= MAX_TERMS) do # do number 2
> array_x_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= MAX_TERMS) do # do number 2
> array_x_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= MAX_TERMS) do # do number 2
> array_x_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= MAX_TERMS) do # do number 2
> array_y_higher[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= MAX_TERMS) do # do number 2
> array_y_higher_work[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= MAX_TERMS) do # do number 2
> array_y_higher_work2[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= MAX_TERMS) do # do number 2
> array_y_set_initial[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_rad_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_ord_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_rad_test_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_ord_test_poles[ord,term] := 0.0;
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=MAX_TERMS) do # do number 1
> term := 1;
> while (term <= MAX_TERMS) do # do number 2
> array_fact_2[ord,term] := 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_x);
> zero_ats_ar(array_t);
> zero_ats_ar(array_m1);
> zero_ats_ar(array_y);
> zero_ats_ar(array_tmp0);
> zero_ats_ar(array_tmp1);
> zero_ats_ar(array_tmp2);
> zero_ats_ar(array_tmp3);
> zero_ats_ar(array_tmp4);
> zero_ats_ar(array_tmp5);
> zero_ats_ar(array_tmp6);
> zero_ats_ar(array_tmp7_c1);
> zero_ats_ar(array_tmp7_a1);
> zero_ats_ar(array_tmp7_a2);
> zero_ats_ar(array_tmp7);
> zero_ats_ar(array_tmp8);
> zero_ats_ar(array_tmp9);
> zero_ats_ar(array_tmp10);
> zero_ats_ar(array_tmp11);
> zero_ats_ar(array_tmp12);
> zero_ats_ar(array_tmp13);
> zero_ats_ar(array_tmp14);
> zero_ats_ar(array_tmp15);
> zero_ats_ar(array_tmp16);
> zero_ats_ar(array_tmp17_c1);
> zero_ats_ar(array_tmp17_a1);
> zero_ats_ar(array_tmp17_a2);
> zero_ats_ar(array_tmp17);
> zero_ats_ar(array_tmp18);
> zero_ats_ar(array_const_2);
> array_const_2[1] := 2;
> zero_ats_ar(array_const_0D0);
> array_const_0D0[1] := 0.0;
> zero_ats_ar(array_const_0D58);
> array_const_0D58[1] := 0.58;
> zero_ats_ar(array_const_1D5);
> array_const_1D5[1] := 1.5;
> zero_ats_ar(array_m1);
> array_m1[1] := -1.0;
> #END SYMBOLS INITIALIZATED
> # before generate factorials init
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= MAX_TERMS) do # do number 1
> jjjf := 0;
> while (jjjf <= 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
> 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(10.0);
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> MAX_UNCHANGED := 10;
> glob_prec := 1.0e-16;
> glob_est_digits := 1;
> glob_check_sign := 1.0;
> glob_desired_digits_correct := 8.0;
> glob_max_estimated_step_error := 0.0;
> glob_ratio_of_radius := 0.1;
> glob_percent_done := 0.0;
> glob_subiter_method := 3;
> glob_total_exp_sec := 0.1;
> glob_optimal_expect_sec := 0.1;
> glob_estimated_size_answer := 100.0;
> glob_html_log := true;
> glob_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 := 60.0;
> glob_hours_in_day := 24.0;
> glob_days_in_year := 365;
> glob_sec_in_hour := 3600;
> glob_sec_in_day := 86400;
> glob_sec_in_year := 31536000;
> glob_almost_1 := 0.9990;
> glob_clock_sec := 0.0;
> glob_clock_start_sec := 0.0;
> 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_disp_incr := 0.1;
> glob_h := 0.1;
> glob_diff_rc_fm := 0.1;
> glob_diff_rc_fmm1 := 0.1;
> glob_diff_rc_fmm2 := 0.1;
> glob_diff_ord_fm := 0.1;
> glob_diff_ord_fmm1 := 0.1;
> glob_diff_ord_fmm2 := 0.1;
> glob_six_term_ord_save := 0.1;
> glob_guess_error_rc := 0.1;
> glob_guess_error_ord := 0.1;
> glob_max_h := 0.1;
> glob_min_h := 0.000001;
> glob_type_given_pole := 0;
> glob_large_float := 1.0e100;
> glob_larger_float := 1.1e100;
> glob_least_given_sing := 9.9e100;
> glob_least_ratio_sing := 9.9e100;
> glob_least_3_sing := 9.9e100;
> glob_least_6_sing := 9.9e100;
> glob_last_good_h := 0.1;
> glob_look_poles := false;
> glob_display_interval := 0.1;
> glob_next_display := 0.0;
> glob_dump_closed_form := false;
> glob_abserr := 0.1e-10;
> glob_relerr := 0.1e-10;
> glob_min_pole_est := 0.1e+10;
> glob_max_hours := 0.0;
> glob_max_iter := 1000;
> glob_max_rel_trunc_err := 0.1e-10;
> glob_max_trunc_err := 0.1e-10;
> glob_no_eqs := 0;
> glob_optimal_clock_start_sec := 0.0;
> glob_optimal_start := 0.0;
> glob_upper_ratio_limit := 1.0001;
> glob_lower_ratio_limit := 0.9999;
> glob_small_float := 0.0;
> glob_smallish_float := 0.0;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_max_sec := 10000.0;
> glob_orig_start_sec := 0.0;
> glob_start := 0;
> glob_iter := 0;
> glob_normmax := 0.0;
> glob_max_minutes := 0.0;
> # before generate set diff initial
> array_x_set_initial[1,1] := true;
> array_x_set_initial[1,2] := true;
> array_x_set_initial[1,3] := false;
> array_x_set_initial[1,4] := false;
> array_x_set_initial[1,5] := false;
> array_x_set_initial[1,6] := false;
> array_x_set_initial[1,7] := false;
> array_x_set_initial[1,8] := false;
> array_x_set_initial[1,9] := false;
> array_x_set_initial[1,10] := false;
> array_x_set_initial[1,11] := false;
> array_x_set_initial[1,12] := false;
> array_x_set_initial[1,13] := false;
> array_x_set_initial[1,14] := false;
> array_x_set_initial[1,15] := false;
> array_x_set_initial[1,16] := false;
> array_x_set_initial[1,17] := false;
> array_x_set_initial[1,18] := false;
> array_x_set_initial[1,19] := false;
> array_x_set_initial[1,20] := false;
> array_x_set_initial[1,21] := false;
> array_x_set_initial[1,22] := false;
> array_x_set_initial[1,23] := false;
> array_x_set_initial[1,24] := false;
> array_x_set_initial[1,25] := false;
> array_x_set_initial[1,26] := false;
> array_x_set_initial[1,27] := false;
> array_x_set_initial[1,28] := false;
> array_x_set_initial[1,29] := false;
> array_x_set_initial[1,30] := false;
> array_y_set_initial[2,1] := true;
> array_y_set_initial[2,2] := true;
> array_y_set_initial[2,3] := false;
> array_y_set_initial[2,4] := false;
> array_y_set_initial[2,5] := false;
> array_y_set_initial[2,6] := false;
> array_y_set_initial[2,7] := false;
> array_y_set_initial[2,8] := false;
> array_y_set_initial[2,9] := false;
> array_y_set_initial[2,10] := false;
> array_y_set_initial[2,11] := false;
> array_y_set_initial[2,12] := false;
> array_y_set_initial[2,13] := false;
> array_y_set_initial[2,14] := false;
> array_y_set_initial[2,15] := false;
> array_y_set_initial[2,16] := false;
> array_y_set_initial[2,17] := false;
> array_y_set_initial[2,18] := false;
> array_y_set_initial[2,19] := false;
> array_y_set_initial[2,20] := false;
> array_y_set_initial[2,21] := false;
> array_y_set_initial[2,22] := false;
> array_y_set_initial[2,23] := false;
> array_y_set_initial[2,24] := false;
> array_y_set_initial[2,25] := false;
> array_y_set_initial[2,26] := false;
> array_y_set_initial[2,27] := false;
> array_y_set_initial[2,28] := false;
> array_y_set_initial[2,29] := false;
> array_y_set_initial[2,30] := false;
> # before generate init omniout const
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> MAX_TERMS := 30;
> glob_iolevel := INFO;
> # set default block
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> glob_display_flag := true;
> glob_no_eqs := 2;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 50000;
> glob_max_hours := 0.0;
> glob_max_minutes := 15.0;
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/chang3_1postode.ode#################");
> omniout_str(ALWAYS,"diff ( x , t , 2 ) = m1 * 0.58 * x * expt ( ( x * x + y * y ) , ( m1 * 1.5 ) ) ; ");
> omniout_str(ALWAYS,"diff ( y , t , 2 ) = m1 * 0.58 * y * expt ( ( x * x + y * y ) , ( m1 * 1.5 ) ) ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"max_terms:=30;");
> omniout_str(ALWAYS,"Digits:=16;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"t_start := 1.00;");
> omniout_str(ALWAYS,"t_end := 12.0;");
> omniout_str(ALWAYS,"array_x_init[0 + 1] := -1.000;");
> omniout_str(ALWAYS,"array_x_init[1 + 1] := 0.000;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := 0.000;");
> omniout_str(ALWAYS,"array_y_init[1 + 1] := 4.300;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_type_given_pole := 0;");
> omniout_str(ALWAYS,"glob_min_h := 0.1;");
> omniout_str(ALWAYS,"glob_max_h := 0.1;");
> omniout_str(ALWAYS,"glob_display_interval := 0.1;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=16;");
> omniout_str(ALWAYS,"glob_max_minutes:=30.0;");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"glob_max_iter:=100000000;");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"exact_soln_x := proc(t)");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"return(0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y := proc(t)");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"return(0);");
> omniout_str(ALWAYS,"");
> 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 := 0.0;
> glob_smallish_float := 0.0;
> glob_large_float := 1.0e100;
> glob_larger_float := 1.1e100;
> glob_almost_1 := 0.99;
> # before second block
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #BEGIN BLOCK 2
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> t_start := 1.00;
> t_end := 12.0;
> array_x_init[0 + 1] := -1.000;
> array_x_init[1 + 1] := 0.000;
> array_y_init[0 + 1] := 0.000;
> array_y_init[1 + 1] := 4.300;
> glob_look_poles := true;
> glob_type_given_pole := 0;
> glob_min_h := 0.1;
> glob_max_h := 0.1;
> glob_display_interval := 0.1;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=16;
> glob_max_minutes:=30.0;
> glob_subiter_method:=3;
> glob_max_iter:=100000000;
> #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
> #BEGIN OPTIMIZE CODE
> omniout_str(ALWAYS,"START of Optimize");
> #Start Series -- INITIALIZE FOR OPTIMIZE
> glob_check_sign := my_check_sign(t_start,t_end);
> 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 := float_abs(glob_display_interval) * glob_check_sign;
> display_max := (t_end - t_start)/10.0;
> if (glob_display_interval > display_max) then # if number 17
> glob_display_interval := display_max;
> fi;# end if 17;
> chk_data();
> min_value := glob_larger_float;
> est_answer := est_size_answer();
> opt_iter := 1;
> glob_prec = expt(10.0,-Digits);
> est_needed_step_err := estimated_needed_step_error(t_start,t_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_t[1] := t_start;
> array_t[2] := glob_h;
> glob_next_display := t_start;
> order_diff := 2;
> #Start Series array_x
> term_no := 1;
> while (term_no <= order_diff) do # do number 2
> array_x[term_no] := array_x_init[term_no] * expt(glob_h , (term_no - 1)) / 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 < MAX_TERMS) then # if number 17
> array_x_higher[r_order,term_no] := array_x_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> fi;# end if 17;
> term_no := term_no + 1;
> od;# end do number 3;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> order_diff := 2;
> #Start Series array_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 , (term_no - 1)) / 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 < MAX_TERMS) then # if number 17
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> fi;# end if 17;
> term_no := term_no + 1;
> od;# end do number 3;
> r_order := r_order + 1;
> od;# end do number 2
> ;
> if (glob_subiter_method = 1 ) then # if number 17
> atomall();
> elif
> (glob_subiter_method = 2 ) then # if number 18
> subiter := 1;
> while (subiter <= 4) do # do number 2
> atomall();
> subiter := subiter + 1;
> od;# end do number 2;
> else
> subiter := 1;
> while (subiter <= 4 + MAX_TERMS) do # do number 2
> atomall();
> subiter := subiter + 1;
> od;# end do number 2;
> fi;# end if 18;
> if (glob_check_sign * glob_max_h <= glob_check_sign * glob_h) then # if number 18
> 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 18;
> if (glob_check_sign * glob_display_interval <= glob_check_sign * glob_h) then # if number 18
> omniout_str(ALWAYS,"SETTING H FOR DISPLAY INTERVAL");
> glob_h_reason := 2;
> glob_h := glob_display_interval;
> found_h := true;
> fi;# end if 18;
> if (glob_look_poles) then # if number 18
> check_for_pole();
> if ((opt_iter > 2) and ( not found_h) and ((glob_min_pole_est < 0.999 * last_min_pole_est) or (glob_min_pole_est > 1.111 * last_min_pole_est))) then # if number 19
> omniout_str(ALWAYS,"SETTING H FOR POLE ACCURACY");
> glob_h_reason := 4;
> found_h := true;
> glob_h := glob_h/2.0;
> last_min_pole_est := glob_min_pole_est;
> else
> last_min_pole_est := glob_min_pole_est;
> fi;# end if 19;
> fi;# end if 18;
> if ( not found_h) then # if number 18
> est_answer := est_size_answer();
> est_needed_step_err := estimated_needed_step_error(t_start,t_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 19
> omniout_str(ALWAYS,"Double H and LOOP");
> glob_h := glob_h*2.0;
> else
> omniout_str(ALWAYS,"Found H for OPTIMAL");
> found_h := true;
> glob_h_reason := 3;
> glob_h := glob_h/2.0;
> fi;# end if 19;
> fi;# end if 18;
> opt_iter := opt_iter + 1;
> od;# end do number 1;
> if (( not found_h) and (opt_iter = 1)) then # if number 18
> omniout_str(ALWAYS,"Beginning glob_h too large.");
> found_h := false;
> fi;# end if 18;
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 18
> html_log_file := fopen("entry.html",WRITE,TEXT);
> fi;# end if 18;
> #BEGIN SOLUTION CODE
> if (found_h) then # if number 18
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_t[1] := t_start;
> array_t[2] := glob_h;
> glob_next_display := t_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 := 2;
> #Start Series array_x
> term_no := 1;
> while (term_no <= order_diff) do # do number 1
> array_x[term_no] := array_x_init[term_no] * expt(glob_h , (term_no - 1)) / 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 < MAX_TERMS) then # if number 19
> array_x_higher[r_order,term_no] := array_x_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> fi;# end if 19;
> term_no := term_no + 1;
> od;# end do number 2;
> r_order := r_order + 1;
> od;# end do number 1
> ;
> order_diff := 2;
> #Start Series array_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 , (term_no - 1)) / 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 < MAX_TERMS) then # if number 19
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , (term_no - 1)) / ((factorial_1(term_no - 1)));
> fi;# end if 19;
> term_no := term_no + 1;
> od;# end do number 2;
> r_order := r_order + 1;
> od;# end do number 1
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> glob_clock_sec := elapsed_time_seconds();
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_iter < glob_max_iter) and (glob_check_sign * array_t[1] < glob_check_sign * t_end ) and (((glob_clock_sec) - (glob_orig_start_sec)) < (glob_max_sec))) do # do number 1
> #left paren 0001C
> if (reached_interval()) then # if number 19
> omniout_str(INFO," ");
> omniout_str(INFO,"TOP MAIN SOLVE Loop");
> fi;# end if 19;
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> track_estimated_error();
> if (glob_subiter_method = 1 ) then # if number 19
> atomall();
> elif
> (glob_subiter_method = 2 ) then # if number 20
> subiter := 1;
> while (subiter <= 4) do # do number 2
> atomall();
> subiter := subiter + 1;
> od;# end do number 2;
> else
> subiter := 1;
> while (subiter <= 4 + MAX_TERMS) do # do number 2
> atomall();
> subiter := subiter + 1;
> od;# end do number 2;
> fi;# end if 20;
> track_estimated_error();
> display_alot(current_iter);
> check_for_pole();
> if (reached_interval()) then # if number 20
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 20;
> array_t[1] := array_t[1] + glob_h;
> array_t[2] := glob_h;
> #Jump Series array_x;
> order_diff := 3;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_x
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 3;
> calc_term := 1;
> #adjust_subseriesarray_x
> iii := MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_x_higher_work[3,iii] := array_x_higher[3,iii] / expt(glob_h , (calc_term - 1)) / 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 := 0.0;
> ord := 3;
> calc_term := 1;
> #sum_subseriesarray_x
> iii := MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_x_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_x_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 2;
> #adjust_subseriesarray_x
> iii := MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_x_higher_work[2,iii] := array_x_higher[2,iii] / expt(glob_h , (calc_term - 1)) / 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 := 0.0;
> ord := 2;
> calc_term := 2;
> #sum_subseriesarray_x
> iii := MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_x_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_x_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_x
> iii := MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_x_higher_work[2,iii] := array_x_higher[2,iii] / expt(glob_h , (calc_term - 1)) / 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 := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_x
> iii := MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_x_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_x_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 3;
> #adjust_subseriesarray_x
> iii := MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_x_higher_work[1,iii] := array_x_higher[1,iii] / expt(glob_h , (calc_term - 1)) / 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 := 0.0;
> ord := 1;
> calc_term := 3;
> #sum_subseriesarray_x
> iii := MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_x_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_x_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_x
> iii := MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_x_higher_work[1,iii] := array_x_higher[1,iii] / expt(glob_h , (calc_term - 1)) / 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 := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_x
> iii := MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_x_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_x_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_x
> iii := MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_x_higher_work[1,iii] := array_x_higher[1,iii] / expt(glob_h , (calc_term - 1)) / 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 := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_x
> iii := MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_x_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_x_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , (calc_term - 1)) / (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 := MAX_TERMS;
> while (term_no >= 1) do # do number 2
> array_x[term_no] := array_x_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 3
> array_x_higher[ord,term_no] := array_x_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 3;
> term_no := term_no - 1;
> od;# end do number 2;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> #Jump Series array_y;
> order_diff := 3;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =2
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 3;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[3,iii] := array_y_higher[3,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 3;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := 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 , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 2;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 2;
> calc_term := 2;
> #sum_subseriesarray_y
> iii := 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 , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := 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 , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 1;
> calc_term := 3;
> #adjust_subseriesarray_y
> iii := MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 1;
> calc_term := 3;
> #sum_subseriesarray_y
> iii := 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 , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y
> iii := 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 , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , (calc_term - 1)) / factorial_3(iii - calc_term , iii - 1);
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := 0.0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := 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 , (calc_term - 1)) / (factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #END SUM AND ADJUST EQ =2
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := 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 20
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 20;
> if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec )) then # if number 20
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 20;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( x , t , 2 ) = m1 * 0.58 * x * expt ( ( x * x + y * y ) , ( m1 * 1.5 ) ) ; ");
> omniout_str(INFO,"diff ( y , t , 2 ) = m1 * 0.58 * y * expt ( ( x * x + y * y ) , ( m1 * 1.5 ) ) ; ");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(t_start,t_end);
> if (glob_html_log) then # if number 20
> logstart(html_log_file);
> logitem_str(html_log_file,"2014-09-23T16:46:14-05:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"chang3_1")
> ;
> logitem_str(html_log_file,"diff ( x , t , 2 ) = m1 * 0.58 * x * expt ( ( x * x + y * y ) , ( m1 * 1.5 ) ) ; ")
> ;
> logitem_float(html_log_file,t_start)
> ;
> logitem_float(html_log_file,t_end)
> ;
> logitem_float(html_log_file,array_t[1])
> ;
> logitem_float(html_log_file,glob_h)
> ;
> logitem_h_reason(html_log_file)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> logitem_float(html_log_file,glob_desired_digits_correct)
> ;
> if (array_est_digits[1] <> -16) then # if number 21
> logitem_integer(html_log_file,array_est_digits[1])
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 21;
> if (array_good_digits[1] <> -16) then # if number 21
> logitem_integer(html_log_file,array_good_digits[1])
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 21;
> logitem_integer(html_log_file,MAX_TERMS)
> ;
> if (glob_type_given_pole = 0) then # if number 21
> logitem_str(html_log_file,"Not Given")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 4) then # if number 22
> logitem_str(html_log_file,"No Solution")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 5) then # if number 23
> logitem_str(html_log_file,"Some Pole")
> ;
> logitem_str(html_log_file,"????")
> ;
> elif
> (glob_type_given_pole = 3) then # if number 24
> logitem_str(html_log_file,"No Pole")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 1) then # if number 25
> logitem_str(html_log_file,"Real Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> elif
> (glob_type_given_pole = 2) then # if number 26
> logitem_str(html_log_file,"Complex Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> fi;# end if 26;
> if (glob_least_ratio_sing < glob_large_float) then # if number 26
> logitem_float(html_log_file,glob_least_ratio_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 26;
> if (glob_least_3_sing < glob_large_float) then # if number 26
> logitem_float(html_log_file,glob_least_3_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 26;
> if (glob_least_6_sing < glob_large_float) then # if number 26
> logitem_float(html_log_file,glob_least_6_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 26;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_time(html_log_file,(glob_clock_sec))
> ;
> if (glob_percent_done < 100.0) then # if number 26
> logitem_time(html_log_file,(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 26;
> log_revs(html_log_file," 269 | ")
> ;
> logitem_str(html_log_file,"chang3_1 diffeq.mxt")
> ;
> logitem_str(html_log_file,"chang3_1 maple results")
> ;
> logitem_str(html_log_file,"from chapter 3")
> ;
> logend(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logitem_str(html_log_file,"diff ( y , t , 2 ) = m1 * 0.58 * y * expt ( ( x * x + y * y ) , ( m1 * 1.5 ) ) ; ")
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> ;
> logditto(html_log_file)
> ;
> if (array_est_digits[2] <> -16) then # if number 26
> logitem_integer(html_log_file,array_est_digits[2])
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 26;
> if (array_good_digits[2] <> -16) then # if number 26
> logitem_integer(html_log_file,array_good_digits[2])
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 26;
> logditto(html_log_file)
> ;
> if (glob_type_given_pole = 0) then # if number 26
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> elif
> (glob_type_given_pole = 4) then # if number 27
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> elif
> (glob_type_given_pole = 5) then # if number 28
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> elif
> (glob_type_given_pole = 3) then # if number 29
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> elif
> (glob_type_given_pole = 1) then # if number 30
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> elif
> (glob_type_given_pole = 2) then # if number 31
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> fi;# end if 31;
> if (glob_least_ratio_sing < glob_large_float) then # if number 31
> logditto(html_log_file)
> ;
> else
> logditto(html_log_file)
> ;
> fi;# end if 31;
> if (glob_least_3_sing < glob_large_float) then # if number 31
> logditto(html_log_file)
> ;
> else
> logditto(html_log_file)
> ;
> fi;# end if 31;
> if (glob_least_6_sing < glob_large_float) then # if number 31
> logditto(html_log_file)
> ;
> else
> logditto(html_log_file)
> ;
> fi;# end if 31;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> if (glob_percent_done < 100.0) then # if number 31
> logditto(html_log_file)
> ;
> 0;
> else
> logditto(html_log_file)
> ;
> 0;
> fi;# end if 31;
> logditto(html_log_file);
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 30;
> if (glob_html_log) then # if number 30
> fclose(html_log_file);
> fi;# end if 30
> ;
> ;;
> fi;# end if 29
> #END OUTFILEMAIN
> end;
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max,
term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order,
sub_iter, calc_term, iii, temp_sum, current_iter, t_start, t_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 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, ALWAYS, INFO, DEBUGL, DEBUGMASSIVE,
MAX_UNCHANGED, glob_prec, glob_est_digits, glob_check_sign,
glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_subiter_method,
glob_total_exp_sec, glob_optimal_expect_sec, glob_estimated_size_answer,
glob_html_log, glob_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_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_not_yet_finished,
glob_initial_pass, glob_not_yet_start_msg, glob_reached_optimal_h,
glob_optimal_done, 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_max_h, glob_min_h, glob_type_given_pole,
glob_large_float, glob_larger_float, glob_least_given_sing,
glob_least_ratio_sing, glob_least_3_sing, glob_least_6_sing,
glob_last_good_h, glob_look_poles, glob_display_interval, glob_next_display,
glob_dump_closed_form, glob_abserr, glob_relerr, glob_min_pole_est,
glob_max_hours, glob_max_iter, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_no_eqs, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_small_float,
glob_smallish_float, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_max_sec, glob_orig_start_sec, glob_start, glob_iter, glob_normmax,
glob_max_minutes, array_const_2, array_const_0D0, array_const_0D58,
array_const_1D5, array_x_init, 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_good_digits, array_x,
array_t, array_y, array_tmp0, array_tmp1, array_tmp2, array_tmp3,
array_tmp4, array_tmp5, array_tmp6, array_tmp7_c1, array_tmp7_a1,
array_tmp7_a2, array_tmp7, array_tmp8, array_tmp9, array_tmp10, array_tmp11,
array_tmp12, array_tmp13, array_tmp14, array_tmp15, array_tmp16,
array_tmp17_c1, array_tmp17_a1, array_tmp17_a2, array_tmp17, array_tmp18,
array_m1, array_x_higher, array_x_higher_work, array_x_higher_work2,
array_x_set_initial, 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, MAX_TERMS, glob_last;
MAX_TERMS := 30;
max_terms := 30;
Digits := 16;
glob_html_log := true;
array_x_init := Array(0 .. MAX_TERMS, []);
array_y_init := Array(0 .. MAX_TERMS, []);
array_norms := Array(0 .. MAX_TERMS, []);
array_fact_1 := Array(0 .. MAX_TERMS, []);
array_1st_rel_error := Array(0 .. 3, []);
array_last_rel_error := Array(0 .. 3, []);
array_est_rel_error := Array(0 .. 3, []);
array_max_est_error := Array(0 .. 3, []);
array_type_pole := Array(0 .. 3, []);
array_type_real_pole := Array(0 .. 3, []);
array_type_complex_pole := Array(0 .. 3, []);
array_est_digits := Array(0 .. 3, []);
array_good_digits := Array(0 .. 3, []);
array_x := Array(0 .. MAX_TERMS, []);
array_t := Array(0 .. MAX_TERMS, []);
array_y := Array(0 .. MAX_TERMS, []);
array_tmp0 := Array(0 .. MAX_TERMS, []);
array_tmp1 := Array(0 .. MAX_TERMS, []);
array_tmp2 := Array(0 .. MAX_TERMS, []);
array_tmp3 := Array(0 .. MAX_TERMS, []);
array_tmp4 := Array(0 .. MAX_TERMS, []);
array_tmp5 := Array(0 .. MAX_TERMS, []);
array_tmp6 := Array(0 .. MAX_TERMS, []);
array_tmp7_c1 := Array(0 .. MAX_TERMS, []);
array_tmp7_a1 := Array(0 .. MAX_TERMS, []);
array_tmp7_a2 := Array(0 .. MAX_TERMS, []);
array_tmp7 := Array(0 .. MAX_TERMS, []);
array_tmp8 := Array(0 .. MAX_TERMS, []);
array_tmp9 := Array(0 .. MAX_TERMS, []);
array_tmp10 := Array(0 .. MAX_TERMS, []);
array_tmp11 := Array(0 .. MAX_TERMS, []);
array_tmp12 := Array(0 .. MAX_TERMS, []);
array_tmp13 := Array(0 .. MAX_TERMS, []);
array_tmp14 := Array(0 .. MAX_TERMS, []);
array_tmp15 := Array(0 .. MAX_TERMS, []);
array_tmp16 := Array(0 .. MAX_TERMS, []);
array_tmp17_c1 := Array(0 .. MAX_TERMS, []);
array_tmp17_a1 := Array(0 .. MAX_TERMS, []);
array_tmp17_a2 := Array(0 .. MAX_TERMS, []);
array_tmp17 := Array(0 .. MAX_TERMS, []);
array_tmp18 := Array(0 .. MAX_TERMS, []);
array_m1 := Array(0 .. MAX_TERMS, []);
array_x_higher := Array(0 .. 3, 0 .. MAX_TERMS + 1, []);
array_x_higher_work := Array(0 .. 3, 0 .. MAX_TERMS + 1, []);
array_x_higher_work2 := Array(0 .. 3, 0 .. MAX_TERMS + 1, []);
array_x_set_initial := Array(0 .. 3, 0 .. MAX_TERMS + 1, []);
array_y_higher := Array(0 .. 3, 0 .. MAX_TERMS + 1, []);
array_y_higher_work := Array(0 .. 3, 0 .. MAX_TERMS + 1, []);
array_y_higher_work2 := Array(0 .. 3, 0 .. MAX_TERMS + 1, []);
array_y_set_initial := Array(0 .. 3, 0 .. MAX_TERMS + 1, []);
array_given_rad_poles := Array(0 .. 3, 0 .. 4, []);
array_given_ord_poles := Array(0 .. 3, 0 .. 4, []);
array_rad_test_poles := Array(0 .. 3, 0 .. 5, []);
array_ord_test_poles := Array(0 .. 3, 0 .. 5, []);
array_fact_2 := Array(0 .. MAX_TERMS, 0 .. MAX_TERMS + 1, []);
term := 1;
while term <= MAX_TERMS do array_x_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= MAX_TERMS do array_y_init[term] := 0.; term := term + 1
end do;
term := 1;
while term <= MAX_TERMS do array_norms[term] := 0.; term := term + 1
end do;
term := 1;
while term <= MAX_TERMS do array_fact_1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 3 do array_1st_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 3 do array_last_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 3 do array_est_rel_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 3 do array_max_est_error[term] := 0.; term := term + 1
end do;
term := 1;
while term <= 3 do array_type_pole[term] := 0; term := term + 1 end do;
term := 1;
while term <= 3 do array_type_real_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 3 do array_type_complex_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 3 do array_est_digits[term] := 0; term := term + 1 end do
;
term := 1;
while term <= 3 do array_good_digits[term] := 0; term := term + 1
end do;
term := 1;
while term <= MAX_TERMS do array_x[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= MAX_TERMS do array_t[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= MAX_TERMS do array_y[term] := 0.; term := term + 1 end do
;
term := 1;
while term <= MAX_TERMS do array_tmp0[term] := 0.; term := term + 1
end do;
term := 1;
while term <= MAX_TERMS do array_tmp1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= MAX_TERMS do array_tmp2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= MAX_TERMS do array_tmp3[term] := 0.; term := term + 1
end do;
term := 1;
while term <= MAX_TERMS do array_tmp4[term] := 0.; term := term + 1
end do;
term := 1;
while term <= MAX_TERMS do array_tmp5[term] := 0.; term := term + 1
end do;
term := 1;
while term <= MAX_TERMS do array_tmp6[term] := 0.; term := term + 1
end do;
term := 1;
while term <= MAX_TERMS do array_tmp7_c1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= MAX_TERMS do array_tmp7_a1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= MAX_TERMS do array_tmp7_a2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= MAX_TERMS do array_tmp7[term] := 0.; term := term + 1
end do;
term := 1;
while term <= MAX_TERMS do array_tmp8[term] := 0.; term := term + 1
end do;
term := 1;
while term <= MAX_TERMS do array_tmp9[term] := 0.; term := term + 1
end do;
term := 1;
while term <= MAX_TERMS do array_tmp10[term] := 0.; term := term + 1
end do;
term := 1;
while term <= MAX_TERMS do array_tmp11[term] := 0.; term := term + 1
end do;
term := 1;
while term <= MAX_TERMS do array_tmp12[term] := 0.; term := term + 1
end do;
term := 1;
while term <= MAX_TERMS do array_tmp13[term] := 0.; term := term + 1
end do;
term := 1;
while term <= MAX_TERMS do array_tmp14[term] := 0.; term := term + 1
end do;
term := 1;
while term <= MAX_TERMS do array_tmp15[term] := 0.; term := term + 1
end do;
term := 1;
while term <= MAX_TERMS do array_tmp16[term] := 0.; term := term + 1
end do;
term := 1;
while term <= MAX_TERMS do array_tmp17_c1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= MAX_TERMS do array_tmp17_a1[term] := 0.; term := term + 1
end do;
term := 1;
while term <= MAX_TERMS do array_tmp17_a2[term] := 0.; term := term + 1
end do;
term := 1;
while term <= MAX_TERMS do array_tmp17[term] := 0.; term := term + 1
end do;
term := 1;
while term <= MAX_TERMS do array_tmp18[term] := 0.; term := term + 1
end do;
term := 1;
while term <= MAX_TERMS do array_m1[term] := 0.; term := term + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= MAX_TERMS do
array_x_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= MAX_TERMS do
array_x_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= MAX_TERMS do
array_x_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= MAX_TERMS do
array_x_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= MAX_TERMS do
array_y_higher[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= MAX_TERMS do
array_y_higher_work[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= MAX_TERMS do
array_y_higher_work2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= MAX_TERMS do
array_y_set_initial[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 3 do
array_given_rad_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 3 do
array_given_ord_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 4 do
array_rad_test_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 4 do
array_ord_test_poles[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= MAX_TERMS do
term := 1;
while term <= MAX_TERMS do
array_fact_2[ord, term] := 0.; term := term + 1
end do;
ord := ord + 1
end do;
zero_ats_ar(array_x);
zero_ats_ar(array_t);
zero_ats_ar(array_m1);
zero_ats_ar(array_y);
zero_ats_ar(array_tmp0);
zero_ats_ar(array_tmp1);
zero_ats_ar(array_tmp2);
zero_ats_ar(array_tmp3);
zero_ats_ar(array_tmp4);
zero_ats_ar(array_tmp5);
zero_ats_ar(array_tmp6);
zero_ats_ar(array_tmp7_c1);
zero_ats_ar(array_tmp7_a1);
zero_ats_ar(array_tmp7_a2);
zero_ats_ar(array_tmp7);
zero_ats_ar(array_tmp8);
zero_ats_ar(array_tmp9);
zero_ats_ar(array_tmp10);
zero_ats_ar(array_tmp11);
zero_ats_ar(array_tmp12);
zero_ats_ar(array_tmp13);
zero_ats_ar(array_tmp14);
zero_ats_ar(array_tmp15);
zero_ats_ar(array_tmp16);
zero_ats_ar(array_tmp17_c1);
zero_ats_ar(array_tmp17_a1);
zero_ats_ar(array_tmp17_a2);
zero_ats_ar(array_tmp17);
zero_ats_ar(array_tmp18);
zero_ats_ar(array_const_2);
array_const_2[1] := 2;
zero_ats_ar(array_const_0D0);
array_const_0D0[1] := 0.;
zero_ats_ar(array_const_0D58);
array_const_0D58[1] := 0.58;
zero_ats_ar(array_const_1D5);
array_const_1D5[1] := 1.5;
zero_ats_ar(array_m1);
array_m1[1] := -1.0;
iiif := 0;
while iiif <= MAX_TERMS do
jjjf := 0;
while jjjf <= MAX_TERMS do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
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(10.0);
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
MAX_UNCHANGED := 10;
glob_prec := 0.10*10^(-15);
glob_est_digits := 1;
glob_check_sign := 1.0;
glob_desired_digits_correct := 8.0;
glob_max_estimated_step_error := 0.;
glob_ratio_of_radius := 0.1;
glob_percent_done := 0.;
glob_subiter_method := 3;
glob_total_exp_sec := 0.1;
glob_optimal_expect_sec := 0.1;
glob_estimated_size_answer := 100.0;
glob_html_log := true;
glob_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 := 60.0;
glob_hours_in_day := 24.0;
glob_days_in_year := 365;
glob_sec_in_hour := 3600;
glob_sec_in_day := 86400;
glob_sec_in_year := 31536000;
glob_almost_1 := 0.9990;
glob_clock_sec := 0.;
glob_clock_start_sec := 0.;
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_disp_incr := 0.1;
glob_h := 0.1;
glob_diff_rc_fm := 0.1;
glob_diff_rc_fmm1 := 0.1;
glob_diff_rc_fmm2 := 0.1;
glob_diff_ord_fm := 0.1;
glob_diff_ord_fmm1 := 0.1;
glob_diff_ord_fmm2 := 0.1;
glob_six_term_ord_save := 0.1;
glob_guess_error_rc := 0.1;
glob_guess_error_ord := 0.1;
glob_max_h := 0.1;
glob_min_h := 0.1*10^(-5);
glob_type_given_pole := 0;
glob_large_float := 0.10*10^101;
glob_larger_float := 0.11*10^101;
glob_least_given_sing := 0.99*10^101;
glob_least_ratio_sing := 0.99*10^101;
glob_least_3_sing := 0.99*10^101;
glob_least_6_sing := 0.99*10^101;
glob_last_good_h := 0.1;
glob_look_poles := false;
glob_display_interval := 0.1;
glob_next_display := 0.;
glob_dump_closed_form := false;
glob_abserr := 0.1*10^(-10);
glob_relerr := 0.1*10^(-10);
glob_min_pole_est := 0.1*10^10;
glob_max_hours := 0.;
glob_max_iter := 1000;
glob_max_rel_trunc_err := 0.1*10^(-10);
glob_max_trunc_err := 0.1*10^(-10);
glob_no_eqs := 0;
glob_optimal_clock_start_sec := 0.;
glob_optimal_start := 0.;
glob_upper_ratio_limit := 1.0001;
glob_lower_ratio_limit := 0.9999;
glob_small_float := 0.;
glob_smallish_float := 0.;
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_max_sec := 10000.0;
glob_orig_start_sec := 0.;
glob_start := 0;
glob_iter := 0;
glob_normmax := 0.;
glob_max_minutes := 0.;
array_x_set_initial[1, 1] := true;
array_x_set_initial[1, 2] := true;
array_x_set_initial[1, 3] := false;
array_x_set_initial[1, 4] := false;
array_x_set_initial[1, 5] := false;
array_x_set_initial[1, 6] := false;
array_x_set_initial[1, 7] := false;
array_x_set_initial[1, 8] := false;
array_x_set_initial[1, 9] := false;
array_x_set_initial[1, 10] := false;
array_x_set_initial[1, 11] := false;
array_x_set_initial[1, 12] := false;
array_x_set_initial[1, 13] := false;
array_x_set_initial[1, 14] := false;
array_x_set_initial[1, 15] := false;
array_x_set_initial[1, 16] := false;
array_x_set_initial[1, 17] := false;
array_x_set_initial[1, 18] := false;
array_x_set_initial[1, 19] := false;
array_x_set_initial[1, 20] := false;
array_x_set_initial[1, 21] := false;
array_x_set_initial[1, 22] := false;
array_x_set_initial[1, 23] := false;
array_x_set_initial[1, 24] := false;
array_x_set_initial[1, 25] := false;
array_x_set_initial[1, 26] := false;
array_x_set_initial[1, 27] := false;
array_x_set_initial[1, 28] := false;
array_x_set_initial[1, 29] := false;
array_x_set_initial[1, 30] := false;
array_y_set_initial[2, 1] := true;
array_y_set_initial[2, 2] := true;
array_y_set_initial[2, 3] := false;
array_y_set_initial[2, 4] := false;
array_y_set_initial[2, 5] := false;
array_y_set_initial[2, 6] := false;
array_y_set_initial[2, 7] := false;
array_y_set_initial[2, 8] := false;
array_y_set_initial[2, 9] := false;
array_y_set_initial[2, 10] := false;
array_y_set_initial[2, 11] := false;
array_y_set_initial[2, 12] := false;
array_y_set_initial[2, 13] := false;
array_y_set_initial[2, 14] := false;
array_y_set_initial[2, 15] := false;
array_y_set_initial[2, 16] := false;
array_y_set_initial[2, 17] := false;
array_y_set_initial[2, 18] := false;
array_y_set_initial[2, 19] := false;
array_y_set_initial[2, 20] := false;
array_y_set_initial[2, 21] := false;
array_y_set_initial[2, 22] := false;
array_y_set_initial[2, 23] := false;
array_y_set_initial[2, 24] := false;
array_y_set_initial[2, 25] := false;
array_y_set_initial[2, 26] := false;
array_y_set_initial[2, 27] := false;
array_y_set_initial[2, 28] := false;
array_y_set_initial[2, 29] := false;
array_y_set_initial[2, 30] := false;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
MAX_TERMS := 30;
glob_iolevel := INFO;
glob_orig_start_sec := elapsed_time_seconds();
glob_display_flag := true;
glob_no_eqs := 2;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 50000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/chang3_1postode.ode#################");
omniout_str(ALWAYS, "diff ( x , t , 2 ) = m1 * 0.58 * x * expt (\
( x * x + y * y ) , ( m1 * 1.5 ) ) ; ");
omniout_str(ALWAYS, "diff ( y , t , 2 ) = m1 * 0.58 * y * expt (\
( x * x + y * y ) , ( m1 * 1.5 ) ) ; ");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "max_terms:=30;");
omniout_str(ALWAYS, "Digits:=16;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "t_start := 1.00;");
omniout_str(ALWAYS, "t_end := 12.0;");
omniout_str(ALWAYS, "array_x_init[0 + 1] := -1.000;");
omniout_str(ALWAYS, "array_x_init[1 + 1] := 0.000;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := 0.000;");
omniout_str(ALWAYS, "array_y_init[1 + 1] := 4.300;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_type_given_pole := 0;");
omniout_str(ALWAYS, "glob_min_h := 0.1;");
omniout_str(ALWAYS, "glob_max_h := 0.1;");
omniout_str(ALWAYS, "glob_display_interval := 0.1;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=16;");
omniout_str(ALWAYS, "glob_max_minutes:=30.0;");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "glob_max_iter:=100000000;");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "exact_soln_x := proc(t)");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "return(0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y := proc(t)");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "return(0);");
omniout_str(ALWAYS, "");
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 := 0.;
glob_smallish_float := 0.;
glob_large_float := 0.10*10^101;
glob_larger_float := 0.11*10^101;
glob_almost_1 := 0.99;
t_start := 1.00;
t_end := 12.0;
array_x_init[1] := -1.000;
array_x_init[2] := 0.;
array_y_init[1] := 0.;
array_y_init[2] := 4.300;
glob_look_poles := true;
glob_type_given_pole := 0;
glob_min_h := 0.1;
glob_max_h := 0.1;
glob_display_interval := 0.1;
glob_desired_digits_correct := 16;
glob_max_minutes := 30.0;
glob_subiter_method := 3;
glob_max_iter := 100000000;
glob_last_good_h := glob_h;
glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours;
omniout_str(ALWAYS, "START of Optimize");
glob_check_sign := my_check_sign(t_start, t_end);
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 :=
float_abs(glob_display_interval)*glob_check_sign;
display_max := (t_end - t_start)/10.0;
if display_max < glob_display_interval then
glob_display_interval := display_max
end if;
chk_data();
min_value := glob_larger_float;
est_answer := est_size_answer();
opt_iter := 1;
glob_prec = expt(10.0, -Digits);
est_needed_step_err :=
estimated_needed_step_error(t_start, t_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_t[1] := t_start;
array_t[2] := glob_h;
glob_next_display := t_start;
order_diff := 2;
term_no := 1;
while term_no <= order_diff do
array_x[term_no] := array_x_init[term_no]*
expt(glob_h, term_no - 1)/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 < MAX_TERMS then
array_x_higher[r_order, term_no] := array_x_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1)
end if;
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
order_diff := 2;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, term_no - 1)/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 < MAX_TERMS then
array_y_higher[r_order, term_no] := array_y_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1)
end if;
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
if glob_subiter_method = 1 then atomall()
elif glob_subiter_method = 2 then
subiter := 1;
while subiter <= 4 do atomall(); subiter := subiter + 1 end do
else
subiter := 1;
while subiter <= 4 + MAX_TERMS do
atomall(); subiter := subiter + 1
end do
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;
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();
if 2 < opt_iter and not found_h and (
glob_min_pole_est < 0.999*last_min_pole_est or
1.111*last_min_pole_est < glob_min_pole_est) then
omniout_str(ALWAYS, "SETTING H FOR POLE ACCURACY");
glob_h_reason := 4;
found_h := true;
glob_h := glob_h/2.0;
last_min_pole_est := glob_min_pole_est
else last_min_pole_est := glob_min_pole_est
end if
end if;
if not found_h then
est_answer := est_size_answer();
est_needed_step_err := estimated_needed_step_error(t_start,
t_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*2.0
else
omniout_str(ALWAYS, "Found H for OPTIMAL");
found_h := true;
glob_h_reason := 3;
glob_h := glob_h/2.0
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_html_log then html_log_file := fopen("entry.html", WRITE, TEXT)
end if;
if found_h then
omniout_str(ALWAYS, "START of Soultion");
array_t[1] := t_start;
array_t[2] := glob_h;
glob_next_display := t_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 := 2;
term_no := 1;
while term_no <= order_diff do
array_x[term_no] := array_x_init[term_no]*
expt(glob_h, term_no - 1)/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 < MAX_TERMS then
array_x_higher[r_order, term_no] := array_x_init[it]*
expt(glob_h, term_no - 1)/factorial_1(term_no - 1)
end if;
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
order_diff := 2;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, term_no - 1)/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 < MAX_TERMS then
array_y_higher[r_order, term_no] := array_y_init[it]*
expt(glob_h, term_no - 1)/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_t[1] < glob_check_sign*t_end and
glob_clock_sec - glob_orig_start_sec < glob_max_sec do
if reached_interval() then
omniout_str(INFO, " ");
omniout_str(INFO, "TOP MAIN SOLVE Loop")
end if;
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
track_estimated_error();
if glob_subiter_method = 1 then atomall()
elif glob_subiter_method = 2 then
subiter := 1;
while subiter <= 4 do atomall(); subiter := subiter + 1
end do
else
subiter := 1;
while subiter <= 4 + MAX_TERMS do
atomall(); subiter := subiter + 1
end do
end if;
track_estimated_error();
display_alot(current_iter);
check_for_pole();
if reached_interval() then glob_next_display :=
glob_next_display + glob_display_interval
end if;
array_t[1] := array_t[1] + glob_h;
array_t[2] := glob_h;
order_diff := 3;
ord := 3;
calc_term := 1;
iii := MAX_TERMS;
while calc_term <= iii do
array_x_higher_work[3, iii] := array_x_higher[3, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 3;
calc_term := 1;
iii := MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_x_higher_work[ord, iii];
iii := iii - 1
end do;
array_x_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
ord := 2;
calc_term := 2;
iii := MAX_TERMS;
while calc_term <= iii do
array_x_higher_work[2, iii] := array_x_higher[2, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 2;
iii := MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_x_higher_work[ord, iii];
iii := iii - 1
end do;
array_x_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
ord := 2;
calc_term := 1;
iii := MAX_TERMS;
while calc_term <= iii do
array_x_higher_work[2, iii] := array_x_higher[2, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_x_higher_work[ord, iii];
iii := iii - 1
end do;
array_x_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
ord := 1;
calc_term := 3;
iii := MAX_TERMS;
while calc_term <= iii do
array_x_higher_work[1, iii] := array_x_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 3;
iii := MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_x_higher_work[ord, iii];
iii := iii - 1
end do;
array_x_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
ord := 1;
calc_term := 2;
iii := MAX_TERMS;
while calc_term <= iii do
array_x_higher_work[1, iii] := array_x_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_x_higher_work[ord, iii];
iii := iii - 1
end do;
array_x_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
ord := 1;
calc_term := 1;
iii := MAX_TERMS;
while calc_term <= iii do
array_x_higher_work[1, iii] := array_x_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_x_higher_work[ord, iii];
iii := iii - 1
end do;
array_x_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, calc_term - 1)/factorial_1(calc_term - 1);
term_no := MAX_TERMS;
while 1 <= term_no do
array_x[term_no] := array_x_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_x_higher[ord, term_no] :=
array_x_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
order_diff := 3;
ord := 3;
calc_term := 1;
iii := MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[3, iii] := array_y_higher[3, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 3;
calc_term := 1;
iii := 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, calc_term - 1)/factorial_1(calc_term - 1);
ord := 2;
calc_term := 2;
iii := MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 2;
iii := 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, calc_term - 1)/factorial_1(calc_term - 1);
ord := 2;
calc_term := 1;
iii := MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 2;
calc_term := 1;
iii := 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, calc_term - 1)/factorial_1(calc_term - 1);
ord := 1;
calc_term := 3;
iii := MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 3;
iii := 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, calc_term - 1)/factorial_1(calc_term - 1);
ord := 1;
calc_term := 2;
iii := MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 2;
iii := 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, calc_term - 1)/factorial_1(calc_term - 1);
ord := 1;
calc_term := 1;
iii := MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, calc_term - 1)*
factorial_3(iii - calc_term, iii - 1));
iii := iii - 1
end do;
temp_sum := 0.;
ord := 1;
calc_term := 1;
iii := 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, calc_term - 1)/factorial_1(calc_term - 1);
term_no := 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 ( x , t , 2 ) = m1 * 0.58 * x * expt\
( ( x * x + y * y ) , ( m1 * 1.5 ) ) ; ");
omniout_str(INFO, "diff ( y , t , 2 ) = m1 * 0.58 * y * expt\
( ( x * x + y * y ) , ( m1 * 1.5 ) ) ; ");
omniout_int(INFO, "Iterations ", 32, glob_iter,
4, " ");
prog_report(t_start, t_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2014-09-23T16:46:14-05:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"chang3_1");
logitem_str(html_log_file, "diff ( x , t , 2 ) = m1 * 0.\
58 * x * expt ( ( x * x + y * y ) , ( m1 * 1.5 ) \
) ; ");
logitem_float(html_log_file, t_start);
logitem_float(html_log_file, t_end);
logitem_float(html_log_file, array_t[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 array_good_digits[1] <> -16 then
logitem_integer(html_log_file, array_good_digits[1])
else logitem_str(html_log_file, "Unknown")
end if;
logitem_integer(html_log_file, 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 glob_percent_done < 100.0 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, " 269 | ");
logitem_str(html_log_file, "chang3_1 diffeq.mxt");
logitem_str(html_log_file, "chang3_1 maple results");
logitem_str(html_log_file, "from chapter 3");
logend(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logitem_str(html_log_file, "diff ( y , t , 2 ) = m1 * 0.\
58 * y * expt ( ( x * x + y * y ) , ( m1 * 1.5 ) \
) ; ");
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
if array_est_digits[2] <> -16 then
logitem_integer(html_log_file, array_est_digits[2])
else logitem_str(html_log_file, "Unknown")
end if;
if array_good_digits[2] <> -16 then
logitem_integer(html_log_file, array_good_digits[2])
else logitem_str(html_log_file, "Unknown")
end if;
logditto(html_log_file);
if glob_type_given_pole = 0 then
logditto(html_log_file); logditto(html_log_file)
elif glob_type_given_pole = 4 then
logditto(html_log_file); logditto(html_log_file)
elif glob_type_given_pole = 5 then
logditto(html_log_file); logditto(html_log_file)
elif glob_type_given_pole = 3 then
logditto(html_log_file); logditto(html_log_file)
elif glob_type_given_pole = 1 then
logditto(html_log_file); logditto(html_log_file)
elif glob_type_given_pole = 2 then
logditto(html_log_file); logditto(html_log_file)
end if;
if glob_least_ratio_sing < glob_large_float then
logditto(html_log_file)
else logditto(html_log_file)
end if;
if glob_least_3_sing < glob_large_float then
logditto(html_log_file)
else logditto(html_log_file)
end if;
if glob_least_6_sing < glob_large_float then
logditto(html_log_file)
else logditto(html_log_file)
end if;
logditto(html_log_file);
logditto(html_log_file);
if glob_percent_done < 100.0 then logditto(html_log_file); 0
else logditto(html_log_file); 0
end if;
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end if
end proc
# End Function number 12
> main();
##############ECHO OF PROBLEM#################
##############temp/chang3_1postode.ode#################
diff ( x , t , 2 ) = m1 * 0.58 * x * expt ( ( x * x + y * y ) , ( m1 * 1.5 ) ) ;
diff ( y , t , 2 ) = m1 * 0.58 * y * expt ( ( x * x + y * y ) , ( m1 * 1.5 ) ) ;
!
#BEGIN FIRST INPUT BLOCK
max_terms:=30;
Digits:=16;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
t_start := 1.00;
t_end := 12.0;
array_x_init[0 + 1] := -1.000;
array_x_init[1 + 1] := 0.000;
array_y_init[0 + 1] := 0.000;
array_y_init[1 + 1] := 4.300;
glob_look_poles := true;
glob_type_given_pole := 0;
glob_min_h := 0.1;
glob_max_h := 0.1;
glob_display_interval := 0.1;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=16;
glob_max_minutes:=30.0;
glob_subiter_method:=3;
glob_max_iter:=100000000;
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_x := proc(t)
return(0);
end;
exact_soln_y := proc(t)
return(0);
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Optimize
min_size = 0
min_size = 1
glob_desired_digits_correct = 16
estimated_h = 0.1
estimated_answer = 1
desired_abs_gbl_error = 1.000000000000000e-16
range = 11
estimated_steps = 110
step_error = 3.178208630818640e-19
est_needed_step_err = 3.178208630818640e-19
opt_iter = 1
memory used=4.0MB, alloc=40.3MB, time=0.14
SETTING H FOR MAX H
SETTING H FOR DISPLAY INTERVAL
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
START of Soultion
TOP MAIN SOLVE Loop
memory used=42.3MB, alloc=40.3MB, time=0.66
t[1] = 1
x[1] (closed_form) = 0
x[1] (numeric) = -1
absolute error = 1
relative error = -1 %
Desired digits = 16
Estimated correct digits = 13
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 0
absolute error = 0
relative error = -1 %
Desired digits = 16
Estimated correct digits = -16
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=81.6MB, alloc=40.3MB, time=1.14
memory used=122.0MB, alloc=40.3MB, time=1.56
t[1] = 1.1
x[1] (closed_form) = 0
x[1] (numeric) = -0.997008569718251
absolute error = 0.997008569718251
relative error = -1 %
Desired digits = 16
Estimated correct digits = 12
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 0.4295601621083651
absolute error = 0.4295601621083651
relative error = -1 %
Desired digits = 16
Estimated correct digits = 11
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=162.5MB, alloc=40.3MB, time=1.98
t[1] = 1.2
x[1] (closed_form) = 0
x[1] (numeric) = -0.9880406544699653
absolute error = 0.9880406544699653
relative error = -1 %
Desired digits = 16
Estimated correct digits = 10
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 0.856532038414645
absolute error = 0.856532038414645
relative error = -1 %
Desired digits = 16
Estimated correct digits = 9
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=203.1MB, alloc=40.3MB, time=2.39
t[1] = 1.3
x[1] (closed_form) = 0
x[1] (numeric) = -0.973238633328199
absolute error = 0.973238633328199
relative error = -1 %
Desired digits = 16
Estimated correct digits = 8
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 1.278486022819548
absolute error = 1.278486022819548
relative error = -1 %
Desired digits = 16
Estimated correct digits = 8
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=243.7MB, alloc=40.3MB, time=2.80
memory used=284.2MB, alloc=40.3MB, time=3.20
t[1] = 1.4
x[1] (closed_form) = 0
x[1] (numeric) = -0.9526550002167084
absolute error = 0.9526550002167084
relative error = -1 %
Desired digits = 16
Estimated correct digits = 6
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 1.692833653887876
absolute error = 1.692833653887876
relative error = -1 %
Desired digits = 16
Estimated correct digits = 6
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=325.0MB, alloc=40.3MB, time=3.61
t[1] = 1.5
x[1] (closed_form) = 0
x[1] (numeric) = -0.9253927417856956
absolute error = 0.9253927417856956
relative error = -1 %
Desired digits = 16
Estimated correct digits = 5
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 2.095221577258679
absolute error = 2.095221577258679
relative error = -1 %
Desired digits = 16
Estimated correct digits = 5
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=365.8MB, alloc=40.3MB, time=4.03
memory used=406.3MB, alloc=40.3MB, time=4.42
t[1] = 1.6
x[1] (closed_form) = 0
x[1] (numeric) = -0.8893038464632661
absolute error = 0.8893038464632661
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 2.477470063664513
absolute error = 2.477470063664513
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=447.1MB, alloc=40.3MB, time=4.86
t[1] = 1.7
x[1] (closed_form) = 0
x[1] (numeric) = -0.8416248911257125
absolute error = 0.8416248911257125
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 2.82734797966292
absolute error = 2.82734797966292
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=487.8MB, alloc=40.3MB, time=5.27
memory used=528.5MB, alloc=40.3MB, time=5.66
t[1] = 1.8
x[1] (closed_form) = 0
x[1] (numeric) = -0.7815511696337904
absolute error = 0.7815511696337904
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 3.135713989079374
absolute error = 3.135713989079374
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=569.4MB, alloc=40.3MB, time=6.06
t[1] = 1.9
x[1] (closed_form) = 0
x[1] (numeric) = -0.7116936394254486
absolute error = 0.7116936394254486
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 3.405026786522452
absolute error = 3.405026786522452
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=610.2MB, alloc=40.3MB, time=6.48
memory used=650.9MB, alloc=40.3MB, time=6.89
t[1] = 2
x[1] (closed_form) = 0
x[1] (numeric) = -0.635235550117286
absolute error = 0.635235550117286
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 3.642924066942093
absolute error = 3.642924066942093
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=691.8MB, alloc=40.3MB, time=7.28
t[1] = 2.1
x[1] (closed_form) = 0
x[1] (numeric) = -0.5544057463088815
absolute error = 0.5544057463088815
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 3.855876038868624
absolute error = 3.855876038868624
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=732.7MB, alloc=40.3MB, time=7.69
memory used=773.5MB, alloc=40.3MB, time=8.08
t[1] = 2.2
x[1] (closed_form) = 0
x[1] (numeric) = -0.4706574578276808
absolute error = 0.4706574578276808
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 4.048629871743554
absolute error = 4.048629871743554
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=814.4MB, alloc=40.3MB, time=8.47
t[1] = 2.3
x[1] (closed_form) = 0
x[1] (numeric) = -0.3849564128970775
absolute error = 0.3849564128970775
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 4.224670354421668
absolute error = 4.224670354421668
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=855.3MB, alloc=40.3MB, time=8.88
memory used=896.1MB, alloc=40.3MB, time=9.26
t[1] = 2.4
x[1] (closed_form) = 0
x[1] (numeric) = -0.2979639550079853
absolute error = 0.2979639550079853
relative error = -1 %
Desired digits = 16
Estimated correct digits = 3
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 4.386614737384148
absolute error = 4.386614737384148
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=937.0MB, alloc=40.3MB, time=9.67
t[1] = 2.5
x[1] (closed_form) = 0
x[1] (numeric) = -0.2101457471420201
absolute error = 0.2101457471420201
relative error = -1 %
Desired digits = 16
Estimated correct digits = 3
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 4.536477538310833
absolute error = 4.536477538310833
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=977.9MB, alloc=40.3MB, time=10.08
memory used=1018.8MB, alloc=40.3MB, time=10.45
t[1] = 2.6
x[1] (closed_form) = 0
x[1] (numeric) = -0.1218374832814874
absolute error = 0.1218374832814874
relative error = -1 %
Desired digits = 16
Estimated correct digits = 3
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 4.675844233571894
absolute error = 4.675844233571894
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=1059.8MB, alloc=40.3MB, time=10.86
t[1] = 2.7
x[1] (closed_form) = 0
x[1] (numeric) = -0.03328591815573923
absolute error = 0.03328591815573923
relative error = -1 %
Desired digits = 16
Estimated correct digits = 3
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 4.805987099374592
absolute error = 4.805987099374592
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=1100.8MB, alloc=40.3MB, time=11.25
memory used=1141.8MB, alloc=40.3MB, time=11.64
t[1] = 2.8
x[1] (closed_form) = 0
x[1] (numeric) = 0.05532466442566612
absolute error = 0.05532466442566612
relative error = -1 %
Desired digits = 16
Estimated correct digits = 3
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 4.927944400221841
absolute error = 4.927944400221841
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=1182.8MB, alloc=40.3MB, time=12.05
t[1] = 2.9
x[1] (closed_form) = 0
x[1] (numeric) = 0.1438548612745791
absolute error = 0.1438548612745791
relative error = -1 %
Desired digits = 16
Estimated correct digits = 3
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 5.042575894211264
absolute error = 5.042575894211264
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=1223.8MB, alloc=40.3MB, time=12.42
memory used=1264.7MB, alloc=40.3MB, time=12.81
t[1] = 3
x[1] (closed_form) = 0
x[1] (numeric) = 0.2321981471704578
absolute error = 0.2321981471704578
relative error = -1 %
Desired digits = 16
Estimated correct digits = 3
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 5.150602655445166
absolute error = 5.150602655445166
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=1305.7MB, alloc=40.3MB, time=13.22
t[1] = 3.1
x[1] (closed_form) = 0
x[1] (numeric) = 0.3202724923659961
absolute error = 0.3202724923659961
relative error = -1 %
Desired digits = 16
Estimated correct digits = 3
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 5.25263625381302
absolute error = 5.25263625381302
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=1346.7MB, alloc=40.3MB, time=13.61
memory used=1387.6MB, alloc=40.3MB, time=14.00
t[1] = 3.2
x[1] (closed_form) = 0
x[1] (numeric) = 0.4080143872547018
absolute error = 0.4080143872547018
relative error = -1 %
Desired digits = 16
Estimated correct digits = 3
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 5.349200544973688
absolute error = 5.349200544973688
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=1428.6MB, alloc=40.3MB, time=14.39
t[1] = 3.3
x[1] (closed_form) = 0
x[1] (numeric) = 0.4953745051493808
absolute error = 0.4953745051493808
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 5.440748220327046
absolute error = 5.440748220327046
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=1469.6MB, alloc=40.3MB, time=14.78
memory used=1510.4MB, alloc=40.3MB, time=15.17
t[1] = 3.4
x[1] (closed_form) = 0
x[1] (numeric) = 0.5823145031086536
absolute error = 0.5823145031086536
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 5.527673569902632
absolute error = 5.527673569902632
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=1551.5MB, alloc=40.3MB, time=15.56
t[1] = 3.5
x[1] (closed_form) = 0
x[1] (numeric) = 0.6688046281685971
absolute error = 0.6688046281685971
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 5.61032246059546
absolute error = 5.61032246059546
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=1592.5MB, alloc=40.3MB, time=15.95
memory used=1633.5MB, alloc=40.3MB, time=16.34
t[1] = 3.6
x[1] (closed_form) = 0
x[1] (numeric) = 0.7548219031187755
absolute error = 0.7548219031187755
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 5.689000234558259
absolute error = 5.689000234558259
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=1674.6MB, alloc=40.3MB, time=16.73
t[1] = 3.7
x[1] (closed_form) = 0
x[1] (numeric) = 0.8403487355971408
absolute error = 0.8403487355971408
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 5.763978031933269
absolute error = 5.763978031933269
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=1715.6MB, alloc=40.3MB, time=17.13
memory used=1756.5MB, alloc=40.3MB, time=17.50
t[1] = 3.8
x[1] (closed_form) = 0
x[1] (numeric) = 0.9253718406139812
absolute error = 0.9253718406139812
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 5.835497904326861
absolute error = 5.835497904326861
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=1797.6MB, alloc=40.3MB, time=17.91
memory used=1838.5MB, alloc=40.3MB, time=18.28
t[1] = 3.9
x[1] (closed_form) = 0
x[1] (numeric) = 1.009881398018334
absolute error = 1.009881398018334
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 5.903776989177088
absolute error = 5.903776989177088
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=1879.5MB, alloc=40.3MB, time=18.67
t[1] = 4
x[1] (closed_form) = 0
x[1] (numeric) = 1.093870388062907
absolute error = 1.093870388062907
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 5.969010946854539
absolute error = 5.969010946854539
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=1920.6MB, alloc=40.3MB, time=19.06
memory used=1961.5MB, alloc=40.3MB, time=19.45
t[1] = 4.1
x[1] (closed_form) = 0
x[1] (numeric) = 1.177334063369868
absolute error = 1.177334063369868
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 6.031376813149824
absolute error = 6.031376813149824
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=2002.6MB, alloc=40.3MB, time=19.84
t[1] = 4.2
x[1] (closed_form) = 0
x[1] (numeric) = 1.260269526350164
absolute error = 1.260269526350164
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 6.091035383906019
absolute error = 6.091035383906019
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=2043.7MB, alloc=40.3MB, time=20.23
memory used=2084.6MB, alloc=40.3MB, time=20.61
t[1] = 4.3
x[1] (closed_form) = 0
x[1] (numeric) = 1.342675388858806
absolute error = 1.342675388858806
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 6.148133222033109
absolute error = 6.148133222033109
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=2125.7MB, alloc=40.3MB, time=21.00
t[1] = 4.4
x[1] (closed_form) = 0
x[1] (numeric) = 1.424551496493388
absolute error = 1.424551496493388
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 6.202804357319811
absolute error = 6.202804357319811
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=2166.8MB, alloc=40.3MB, time=21.39
memory used=2207.7MB, alloc=40.3MB, time=21.78
t[1] = 4.5
x[1] (closed_form) = 0
x[1] (numeric) = 1.50589870408192
absolute error = 1.50589870408192
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 6.255171734484876
absolute error = 6.255171734484876
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=2248.8MB, alloc=40.3MB, time=22.17
t[1] = 4.6
x[1] (closed_form) = 0
x[1] (numeric) = 1.586718691982815
absolute error = 1.586718691982815
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 6.305348453486371
absolute error = 6.305348453486371
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=2289.9MB, alloc=40.3MB, time=22.55
memory used=2330.9MB, alloc=40.3MB, time=22.94
t[1] = 4.7
x[1] (closed_form) = 0
x[1] (numeric) = 1.667013815129221
absolute error = 1.667013815129221
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 6.353438837310861
absolute error = 6.353438837310861
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=2372.0MB, alloc=40.3MB, time=23.33
t[1] = 4.8
x[1] (closed_form) = 0
x[1] (numeric) = 1.746786978498665
absolute error = 1.746786978498665
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 6.399539355631865
absolute error = 6.399539355631865
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=2413.1MB, alloc=40.3MB, time=23.72
memory used=2454.0MB, alloc=40.3MB, time=24.11
t[1] = 4.9
x[1] (closed_form) = 0
x[1] (numeric) = 1.826041534024416
absolute error = 1.826041534024416
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 6.443739427376632
absolute error = 6.443739427376632
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=2495.2MB, alloc=40.3MB, time=24.48
memory used=2536.1MB, alloc=40.3MB, time=24.87
t[1] = 5
x[1] (closed_form) = 0
x[1] (numeric) = 1.904781194992713
absolute error = 1.904781194992713
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 6.486122121018702
absolute error = 6.486122121018702
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=2577.3MB, alloc=40.3MB, time=25.27
t[1] = 5.1
x[1] (closed_form) = 0
x[1] (numeric) = 1.983009964766759
absolute error = 1.983009964766759
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 6.526764768058709
absolute error = 6.526764768058709
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=2618.3MB, alloc=40.3MB, time=25.66
memory used=2659.3MB, alloc=40.3MB, time=26.05
t[1] = 5.2
x[1] (closed_form) = 0
x[1] (numeric) = 2.060732077300328
absolute error = 2.060732077300328
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 6.565739502471596
absolute error = 6.565739502471596
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=2700.4MB, alloc=40.3MB, time=26.42
t[1] = 5.3
x[1] (closed_form) = 0
x[1] (numeric) = 2.137951947392468
absolute error = 2.137951947392468
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 6.603113736737003
absolute error = 6.603113736737003
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=2741.6MB, alloc=40.3MB, time=26.81
memory used=2782.6MB, alloc=40.3MB, time=27.20
t[1] = 5.4
x[1] (closed_form) = 0
x[1] (numeric) = 2.214674129021013
absolute error = 2.214674129021013
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 6.63895058331873
absolute error = 6.63895058331873
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=2823.8MB, alloc=40.3MB, time=27.59
t[1] = 5.5
x[1] (closed_form) = 0
x[1] (numeric) = 2.290903280399685
absolute error = 2.290903280399685
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 6.673309229032762
absolute error = 6.673309229032762
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=2865.0MB, alloc=40.3MB, time=27.97
memory used=2906.1MB, alloc=40.3MB, time=28.36
t[1] = 5.6
x[1] (closed_form) = 0
x[1] (numeric) = 2.366644134649004
absolute error = 2.366644134649004
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 6.706245268574996
absolute error = 6.706245268574996
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=2947.3MB, alloc=40.3MB, time=28.73
memory used=2988.4MB, alloc=40.3MB, time=29.13
t[1] = 5.7
x[1] (closed_form) = 0
x[1] (numeric) = 2.441901475168425
absolute error = 2.441901475168425
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 6.737811002517889
absolute error = 6.737811002517889
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=3029.5MB, alloc=40.3MB, time=29.52
t[1] = 5.8
x[1] (closed_form) = 0
x[1] (numeric) = 2.51668011495631
absolute error = 2.51668011495631
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 6.768055704289458
absolute error = 6.768055704289458
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=3070.6MB, alloc=40.3MB, time=29.89
memory used=3111.7MB, alloc=40.3MB, time=30.28
t[1] = 5.9
x[1] (closed_form) = 0
x[1] (numeric) = 2.590984879253479
absolute error = 2.590984879253479
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 6.797025859986624
absolute error = 6.797025859986624
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=3152.8MB, alloc=40.3MB, time=30.66
t[1] = 6
x[1] (closed_form) = 0
x[1] (numeric) = 2.664820590991266
absolute error = 2.664820590991266
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 6.824765384322709
absolute error = 6.824765384322709
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=3193.9MB, alloc=40.3MB, time=31.05
memory used=3234.9MB, alloc=40.3MB, time=31.42
t[1] = 6.1
x[1] (closed_form) = 0
x[1] (numeric) = 2.738192058611034
absolute error = 2.738192058611034
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 6.851315815545968
absolute error = 6.851315815545968
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=3276.1MB, alloc=40.3MB, time=31.81
t[1] = 6.2
x[1] (closed_form) = 0
x[1] (numeric) = 2.811104065892779
absolute error = 2.811104065892779
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 6.876716491776387
absolute error = 6.876716491776387
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=3317.2MB, alloc=40.3MB, time=32.20
memory used=3358.3MB, alloc=40.3MB, time=32.58
t[1] = 6.3
x[1] (closed_form) = 0
x[1] (numeric) = 2.883561363488666
absolute error = 2.883561363488666
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 6.901004710878739
absolute error = 6.901004710878739
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=3399.3MB, alloc=40.3MB, time=32.97
memory used=3440.3MB, alloc=40.3MB, time=33.34
t[1] = 6.4
x[1] (closed_form) = 0
x[1] (numeric) = 2.955568661905535
absolute error = 2.955568661905535
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 6.924215875710663
absolute error = 6.924215875710663
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=3481.5MB, alloc=40.3MB, time=33.75
t[1] = 6.5
x[1] (closed_form) = 0
x[1] (numeric) = 3.027130625720395
absolute error = 3.027130625720395
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 6.9463836263469
absolute error = 6.9463836263469
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=3522.6MB, alloc=40.3MB, time=34.14
memory used=3563.7MB, alloc=40.3MB, time=34.52
t[1] = 6.6
x[1] (closed_form) = 0
x[1] (numeric) = 3.098251868846217
absolute error = 3.098251868846217
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 6.967539960677904
absolute error = 6.967539960677904
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=3604.8MB, alloc=40.3MB, time=34.91
t[1] = 6.7
x[1] (closed_form) = 0
x[1] (numeric) = 3.16893695069315
absolute error = 3.16893695069315
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 6.98771534460719
absolute error = 6.98771534460719
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=3646.1MB, alloc=40.3MB, time=35.30
memory used=3687.2MB, alloc=40.3MB, time=35.67
t[1] = 6.8
x[1] (closed_form) = 0
x[1] (numeric) = 3.239190373093575
absolute error = 3.239190373093575
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.006938812922408
absolute error = 7.006938812922408
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=3728.5MB, alloc=40.3MB, time=36.06
t[1] = 6.9
x[1] (closed_form) = 0
x[1] (numeric) = 3.309016577878986
absolute error = 3.309016577878986
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.025238061786338
absolute error = 7.025238061786338
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=3769.7MB, alloc=40.3MB, time=36.44
memory used=3810.8MB, alloc=40.3MB, time=36.81
t[1] = 7
x[1] (closed_form) = 0
x[1] (numeric) = 3.378419945013156
absolute error = 3.378419945013156
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.042639533682725
absolute error = 7.042639533682725
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=3852.0MB, alloc=40.3MB, time=37.20
memory used=3893.1MB, alloc=40.3MB, time=37.59
t[1] = 7.1
x[1] (closed_form) = 0
x[1] (numeric) = 3.447404791199976
absolute error = 3.447404791199976
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.059168495555372
absolute error = 7.059168495555372
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=3934.3MB, alloc=40.3MB, time=37.97
t[1] = 7.2
x[1] (closed_form) = 0
x[1] (numeric) = 3.515975368896117
absolute error = 3.515975368896117
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.074849110795069
absolute error = 7.074849110795069
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=3975.5MB, alloc=40.3MB, time=38.36
memory used=4016.6MB, alloc=40.3MB, time=38.72
t[1] = 7.3
x[1] (closed_form) = 0
x[1] (numeric) = 3.584135865668666
absolute error = 3.584135865668666
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.08970450565587
absolute error = 7.08970450565587
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=4057.8MB, alloc=40.3MB, time=39.09
t[1] = 7.4
x[1] (closed_form) = 0
x[1] (numeric) = 3.651890403846374
absolute error = 3.651890403846374
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.103756830618423
absolute error = 7.103756830618423
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=4098.9MB, alloc=40.3MB, time=39.48
memory used=4140.0MB, alloc=40.3MB, time=39.86
t[1] = 7.5
x[1] (closed_form) = 0
x[1] (numeric) = 3.71924304042039
absolute error = 3.71924304042039
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.117027317162169
absolute error = 7.117027317162169
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=4181.2MB, alloc=40.3MB, time=40.25
memory used=4222.4MB, alloc=40.3MB, time=40.63
t[1] = 7.6
x[1] (closed_form) = 0
x[1] (numeric) = 3.786197767156534
absolute error = 3.786197767156534
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.129536330359199
absolute error = 7.129536330359199
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=4263.6MB, alloc=40.3MB, time=41.00
t[1] = 7.7
x[1] (closed_form) = 0
x[1] (numeric) = 3.85275851088644
absolute error = 3.85275851088644
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.141303417659422
absolute error = 7.141303417659422
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=4304.8MB, alloc=40.3MB, time=41.39
memory used=4345.8MB, alloc=40.3MB, time=41.77
t[1] = 7.8
x[1] (closed_form) = 0
x[1] (numeric) = 3.918929133949421
absolute error = 3.918929133949421
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.152347354198693
absolute error = 7.152347354198693
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=4387.1MB, alloc=40.3MB, time=42.16
t[1] = 7.9
x[1] (closed_form) = 0
x[1] (numeric) = 3.984713434760796
absolute error = 3.984713434760796
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.162686184927961
absolute error = 7.162686184927961
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=4428.3MB, alloc=40.3MB, time=42.56
memory used=4469.4MB, alloc=40.3MB, time=42.94
t[1] = 8
x[1] (closed_form) = 0
x[1] (numeric) = 4.05011514848575
absolute error = 4.05011514848575
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.172337263831785
absolute error = 7.172337263831785
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=4510.7MB, alloc=40.3MB, time=43.33
t[1] = 8.1
x[1] (closed_form) = 0
x[1] (numeric) = 4.115137947800674
absolute error = 4.115137947800674
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.181317290478211
absolute error = 7.181317290478211
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=4551.9MB, alloc=40.3MB, time=43.72
memory used=4593.0MB, alloc=40.3MB, time=44.09
t[1] = 8.2
x[1] (closed_form) = 0
x[1] (numeric) = 4.179785443726397
absolute error = 4.179785443726397
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.189642344118601
absolute error = 7.189642344118601
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=4634.2MB, alloc=40.3MB, time=44.48
memory used=4675.2MB, alloc=40.3MB, time=44.86
t[1] = 8.3
x[1] (closed_form) = 0
x[1] (numeric) = 4.244061186519869
absolute error = 4.244061186519869
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.197327915535151
absolute error = 7.197327915535151
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=4716.4MB, alloc=40.3MB, time=45.27
t[1] = 8.4
x[1] (closed_form) = 0
x[1] (numeric) = 4.307968666612692
absolute error = 4.307968666612692
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.204388936815259
absolute error = 7.204388936815259
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=4757.6MB, alloc=40.3MB, time=45.64
memory used=4798.7MB, alloc=40.3MB, time=46.02
t[1] = 8.5
x[1] (closed_form) = 0
x[1] (numeric) = 4.371511315586496
absolute error = 4.371511315586496
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.210839809215321
absolute error = 7.210839809215321
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=4840.0MB, alloc=40.3MB, time=46.41
t[1] = 8.6
x[1] (closed_form) = 0
x[1] (numeric) = 4.434692507176531
absolute error = 4.434692507176531
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.216694429261666
absolute error = 7.216694429261666
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=4881.2MB, alloc=40.3MB, time=46.78
memory used=4922.3MB, alloc=40.3MB, time=47.17
t[1] = 8.7
x[1] (closed_form) = 0
x[1] (numeric) = 4.497515558296053
absolute error = 4.497515558296053
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.221966213223047
absolute error = 7.221966213223047
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=4963.5MB, alloc=40.3MB, time=47.55
memory used=5004.7MB, alloc=40.3MB, time=47.92
t[1] = 8.8
x[1] (closed_form) = 0
x[1] (numeric) = 4.55998373007512
absolute error = 4.55998373007512
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.226668120077158
absolute error = 7.226668120077158
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=5045.9MB, alloc=40.3MB, time=48.33
t[1] = 8.9
x[1] (closed_form) = 0
x[1] (numeric) = 4.622100228908305
absolute error = 4.622100228908305
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.230812673082917
absolute error = 7.230812673082917
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=5087.1MB, alloc=40.3MB, time=48.70
memory used=5128.3MB, alloc=40.3MB, time=49.09
t[1] = 9
x[1] (closed_form) = 0
x[1] (numeric) = 4.683868207506631
absolute error = 4.683868207506631
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.234411980060587
absolute error = 7.234411980060587
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=5169.5MB, alloc=40.3MB, time=49.47
t[1] = 9.1
x[1] (closed_form) = 0
x[1] (numeric) = 4.7452907659497
absolute error = 4.7452907659497
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.237477752473088
absolute error = 7.237477752473088
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=5210.7MB, alloc=40.3MB, time=49.86
memory used=5251.9MB, alloc=40.3MB, time=50.23
t[1] = 9.2
x[1] (closed_form) = 0
x[1] (numeric) = 4.806370952734594
absolute error = 4.806370952734594
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.240021323394006
absolute error = 7.240021323394006
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=5293.2MB, alloc=40.3MB, time=50.61
t[1] = 9.3
x[1] (closed_form) = 0
x[1] (numeric) = 4.867111765818629
absolute error = 4.867111765818629
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.242053664440665
absolute error = 7.242053664440665
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=5334.5MB, alloc=40.3MB, time=51.00
TOP MAIN SOLVE Loop
memory used=5375.5MB, alloc=40.3MB, time=51.38
t[1] = 9.4
x[1] (closed_form) = 0
x[1] (numeric) = 4.92751615365349
absolute error = 4.92751615365349
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.243585401744222
absolute error = 7.243585401744222
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=5416.7MB, alloc=40.3MB, time=51.77
memory used=5457.9MB, alloc=40.3MB, time=52.14
t[1] = 9.5
x[1] (closed_form) = 0
x[1] (numeric) = 4.987587016208681
absolute error = 4.987587016208681
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.244626831022883
absolute error = 7.244626831022883
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=5499.1MB, alloc=40.3MB, time=52.53
t[1] = 9.6
x[1] (closed_form) = 0
x[1] (numeric) = 5.047327205982544
absolute error = 5.047327205982544
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.245187931819056
absolute error = 7.245187931819056
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=5540.4MB, alloc=40.3MB, time=52.91
memory used=5581.5MB, alloc=40.3MB, time=53.28
t[1] = 9.7
x[1] (closed_form) = 0
x[1] (numeric) = 5.106739528999402
absolute error = 5.106739528999402
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.245278380956436
absolute error = 7.245278380956436
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=5622.8MB, alloc=40.3MB, time=53.66
memory used=5663.9MB, alloc=40.3MB, time=54.03
t[1] = 9.8
x[1] (closed_form) = 0
x[1] (numeric) = 5.165826745791646
absolute error = 5.165826745791646
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.244907565268654
absolute error = 7.244907565268654
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=5705.2MB, alloc=40.3MB, time=54.41
t[1] = 9.9
x[1] (closed_form) = 0
x[1] (numeric) = 5.224591572365797
absolute error = 5.224591572365797
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.244084593647108
absolute error = 7.244084593647108
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=5746.5MB, alloc=40.3MB, time=54.80
memory used=5787.7MB, alloc=40.3MB, time=55.17
t[1] = 10
x[1] (closed_form) = 0
x[1] (numeric) = 5.283036681151771
absolute error = 5.283036681151771
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.242818308451981
absolute error = 7.242818308451981
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=5829.0MB, alloc=40.3MB, time=55.55
t[1] = 10.1
x[1] (closed_form) = 0
x[1] (numeric) = 5.34116470193475
absolute error = 5.34116470193475
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.241117296327115
absolute error = 7.241117296327115
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=5870.3MB, alloc=40.3MB, time=55.94
memory used=5911.5MB, alloc=40.3MB, time=56.31
t[1] = 10.2
x[1] (closed_form) = 0
x[1] (numeric) = 5.398978222769199
absolute error = 5.398978222769199
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.238989898456385
absolute error = 7.238989898456385
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=5952.7MB, alloc=40.3MB, time=56.69
memory used=5994.0MB, alloc=40.3MB, time=57.06
t[1] = 10.3
x[1] (closed_form) = 0
x[1] (numeric) = 5.456479790874697
absolute error = 5.456479790874697
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.236444220296429
absolute error = 7.236444220296429
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=6035.3MB, alloc=40.3MB, time=57.45
t[1] = 10.4
x[1] (closed_form) = 0
x[1] (numeric) = 5.513671913513362
absolute error = 5.513671913513362
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.233488140818066
absolute error = 7.233488140818066
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=6076.6MB, alloc=40.3MB, time=57.84
memory used=6117.8MB, alloc=40.3MB, time=58.22
t[1] = 10.5
x[1] (closed_form) = 0
x[1] (numeric) = 5.570557058848743
absolute error = 5.570557058848743
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.230129321286377
absolute error = 7.230129321286377
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=6159.0MB, alloc=40.3MB, time=58.58
t[1] = 10.6
x[1] (closed_form) = 0
x[1] (numeric) = 5.627137656786134
absolute error = 5.627137656786134
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.22637521360731
absolute error = 7.22637521360731
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=6200.3MB, alloc=40.3MB, time=58.97
memory used=6241.5MB, alloc=40.3MB, time=59.34
t[1] = 10.7
x[1] (closed_form) = 0
x[1] (numeric) = 5.683416099794328
absolute error = 5.683416099794328
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.222233068266685
absolute error = 7.222233068266685
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=6282.8MB, alloc=40.3MB, time=59.72
t[1] = 10.8
x[1] (closed_form) = 0
x[1] (numeric) = 5.739394743708894
absolute error = 5.739394743708894
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.217709941885682
absolute error = 7.217709941885682
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=6324.0MB, alloc=40.3MB, time=60.11
memory used=6365.1MB, alloc=40.3MB, time=60.48
t[1] = 10.9
x[1] (closed_form) = 0
x[1] (numeric) = 5.795075908517117
absolute error = 5.795075908517117
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.212812704415224
absolute error = 7.212812704415224
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=6406.4MB, alloc=40.3MB, time=60.88
memory used=6447.5MB, alloc=40.3MB, time=61.25
t[1] = 11
x[1] (closed_form) = 0
x[1] (numeric) = 5.850461879124772
absolute error = 5.850461879124772
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.207548045990134
absolute error = 7.207548045990134
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=6488.7MB, alloc=40.3MB, time=61.64
t[1] = 11.1
x[1] (closed_form) = 0
x[1] (numeric) = 5.905554906104937
absolute error = 5.905554906104937
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.20192248346254
absolute error = 7.20192248346254
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=6530.0MB, alloc=40.3MB, time=62.02
memory used=6571.2MB, alloc=40.3MB, time=62.39
t[1] = 11.2
x[1] (closed_form) = 0
x[1] (numeric) = 5.960357206429104
absolute error = 5.960357206429104
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.195942366632697
absolute error = 7.195942366632697
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=6612.5MB, alloc=40.3MB, time=62.78
t[1] = 11.3
x[1] (closed_form) = 0
x[1] (numeric) = 6.01487096418084
absolute error = 6.01487096418084
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.189613884194178
absolute error = 7.189613884194178
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=6653.7MB, alloc=40.3MB, time=63.16
memory used=6694.9MB, alloc=40.3MB, time=63.55
t[1] = 11.4
x[1] (closed_form) = 0
x[1] (numeric) = 6.069098331252297
absolute error = 6.069098331252297
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.182943069409299
absolute error = 7.182943069409299
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=6736.1MB, alloc=40.3MB, time=63.92
memory used=6777.3MB, alloc=40.3MB, time=64.30
t[1] = 11.5
x[1] (closed_form) = 0
x[1] (numeric) = 6.123041428023867
absolute error = 6.123041428023867
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.175935805529587
absolute error = 7.175935805529587
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=6818.6MB, alloc=40.3MB, time=64.69
t[1] = 11.6
x[1] (closed_form) = 0
x[1] (numeric) = 6.176702344027311
absolute error = 6.176702344027311
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.168597830975163
absolute error = 7.168597830975163
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=6859.9MB, alloc=40.3MB, time=65.06
memory used=6901.1MB, alloc=40.3MB, time=65.44
t[1] = 11.7
x[1] (closed_form) = 0
x[1] (numeric) = 6.230083138592681
absolute error = 6.230083138592681
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.160934744286029
absolute error = 7.160934744286029
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=6942.4MB, alloc=40.3MB, time=65.83
t[1] = 11.8
x[1] (closed_form) = 0
x[1] (numeric) = 6.283185841479377
absolute error = 6.283185841479377
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.152952008857422
absolute error = 7.152952008857422
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
TOP MAIN SOLVE Loop
memory used=6983.6MB, alloc=40.3MB, time=66.20
memory used=7024.7MB, alloc=40.3MB, time=66.58
t[1] = 11.9
x[1] (closed_form) = 0
x[1] (numeric) = 6.336012453491681
absolute error = 6.336012453491681
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
y[1] (closed_form) = 0
y[1] (numeric) = 7.14465495747064
absolute error = 7.14465495747064
relative error = -1 %
Desired digits = 16
Estimated correct digits = 4
Correct digits = -16
h = 0.1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
Finished!
diff ( x , t , 2 ) = m1 * 0.58 * x * expt ( ( x * x + y * y ) , ( m1 * 1.5 ) ) ;
diff ( y , t , 2 ) = m1 * 0.58 * y * expt ( ( x * x + y * y ) , ( m1 * 1.5 ) ) ;
Iterations = 110
Total Elapsed Time = 1 Minutes 6 Seconds
Elapsed Time(since restart) = 1 Minutes 6 Seconds
Time to Timeout = 28 Minutes 53 Seconds
Percent Done = 100.9 %
> quit
memory used=7047.9MB, alloc=40.3MB, time=66.80