|\^/| Maple 2016 (X86 64 LINUX)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2016
\ 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_complex := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> if vallen = 4 then
> printf("%-30s = %-20.4g %-20g %s \n",prelabel,Re(value), Im(value), postlabel);
> else
> printf("%-30s = %-20.12g %-20.12g %s \n",prelabel,Re(value),Im(value), postlabel);
> fi;# end if 0;
> fi;# end if -1;
> end;
omniout_complex := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then printf("%-30s = %-20.4g %-20g %s \n", prelabel,
Re(value), Im(value), postlabel)
else printf("%-30s = %-20.12g %-20.12g %s \n", prelabel, Re(value),
Im(value), postlabel)
end if
end if
end proc
# End Function number 6
# Begin Function number 7
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number -1
> if vallen = 5 then # if number 0
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;# end if 0;
> fi;# end if -1;
> 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 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 -1
> 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 0
> 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 1
> 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 2
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 3
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 3
> else
> fprintf(fd," 0.0 Seconds");
> fi;# end if 2
> 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 2
> 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 3
> 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 4
> 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 5
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 6
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 6
> else
> printf(" 0.0 Seconds\n");
> fi;# end if 5
> end;
omniout_timestr := proc(secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" 0.0 Seconds\n")
end if
end proc
# End Function number 9
# Begin Function number 10
> zero_ats_ar := proc(arr_a)
> global ATS_MAX_TERMS;
> local iii;
> iii := 1;
> while (iii <= ATS_MAX_TERMS) do # do number 1
> arr_a [iii] := glob__0;
> iii := iii + 1;
> od;# end do number 1
> end;
zero_ats_ar := proc(arr_a)
local iii;
global ATS_MAX_TERMS;
iii := 1;
while iii <= ATS_MAX_TERMS do arr_a[iii] := glob__0; iii := iii + 1
end do
end proc
# End Function number 10
# Begin Function number 11
> ats := proc(mmm_ats,arr_a,arr_b,jjj_ats)
> global ATS_MAX_TERMS;
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := glob__0;
> if (jjj_ats <= mmm_ats) then # if number 5
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> if ((lll_ats <= ATS_MAX_TERMS and (iii_ats <= ATS_MAX_TERMS) )) then # if number 6
> ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]);
> fi;# end if 6;
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 5;
> ret_ats;
> end;
ats := proc(mmm_ats, arr_a, arr_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
global ATS_MAX_TERMS;
ret_ats := glob__0;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
if lll_ats <= ATS_MAX_TERMS and iii_ats <= ATS_MAX_TERMS then
ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats])
end if;
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
# End Function number 11
# Begin Function number 12
> att := proc(mmm_att,arr_aa,arr_bb,jjj_att)
> global ATS_MAX_TERMS;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := glob__0;
> if (jjj_att < mmm_att) then # if number 5
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while ((iii_att < mmm_att) and (iii_att <= ATS_MAX_TERMS) ) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if ((lll_att <= ATS_MAX_TERMS and (iii_att <= ATS_MAX_TERMS) )) then # if number 6
> ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att);
> fi;# end if 6;
> iii_att := iii_att + 1;
> od;# end do number 1;
> ret_att := ret_att / c(mmm_att) ;
> fi;# end if 5;
> ret_att;
> end;
att := proc(mmm_att, arr_aa, arr_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global ATS_MAX_TERMS;
ret_att := glob__0;
if jjj_att < mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att < mmm_att and iii_att <= ATS_MAX_TERMS do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= ATS_MAX_TERMS and iii_att <= ATS_MAX_TERMS then
ret_att :=
ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])*c(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/c(mmm_att)
end if;
ret_att
end proc
# End Function number 12
# Begin Function number 13
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
# End Function number 13
# Begin Function number 14
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
# End Function number 14
# Begin Function number 15
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
# End Function number 15
# Begin Function number 16
> logitem_good_digits := proc(file,rel_error)
> global glob_small_float,glob_prec;
> local good_digits;
> fprintf(file,"");
> fprintf(file,"%d",glob_min_good_digits);
> fprintf(file," | ");
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float, glob_prec;
fprintf(file, "");
fprintf(file, "%d", glob_min_good_digits);
fprintf(file, " | ")
end proc
# End Function number 16
# Begin Function number 17
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
# End Function number 17
# Begin Function number 18
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
# End Function number 18
# Begin Function number 19
> logitem_complex := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g + %g I",Re(x),Im(x));
> fprintf(file," | ");
> end;
logitem_complex := proc(file, x)
fprintf(file, "");
fprintf(file, "%g + %g I", Re(x), Im(x));
fprintf(file, " | ")
end proc
# End Function number 19
# Begin Function number 20
> logitem_h_reason := proc(file)
> global glob_h_reason;
> fprintf(file,"");
> if (glob_h_reason = 1) then # if number 5
> fprintf(file,"Max H");
> elif
> (glob_h_reason = 2) then # if number 6
> fprintf(file,"Display Interval");
> elif
> (glob_h_reason = 3) then # if number 7
> fprintf(file,"Optimal");
> elif
> (glob_h_reason = 4) then # if number 8
> fprintf(file,"Pole Accuracy");
> elif
> (glob_h_reason = 5) then # if number 9
> fprintf(file,"Min H (Pole)");
> elif
> (glob_h_reason = 6) then # if number 10
> fprintf(file,"Pole");
> elif
> (glob_h_reason = 7) then # if number 11
> fprintf(file,"Opt Iter");
> else
> fprintf(file,"Impossible");
> fi;# end if 11
> 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 20
# Begin Function number 21
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
# End Function number 21
# Begin Function number 22
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file) fprintf(file, "\n") end proc
# End Function number 22
# Begin Function number 23
> chk_data := proc()
> global glob_max_iter,ALWAYS, ATS_MAX_TERMS;
> local errflag;
> errflag := false;
> if (glob_max_iter < 2) then # if number 11
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 11;
> if (errflag) then # if number 11
> quit;
> fi;# end if 11
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, ATS_MAX_TERMS;
errflag := false;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
# End Function number 23
# Begin Function number 24
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := c(clock_sec2);
> sub1 := c(t_end2-t_start2);
> sub2 := c(t2-t_start2);
> if (sub1 = glob__0) then # if number 11
> sec_left := glob__0;
> else
> if (sub2 > glob__0) then # if number 12
> rrr := (sub1/sub2);
> sec_left := rrr * c(ms2) - c(ms2);
> else
> sec_left := glob__0;
> fi;# end if 12
> fi;# end if 11;
> sec_left;
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := c(clock_sec2);
sub1 := c(t_end2 - t_start2);
sub2 := c(t2 - t_start2);
if sub1 = glob__0 then sec_left := glob__0
else
if glob__0 < sub2 then
rrr := sub1/sub2; sec_left := rrr*c(ms2) - c(ms2)
else sec_left := glob__0
end if
end if;
sec_left
end proc
# End Function number 24
# Begin Function number 25
> 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 11
> rrr := (glob__100*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 11;
> rrr;
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < sub2 then rrr := glob__100*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
# End Function number 25
# Begin Function number 26
> comp_rad_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 11
> ret := float_abs(term1 * glob_h / term2);
> else
> ret := glob_larger_float;
> fi;# end if 11;
> ret;
> #BOTTOM TWO TERM RADIUS ANALYSIS
> end;
comp_rad_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := float_abs(term1*glob_h/term2)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 26
# Begin Function number 27
> comp_ord_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM ORDER ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 11
> ret := glob__1 + float_abs(term2) * c(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(c(last_no));
> else
> ret := glob_larger_float;
> fi;# end if 11;
> ret;
> #BOTTOM TWO TERM ORDER ANALYSIS
> end;
comp_ord_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := glob__1 + float_abs(term2)*
c(last_no)*ln(float_abs(term1*glob_h/term2))/ln(c(last_no))
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 27
# Begin Function number 28
> c := proc(in_val)
> #To Force Conversion when needed
> local ret;
> ret := evalc(in_val);
> ret;
> #End Conversion
> end;
c := proc(in_val) local ret; ret := evalc(in_val); ret end proc
# End Function number 28
# Begin Function number 29
> comp_rad_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret,temp;
> temp := float_abs(term2*term2*c(last_no)+glob__m2*term2*term2-term1*term3*c(last_no)+term1*term3);
> if (float_abs(temp) > glob__0) then # if number 11
> ret := float_abs((term2*glob_h*term1)/(temp));
> else
> ret := glob_larger_float;
> fi;# end if 11;
> ret;
> #BOTTOM THREE TERM RADIUS ANALYSIS
> end;
comp_rad_from_three_terms := proc(term1, term2, term3, last_no)
local ret, temp;
global glob_h, glob_larger_float;
temp := float_abs(term2*term2*c(last_no) + glob__m2*term2*term2
- term1*term3*c(last_no) + term1*term3);
if glob__0 < float_abs(temp) then
ret := float_abs(term2*glob_h*term1/temp)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 29
# Begin Function number 30
> comp_ord_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM ORDER ANALYSIS
> local ret;
> ret := float_abs((glob__4*term1*term3*c(last_no)-glob__3*term1*term3-glob__4*term2*term2*c(last_no)+glob__4*term2*term2+term2*term2*c(last_no*last_no)-term1*term3*c(last_no*last_no))/(term2*term2*c(last_no)-glob__2*term2*term2-term1*term3*c(last_no)+term1*term3));
> ret;
> #TOP THREE TERM ORDER ANALYSIS
> end;
comp_ord_from_three_terms := proc(term1, term2, term3, last_no)
local ret;
ret := float_abs((glob__4*term1*term3*c(last_no) - glob__3*term1*term3
- glob__4*term2*term2*c(last_no) + glob__4*term2*term2
+ term2*term2*c(last_no*last_no) - term1*term3*c(last_no*last_no))
/(term2*term2*c(last_no) - glob__2*term2*term2
- term1*term3*c(last_no) + term1*term3));
ret
end proc
# End Function number 30
# Begin Function number 31
> comp_rad_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> #TOP SIX TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float,glob_six_term_ord_save;
> local ret,rm0,rm1,rm2,rm3,rm4,nr1,nr2,dr1,dr2,ds2,rad_c,ord_no,ds1,rcs;
> if ((term5 <> glob__0) and (term4 <> glob__0) and (term3 <> glob__0) and (term2 <> glob__0) and (term1 <> glob__0)) then # if number 11
> rm0 := term6/term5;
> rm1 := term5/term4;
> rm2 := term4/term3;
> rm3 := term3/term2;
> rm4 := term2/term1;
> nr1 := c(last_no-1)*rm0 - glob__2*c(last_no-2)*rm1 + c(last_no-3)*rm2;
> nr2 := c(last_no-2)*rm1 - glob__2*c(last_no-3)*rm2 + c(last_no-4)*rm3;
> dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
> dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
> ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
> ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
> if ((float_abs(nr1 * dr2 - nr2 * dr1) = glob__0) or (float_abs(dr1) = glob__0)) then # if number 12
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> else
> if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0) then # if number 13
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) -c(last_no)/glob__2;
> if (float_abs(rcs) <> glob__0) then # if number 14
> if (rcs > glob__0) then # if number 15
> rad_c := float_abs( sqrt(rcs) * float_abs(glob_h));
> 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
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 13
> fi;# end if 12
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 11;
> glob_six_term_ord_save := ord_no;
> rad_c;
> #BOTTOM SIX TERM RADIUS ANALYSIS
> end;
comp_rad_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
local ret, rm0, rm1, rm2, rm3, rm4, nr1, nr2, dr1, dr2, ds2, rad_c, ord_no,
ds1, rcs;
global glob_h, glob_larger_float, glob_six_term_ord_save;
if term5 <> glob__0 and term4 <> glob__0 and term3 <> glob__0 and
term2 <> glob__0 and term1 <> glob__0 then
rm0 := term6/term5;
rm1 := term5/term4;
rm2 := term4/term3;
rm3 := term3/term2;
rm4 := term2/term1;
nr1 := c(last_no - 1)*rm0 - glob__2*c(last_no - 2)*rm1
+ c(last_no - 3)*rm2;
nr2 := c(last_no - 2)*rm1 - glob__2*c(last_no - 3)*rm2
+ c(last_no - 4)*rm3;
dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
if
float_abs(nr1*dr2 - nr2*dr1) = glob__0 or float_abs(dr1) = glob__0
then rad_c := glob_larger_float; ord_no := glob_larger_float
else
if glob__0 < float_abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no :=
(rcs*nr1 - ds1)/(glob__2*dr1) - c(last_no)/glob__2;
if float_abs(rcs) <> glob__0 then
if glob__0 < rcs then
rad_c := float_abs(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 31
# Begin Function number 32
> 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 32
# Begin Function number 33
> 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 33
# Begin Function number 34
> factorial_1 := proc(nnn)
> global ATS_MAX_TERMS,array_fact_1;
> local ret;
> if (nnn <= ATS_MAX_TERMS) then # if number 11
> if (array_fact_1[nnn] = 0) then # if number 12
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 12;
> else
> ret := factorial_2(nnn);
> fi;# end if 11;
> ret;
> end;
factorial_1 := proc(nnn)
local ret;
global ATS_MAX_TERMS, array_fact_1;
if nnn <= ATS_MAX_TERMS then
if array_fact_1[nnn] = 0 then
ret := factorial_2(nnn); array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := factorial_2(nnn)
end if;
ret
end proc
# End Function number 34
# Begin Function number 35
> factorial_3 := proc(mmm,nnn)
> global ATS_MAX_TERMS,array_fact_2;
> local ret;
> if ((nnn <= ATS_MAX_TERMS) and (mmm <= ATS_MAX_TERMS)) then # if number 11
> if (array_fact_2[mmm,nnn] = 0) then # if number 12
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 12;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 11;
> ret;
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global ATS_MAX_TERMS, array_fact_2;
if nnn <= ATS_MAX_TERMS and mmm <= ATS_MAX_TERMS then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := factorial_2(mmm)/factorial_2(nnn)
end if;
ret
end proc
# End Function number 35
# Begin Function number 36
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
# End Function number 36
# Begin Function number 37
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
# End Function number 37
# Begin Function number 38
> float_abs := proc(x)
> abs(x);
> end;
float_abs := proc(x) abs(x) end proc
# End Function number 38
# Begin Function number 39
> expt := proc(x,y)
> x^y;
> end;
expt := proc(x, y) x^y end proc
# End Function number 39
# Begin Function number 40
> neg := proc(x)
> -x;
> end;
neg := proc(x) -x end proc
# End Function number 40
# Begin Function number 41
> int_trunc := proc(x)
> trunc(x);
> end;
int_trunc := proc(x) trunc(x) end proc
# End Function number 41
# Begin Function number 42
> estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer)
> local desired_abs_gbl_error,range,estimated_steps,step_error;
> global glob_desired_digits_correct,ALWAYS,ATS_MAX_TERMS;
> omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
> desired_abs_gbl_error := expt(glob__10,c( -glob_desired_digits_correct)) * c(float_abs(c(estimated_answer)));
> omniout_float(ALWAYS,"estimated_h",32,estimated_h,32,"");
> omniout_float(ALWAYS,"estimated_answer",32,estimated_answer,32,"");
> omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,"");
> range := (x_end - x_start);
> omniout_float(ALWAYS,"range",32,range,32,"");
> estimated_steps := range / estimated_h;
> omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,"");
> step_error := (c(float_abs(desired_abs_gbl_error) /sqrt(c( estimated_steps))/c(ATS_MAX_TERMS)));
> omniout_float(ALWAYS,"step_error",32,step_error,32,"");
> (step_error);;
> end;
estimated_needed_step_error := proc(
x_start, x_end, estimated_h, estimated_answer)
local desired_abs_gbl_error, range, estimated_steps, step_error;
global glob_desired_digits_correct, ALWAYS, ATS_MAX_TERMS;
omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, "");
desired_abs_gbl_error :=
expt(glob__10, c(-glob_desired_digits_correct))*
c(float_abs(c(estimated_answer)));
omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, "");
omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, "")
;
omniout_float(ALWAYS, "desired_abs_gbl_error", 32,
desired_abs_gbl_error, 32, "");
range := x_end - x_start;
omniout_float(ALWAYS, "range", 32, range, 32, "");
estimated_steps := range/estimated_h;
omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, "");
step_error := c(float_abs(desired_abs_gbl_error)/(
sqrt(c(estimated_steps))*c(ATS_MAX_TERMS)));
omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
step_error
end proc
# End Function number 42
#END ATS LIBRARY BLOCK
#BEGIN USER FUNCTION BLOCK
#BEGIN BLOCK 3
#BEGIN USER DEF BLOCK
> exact_soln_y1 := proc(x)
> return(cos(c(x)));
> end;
exact_soln_y1 := proc(x) return cos(c(x)) end proc
> exact_soln_y2 := proc(x)
> return(sin(c(x)));
> end;
exact_soln_y2 := proc(x) return sin(c(x)) end proc
> next_delta := proc()
> global glob_nxt, x_delta;
> x_delta := [ 0.001 + 0.00004 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.000 + 0.000 * I ];
> glob_nxt := glob_nxt + 1;
> it := x_delta[glob_nxt];
> return it;
> end;
Warning, `it` is implicitly declared local to procedure `next_delta`
next_delta := proc()
local it;
global glob_nxt, x_delta;
x_delta := [0.001 + 0.00004*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0. + 0.*I];
glob_nxt := glob_nxt + 1;
it := x_delta[glob_nxt];
return it
end proc
#END USER DEF BLOCK
#END BLOCK 3
#END USER FUNCTION BLOCK
# before write_aux functions
# Begin Function number 2
> display_poles := proc()
> local rad_given;
> global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ;
> if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1
> rad_given := float_abs(array_x[1] - (array_given_rad_poles[1,1] + array_given_rad_poles[1,2] * I ));
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," ");
> omniout_complex(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," ");
> if ((float_abs(rad_given) < float_abs(glob_least_given_sing)) and
> (float_abs(rad_given) > 0.0)) 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 ((float_abs(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_complex(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," ");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," ");
> if ((float_abs(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_complex(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," ");
> if ((float_abs(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_complex(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 := float_abs(array_x[1] - (array_given_rad_poles[2,1] + array_given_rad_poles[2,2] * I ));
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 2 ",4,rad_given,4," ");
> omniout_complex(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[2,1],4," ");
> if ((float_abs(rad_given) < float_abs(glob_least_given_sing)) and
> (float_abs(rad_given) > 0.0)) 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 ((float_abs(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_complex(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[2,1],4," ");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 2");
> fi;# end if 5;
> if ((array_rad_test_poles[2,2] > glob__small) and (array_rad_test_poles[2,2] < glob_large_float)) then # if number 5
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 2 ",4,array_rad_test_poles[2,2],4," ");
> if ((float_abs(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_complex(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[2,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 2");
> fi;# end if 5;
> if ((array_rad_test_poles[2,3] > glob__small) and (array_rad_test_poles[2,3] < glob_large_float)) then # if number 5
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 2 ",4,array_rad_test_poles[2,3],4," ");
> if ((float_abs(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_complex(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[2,3],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 2");
> fi;# end if 5
> ;
> end;
display_poles := proc()
local rad_given;
global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float,
glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord,
glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
glob_least_3_sing, glob_least_6_sing, glob_least_given_sing,
glob_least_ratio_sing, array_x;
if glob_type_given_pole = 1 or glob_type_given_pole = 2 then
rad_given := float_abs(array_x[1] - array_given_rad_poles[1, 1]
- array_given_rad_poles[1, 2]*I);
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 1 ", 4,
rad_given, 4, " ");
omniout_complex(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles[1, 1], 4, " ");
if float_abs(rad_given) < float_abs(glob_least_given_sing) and
0. < float_abs(rad_given) 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 float_abs(array_rad_test_poles[1, 1]) < glob_least_ratio_sing
then glob_least_ratio_sing := array_rad_test_poles[1, 1]
end if;
omniout_complex(ALWAYS,
"Order of pole (ratio test) ", 4,
array_ord_test_poles[1, 1], 4, " ")
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 2] and
array_rad_test_poles[1, 2] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 1 ", 4,
array_rad_test_poles[1, 2], 4, " ");
if float_abs(array_rad_test_poles[1, 2]) < glob_least_3_sing then
glob_least_3_sing := array_rad_test_poles[1, 2]
end if;
omniout_complex(ALWAYS,
"Order of pole (three term test) ", 4,
array_ord_test_poles[1, 2], 4, " ")
else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 3] and
array_rad_test_poles[1, 3] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 1 ", 4,
array_rad_test_poles[1, 3], 4, " ");
if float_abs(array_rad_test_poles[1, 3]) < glob_least_6_sing then
glob_least_6_sing := array_rad_test_poles[1, 3]
end if;
omniout_complex(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 := float_abs(array_x[1] - array_given_rad_poles[2, 1]
- array_given_rad_poles[2, 2]*I);
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 2 ", 4,
rad_given, 4, " ");
omniout_complex(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles[2, 1], 4, " ");
if float_abs(rad_given) < float_abs(glob_least_given_sing) and
0. < float_abs(rad_given) 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 float_abs(array_rad_test_poles[2, 1]) < glob_least_ratio_sing
then glob_least_ratio_sing := array_rad_test_poles[2, 1]
end if;
omniout_complex(ALWAYS,
"Order of pole (ratio test) ", 4,
array_ord_test_poles[2, 1], 4, " ")
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 2")
end if;
if glob__small < array_rad_test_poles[2, 2] and
array_rad_test_poles[2, 2] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 2 ", 4,
array_rad_test_poles[2, 2], 4, " ");
if float_abs(array_rad_test_poles[2, 2]) < glob_least_3_sing then
glob_least_3_sing := array_rad_test_poles[2, 2]
end if;
omniout_complex(ALWAYS,
"Order of pole (three term test) ", 4,
array_ord_test_poles[2, 2], 4, " ")
else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 2")
end if;
if glob__small < array_rad_test_poles[2, 3] and
array_rad_test_poles[2, 3] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 2 ", 4,
array_rad_test_poles[2, 3], 4, " ");
if float_abs(array_rad_test_poles[2, 3]) < glob_least_6_sing then
glob_least_6_sing := array_rad_test_poles[2, 3]
end if;
omniout_complex(ALWAYS,
"Order of pole (six term test) ", 4,
array_ord_test_poles[2, 3], 4, " ")
else omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 2")
end if
end proc
# End Function number 2
# Begin Function number 3
> my_check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 5
> ret := glob__1;
> else
> ret := glob__m1;
> fi;# end if 5;
> ret;;
> end;
my_check_sign := proc(x0, xf)
local ret;
if x0 < xf then ret := glob__1 else ret := glob__m1 end if; ret
end proc
# End Function number 3
# Begin Function number 4
> est_size_answer := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#END CONST
> array_y1_init,
> array_y2_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local min_size;
> min_size := glob_estimated_size_answer;
> if (float_abs(array_y1[1]) < min_size) then # if number 5
> min_size := float_abs(array_y1[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 5;
> if (float_abs(array_y2[1]) < min_size) then # if number 5
> min_size := float_abs(array_y2[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 5;
> if (min_size < glob__1) then # if number 5
> min_size := glob__1;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 5;
> min_size;
> end;
est_size_answer := proc()
local min_size;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_y1_init,
array_y2_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y1, array_x, array_y2, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_m1, array_y1_higher, array_y1_higher_work,
array_y1_higher_work2, array_y1_set_initial, array_y2_higher,
array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
min_size := glob_estimated_size_answer;
if float_abs(array_y1[1]) < min_size then
min_size := float_abs(array_y1[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if float_abs(array_y2[1]) < min_size then
min_size := float_abs(array_y2[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if min_size < glob__1 then
min_size := glob__1;
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
min_size
end proc
# End Function number 4
# Begin Function number 5
> test_suggested_h := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#END CONST
> array_y1_init,
> array_y2_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> max_estimated_step_error := glob__small;
> no_terms := ATS_MAX_TERMS;
> hn_div_ho := glob__0_5;
> hn_div_ho_2 := glob__0_25;
> hn_div_ho_3 := glob__0_125;
> omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,"");
> omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,"");
> omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,"");
> est_tmp := float_abs(array_y1[no_terms-3] + array_y1[no_terms - 2] * hn_div_ho + array_y1[no_terms - 1] * hn_div_ho_2 + array_y1[no_terms] * hn_div_ho_3);
> if (est_tmp >= max_estimated_step_error) then # if number 5
> max_estimated_step_error := est_tmp;
> fi;# end if 5;
> est_tmp := float_abs(array_y2[no_terms-3] + array_y2[no_terms - 2] * hn_div_ho + array_y2[no_terms - 1] * hn_div_ho_2 + array_y2[no_terms] * hn_div_ho_3);
> if (est_tmp >= max_estimated_step_error) then # if number 5
> max_estimated_step_error := est_tmp;
> fi;# end if 5;
> omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,"");
> max_estimated_step_error;
> end;
test_suggested_h := proc()
local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3,
no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_y1_init,
array_y2_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y1, array_x, array_y2, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_m1, array_y1_higher, array_y1_higher_work,
array_y1_higher_work2, array_y1_set_initial, array_y2_higher,
array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
max_estimated_step_error := glob__small;
no_terms := ATS_MAX_TERMS;
hn_div_ho := glob__0_5;
hn_div_ho_2 := glob__0_25;
hn_div_ho_3 := glob__0_125;
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, "");
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, "");
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, "");
est_tmp := float_abs(array_y1[no_terms - 3]
+ array_y1[no_terms - 2]*hn_div_ho
+ array_y1[no_terms - 1]*hn_div_ho_2
+ array_y1[no_terms]*hn_div_ho_3);
if max_estimated_step_error <= est_tmp then
max_estimated_step_error := est_tmp
end if;
est_tmp := float_abs(array_y2[no_terms - 3]
+ array_y2[no_terms - 2]*hn_div_ho
+ array_y2[no_terms - 1]*hn_div_ho_2
+ array_y2[no_terms]*hn_div_ho_3);
if max_estimated_step_error <= est_tmp then
max_estimated_step_error := est_tmp
end if;
omniout_float(ALWAYS, "max_estimated_step_error", 32,
max_estimated_step_error, 32, "");
max_estimated_step_error
end proc
# End Function number 5
# Begin Function number 6
> track_estimated_error := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#END CONST
> array_y1_init,
> array_y2_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> no_terms := ATS_MAX_TERMS;
> hn_div_ho := glob__0_5;
> hn_div_ho_2 := glob__0_25;
> hn_div_ho_3 := glob__0_125;
> est_tmp := c(float_abs(array_y1[no_terms-3])) + c(float_abs(array_y1[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y1[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y1[no_terms])) * c(hn_div_ho_3);
> if (glob_prec * c(float_abs(array_y1[1])) > c(est_tmp)) then # if number 5
> est_tmp := c(glob_prec) * c(float_abs(array_y1[1]));
> fi;# end if 5;
> if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 5
> array_max_est_error[1] := c(est_tmp);
> fi;# end if 5
> ;
> est_tmp := c(float_abs(array_y2[no_terms-3])) + c(float_abs(array_y2[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y2[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y2[no_terms])) * c(hn_div_ho_3);
> if (glob_prec * c(float_abs(array_y2[1])) > c(est_tmp)) then # if number 5
> est_tmp := c(glob_prec) * c(float_abs(array_y2[1]));
> fi;# end if 5;
> if (c(est_tmp) >= c(array_max_est_error[2])) then # if number 5
> array_max_est_error[2] := c(est_tmp);
> fi;# end if 5
> ;
> end;
track_estimated_error := proc()
local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_y1_init,
array_y2_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y1, array_x, array_y2, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_m1, array_y1_higher, array_y1_higher_work,
array_y1_higher_work2, array_y1_set_initial, array_y2_higher,
array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
no_terms := ATS_MAX_TERMS;
hn_div_ho := glob__0_5;
hn_div_ho_2 := glob__0_25;
hn_div_ho_3 := glob__0_125;
est_tmp := c(float_abs(array_y1[no_terms - 3]))
+ c(float_abs(array_y1[no_terms - 2]))*c(hn_div_ho)
+ c(float_abs(array_y1[no_terms - 1]))*c(hn_div_ho_2)
+ c(float_abs(array_y1[no_terms]))*c(hn_div_ho_3);
if c(est_tmp) < glob_prec*c(float_abs(array_y1[1])) then
est_tmp := c(glob_prec)*c(float_abs(array_y1[1]))
end if;
if c(array_max_est_error[1]) <= c(est_tmp) then
array_max_est_error[1] := c(est_tmp)
end if;
est_tmp := c(float_abs(array_y2[no_terms - 3]))
+ c(float_abs(array_y2[no_terms - 2]))*c(hn_div_ho)
+ c(float_abs(array_y2[no_terms - 1]))*c(hn_div_ho_2)
+ c(float_abs(array_y2[no_terms]))*c(hn_div_ho_3);
if c(est_tmp) < glob_prec*c(float_abs(array_y2[1])) then
est_tmp := c(glob_prec)*c(float_abs(array_y2[1]))
end if;
if c(array_max_est_error[2]) <= c(est_tmp) then
array_max_est_error[2] := c(est_tmp)
end if
end proc
# End Function number 6
# Begin Function number 7
> reached_interval := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#END CONST
> array_y1_init,
> array_y2_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local ret;
> if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 5
> ret := true;
> else
> ret := false;
> fi;# end if 5;
> return(ret);
> end;
reached_interval := proc()
local ret;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_y1_init,
array_y2_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y1, array_x, array_y2, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_m1, array_y1_higher, array_y1_higher_work,
array_y1_higher_work2, array_y1_set_initial, array_y2_higher,
array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
if glob_check_sign*glob_next_display - glob_h/glob__10 <=
glob_check_sign*array_x[1] then ret := true
else ret := false
end if;
return ret
end proc
# End Function number 7
# Begin Function number 8
> display_alot := proc(iter)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#END CONST
> array_y1_init,
> array_y2_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err;
> #TOP DISPLAY ALOT
> ind_var := array_x[1];
> omniout_complex(ALWAYS,"x[1] ",33,ind_var,20," ");
> term_no := 1;
> numeric_val := array_y1[term_no];
> omniout_complex(ALWAYS,"h ",33,glob_h,20," ");
> omniout_complex(ALWAYS,"y1[1] (numeric) ",33,numeric_val,20," ");
> closed_form_val_y := evalf(exact_soln_y1(ind_var));
> omniout_complex(ALWAYS,"y1[1] (closed_form) ",33,closed_form_val_y,20," ");
> abserr := float_abs(numeric_val - closed_form_val_y);
> if (float_abs(closed_form_val_y) > 0.0) then # if number 5
> relerr := abserr/float_abs(closed_form_val_y);
> if (float_abs(c(relerr)) > 0.0) then # if number 6
> glob_good_digits := round(-log10(relerr));
> else
> relerr := 0.0 ;
> glob_good_digits := Digits - 2;
> fi;# end if 6;
> else
> ;
> relerr := glob__m1 ;
> glob_good_digits := -16;
> fi;# end if 5;
> if (glob_good_digits < glob_min_good_digits) then # if number 5
> glob_min_good_digits := glob_good_digits;
> fi;# end if 5;
> omniout_float(ALWAYS,"absolute error ",4,abserr,4," ");
> omniout_float(ALWAYS,"relative error ",4,relerr * glob__100 ,4,"%");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> ;
> term_no := 1;
> numeric_val := array_y2[term_no];
> omniout_complex(ALWAYS,"h ",33,glob_h,20," ");
> omniout_complex(ALWAYS,"y2[1] (numeric) ",33,numeric_val,20," ");
> closed_form_val_y := evalf(exact_soln_y2(ind_var));
> omniout_complex(ALWAYS,"y2[1] (closed_form) ",33,closed_form_val_y,20," ");
> abserr := float_abs(numeric_val - closed_form_val_y);
> if (float_abs(closed_form_val_y) > 0.0) then # if number 5
> relerr := abserr/float_abs(closed_form_val_y);
> if (float_abs(c(relerr)) > 0.0) then # if number 6
> glob_good_digits := round(-log10(relerr));
> else
> relerr := 0.0 ;
> glob_good_digits := Digits - 2;
> fi;# end if 6;
> else
> ;
> relerr := glob__m1 ;
> glob_good_digits := -16;
> fi;# end if 5;
> if (glob_good_digits < glob_min_good_digits) then # if number 5
> glob_min_good_digits := glob_good_digits;
> fi;# end if 5;
> omniout_float(ALWAYS,"absolute error ",4,abserr,4," ");
> omniout_float(ALWAYS,"relative error ",4,relerr * glob__100 ,4,"%");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> #BOTTOM DISPLAY ALOT
> end;
display_alot := proc(iter)
local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no,
est_rel_err;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_y1_init,
array_y2_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y1, array_x, array_y2, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_m1, array_y1_higher, array_y1_higher_work,
array_y1_higher_work2, array_y1_set_initial, array_y2_higher,
array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
ind_var := array_x[1];
omniout_complex(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
term_no := 1;
numeric_val := array_y1[term_no];
omniout_complex(ALWAYS, "h ", 33, glob_h,
20, " ");
omniout_complex(ALWAYS, "y1[1] (numeric) ", 33,
numeric_val, 20, " ");
closed_form_val_y := evalf(exact_soln_y1(ind_var));
omniout_complex(ALWAYS, "y1[1] (closed_form) ", 33,
closed_form_val_y, 20, " ");
abserr := float_abs(numeric_val - closed_form_val_y);
if 0. < float_abs(closed_form_val_y) then
relerr := abserr/float_abs(closed_form_val_y);
if 0. < float_abs(c(relerr)) then
glob_good_digits := round(-log10(relerr))
else relerr := 0.; glob_good_digits := Digits - 2
end if
else relerr := glob__m1; glob_good_digits := -16
end if;
if glob_good_digits < glob_min_good_digits then
glob_min_good_digits := glob_good_digits
end if;
omniout_float(ALWAYS, "absolute error ", 4, abserr, 4,
" ");
omniout_float(ALWAYS, "relative error ", 4,
relerr*glob__100, 4, "%");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ");
term_no := 1;
numeric_val := array_y2[term_no];
omniout_complex(ALWAYS, "h ", 33, glob_h,
20, " ");
omniout_complex(ALWAYS, "y2[1] (numeric) ", 33,
numeric_val, 20, " ");
closed_form_val_y := evalf(exact_soln_y2(ind_var));
omniout_complex(ALWAYS, "y2[1] (closed_form) ", 33,
closed_form_val_y, 20, " ");
abserr := float_abs(numeric_val - closed_form_val_y);
if 0. < float_abs(closed_form_val_y) then
relerr := abserr/float_abs(closed_form_val_y);
if 0. < float_abs(c(relerr)) then
glob_good_digits := round(-log10(relerr))
else relerr := 0.; glob_good_digits := Digits - 2
end if
else relerr := glob__m1; glob_good_digits := -16
end if;
if glob_good_digits < glob_min_good_digits then
glob_min_good_digits := glob_good_digits
end if;
omniout_float(ALWAYS, "absolute error ", 4, abserr, 4,
" ");
omniout_float(ALWAYS, "relative error ", 4,
relerr*glob__100, 4, "%");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ")
end proc
# End Function number 8
# Begin Function number 9
> prog_report := proc(x_start,x_end)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#END CONST
> array_y1_init,
> array_y2_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := (clock_sec1) - (glob_orig_start_sec);
> glob_clock_sec := (clock_sec1) - (glob_clock_start_sec);
> left_sec := (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1);
> expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h) ,( clock_sec1) - (glob_orig_start_sec));
> opt_clock_sec := ( clock_sec1) - (glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec));
> glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
> percent_done := comp_percent((x_end),(x_start),(array_x[1]) + (glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr((total_clock_sec));
> if (c(percent_done) < glob__100) then # if number 5
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr((expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr((glob_optimal_expect_sec));
> omniout_str_noeol(INFO,"Expected Total Time ");
> omniout_timestr((glob_total_exp_sec));
> fi;# end if 5;
> #BOTTOM PROGRESS REPORT
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_y1_init,
array_y2_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y1, array_x, array_y2, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_m1, array_y1_higher, array_y1_higher_work,
array_y1_higher_work2, array_y1_set_initial, array_y2_higher,
array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec := clock_sec1 - glob_orig_start_sec;
glob_clock_sec := clock_sec1 - glob_clock_start_sec;
left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1;
expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h,
clock_sec1 - glob_orig_start_sec);
opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec;
glob_optimal_expect_sec :=
comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec)
;
glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h);
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(total_clock_sec);
if c(percent_done) < glob__100 then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(expect_sec);
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(glob_optimal_expect_sec);
omniout_str_noeol(INFO, "Expected Total Time ");
omniout_timestr(glob_total_exp_sec)
end if
end proc
# End Function number 9
# Begin Function number 10
> check_for_pole := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#END CONST
> array_y1_init,
> array_y2_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad, last_no;
> #TOP CHECK FOR POLE
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,1] := glob_larger_float;
> array_ord_test_poles[1,1] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_ratio(array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 5
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 5;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 6
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 7
> found_sing := 0;
> fi;# end if 7;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 7
> if (rad_c < array_rad_test_poles[1,1]) then # if number 8
> array_rad_test_poles[1,1] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_ratio(array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
> array_rad_test_poles[1,1] := rad_c;
> array_ord_test_poles[1,1] := tmp_ord;
> fi;# end if 8;
> fi;# end if 7;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[2,1] := glob_larger_float;
> array_ord_test_poles[2,1] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_ratio(array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 7
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 7;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 8
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 9
> found_sing := 0;
> fi;# end if 9;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 9
> if (rad_c < array_rad_test_poles[2,1]) then # if number 10
> array_rad_test_poles[2,1] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_ratio(array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
> array_rad_test_poles[2,1] := rad_c;
> array_ord_test_poles[2,1] := tmp_ord;
> fi;# end if 10;
> fi;# end if 9;
> #BOTTOM general radius test2
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,2] := glob_larger_float;
> array_ord_test_poles[1,2] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_three_terms(array_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 9
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 9;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 9
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 10
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 11
> found_sing := 0;
> fi;# end if 11;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 11
> if (rad_c < array_rad_test_poles[1,2]) then # if number 12
> array_rad_test_poles[1,2] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_three_terms(array_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
> array_rad_test_poles[1,2] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 13
> glob_min_pole_est := rad_c;
> fi;# end if 13;
> array_ord_test_poles[1,2] := tmp_ord;
> fi;# end if 12;
> fi;# end if 11;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[2,2] := glob_larger_float;
> array_ord_test_poles[2,2] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_three_terms(array_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 11
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 11;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 11
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 12
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 13
> found_sing := 0;
> fi;# end if 13;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 13
> if (rad_c < array_rad_test_poles[2,2]) then # if number 14
> array_rad_test_poles[2,2] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_three_terms(array_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
> array_rad_test_poles[2,2] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 15
> glob_min_pole_est := rad_c;
> fi;# end if 15;
> array_ord_test_poles[2,2] := tmp_ord;
> fi;# end if 14;
> fi;# end if 13;
> #BOTTOM general radius test2
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,3] := glob_larger_float;
> array_ord_test_poles[1,3] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_six_terms(array_y1_higher[1,last_no-5],array_y1_higher[1,last_no-4],array_y1_higher[1,last_no-3],array_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 13
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 13;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 13
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 14
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 15
> found_sing := 0;
> fi;# end if 15;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 15
> if (rad_c < array_rad_test_poles[1,3]) then # if number 16
> array_rad_test_poles[1,3] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_six_terms(array_y1_higher[1,last_no-5],array_y1_higher[1,last_no-4],array_y1_higher[1,last_no-3],array_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
> array_rad_test_poles[1,3] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 17
> glob_min_pole_est := rad_c;
> fi;# end if 17;
> array_ord_test_poles[1,3] := tmp_ord;
> fi;# end if 16;
> fi;# end if 15;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[2,3] := glob_larger_float;
> array_ord_test_poles[2,3] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_six_terms(array_y2_higher[1,last_no-5],array_y2_higher[1,last_no-4],array_y2_higher[1,last_no-3],array_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 15
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 15;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 15
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 16
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 17
> found_sing := 0;
> fi;# end if 17;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 17
> if (rad_c < array_rad_test_poles[2,3]) then # if number 18
> array_rad_test_poles[2,3] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_six_terms(array_y2_higher[1,last_no-5],array_y2_higher[1,last_no-4],array_y2_higher[1,last_no-3],array_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
> array_rad_test_poles[2,3] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 19
> glob_min_pole_est := rad_c;
> fi;# end if 19;
> array_ord_test_poles[2,3] := tmp_ord;
> fi;# end if 18;
> fi;# end if 17;
> #BOTTOM general radius test2
> ;
> if (true) then # if number 17
> display_poles();
> fi;# end if 17
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2,
term3, part1, part2, part3, part4, part5, part6, part7, part8, part9,
part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4,
found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio,
prev_tmp_rad, last_no;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_y1_init,
array_y2_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y1, array_x, array_y2, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_m1, array_y1_higher, array_y1_higher_work,
array_y1_higher_work2, array_y1_set_initial, array_y2_higher,
array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 1] := glob_larger_float;
array_ord_test_poles[1, 1] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do
tmp_rad := comp_rad_from_ratio(array_y1_higher[1, last_no - 1],
array_y1_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 1] then
array_rad_test_poles[1, 1] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_ratio(array_y1_higher[1, last_no - 1],
array_y1_higher[1, last_no], last_no);
array_rad_test_poles[1, 1] := rad_c;
array_ord_test_poles[1, 1] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[2, 1] := glob_larger_float;
array_ord_test_poles[2, 1] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do
tmp_rad := comp_rad_from_ratio(array_y2_higher[1, last_no - 1],
array_y2_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[2, 1] then
array_rad_test_poles[2, 1] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_ratio(array_y2_higher[1, last_no - 1],
array_y2_higher[1, last_no], last_no);
array_rad_test_poles[2, 1] := rad_c;
array_ord_test_poles[2, 1] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 2] := glob_larger_float;
array_ord_test_poles[1, 2] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do
tmp_rad := comp_rad_from_three_terms(
array_y1_higher[1, last_no - 2],
array_y1_higher[1, last_no - 1], array_y1_higher[1, last_no],
last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 2] then
array_rad_test_poles[1, 2] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_three_terms(
array_y1_higher[1, last_no - 2],
array_y1_higher[1, last_no - 1],
array_y1_higher[1, last_no], last_no);
array_rad_test_poles[1, 2] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 2] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[2, 2] := glob_larger_float;
array_ord_test_poles[2, 2] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do
tmp_rad := comp_rad_from_three_terms(
array_y2_higher[1, last_no - 2],
array_y2_higher[1, last_no - 1], array_y2_higher[1, last_no],
last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[2, 2] then
array_rad_test_poles[2, 2] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_three_terms(
array_y2_higher[1, last_no - 2],
array_y2_higher[1, last_no - 1],
array_y2_higher[1, last_no], last_no);
array_rad_test_poles[2, 2] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[2, 2] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 3] := glob_larger_float;
array_ord_test_poles[1, 3] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do
tmp_rad := comp_rad_from_six_terms(array_y1_higher[1, last_no - 5],
array_y1_higher[1, last_no - 4],
array_y1_higher[1, last_no - 3],
array_y1_higher[1, last_no - 2],
array_y1_higher[1, last_no - 1], array_y1_higher[1, last_no],
last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 3] then
array_rad_test_poles[1, 3] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_six_terms(
array_y1_higher[1, last_no - 5],
array_y1_higher[1, last_no - 4],
array_y1_higher[1, last_no - 3],
array_y1_higher[1, last_no - 2],
array_y1_higher[1, last_no - 1],
array_y1_higher[1, last_no], last_no);
array_rad_test_poles[1, 3] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 3] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[2, 3] := glob_larger_float;
array_ord_test_poles[2, 3] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do
tmp_rad := comp_rad_from_six_terms(array_y2_higher[1, last_no - 5],
array_y2_higher[1, last_no - 4],
array_y2_higher[1, last_no - 3],
array_y2_higher[1, last_no - 2],
array_y2_higher[1, last_no - 1], array_y2_higher[1, last_no],
last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[2, 3] then
array_rad_test_poles[2, 3] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_six_terms(
array_y2_higher[1, last_no - 5],
array_y2_higher[1, last_no - 4],
array_y2_higher[1, last_no - 3],
array_y2_higher[1, last_no - 2],
array_y2_higher[1, last_no - 1],
array_y2_higher[1, last_no], last_no);
array_rad_test_poles[2, 3] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[2, 3] := tmp_ord
end if
end if;
display_poles()
end proc
# End Function number 10
# Begin Function number 11
> atomall := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#END CONST
> array_y1_init,
> array_y2_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> # before write maple main top matter
> # before generate constants assign
> # before generate globals assign
> #END OUTFILE1
> #BEGIN OUTFILE2
> #END OUTFILE2
> #BEGIN ATOMHDR1
> #emit pre neg FULL $eq_no = 1
> array_tmp1[1] := neg(array_y2[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y1_set_initial[1,2]) then # if number 1
> if (1 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
> if (2 <= ATS_MAX_TERMS) then # if number 3
> array_y1[2] := temporary;
> array_y1_higher[1,2] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(1);
> array_y1_higher[2,1] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5
> if ( not array_y2_set_initial[2,2]) then # if number 1
> if (1 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp3[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
> if (2 <= ATS_MAX_TERMS) then # if number 3
> array_y2[2] := temporary;
> array_y2_higher[1,2] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(1);
> array_y2_higher[2,1] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre neg FULL $eq_no = 1
> array_tmp1[2] := neg(array_y2[2]);
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y1_set_initial[1,3]) then # if number 1
> if (2 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2));
> if (3 <= ATS_MAX_TERMS) then # if number 3
> array_y1[3] := temporary;
> array_y1_higher[1,3] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y1_higher[2,2] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5
> if ( not array_y2_set_initial[2,3]) then # if number 1
> if (2 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp3[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2));
> if (3 <= ATS_MAX_TERMS) then # if number 3
> array_y2[3] := temporary;
> array_y2_higher[1,3] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y2_higher[2,2] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre neg FULL $eq_no = 1
> array_tmp1[3] := neg(array_y2[3]);
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp2[3] := array_tmp1[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y1_set_initial[1,4]) then # if number 1
> if (3 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3));
> if (4 <= ATS_MAX_TERMS) then # if number 3
> array_y1[4] := temporary;
> array_y1_higher[1,4] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y1_higher[2,3] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5
> if ( not array_y2_set_initial[2,4]) then # if number 1
> if (3 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp3[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3));
> if (4 <= ATS_MAX_TERMS) then # if number 3
> array_y2[4] := temporary;
> array_y2_higher[1,4] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y2_higher[2,3] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre neg FULL $eq_no = 1
> array_tmp1[4] := neg(array_y2[4]);
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp2[4] := array_tmp1[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y1_set_initial[1,5]) then # if number 1
> if (4 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4));
> if (5 <= ATS_MAX_TERMS) then # if number 3
> array_y1[5] := temporary;
> array_y1_higher[1,5] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y1_higher[2,4] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5
> if ( not array_y2_set_initial[2,5]) then # if number 1
> if (4 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp3[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4));
> if (5 <= ATS_MAX_TERMS) then # if number 3
> array_y2[5] := temporary;
> array_y2_higher[1,5] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y2_higher[2,4] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre neg FULL $eq_no = 1
> array_tmp1[5] := neg(array_y2[5]);
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp2[5] := array_tmp1[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y1_set_initial[1,6]) then # if number 1
> if (5 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5));
> if (6 <= ATS_MAX_TERMS) then # if number 3
> array_y1[6] := temporary;
> array_y1_higher[1,6] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y1_higher[2,5] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5
> if ( not array_y2_set_initial[2,6]) then # if number 1
> if (5 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp3[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5));
> if (6 <= ATS_MAX_TERMS) then # if number 3
> array_y2[6] := temporary;
> array_y2_higher[1,6] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y2_higher[2,5] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= ATS_MAX_TERMS) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit neg FULL $eq_no = 1
> array_tmp1[kkk] := neg(array_y2[kkk]);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp2[kkk] := array_tmp1[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1
> if ( not array_y1_set_initial[1,kkk + order_d]) then # if number 2
> temporary := c(array_tmp2[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
> array_y1[kkk + order_d] := c(temporary);
> array_y1_higher[1,kkk + order_d] := c(temporary);
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := c(temporary) / c(glob_h) * c(adj2);
> else
> temporary := c(temporary);
> fi;# end if 4;
> array_y1_higher[adj3,term] := c(temporary);
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 1
> fi;# end if 2
> fi;# end if 1;
> #emit assign $eq_no = 2
> order_d := 1;
> if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1
> if ( not array_y2_set_initial[2,kkk + order_d]) then # if number 2
> temporary := c(array_tmp3[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
> array_y2[kkk + order_d] := c(temporary);
> array_y2_higher[1,kkk + order_d] := c(temporary);
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := c(temporary) / c(glob_h) * c(adj2);
> else
> temporary := c(temporary);
> fi;# end if 4;
> array_y2_higher[adj3,term] := c(temporary);
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 1
> fi;# end if 2
> fi;# end if 1;
> kkk := kkk + 1;
> od;# end do number 1;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_y1_init,
array_y2_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y1, array_x, array_y2, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_m1, array_y1_higher, array_y1_higher_work,
array_y1_higher_work2, array_y1_set_initial, array_y2_higher,
array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
array_tmp1[1] := neg(array_y2[1]);
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
if not array_y1_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
if 2 <= ATS_MAX_TERMS then
array_y1[2] := temporary;
array_y1_higher[1, 2] := temporary
end if;
temporary := c(temporary)*c(1)/c(glob_h);
array_y1_higher[2, 1] := c(temporary)
end if
end if;
kkk := 2;
if not array_y2_set_initial[2, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp3[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
if 2 <= ATS_MAX_TERMS then
array_y2[2] := temporary;
array_y2_higher[1, 2] := temporary
end if;
temporary := c(temporary)*c(1)/c(glob_h);
array_y2_higher[2, 1] := c(temporary)
end if
end if;
kkk := 2;
array_tmp1[2] := neg(array_y2[2]);
array_tmp2[2] := array_tmp1[2];
if not array_y1_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
if 3 <= ATS_MAX_TERMS then
array_y1[3] := temporary;
array_y1_higher[1, 3] := temporary
end if;
temporary := c(temporary)*c(2)/c(glob_h);
array_y1_higher[2, 2] := c(temporary)
end if
end if;
kkk := 3;
if not array_y2_set_initial[2, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp3[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
if 3 <= ATS_MAX_TERMS then
array_y2[3] := temporary;
array_y2_higher[1, 3] := temporary
end if;
temporary := c(temporary)*c(2)/c(glob_h);
array_y2_higher[2, 2] := c(temporary)
end if
end if;
kkk := 3;
array_tmp1[3] := neg(array_y2[3]);
array_tmp2[3] := array_tmp1[3];
if not array_y1_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[3])*expt(glob_h, c(1))*c(factorial_3(2, 3));
if 4 <= ATS_MAX_TERMS then
array_y1[4] := temporary;
array_y1_higher[1, 4] := temporary
end if;
temporary := c(temporary)*c(3)/c(glob_h);
array_y1_higher[2, 3] := c(temporary)
end if
end if;
kkk := 4;
if not array_y2_set_initial[2, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp3[3])*expt(glob_h, c(1))*c(factorial_3(2, 3));
if 4 <= ATS_MAX_TERMS then
array_y2[4] := temporary;
array_y2_higher[1, 4] := temporary
end if;
temporary := c(temporary)*c(3)/c(glob_h);
array_y2_higher[2, 3] := c(temporary)
end if
end if;
kkk := 4;
array_tmp1[4] := neg(array_y2[4]);
array_tmp2[4] := array_tmp1[4];
if not array_y1_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[4])*expt(glob_h, c(1))*c(factorial_3(3, 4));
if 5 <= ATS_MAX_TERMS then
array_y1[5] := temporary;
array_y1_higher[1, 5] := temporary
end if;
temporary := c(temporary)*c(4)/c(glob_h);
array_y1_higher[2, 4] := c(temporary)
end if
end if;
kkk := 5;
if not array_y2_set_initial[2, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp3[4])*expt(glob_h, c(1))*c(factorial_3(3, 4));
if 5 <= ATS_MAX_TERMS then
array_y2[5] := temporary;
array_y2_higher[1, 5] := temporary
end if;
temporary := c(temporary)*c(4)/c(glob_h);
array_y2_higher[2, 4] := c(temporary)
end if
end if;
kkk := 5;
array_tmp1[5] := neg(array_y2[5]);
array_tmp2[5] := array_tmp1[5];
if not array_y1_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[5])*expt(glob_h, c(1))*c(factorial_3(4, 5));
if 6 <= ATS_MAX_TERMS then
array_y1[6] := temporary;
array_y1_higher[1, 6] := temporary
end if;
temporary := c(temporary)*c(5)/c(glob_h);
array_y1_higher[2, 5] := c(temporary)
end if
end if;
kkk := 6;
if not array_y2_set_initial[2, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp3[5])*expt(glob_h, c(1))*c(factorial_3(4, 5));
if 6 <= ATS_MAX_TERMS then
array_y2[6] := temporary;
array_y2_higher[1, 6] := temporary
end if;
temporary := c(temporary)*c(5)/c(glob_h);
array_y2_higher[2, 5] := c(temporary)
end if
end if;
kkk := 6;
while kkk <= ATS_MAX_TERMS do
array_tmp1[kkk] := neg(array_y2[kkk]);
array_tmp2[kkk] := array_tmp1[kkk];
order_d := 1;
if kkk + order_d <= ATS_MAX_TERMS then
if not array_y1_set_initial[1, kkk + order_d] then
temporary := c(array_tmp2[kkk])*expt(glob_h, c(order_d))*
c(factorial_3(kkk - 1, kkk + order_d - 1));
array_y1[kkk + order_d] := c(temporary);
array_y1_higher[1, kkk + order_d] := c(temporary);
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while
1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1
do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := c(temporary)*c(adj2)/c(glob_h)
else temporary := c(temporary)
end if;
array_y1_higher[adj3, term] := c(temporary)
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
order_d := 1;
if kkk + order_d <= ATS_MAX_TERMS then
if not array_y2_set_initial[2, kkk + order_d] then
temporary := c(array_tmp3[kkk])*expt(glob_h, c(order_d))*
c(factorial_3(kkk - 1, kkk + order_d - 1));
array_y2[kkk + order_d] := c(temporary);
array_y2_higher[1, kkk + order_d] := c(temporary);
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while
1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1
do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := c(temporary)*c(adj2)/c(glob_h)
else temporary := c(temporary)
end if;
array_y2_higher[adj3, term] := c(temporary)
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
# End Function number 12
#END OUTFILE5
# Begin Function number 12
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it;
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #END CONST
> array_y1_init,
> array_y2_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> ATS_MAX_TERMS := 40;
> # before first input block
> #BEGIN FIRST INPUT BLOCK
> #BEGIN BLOCK 1
> #BEGIN FIRST INPUT BLOCK
> Digits:=64;
> max_terms:=40;
> #END BLOCK 1
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> # before generate arrays
> array_y1_init:= Array(0..(40),[]);
> array_y2_init:= Array(0..(40),[]);
> array_norms:= Array(0..(40),[]);
> array_fact_1:= Array(0..(40),[]);
> array_1st_rel_error:= Array(0..(3),[]);
> array_last_rel_error:= Array(0..(3),[]);
> array_est_rel_error:= Array(0..(3),[]);
> array_max_est_error:= Array(0..(3),[]);
> array_type_pole:= Array(0..(3),[]);
> array_type_real_pole:= Array(0..(3),[]);
> array_type_complex_pole:= Array(0..(3),[]);
> array_est_digits:= Array(0..(3),[]);
> array_y1:= Array(0..(40),[]);
> array_x:= Array(0..(40),[]);
> array_y2:= Array(0..(40),[]);
> array_tmp0:= Array(0..(40),[]);
> array_tmp1:= Array(0..(40),[]);
> array_tmp2:= Array(0..(40),[]);
> array_tmp3:= Array(0..(40),[]);
> array_m1:= Array(0..(40),[]);
> array_y1_higher := Array(0..(2) ,(0..40+ 1),[]);
> array_y1_higher_work := Array(0..(2) ,(0..40+ 1),[]);
> array_y1_higher_work2 := Array(0..(2) ,(0..40+ 1),[]);
> array_y1_set_initial := Array(0..(3) ,(0..40+ 1),[]);
> array_y2_higher := Array(0..(2) ,(0..40+ 1),[]);
> array_y2_higher_work := Array(0..(2) ,(0..40+ 1),[]);
> array_y2_higher_work2 := Array(0..(2) ,(0..40+ 1),[]);
> array_y2_set_initial := Array(0..(3) ,(0..40+ 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..(40) ,(0..40+ 1),[]);
> # before generate constants
> # before generate globals definition
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> # before generate const definition
> # before arrays initialized
> term := 1;
> while (term <= 40) do # do number 1
> array_y1_init[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_y2_init[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_norms[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_fact_1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_1st_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_last_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_est_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_max_est_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_type_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_type_real_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_type_complex_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_est_digits[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_y1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_x[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_y2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp0[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp3[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_m1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_y1_higher[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_y1_higher_work[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_y1_higher_work2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_y1_set_initial[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_y2_higher[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_y2_higher_work[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_y2_higher_work2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_y2_set_initial[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_rad_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_ord_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_rad_test_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_ord_test_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=40) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_fact_2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> # before symbols initialized
> #BEGIN SYMBOLS INITIALIZATED
> zero_ats_ar(array_y1);
> zero_ats_ar(array_x);
> zero_ats_ar(array_y2);
> zero_ats_ar(array_tmp0);
> zero_ats_ar(array_tmp1);
> zero_ats_ar(array_tmp2);
> zero_ats_ar(array_tmp3);
> zero_ats_ar(array_m1);
> zero_ats_ar(array_const_1);
> array_const_1[1] := c(1);
> zero_ats_ar(array_const_0D0);
> array_const_0D0[1] := c(0.0);
> zero_ats_ar(array_m1);
> array_m1[1] := glob__m1;
> #END SYMBOLS INITIALIZATED
> # before generate factorials init
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= ATS_MAX_TERMS) do # do number 1
> jjjf := 0;
> while (jjjf <= ATS_MAX_TERMS) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Table
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> glob_yes_pole := 4;
> glob_no_pole := 3;
> glob_not_given := 0;
> glob_no_sing_tests := 4;
> glob_ratio_test := 1;
> glob_three_term_test := 2;
> glob_six_term_test := 3;
> glob_log_10 := log(c(10.0));
> MAX_UNCHANGED := 10;
> glob__small := c(0.1e-50);
> glob_small_float := c(0.1e-50);
> glob_smallish_float := c(0.1e-60);
> glob_large_float := c(1.0e100);
> glob_larger_float := c(1.1e100);
> glob__m2 := c(-2);
> glob__m1 := c(-1);
> glob__0 := c(0);
> glob__1 := c(1);
> glob__2 := c(2);
> glob__3 := c(3);
> glob__4 := c(4);
> glob__5 := c(5);
> glob__8 := c(8);
> glob__10 := c(10);
> glob__100 := c(100);
> glob__pi := c(0.0);
> glob__0_5 := c(0.5);
> glob__0_8 := c(0.8);
> glob__m0_8 := c(-0.8);
> glob__0_25 := c(0.25);
> glob__0_125 := c(0.125);
> glob_h := 0.1;
> glob_nxt := 1;
> glob_prec := c(1.0e-16);
> glob_check_sign := c(1.0);
> glob_desired_digits_correct := c(8.0);
> glob_max_estimated_step_error := c(0.0);
> glob_ratio_of_radius := c(0.1);
> glob_percent_done := c(0.0);
> glob_total_exp_sec := c(0.1);
> glob_optimal_expect_sec := c(0.1);
> glob_estimated_size_answer := c(100.0);
> glob_almost_1 := c(0.9990);
> glob_clock_sec := c(0.0);
> glob_clock_start_sec := c(0.0);
> glob_disp_incr := c(0.1);
> glob_diff_rc_fm := c(0.1);
> glob_diff_rc_fmm1 := c(0.1);
> glob_diff_rc_fmm2 := c(0.1);
> glob_diff_ord_fm := c(0.1);
> glob_diff_ord_fmm1 := c(0.1);
> glob_diff_ord_fmm2 := c(0.1);
> glob_six_term_ord_save := c(0.1);
> glob_guess_error_rc := c(0.1);
> glob_guess_error_ord := c(0.1);
> glob_least_given_sing := c(9.9e200);
> glob_least_ratio_sing := c(9.9e200);
> glob_least_3_sing := c(9.9e100);
> glob_least_6_sing := c(9.9e100);
> glob_last_good_h := c(0.1);
> glob_max_h := c(0.1);
> glob_min_h := c(0.000001);
> glob_display_interval := c(0.1);
> glob_abserr := c(0.1e-10);
> glob_relerr := c(0.1e-10);
> glob_min_pole_est := c(0.1e+10);
> glob_max_rel_trunc_err := c(0.1e-10);
> glob_max_trunc_err := c(0.1e-10);
> glob_max_hours := c(0.0);
> glob_optimal_clock_start_sec := c(0.0);
> glob_optimal_start := c(0.0);
> glob_upper_ratio_limit := c(1.0001);
> glob_lower_ratio_limit := c(0.9999);
> glob_max_sec := c(10000.0);
> glob_orig_start_sec := c(0.0);
> glob_normmax := c(0.0);
> glob_max_minutes := c(0.0);
> glob_next_display := c(0.0);
> glob_est_digits := 1;
> glob_subiter_method := 3;
> glob_html_log := true;
> glob_min_good_digits := 99999;
> glob_good_digits := 0;
> glob_min_apfp_est_good_digits := 99999;
> glob_apfp_est_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> glob_h_reason := 0;
> glob_sec_in_minute := 60 ;
> glob_min_in_hour := 60;
> glob_hours_in_day := 24;
> glob_days_in_year := 365;
> glob_sec_in_hour := 3600;
> glob_sec_in_day := 86400;
> glob_sec_in_year := 31536000;
> glob_not_yet_finished := true;
> glob_initial_pass := true;
> glob_not_yet_start_msg := true;
> glob_reached_optimal_h := false;
> glob_optimal_done := false;
> glob_type_given_pole := 0;
> glob_optimize := false;
> glob_look_poles := false;
> glob_dump_closed_form := false;
> glob_max_iter := 10000;
> glob_no_eqs := 0;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_start := 0;
> glob_iter := 0;
> # before generate set diff initial
> array_y1_set_initial[1,1] := true;
> array_y1_set_initial[1,2] := false;
> array_y1_set_initial[1,3] := false;
> array_y1_set_initial[1,4] := false;
> array_y1_set_initial[1,5] := false;
> array_y1_set_initial[1,6] := false;
> array_y1_set_initial[1,7] := false;
> array_y1_set_initial[1,8] := false;
> array_y1_set_initial[1,9] := false;
> array_y1_set_initial[1,10] := false;
> array_y1_set_initial[1,11] := false;
> array_y1_set_initial[1,12] := false;
> array_y1_set_initial[1,13] := false;
> array_y1_set_initial[1,14] := false;
> array_y1_set_initial[1,15] := false;
> array_y1_set_initial[1,16] := false;
> array_y1_set_initial[1,17] := false;
> array_y1_set_initial[1,18] := false;
> array_y1_set_initial[1,19] := false;
> array_y1_set_initial[1,20] := false;
> array_y1_set_initial[1,21] := false;
> array_y1_set_initial[1,22] := false;
> array_y1_set_initial[1,23] := false;
> array_y1_set_initial[1,24] := false;
> array_y1_set_initial[1,25] := false;
> array_y1_set_initial[1,26] := false;
> array_y1_set_initial[1,27] := false;
> array_y1_set_initial[1,28] := false;
> array_y1_set_initial[1,29] := false;
> array_y1_set_initial[1,30] := false;
> array_y1_set_initial[1,31] := false;
> array_y1_set_initial[1,32] := false;
> array_y1_set_initial[1,33] := false;
> array_y1_set_initial[1,34] := false;
> array_y1_set_initial[1,35] := false;
> array_y1_set_initial[1,36] := false;
> array_y1_set_initial[1,37] := false;
> array_y1_set_initial[1,38] := false;
> array_y1_set_initial[1,39] := false;
> array_y1_set_initial[1,40] := false;
> array_y2_set_initial[2,1] := true;
> array_y2_set_initial[2,2] := false;
> array_y2_set_initial[2,3] := false;
> array_y2_set_initial[2,4] := false;
> array_y2_set_initial[2,5] := false;
> array_y2_set_initial[2,6] := false;
> array_y2_set_initial[2,7] := false;
> array_y2_set_initial[2,8] := false;
> array_y2_set_initial[2,9] := false;
> array_y2_set_initial[2,10] := false;
> array_y2_set_initial[2,11] := false;
> array_y2_set_initial[2,12] := false;
> array_y2_set_initial[2,13] := false;
> array_y2_set_initial[2,14] := false;
> array_y2_set_initial[2,15] := false;
> array_y2_set_initial[2,16] := false;
> array_y2_set_initial[2,17] := false;
> array_y2_set_initial[2,18] := false;
> array_y2_set_initial[2,19] := false;
> array_y2_set_initial[2,20] := false;
> array_y2_set_initial[2,21] := false;
> array_y2_set_initial[2,22] := false;
> array_y2_set_initial[2,23] := false;
> array_y2_set_initial[2,24] := false;
> array_y2_set_initial[2,25] := false;
> array_y2_set_initial[2,26] := false;
> array_y2_set_initial[2,27] := false;
> array_y2_set_initial[2,28] := false;
> array_y2_set_initial[2,29] := false;
> array_y2_set_initial[2,30] := false;
> array_y2_set_initial[2,31] := false;
> array_y2_set_initial[2,32] := false;
> array_y2_set_initial[2,33] := false;
> array_y2_set_initial[2,34] := false;
> array_y2_set_initial[2,35] := false;
> array_y2_set_initial[2,36] := false;
> array_y2_set_initial[2,37] := false;
> array_y2_set_initial[2,38] := false;
> array_y2_set_initial[2,39] := false;
> array_y2_set_initial[2,40] := false;
> # before generate init omniout const
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> ATS_MAX_TERMS := 40;
> glob_iolevel := INFO;
> # set default block
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> glob_display_flag := true;
> glob_no_eqs := 2;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 10000;
> glob_max_hours := (0.0);
> glob_max_minutes := (15.0);
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/mtest2postcpx.cpx#################");
> omniout_str(ALWAYS,"diff ( y1 , x , 1 ) = neg ( y2 ) ; ");
> omniout_str(ALWAYS,"diff ( y2 , x , 1 ) = y1 ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=64;");
> omniout_str(ALWAYS,"max_terms:=40;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := 0.2 + 0.1 * I;");
> omniout_str(ALWAYS,"x_end := 99.0 + 99.0 * I;");
> omniout_str(ALWAYS,"array_y1_init[0 + 1] := exact_soln_y1(x_start);");
> omniout_str(ALWAYS,"array_y2_init[0 + 1] := exact_soln_y2(x_start);");
> omniout_str(ALWAYS,"glob_max_h := 0.00001;");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_type_given_pole := 3;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=8;");
> omniout_str(ALWAYS,"glob_max_minutes:=(3.0);");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"glob_max_iter:=10000;");
> omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);");
> omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);");
> omniout_str(ALWAYS,"glob_look_poles:=true;");
> omniout_str(ALWAYS,"glob_h:=c(0.001);");
> omniout_str(ALWAYS,"glob_display_interval:=c(0.01);");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y1 := proc(x)");
> omniout_str(ALWAYS,"return(cos(c(x)));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2 := proc(x)");
> omniout_str(ALWAYS,"return(sin(c(x)));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"next_delta := proc()");
> omniout_str(ALWAYS,"global glob_nxt, x_delta;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"x_delta := [ 0.001 + 0.00004 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.000 + 0.000 * I ];");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_nxt := glob_nxt + 1;");
> omniout_str(ALWAYS,"it := x_delta[glob_nxt];");
> omniout_str(ALWAYS,"return it;");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := glob__0;
> glob_smallish_float := glob__0;
> glob_large_float := c(1.0e100);
> glob_larger_float := c( 1.1e100);
> glob_almost_1 := c( 0.99);
> # before second block
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #BEGIN BLOCK 2
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := 0.2 + 0.1 * I;
> x_end := 99.0 + 99.0 * I;
> array_y1_init[0 + 1] := exact_soln_y1(x_start);
> array_y2_init[0 + 1] := exact_soln_y2(x_start);
> glob_max_h := 0.00001;
> glob_look_poles := true;
> glob_type_given_pole := 3;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=8;
> glob_max_minutes:=(3.0);
> glob_subiter_method:=3;
> glob_max_iter:=10000;
> glob_upper_ratio_limit:=c(1.000001);
> glob_lower_ratio_limit:=c(0.999999);
> glob_look_poles:=true;
> glob_h:=c(0.001);
> glob_display_interval:=c(0.01);
> #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
> found_h := true;
> glob_h := next_delta();
> #START ADJUST ALL SERIES
> if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 17
> h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius;
> omniout_str(ALWAYS,"SETTING H FOR POLE");
> glob_h_reason := 6;
> if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 18
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> h_new := glob_min_h;
> glob_h_reason := 5;
> fi;# end if 18;
> term := 1;
> ratio := c(1.0);
> while (term <= ATS_MAX_TERMS) do # do number 1
> array_y1[term] := array_y1[term]* ratio;
> array_y1_higher[1,term] := array_y1_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> array_y2[term] := array_y2[term]* ratio;
> array_y2_higher[1,term] := array_y2_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / float_abs(glob_h);
> term := term + 1;
> od;# end do number 1;
> glob_h := h_new;
> fi;# end if 17;
> #BOTTOM ADJUST ALL SERIES
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 17
> html_log_file := fopen("entry.html",WRITE,TEXT);
> fi;# end if 17;
> #BEGIN SOLUTION CODE
> found_h := true;
> if (found_h) then # if number 17
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := c(x_start);
> array_x[2] := c(glob_h);
> glob_next_display := c(x_start);
> glob_min_pole_est := glob_larger_float;
> glob_least_given_sing := glob_larger_float;
> glob_least_ratio_sing := glob_larger_float;
> glob_least_3_sing := glob_larger_float;
> glob_least_6_sing := glob_larger_float;
> order_diff := 1;
> #Start Series array_y1
> term_no := 1;
> while (term_no <= order_diff) do # do number 1
> array_y1[term_no] := array_y1_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1));
> term_no := term_no + 1;
> od;# end do number 1;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 1
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 2
> it := term_no + r_order - 1;
> if (term_no < ATS_MAX_TERMS) then # if number 18
> array_y1_higher[r_order,term_no] := array_y1_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 18;
> term_no := term_no + 1;
> od;# end do number 2;
> r_order := r_order + 1;
> od;# end do number 1
> ;
> order_diff := 1;
> #Start Series array_y2
> term_no := 1;
> while (term_no <= order_diff) do # do number 1
> array_y2[term_no] := array_y2_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1));
> term_no := term_no + 1;
> od;# end do number 1;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 1
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 2
> it := term_no + r_order - 1;
> if (term_no < ATS_MAX_TERMS) then # if number 18
> array_y2_higher[r_order,term_no] := array_y2_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 18;
> term_no := term_no + 1;
> od;# end do number 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;
> found_h := true;
> glob_h := next_delta();
> #START ADJUST ALL SERIES
> if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 18
> 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 19
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> h_new := glob_min_h;
> glob_h_reason := 5;
> fi;# end if 19;
> term := 1;
> ratio := c(1.0);
> while (term <= ATS_MAX_TERMS) do # do number 1
> array_y1[term] := array_y1[term]* ratio;
> array_y1_higher[1,term] := array_y1_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> array_y2[term] := array_y2[term]* ratio;
> array_y2_higher[1,term] := array_y2_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / float_abs(glob_h);
> term := term + 1;
> od;# end do number 1;
> glob_h := h_new;
> fi;# end if 18;
> #BOTTOM ADJUST ALL SERIES
> #END OPTIMIZE CODE
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_iter < glob_max_iter) and ((glob_iter < 10) or ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0))))) do # do number 1
> #left paren 0001C
> if (true) then # if number 18
> omniout_str(INFO," ");
> fi;# end if 18;
> found_h := true;
> glob_h := next_delta();
> #START ADJUST ALL SERIES
> if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 18
> 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 19
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> h_new := glob_min_h;
> glob_h_reason := 5;
> fi;# end if 19;
> term := 1;
> ratio := c(1.0);
> while (term <= ATS_MAX_TERMS) do # do number 2
> array_y1[term] := array_y1[term]* ratio;
> array_y1_higher[1,term] := array_y1_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> array_y2[term] := array_y2[term]* ratio;
> array_y2_higher[1,term] := array_y2_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / float_abs(glob_h);
> term := term + 1;
> od;# end do number 2;
> glob_h := h_new;
> fi;# end if 18;
> #BOTTOM ADJUST ALL SERIES
> #END OPTIMIZE CODE
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> if (glob_subiter_method = 1 ) then # if number 18
> atomall();
> elif
> (glob_subiter_method = 2 ) then # if number 19
> subiter := 1;
> while (subiter <= 2) do # do number 2
> atomall();
> subiter := subiter + 1;
> od;# end do number 2;
> else
> subiter := 1;
> while (subiter <= 2 + ATS_MAX_TERMS) do # do number 2
> atomall();
> subiter := subiter + 1;
> od;# end do number 2;
> fi;# end if 19;
> if ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0))) then # if number 19
> display_alot(current_iter);
> fi;# end if 19;
> if ((glob_look_poles) and ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0)))) then # if number 19
> check_for_pole();
> fi;# end if 19;
> if (true) then # if number 19
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 19;
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y1;
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y1
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y1_higher_work[2,iii] := array_y1_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y1
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y1
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y1
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y1
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y1
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := ATS_MAX_TERMS;
> while (term_no >= 1) do # do number 2
> array_y1[term_no] := array_y1_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 3
> array_y1_higher[ord,term_no] := array_y1_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 3;
> term_no := term_no - 1;
> od;# end do number 2;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> #Jump Series array_y2;
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =2
> #sum_and_adjust array_y2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := glob__0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := glob__0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := glob__0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #END SUM AND ADJUST EQ =2
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := ATS_MAX_TERMS;
> while (term_no >= 1) do # do number 2
> array_y2[term_no] := array_y2_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 3
> array_y2_higher[ord,term_no] := array_y2_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 3;
> term_no := term_no - 1;
> od;# end do number 2;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> ;
> od;# end do number 1;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 19
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 19;
> if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec )) then # if number 19
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 19;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y1 , x , 1 ) = neg ( y2 ) ; ");
> omniout_str(INFO,"diff ( y2 , x , 1 ) = y1 ; ");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 19
> logstart(html_log_file);
> logitem_str(html_log_file,"2017-11-26T15:12:47-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"mtest2")
> ;
> logitem_str(html_log_file,"diff ( y1 , x , 1 ) = neg ( y2 ) ; ")
> ;
> logitem_complex(html_log_file,x_start)
> ;
> logitem_complex(html_log_file,x_end)
> ;
> logitem_complex(html_log_file,array_x[1])
> ;
> logitem_complex(html_log_file,glob_h)
> ;
> logitem_h_reason(html_log_file)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> glob_desired_digits_correct := 0.0;
> logitem_float(html_log_file,glob_desired_digits_correct)
> ;
> if (array_est_digits[1] <> -16) then # if number 20
> logitem_integer(html_log_file,array_est_digits[1])
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 20;
> if (glob_min_good_digits <> -16) then # if number 20
> logitem_integer(html_log_file,glob_min_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 20;
> if (glob_good_digits <> -16) then # if number 20
> logitem_integer(html_log_file,glob_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 20;
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> logitem_integer(html_log_file,ATS_MAX_TERMS)
> ;
> if (glob_type_given_pole = 0) then # if number 20
> logitem_str(html_log_file,"Not Given")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 4) then # if number 21
> logitem_str(html_log_file,"No Solution")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 5) then # if number 22
> logitem_str(html_log_file,"Some Pole")
> ;
> logitem_str(html_log_file,"????")
> ;
> elif
> (glob_type_given_pole = 3) then # if number 23
> logitem_str(html_log_file,"No Pole")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 1) then # if number 24
> 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 25
> logitem_str(html_log_file,"Complex Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> fi;# end if 25;
> if (glob_least_ratio_sing < glob_large_float) then # if number 25
> glob_least_ratio_sing := 0;
> logitem_float(html_log_file,glob_least_ratio_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 25;
> if (glob_least_3_sing < glob_large_float) then # if number 25
> logitem_float(html_log_file,glob_least_3_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 25;
> if (glob_least_6_sing < glob_large_float) then # if number 25
> glob_least_6_sing := 0.0;
> logitem_float(html_log_file,glob_least_6_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 25;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_time(html_log_file,(glob_clock_sec))
> ;
> if (c(glob_percent_done) < glob__100) then # if number 25
> logitem_time(html_log_file,(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 25;
> log_revs(html_log_file," 309 | ")
> ;
> logitem_str(html_log_file,"mtest2 diffeq.mxt")
> ;
> logitem_str(html_log_file,"mtest2 maple results")
> ;
> logitem_str(html_log_file,"Poor Accuracy - Not sure of algorithm for multiple equations")
> ;
> logend(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logitem_str(html_log_file,"diff ( y2 , x , 1 ) = y1 ; ")
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> ;
> glob_desired_digits_correct := 0.0;
> logditto(html_log_file)
> ;
> if (array_est_digits[2] <> -16) then # if number 25
> logitem_integer(html_log_file,array_est_digits[2])
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 25;
> if (glob_min_good_digits <> -16) then # if number 25
> logitem_integer(html_log_file,glob_min_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 25;
> if (glob_good_digits <> -16) then # if number 25
> logitem_integer(html_log_file,glob_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 25;
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> logditto(html_log_file)
> ;
> if (glob_type_given_pole = 0) then # if number 25
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> elif
> (glob_type_given_pole = 4) then # if number 26
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> elif
> (glob_type_given_pole = 5) then # if number 27
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> elif
> (glob_type_given_pole = 3) then # if number 28
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> elif
> (glob_type_given_pole = 1) then # if number 29
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> elif
> (glob_type_given_pole = 2) then # if number 30
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> fi;# end if 30;
> if (glob_least_ratio_sing < glob_large_float) then # if number 30
> glob_least_ratio_sing := 0;
> logditto(html_log_file)
> ;
> else
> logditto(html_log_file)
> ;
> fi;# end if 30;
> if (glob_least_3_sing < glob_large_float) then # if number 30
> logditto(html_log_file)
> ;
> else
> logditto(html_log_file)
> ;
> fi;# end if 30;
> if (glob_least_6_sing < glob_large_float) then # if number 30
> glob_least_6_sing := 0.0;
> logditto(html_log_file)
> ;
> else
> logditto(html_log_file)
> ;
> fi;# end if 30;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> if (c(glob_percent_done) < glob__100) then # if number 30
> logditto(html_log_file)
> ;
> 0;
> else
> logditto(html_log_file)
> ;
> 0;
> fi;# end if 30;
> logditto(html_log_file);
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 29;
> if (glob_html_log) then # if number 29
> fclose(html_log_file);
> fi;# end if 29
> ;
> ;;
> end;
> # End Function number 12
> #END OUTFILEMAIN
> end;
Warning, `h_new` is implicitly declared local to procedure `main`
Warning, `ratio` is implicitly declared local to procedure `main`
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max,
term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order,
sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it,
last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err,
estimated_step_error, min_value, est_answer, found_h, repeat_it, h_new,
ratio;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_y1_init,
array_y2_init, array_norms, array_fact_1, array_1st_rel_error,
array_last_rel_error, array_est_rel_error, array_max_est_error,
array_type_pole, array_type_real_pole, array_type_complex_pole,
array_est_digits, array_y1, array_x, array_y2, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_m1, array_y1_higher, array_y1_higher_work,
array_y1_higher_work2, array_y1_set_initial, array_y2_higher,
array_y2_higher_work, array_y2_higher_work2, array_y2_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
ATS_MAX_TERMS := 40;
Digits := 64;
max_terms := 40;
glob_html_log := true;
array_y1_init := Array(0 .. 40, []);
array_y2_init := Array(0 .. 40, []);
array_norms := Array(0 .. 40, []);
array_fact_1 := Array(0 .. 40, []);
array_1st_rel_error := Array(0 .. 3, []);
array_last_rel_error := Array(0 .. 3, []);
array_est_rel_error := Array(0 .. 3, []);
array_max_est_error := Array(0 .. 3, []);
array_type_pole := Array(0 .. 3, []);
array_type_real_pole := Array(0 .. 3, []);
array_type_complex_pole := Array(0 .. 3, []);
array_est_digits := Array(0 .. 3, []);
array_y1 := Array(0 .. 40, []);
array_x := Array(0 .. 40, []);
array_y2 := Array(0 .. 40, []);
array_tmp0 := Array(0 .. 40, []);
array_tmp1 := Array(0 .. 40, []);
array_tmp2 := Array(0 .. 40, []);
array_tmp3 := Array(0 .. 40, []);
array_m1 := Array(0 .. 40, []);
array_y1_higher := Array(0 .. 2, 0 .. 41, []);
array_y1_higher_work := Array(0 .. 2, 0 .. 41, []);
array_y1_higher_work2 := Array(0 .. 2, 0 .. 41, []);
array_y1_set_initial := Array(0 .. 3, 0 .. 41, []);
array_y2_higher := Array(0 .. 2, 0 .. 41, []);
array_y2_higher_work := Array(0 .. 2, 0 .. 41, []);
array_y2_higher_work2 := Array(0 .. 2, 0 .. 41, []);
array_y2_set_initial := Array(0 .. 3, 0 .. 41, []);
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 .. 40, 0 .. 41, []);
term := 1;
while term <= 40 do array_y1_init[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 40 do array_y2_init[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 40 do array_norms[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 40 do array_fact_1[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 3 do array_1st_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 3 do
array_last_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 3 do array_est_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 3 do array_max_est_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 3 do array_type_pole[term] := 0; term := term + 1 end do;
term := 1;
while term <= 3 do array_type_real_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 3 do array_type_complex_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 3 do array_est_digits[term] := 0; term := term + 1 end do
;
term := 1;
while term <= 40 do array_y1[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_x[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_y2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp0[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp1[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp3[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_m1[term] := c(0.); term := term + 1 end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 40 do
array_y1_higher[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 40 do
array_y1_higher_work[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 40 do
array_y1_higher_work2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 40 do
array_y1_set_initial[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 40 do
array_y2_higher[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 40 do
array_y2_higher_work[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 40 do
array_y2_higher_work2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 40 do
array_y2_set_initial[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 3 do
array_given_rad_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 3 do
array_given_ord_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 4 do
array_rad_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 4 do
array_ord_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 40 do
term := 1;
while term <= 40 do
array_fact_2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
zero_ats_ar(array_y1);
zero_ats_ar(array_x);
zero_ats_ar(array_y2);
zero_ats_ar(array_tmp0);
zero_ats_ar(array_tmp1);
zero_ats_ar(array_tmp2);
zero_ats_ar(array_tmp3);
zero_ats_ar(array_m1);
zero_ats_ar(array_const_1);
array_const_1[1] := c(1);
zero_ats_ar(array_const_0D0);
array_const_0D0[1] := c(0.);
zero_ats_ar(array_m1);
array_m1[1] := glob__m1;
iiif := 0;
while iiif <= ATS_MAX_TERMS do
jjjf := 0;
while jjjf <= ATS_MAX_TERMS do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
glob_yes_pole := 4;
glob_no_pole := 3;
glob_not_given := 0;
glob_no_sing_tests := 4;
glob_ratio_test := 1;
glob_three_term_test := 2;
glob_six_term_test := 3;
glob_log_10 := log(c(10.0));
MAX_UNCHANGED := 10;
glob__small := c(0.1*10^(-50));
glob_small_float := c(0.1*10^(-50));
glob_smallish_float := c(0.1*10^(-60));
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob__m2 := c(-2);
glob__m1 := c(-1);
glob__0 := c(0);
glob__1 := c(1);
glob__2 := c(2);
glob__3 := c(3);
glob__4 := c(4);
glob__5 := c(5);
glob__8 := c(8);
glob__10 := c(10);
glob__100 := c(100);
glob__pi := c(0.);
glob__0_5 := c(0.5);
glob__0_8 := c(0.8);
glob__m0_8 := c(-0.8);
glob__0_25 := c(0.25);
glob__0_125 := c(0.125);
glob_h := 0.1;
glob_nxt := 1;
glob_prec := c(0.10*10^(-15));
glob_check_sign := c(1.0);
glob_desired_digits_correct := c(8.0);
glob_max_estimated_step_error := c(0.);
glob_ratio_of_radius := c(0.1);
glob_percent_done := c(0.);
glob_total_exp_sec := c(0.1);
glob_optimal_expect_sec := c(0.1);
glob_estimated_size_answer := c(100.0);
glob_almost_1 := c(0.9990);
glob_clock_sec := c(0.);
glob_clock_start_sec := c(0.);
glob_disp_incr := c(0.1);
glob_diff_rc_fm := c(0.1);
glob_diff_rc_fmm1 := c(0.1);
glob_diff_rc_fmm2 := c(0.1);
glob_diff_ord_fm := c(0.1);
glob_diff_ord_fmm1 := c(0.1);
glob_diff_ord_fmm2 := c(0.1);
glob_six_term_ord_save := c(0.1);
glob_guess_error_rc := c(0.1);
glob_guess_error_ord := c(0.1);
glob_least_given_sing := c(0.99*10^201);
glob_least_ratio_sing := c(0.99*10^201);
glob_least_3_sing := c(0.99*10^101);
glob_least_6_sing := c(0.99*10^101);
glob_last_good_h := c(0.1);
glob_max_h := c(0.1);
glob_min_h := c(0.1*10^(-5));
glob_display_interval := c(0.1);
glob_abserr := c(0.1*10^(-10));
glob_relerr := c(0.1*10^(-10));
glob_min_pole_est := c(0.1*10^10);
glob_max_rel_trunc_err := c(0.1*10^(-10));
glob_max_trunc_err := c(0.1*10^(-10));
glob_max_hours := c(0.);
glob_optimal_clock_start_sec := c(0.);
glob_optimal_start := c(0.);
glob_upper_ratio_limit := c(1.0001);
glob_lower_ratio_limit := c(0.9999);
glob_max_sec := c(10000.0);
glob_orig_start_sec := c(0.);
glob_normmax := c(0.);
glob_max_minutes := c(0.);
glob_next_display := c(0.);
glob_est_digits := 1;
glob_subiter_method := 3;
glob_html_log := true;
glob_min_good_digits := 99999;
glob_good_digits := 0;
glob_min_apfp_est_good_digits := 99999;
glob_apfp_est_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
glob_h_reason := 0;
glob_sec_in_minute := 60;
glob_min_in_hour := 60;
glob_hours_in_day := 24;
glob_days_in_year := 365;
glob_sec_in_hour := 3600;
glob_sec_in_day := 86400;
glob_sec_in_year := 31536000;
glob_not_yet_finished := true;
glob_initial_pass := true;
glob_not_yet_start_msg := true;
glob_reached_optimal_h := false;
glob_optimal_done := false;
glob_type_given_pole := 0;
glob_optimize := false;
glob_look_poles := false;
glob_dump_closed_form := false;
glob_max_iter := 10000;
glob_no_eqs := 0;
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_start := 0;
glob_iter := 0;
array_y1_set_initial[1, 1] := true;
array_y1_set_initial[1, 2] := false;
array_y1_set_initial[1, 3] := false;
array_y1_set_initial[1, 4] := false;
array_y1_set_initial[1, 5] := false;
array_y1_set_initial[1, 6] := false;
array_y1_set_initial[1, 7] := false;
array_y1_set_initial[1, 8] := false;
array_y1_set_initial[1, 9] := false;
array_y1_set_initial[1, 10] := false;
array_y1_set_initial[1, 11] := false;
array_y1_set_initial[1, 12] := false;
array_y1_set_initial[1, 13] := false;
array_y1_set_initial[1, 14] := false;
array_y1_set_initial[1, 15] := false;
array_y1_set_initial[1, 16] := false;
array_y1_set_initial[1, 17] := false;
array_y1_set_initial[1, 18] := false;
array_y1_set_initial[1, 19] := false;
array_y1_set_initial[1, 20] := false;
array_y1_set_initial[1, 21] := false;
array_y1_set_initial[1, 22] := false;
array_y1_set_initial[1, 23] := false;
array_y1_set_initial[1, 24] := false;
array_y1_set_initial[1, 25] := false;
array_y1_set_initial[1, 26] := false;
array_y1_set_initial[1, 27] := false;
array_y1_set_initial[1, 28] := false;
array_y1_set_initial[1, 29] := false;
array_y1_set_initial[1, 30] := false;
array_y1_set_initial[1, 31] := false;
array_y1_set_initial[1, 32] := false;
array_y1_set_initial[1, 33] := false;
array_y1_set_initial[1, 34] := false;
array_y1_set_initial[1, 35] := false;
array_y1_set_initial[1, 36] := false;
array_y1_set_initial[1, 37] := false;
array_y1_set_initial[1, 38] := false;
array_y1_set_initial[1, 39] := false;
array_y1_set_initial[1, 40] := false;
array_y2_set_initial[2, 1] := true;
array_y2_set_initial[2, 2] := false;
array_y2_set_initial[2, 3] := false;
array_y2_set_initial[2, 4] := false;
array_y2_set_initial[2, 5] := false;
array_y2_set_initial[2, 6] := false;
array_y2_set_initial[2, 7] := false;
array_y2_set_initial[2, 8] := false;
array_y2_set_initial[2, 9] := false;
array_y2_set_initial[2, 10] := false;
array_y2_set_initial[2, 11] := false;
array_y2_set_initial[2, 12] := false;
array_y2_set_initial[2, 13] := false;
array_y2_set_initial[2, 14] := false;
array_y2_set_initial[2, 15] := false;
array_y2_set_initial[2, 16] := false;
array_y2_set_initial[2, 17] := false;
array_y2_set_initial[2, 18] := false;
array_y2_set_initial[2, 19] := false;
array_y2_set_initial[2, 20] := false;
array_y2_set_initial[2, 21] := false;
array_y2_set_initial[2, 22] := false;
array_y2_set_initial[2, 23] := false;
array_y2_set_initial[2, 24] := false;
array_y2_set_initial[2, 25] := false;
array_y2_set_initial[2, 26] := false;
array_y2_set_initial[2, 27] := false;
array_y2_set_initial[2, 28] := false;
array_y2_set_initial[2, 29] := false;
array_y2_set_initial[2, 30] := false;
array_y2_set_initial[2, 31] := false;
array_y2_set_initial[2, 32] := false;
array_y2_set_initial[2, 33] := false;
array_y2_set_initial[2, 34] := false;
array_y2_set_initial[2, 35] := false;
array_y2_set_initial[2, 36] := false;
array_y2_set_initial[2, 37] := false;
array_y2_set_initial[2, 38] := false;
array_y2_set_initial[2, 39] := false;
array_y2_set_initial[2, 40] := false;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
ATS_MAX_TERMS := 40;
glob_iolevel := INFO;
glob_orig_start_sec := elapsed_time_seconds();
glob_display_flag := true;
glob_no_eqs := 2;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 10000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/mtest2postcpx.cpx#################");
omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = neg ( y2 ) ; ");
omniout_str(ALWAYS, "diff ( y2 , x , 1 ) = y1 ; ");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=64;");
omniout_str(ALWAYS, "max_terms:=40;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := 0.2 + 0.1 * I;");
omniout_str(ALWAYS, "x_end := 99.0 + 99.0 * I;");
omniout_str(ALWAYS, "array_y1_init[0 + 1] := exact_soln_y1(x_start);");
omniout_str(ALWAYS, "array_y2_init[0 + 1] := exact_soln_y2(x_start);");
omniout_str(ALWAYS, "glob_max_h := 0.00001;");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_type_given_pole := 3;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=8;");
omniout_str(ALWAYS, "glob_max_minutes:=(3.0);");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "glob_max_iter:=10000;");
omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);");
omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);");
omniout_str(ALWAYS, "glob_look_poles:=true;");
omniout_str(ALWAYS, "glob_h:=c(0.001);");
omniout_str(ALWAYS, "glob_display_interval:=c(0.01);");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y1 := proc(x)");
omniout_str(ALWAYS, "return(cos(c(x)));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2 := proc(x)");
omniout_str(ALWAYS, "return(sin(c(x)));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "next_delta := proc()");
omniout_str(ALWAYS, "global glob_nxt, x_delta;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "x_delta := [ 0.001 + 0.00004 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
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omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.000 + 0.000 * I ];");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_nxt := glob_nxt + 1;");
omniout_str(ALWAYS, "it := x_delta[glob_nxt];");
omniout_str(ALWAYS, "return it;");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := glob__0;
glob_smallish_float := glob__0;
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob_almost_1 := c(0.99);
x_start := 0.2 + 0.1*I;
x_end := 99.0 + 99.0*I;
array_y1_init[1] := exact_soln_y1(x_start);
array_y2_init[1] := exact_soln_y2(x_start);
glob_max_h := 0.00001;
glob_look_poles := true;
glob_type_given_pole := 3;
glob_desired_digits_correct := 8;
glob_max_minutes := 3.0;
glob_subiter_method := 3;
glob_max_iter := 10000;
glob_upper_ratio_limit := c(1.000001);
glob_lower_ratio_limit := c(0.999999);
glob_look_poles := true;
glob_h := c(0.001);
glob_display_interval := c(0.01);
glob_last_good_h := glob_h;
glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours;
found_h := true;
glob_h := next_delta();
if
float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h)
then
h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius;
omniout_str(ALWAYS, "SETTING H FOR POLE");
glob_h_reason := 6;
if glob_check_sign*h_new < glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
h_new := glob_min_h;
glob_h_reason := 5
end if;
term := 1;
ratio := c(1.0);
while term <= ATS_MAX_TERMS do
array_y1[term] := array_y1[term]*ratio;
array_y1_higher[1, term] := array_y1_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
array_y2[term] := array_y2[term]*ratio;
array_y2_higher[1, term] := array_y2_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/float_abs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT)
end if;
found_h := true;
if found_h then
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := c(x_start);
array_x[2] := c(glob_h);
glob_next_display := c(x_start);
glob_min_pole_est := glob_larger_float;
glob_least_given_sing := glob_larger_float;
glob_least_ratio_sing := glob_larger_float;
glob_least_3_sing := glob_larger_float;
glob_least_6_sing := glob_larger_float;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y1[term_no] := array_y1_init[term_no]*
expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1));
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
if term_no < ATS_MAX_TERMS then
array_y1_higher[r_order, term_no] := array_y1_init[it]*
expt(glob_h, c(term_no - 1))/
c(factorial_1(term_no - 1))
end if;
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y2[term_no] := array_y2_init[term_no]*
expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1));
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
if term_no < ATS_MAX_TERMS then
array_y2_higher[r_order, term_no] := array_y2_init[it]*
expt(glob_h, c(term_no - 1))/
c(factorial_1(term_no - 1))
end if;
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
glob_clock_sec := elapsed_time_seconds();
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
found_h := true;
glob_h := next_delta();
if float_abs(glob_min_pole_est)*glob_ratio_of_radius <
float_abs(glob_h) then
h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius
;
omniout_str(ALWAYS, "SETTING H FOR POLE");
glob_h_reason := 6;
if glob_check_sign*h_new < glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
h_new := glob_min_h;
glob_h_reason := 5
end if;
term := 1;
ratio := c(1.0);
while term <= ATS_MAX_TERMS do
array_y1[term] := array_y1[term]*ratio;
array_y1_higher[1, term] := array_y1_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
array_y2[term] := array_y2[term]*ratio;
array_y2_higher[1, term] := array_y2_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/float_abs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_iter < glob_max_iter and
(glob_iter < 10 or not (Re(glob_h) = 0. and Im(glob_h) = 0.)) do
omniout_str(INFO, " ");
found_h := true;
glob_h := next_delta();
if float_abs(glob_min_pole_est)*glob_ratio_of_radius <
float_abs(glob_h) then
h_new :=
glob_check_sign*glob_min_pole_est*glob_ratio_of_radius;
omniout_str(ALWAYS, "SETTING H FOR POLE");
glob_h_reason := 6;
if glob_check_sign*h_new < glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
h_new := glob_min_h;
glob_h_reason := 5
end if;
term := 1;
ratio := c(1.0);
while term <= ATS_MAX_TERMS do
array_y1[term] := array_y1[term]*ratio;
array_y1_higher[1, term] :=
array_y1_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
array_y2[term] := array_y2[term]*ratio;
array_y2_higher[1, term] :=
array_y2_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/float_abs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
if glob_subiter_method = 1 then atomall()
elif glob_subiter_method = 2 then
subiter := 1;
while subiter <= 2 do atomall(); subiter := subiter + 1
end do
else
subiter := 1;
while subiter <= 2 + ATS_MAX_TERMS do
atomall(); subiter := subiter + 1
end do
end if;
if not (Re(glob_h) = 0. and Im(glob_h) = 0.) then
display_alot(current_iter)
end if;
if
glob_look_poles and not (Re(glob_h) = 0. and Im(glob_h) = 0.)
then check_for_pole()
end if;
glob_next_display := glob_next_display + glob_display_interval;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y1_higher_work[2, iii] := array_y1_higher[2, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
term_no := ATS_MAX_TERMS;
while 1 <= term_no do
array_y1[term_no] := array_y1_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y1_higher[ord, term_no] :=
array_y1_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
term_no := ATS_MAX_TERMS;
while 1 <= term_no do
array_y2[term_no] := array_y2_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y2_higher[ord, term_no] :=
array_y2_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if glob_max_sec <= elapsed_time_seconds() - glob_orig_start_sec
then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff ( y1 , x , 1 ) = neg ( y2 ) ; ")
;
omniout_str(INFO, "diff ( y2 , x , 1 ) = y1 ; ");
omniout_int(INFO, "Iterations ", 32, glob_iter,
4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2017-11-26T15:12:47-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"mtest2");
logitem_str(html_log_file,
"diff ( y1 , x , 1 ) = neg ( y2 ) ; ");
logitem_complex(html_log_file, x_start);
logitem_complex(html_log_file, x_end);
logitem_complex(html_log_file, array_x[1]);
logitem_complex(html_log_file, glob_h);
logitem_h_reason(html_log_file);
logitem_integer(html_log_file, Digits);
glob_desired_digits_correct := 0.;
logitem_float(html_log_file, glob_desired_digits_correct);
if array_est_digits[1] <> -16 then
logitem_integer(html_log_file, array_est_digits[1])
else logitem_str(html_log_file, "Unknown")
end if;
if glob_min_good_digits <> -16 then
logitem_integer(html_log_file, glob_min_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
if glob_good_digits <> -16 then
logitem_integer(html_log_file, glob_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
logitem_integer(html_log_file, ATS_MAX_TERMS);
if glob_type_given_pole = 0 then
logitem_str(html_log_file, "Not Given");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 4 then
logitem_str(html_log_file, "No Solution");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 5 then
logitem_str(html_log_file, "Some Pole");
logitem_str(html_log_file, "????")
elif glob_type_given_pole = 3 then
logitem_str(html_log_file, "No Pole");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 1 then
logitem_str(html_log_file, "Real Sing");
logitem_float(html_log_file, glob_least_given_sing)
elif glob_type_given_pole = 2 then
logitem_str(html_log_file, "Complex Sing");
logitem_float(html_log_file, glob_least_given_sing)
end if;
if glob_least_ratio_sing < glob_large_float then
glob_least_ratio_sing := 0;
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
glob_least_6_sing := 0.;
logitem_float(html_log_file, glob_least_6_sing)
else logitem_str(html_log_file, "NONE")
end if;
logitem_integer(html_log_file, glob_iter);
logitem_time(html_log_file, glob_clock_sec);
if c(glob_percent_done) < glob__100 then
logitem_time(html_log_file, glob_total_exp_sec); 0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 309 | ");
logitem_str(html_log_file,
"mtest2 diffeq.mxt");
logitem_str(html_log_file, "mtest2 maple results");
logitem_str(html_log_file, "Poor Accuracy - Not sure of algor\
ithm for multiple equations");
logend(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logitem_str(html_log_file,
"diff ( y2 , x , 1 ) = y1 ; ");
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
glob_desired_digits_correct := 0.;
logditto(html_log_file);
if array_est_digits[2] <> -16 then
logitem_integer(html_log_file, array_est_digits[2])
else logitem_str(html_log_file, "Unknown")
end if;
if glob_min_good_digits <> -16 then
logitem_integer(html_log_file, glob_min_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
if glob_good_digits <> -16 then
logitem_integer(html_log_file, glob_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
logditto(html_log_file);
if glob_type_given_pole = 0 then
logditto(html_log_file); logditto(html_log_file)
elif glob_type_given_pole = 4 then
logditto(html_log_file); logditto(html_log_file)
elif glob_type_given_pole = 5 then
logditto(html_log_file); logditto(html_log_file)
elif glob_type_given_pole = 3 then
logditto(html_log_file); logditto(html_log_file)
elif glob_type_given_pole = 1 then
logditto(html_log_file); logditto(html_log_file)
elif glob_type_given_pole = 2 then
logditto(html_log_file); logditto(html_log_file)
end if;
if glob_least_ratio_sing < glob_large_float then
glob_least_ratio_sing := 0; 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
glob_least_6_sing := 0.; logditto(html_log_file)
else logditto(html_log_file)
end if;
logditto(html_log_file);
logditto(html_log_file);
if c(glob_percent_done) < glob__100 then
logditto(html_log_file); 0
else logditto(html_log_file); 0
end if;
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end if
end proc
# End Function number 12
> main();
memory used=4.0MB, alloc=40.3MB, time=0.08
##############ECHO OF PROBLEM#################
##############temp/mtest2postcpx.cpx#################
diff ( y1 , x , 1 ) = neg ( y2 ) ;
diff ( y2 , x , 1 ) = y1 ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=64;
max_terms:=40;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.2 + 0.1 * I;
x_end := 99.0 + 99.0 * I;
array_y1_init[0 + 1] := exact_soln_y1(x_start);
array_y2_init[0 + 1] := exact_soln_y2(x_start);
glob_max_h := 0.00001;
glob_look_poles := true;
glob_type_given_pole := 3;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=8;
glob_max_minutes:=(3.0);
glob_subiter_method:=3;
glob_max_iter:=10000;
glob_upper_ratio_limit:=c(1.000001);
glob_lower_ratio_limit:=c(0.999999);
glob_look_poles:=true;
glob_h:=c(0.001);
glob_display_interval:=c(0.01);
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y1 := proc(x)
return(cos(c(x)));
end;
exact_soln_y2 := proc(x)
return(sin(c(x)));
end;
next_delta := proc()
global glob_nxt, x_delta;
x_delta := [ 0.001 + 0.00004 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.000 + 0.000 * I ];
glob_nxt := glob_nxt + 1;
it := x_delta[glob_nxt];
return it;
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = 0.2 0.1
h = 0.0001 0.005
y1[1] (numeric) = 0.984970995703 -0.0199000611944
y1[1] (closed_form) = 0.984970995703 -0.0199000611944
absolute error = 0
relative error = 0 %
Correct digits = 62
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.199663505514 0.0981700839054
absolute error = 0
relative error = 0 %
Correct digits = 62
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=56.3MB, alloc=40.3MB, time=0.76
x[1] = 0.2001 0.105
h = 0.0001 0.003
y1[1] (numeric) = 0.985441879772 -0.0209081957303
y1[1] (closed_form) = 0.985454178853 -0.020908941147
absolute error = 1.232e-05
relative error = 0.00125 %
Correct digits = 5
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.199864048451 0.103094096154
absolute error = 0.004928
relative error = 2.191 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2002 0.108
h = 0.001 0.001
y1[1] (numeric) = 0.985716423673 -0.0215170032553
y1[1] (closed_form) = 0.985747898456 -0.0215192332672
absolute error = 3.155e-05
relative error = 0.0032 %
Correct digits = 4
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.200026250547 0.106048775656
absolute error = 0.007887
relative error = 3.484 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=105.7MB, alloc=44.3MB, time=1.43
x[1] = 0.2012 0.109
h = 0.001 0.003
y1[1] (numeric) = 0.985614930251 -0.0218148368447
y1[1] (closed_form) = 0.98565389936 -0.02182629401
absolute error = 4.062e-05
relative error = 0.00412 %
Correct digits = 4
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.201033624049 0.107012803959
absolute error = 0.008948
relative error = 3.929 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=155.1MB, alloc=44.3MB, time=2.08
x[1] = 0.2022 0.112
h = 0.0001 0.004
y1[1] (numeric) = 0.985709776997 -0.0225119974451
y1[1] (closed_form) = 0.985777780735 -0.0225394530237
absolute error = 7.334e-05
relative error = 0.007438 %
Correct digits = 4
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.20208588634 0.109947767175
absolute error = 0.01202
relative error = 5.227 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2023 0.116
h = 0.003 0.006
y1[1] (numeric) = 0.986082490982 -0.0233204684756
y1[1] (closed_form) = 0.986205236512 -0.0233593681006
absolute error = 0.0001288
relative error = 0.01305 %
Correct digits = 4
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.202276282617 0.113889433029
absolute error = 0.01594
relative error = 6.865 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=204.4MB, alloc=44.3MB, time=2.74
x[1] = 0.2053 0.122
h = 0.0001 0.005
y1[1] (numeric) = 0.986072520969 -0.0248129597604
y1[1] (closed_form) = 0.986294628552 -0.0249327686785
absolute error = 0.0002524
relative error = 0.02558 %
Correct digits = 4
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.205379884307 0.119734490579
absolute error = 0.02231
relative error = 9.384 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=253.8MB, alloc=44.3MB, time=3.40
x[1] = 0.2054 0.127
h = 0.0001 0.003
y1[1] (numeric) = 0.986543405038 -0.0258210942963
y1[1] (closed_form) = 0.986885076562 -0.0259724506573
absolute error = 0.0003737
relative error = 0.03785 %
Correct digits = 3
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.205605805459 0.124664884332
absolute error = 0.02715
relative error = 11.29 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2055 0.13
h = 0.001 0.001
y1[1] (numeric) = 0.986817948939 -0.0264299018213
y1[1] (closed_form) = 0.987242939361 -0.0266021483526
absolute error = 0.0004586
relative error = 0.04643 %
Correct digits = 3
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.205783373477 0.127623445418
absolute error = 0.03008
relative error = 12.42 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=303.4MB, alloc=44.3MB, time=4.06
x[1] = 0.2065 0.131
h = 0.001 0.003
y1[1] (numeric) = 0.986716455518 -0.0267277354107
y1[1] (closed_form) = 0.987164752719 -0.0269365423883
absolute error = 0.0004945
relative error = 0.05008 %
Correct digits = 3
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.206797346508 0.128583880088
absolute error = 0.03124
relative error = 12.83 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=352.9MB, alloc=44.3MB, time=4.72
x[1] = 0.2075 0.134
h = 0.0001 0.004
y1[1] (numeric) = 0.986811302264 -0.0274248960111
y1[1] (closed_form) = 0.987347574353 -0.0276885887299
absolute error = 0.0005976
relative error = 0.0605 %
Correct digits = 3
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.207866538189 0.131518334591
absolute error = 0.03434
relative error = 13.96 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2076 0.138
h = 0.003 0.006
y1[1] (numeric) = 0.987184016249 -0.0282333670416
y1[1] (closed_form) = 0.98786074505 -0.0285338253451
absolute error = 0.0007404
relative error = 0.07492 %
Correct digits = 3
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.208077742888 0.135465934863
absolute error = 0.03823
relative error = 15.4 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=402.3MB, alloc=44.3MB, time=5.38
x[1] = 0.2106 0.144
h = 0.0001 0.005
y1[1] (numeric) = 0.987174046236 -0.0297258583264
y1[1] (closed_form) = 0.988062120836 -0.0302068649647
absolute error = 0.00101
relative error = 0.1022 %
Correct digits = 3
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.211217824674 0.141305588706
absolute error = 0.04466
relative error = 17.57 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=451.8MB, alloc=44.3MB, time=6.04
x[1] = 0.2107 0.149
h = 0.0001 0.003
y1[1] (numeric) = 0.987644930305 -0.0307339928623
y1[1] (closed_form) = 0.988759860432 -0.0312779606873
absolute error = 0.001241
relative error = 0.1254 %
Correct digits = 3
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.211470376899 0.146244559154
absolute error = 0.0495
relative error = 19.25 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2108 0.152
h = 0.001 0.001
y1[1] (numeric) = 0.987919474206 -0.0313428003873
y1[1] (closed_form) = 0.989181882728 -0.0319274345111
absolute error = 0.001391
relative error = 0.1406 %
Correct digits = 3
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.211664081786 0.149208309288
absolute error = 0.05243
relative error = 20.25 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=501.3MB, alloc=44.3MB, time=6.70
x[1] = 0.2118 0.153
h = 0.001 0.003
y1[1] (numeric) = 0.987817980785 -0.0316406339767
y1[1] (closed_form) = 0.989119394907 -0.0322892960632
absolute error = 0.001454
relative error = 0.1469 %
Correct digits = 3
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.212685340631 0.150165351732
absolute error = 0.0536
relative error = 20.59 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2128 0.156
h = 0.0001 0.004
y1[1] (numeric) = 0.987912827531 -0.0323377945771
y1[1] (closed_form) = 0.989361064761 -0.033080615245
absolute error = 0.001628
relative error = 0.1644 %
Correct digits = 3
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.213772633535 0.153100386053
absolute error = 0.05671
relative error = 21.57 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=550.7MB, alloc=44.3MB, time=7.36
x[1] = 0.2129 0.16
h = 0.003 0.006
y1[1] (numeric) = 0.988285541516 -0.0331462656076
y1[1] (closed_form) = 0.989959987221 -0.0339516784415
absolute error = 0.001858
relative error = 0.1876 %
Correct digits = 3
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.214005663601 0.157055671287
absolute error = 0.06061
relative error = 22.83 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=600.2MB, alloc=44.3MB, time=8.02
x[1] = 0.2159 0.166
h = 0.0001 0.005
y1[1] (numeric) = 0.988275571503 -0.0346387568924
y1[1] (closed_form) = 0.990273048382 -0.0357251668441
absolute error = 0.002274
relative error = 0.2295 %
Correct digits = 3
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.217185019028 0.162891851533
absolute error = 0.06705
relative error = 24.7 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.216 0.171
h = 0.0001 0.003
y1[1] (numeric) = 0.988746455572 -0.0356468914283
y1[1] (closed_form) = 0.99107814788 -0.0368283273727
absolute error = 0.002614
relative error = 0.2636 %
Correct digits = 3
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.217465469327 0.167841591564
absolute error = 0.07191
relative error = 26.18 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=649.6MB, alloc=44.3MB, time=8.68
x[1] = 0.2161 0.174
h = 0.001 0.001
y1[1] (numeric) = 0.989020999473 -0.0362556989533
y1[1] (closed_form) = 0.991564370614 -0.037497971858
absolute error = 0.002831
relative error = 0.2853 %
Correct digits = 3
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.217676090595 0.170811836812
absolute error = 0.07484
relative error = 27.05 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=699.2MB, alloc=44.3MB, time=9.34
x[1] = 0.2171 0.175
h = 0.001 0.003
y1[1] (numeric) = 0.988919506051 -0.0365535325427
y1[1] (closed_form) = 0.991517468733 -0.0378874513342
absolute error = 0.00292
relative error = 0.2943 %
Correct digits = 3
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.218705324068 0.171765685192
absolute error = 0.07602
relative error = 27.34 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2181 0.178
h = 0.0001 0.004
y1[1] (numeric) = 0.989014352797 -0.0372506931431
y1[1] (closed_form) = 0.99181791244 -0.0387184604982
absolute error = 0.003165
relative error = 0.3188 %
Correct digits = 2
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.21981189842 0.174702383903
absolute error = 0.07914
relative error = 28.19 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=748.7MB, alloc=44.3MB, time=10.00
x[1] = 0.2182 0.182
h = 0.003 0.006
y1[1] (numeric) = 0.989387066783 -0.0380591641736
y1[1] (closed_form) = 0.992502656578 -0.039615887093
absolute error = 0.003483
relative error = 0.3506 %
Correct digits = 2
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.220067782538 0.178667103058
absolute error = 0.08304
relative error = 29.3 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=798.1MB, alloc=44.3MB, time=10.65
x[1] = 0.2212 0.188
h = 0.0001 0.005
y1[1] (numeric) = 0.989377096769 -0.0395516554584
y1[1] (closed_form) = 0.992927132236 -0.0414907058638
absolute error = 0.004045
relative error = 0.407 %
Correct digits = 2
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.223289222248 0.184501729071
absolute error = 0.08951
relative error = 30.9 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2213 0.193
h = 0.0001 0.003
y1[1] (numeric) = 0.989847980838 -0.0405597899943
y1[1] (closed_form) = 0.993839701424 -0.0426266219179
absolute error = 0.004495
relative error = 0.4519 %
Correct digits = 2
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.223598852851 0.18946442998
absolute error = 0.09438
relative error = 32.2 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=847.5MB, alloc=44.3MB, time=11.31
x[1] = 0.2214 0.196
h = 0.001 0.001
y1[1] (numeric) = 0.99012252474 -0.0411685975193
y1[1] (closed_form) = 0.994390190103 -0.0433168557667
absolute error = 0.004778
relative error = 0.48 %
Correct digits = 2
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.223827179242 0.192442475424
absolute error = 0.09732
relative error = 32.97 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2224 0.197
h = 0.0001 0.004
y1[1] (numeric) = 0.990021031318 -0.0414664311087
y1[1] (closed_form) = 0.994358761943 -0.0437341198011
absolute error = 0.004895
relative error = 0.4918 %
Correct digits = 2
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.224865079048 0.193393324585
absolute error = 0.0985
relative error = 33.21 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=897.0MB, alloc=44.3MB, time=11.98
x[1] = 0.2225 0.201
h = 0.003 0.006
y1[1] (numeric) = 0.990393745303 -0.0422749021391
y1[1] (closed_form) = 0.995117783028 -0.0446536693978
absolute error = 0.005289
relative error = 0.531 %
Correct digits = 2
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.22514132782 0.197367853008
absolute error = 0.1024
relative error = 34.21 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=946.4MB, alloc=44.3MB, time=12.63
x[1] = 0.2255 0.207
h = 0.0001 0.005
y1[1] (numeric) = 0.99038377529 -0.0437673934239
y1[1] (closed_form) = 0.995639187091 -0.0466151477439
absolute error = 0.005977
relative error = 0.5997 %
Correct digits = 2
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.228401244886 0.203203217343
absolute error = 0.1089
relative error = 35.62 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2256 0.212
h = 0.0001 0.003
y1[1] (numeric) = 0.990854659359 -0.0447755279599
y1[1] (closed_form) = 0.996644784226 -0.0477785595758
absolute error = 0.006523
relative error = 0.6537 %
Correct digits = 2
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.228736842239 0.208179197251
absolute error = 0.1138
relative error = 36.79 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=995.8MB, alloc=44.3MB, time=13.30
x[1] = 0.2257 0.215
h = 0.001 0.001
y1[1] (numeric) = 0.99112920326 -0.0453843354848
y1[1] (closed_form) = 0.997250914553 -0.0484861029005
absolute error = 0.006863
relative error = 0.6873 %
Correct digits = 2
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.228980933686 0.211165225341
absolute error = 0.1167
relative error = 37.48 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=1045.4MB, alloc=44.3MB, time=13.96
x[1] = 0.2267 0.216
h = 0.001 0.003
y1[1] (numeric) = 0.991027709838 -0.0456821690742
y1[1] (closed_form) = 0.997233050211 -0.0489272463045
absolute error = 0.007003
relative error = 0.7014 %
Correct digits = 2
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.230026882185 0.212113760823
absolute error = 0.1179
relative error = 37.69 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2277 0.219
h = 0.0001 0.004
y1[1] (numeric) = 0.991122556585 -0.0463793296747
y1[1] (closed_form) = 0.997643206403 -0.0498326297333
absolute error = 0.007379
relative error = 0.7387 %
Correct digits = 2
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.231172457892 0.215056693881
absolute error = 0.1211
relative error = 38.34 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=1094.8MB, alloc=44.3MB, time=14.61
x[1] = 0.2278 0.223
h = 0.003 0.006
y1[1] (numeric) = 0.99149527057 -0.0471878007051
y1[1] (closed_form) = 0.998488274272 -0.0507796253382
absolute error = 0.007862
relative error = 0.7863 %
Correct digits = 2
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.231473488309 0.219043920937
absolute error = 0.125
relative error = 39.22 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=1144.2MB, alloc=44.3MB, time=15.27
x[1] = 0.2308 0.229
h = 0.0001 0.005
y1[1] (numeric) = 0.991485300557 -0.0486802919899
y1[1] (closed_form) = 0.999120673377 -0.0528442693503
absolute error = 0.008697
relative error = 0.8692 %
Correct digits = 2
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.234780748461 0.224881308725
absolute error = 0.1315
relative error = 40.44 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2309 0.234
h = 0.0001 0.003
y1[1] (numeric) = 0.991956184626 -0.0496884265259
y1[1] (closed_form) = 1.00023406385 -0.0540418262429
absolute error = 0.009353
relative error = 0.9337 %
Correct digits = 2
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.235147930256 0.229874340896
absolute error = 0.1364
relative error = 41.48 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=1193.7MB, alloc=44.3MB, time=15.93
x[1] = 0.231 0.237
h = 0.001 0.001
y1[1] (numeric) = 0.992230728527 -0.0502972340508
y1[1] (closed_form) = 1.00090465285 -0.0547708016147
absolute error = 0.00976
relative error = 0.9736 %
Correct digits = 2
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.235411205787 0.232870606108
absolute error = 0.1394
relative error = 42.09 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.232 0.238
h = 0.001 0.003
y1[1] (numeric) = 0.992129235105 -0.0505950676402
y1[1] (closed_form) = 1.00090205732 -0.0552400843304
absolute error = 0.009927
relative error = 0.9903 %
Correct digits = 2
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.236467114427 0.233816504196
absolute error = 0.1406
relative error = 42.26 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=1243.3MB, alloc=44.3MB, time=16.59
x[1] = 0.233 0.241
h = 0.0001 0.004
y1[1] (numeric) = 0.992224081851 -0.0512922282407
y1[1] (closed_form) = 1.00137087728 -0.056186527571
absolute error = 0.01037
relative error = 1.034 %
Correct digits = 2
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.23763538856 0.236764198911
absolute error = 0.1437
relative error = 42.84 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=1292.7MB, alloc=44.3MB, time=17.24
x[1] = 0.2331 0.245
h = 0.003 0.006
y1[1] (numeric) = 0.992596795836 -0.0521006992711
y1[1] (closed_form) = 1.00230215637 -0.0571615980259
absolute error = 0.01095
relative error = 1.09 %
Correct digits = 2
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.23796226776 0.240765872262
absolute error = 0.1476
relative error = 43.62 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2361 0.251
h = 0.0001 0.005
y1[1] (numeric) = 0.992586825823 -0.0535931905559
y1[1] (closed_form) = 1.00304535733 -0.059330496509
absolute error = 0.01193
relative error = 1.187 %
Correct digits = 2
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.241319740236 0.246607173591
absolute error = 0.1542
relative error = 44.68 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=1342.0MB, alloc=44.3MB, time=17.90
x[1] = 0.2362 0.256
h = 0.0001 0.003
y1[1] (numeric) = 0.993057709892 -0.0546013250919
y1[1] (closed_form) = 1.00426676946 -0.0605630041181
absolute error = 0.0127
relative error = 1.262 %
Correct digits = 2
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.241719838343 0.251619448828
absolute error = 0.1591
relative error = 45.6 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=1391.4MB, alloc=44.3MB, time=18.56
x[1] = 0.2363 0.259
h = 0.001 0.001
y1[1] (numeric) = 0.993332253793 -0.0552101326168
y1[1] (closed_form) = 1.00500195286 -0.0613139002867
absolute error = 0.01317
relative error = 1.308 %
Correct digits = 2
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.242003116773 0.254627255827
absolute error = 0.1621
relative error = 46.14 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2373 0.26
h = 0.001 0.003
y1[1] (numeric) = 0.993230760372 -0.0555079662063
y1[1] (closed_form) = 1.00501451552 -0.0618115356655
absolute error = 0.01336
relative error = 1.327 %
Correct digits = 2
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.243069687568 0.255570701521
absolute error = 0.1633
relative error = 46.29 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=1440.7MB, alloc=44.3MB, time=19.22
x[1] = 0.2383 0.263
h = 0.0001 0.004
y1[1] (numeric) = 0.993325607118 -0.0562051268067
y1[1] (closed_form) = 1.00554199227 -0.0627995795601
absolute error = 0.01388
relative error = 1.378 %
Correct digits = 2
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.244261880223 0.258524229352
absolute error = 0.1664
relative error = 46.8 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=1490.1MB, alloc=44.3MB, time=19.87
x[1] = 0.2384 0.267
h = 0.003 0.006
y1[1] (numeric) = 0.993698321103 -0.0570135978371
y1[1] (closed_form) = 1.00655967976 -0.0638033866125
absolute error = 0.01454
relative error = 1.442 %
Correct digits = 2
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.2446156905 0.262542097218
absolute error = 0.1704
relative error = 47.49 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2414 0.273
h = 0.0001 0.005
y1[1] (numeric) = 0.99368835109 -0.0585060891219
y1[1] (closed_form) = 1.00741351559 -0.0660777017445
absolute error = 0.01568
relative error = 1.553 %
Correct digits = 2
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.248026268343 0.268389192247
absolute error = 0.177
relative error = 48.42 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=1539.4MB, alloc=44.3MB, time=20.53
x[1] = 0.2415 0.278
h = 0.0001 0.003
y1[1] (numeric) = 0.994159235159 -0.0595142236579
y1[1] (closed_form) = 1.00874321882 -0.0673460068534
absolute error = 0.01655
relative error = 1.637 %
Correct digits = 2
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.248460634127 0.273422902451
absolute error = 0.1819
relative error = 49.24 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2416 0.281
h = 0.001 0.001
y1[1] (numeric) = 0.99443377906 -0.0601230311828
y1[1] (closed_form) = 1.00954315668 -0.0681193376273
absolute error = 0.01709
relative error = 1.689 %
Correct digits = 2
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.248764746084 0.276443556499
absolute error = 0.1849
relative error = 49.72 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=1588.9MB, alloc=44.3MB, time=21.19
x[1] = 0.2426 0.282
h = 0.001 0.003
y1[1] (numeric) = 0.994332285639 -0.0604208647723
y1[1] (closed_form) = 1.00957076719 -0.0686455554822
absolute error = 0.01732
relative error = 1.711 %
Correct digits = 2
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.249842685335 0.277384731194
absolute error = 0.1861
relative error = 49.85 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=1638.4MB, alloc=44.3MB, time=21.84
x[1] = 0.2436 0.285
h = 0.0001 0.004
y1[1] (numeric) = 0.994427132385 -0.0611180253727
y1[1] (closed_form) = 1.0101569108 -0.0696757735196
absolute error = 0.01791
relative error = 1.768 %
Correct digits = 2
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.251060028876 0.280345160682
absolute error = 0.1893
relative error = 50.3 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2437 0.289
h = 0.003 0.006
y1[1] (numeric) = 0.99479984637 -0.0619264964032
y1[1] (closed_form) = 1.01126123657 -0.0707090121708
absolute error = 0.01866
relative error = 1.84 %
Correct digits = 2
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.251441868577 0.284380972385
absolute error = 0.1933
relative error = 50.92 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=1687.9MB, alloc=44.3MB, time=22.50
x[1] = 0.2467 0.295
h = 0.0001 0.005
y1[1] (numeric) = 0.994789876357 -0.063418987688
y1[1] (closed_form) = 1.01222556614 -0.0730899799934
absolute error = 0.01994
relative error = 1.965 %
Correct digits = 2
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.254908470393 0.290235731532
absolute error = 0.1999
relative error = 51.74 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=1737.4MB, alloc=44.3MB, time=23.16
x[1] = 0.2468 0.3
h = 0.0001 0.003
y1[1] (numeric) = 0.995260760426 -0.0644271222239
y1[1] (closed_form) = 1.01366387091 -0.0743949709616
absolute error = 0.02093
relative error = 2.059 %
Correct digits = 2
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.255378475842 0.295293070384
absolute error = 0.2048
relative error = 52.47 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2469 0.303
h = 0.001 0.001
y1[1] (numeric) = 0.995535304327 -0.0650359297488
y1[1] (closed_form) = 1.01452874759 -0.0751912754796
absolute error = 0.02154
relative error = 2.117 %
Correct digits = 2
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.255704264447 0.298327877742
absolute error = 0.2079
relative error = 52.9 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=1786.9MB, alloc=44.3MB, time=23.82
x[1] = 0.2479 0.304
h = 0.0001 0.004
y1[1] (numeric) = 0.995433810905 -0.0653337633383
y1[1] (closed_form) = 1.01457129583 -0.0757463221647
absolute error = 0.02179
relative error = 2.141 %
Correct digits = 2
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.256794283111 0.299266959147
absolute error = 0.2091
relative error = 53.01 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=1836.2MB, alloc=44.3MB, time=24.47
x[1] = 0.248 0.308
h = 0.003 0.006
y1[1] (numeric) = 0.99580652489 -0.0661422343687
y1[1] (closed_form) = 1.01575076843 -0.0768044403887
absolute error = 0.02262
relative error = 2.22 %
Correct digits = 2
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.257200899928 0.303319970363
absolute error = 0.2131
relative error = 53.58 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.251 0.314
h = 0.0001 0.005
y1[1] (numeric) = 0.995796554877 -0.0676347256535
y1[1] (closed_form) = 1.01681140567 -0.0792769434828
absolute error = 0.02402
relative error = 2.356 %
Correct digits = 2
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.260717961836 0.309183532168
absolute error = 0.2197
relative error = 54.31 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=1885.5MB, alloc=44.3MB, time=25.13
x[1] = 0.2511 0.319
h = 0.0001 0.003
y1[1] (numeric) = 0.996267438946 -0.0686428601895
y1[1] (closed_form) = 1.01834392309 -0.080612956432
absolute error = 0.02511
relative error = 2.458 %
Correct digits = 2
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.261219442885 0.314263415458
absolute error = 0.2247
relative error = 54.98 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2512 0.322
h = 0.001 0.001
y1[1] (numeric) = 0.996541982847 -0.0692516677144
y1[1] (closed_form) = 1.01926514596 -0.0814287102743
absolute error = 0.02578
relative error = 2.521 %
Correct digits = 2
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.261564385427 0.317311724712
absolute error = 0.2277
relative error = 55.38 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=1935.0MB, alloc=44.3MB, time=25.79
x[1] = 0.2522 0.323
h = 0.001 0.003
y1[1] (numeric) = 0.996440489426 -0.0695495013038
y1[1] (closed_form) = 1.01932081168 -0.0820086056681
absolute error = 0.02605
relative error = 2.548 %
Correct digits = 2
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.262665396908 0.318249299216
absolute error = 0.2289
relative error = 55.48 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=1984.5MB, alloc=44.3MB, time=26.44
x[1] = 0.2532 0.326
h = 0.0001 0.004
y1[1] (numeric) = 0.996535336172 -0.0702466619043
y1[1] (closed_form) = 1.02001672525 -0.0831182393262
absolute error = 0.02678
relative error = 2.617 %
Correct digits = 2
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.263932753611 0.321225740748
absolute error = 0.2321
relative error = 55.83 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2533 0.33
h = 0.003 0.006
y1[1] (numeric) = 0.996908050157 -0.0710551329347
y1[1] (closed_form) = 1.02128335995 -0.0842071685206
absolute error = 0.0277
relative error = 2.703 %
Correct digits = 2
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.264369468577 0.325299969249
absolute error = 0.2362
relative error = 56.34 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=2033.8MB, alloc=44.3MB, time=27.10
x[1] = 0.2563 0.336
h = 0.0001 0.005
y1[1] (numeric) = 0.996898080144 -0.0725476242195
y1[1] (closed_form) = 1.02245431276 -0.0867888236995
absolute error = 0.02926
relative error = 2.851 %
Correct digits = 2
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.267948037387 0.331174685796
absolute error = 0.2428
relative error = 57 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=2083.3MB, alloc=44.3MB, time=27.76
x[1] = 0.2564 0.341
h = 0.0001 0.003
y1[1] (numeric) = 0.997368964213 -0.0735557587555
y1[1] (closed_form) = 1.02409613015 -0.0881632830024
absolute error = 0.03046
relative error = 2.963 %
Correct digits = 2
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.268487743626 0.336282303706
absolute error = 0.2479
relative error = 57.6 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2565 0.344
h = 0.001 0.001
y1[1] (numeric) = 0.997643508114 -0.0741645662804
y1[1] (closed_form) = 1.02508270654 -0.0890030793426
absolute error = 0.03119
relative error = 3.032 %
Correct digits = 2
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.268855951683 0.339347211366
absolute error = 0.2509
relative error = 57.95 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=2132.7MB, alloc=44.3MB, time=28.42
x[1] = 0.2575 0.345
h = 0.001 0.003
y1[1] (numeric) = 0.997542014692 -0.0744623998698
y1[1] (closed_form) = 1.02515310859 -0.0896123076118
absolute error = 0.03149
relative error = 3.06 %
Correct digits = 2
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.269970377128 0.340283021765
absolute error = 0.2521
relative error = 58.04 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=2182.1MB, alloc=44.3MB, time=29.07
x[1] = 0.2585 0.348
h = 0.0001 0.004
y1[1] (numeric) = 0.997636861439 -0.0751595604703
y1[1] (closed_form) = 1.02590781891 -0.0907659379622
absolute error = 0.03229
relative error = 3.135 %
Correct digits = 2
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.271266472603 0.343269422691
absolute error = 0.2553
relative error = 58.36 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2586 0.352
h = 0.003 0.006
y1[1] (numeric) = 0.998009575424 -0.0759680315007
y1[1] (closed_form) = 1.02726193922 -0.0918864699964
absolute error = 0.0333
relative error = 3.229 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.27173443501 0.347366624158
absolute error = 0.2594
relative error = 58.82 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=2231.4MB, alloc=44.3MB, time=29.73
x[1] = 0.2616 0.358
h = 0.0001 0.005
y1[1] (numeric) = 0.997999605411 -0.0774605227855
y1[1] (closed_form) = 1.02854313939 -0.0945787273825
absolute error = 0.03501
relative error = 3.39 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.27537751236 0.35325433928
absolute error = 0.2661
relative error = 59.41 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2617 0.363
h = 0.0001 0.003
y1[1] (numeric) = 0.99847048948 -0.0784686573215
y1[1] (closed_form) = 1.03029468472 -0.0959926425872
absolute error = 0.03633
relative error = 3.511 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.275956881041 0.358391894621
absolute error = 0.2712
relative error = 59.95 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=2280.9MB, alloc=44.3MB, time=30.38
x[1] = 0.2618 0.366
h = 0.001 0.001
y1[1] (numeric) = 0.998745033381 -0.0790774648464
y1[1] (closed_form) = 1.03134686858 -0.0968570943948
absolute error = 0.03713
relative error = 3.585 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.276349237276 0.361474712174
absolute error = 0.2742
relative error = 60.27 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=2330.4MB, alloc=44.3MB, time=31.04
x[1] = 0.2628 0.367
h = 0.001 0.003
y1[1] (numeric) = 0.998643539959 -0.0793752984358
y1[1] (closed_form) = 1.03143189699 -0.0974959497195
absolute error = 0.03746
relative error = 3.616 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.277477803025 0.362408925223
absolute error = 0.2755
relative error = 60.35 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2638 0.37
h = 0.0001 0.004
y1[1] (numeric) = 0.998738386705 -0.0800724590363
y1[1] (closed_form) = 1.03224547908 -0.0986942787404
absolute error = 0.03833
relative error = 3.697 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.278803924673 0.365406344838
absolute error = 0.2787
relative error = 60.64 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=2379.6MB, alloc=44.3MB, time=31.70
x[1] = 0.2639 0.374
h = 0.003 0.006
y1[1] (numeric) = 0.99911110069 -0.0808809300667
y1[1] (closed_form) = 1.03368744107 -0.0998472402953
absolute error = 0.03944
relative error = 3.797 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.279304303416 0.369528278143
absolute error = 0.2828
relative error = 61.05 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=2429.1MB, alloc=44.3MB, time=32.36
x[1] = 0.2669 0.38
h = 0.0001 0.005
y1[1] (numeric) = 0.999101130677 -0.0823734213515
y1[1] (closed_form) = 1.03507884483 -0.102651626149
absolute error = 0.0413
relative error = 3.97 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.283014923387 0.375430826552
absolute error = 0.2895
relative error = 61.58 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.267 0.385
h = 0.0001 0.003
y1[1] (numeric) = 0.999572014746 -0.0833815558875
y1[1] (closed_form) = 1.03694058694 -0.104106050383
absolute error = 0.04273
relative error = 4.1 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.283635416827 0.380600526534
absolute error = 0.2946
relative error = 62.08 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=2478.6MB, alloc=44.3MB, time=33.02
x[1] = 0.2671 0.388
h = 0.001 0.001
y1[1] (numeric) = 0.999846558647 -0.0839903634124
y1[1] (closed_form) = 1.03805865638 -0.104995797169
absolute error = 0.0436
relative error = 4.179 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.284052819093 0.383702568003
absolute error = 0.2977
relative error = 62.37 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=2528.1MB, alloc=44.3MB, time=33.67
x[1] = 0.2681 0.389
h = 0.001 0.003
y1[1] (numeric) = 0.999745065226 -0.0842881970018
y1[1] (closed_form) = 1.03815820091 -0.105664590648
absolute error = 0.04396
relative error = 4.213 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.28519625756 0.384635346429
absolute error = 0.299
relative error = 62.44 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2691 0.392
h = 0.0001 0.004
y1[1] (numeric) = 0.999839911972 -0.0849853576023
y1[1] (closed_form) = 1.03903074625 -0.106908354427
absolute error = 0.04491
relative error = 4.299 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.286553709042 0.387644842049
absolute error = 0.3022
relative error = 62.7 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=2577.6MB, alloc=44.3MB, time=34.34
x[1] = 0.2692 0.396
h = 0.003 0.006
y1[1] (numeric) = 1.00021262596 -0.0857938286327
y1[1] (closed_form) = 1.04056093844 -0.108094607455
absolute error = 0.0461
relative error = 4.407 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.287087693562 0.391793269778
absolute error = 0.3064
relative error = 63.07 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=2627.0MB, alloc=44.3MB, time=35.02
x[1] = 0.2722 0.402
h = 0.0001 0.005
y1[1] (numeric) = 1.00020265594 -0.0872863199175
y1[1] (closed_form) = 1.04206252613 -0.111012724859
absolute error = 0.04812
relative error = 4.591 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.29086892449 0.397712477199
absolute error = 0.3131
relative error = 63.55 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2723 0.407
h = 0.0001 0.003
y1[1] (numeric) = 1.00067354001 -0.0882944544535
y1[1] (closed_form) = 1.04403497463 -0.112508755419
absolute error = 0.04966
relative error = 4.73 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.291532031251 0.402916534095
absolute error = 0.3183
relative error = 64 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=2676.4MB, alloc=44.3MB, time=35.71
x[1] = 0.2724 0.41
h = 0.001 0.001
y1[1] (numeric) = 1.00094808391 -0.0889032619784
y1[1] (closed_form) = 1.04521923189 -0.113424463593
absolute error = 0.05061
relative error = 4.814 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.291975393302 0.406039116426
absolute error = 0.3214
relative error = 64.27 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2734 0.411
h = 0.0001 0.004
y1[1] (numeric) = 1.00084659049 -0.0892010955678
y1[1] (closed_form) = 1.04533318196 -0.11412352336
absolute error = 0.05099
relative error = 4.849 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.293134443347 0.406970618833
absolute error = 0.3226
relative error = 64.33 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=2725.9MB, alloc=44.3MB, time=36.39
x[1] = 0.2735 0.415
h = 0.003 0.006
y1[1] (numeric) = 1.00121930448 -0.0900095665983
y1[1] (closed_form) = 1.04694006689 -0.115338092195
absolute error = 0.05227
relative error = 4.962 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.293697979211 0.411143686727
absolute error = 0.3268
relative error = 64.68 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=2775.3MB, alloc=44.3MB, time=37.06
x[1] = 0.2765 0.421
h = 0.0001 0.005
y1[1] (numeric) = 1.00120933446 -0.0915020578831
y1[1] (closed_form) = 1.0485378818 -0.118354136193
absolute error = 0.05442
relative error = 5.157 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.297542246362 0.417079580407
absolute error = 0.3336
relative error = 65.11 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2766 0.426
h = 0.0001 0.003
y1[1] (numeric) = 1.00168021853 -0.092510192419
y1[1] (closed_form) = 1.05060657612 -0.119885565204
absolute error = 0.05606
relative error = 5.302 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.298242800943 0.422315518722
absolute error = 0.3388
relative error = 65.53 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=2824.8MB, alloc=44.3MB, time=37.74
x[1] = 0.2767 0.429
h = 0.001 0.001
y1[1] (numeric) = 1.00195476243 -0.093118999944
y1[1] (closed_form) = 1.05184838667 -0.120823380755
absolute error = 0.05707
relative error = 5.39 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.298708986604 0.425457163388
absolute error = 0.3419
relative error = 65.78 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=2874.3MB, alloc=44.3MB, time=38.43
x[1] = 0.2777 0.43
h = 0.001 0.003
y1[1] (numeric) = 1.00185326901 -0.0934168335334
y1[1] (closed_form) = 1.05197501378 -0.121548598796
absolute error = 0.05748
relative error = 5.428 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.299882084139 0.426387889294
absolute error = 0.3432
relative error = 65.83 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2787 0.433
h = 0.0001 0.004
y1[1] (numeric) = 1.00194811576 -0.0941139941338
y1[1] (closed_form) = 1.0529581386 -0.122878277809
absolute error = 0.05856
relative error = 5.524 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.301301188566 0.42942307427
absolute error = 0.3465
relative error = 66.05 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=2923.7MB, alloc=44.3MB, time=39.12
x[1] = 0.2788 0.437
h = 0.003 0.006
y1[1] (numeric) = 1.00232082974 -0.0949224651643
y1[1] (closed_form) = 1.05465407437 -0.124127832019
absolute error = 0.05993
relative error = 5.644 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.301900580318 0.433625942831
absolute error = 0.3507
relative error = 66.37 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=2973.0MB, alloc=44.3MB, time=39.80
x[1] = 0.2818 0.443
h = 0.0001 0.005
y1[1] (numeric) = 1.00231085973 -0.0964149564491
y1[1] (closed_form) = 1.05636212074 -0.127260797093
absolute error = 0.06223
relative error = 5.849 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.305821243808 0.439581906833
absolute error = 0.3575
relative error = 66.77 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2819 0.448
h = 0.0001 0.003
y1[1] (numeric) = 1.0027817438 -0.097423090985
y1[1] (closed_form) = 1.05854259255 -0.128835986726
absolute error = 0.064
relative error = 6.002 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.306567229011 0.444856352855
absolute error = 0.3628
relative error = 67.15 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=3022.5MB, alloc=44.3MB, time=40.49
x[1] = 0.282 0.451
h = 0.001 0.001
y1[1] (numeric) = 1.0030562877 -0.09803189851
y1[1] (closed_form) = 1.05985122625 -0.129801072304
absolute error = 0.06508
relative error = 6.095 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.307061103762 0.448021009385
absolute error = 0.366
relative error = 67.38 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.283 0.452
h = 0.001 0.003
y1[1] (numeric) = 1.00295479428 -0.0983297320994
y1[1] (closed_form) = 1.0599920561 -0.130557214316
absolute error = 0.06551
relative error = 6.134 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.308251204391 0.448950752081
absolute error = 0.3672
relative error = 67.43 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=3072.1MB, alloc=44.3MB, time=41.18
x[1] = 0.284 0.455
h = 0.0001 0.004
y1[1] (numeric) = 1.00304964103 -0.0990268926998
y1[1] (closed_form) = 1.06103450546 -0.131934623761
absolute error = 0.06667
relative error = 6.236 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.309705452935 0.452001044698
absolute error = 0.3705
relative error = 67.63 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=3121.4MB, alloc=44.3MB, time=41.86
x[1] = 0.2841 0.459
h = 0.003 0.006
y1[1] (numeric) = 1.00342235501 -0.0998353637303
y1[1] (closed_form) = 1.06281997387 -0.133220128569
absolute error = 0.06814
relative error = 6.361 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.310341954033 0.456235490319
absolute error = 0.3748
relative error = 67.92 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2871 0.465
h = 0.0001 0.005
y1[1] (numeric) = 1.003412385 -0.101327855015
y1[1] (closed_form) = 1.06463829976 -0.136471841456
absolute error = 0.0706
relative error = 6.577 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.314342190419 0.462213325735
absolute error = 0.3817
relative error = 68.28 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=3170.8MB, alloc=44.3MB, time=42.55
x[1] = 0.2872 0.47
h = 0.0001 0.003
y1[1] (numeric) = 1.00388326907 -0.102335989551
y1[1] (closed_form) = 1.06693117584 -0.138092018399
absolute error = 0.07248
relative error = 6.737 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.315135176448 0.467528510228
absolute error = 0.387
relative error = 68.64 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=3220.3MB, alloc=44.3MB, time=43.24
x[1] = 0.2873 0.473
h = 0.001 0.001
y1[1] (numeric) = 1.00415781297 -0.102944797076
y1[1] (closed_form) = 1.06830700424 -0.139085119207
absolute error = 0.07363
relative error = 6.834 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.315657703513 0.470717506279
absolute error = 0.3902
relative error = 68.85 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2883 0.474
h = 0.001 0.003
y1[1] (numeric) = 1.00405631955 -0.103242630665
y1[1] (closed_form) = 1.0684619247 -0.139872562776
absolute error = 0.07409
relative error = 6.876 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.316865566664 0.471646412103
absolute error = 0.3914
relative error = 68.89 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=3269.8MB, alloc=44.3MB, time=43.94
x[1] = 0.2893 0.477
h = 0.0001 0.004
y1[1] (numeric) = 1.00415116629 -0.103939791266
y1[1] (closed_form) = 1.06956385264 -0.141298573763
absolute error = 0.07533
relative error = 6.982 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.31835633373 0.474712863902
absolute error = 0.3948
relative error = 69.07 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=3319.2MB, alloc=44.3MB, time=44.62
x[1] = 0.2894 0.481
h = 0.003 0.006
y1[1] (numeric) = 1.00452388028 -0.104748262296
y1[1] (closed_form) = 1.07143936792 -0.142621031664
absolute error = 0.07689
relative error = 7.114 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.319031221918 0.478980668721
absolute error = 0.3991
relative error = 69.34 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2924 0.487
h = 0.0001 0.005
y1[1] (numeric) = 1.00451391026 -0.106240753581
y1[1] (closed_form) = 1.073368044 -0.145993398958
absolute error = 0.07951
relative error = 7.34 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.323114249137 0.484982168057
absolute error = 0.406
relative error = 69.67 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=3368.6MB, alloc=44.3MB, time=45.30
x[1] = 0.2925 0.492
h = 0.0001 0.003
y1[1] (numeric) = 1.00498479433 -0.107248888117
y1[1] (closed_form) = 1.07577399187 -0.147659836628
absolute error = 0.08151
relative error = 7.507 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.323955837128 0.490340329396
absolute error = 0.4114
relative error = 70 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2926 0.495
h = 0.001 0.001
y1[1] (numeric) = 1.00525933823 -0.107857695642
y1[1] (closed_form) = 1.07721741063 -0.14868172631
absolute error = 0.08273
relative error = 7.608 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.324507998468 0.493554997041
absolute error = 0.4146
relative error = 70.19 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=3418.2MB, alloc=44.3MB, time=45.99
x[1] = 0.2936 0.496
h = 0.001 0.003
y1[1] (numeric) = 1.00515784481 -0.108155529231
y1[1] (closed_form) = 1.07738630868 -0.149500866579
absolute error = 0.08322
relative error = 7.651 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.32573439147 0.494483207809
absolute error = 0.4159
relative error = 70.24 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=3467.8MB, alloc=44.3MB, time=46.67
x[1] = 0.2946 0.499
h = 0.0001 0.004
y1[1] (numeric) = 1.00525269156 -0.108852689832
y1[1] (closed_form) = 1.07854788503 -0.150976386248
absolute error = 0.08454
relative error = 7.762 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.327263071885 0.497566869182
absolute error = 0.4193
relative error = 70.4 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2947 0.503
h = 0.003 0.006
y1[1] (numeric) = 1.00562540554 -0.109661160862
y1[1] (closed_form) = 1.08051399384 -0.152336837583
absolute error = 0.08619
relative error = 7.899 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.327977650187 0.501869821592
absolute error = 0.4236
relative error = 70.65 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=3517.1MB, alloc=44.3MB, time=47.35
x[1] = 0.2977 0.509
h = 0.0001 0.005
y1[1] (numeric) = 1.00561543553 -0.111153652147
y1[1] (closed_form) = 1.08255311294 -0.155831846626
absolute error = 0.08897
relative error = 8.135 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.332146729439 0.507896768833
absolute error = 0.4306
relative error = 70.96 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=3566.5MB, alloc=44.3MB, time=48.03
x[1] = 0.2978 0.514
h = 0.0001 0.003
y1[1] (numeric) = 1.0060863196 -0.112161786683
y1[1] (closed_form) = 1.08507284088 -0.157545865898
absolute error = 0.0911
relative error = 8.308 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.33303855271 0.513300153653
absolute error = 0.436
relative error = 71.26 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.2979 0.517
h = 0.001 0.001
y1[1] (numeric) = 1.0063608635 -0.112770594208
y1[1] (closed_form) = 1.08658426978 -0.158597346988
absolute error = 0.09239
relative error = 8.414 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.333621349787 0.516541829759
absolute error = 0.4393
relative error = 71.44 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=3616.1MB, alloc=44.3MB, time=48.72
x[1] = 0.2989 0.518
h = 0.0001 0.004
y1[1] (numeric) = 1.00625937008 -0.113068427797
y1[1] (closed_form) = 1.08676703138 -0.159448596813
absolute error = 0.09291
relative error = 8.459 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.334867048254 0.517469482646
absolute error = 0.4406
relative error = 71.48 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=3665.6MB, alloc=44.3MB, time=49.41
x[1] = 0.299 0.522
h = 0.003 0.006
y1[1] (numeric) = 1.00663208406 -0.113876898828
y1[1] (closed_form) = 1.08881205278 -0.160841525434
absolute error = 0.09465
relative error = 8.6 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.335616406166 0.521804620581
absolute error = 0.4449
relative error = 71.71 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.302 0.528
h = 0.0001 0.005
y1[1] (numeric) = 1.00662211405 -0.115369390113
y1[1] (closed_form) = 1.09094782314 -0.164442436645
absolute error = 0.09757
relative error = 8.843 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.339861870159 0.527855973387
absolute error = 0.452
relative error = 71.99 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=3715.0MB, alloc=44.3MB, time=50.10
x[1] = 0.3021 0.533
h = 0.0001 0.003
y1[1] (numeric) = 1.00709299812 -0.116377524649
y1[1] (closed_form) = 1.09356667658 -0.166197139513
absolute error = 0.0998
relative error = 9.022 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.340797692422 0.533300716397
absolute error = 0.4574
relative error = 72.28 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3022 0.536
h = 0.001 0.001
y1[1] (numeric) = 1.00736754202 -0.116986332174
y1[1] (closed_form) = 1.09513736693 -0.167273939558
absolute error = 0.1012
relative error = 9.131 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.341407333623 0.536567096491
absolute error = 0.4607
relative error = 72.45 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=3764.5MB, alloc=44.3MB, time=50.79
x[1] = 0.3032 0.537
h = 0.001 0.003
y1[1] (numeric) = 1.0072660486 -0.117284165763
y1[1] (closed_form) = 1.09533235912 -0.16815300919
absolute error = 0.1017
relative error = 9.178 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.342670281806 0.53749461809
absolute error = 0.462
relative error = 72.48 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=3814.0MB, alloc=44.3MB, time=51.49
x[1] = 0.3042 0.54
h = 0.0001 0.004
y1[1] (numeric) = 1.00736089535 -0.117981326363
y1[1] (closed_form) = 1.09660604969 -0.169722476625
absolute error = 0.1032
relative error = 9.296 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.344273061611 0.540613586683
absolute error = 0.4655
relative error = 72.63 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3043 0.544
h = 0.003 0.006
y1[1] (numeric) = 1.00773360933 -0.118789797394
y1[1] (closed_form) = 1.0987427817 -0.171155429904
absolute error = 0.105
relative error = 9.442 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.345064583519 0.544987234675
absolute error = 0.4699
relative error = 72.84 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=3863.5MB, alloc=44.3MB, time=52.18
x[1] = 0.3073 0.55
h = 0.0001 0.005
y1[1] (numeric) = 1.00772363932 -0.120282288679
y1[1] (closed_form) = 1.10098925137 -0.174882897245
absolute error = 0.1081
relative error = 9.694 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.34940226855 0.551067372616
absolute error = 0.477
relative error = 73.1 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=3912.8MB, alloc=44.3MB, time=52.87
x[1] = 0.3074 0.555
h = 0.0001 0.003
y1[1] (numeric) = 1.00819452339 -0.121290423215
y1[1] (closed_form) = 1.10372332849 -0.176687758948
absolute error = 0.1104
relative error = 9.879 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.350391428302 0.556561564174
absolute error = 0.4825
relative error = 73.37 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3075 0.558
h = 0.001 0.001
y1[1] (numeric) = 1.00846906729 -0.12189923074
y1[1] (closed_form) = 1.10536288461 -0.17779571654
absolute error = 0.1119
relative error = 9.991 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.35103360718 0.559857466883
absolute error = 0.4859
relative error = 73.53 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=3962.4MB, alloc=44.3MB, time=53.57
x[1] = 0.3085 0.559
h = 0.001 0.003
y1[1] (numeric) = 1.00836757387 -0.122197064329
y1[1] (closed_form) = 1.10557153037 -0.178707713047
absolute error = 0.1124
relative error = 10.04 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.352317325948 0.560784682589
absolute error = 0.4872
relative error = 73.56 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=4012.0MB, alloc=44.3MB, time=54.26
x[1] = 0.3095 0.562
h = 0.0001 0.004
y1[1] (numeric) = 1.00846242061 -0.122894224929
y1[1] (closed_form) = 1.10690545341 -0.180329484744
absolute error = 0.114
relative error = 10.16 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.35396211757 0.563923878196
absolute error = 0.4906
relative error = 73.69 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3096 0.566
h = 0.003 0.006
y1[1] (numeric) = 1.0088351346 -0.12370269596
y1[1] (closed_form) = 1.10913453602 -0.181803614322
absolute error = 0.1159
relative error = 10.31 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.354797184361 0.568337845694
absolute error = 0.4951
relative error = 73.9 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=4061.4MB, alloc=44.3MB, time=54.95
x[1] = 0.3126 0.572
h = 0.0001 0.005
y1[1] (numeric) = 1.00882516459 -0.125195187245
y1[1] (closed_form) = 1.11149185991 -0.185659861147
absolute error = 0.1191
relative error = 10.57 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.359230486074 0.574448529219
absolute error = 0.5023
relative error = 74.14 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3127 0.577
h = 0.0001 0.003
y1[1] (numeric) = 1.00929604865 -0.126203321781
y1[1] (closed_form) = 1.1143419863 -0.187516342196
absolute error = 0.1216
relative error = 10.76 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.360274715638 0.579994443562
absolute error = 0.5079
relative error = 74.39 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=4110.8MB, alloc=44.3MB, time=55.63
x[1] = 0.3128 0.58
h = 0.001 0.001
y1[1] (numeric) = 1.00957059256 -0.126812129306
y1[1] (closed_form) = 1.11605089731 -0.188656344854
absolute error = 0.1231
relative error = 10.88 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.36095049364 0.583321221795
absolute error = 0.5113
relative error = 74.53 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=4160.3MB, alloc=44.3MB, time=56.86
x[1] = 0.3138 0.581
h = 0.001 0.003
y1[1] (numeric) = 1.00946909913 -0.127109962895
y1[1] (closed_form) = 1.11627307907 -0.189601732694
absolute error = 0.1237
relative error = 10.93 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.362255784512 0.584248254962
absolute error = 0.5126
relative error = 74.56 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3148 0.584
h = 0.0001 0.004
y1[1] (numeric) = 1.00956394588 -0.127807123495
y1[1] (closed_form) = 1.11766746452 -0.191276859152
absolute error = 0.1254
relative error = 11.06 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.363944069966 0.587408725218
absolute error = 0.5161
relative error = 74.68 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=4209.9MB, alloc=44.3MB, time=57.76
x[1] = 0.3149 0.588
h = 0.003 0.006
y1[1] (numeric) = 1.00993665986 -0.128615594526
y1[1] (closed_form) = 1.11998957023 -0.192793356978
absolute error = 0.1274
relative error = 11.21 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.364824091781 0.591864829898
absolute error = 0.5206
relative error = 74.88 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=4259.3MB, alloc=44.3MB, time=58.49
x[1] = 0.3179 0.594
h = 0.0001 0.005
y1[1] (numeric) = 1.00992668985 -0.130108085811
y1[1] (closed_form) = 1.12245792374 -0.196780691208
absolute error = 0.1308
relative error = 11.48 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.369356456539 0.598007811083
absolute error = 0.5279
relative error = 75.1 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.318 0.599
h = 0.0001 0.003
y1[1] (numeric) = 1.01039757392 -0.131116220347
y1[1] (closed_form) = 1.12542496588 -0.198690302716
absolute error = 0.1334
relative error = 11.67 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.370457525409 0.603607733187
absolute error = 0.5335
relative error = 75.33 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=4308.8MB, alloc=44.3MB, time=59.17
x[1] = 0.3181 0.602
h = 0.001 0.001
y1[1] (numeric) = 1.01067211782 -0.131725027872
y1[1] (closed_form) = 1.12720374505 -0.19986326874
absolute error = 0.135
relative error = 11.79 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.371167986501 0.606966746094
absolute error = 0.5369
relative error = 75.47 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=4358.3MB, alloc=44.3MB, time=59.86
x[1] = 0.3191 0.603
h = 0.001 0.003
y1[1] (numeric) = 1.0105706244 -0.132022861461
y1[1] (closed_form) = 1.12743934362 -0.200842530755
absolute error = 0.1356
relative error = 11.84 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.372495660791 0.60789371496
absolute error = 0.5382
relative error = 75.49 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3201 0.606
h = 0.0001 0.004
y1[1] (numeric) = 1.01066547115 -0.132720022061
y1[1] (closed_form) = 1.12889443654 -0.202572100897
absolute error = 0.1373
relative error = 11.97 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.374228946882 0.611076507059
absolute error = 0.5418
relative error = 75.61 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=4407.8MB, alloc=44.3MB, time=60.65
x[1] = 0.3202 0.61
h = 0.003 0.006
y1[1] (numeric) = 1.01103818513 -0.133528493092
y1[1] (closed_form) = 1.13131027038 -0.204132199933
absolute error = 0.1395
relative error = 12.13 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.375155364184 0.615576575323
absolute error = 0.5464
relative error = 75.79 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3232 0.616
h = 0.0001 0.005
y1[1] (numeric) = 1.01102821512 -0.135020984377
y1[1] (closed_form) = 1.13388984897 -0.208253015148
absolute error = 0.143
relative error = 12.41 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.379790291049 0.621753597865
absolute error = 0.5537
relative error = 76 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=4457.3MB, alloc=44.3MB, time=61.33
x[1] = 0.3233 0.621
h = 0.0001 0.003
y1[1] (numeric) = 1.01149909919 -0.136029118913
y1[1] (closed_form) = 1.13697471425 -0.210217319717
absolute error = 0.1458
relative error = 12.61 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.380950007228 0.627409824074
absolute error = 0.5594
relative error = 76.22 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=4506.7MB, alloc=44.3MB, time=62.00
x[1] = 0.3234 0.624
h = 0.001 0.001
y1[1] (numeric) = 1.01177364309 -0.136637926438
y1[1] (closed_form) = 1.13882389901 -0.211424198732
absolute error = 0.1474
relative error = 12.73 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.381696258707 0.630802437414
absolute error = 0.5629
relative error = 76.34 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3244 0.625
h = 0.0001 0.004
y1[1] (numeric) = 1.01167214967 -0.136935760027
y1[1] (closed_form) = 1.13907279342 -0.212437836335
absolute error = 0.1481
relative error = 12.78 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.383047137917 0.631729454968
absolute error = 0.5642
relative error = 76.37 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=4556.3MB, alloc=44.3MB, time=62.68
x[1] = 0.3245 0.629
h = 0.003 0.006
y1[1] (numeric) = 1.01204486365 -0.137744231057
y1[1] (closed_form) = 1.14157043487 -0.214035356489
absolute error = 0.1503
relative error = 12.94 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.384014114873 0.63626941178
absolute error = 0.5688
relative error = 76.54 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=4605.6MB, alloc=44.3MB, time=63.35
x[1] = 0.3275 0.635
h = 0.0001 0.005
y1[1] (numeric) = 1.01203489364 -0.139236722342
y1[1] (closed_form) = 1.14424755424 -0.218271722198
absolute error = 0.154
relative error = 13.22 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.388739733833 0.642478405335
absolute error = 0.5762
relative error = 76.73 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3276 0.64
h = 0.0001 0.003
y1[1] (numeric) = 1.01250577771 -0.140244856878
y1[1] (closed_form) = 1.14743527344 -0.220282977036
absolute error = 0.1569
relative error = 13.43 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.389950701725 0.648185672885
absolute error = 0.582
relative error = 76.94 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=4655.1MB, alloc=44.3MB, time=64.02
x[1] = 0.3277 0.643
h = 0.001 0.001
y1[1] (numeric) = 1.01278032161 -0.140853664403
y1[1] (closed_form) = 1.14934592976 -0.221518984153
absolute error = 0.1586
relative error = 13.55 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.390728242973 0.651608752066
absolute error = 0.5855
relative error = 77.06 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=4704.5MB, alloc=44.3MB, time=64.70
x[1] = 0.3287 0.644
h = 0.001 0.003
y1[1] (numeric) = 1.01267882819 -0.141151497993
y1[1] (closed_form) = 1.1496065884 -0.222562470581
absolute error = 0.1593
relative error = 13.6 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.392099759805 0.652536187827
absolute error = 0.5868
relative error = 77.08 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3297 0.647
h = 0.0001 0.004
y1[1] (numeric) = 1.01277367493 -0.141848658593
y1[1] (closed_form) = 1.1511760282 -0.224395649127
absolute error = 0.1611
relative error = 13.74 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.393920585465 0.65576388145
absolute error = 0.5905
relative error = 77.19 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=4753.9MB, alloc=44.3MB, time=65.37
x[1] = 0.3298 0.651
h = 0.003 0.006
y1[1] (numeric) = 1.01314638892 -0.142657129623
y1[1] (closed_form) = 1.15376881224 -0.226039167092
absolute error = 0.1635
relative error = 13.91 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.39493670068 0.660351243345
absolute error = 0.5951
relative error = 77.35 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3328 0.657
h = 0.0001 0.005
y1[1] (numeric) = 1.01313641891 -0.144149620908
y1[1] (closed_form) = 1.15655760312 -0.230413696724
absolute error = 0.1674
relative error = 14.19 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.399771519277 0.666597543746
absolute error = 0.6026
relative error = 77.53 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=4803.3MB, alloc=44.3MB, time=66.04
x[1] = 0.3329 0.662
h = 0.0001 0.003
y1[1] (numeric) = 1.01360730297 -0.145157755444
y1[1] (closed_form) = 1.15986496307 -0.232482680533
absolute error = 0.1703
relative error = 14.4 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.401044578217 0.672365443437
absolute error = 0.6085
relative error = 77.72 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=4852.8MB, alloc=44.3MB, time=66.72
x[1] = 0.333 0.665
h = 0.001 0.001
y1[1] (numeric) = 1.01388184688 -0.145766562969
y1[1] (closed_form) = 1.16184710163 -0.233754445883
absolute error = 0.1721
relative error = 14.53 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.401860018726 0.675824697127
absolute error = 0.612
relative error = 77.84 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.334 0.666
h = 0.001 0.003
y1[1] (numeric) = 1.01378035345 -0.146064396559
y1[1] (closed_form) = 1.16212083219 -0.234833292537
absolute error = 0.1729
relative error = 14.58 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.403256296407 0.676752387458
absolute error = 0.6134
relative error = 77.86 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=4902.4MB, alloc=44.3MB, time=67.39
x[1] = 0.335 0.669
h = 0.0001 0.004
y1[1] (numeric) = 1.0138752002 -0.146761557159
y1[1] (closed_form) = 1.16375177733 -0.236724243657
absolute error = 0.1748
relative error = 14.72 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.405126566143 0.68000541637
absolute error = 0.617
relative error = 77.96 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=4951.8MB, alloc=44.3MB, time=68.06
x[1] = 0.3351 0.673
h = 0.003 0.006
y1[1] (numeric) = 1.01424791419 -0.147570028189
y1[1] (closed_form) = 1.16644050277 -0.238415113435
absolute error = 0.1772
relative error = 14.89 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.40619335274 0.684642037855
absolute error = 0.6218
relative error = 78.11 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3381 0.679
h = 0.0001 0.005
y1[1] (numeric) = 1.01423794417 -0.149062519474
y1[1] (closed_form) = 1.16934121642 -0.242930451833
absolute error = 0.1813
relative error = 15.18 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.411141032027 0.690927365366
absolute error = 0.6294
relative error = 78.28 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=5001.3MB, alloc=44.3MB, time=68.73
x[1] = 0.3382 0.684
h = 0.0001 0.003
y1[1] (numeric) = 1.01470882824 -0.15007065401
y1[1] (closed_form) = 1.17276924249 -0.245058879243
absolute error = 0.1844
relative error = 15.39 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.412478107607 0.696758230015
absolute error = 0.6353
relative error = 78.46 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=5050.8MB, alloc=44.3MB, time=69.41
x[1] = 0.3383 0.687
h = 0.001 0.001
y1[1] (numeric) = 1.01498337214 -0.150679461535
y1[1] (closed_form) = 1.17482347039 -0.246367444924
absolute error = 0.1863
relative error = 15.52 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.413332625914 0.700255045192
absolute error = 0.6389
relative error = 78.57 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3393 0.688
h = 0.001 0.003
y1[1] (numeric) = 1.01488187872 -0.150977295125
y1[1] (closed_form) = 1.17511014608 -0.247482207515
absolute error = 0.187
relative error = 15.58 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.414754517394 0.701183087411
absolute error = 0.6402
relative error = 78.59 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=5100.2MB, alloc=44.3MB, time=70.09
x[1] = 0.3403 0.691
h = 0.0001 0.004
y1[1] (numeric) = 1.01497672547 -0.151674455725
y1[1] (closed_form) = 1.17680289912 -0.249432173701
absolute error = 0.1891
relative error = 15.72 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.416675842567 0.704462498562
absolute error = 0.644
relative error = 78.68 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3404 0.695
h = 0.003 0.006
y1[1] (numeric) = 1.01534943945 -0.152482926755
y1[1] (closed_form) = 1.17958839748 -0.251171793256
absolute error = 0.1916
relative error = 15.89 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.417794868263 0.709150244785
absolute error = 0.6488
relative error = 78.82 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=5149.6MB, alloc=44.3MB, time=70.76
x[1] = 0.3434 0.701
h = 0.0001 0.005
y1[1] (numeric) = 1.01533946944 -0.15397541804
y1[1] (closed_form) = 1.18260130334 -0.255830675563
absolute error = 0.1958
relative error = 16.19 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.422859129847 0.715476311144
absolute error = 0.6564
relative error = 78.98 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=5199.0MB, alloc=44.3MB, time=71.44
x[1] = 0.3435 0.706
h = 0.0001 0.003
y1[1] (numeric) = 1.01581035351 -0.154983552576
y1[1] (closed_form) = 1.18615106206 -0.258020316451
absolute error = 0.1991
relative error = 16.4 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.424262191533 0.721372487346
absolute error = 0.6624
relative error = 79.16 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3436 0.709
h = 0.001 0.001
y1[1] (numeric) = 1.01608489741 -0.155592360101
y1[1] (closed_form) = 1.1882780107 -0.25936675815
absolute error = 0.201
relative error = 16.53 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.425156992751 0.724908258997
absolute error = 0.6661
relative error = 79.26 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=5248.6MB, alloc=44.3MB, time=72.12
x[1] = 0.3446 0.71
h = 0.001 0.003
y1[1] (numeric) = 1.01598340399 -0.155890193691
y1[1] (closed_form) = 1.18857750221 -0.260518011779
absolute error = 0.2018
relative error = 16.59 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.426605362738 0.72583674461
absolute error = 0.6674
relative error = 79.28 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=5298.0MB, alloc=44.3MB, time=73.16
x[1] = 0.3456 0.713
h = 0.0001 0.004
y1[1] (numeric) = 1.01607825073 -0.156587354291
y1[1] (closed_form) = 1.19033238017 -0.262528276847
absolute error = 0.2039
relative error = 16.73 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.428579384142 0.729143585071
absolute error = 0.6712
relative error = 79.36 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3457 0.717
h = 0.003 0.006
y1[1] (numeric) = 1.01645096472 -0.157395825321
y1[1] (closed_form) = 1.1932155157 -0.264318088939
absolute error = 0.2066
relative error = 16.9 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.42975225239 0.733884332306
absolute error = 0.6761
relative error = 79.5 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=5347.3MB, alloc=44.3MB, time=74.21
x[1] = 0.3487 0.723
h = 0.0001 0.005
y1[1] (numeric) = 1.01644099471 -0.158888316606
y1[1] (closed_form) = 1.1963409009 -0.269123341909
absolute error = 0.211
relative error = 17.21 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.434936880536 0.740252840634
absolute error = 0.6838
relative error = 79.65 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=5396.9MB, alloc=44.3MB, time=75.50
x[1] = 0.3488 0.728
h = 0.0001 0.003
y1[1] (numeric) = 1.01691187877 -0.159896451142
y1[1] (closed_form) = 1.20001350003 -0.271376022447
absolute error = 0.2144
relative error = 17.42 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.436407943107 0.746216689371
absolute error = 0.6899
relative error = 79.81 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3489 0.731
h = 0.001 0.001
y1[1] (numeric) = 1.01718642268 -0.160505258667
y1[1] (closed_form) = 1.2022138251 -0.272761450079
absolute error = 0.2164
relative error = 17.56 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.437344259802 0.749792820853
absolute error = 0.6936
relative error = 79.91 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=5446.4MB, alloc=44.3MB, time=76.82
x[1] = 0.3499 0.732
h = 0.0001 0.004
y1[1] (numeric) = 1.01708492925 -0.160803092257
y1[1] (closed_form) = 1.20252600051 -0.273949789478
absolute error = 0.2172
relative error = 17.61 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.438819985179 0.750721835392
absolute error = 0.695
relative error = 79.92 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=5495.8MB, alloc=44.3MB, time=77.61
x[1] = 0.35 0.736
h = 0.003 0.006
y1[1] (numeric) = 1.01745764324 -0.161611563287
y1[1] (closed_form) = 1.20549451812 -0.275782818118
absolute error = 0.22
relative error = 17.79 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.440039849476 0.7555103835
absolute error = 0.6999
relative error = 80.05 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.353 0.742
h = 0.0001 0.005
y1[1] (numeric) = 1.01744767323 -0.163104054572
y1[1] (closed_form) = 1.20871875592 -0.280715051784
absolute error = 0.2245
relative error = 18.09 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.445330631869 0.761918277971
absolute error = 0.7078
relative error = 80.2 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=5545.2MB, alloc=44.3MB, time=78.30
x[1] = 0.3531 0.747
h = 0.0001 0.003
y1[1] (numeric) = 1.0179185573 -0.164112189108
y1[1] (closed_form) = 1.21249879216 -0.283022018893
absolute error = 0.228
relative error = 18.31 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.446861031734 0.767943122569
absolute error = 0.7139
relative error = 80.35 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3532 0.75
h = 0.001 0.001
y1[1] (numeric) = 1.0181931012 -0.164720996633
y1[1] (closed_form) = 1.21476330395 -0.284441034586
absolute error = 0.2302
relative error = 18.45 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.447833588509 0.771555639903
absolute error = 0.7177
relative error = 80.45 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=5594.8MB, alloc=44.3MB, time=78.99
x[1] = 0.3542 0.751
h = 0.001 0.003
y1[1] (numeric) = 1.01809160777 -0.165018830222
y1[1] (closed_form) = 1.21508674115 -0.285661638685
absolute error = 0.231
relative error = 18.51 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.449333564714 0.772485513839
absolute error = 0.7191
relative error = 80.46 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=5644.4MB, alloc=44.3MB, time=79.68
x[1] = 0.3552 0.754
h = 0.0001 0.004
y1[1] (numeric) = 1.01818645452 -0.165715990823
y1[1] (closed_form) = 1.21695886786 -0.287786917501
absolute error = 0.2333
relative error = 18.65 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.451409757288 0.775846856771
absolute error = 0.7229
relative error = 80.54 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3553 0.758
h = 0.0001 0.004
y1[1] (numeric) = 1.01855916851 -0.166524461853
y1[1] (closed_form) = 1.2200267367 -0.289672934286
absolute error = 0.2361
relative error = 18.83 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.452686524247 0.780691948617
absolute error = 0.7279
relative error = 80.66 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=5693.8MB, alloc=44.3MB, time=80.36
x[1] = 0.3554 0.762
h = 0.003 0.006
y1[1] (numeric) = 1.01893188249 -0.167332932883
y1[1] (closed_form) = 1.22311388205 -0.291564558972
absolute error = 0.239
relative error = 19.01 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.453971154229 0.785549161593
absolute error = 0.7329
relative error = 80.78 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=5743.3MB, alloc=44.3MB, time=81.03
x[1] = 0.3584 0.768
h = 0.0001 0.005
y1[1] (numeric) = 1.01892191248 -0.168825424168
y1[1] (closed_form) = 1.22647651198 -0.296671028616
absolute error = 0.2438
relative error = 19.32 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.459410214946 0.792015581161
absolute error = 0.7409
relative error = 80.92 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3585 0.773
h = 0.0001 0.003
y1[1] (numeric) = 1.01939279655 -0.169833558704
y1[1] (closed_form) = 1.23040584129 -0.299051611952
absolute error = 0.2474
relative error = 19.54 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.461022361798 0.798127988318
absolute error = 0.7472
relative error = 81.06 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=5793.0MB, alloc=44.3MB, time=81.70
x[1] = 0.3586 0.776
h = 0.001 0.001
y1[1] (numeric) = 1.01966734045 -0.170442366229
y1[1] (closed_form) = 1.23275956735 -0.300516207623
absolute error = 0.2497
relative error = 19.68 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.462044870849 0.801792755345
absolute error = 0.751
relative error = 81.15 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3596 0.777
h = 0.001 0.003
y1[1] (numeric) = 1.01956584703 -0.170740199819
y1[1] (closed_form) = 1.2330990143 -0.301781278122
absolute error = 0.2505
relative error = 19.74 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.463578948727 0.802724536149
memory used=5842.6MB, alloc=44.3MB, time=82.36
absolute error = 0.7524
relative error = 81.16 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3606 0.78
h = 0.0001 0.004
y1[1] (numeric) = 1.01966069377 -0.171437360419
y1[1] (closed_form) = 1.23504763641 -0.303979650801
absolute error = 0.2529
relative error = 19.88 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.465721660318 0.806123874466
absolute error = 0.7563
relative error = 81.24 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=5891.9MB, alloc=44.3MB, time=83.04
x[1] = 0.3607 0.784
h = 0.003 0.006
y1[1] (numeric) = 1.02003340776 -0.172245831449
y1[1] (closed_form) = 1.23823532058 -0.305926079774
absolute error = 0.2559
relative error = 20.06 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.467065133809 0.811039938632
absolute error = 0.7614
relative error = 81.35 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3637 0.79
h = 0.0001 0.005
y1[1] (numeric) = 1.02002343774 -0.173738322734
y1[1] (closed_form) = 1.24171155844 -0.311188053074
absolute error = 0.2608
relative error = 20.38 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.472636364448 0.817554110127
absolute error = 0.7694
relative error = 81.48 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=5941.4MB, alloc=44.3MB, time=83.71
x[1] = 0.3638 0.795
h = 0.0001 0.003
y1[1] (numeric) = 1.02049432181 -0.17474645727
y1[1] (closed_form) = 1.2457674414 -0.313637510325
absolute error = 0.2646
relative error = 20.6 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.474322798279 0.823741553603
absolute error = 0.7758
relative error = 81.62 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=5991.0MB, alloc=44.3MB, time=84.88
x[1] = 0.3639 0.798
h = 0.001 0.001
y1[1] (numeric) = 1.02076886571 -0.175355264795
y1[1] (closed_form) = 1.2481967429 -0.315144638905
absolute error = 0.267
relative error = 20.74 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.475390668726 0.827451058047
absolute error = 0.7797
relative error = 81.7 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3649 0.799
h = 0.001 0.003
y1[1] (numeric) = 1.02066737229 -0.175653098385
y1[1] (closed_form) = 1.24854848771 -0.316448728946
absolute error = 0.2679
relative error = 20.8 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.47695483787 0.828383634239
absolute error = 0.7811
relative error = 81.71 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=6040.6MB, alloc=44.3MB, time=86.10
x[1] = 0.3659 0.802
h = 0.0001 0.004
y1[1] (numeric) = 1.02076221904 -0.176350258985
y1[1] (closed_form) = 1.25056072904 -0.31871299356
absolute error = 0.2703
relative error = 20.95 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.479157131879 0.831814716016
absolute error = 0.7851
relative error = 81.78 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=6089.9MB, alloc=44.3MB, time=86.77
x[1] = 0.366 0.806
h = 0.003 0.006
y1[1] (numeric) = 1.02113493302 -0.177158730015
y1[1] (closed_form) = 1.25384995142 -0.320715857665
absolute error = 0.2734
relative error = 21.13 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.480561207912 0.836791559397
absolute error = 0.7902
relative error = 81.89 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.369 0.812
h = 0.0001 0.005
y1[1] (numeric) = 1.02112496301 -0.1786512213
y1[1] (closed_form) = 1.25744015493 -0.326136544394
absolute error = 0.2786
relative error = 21.44 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.486268667745 0.843355153467
absolute error = 0.7984
relative error = 82.01 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=6139.4MB, alloc=44.3MB, time=87.44
x[1] = 0.3691 0.817
h = 0.0001 0.003
y1[1] (numeric) = 1.02159584708 -0.179659355836
y1[1] (closed_form) = 1.26162386945 -0.328656938228
absolute error = 0.2825
relative error = 21.67 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.48803160046 0.849620060954
absolute error = 0.8049
relative error = 82.15 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=6189.0MB, alloc=44.3MB, time=88.12
x[1] = 0.3692 0.82
h = 0.001 0.001
y1[1] (numeric) = 1.02187039098 -0.180268163361
y1[1] (closed_form) = 1.26412950247 -0.330207853409
absolute error = 0.2849
relative error = 21.81 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.489146184293 0.853375745014
absolute error = 0.8088
relative error = 82.23 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3702 0.821
h = 0.001 0.003
y1[1] (numeric) = 1.02176889756 -0.180565996951
y1[1] (closed_form) = 1.26449340138 -0.331551639589
absolute error = 0.2859
relative error = 21.87 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.490741375336 0.854309176986
absolute error = 0.8102
relative error = 82.24 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=6238.6MB, alloc=44.3MB, time=88.80
x[1] = 0.3712 0.824
h = 0.0001 0.004
y1[1] (numeric) = 1.02186374431 -0.181263157551
y1[1] (closed_form) = 1.26656965129 -0.333883297758
absolute error = 0.2884
relative error = 22.02 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.493005056027 0.857773052919
absolute error = 0.8143
relative error = 82.3 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3713 0.828
h = 0.003 0.006
y1[1] (numeric) = 1.02223645829 -0.182071628581
y1[1] (closed_form) = 1.26996144442 -0.335944277252
absolute error = 0.2916
relative error = 22.2 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.494471535442 0.862812617114
absolute error = 0.8195
relative error = 82.41 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=6288.0MB, alloc=44.3MB, time=89.49
x[1] = 0.3743 0.834
h = 0.0001 0.005
y1[1] (numeric) = 1.02222648828 -0.183564119866
y1[1] (closed_form) = 1.27366598623 -0.341526986124
absolute error = 0.2969
relative error = 22.52 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.500319357376 0.869427295171
absolute error = 0.8278
relative error = 82.52 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=6337.5MB, alloc=44.3MB, time=90.19
x[1] = 0.3744 0.839
h = 0.0001 0.003
y1[1] (numeric) = 1.02269737235 -0.184572254402
y1[1] (closed_form) = 1.27797885196 -0.344120441362
absolute error = 0.301
relative error = 22.75 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.502161053823 0.875772111836
absolute error = 0.8344
relative error = 82.65 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3745 0.842
h = 0.001 0.001
y1[1] (numeric) = 1.02297191625 -0.185181061927
y1[1] (closed_form) = 1.28056159717 -0.345716434598
absolute error = 0.3035
relative error = 22.88 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.503323735098 0.879575427874
absolute error = 0.8383
relative error = 82.72 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=6387.1MB, alloc=44.3MB, time=90.88
x[1] = 0.3755 0.843
h = 0.001 0.003
y1[1] (numeric) = 1.02287042283 -0.185478895517
y1[1] (closed_form) = 1.28093750269 -0.347100614448
absolute error = 0.3045
relative error = 22.94 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.504950893017 0.880509769171
absolute error = 0.8398
relative error = 82.74 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=6436.7MB, alloc=44.3MB, time=91.58
x[1] = 0.3765 0.846
h = 0.0001 0.004
y1[1] (numeric) = 1.02296526957 -0.186176056117
y1[1] (closed_form) = 1.28307816401 -0.349501213447
absolute error = 0.3071
relative error = 23.1 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.507277800292 0.884007490589
absolute error = 0.8439
relative error = 82.8 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3766 0.85
h = 0.003 0.006
y1[1] (numeric) = 1.02333798356 -0.186984527147
y1[1] (closed_form) = 1.28657359362 -0.351622039004
absolute error = 0.3105
relative error = 23.28 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.508808527005 0.889111731242
absolute error = 0.8492
relative error = 82.9 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=6486.2MB, alloc=44.3MB, time=92.29
x[1] = 0.3796 0.856
h = 0.0001 0.005
y1[1] (numeric) = 1.02332801354 -0.188477018432
y1[1] (closed_form) = 1.29039286073 -0.357370179268
absolute error = 0.316
relative error = 23.6 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.514800919856 0.895779145253
absolute error = 0.8576
relative error = 83.01 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=6535.8MB, alloc=44.3MB, time=92.99
x[1] = 0.3797 0.861
h = 0.0001 0.003
y1[1] (numeric) = 1.02379889761 -0.189485152968
y1[1] (closed_form) = 1.29483623916 -0.360038884162
absolute error = 0.3202
relative error = 23.83 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.51672369943 0.902206334325
absolute error = 0.8643
relative error = 83.13 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3798 0.864
h = 0.001 0.001
y1[1] (numeric) = 1.02407344151 -0.190093960493
y1[1] (closed_form) = 1.29749690189 -0.361681285445
absolute error = 0.3228
relative error = 23.97 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.517935895241 0.906058745203
absolute error = 0.8683
relative error = 83.2 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=6585.5MB, alloc=44.3MB, time=93.70
x[1] = 0.3808 0.865
h = 0.0001 0.004
y1[1] (numeric) = 1.02397194809 -0.190391794083
y1[1] (closed_form) = 1.29788466259 -0.363106577711
absolute error = 0.3238
relative error = 24.03 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.519595979798 0.90699404233
absolute error = 0.8698
relative error = 83.21 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3809 0.869
h = 0.003 0.006
y1[1] (numeric) = 1.02434466208 -0.191200265113
y1[1] (closed_form) = 1.30147091976 -0.365279089488
absolute error = 0.3273
relative error = 24.21 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.521182716454 0.912156327438
absolute error = 0.8752
relative error = 83.31 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=6635.0MB, alloc=44.3MB, time=94.40
x[1] = 0.3839 0.875
h = 0.0001 0.005
y1[1] (numeric) = 1.02433469207 -0.192692756398
y1[1] (closed_form) = 1.30539128676 -0.371171062453
absolute error = 0.3329
relative error = 24.53 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.527302326302 0.918872242078
absolute error = 0.8837
relative error = 83.41 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=6684.4MB, alloc=44.3MB, time=95.10
x[1] = 0.384 0.88
h = 0.0001 0.003
y1[1] (numeric) = 1.02480557613 -0.193700890934
y1[1] (closed_form) = 1.30994906151 -0.37390476392
absolute error = 0.3373
relative error = 24.76 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.529295778192 0.925373325785
absolute error = 0.8905
relative error = 83.53 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3841 0.883
h = 0.001 0.001
y1[1] (numeric) = 1.02508012004 -0.194309698459
y1[1] (closed_form) = 1.31267803187 -0.375587265066
absolute error = 0.34
relative error = 24.9 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.530551146455 0.929269788967
absolute error = 0.8945
relative error = 83.6 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=6734.0MB, alloc=44.3MB, time=95.79
x[1] = 0.3851 0.884
h = 0.001 0.003
y1[1] (numeric) = 1.02497862661 -0.194607532048
y1[1] (closed_form) = 1.31307637444 -0.377048398812
absolute error = 0.341
relative error = 24.96 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.532240341334 0.93020634862
absolute error = 0.896
relative error = 83.61 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=6783.6MB, alloc=44.3MB, time=96.49
x[1] = 0.3861 0.887
h = 0.0001 0.004
y1[1] (numeric) = 1.02507347336 -0.195304692649
y1[1] (closed_form) = 1.31533887479 -0.379580779241
absolute error = 0.3438
relative error = 25.11 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.534689489311 0.933770655753
absolute error = 0.9003
relative error = 83.67 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3862 0.891
h = 0.003 0.006
y1[1] (numeric) = 1.02544618735 -0.196113163679
y1[1] (closed_form) = 1.31903086229 -0.381816481592
absolute error = 0.3474
relative error = 25.3 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.536343999766 0.939001318505
absolute error = 0.9057
relative error = 83.76 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=6833.0MB, alloc=44.3MB, time=97.18
x[1] = 0.3892 0.897
h = 0.0001 0.005
y1[1] (numeric) = 1.02543621733 -0.197605654964
y1[1] (closed_form) = 1.32306675427 -0.38788049803
absolute error = 0.3533
relative error = 25.62 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.542616202702 0.945773069465
absolute error = 0.9144
relative error = 83.86 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=6882.5MB, alloc=44.3MB, time=97.88
x[1] = 0.3893 0.902
h = 0.0001 0.003
y1[1] (numeric) = 1.0259071014 -0.1986137895
y1[1] (closed_form) = 1.32775771481 -0.390693676936
absolute error = 0.3578
relative error = 25.85 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.544695174485 0.952361188383
absolute error = 0.9212
relative error = 83.97 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3894 0.905
h = 0.001 0.001
y1[1] (numeric) = 1.0261816453 -0.199222597025
y1[1] (closed_form) = 1.33056618395 -0.392425155947
absolute error = 0.3605
relative error = 25.99 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.546002767752 0.956309515397
absolute error = 0.9254
relative error = 84.03 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=6932.0MB, alloc=44.3MB, time=98.57
x[1] = 0.3904 0.906
h = 0.001 0.003
y1[1] (numeric) = 1.02608015188 -0.199520430614
y1[1] (closed_form) = 1.33097609777 -0.393928798933
absolute error = 0.3616
relative error = 26.05 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.547726715714 0.957247109847
absolute error = 0.9269
relative error = 84.05 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3914 0.909
h = 0.0001 0.004
y1[1] (numeric) = 1.02617499863 -0.200217591215
y1[1] (closed_form) = 1.333304255 -0.396534800631
absolute error = 0.3645
relative error = 26.2 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.550244547811 0.960848297435
absolute error = 0.9312
relative error = 84.1 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=6981.3MB, alloc=44.3MB, time=99.25
x[1] = 0.3915 0.913
h = 0.003 0.006
y1[1] (numeric) = 1.02654771261 -0.201026062245
y1[1] (closed_form) = 1.33710313469 -0.398835573902
absolute error = 0.3682
relative error = 26.39 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.551968806278 0.966149336747
absolute error = 0.9368
relative error = 84.19 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=7030.8MB, alloc=44.3MB, time=99.92
x[1] = 0.3945 0.919
h = 0.0001 0.005
y1[1] (numeric) = 1.0265377426 -0.20251855353
y1[1] (closed_form) = 1.34125497745 -0.405075339777
absolute error = 0.3743
relative error = 26.71 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.558398041234 0.972978548635
absolute error = 0.9455
relative error = 84.28 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3946 0.924
h = 0.0001 0.003
y1[1] (numeric) = 1.02700862667 -0.203526688066
y1[1] (closed_form) = 1.34608060642 -0.407970372731
absolute error = 0.379
relative error = 26.94 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.560565017225 0.979656221583
absolute error = 0.9525
relative error = 84.39 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=7080.3MB, alloc=44.3MB, time=100.60
x[1] = 0.3947 0.927
h = 0.001 0.001
y1[1] (numeric) = 1.02728317057 -0.204135495591
y1[1] (closed_form) = 1.34896945097 -0.409752274013
absolute error = 0.3818
relative error = 27.08 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.561926352478 0.983657907607
absolute error = 0.9567
relative error = 84.45 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=7129.8MB, alloc=44.3MB, time=101.27
x[1] = 0.3957 0.928
h = 0.001 0.003
y1[1] (numeric) = 1.02718167715 -0.20443332918
y1[1] (closed_form) = 1.34939077226 -0.411299207383
absolute error = 0.3829
relative error = 27.14 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.563686058174 0.984596562271
absolute error = 0.9583
relative error = 84.46 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3967 0.931
h = 0.0001 0.004
y1[1] (numeric) = 1.02727652389 -0.205130489781
y1[1] (closed_form) = 1.35178504006 -0.413980561452
absolute error = 0.3859
relative error = 27.3 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.566274562188 0.988235684973
absolute error = 0.9626
relative error = 84.52 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=7179.2MB, alloc=44.3MB, time=101.94
x[1] = 0.3968 0.935
h = 0.003 0.006
y1[1] (numeric) = 1.02764923788 -0.205938960811
y1[1] (closed_form) = 1.35569200736 -0.416348340583
absolute error = 0.3897
relative error = 27.48 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.568070591093 0.993609115583
absolute error = 0.9683
relative error = 84.6 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=7228.7MB, alloc=44.3MB, time=102.62
x[1] = 0.3998 0.941
h = 0.0001 0.005
y1[1] (numeric) = 1.02763926787 -0.207431452096
y1[1] (closed_form) = 1.35996023861 -0.422767669032
absolute error = 0.396
relative error = 27.81 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.574661381997 1.00049740258
absolute error = 0.9771
relative error = 84.69 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.3999 0.946
h = 0.0001 0.003
y1[1] (numeric) = 1.02811015193 -0.208439586632
y1[1] (closed_form) = 1.36492206093 -0.425747001366
absolute error = 0.4008
relative error = 28.03 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.576918907523 1.00726716869
absolute error = 0.9843
relative error = 84.79 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=7278.2MB, alloc=44.3MB, time=103.30
x[1] = 0.4 0.949
h = 0.001 0.001
y1[1] (numeric) = 1.02838469584 -0.209048394157
y1[1] (closed_form) = 1.36789218241 -0.427580811057
absolute error = 0.4038
relative error = 28.17 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.578335538689 1.01132372069
absolute error = 0.9886
relative error = 84.85 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.401 0.95
h = 0.001 0.003
y1[1] (numeric) = 1.02828320241 -0.209346227746
y1[1] (closed_form) = 1.36832474248 -0.429171838353
absolute error = 0.4049
relative error = 28.24 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.58013202332 1.01226345313
absolute error = 0.9901
relative error = 84.86 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=7327.6MB, alloc=44.3MB, time=103.98
x[1] = 0.402 0.953
h = 0.0001 0.004
y1[1] (numeric) = 1.02837804916 -0.210043388347
y1[1] (closed_form) = 1.37078558713 -0.431930325671
absolute error = 0.408
relative error = 28.39 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.582793228117 1.01594156642
absolute error = 0.9945
relative error = 84.91 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=7377.1MB, alloc=44.3MB, time=104.65
x[1] = 0.4021 0.957
h = 0.003 0.006
y1[1] (numeric) = 1.02875076315 -0.210851859377
y1[1] (closed_form) = 1.37480187109 -0.434367101361
absolute error = 0.412
relative error = 28.57 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.58466309949 1.02138941933
absolute error = 1
relative error = 84.99 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4051 0.963
h = 0.0001 0.005
y1[1] (numeric) = 1.02874079313 -0.212344350662
y1[1] (closed_form) = 1.37918693971 -0.440969914527
absolute error = 0.4184
relative error = 28.9 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.591420057703 1.02833838487
absolute error = 1.009
relative error = 85.08 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=7426.7MB, alloc=44.3MB, time=105.31
x[1] = 0.4052 0.968
h = 0.0001 0.003
y1[1] (numeric) = 1.0292116772 -0.213352485198
y1[1] (closed_form) = 1.38428652278 -0.444036061772
absolute error = 0.4234
relative error = 29.13 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.59377074085 1.03520280413
absolute error = 1.017
relative error = 85.18 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=7476.2MB, alloc=44.3MB, time=105.98
x[1] = 0.4053 0.971
h = 0.001 0.001
y1[1] (numeric) = 1.0294862211 -0.213961292723
y1[1] (closed_form) = 1.38733884766 -0.445923308634
absolute error = 0.4265
relative error = 29.26 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.595244259865 1.03931574121
absolute error = 1.021
relative error = 85.24 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4063 0.972
h = 0.0001 0.004
y1[1] (numeric) = 1.02938472768 -0.214259126312
y1[1] (closed_form) = 1.38778247267 -0.447559256122
absolute error = 0.4276
relative error = 29.33 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.59707856165 1.0402565609
absolute error = 1.022
relative error = 85.25 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=7525.5MB, alloc=44.3MB, time=106.65
x[1] = 0.4064 0.976
h = 0.003 0.006
y1[1] (numeric) = 1.02975744167 -0.215067597343
y1[1] (closed_form) = 1.39189471796 -0.450055736569
absolute error = 0.4317
relative error = 29.51 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.59901277255 1.04577102731
absolute error = 1.028
relative error = 85.32 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=7574.8MB, alloc=44.3MB, time=107.31
x[1] = 0.4094 0.982
h = 0.0001 0.005
y1[1] (numeric) = 1.02974747165 -0.216560088627
y1[1] (closed_form) = 1.39638297508 -0.456818313403
absolute error = 0.4383
relative error = 29.84 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.605915774694 1.05277555426
absolute error = 1.037
relative error = 85.41 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4095 0.987
h = 0.0001 0.003
y1[1] (numeric) = 1.03021835572 -0.217568223163
y1[1] (closed_form) = 1.40160350185 -0.459959589907
absolute error = 0.4435
relative error = 30.06 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.608347613133 1.05972466729
absolute error = 1.045
relative error = 85.5 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=7624.3MB, alloc=44.3MB, time=107.98
x[1] = 0.4096 0.99
h = 0.001 0.001
y1[1] (numeric) = 1.03049289962 -0.218177030688
y1[1] (closed_form) = 1.4047280078 -0.46189309642
absolute error = 0.4466
relative error = 30.2 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.609870707389 1.06388806888
absolute error = 1.049
relative error = 85.56 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4106 0.991
h = 0.001 0.003
y1[1] (numeric) = 1.0303914062 -0.218474864278
y1[1] (closed_form) = 1.40518156271 -0.463568260075
absolute error = 0.4478
relative error = 30.26 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.611738392695 1.06483029329
absolute error = 1.051
relative error = 85.57 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=7673.9MB, alloc=44.3MB, time=108.65
x[1] = 0.4116 0.994
h = 0.0001 0.004
y1[1] (numeric) = 1.03048625295 -0.219172024878
y1[1] (closed_form) = 1.40776854576 -0.46647438182
absolute error = 0.4511
relative error = 30.42 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.614539927967 1.06858469603
absolute error = 1.055
relative error = 85.62 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=7723.4MB, alloc=44.3MB, time=109.32
x[1] = 0.4117 0.998
h = 0.003 0.006
y1[1] (numeric) = 1.03085896693 -0.219980495909
y1[1] (closed_form) = 1.41199250997 -0.469043699975
absolute error = 0.4553
relative error = 30.6 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.61655194913 1.07417743492
absolute error = 1.061
relative error = 85.69 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4147 1.004
h = 0.0001 0.005
y1[1] (numeric) = 1.03084899692 -0.221472987193
y1[1] (closed_form) = 1.41659851692 -0.475997350754
absolute error = 0.4622
relative error = 30.93 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.623629921692 1.08124565176
absolute error = 1.071
relative error = 85.77 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=7772.8MB, alloc=44.3MB, time=109.99
x[1] = 0.4148 1.009
h = 0.0001 0.003
y1[1] (numeric) = 1.03131988099 -0.222481121729
y1[1] (closed_form) = 1.42195986634 -0.479230295157
absolute error = 0.4675
relative error = 31.15 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.62615991287 1.08829427187
absolute error = 1.078
relative error = 85.86 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=7822.3MB, alloc=44.3MB, time=110.66
x[1] = 0.4149 1.012
h = 0.001 0.001
y1[1] (numeric) = 1.03159442489 -0.223089929254
y1[1] (closed_form) = 1.42516838571 -0.481220188351
absolute error = 0.4707
relative error = 31.29 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.627742943611 1.09251693864
absolute error = 1.083
relative error = 85.92 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4159 1.013
h = 0.001 0.003
y1[1] (numeric) = 1.03149293147 -0.223387762844
y1[1] (closed_form) = 1.42563267791 -0.482941873557
absolute error = 0.4719
relative error = 31.35 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.629650425017 1.09346025845
absolute error = 1.084
relative error = 85.93 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=7871.8MB, alloc=44.3MB, time=111.34
x[1] = 0.4169 1.016
h = 0.0001 0.004
y1[1] (numeric) = 1.03158777821 -0.224084923444
y1[1] (closed_form) = 1.42828766252 -0.485930500389
absolute error = 0.4753
relative error = 31.51 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.632530689929 1.09725670169
absolute error = 1.089
relative error = 85.97 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=7921.2MB, alloc=44.3MB, time=112.00
x[1] = 0.417 1.02
h = 0.003 0.006
y1[1] (numeric) = 1.0319604922 -0.224893394475
y1[1] (closed_form) = 1.43262467224 -0.488574812767
absolute error = 0.4796
relative error = 31.69 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.634622743007 1.10292979367
absolute error = 1.095
relative error = 86.04 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.42 1.026
h = 0.0001 0.005
y1[1] (numeric) = 1.03195052219 -0.226385885759
y1[1] (closed_form) = 1.43734890729 -0.495723782022
absolute error = 0.4867
relative error = 32.01 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.64188056143 1.11006327224
absolute error = 1.104
relative error = 86.12 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=7970.6MB, alloc=44.3MB, time=112.66
x[1] = 0.4201 1.031
h = 0.0001 0.003
y1[1] (numeric) = 1.03242140625 -0.227394020295
y1[1] (closed_form) = 1.44285276974 -0.499051118659
absolute error = 0.4922
relative error = 32.24 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.64451150269 1.11721402302
absolute error = 1.112
relative error = 86.21 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4202 1.034
h = 0.001 0.001
y1[1] (numeric) = 1.03269595016 -0.22800282782
y1[1] (closed_form) = 1.4461463013 -0.501099054055
absolute error = 0.4955
relative error = 32.38 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.646156176457 1.12149751099
absolute error = 1.116
relative error = 86.26 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=8020.3MB, alloc=44.3MB, time=113.34
x[1] = 0.4212 1.035
h = 0.001 0.003
y1[1] (numeric) = 1.03259445673 -0.22830066141
y1[1] (closed_form) = 1.44662114094 -0.502868154048
absolute error = 0.4968
relative error = 32.44 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.648104543624 1.12244191143
absolute error = 1.118
relative error = 86.27 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=8069.7MB, alloc=44.3MB, time=114.00
x[1] = 0.4222 1.038
h = 0.0001 0.004
y1[1] (numeric) = 1.03268930348 -0.22899782201
y1[1] (closed_form) = 1.44934464057 -0.505941267741
absolute error = 0.5003
relative error = 32.59 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.651065736754 1.12628145431
absolute error = 1.123
relative error = 86.31 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4223 1.042
h = 0.003 0.006
y1[1] (numeric) = 1.03306201747 -0.229806293041
y1[1] (closed_form) = 1.45379605643 -0.508662791411
absolute error = 0.5048
relative error = 32.77 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.653240098626 1.13203699798
absolute error = 1.129
relative error = 86.38 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=8119.1MB, alloc=44.3MB, time=114.67
x[1] = 0.4253 1.048
h = 0.0001 0.005
y1[1] (numeric) = 1.03305204745 -0.231298784325
y1[1] (closed_form) = 1.45863900622 -0.516011440294
absolute error = 0.512
relative error = 33.09 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.660682735568 1.13923729795
absolute error = 1.139
relative error = 86.46 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=8168.6MB, alloc=44.3MB, time=115.34
x[1] = 0.4254 1.053
h = 0.0001 0.003
y1[1] (numeric) = 1.03352293152 -0.232306918861
y1[1] (closed_form) = 1.46428711504 -0.519435969772
absolute error = 0.5177
relative error = 33.32 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.6634174941 1.146492826
absolute error = 1.146
relative error = 86.54 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4255 1.056
h = 0.001 0.001
y1[1] (numeric) = 1.03379747542 -0.232915726386
y1[1] (closed_form) = 1.46766668276 -0.521543649181
absolute error = 0.5211
relative error = 33.46 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.665125559721 1.15083870454
absolute error = 1.151
relative error = 86.59 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=8218.2MB, alloc=44.3MB, time=116.01
x[1] = 0.4265 1.057
h = 0.001 0.003
y1[1] (numeric) = 1.033695982 -0.233213559976
y1[1] (closed_form) = 1.46815187375 -0.523361081274
absolute error = 0.5224
relative error = 33.52 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.667115921207 1.15178416179
absolute error = 1.153
relative error = 86.6 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=8267.6MB, alloc=44.3MB, time=116.68
x[1] = 0.4275 1.06
h = 0.0001 0.004
y1[1] (numeric) = 1.03379082875 -0.233910720576
y1[1] (closed_form) = 1.47094441341 -0.526520718098
absolute error = 0.526
relative error = 33.67 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.670160288078 1.15566786425
absolute error = 1.157
relative error = 86.64 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4276 1.064
h = 0.003 0.006
y1[1] (numeric) = 1.03416354273 -0.234719191607
y1[1] (closed_form) = 1.47551163021 -0.529321732014
absolute error = 0.5306
relative error = 33.85 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.672419292381 1.16150797658
absolute error = 1.164
relative error = 86.71 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=8317.1MB, alloc=44.3MB, time=117.34
x[1] = 0.4306 1.07
h = 0.0001 0.005
y1[1] (numeric) = 1.03415357272 -0.236211682891
y1[1] (closed_form) = 1.4804737889 -0.536874540405
absolute error = 0.5381
relative error = 34.17 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.680051820348 1.16877664498
absolute error = 1.173
relative error = 86.78 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4307 1.075
h = 0.0001 0.003
y1[1] (numeric) = 1.03462445679 -0.237219817427
y1[1] (closed_form) = 1.48626792053 -0.540399141284
absolute error = 0.544
relative error = 34.4 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.682893335107 1.17613962047
absolute error = 1.181
relative error = 86.86 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=8366.7MB, alloc=44.3MB, time=118.01
x[1] = 0.4308 1.078
h = 0.001 0.001
y1[1] (numeric) = 1.03489900069 -0.237828624952
y1[1] (closed_form) = 1.48973457369 -0.54256831382
absolute error = 0.5475
relative error = 34.53 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.684666584865 1.18054947262
absolute error = 1.186
relative error = 86.91 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=8416.2MB, alloc=44.3MB, time=118.68
x[1] = 0.4318 1.079
h = 0.0001 0.004
y1[1] (numeric) = 1.03479750727 -0.238126458542
y1[1] (closed_form) = 1.49022991339 -0.544435019777
absolute error = 0.5489
relative error = 34.59 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.686700068618 1.18149595354
absolute error = 1.188
relative error = 86.92 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4319 1.083
h = 0.003 0.006
y1[1] (numeric) = 1.03517022125 -0.238934929572
y1[1] (closed_form) = 1.49489893585 -0.54730492676
absolute error = 0.5536
relative error = 34.77 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.689032801451 1.18741161651
absolute error = 1.194
relative error = 86.98 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=8465.6MB, alloc=44.3MB, time=119.34
x[1] = 0.4349 1.089
h = 0.0001 0.005
y1[1] (numeric) = 1.03516025124 -0.240427420857
y1[1] (closed_form) = 1.49996661329 -0.555035720302
absolute error = 0.5613
relative error = 35.09 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.696832082174 1.19474270909
absolute error = 1.204
relative error = 87.05 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=8515.1MB, alloc=44.3MB, time=120.01
x[1] = 0.435 1.094
h = 0.0001 0.003
y1[1] (numeric) = 1.03563113531 -0.241435555393
y1[1] (closed_form) = 1.50588913222 -0.55864705615
absolute error = 0.5672
relative error = 35.32 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.69976657517 1.20220164903
absolute error = 1.212
relative error = 87.13 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4351 1.097
h = 0.001 0.001
y1[1] (numeric) = 1.03590567921 -0.242044362918
y1[1] (closed_form) = 1.50943236697 -0.560869542607
absolute error = 0.5709
relative error = 35.45 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.701596614548 1.20666865219
absolute error = 1.217
relative error = 87.18 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=8564.6MB, alloc=44.3MB, time=120.68
x[1] = 0.4361 1.098
h = 0.001 0.003
y1[1] (numeric) = 1.03580418579 -0.242342196507
y1[1] (closed_form) = 1.5099368775 -0.562779317474
absolute error = 0.5723
relative error = 35.51 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.703668123443 1.20761651273
absolute error = 1.219
relative error = 87.19 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=8614.1MB, alloc=44.3MB, time=121.34
x[1] = 0.4371 1.101
h = 0.0001 0.004
y1[1] (numeric) = 1.03589903253 -0.243039357108
y1[1] (closed_form) = 1.5128604109 -0.566104726636
absolute error = 0.5761
relative error = 35.66 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.706872844032 1.2115862656
absolute error = 1.224
relative error = 87.22 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4372 1.105
h = 0.003 0.006
y1[1] (numeric) = 1.03627174652 -0.243847828138
y1[1] (closed_form) = 1.51764794991 -0.569058516293
absolute error = 0.5809
relative error = 35.84 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.709294692308 1.21759051632
absolute error = 1.23
relative error = 87.29 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=8663.6MB, alloc=44.3MB, time=122.00
x[1] = 0.4402 1.111
h = 0.0001 0.005
y1[1] (numeric) = 1.03626177651 -0.245340319423
y1[1] (closed_form) = 1.52283582989 -0.577002122713
absolute error = 0.5889
relative error = 36.16 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.71729355969 1.22499288404
absolute error = 1.24
relative error = 87.35 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4403 1.116
h = 0.0001 0.003
y1[1] (numeric) = 1.03673266058 -0.246348453959
y1[1] (closed_form) = 1.52890782892 -0.580719077334
absolute error = 0.595
relative error = 36.38 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.720340442897 1.23256434161
absolute error = 1.248
relative error = 87.43 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=8713.1MB, alloc=44.3MB, time=122.67
x[1] = 0.4404 1.119
h = 0.001 0.001
y1[1] (numeric) = 1.03700720448 -0.246957261484
y1[1] (closed_form) = 1.53254019133 -0.583006427889
absolute error = 0.5987
relative error = 36.52 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.722239101907 1.23709832407
absolute error = 1.253
relative error = 87.48 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=8762.7MB, alloc=44.3MB, time=123.34
x[1] = 0.4414 1.12
h = 0.001 0.003
y1[1] (numeric) = 1.03690571106 -0.247255095073
y1[1] (closed_form) = 1.53305446689 -0.584967298027
absolute error = 0.6002
relative error = 36.58 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.724355885941 1.23804713488
absolute error = 1.255
relative error = 87.48 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4424 1.123
h = 0.0001 0.004
y1[1] (numeric) = 1.0370005578 -0.247952255674
y1[1] (closed_form) = 1.5360486303 -0.588385359397
absolute error = 0.6041
relative error = 36.73 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.727650462271 1.24206411217
absolute error = 1.26
relative error = 87.52 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=8812.3MB, alloc=44.3MB, time=124.00
x[1] = 0.4425 1.127
h = 0.003 0.006
y1[1] (numeric) = 1.03737327179 -0.248760726704
y1[1] (closed_form) = 1.54095617972 -0.591425494966
absolute error = 0.6091
relative error = 36.9 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.730163930464 1.24815912329
absolute error = 1.266
relative error = 87.58 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=8861.9MB, alloc=44.3MB, time=124.67
x[1] = 0.4455 1.133
h = 0.0001 0.005
y1[1] (numeric) = 1.03736330177 -0.250253217989
y1[1] (closed_form) = 1.54626477492 -0.59958674584
absolute error = 0.6173
relative error = 37.22 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.738367757735 1.25563427559
absolute error = 1.277
relative error = 87.65 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4456 1.138
h = 0.0001 0.003
y1[1] (numeric) = 1.03783418584 -0.251261352525
y1[1] (closed_form) = 1.55248815555 -0.603412429978
absolute error = 0.6236
relative error = 37.44 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.741530186095 1.26332099221
absolute error = 1.285
relative error = 87.72 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=8911.3MB, alloc=44.3MB, time=125.34
x[1] = 0.4457 1.141
h = 0.001 0.001
y1[1] (numeric) = 1.03810872974 -0.25187016005
y1[1] (closed_form) = 1.55621076826 -0.605766534617
absolute error = 0.6274
relative error = 37.57 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.743499387782 1.2679235783
absolute error = 1.29
relative error = 87.76 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=8961.0MB, alloc=44.3MB, time=126.01
x[1] = 0.4467 1.142
h = 0.001 0.003
y1[1] (numeric) = 1.03800723632 -0.252167993639
y1[1] (closed_form) = 1.55673458601 -0.607779513969
absolute error = 0.6289
relative error = 37.63 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.745662633325 1.26887327831
absolute error = 1.292
relative error = 87.77 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4477 1.145
h = 0.0001 0.004
y1[1] (numeric) = 1.03810208307 -0.25286515424
y1[1] (closed_form) = 1.55979994739 -0.611292484211
absolute error = 0.633
relative error = 37.78 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.749049504299 1.2729385431
absolute error = 1.297
relative error = 87.81 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=9010.5MB, alloc=44.3MB, time=126.67
x[1] = 0.4478 1.149
h = 0.003 0.006
y1[1] (numeric) = 1.03847479705 -0.25367362527
y1[1] (closed_form) = 1.56482903566 -0.614421496287
absolute error = 0.6381
relative error = 37.96 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.751657159822 1.27912650729
absolute error = 1.304
relative error = 87.87 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4508 1.155
h = 0.0001 0.005
y1[1] (numeric) = 1.03846482704 -0.255166116555
y1[1] (closed_form) = 1.57025886305 -0.622805350575
absolute error = 0.6465
relative error = 38.27 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.76007143063 1.28667593898
absolute error = 1.314
relative error = 87.93 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=9059.9MB, alloc=44.3MB, time=127.34
x[1] = 0.4509 1.16
h = 0.0001 0.003
y1[1] (numeric) = 1.03893571111 -0.256174251091
y1[1] (closed_form) = 1.57663557045 -0.626742959848
absolute error = 0.653
relative error = 38.49 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.763352638644 1.29448068166
absolute error = 1.322
relative error = 88 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=9109.5MB, alloc=44.3MB, time=128.00
x[1] = 0.451 1.163
h = 0.001 0.001
y1[1] (numeric) = 1.03921025501 -0.256783058616
y1[1] (closed_form) = 1.58044958165 -0.629165760041
absolute error = 0.657
relative error = 38.62 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.765394354218 1.29915351056
absolute error = 1.328
relative error = 88.04 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.452 1.164
h = 0.001 0.003
y1[1] (numeric) = 1.03910876159 -0.257080892205
y1[1] (closed_form) = 1.58098271095 -0.631231888533
absolute error = 0.6585
relative error = 38.68 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.767605269031 1.30010402825
absolute error = 1.329
relative error = 88.05 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=9159.0MB, alloc=44.3MB, time=128.68
x[1] = 0.453 1.167
h = 0.0001 0.004
y1[1] (numeric) = 1.03920360833 -0.257778052806
y1[1] (closed_form) = 1.58411984857 -0.634842084188
absolute error = 0.6627
relative error = 38.83 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.771086926891 1.3042186441
absolute error = 1.335
relative error = 88.08 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=9208.6MB, alloc=44.3MB, time=129.35
x[1] = 0.4531 1.171
h = 0.003 0.006
y1[1] (numeric) = 1.03957632232 -0.258586523836
y1[1] (closed_form) = 1.58927203884 -0.638062572231
absolute error = 0.668
relative error = 39 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.773791401776 1.31050177445
absolute error = 1.341
relative error = 88.14 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4561 1.177
h = 0.0001 0.005
y1[1] (numeric) = 1.03956635231 -0.260079015121
y1[1] (closed_form) = 1.59482361873 -0.646674118654
absolute error = 0.6766
relative error = 39.31 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.782421713041 1.31812696512
absolute error = 1.352
relative error = 88.2 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=9258.0MB, alloc=44.3MB, time=130.03
x[1] = 0.4562 1.182
h = 0.0001 0.003
y1[1] (numeric) = 1.04003723638 -0.261087149657
y1[1] (closed_form) = 1.60135564186 -0.650726935469
absolute error = 0.6833
relative error = 39.53 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.785825016891 1.326052527
absolute error = 1.361
relative error = 88.27 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=9307.6MB, alloc=44.3MB, time=130.70
x[1] = 0.4563 1.185
h = 0.001 0.001
y1[1] (numeric) = 1.04031178028 -0.261695957182
y1[1] (closed_form) = 1.60526222542 -0.653220425321
absolute error = 0.6874
relative error = 39.66 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.787941267003 1.33079725298
absolute error = 1.366
relative error = 88.31 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4573 1.186
h = 0.0001 0.004
y1[1] (numeric) = 1.04021028686 -0.261993790771
y1[1] (closed_form) = 1.60580442748 -0.655340769284
absolute error = 0.6889
relative error = 39.72 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.790201080769 1.33174850609
absolute error = 1.368
relative error = 88.32 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=9357.1MB, alloc=44.3MB, time=131.36
x[1] = 0.4574 1.19
h = 0.003 0.006
y1[1] (numeric) = 1.04058300084 -0.262802261802
y1[1] (closed_form) = 1.61106499123 -0.658640639716
absolute error = 0.6944
relative error = 39.89 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.792989882917 1.33811653755
absolute error = 1.375
relative error = 88.37 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4604 1.196
h = 0.0001 0.005
y1[1] (numeric) = 1.04057303083 -0.264294753087
y1[1] (closed_form) = 1.61672458735 -0.667450892933
absolute error = 0.7032
relative error = 40.2 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.801809798955 1.34581077814
absolute error = 1.385
relative error = 88.43 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=9406.6MB, alloc=44.3MB, time=132.02
x[1] = 0.4605 1.201
h = 0.0001 0.003
y1[1] (numeric) = 1.0410439149 -0.265302887623
y1[1] (closed_form) = 1.62339335455 -0.671603689554
absolute error = 0.7101
relative error = 40.42 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.80531943333 1.35384410383
absolute error = 1.394
relative error = 88.5 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=9456.2MB, alloc=44.3MB, time=132.69
x[1] = 0.4606 1.204
h = 0.001 0.001
y1[1] (numeric) = 1.0413184588 -0.265911695147
y1[1] (closed_form) = 1.6273814563 -0.674158542365
absolute error = 0.7142
relative error = 40.55 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.807500613544 1.35865297444
absolute error = 1.399
relative error = 88.54 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4616 1.205
h = 0.001 0.003
y1[1] (numeric) = 1.04121696538 -0.266209528737
y1[1] (closed_form) = 1.62793193378 -0.676326323518
absolute error = 0.7158
relative error = 40.61 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.809803512513 1.35960538908
absolute error = 1.401
relative error = 88.55 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=9505.7MB, alloc=44.3MB, time=133.36
x[1] = 0.4626 1.208
h = 0.0001 0.004
y1[1] (numeric) = 1.04131181212 -0.266906689337
y1[1] (closed_form) = 1.63120542976 -0.680122936874
absolute error = 0.7202
relative error = 40.75 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.813467750538 1.36381586952
absolute error = 1.407
relative error = 88.58 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=9555.3MB, alloc=44.3MB, time=134.02
x[1] = 0.4627 1.212
h = 0.003 0.006
y1[1] (numeric) = 1.04168452611 -0.267715160368
y1[1] (closed_form) = 1.63659212978 -0.683519289288
absolute error = 0.7258
relative error = 40.92 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.816358420585 1.37028327411
absolute error = 1.414
relative error = 88.63 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4657 1.218
h = 0.0001 0.005
y1[1] (numeric) = 1.04167455609 -0.269207651653
y1[1] (closed_form) = 1.64237451664 -0.692567051096
absolute error = 0.7349
relative error = 41.23 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.825405085902 1.37805605419
absolute error = 1.425
relative error = 88.69 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=9604.9MB, alloc=44.3MB, time=134.68
x[1] = 0.4658 1.223
h = 0.0001 0.003
y1[1] (numeric) = 1.04214544016 -0.270215786189
y1[1] (closed_form) = 1.64920245927 -0.696841375862
absolute error = 0.742
relative error = 41.44 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.829043177562 1.38621550952
absolute error = 1.434
relative error = 88.76 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=9654.4MB, alloc=44.3MB, time=135.34
x[1] = 0.4659 1.226
h = 0.001 0.001
y1[1] (numeric) = 1.04241998406 -0.270824593713
y1[1] (closed_form) = 1.65328541145 -0.699470758353
absolute error = 0.7463
relative error = 41.57 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.83130276822 1.39109942217
absolute error = 1.439
relative error = 88.79 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4669 1.227
h = 0.001 0.003
y1[1] (numeric) = 1.04231849064 -0.271122427303
y1[1] (closed_form) = 1.65384450789 -0.701694814016
absolute error = 0.7479
relative error = 41.63 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.833656915807 1.39205240474
absolute error = 1.441
relative error = 88.8 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=9704.0MB, alloc=44.3MB, time=136.00
x[1] = 0.4679 1.23
h = 0.0001 0.004
y1[1] (numeric) = 1.04241333739 -0.271819587903
y1[1] (closed_form) = 1.65719151904 -0.705595614021
absolute error = 0.7524
relative error = 41.77 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.83742336482 1.3963153126
absolute error = 1.446
relative error = 88.83 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.468 1.234
h = 0.003 0.006
y1[1] (numeric) = 1.04278605137 -0.272628058934
y1[1] (closed_form) = 1.66270601918 -0.709091253167
absolute error = 0.7582
relative error = 41.94 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.840418729002 1.40288436478
absolute error = 1.454
relative error = 88.88 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=9753.5MB, alloc=44.3MB, time=136.66
x[1] = 0.471 1.24
h = 0.0001 0.005
y1[1] (numeric) = 1.04277608136 -0.274120550219
y1[1] (closed_form) = 1.668611723 -0.7183819972
absolute error = 0.7675
relative error = 42.25 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.84969808093 1.4107371183
absolute error = 1.465
relative error = 88.94 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=9803.1MB, alloc=44.3MB, time=137.32
x[1] = 0.4711 1.245
h = 0.0001 0.003
y1[1] (numeric) = 1.04324696543 -0.275128684755
y1[1] (closed_form) = 1.67560095723 -0.722781391272
absolute error = 0.7748
relative error = 42.46 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.853468191493 1.41902557489
absolute error = 1.474
relative error = 89 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4712 1.248
h = 0.001 0.001
y1[1] (numeric) = 1.04352150933 -0.275737492279
y1[1] (closed_form) = 1.67978000811 -0.725487454456
absolute error = 0.7792
relative error = 42.58 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.855808361809 1.42398622929
absolute error = 1.479
relative error = 89.04 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=9852.7MB, alloc=44.3MB, time=137.98
x[1] = 0.4722 1.249
h = 0.001 0.003
y1[1] (numeric) = 1.04342001591 -0.276035325869
y1[1] (closed_form) = 1.68034745973 -0.727768929016
absolute error = 0.7809
relative error = 42.64 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.858215053576 1.42493966524
absolute error = 1.481
relative error = 89.05 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=9902.3MB, alloc=44.3MB, time=138.64
x[1] = 0.4732 1.252
h = 0.0001 0.004
y1[1] (numeric) = 1.04351486266 -0.276732486469
y1[1] (closed_form) = 1.68376860231 -0.731776474717
absolute error = 0.7855
relative error = 42.78 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.862086424973 1.42925606569
absolute error = 1.487
relative error = 89.08 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4733 1.256
h = 0.003 0.006
y1[1] (numeric) = 1.04388757664 -0.2775409575
y1[1] (closed_form) = 1.6894126015 -0.735374280415
absolute error = 0.7914
relative error = 42.95 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.865189380964 1.43592906187
absolute error = 1.494
relative error = 89.13 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=9951.9MB, alloc=44.3MB, time=139.30
x[1] = 0.4763 1.262
h = 0.0001 0.005
y1[1] (numeric) = 1.04387760663 -0.279033448785
y1[1] (closed_form) = 1.69544214805 -0.744913619851
absolute error = 0.801
relative error = 43.25 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.874707481571 1.44386320497
absolute error = 1.506
relative error = 89.18 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=10001.4MB, alloc=44.3MB, time=139.96
x[1] = 0.4764 1.267
h = 0.0001 0.003
y1[1] (numeric) = 1.0443484907 -0.280041583321
y1[1] (closed_form) = 1.70259483442 -0.749441719025
absolute error = 0.8085
relative error = 43.46 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.878613262932 1.45228356245
absolute error = 1.515
relative error = 89.24 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4765 1.27
h = 0.001 0.001
y1[1] (numeric) = 1.0446230346 -0.280650390845
y1[1] (closed_form) = 1.70687125823 -0.752226671286
absolute error = 0.813
relative error = 43.59 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.881036236755 1.45732267452
absolute error = 1.52
relative error = 89.28 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=10051.1MB, alloc=44.3MB, time=140.62
x[1] = 0.4775 1.271
h = 0.001 0.003
y1[1] (numeric) = 1.04452154118 -0.280948224435
y1[1] (closed_form) = 1.70744679166 -0.75456673726
absolute error = 0.8147
relative error = 43.64 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.883496792325 1.45827643725
absolute error = 1.522
relative error = 89.29 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4785 1.274
h = 0.0001 0.004
y1[1] (numeric) = 1.04461638792 -0.281645385035
y1[1] (closed_form) = 1.71094269082 -0.758683653659
absolute error = 0.8195
relative error = 43.79 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.887475857814 1.46264739535
absolute error = 1.528
relative error = 89.32 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=10100.6MB, alloc=44.3MB, time=141.28
x[1] = 0.4786 1.278
h = 0.003 0.006
y1[1] (numeric) = 1.04498910191 -0.282453856066
y1[1] (closed_form) = 1.7167179232 -0.762386582511
absolute error = 0.8256
relative error = 43.95 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.890689376583 1.46942665425
absolute error = 1.536
relative error = 89.36 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=10150.0MB, alloc=44.3MB, time=141.93
x[1] = 0.4816 1.284
h = 0.0001 0.005
y1[1] (numeric) = 1.04497913189 -0.283946347351
y1[1] (closed_form) = 1.72287183677 -0.772180272749
absolute error = 0.8354
relative error = 44.25 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.900452415772 1.4774435845
absolute error = 1.547
relative error = 89.42 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4817 1.289
h = 0.0001 0.003
y1[1] (numeric) = 1.04545001596 -0.284954481887
y1[1] (closed_form) = 1.7301901803 -0.776840809622
absolute error = 0.8431
relative error = 44.45 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.904497612441 1.48599877101
absolute error = 1.557
relative error = 89.48 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=10199.6MB, alloc=44.3MB, time=142.60
x[1] = 0.4818 1.292
h = 0.001 0.001
y1[1] (numeric) = 1.04572455986 -0.285563289411
y1[1] (closed_form) = 1.73456527727 -0.779706918021
absolute error = 0.8477
relative error = 44.58 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.907005669671 1.4911180731
absolute error = 1.562
relative error = 89.51 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=10249.4MB, alloc=44.3MB, time=143.26
x[1] = 0.4828 1.293
h = 0.0001 0.004
y1[1] (numeric) = 1.04562306644 -0.285861123001
y1[1] (closed_form) = 1.73514860917 -0.782106776524
absolute error = 0.8495
relative error = 44.64 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.909521433302 1.49207202361
absolute error = 1.564
relative error = 89.52 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4829 1.297
h = 0.003 0.006
y1[1] (numeric) = 1.04599578043 -0.286669594031
y1[1] (closed_form) = 1.74103951996 -0.78590102735
absolute error = 0.8558
relative error = 44.8 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.912831253448 1.49894599054
absolute error = 1.572
relative error = 89.56 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=10298.9MB, alloc=44.3MB, time=143.92
x[1] = 0.4859 1.303
h = 0.0001 0.005
y1[1] (numeric) = 1.04598581041 -0.288162085316
y1[1] (closed_form) = 1.74730402816 -0.795916883753
absolute error = 0.8658
relative error = 45.09 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.922809175776 1.50703830604
absolute error = 1.584
relative error = 89.62 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=10348.5MB, alloc=44.3MB, time=144.58
x[1] = 0.486 1.308
h = 0.0001 0.003
y1[1] (numeric) = 1.04645669448 -0.289170219852
y1[1] (closed_form) = 1.75476840363 -0.800692473206
absolute error = 0.8737
relative error = 45.3 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.92697579339 1.51571363894
absolute error = 1.593
relative error = 89.67 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4861 1.311
h = 0.001 0.001
y1[1] (numeric) = 1.04673123838 -0.289779027377
y1[1] (closed_form) = 1.75923050083 -0.803629102336
absolute error = 0.8785
relative error = 45.42 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.929557973505 1.52090441746
absolute error = 1.599
relative error = 89.71 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=10398.2MB, alloc=44.3MB, time=145.24
x[1] = 0.4871 1.312
h = 0.001 0.003
y1[1] (numeric) = 1.04662974496 -0.290076860966
y1[1] (closed_form) = 1.75982104283 -0.806081324154
absolute error = 0.8803
relative error = 45.48 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.932122354331 1.52185908844
absolute error = 1.601
relative error = 89.71 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4881 1.315
h = 0.0001 0.004
y1[1] (numeric) = 1.04672459171 -0.290774021567
y1[1] (closed_form) = 1.7634591193 -0.810408063493
absolute error = 0.8853
relative error = 45.62 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.936308723464 1.5263357631
absolute error = 1.607
relative error = 89.74 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=10447.7MB, alloc=44.3MB, time=145.90
x[1] = 0.4882 1.319
h = 0.003 0.006
y1[1] (numeric) = 1.04709730569 -0.291582492597
y1[1] (closed_form) = 1.7694846217 -0.81431312776
absolute error = 0.8917
relative error = 45.78 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.939734808003 1.53332040544
absolute error = 1.615
relative error = 89.79 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=10497.1MB, alloc=44.3MB, time=146.56
x[1] = 0.4912 1.325
h = 0.0001 0.005
y1[1] (numeric) = 1.04708733568 -0.293074983882
y1[1] (closed_form) = 1.77587453729 -0.824594426255
absolute error = 0.902
relative error = 46.07 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.949969521842 1.54149813389
absolute error = 1.627
relative error = 89.84 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4913 1.33
h = 0.0001 0.003
y1[1] (numeric) = 1.04755821975 -0.294083118418
y1[1] (closed_form) = 1.78350883919 -0.829509636642
absolute error = 0.9101
relative error = 46.27 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.954282741451 1.55031386913
absolute error = 1.637
relative error = 89.89 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=10546.6MB, alloc=44.3MB, time=147.22
x[1] = 0.4914 1.333
h = 0.001 0.001
y1[1] (numeric) = 1.04783276365 -0.294691925943
y1[1] (closed_form) = 1.78807212707 -0.832531784932
absolute error = 0.915
relative error = 46.39 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.956954380366 1.55558813469
absolute error = 1.642
relative error = 89.93 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=10596.2MB, alloc=44.3MB, time=147.88
x[1] = 0.4924 1.334
h = 0.001 0.003
y1[1] (numeric) = 1.04773127023 -0.294989759532
y1[1] (closed_form) = 1.78866992746 -0.835046115719
absolute error = 0.9169
relative error = 46.45 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.959576540185 1.55654271721
absolute error = 1.644
relative error = 89.93 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4934 1.337
h = 0.0001 0.004
y1[1] (numeric) = 1.04782611698 -0.295686920133
y1[1] (closed_form) = 1.79238462912 -0.839490103883
absolute error = 0.922
relative error = 46.58 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.963878866657 1.56107703006
absolute error = 1.65
relative error = 89.96 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=10645.7MB, alloc=44.3MB, time=148.54
x[1] = 0.4935 1.341
h = 0.003 0.006
y1[1] (numeric) = 1.04819883096 -0.296495391163
y1[1] (closed_form) = 1.79854655954 -0.843509167251
absolute error = 0.9286
relative error = 46.74 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.967424406561 1.56817473325
absolute error = 1.658
relative error = 90.01 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=10695.1MB, alloc=44.3MB, time=149.20
x[1] = 0.4965 1.347
h = 0.0001 0.005
y1[1] (numeric) = 1.04818886095 -0.297987882448
y1[1] (closed_form) = 1.80506239805 -0.854062085559
absolute error = 0.9392
relative error = 47.03 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.977922485342 1.57643921615
absolute error = 1.671
relative error = 90.05 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4966 1.352
h = 0.0001 0.003
y1[1] (numeric) = 1.04865974502 -0.298996016984
y1[1] (closed_form) = 1.81286896073 -0.85912093829
absolute error = 0.9475
relative error = 47.23 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.982386329427 1.58539836711
absolute error = 1.681
relative error = 90.11 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=10744.5MB, alloc=44.3MB, time=149.85
x[1] = 0.4967 1.355
h = 0.001 0.001
y1[1] (numeric) = 1.04893428892 -0.299604824509
y1[1] (closed_form) = 1.81753481498 -0.862231047847
absolute error = 0.9525
relative error = 47.35 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.985149875257 1.59075790129
absolute error = 1.687
relative error = 90.14 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.4977 1.356
h = 0.001 0.003
y1[1] (numeric) = 1.0488327955 -0.299902658098
y1[1] (closed_form) = 1.81813955992 -0.86480877336
absolute error = 0.9544
relative error = 47.41 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.987831232196 1.59171221902
absolute error = 1.689
relative error = 90.15 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=10794.1MB, alloc=44.3MB, time=150.52
x[1] = 0.4987 1.359
h = 0.0001 0.004
y1[1] (numeric) = 1.04892764224 -0.300599818699
y1[1] (closed_form) = 1.82193154397 -0.869372902799
absolute error = 0.9597
relative error = 47.54 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.992252535018 1.59630523398
absolute error = 1.695
relative error = 90.17 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=10843.5MB, alloc=44.3MB, time=151.17
x[1] = 0.4988 1.363
h = 0.003 0.006
y1[1] (numeric) = 1.04930035623 -0.301408289729
y1[1] (closed_form) = 1.82823177447 -0.873509234723
absolute error = 0.9665
relative error = 47.7 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 0.99592080209 1.60351840715
absolute error = 1.703
relative error = 90.22 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5018 1.369
h = 0.0001 0.005
y1[1] (numeric) = 1.04929038621 -0.302900781014
y1[1] (closed_form) = 1.83487404548 -0.884340103769
absolute error = 0.9774
relative error = 47.98 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.00668895955 1.61187096411
absolute error = 1.715
relative error = 90.26 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=10893.0MB, alloc=44.3MB, time=151.83
x[1] = 0.5019 1.374
h = 0.0001 0.003
y1[1] (numeric) = 1.04976127028 -0.30390891555
y1[1] (closed_form) = 1.84285524832 -0.889546725919
absolute error = 0.9859
relative error = 48.18 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.01130755271 1.62097657442
absolute error = 1.726
relative error = 90.32 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=10942.6MB, alloc=44.3MB, time=152.49
x[1] = 0.502 1.377
h = 0.001 0.001
y1[1] (numeric) = 1.05003581418 -0.304517723075
y1[1] (closed_form) = 1.84762507088 -0.892747302872
absolute error = 0.991
relative error = 48.3 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.01416551536 1.62642317626
absolute error = 1.732
relative error = 90.35 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.503 1.378
h = 0.001 0.003
y1[1] (numeric) = 1.04993432076 -0.304815556664
y1[1] (closed_form) = 1.84823643491 -0.895389739393
absolute error = 0.993
relative error = 48.35 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.01690751447 1.62737703895
absolute error = 1.734
relative error = 90.35 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=10992.2MB, alloc=44.3MB, time=153.15
x[1] = 0.504 1.381
h = 0.0001 0.004
y1[1] (numeric) = 1.05002916751 -0.305512717265
y1[1] (closed_form) = 1.85210636576 -0.900076975354
absolute error = 0.9984
relative error = 48.48 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.02145088059 1.63202981897
absolute error = 1.74
relative error = 90.38 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=11041.8MB, alloc=44.3MB, time=153.81
x[1] = 0.5041 1.385
h = 0.003 0.006
y1[1] (numeric) = 1.05040188149 -0.306321188295
y1[1] (closed_form) = 1.85854680409 -0.904333931009
absolute error = 1.005
relative error = 48.64 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.02524522952 1.63936089525
absolute error = 1.748
relative error = 90.42 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5071 1.391
h = 0.0001 0.005
y1[1] (numeric) = 1.05039191148 -0.30781367958
y1[1] (closed_form) = 1.86531601003 -0.915449237927
absolute error = 1.017
relative error = 48.92 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.03629032307 1.64780282308
absolute error = 1.761
relative error = 90.47 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=11091.2MB, alloc=44.3MB, time=154.47
x[1] = 0.5072 1.396
h = 0.0001 0.003
y1[1] (numeric) = 1.05086279555 -0.308821814116
y1[1] (closed_form) = 1.87347427755 -0.920807864671
absolute error = 1.025
relative error = 49.11 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.04106789462 1.65705796706
absolute error = 1.771
relative error = 90.52 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5073 1.399
h = 0.001 0.001
y1[1] (numeric) = 1.05113733945 -0.309430621641
y1[1] (closed_form) = 1.87834949666 -0.924101480644
absolute error = 1.031
relative error = 49.23 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.04402284733 1.66259345326
absolute error = 1.778
relative error = 90.55 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=11140.8MB, alloc=44.3MB, time=155.13
x[1] = 0.5083 1.4
h = 0.003 0.006
y1[1] (numeric) = 1.05103584603 -0.30972845523
y1[1] (closed_form) = 1.87896714226 -0.9268099755
absolute error = 1.033
relative error = 49.29 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.04682696122 1.66354665632
absolute error = 1.78
relative error = 90.56 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=11190.3MB, alloc=44.3MB, time=155.78
x[1] = 0.5113 1.406
h = 0.0001 0.005
y1[1] (numeric) = 1.05102587602 -0.311220946515
y1[1] (closed_form) = 1.88581658782 -0.938128002477
absolute error = 1.044
relative error = 49.57 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.05806889997 1.67204361515
absolute error = 1.793
relative error = 90.6 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5114 1.411
h = 0.0001 0.003
y1[1] (numeric) = 1.05149676009 -0.312229081051
y1[1] (closed_form) = 1.89409412674 -0.943598240291
absolute error = 1.053
relative error = 49.76 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.06296220014 1.68139928655
absolute error = 1.803
relative error = 90.65 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=11239.7MB, alloc=44.3MB, time=156.44
x[1] = 0.5115 1.414
h = 0.001 0.001
y1[1] (numeric) = 1.05177130399 -0.312837888576
y1[1] (closed_form) = 1.89904026632 -0.94696008205
absolute error = 1.058
relative error = 49.87 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.06598769179 1.68699445618
absolute error = 1.81
relative error = 90.68 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=11289.4MB, alloc=44.3MB, time=157.10
x[1] = 0.5125 1.415
h = 0.001 0.003
y1[1] (numeric) = 1.05166981057 -0.313135722166
y1[1] (closed_form) = 1.89966032521 -0.949714963445
absolute error = 1.06
relative error = 49.93 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.06883537945 1.68794546943
absolute error = 1.812
relative error = 90.69 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5135 1.418
h = 0.0001 0.004
y1[1] (numeric) = 1.05176465731 -0.313832882766
y1[1] (closed_form) = 1.90366007617 -0.954618923423
absolute error = 1.066
relative error = 50.06 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.07359353494 1.6926982823
absolute error = 1.818
relative error = 90.71 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=11338.9MB, alloc=44.3MB, time=157.76
x[1] = 0.5136 1.422
h = 0.003 0.006
y1[1] (numeric) = 1.0521373713 -0.314641353796
y1[1] (closed_form) = 1.91033836504 -0.95909097383
absolute error = 1.073
relative error = 50.21 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.0776116488 1.70023058392
absolute error = 1.827
relative error = 90.75 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=11388.4MB, alloc=44.3MB, time=158.42
x[1] = 0.5166 1.428
h = 0.0001 0.005
y1[1] (numeric) = 1.05212740128 -0.316133845081
y1[1] (closed_form) = 1.91731540136 -0.970704763285
absolute error = 1.085
relative error = 50.48 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.08914246495 1.70881886688
absolute error = 1.84
relative error = 90.8 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5167 1.433
h = 0.0001 0.003
y1[1] (numeric) = 1.05259828535 -0.317141979617
y1[1] (closed_form) = 1.9257740872 -0.976334469939
absolute error = 1.094
relative error = 50.67 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.09420220618 1.71832921925
absolute error = 1.851
relative error = 90.85 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=11438.0MB, alloc=44.3MB, time=159.08
x[1] = 0.5168 1.436
h = 0.001 0.001
y1[1] (numeric) = 1.05287282925 -0.317750787142
y1[1] (closed_form) = 1.93082802531 -0.979793881519
absolute error = 1.1
relative error = 50.78 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.09732922618 1.7240163119
absolute error = 1.857
relative error = 90.88 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5178 1.437
h = 0.001 0.003
y1[1] (numeric) = 1.05277133583 -0.318048620732
y1[1] (closed_form) = 1.93145373166 -0.982617158094
absolute error = 1.102
relative error = 50.84 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.10024157242 1.72496624774
absolute error = 1.859
relative error = 90.88 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=11487.6MB, alloc=44.3MB, time=159.74
x[1] = 0.5188 1.44
h = 0.0001 0.004
y1[1] (numeric) = 1.05286618258 -0.318745781332
y1[1] (closed_form) = 1.9355331672 -0.987652584673
absolute error = 1.107
relative error = 50.97 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.10513046482 1.72978159246
absolute error = 1.866
relative error = 90.91 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=11537.1MB, alloc=44.3MB, time=160.39
x[1] = 0.5189 1.444
h = 0.003 0.006
y1[1] (numeric) = 1.05323889656 -0.319554252362
y1[1] (closed_form) = 1.9423568776 -0.99225476835
absolute error = 1.115
relative error = 51.12 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.10928416798 1.73743836725
absolute error = 1.875
relative error = 90.95 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5219 1.45
h = 0.0001 0.005
y1[1] (numeric) = 1.05322892655 -0.321046743647
y1[1] (closed_form) = 1.94946197714 -1.00417124244
absolute error = 1.127
relative error = 51.39 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.12111112164 1.74611920075
absolute error = 1.888
relative error = 90.99 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=11586.5MB, alloc=44.3MB, time=161.05
x[1] = 0.522 1.455
h = 0.0001 0.003
y1[1] (numeric) = 1.05369981062 -0.322054878183
y1[1] (closed_form) = 1.95810435345 -1.00996495736
absolute error = 1.136
relative error = 51.57 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.12634182876 1.75578739007
absolute error = 1.899
relative error = 91.04 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=11636.2MB, alloc=44.3MB, time=161.71
x[1] = 0.5221 1.458
h = 0.001 0.001
y1[1] (numeric) = 1.05397435452 -0.322663685708
y1[1] (closed_form) = 1.9632675875 -1.01352469466
absolute error = 1.142
relative error = 51.69 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.12957312913 1.76156826933
absolute error = 1.906
relative error = 91.07 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5231 1.459
h = 0.001 0.003
y1[1] (numeric) = 1.0538728611 -0.322961519298
y1[1] (closed_form) = 1.96389856815 -1.01641779953
absolute error = 1.144
relative error = 51.74 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.13255168329 1.76251688165
absolute error = 1.908
relative error = 91.07 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=11685.7MB, alloc=44.3MB, time=162.37
x[1] = 0.5241 1.462
h = 0.0001 0.004
y1[1] (numeric) = 1.05396770784 -0.323658679898
y1[1] (closed_form) = 1.96805837383 -1.02158793988
absolute error = 1.15
relative error = 51.87 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.13757466459 1.76739581346
absolute error = 1.915
relative error = 91.09 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=11735.2MB, alloc=44.3MB, time=163.03
x[1] = 0.5242 1.466
h = 0.003 0.006
y1[1] (numeric) = 1.05434042183 -0.324467150928
y1[1] (closed_form) = 1.97502954354 -1.02632394647
absolute error = 1.158
relative error = 52.01 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.14186763652 1.77517958361
absolute error = 1.924
relative error = 91.13 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5272 1.472
h = 0.0001 0.005
y1[1] (numeric) = 1.05433045182 -0.325959642213
y1[1] (closed_form) = 1.98226316652 -1.03855019523
absolute error = 1.17
relative error = 52.28 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.15399814439 1.78395416718
absolute error = 1.937
relative error = 91.18 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=11784.7MB, alloc=44.3MB, time=163.68
x[1] = 0.5273 1.477
h = 0.0001 0.003
y1[1] (numeric) = 1.05480133589 -0.326967776749
y1[1] (closed_form) = 1.99109182238 -1.04451257546
absolute error = 1.18
relative error = 52.46 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.15940445699 1.79378338149
absolute error = 1.948
relative error = 91.22 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5274 1.48
h = 0.001 0.001
y1[1] (numeric) = 1.05507587979 -0.327576584274
y1[1] (closed_form) = 1.99636587621 -1.04817546559
absolute error = 1.185
relative error = 52.57 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.16274285914 1.7996599294
absolute error = 1.955
relative error = 91.25 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=11834.3MB, alloc=44.3MB, time=164.34
x[1] = 0.5284 1.481
h = 0.0001 0.004
y1[1] (numeric) = 1.05497438637 -0.327874417864
y1[1] (closed_form) = 1.99700174412 -1.05113986496
absolute error = 1.188
relative error = 52.63 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.16578920046 1.80060695606
absolute error = 1.957
relative error = 91.26 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=11883.8MB, alloc=44.3MB, time=165.00
x[1] = 0.5285 1.485
h = 0.003 0.006
y1[1] (numeric) = 1.05534710035 -0.328682888894
y1[1] (closed_form) = 2.00410315685 -1.05599229899
absolute error = 1.195
relative error = 52.77 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.17020351362 1.80850379902
absolute error = 1.967
relative error = 91.29 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5315 1.491
h = 0.0001 0.005
y1[1] (numeric) = 1.05533713034 -0.330175380179
y1[1] (closed_form) = 2.01145157485 -1.06848946141
absolute error = 1.208
relative error = 53.04 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.18260023653 1.81736375783
absolute error = 1.98
relative error = 91.33 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=11933.3MB, alloc=44.3MB, time=165.66
x[1] = 0.5316 1.496
h = 0.0001 0.003
y1[1] (numeric) = 1.05580801441 -0.331183514715
y1[1] (closed_form) = 2.02044476885 -1.07459858238
absolute error = 1.218
relative error = 53.22 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.18815953904 1.82733632398
absolute error = 1.992
relative error = 91.38 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=11982.9MB, alloc=44.3MB, time=166.32
x[1] = 0.5317 1.499
h = 0.001 0.001
y1[1] (numeric) = 1.05608255831 -0.33179232224
y1[1] (closed_form) = 2.02581672906 -1.07835123724
absolute error = 1.224
relative error = 53.33 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.19159127398 1.83329806444
absolute error = 1.999
relative error = 91.41 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5327 1.5
h = 0.001 0.003
y1[1] (numeric) = 1.05598106489 -0.332090155829
y1[1] (closed_form) = 2.02645735649 -1.08137815261
absolute error = 1.226
relative error = 53.38 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.19469727556 1.83424433731
absolute error = 2.001
relative error = 91.41 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=12032.5MB, alloc=44.3MB, time=166.98
x[1] = 0.5337 1.503
h = 0.0001 0.004
y1[1] (numeric) = 1.05607591163 -0.33278731643
y1[1] (closed_form) = 2.03077025424 -1.0868069052
absolute error = 1.232
relative error = 53.5 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.19997816093 1.8392460855
absolute error = 2.008
relative error = 91.43 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=12081.9MB, alloc=44.3MB, time=167.64
x[1] = 0.5338 1.507
h = 0.003 0.006
y1[1] (numeric) = 1.05644862562 -0.33359578746
y1[1] (closed_form) = 2.0380230607 -1.09180025804
absolute error = 1.24
relative error = 53.65 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.20453880831 1.84727473138
absolute error = 2.017
relative error = 91.47 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5368 1.513
h = 0.0001 0.005
y1[1] (numeric) = 1.0564386556 -0.335088278745
y1[1] (closed_form) = 2.04550091043 -1.10462084122
absolute error = 1.253
relative error = 53.91 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.21725330209 1.85623068964
absolute error = 2.031
relative error = 91.51 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=12131.5MB, alloc=44.3MB, time=168.30
x[1] = 0.5369 1.518
h = 0.0001 0.003
y1[1] (numeric) = 1.05690953967 -0.336096413281
y1[1] (closed_form) = 2.05468538193 -1.11090758347
absolute error = 1.263
relative error = 54.08 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.22299711966 1.86637035831
absolute error = 2.043
relative error = 91.56 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.537 1.521
h = 0.001 0.001
y1[1] (numeric) = 1.05718408357 -0.336705220806
y1[1] (closed_form) = 2.06017110365 -1.11476882813
absolute error = 1.269
relative error = 54.19 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.22654137414 1.87243135485
absolute error = 2.05
relative error = 91.58 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=12181.0MB, alloc=44.3MB, time=168.95
x[1] = 0.538 1.522
h = 0.001 0.003
y1[1] (numeric) = 1.05708259015 -0.337003054395
y1[1] (closed_form) = 2.06081587783 -1.11786986125
absolute error = 1.272
relative error = 54.24 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.22971818682 1.87337552953
absolute error = 2.052
relative error = 91.59 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=12230.7MB, alloc=44.3MB, time=169.61
x[1] = 0.539 1.525
h = 0.0001 0.004
y1[1] (numeric) = 1.0571774369 -0.337700214996
y1[1] (closed_form) = 2.06521117618 -1.12344305708
absolute error = 1.278
relative error = 54.36 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.23514316357 1.87844391299
absolute error = 2.06
relative error = 91.61 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5391 1.529
h = 0.003 0.006
y1[1] (numeric) = 1.05755015088 -0.338508686026
y1[1] (closed_form) = 2.07261751853 -1.1285812968
absolute error = 1.286
relative error = 54.51 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.2398540969 1.88660695859
absolute error = 2.069
relative error = 91.65 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=12280.2MB, alloc=44.3MB, time=170.27
x[1] = 0.5421 1.535
h = 0.0001 0.005
y1[1] (numeric) = 1.05754018087 -0.340001177311
y1[1] (closed_form) = 2.08022521933 -1.14173288991
absolute error = 1.299
relative error = 54.76 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.25289424706 1.89566003428
absolute error = 2.083
relative error = 91.68 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=12329.6MB, alloc=44.3MB, time=170.93
x[1] = 0.5422 1.54
h = 0.0001 0.003
y1[1] (numeric) = 1.05801106494 -0.341009311847
y1[1] (closed_form) = 2.08960368956 -1.14820226169
absolute error = 1.31
relative error = 54.94 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.25882756317 1.90597008882
absolute error = 2.095
relative error = 91.73 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5423 1.543
h = 0.001 0.001
y1[1] (numeric) = 1.05828560884 -0.341618119372
y1[1] (closed_form) = 2.09520477336 -1.15217513595
absolute error = 1.316
relative error = 55.04 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.26248736664 1.91213227821
absolute error = 2.102
relative error = 91.75 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=12379.3MB, alloc=44.3MB, time=171.59
x[1] = 0.5433 1.544
h = 0.001 0.003
y1[1] (numeric) = 1.05818411542 -0.341915952961
y1[1] (closed_form) = 2.09585326504 -1.15535185101
absolute error = 1.318
relative error = 55.09 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.265736659 1.91307404427
absolute error = 2.105
relative error = 91.76 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=12428.9MB, alloc=44.3MB, time=172.25
x[1] = 0.5443 1.547
h = 0.0001 0.004
y1[1] (numeric) = 1.05827896217 -0.342613113562
y1[1] (closed_form) = 2.10033166812 -1.1610730561
absolute error = 1.325
relative error = 55.21 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.27130938254 1.91821010858
absolute error = 2.112
relative error = 91.78 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5444 1.551
h = 0.003 0.006
y1[1] (numeric) = 1.05865167615 -0.343421584592
y1[1] (closed_form) = 2.10789372477 -1.16636025263
absolute error = 1.333
relative error = 55.35 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.27617465339 1.92651017697
absolute error = 2.122
relative error = 91.82 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=12478.4MB, alloc=44.3MB, time=172.90
x[1] = 0.5474 1.557
h = 0.0001 0.005
y1[1] (numeric) = 1.05864170614 -0.344914075877
y1[1] (closed_form) = 2.11563167798 -1.17985062603
absolute error = 1.347
relative error = 55.61 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.28954851659 1.93566145639
absolute error = 2.136
relative error = 91.85 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5475 1.562
h = 0.0001 0.003
y1[1] (numeric) = 1.05911259021 -0.345922210413
y1[1] (closed_form) = 2.12520691402 -1.18650776409
absolute error = 1.358
relative error = 55.78 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.29567644086 1.94614521363
absolute error = 2.149
relative error = 91.9 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=12527.9MB, alloc=44.3MB, time=173.56
x[1] = 0.5476 1.565
h = 0.001 0.001
y1[1] (numeric) = 1.05938713411 -0.346531017938
y1[1] (closed_form) = 2.13092498702 -1.19059538554
absolute error = 1.364
relative error = 55.88 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.29945489903 1.95241055182
absolute error = 2.156
relative error = 91.92 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=12577.5MB, alloc=44.3MB, time=174.22
x[1] = 0.5486 1.566
h = 0.001 0.003
y1[1] (numeric) = 1.05928564069 -0.346828851527
y1[1] (closed_form) = 2.13157675099 -1.19384938214
absolute error = 1.366
relative error = 55.93 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.30277837213 1.95334958086
absolute error = 2.158
relative error = 91.93 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5496 1.569
h = 0.0001 0.004
y1[1] (numeric) = 1.05938048743 -0.347526012128
y1[1] (closed_form) = 2.13613896633 -1.19972224934
absolute error = 1.373
relative error = 56.05 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.30850258102 1.95855436801
absolute error = 2.166
relative error = 91.95 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=12627.1MB, alloc=44.3MB, time=174.88
x[1] = 0.5497 1.573
h = 0.003 0.006
y1[1] (numeric) = 1.05975320142 -0.348334483158
y1[1] (closed_form) = 2.14385895192 -1.20516257685
absolute error = 1.382
relative error = 56.19 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.31352634331 1.96699410869
absolute error = 2.176
relative error = 91.98 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=12676.7MB, alloc=44.3MB, time=175.58
x[1] = 0.5527 1.579
h = 0.0001 0.005
y1[1] (numeric) = 1.0597432314 -0.349826974443
y1[1] (closed_form) = 2.15172753924 -1.21899968573
absolute error = 1.396
relative error = 56.44 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.32724215122 1.97624464511
absolute error = 2.191
relative error = 92.02 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5528 1.584
h = 0.0001 0.003
y1[1] (numeric) = 1.06021411547 -0.350835108979
y1[1] (closed_form) = 2.16150235411 -1.22584985834
absolute error = 1.407
relative error = 56.61 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.33356992251 1.98690545569
absolute error = 2.203
relative error = 92.06 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=12726.4MB, alloc=44.3MB, time=176.24
x[1] = 0.5529 1.587
h = 0.001 0.001
y1[1] (numeric) = 1.06048865937 -0.351443916504
y1[1] (closed_form) = 2.16733907 -1.23005542418
absolute error = 1.413
relative error = 56.71 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.33747021926 1.99327591798
absolute error = 2.21
relative error = 92.09 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=12776.0MB, alloc=44.3MB, time=176.90
x[1] = 0.5539 1.588
h = 0.0001 0.004
y1[1] (numeric) = 1.06038716595 -0.351741750093
y1[1] (closed_form) = 2.16799364453 -1.23338833787
absolute error = 1.416
relative error = 56.76 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.34086960735 1.99421186303
absolute error = 2.213
relative error = 92.09 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.554 1.592
h = 0.003 0.006
y1[1] (numeric) = 1.06075987994 -0.352550221124
y1[1] (closed_form) = 2.17585326496 -1.23896198151
absolute error = 1.424
relative error = 56.89 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.34603149288 2.00277592826
absolute error = 2.223
relative error = 92.12 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=12825.5MB, alloc=44.3MB, time=177.55
x[1] = 0.557 1.598
h = 0.0001 0.005
y1[1] (numeric) = 1.06074990992 -0.354042712408
y1[1] (closed_form) = 2.18383885 -1.253102501
absolute error = 1.439
relative error = 57.14 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.36004716494 2.01211692891
absolute error = 2.238
relative error = 92.16 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5571 1.603
h = 0.0001 0.003
y1[1] (numeric) = 1.06122079399 -0.355050846944
y1[1] (closed_form) = 2.19379013066 -1.2601207288
absolute error = 1.45
relative error = 57.3 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.36654909002 2.02293531822
absolute error = 2.251
relative error = 92.2 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=12875.2MB, alloc=44.3MB, time=178.22
x[1] = 0.5572 1.606
h = 0.001 0.001
y1[1] (numeric) = 1.06149533789 -0.355659654469
y1[1] (closed_form) = 2.19973177322 -1.26442899903
absolute error = 1.457
relative error = 57.41 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.37055558739 2.02939936894
absolute error = 2.258
relative error = 92.23 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=12924.8MB, alloc=44.3MB, time=178.88
x[1] = 0.5582 1.607
h = 0.001 0.003
y1[1] (numeric) = 1.06139384447 -0.355957488059
y1[1] (closed_form) = 2.20038935144 -1.26783115393
absolute error = 1.459
relative error = 57.45 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.37402177787 2.03033330001
absolute error = 2.261
relative error = 92.23 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5592 1.61
h = 0.0001 0.004
y1[1] (numeric) = 1.06148869122 -0.356654648659
y1[1] (closed_form) = 2.20511132776 -1.27399523799
absolute error = 1.466
relative error = 57.57 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.38003726112 2.03567063728
absolute error = 2.269
relative error = 92.25 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=12974.2MB, alloc=44.3MB, time=179.53
x[1] = 0.5593 1.614
h = 0.003 0.006
y1[1] (numeric) = 1.0618614052 -0.35746311969
y1[1] (closed_form) = 2.21313314744 -1.27973003807
absolute error = 1.475
relative error = 57.7 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.38536561621 2.04437942872
absolute error = 2.279
relative error = 92.28 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=13023.7MB, alloc=44.3MB, time=180.19
x[1] = 0.5623 1.62
h = 0.0001 0.005
y1[1] (numeric) = 1.06185143519 -0.358955610974
y1[1] (closed_form) = 2.22125011899 -1.29423259662
absolute error = 1.49
relative error = 57.94 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.39973901835 2.05382165644
absolute error = 2.295
relative error = 92.32 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5624 1.625
h = 0.0001 0.003
y1[1] (numeric) = 1.06232231926 -0.35996374551
y1[1] (closed_form) = 2.23140640182 -1.30145398767
absolute error = 1.501
relative error = 58.11 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.40645085274 2.06482349106
absolute error = 2.307
relative error = 92.36 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=13073.5MB, alloc=44.3MB, time=180.85
x[1] = 0.5625 1.628
h = 0.001 0.001
y1[1] (numeric) = 1.06259686316 -0.360572553035
y1[1] (closed_form) = 2.23746987558 -1.30588634928
absolute error = 1.508
relative error = 58.21 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.41058530364 2.07139643374
absolute error = 2.315
relative error = 92.38 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=13123.0MB, alloc=44.3MB, time=181.51
x[1] = 0.5635 1.629
h = 0.001 0.003
y1[1] (numeric) = 1.06249536974 -0.360870386625
y1[1] (closed_form) = 2.23812937966 -1.30937056871
absolute error = 1.511
relative error = 58.25 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.41413073157 2.0723266055
absolute error = 2.318
relative error = 92.39 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5645 1.632
h = 0.0001 0.004
y1[1] (numeric) = 1.06259021649 -0.361567547225
y1[1] (closed_form) = 2.24293725324 -1.31569725261
absolute error = 1.518
relative error = 58.37 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.42030885979 2.07773567102
absolute error = 2.326
relative error = 92.41 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=13172.5MB, alloc=44.3MB, time=182.17
x[1] = 0.5646 1.636
h = 0.003 0.006
y1[1] (numeric) = 1.06296293047 -0.362376018256
y1[1] (closed_form) = 2.25112359205 -1.32159769459
absolute error = 1.527
relative error = 58.5 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.42580814481 2.08659191653
absolute error = 2.336
relative error = 92.44 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5676 1.642
h = 0.0001 0.005
y1[1] (numeric) = 1.06295296046 -0.36386850954
y1[1] (closed_form) = 2.25937226856 -1.33647079727
absolute error = 1.542
relative error = 58.74 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.44054803228 2.09613632412
absolute error = 2.352
relative error = 92.47 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=13222.1MB, alloc=44.3MB, time=182.83
x[1] = 0.5677 1.647
h = 0.0001 0.003
y1[1] (numeric) = 1.06342384453 -0.364876644076
y1[1] (closed_form) = 2.26973649987 -1.34390101259
absolute error = 1.554
relative error = 58.9 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.44747540188 2.10732505473
absolute error = 2.365
relative error = 92.51 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=13271.8MB, alloc=44.3MB, time=183.49
x[1] = 0.5678 1.65
h = 0.001 0.001
y1[1] (numeric) = 1.06369838843 -0.365485451601
y1[1] (closed_form) = 2.2759235356 -1.3484609005
absolute error = 1.561
relative error = 59 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.45174122423 2.11400892189
absolute error = 2.373
relative error = 92.53 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5688 1.651
h = 0.001 0.003
y1[1] (numeric) = 1.06359689501 -0.365783285191
y1[1] (closed_form) = 2.27658445365 -1.35202892679
absolute error = 1.563
relative error = 59.04 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.45536772298 2.11493493158
absolute error = 2.376
relative error = 92.54 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=13321.4MB, alloc=44.3MB, time=184.15
x[1] = 0.5698 1.654
h = 0.0001 0.004
y1[1] (numeric) = 1.06369174175 -0.366480445791
y1[1] (closed_form) = 2.28147894101 -1.3585222163
absolute error = 1.571
relative error = 59.15 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.46171257442 2.12041675061
absolute error = 2.384
relative error = 92.56 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=13370.9MB, alloc=44.3MB, time=184.80
x[1] = 0.5699 1.658
h = 0.003 0.006
y1[1] (numeric) = 1.06406445574 -0.367288916822
y1[1] (closed_form) = 2.2898321552 -1.36459289953
absolute error = 1.58
relative error = 59.28 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.46738736205 2.12942320543
absolute error = 2.394
relative error = 92.59 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5729 1.664
h = 0.0001 0.005
y1[1] (numeric) = 1.06405448572 -0.368781408106
y1[1] (closed_form) = 2.29821282877 -1.37984525107
absolute error = 1.595
relative error = 59.52 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.48250268102 2.13907070679
absolute error = 2.411
relative error = 92.62 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=13420.6MB, alloc=44.3MB, time=185.47
x[1] = 0.573 1.669
h = 0.0001 0.003
y1[1] (numeric) = 1.06452536979 -0.369789542642
y1[1] (closed_form) = 2.30878800099 -1.38749009538
absolute error = 1.607
relative error = 59.68 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.48965135359 2.150449819
absolute error = 2.424
relative error = 92.66 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=13470.3MB, alloc=44.3MB, time=186.13
x[1] = 0.5731 1.672
h = 0.001 0.001
y1[1] (numeric) = 1.06479991369 -0.370398350167
y1[1] (closed_form) = 2.31510035605 -1.39218103148
absolute error = 1.615
relative error = 59.77 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.49405205106 2.15724666311
absolute error = 2.432
relative error = 92.68 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5741 1.673
h = 0.001 0.003
y1[1] (numeric) = 1.06469842027 -0.370696183757
y1[1] (closed_form) = 2.31576215727 -1.39583464551
absolute error = 1.617
relative error = 59.82 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.49776149001 2.15816808714
absolute error = 2.435
relative error = 92.69 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=13519.9MB, alloc=44.3MB, time=186.78
x[1] = 0.5751 1.676
h = 0.0001 0.004
y1[1] (numeric) = 1.06479326702 -0.371393344357
y1[1] (closed_form) = 2.32074397556 -1.40249864255
absolute error = 1.625
relative error = 59.93 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.50427723588 2.16372367925
absolute error = 2.443
relative error = 92.71 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5752 1.68
h = 0.003 0.006
y1[1] (numeric) = 1.065165981 -0.372201815388
y1[1] (closed_form) = 2.32926645776 -1.4087442829
absolute error = 1.635
relative error = 60.05 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.51013221384 2.17288312616
absolute error = 2.454
relative error = 92.74 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=13569.4MB, alloc=44.3MB, time=187.44
x[1] = 0.5782 1.686
h = 0.0001 0.005
y1[1] (numeric) = 1.06515601099 -0.373694306672
y1[1] (closed_form) = 2.33777939221 -1.42438479171
absolute error = 1.65
relative error = 60.28 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.52563210571 2.18263459465
absolute error = 2.47
relative error = 92.77 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=13619.1MB, alloc=44.3MB, time=188.10
x[1] = 0.5783 1.691
h = 0.0001 0.003
y1[1] (numeric) = 1.06562689506 -0.374702441208
y1[1] (closed_form) = 2.34856854391 -1.43225021679
absolute error = 1.663
relative error = 60.44 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.53300799431 2.19420760926
absolute error = 2.484
relative error = 92.81 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5784 1.694
h = 0.001 0.001
y1[1] (numeric) = 1.06590143896 -0.375311248733
y1[1] (closed_form) = 2.35500800223 -1.43707581194
absolute error = 1.67
relative error = 60.54 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.53754715843 2.20111950282
absolute error = 2.492
relative error = 92.83 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=13668.8MB, alloc=44.3MB, time=188.76
x[1] = 0.5794 1.695
h = 0.0001 0.004
y1[1] (numeric) = 1.06579994554 -0.375609082323
y1[1] (closed_form) = 2.35567013625 -1.44081683383
absolute error = 1.673
relative error = 60.58 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.54134144367 2.2020358962
absolute error = 2.495
relative error = 92.83 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=13718.3MB, alloc=44.3MB, time=189.42
x[1] = 0.5795 1.699
h = 0.003 0.006
y1[1] (numeric) = 1.06617265952 -0.376417553353
y1[1] (closed_form) = 2.36434242519 -1.44721488298
absolute error = 1.683
relative error = 60.71 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.5473534991 2.21133150775
absolute error = 2.506
relative error = 92.86 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5825 1.705
h = 0.0001 0.005
y1[1] (numeric) = 1.06616268951 -0.377910044638
y1[1] (closed_form) = 2.37297416562 -1.46319521761
absolute error = 1.699
relative error = 60.93 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.56319063912 2.22117786773
absolute error = 2.523
relative error = 92.9 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=13767.8MB, alloc=44.3MB, time=190.08
x[1] = 0.5826 1.71
h = 0.0001 0.003
y1[1] (numeric) = 1.06663357358 -0.378918179174
y1[1] (closed_form) = 2.38395269894 -1.47125279305
absolute error = 1.711
relative error = 61.09 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.57076458873 2.23292343867
absolute error = 2.537
relative error = 92.93 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=13817.5MB, alloc=44.3MB, time=190.74
x[1] = 0.5827 1.713
h = 0.001 0.001
y1[1] (numeric) = 1.06690811748 -0.379526986699
y1[1] (closed_form) = 2.3905046766 -1.47619571568
absolute error = 1.719
relative error = 61.18 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.57542448052 2.23993774728
absolute error = 2.546
relative error = 92.96 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5837 1.714
h = 0.001 0.003
y1[1] (numeric) = 1.06680662406 -0.379824820288
y1[1] (closed_form) = 2.3911677124 -1.48001346864
absolute error = 1.722
relative error = 61.22 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.57929342116 2.24085047953
absolute error = 2.548
relative error = 92.96 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=13867.1MB, alloc=44.3MB, time=191.40
x[1] = 0.5847 1.717
h = 0.0001 0.004
y1[1] (numeric) = 1.06690147081 -0.380521980889
y1[1] (closed_form) = 2.39631609492 -1.4870053074
absolute error = 1.73
relative error = 61.33 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.58613768382 2.24654819548
absolute error = 2.557
relative error = 92.98 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5848 1.721
h = 0.003 0.006
y1[1] (numeric) = 1.06727418479 -0.381330451919
y1[1] (closed_form) = 2.40516226036 -1.49358737879
absolute error = 1.74
relative error = 61.45 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.59233893421 2.25600211037
absolute error = 2.568
relative error = 93.01 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=13916.7MB, alloc=44.3MB, time=192.05
x[1] = 0.5878 1.727
h = 0.0001 0.005
y1[1] (numeric) = 1.06726421478 -0.382822943204
y1[1] (closed_form) = 2.41392678264 -1.50997300124
absolute error = 1.756
relative error = 61.68 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.60857818252 2.26595406325
absolute error = 2.585
relative error = 93.04 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=13966.1MB, alloc=44.3MB, time=192.72
x[1] = 0.5879 1.732
h = 0.0001 0.003
y1[1] (numeric) = 1.06773509885 -0.38383107774
y1[1] (closed_form) = 2.42512514737 -1.51826259798
absolute error = 1.769
relative error = 61.83 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.61639070685 2.27790025707
absolute error = 2.6
relative error = 93.07 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.588 1.735
h = 0.001 0.001
y1[1] (numeric) = 1.06800964275 -0.384439885265
y1[1] (closed_form) = 2.43180766402 -1.52334712053
absolute error = 1.777
relative error = 61.92 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.62119596411 2.2850335707
absolute error = 2.608
relative error = 93.1 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=14015.8MB, alloc=44.3MB, time=193.38
x[1] = 0.589 1.736
h = 0.001 0.003
y1[1] (numeric) = 1.06790814933 -0.384737718854
y1[1] (closed_form) = 2.43246997698 -1.5272557821
absolute error = 1.78
relative error = 61.96 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.62515340423 2.28594040873
absolute error = 2.611
relative error = 93.1 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=14065.4MB, alloc=44.3MB, time=194.04
x[1] = 0.59 1.739
h = 0.0001 0.004
y1[1] (numeric) = 1.06800299607 -0.385434879455
y1[1] (closed_form) = 2.43770779273 -1.53443060394
absolute error = 1.788
relative error = 62.07 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.63218101513 2.29171483185
absolute error = 2.62
relative error = 93.12 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5901 1.743
h = 0.003 0.006
y1[1] (numeric) = 1.06837571006 -0.386243350485
y1[1] (closed_form) = 2.44673033277 -1.54120176157
absolute error = 1.798
relative error = 62.19 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.6385764926 2.3013299141
absolute error = 2.631
relative error = 93.15 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=14114.9MB, alloc=44.3MB, time=194.70
x[1] = 0.5931 1.749
h = 0.0001 0.005
y1[1] (numeric) = 1.06836574005 -0.38773584177
y1[1] (closed_form) = 2.45562781142 -1.55800218647
absolute error = 1.815
relative error = 62.41 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.65522757402 2.31138820993
absolute error = 2.649
relative error = 93.18 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=14164.6MB, alloc=44.3MB, time=195.36
x[1] = 0.5932 1.754
h = 0.0001 0.003
y1[1] (numeric) = 1.06883662411 -0.388743976306
y1[1] (closed_form) = 2.46704917987 -1.56653019558
absolute error = 1.828
relative error = 62.56 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.66328502103 2.32353865116
absolute error = 2.664
relative error = 93.21 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5933 1.757
h = 0.001 0.001
y1[1] (numeric) = 1.06911116802 -0.389352783831
y1[1] (closed_form) = 2.47386409643 -1.57176019469
absolute error = 1.836
relative error = 62.65 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.66823949821 2.33079310137
absolute error = 2.672
relative error = 93.23 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=14214.2MB, alloc=44.3MB, time=196.02
x[1] = 0.5943 1.758
h = 0.001 0.003
y1[1] (numeric) = 1.06900967459 -0.38965061742
y1[1] (closed_form) = 2.47452507694 -1.57576170138
absolute error = 1.839
relative error = 62.69 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.67228745359 2.33169353568
absolute error = 2.675
relative error = 93.24 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5953 1.761
h = 0.0001 0.004
y1[1] (numeric) = 1.06910452134 -0.390347778021
y1[1] (closed_form) = 2.47985304066 -1.58312399903
absolute error = 1.847
relative error = 62.79 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.67950296347 2.33754565971
absolute error = 2.684
relative error = 93.25 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=14263.8MB, alloc=44.3MB, time=196.68
x[1] = 0.5954 1.765
h = 0.003 0.006
y1[1] (numeric) = 1.06947723532 -0.391156249051
y1[1] (closed_form) = 2.48905448974 -1.59008943424
absolute error = 1.858
relative error = 62.91 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.68609782627 2.34732480151
absolute error = 2.696
relative error = 93.28 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=14313.3MB, alloc=44.3MB, time=197.33
x[1] = 0.5984 1.771
h = 0.0001 0.005
y1[1] (numeric) = 1.06946726531 -0.392648740336
y1[1] (closed_form) = 2.49808506317 -1.60731439632
absolute error = 1.875
relative error = 63.13 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.70317067818 2.35749014277
absolute error = 2.714
relative error = 93.31 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5985 1.776
h = 0.0001 0.003
y1[1] (numeric) = 1.06993814938 -0.393656874872
y1[1] (closed_form) = 2.50973265372 -1.61608736959
absolute error = 1.889
relative error = 63.27 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.71147955515 2.36984849193
absolute error = 2.729
relative error = 93.35 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=14362.8MB, alloc=44.3MB, time=197.99
x[1] = 0.5986 1.779
h = 0.001 0.001
y1[1] (numeric) = 1.07021269328 -0.394265682397
y1[1] (closed_form) = 2.51668185753 -1.62146681909
absolute error = 1.897
relative error = 63.36 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.71658720296 2.37722623072
absolute error = 2.738
relative error = 93.37 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=14412.4MB, alloc=44.3MB, time=198.65
x[1] = 0.5996 1.78
h = 0.001 0.003
y1[1] (numeric) = 1.07011119986 -0.394563515986
y1[1] (closed_form) = 2.51734087373 -1.62556314942
absolute error = 1.9
relative error = 63.4 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.72072772916 2.37811972779
absolute error = 2.741
relative error = 93.37 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6006 1.783
h = 0.0001 0.004
y1[1] (numeric) = 1.07020604661 -0.395260676587
y1[1] (closed_form) = 2.52275969753 -1.63311752209
absolute error = 1.908
relative error = 63.5 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.72813579255 2.38405053806
absolute error = 2.75
relative error = 93.39 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=14461.9MB, alloc=44.3MB, time=199.31
x[1] = 0.6007 1.787
h = 0.003 0.006
y1[1] (numeric) = 1.07057876059 -0.396069147617
y1[1] (closed_form) = 2.53214262635 -1.64028255652
absolute error = 1.919
relative error = 63.62 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.7349353281 2.3939966599
absolute error = 2.762
relative error = 93.41 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=14511.5MB, alloc=44.3MB, time=199.97
x[1] = 0.6037 1.793
h = 0.0001 0.005
y1[1] (numeric) = 1.07056879058 -0.397561638902
y1[1] (closed_form) = 2.54130639463 -1.65794201514
absolute error = 1.937
relative error = 63.83 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.75244010514 2.40426969951
absolute error = 2.78
relative error = 93.45 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6038 1.798
h = 0.0001 0.003
y1[1] (numeric) = 1.07103967465 -0.398569773438
y1[1] (closed_form) = 2.55318347168 -1.66696666879
absolute error = 1.951
relative error = 63.98 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.76100708246 2.41683965328
absolute error = 2.795
relative error = 93.48 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=14561.2MB, alloc=44.3MB, time=200.63
x[1] = 0.6039 1.801
h = 0.001 0.001
y1[1] (numeric) = 1.07131421855 -0.399178580963
y1[1] (closed_form) = 2.56026887645 -1.67249964196
absolute error = 1.959
relative error = 64.06 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.76627195022 2.42434285313
absolute error = 2.805
relative error = 93.5 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6049 1.802
h = 0.0001 0.004
y1[1] (numeric) = 1.07121272513 -0.399476414552
y1[1] (closed_form) = 2.56092527346 -1.67669281725
absolute error = 1.962
relative error = 64.11 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.77050714338 2.42522885468
absolute error = 2.808
relative error = 93.5 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=14610.6MB, alloc=44.3MB, time=201.29
x[1] = 0.605 1.806
h = 0.003 0.006
y1[1] (numeric) = 1.07158543911 -0.400284885583
y1[1] (closed_form) = 2.57046896651 -1.68403181905
absolute error = 1.973
relative error = 64.22 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.77748515239 2.43532359394
absolute error = 2.82
relative error = 93.53 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=14660.2MB, alloc=44.3MB, time=201.95
x[1] = 0.608 1.812
h = 0.0001 0.005
y1[1] (numeric) = 1.0715754691 -0.401777376868
y1[1] (closed_form) = 2.57975277511 -1.70207184033
absolute error = 1.991
relative error = 64.43 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.79536872463 2.44569513399
absolute error = 2.839
relative error = 93.56 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6081 1.817
h = 0.0001 0.003
y1[1] (numeric) = 1.07204635317 -0.402785511404
y1[1] (closed_form) = 2.5918331456 -1.7113158512
absolute error = 2.005
relative error = 64.57 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.80416075378 2.45845340357
absolute error = 2.854
relative error = 93.59 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=14709.7MB, alloc=44.3MB, time=202.61
x[1] = 0.6082 1.82
h = 0.001 0.001
y1[1] (numeric) = 1.07232089707 -0.403394318928
y1[1] (closed_form) = 2.59903923685 -1.71698265792
absolute error = 2.014
relative error = 64.66 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.80956274074 2.46606829178
absolute error = 2.863
relative error = 93.61 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=14759.3MB, alloc=44.3MB, time=203.27
x[1] = 0.6092 1.821
h = 0.001 0.003
y1[1] (numeric) = 1.07221940365 -0.403692152518
y1[1] (closed_form) = 2.59969402399 -1.72126088821
absolute error = 2.017
relative error = 64.7 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.81388122899 2.46694853736
absolute error = 2.866
relative error = 93.61 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6102 1.824
h = 0.0001 0.004
y1[1] (numeric) = 1.07231425039 -0.404389313118
y1[1] (closed_form) = 2.6052862229 -1.72918418071
absolute error = 2.026
relative error = 64.8 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.82165937849 2.47303078503
absolute error = 2.876
relative error = 93.63 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=14808.9MB, alloc=44.3MB, time=203.93
x[1] = 0.6103 1.828
h = 0.003 0.006
y1[1] (numeric) = 1.07268696438 -0.405197784149
y1[1] (closed_form) = 2.61501634259 -1.73673300963
absolute error = 2.038
relative error = 64.91 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.82885221773 2.4832980811
absolute error = 2.888
relative error = 93.66 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=14858.4MB, alloc=44.3MB, time=204.59
x[1] = 0.6133 1.834
h = 0.0001 0.005
y1[1] (numeric) = 1.07267699437 -0.406690275434
y1[1] (closed_form) = 2.62443354757 -1.75522667293
absolute error = 2.056
relative error = 65.11 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.84718719892 2.49377852267
absolute error = 2.907
relative error = 93.69 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6134 1.839
h = 0.0001 0.003
y1[1] (numeric) = 1.07314787843 -0.40769840997
y1[1] (closed_form) = 2.6367496858 -1.76473527215
absolute error = 2.07
relative error = 65.25 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.85625014299 2.50675545639
absolute error = 2.923
relative error = 93.72 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=14908.0MB, alloc=44.3MB, time=205.25
x[1] = 0.6135 1.842
h = 0.001 0.001
y1[1] (numeric) = 1.07342242234 -0.408307217494
y1[1] (closed_form) = 2.64409566034 -1.7705634311
absolute error = 2.079
relative error = 65.34 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.86181712876 2.51449995395
absolute error = 2.933
relative error = 93.74 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6145 1.843
h = 0.001 0.003
y1[1] (numeric) = 1.07332092891 -0.408605051084
y1[1] (closed_form) = 2.64474657114 -1.77494239249
absolute error = 2.082
relative error = 65.38 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.86623430264 2.51537162289
absolute error = 2.936
relative error = 93.74 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=14957.6MB, alloc=44.3MB, time=205.91
x[1] = 0.6155 1.846
h = 0.0001 0.004
y1[1] (numeric) = 1.07341577566 -0.409302211684
y1[1] (closed_form) = 2.65043170532 -1.78307151754
absolute error = 2.091
relative error = 65.47 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.87421890424 2.52153538323
absolute error = 2.946
relative error = 93.76 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=15007.1MB, alloc=44.3MB, time=206.57
x[1] = 0.6156 1.85
h = 0.003 0.006
y1[1] (numeric) = 1.07378848965 -0.410110682715
y1[1] (closed_form) = 2.66035092731 -1.79083588452
absolute error = 2.103
relative error = 65.58 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.8816322476 2.53197823971
absolute error = 2.958
relative error = 93.78 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6186 1.856
h = 0.0001 0.005
y1[1] (numeric) = 1.07377851963 -0.411603174
y1[1] (closed_form) = 2.66990150913 -1.80979381777
absolute error = 2.122
relative error = 65.79 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.9004294413 2.54256808503
absolute error = 2.978
relative error = 93.81 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=15056.6MB, alloc=44.3MB, time=207.22
x[1] = 0.6187 1.861
h = 0.0001 0.003
y1[1] (numeric) = 1.0742494037 -0.412611308536
y1[1] (closed_form) = 2.68245681274 -1.81957421288
absolute error = 2.137
relative error = 65.92 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.90977045874 2.55576748572
absolute error = 2.994
relative error = 93.84 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=15106.2MB, alloc=44.3MB, time=207.88
x[1] = 0.6188 1.864
h = 0.001 0.001
y1[1] (numeric) = 1.0745239476 -0.41322011606
y1[1] (closed_form) = 2.68994466053 -1.82556809445
absolute error = 2.146
relative error = 66 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.91550678758 2.5636438252
absolute error = 3.004
relative error = 93.86 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6198 1.865
h = 0.001 0.003
y1[1] (numeric) = 1.07442245418 -0.41351794965
y1[1] (closed_form) = 2.69059097051 -1.83004993523
absolute error = 2.149
relative error = 66.04 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.92002486427 2.56450628475
absolute error = 3.007
relative error = 93.86 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=15155.7MB, alloc=44.3MB, time=208.54
x[1] = 0.6208 1.868
h = 0.0001 0.004
y1[1] (numeric) = 1.07451730093 -0.41421511025
y1[1] (closed_form) = 2.69636973608 -1.83838992496
absolute error = 2.158
relative error = 66.14 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.92822099582 2.57075250582
absolute error = 3.017
relative error = 93.88 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=15205.1MB, alloc=44.3MB, time=209.20
x[1] = 0.6209 1.872
h = 0.003 0.006
y1[1] (numeric) = 1.07489001491 -0.415023581281
y1[1] (closed_form) = 2.70648077198 -1.84637568328
absolute error = 2.17
relative error = 66.25 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.93586065868 2.58137395491
absolute error = 3.03
relative error = 93.91 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6239 1.878
h = 0.0001 0.005
y1[1] (numeric) = 1.0748800449 -0.416516072566
y1[1] (closed_form) = 2.71616466365 -1.8658087572
absolute error = 2.19
relative error = 66.45 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.95513110469 2.59207364829
absolute error = 3.05
relative error = 93.93 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=15254.6MB, alloc=44.3MB, time=209.86
x[1] = 0.624 1.883
h = 0.0001 0.003
y1[1] (numeric) = 1.07535092897 -0.417524207102
y1[1] (closed_form) = 2.72896257592 -1.87586833543
absolute error = 2.205
relative error = 66.58 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.96475753262 2.60549935538
absolute error = 3.066
relative error = 93.96 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6241 1.886
h = 0.001 0.001
y1[1] (numeric) = 1.07562547287 -0.418133014626
y1[1] (closed_form) = 2.73659431297 -1.88203241867
absolute error = 2.214
relative error = 66.66 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.97066765677 2.61350978997
absolute error = 3.076
relative error = 93.98 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=15304.3MB, alloc=44.3MB, time=210.52
x[1] = 0.6251 1.887
h = 0.001 0.003
y1[1] (numeric) = 1.07552397945 -0.418430848216
y1[1] (closed_form) = 2.73723527154 -1.88661933292
absolute error = 2.217
relative error = 66.7 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.97528889729 2.61436237966
absolute error = 3.08
relative error = 93.99 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=15353.9MB, alloc=44.3MB, time=211.18
x[1] = 0.6261 1.89
h = 0.0001 0.004
y1[1] (numeric) = 1.07561882619 -0.419128008816
y1[1] (closed_form) = 2.74310835814 -1.89517533745
absolute error = 2.227
relative error = 66.79 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.98370175234 2.62069199775
absolute error = 3.09
relative error = 94 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6262 1.894
h = 0.003 0.006
y1[1] (numeric) = 1.07599154018 -0.419936479847
y1[1] (closed_form) = 2.75341395538 -1.90338848606
absolute error = 2.239
relative error = 66.9 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 1.9915736949 2.63149510032
absolute error = 3.103
relative error = 94.03 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=15403.4MB, alloc=44.3MB, time=211.84
x[1] = 0.6292 1.9
h = 0.0001 0.005
y1[1] (numeric) = 1.07598157017 -0.421428971132
y1[1] (closed_form) = 2.76323103987 -1.92330781909
absolute error = 2.259
relative error = 67.09 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.01132867442 2.64230502579
absolute error = 3.123
relative error = 94.05 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=15452.9MB, alloc=44.3MB, time=212.50
x[1] = 0.6293 1.905
h = 0.0001 0.003
y1[1] (numeric) = 1.07645245423 -0.422437105668
y1[1] (closed_form) = 2.77627504959 -1.93365415152
absolute error = 2.274
relative error = 67.23 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.02124803286 2.6559609153
absolute error = 3.14
relative error = 94.08 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6294 1.908
h = 0.001 0.001
y1[1] (numeric) = 1.07672699814 -0.423045913192
y1[1] (closed_form) = 2.7840527178 -1.93999302664
absolute error = 2.284
relative error = 67.31 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.02733651505 2.6641077188
absolute error = 3.15
relative error = 94.1 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=15502.6MB, alloc=44.3MB, time=213.16
x[1] = 0.6304 1.909
h = 0.0001 0.004
y1[1] (numeric) = 1.07662550471 -0.423343746782
y1[1] (closed_form) = 2.78468754745 -1.94468725514
absolute error = 2.287
relative error = 67.34 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.03206322518 2.66494974958
absolute error = 3.154
relative error = 94.1 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=15552.1MB, alloc=44.3MB, time=213.82
x[1] = 0.6305 1.913
h = 0.003 0.006
y1[1] (numeric) = 1.0769982187 -0.424152217812
y1[1] (closed_form) = 2.7951656526 -1.95309868845
absolute error = 2.3
relative error = 67.45 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.04013777824 2.67591455261
absolute error = 3.167
relative error = 94.13 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6335 1.919
h = 0.0001 0.005
y1[1] (numeric) = 1.07698824869 -0.425644709097
y1[1] (closed_form) = 2.80510322842 -1.97344408959
absolute error = 2.32
relative error = 67.64 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.06031773176 2.68682558107
absolute error = 3.188
relative error = 94.16 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=15601.6MB, alloc=44.3MB, time=214.48
x[1] = 0.6336 1.924
h = 0.0001 0.003
y1[1] (numeric) = 1.07745913276 -0.426652843633
y1[1] (closed_form) = 2.81836544099 -1.98404046783
absolute error = 2.336
relative error = 67.77 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.07049259424 2.7006863505
absolute error = 3.205
relative error = 94.19 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6337 1.927
h = 0.001 0.001
y1[1] (numeric) = 1.07773367666 -0.427261651158
y1[1] (closed_form) = 2.82627253532 -1.99053178853
absolute error = 2.345
relative error = 67.85 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.07673667943 2.70895457297
absolute error = 3.216
relative error = 94.2 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=15651.3MB, alloc=44.3MB, time=215.14
x[1] = 0.6347 1.928
h = 0.001 0.003
y1[1] (numeric) = 1.07763218323 -0.427559484747
y1[1] (closed_form) = 2.82690276108 -1.99532030627
absolute error = 2.349
relative error = 67.89 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.08155619299 2.70978823537
absolute error = 3.219
relative error = 94.21 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=15700.8MB, alloc=44.3MB, time=215.80
x[1] = 0.6357 1.931
h = 0.0001 0.004
y1[1] (numeric) = 1.07772702998 -0.428256645348
y1[1] (closed_form) = 2.83295589035 -2.00429124307
absolute error = 2.359
relative error = 67.98 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.09038553051 2.71627821766
absolute error = 3.229
relative error = 94.22 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6358 1.935
h = 0.003 0.006
y1[1] (numeric) = 1.07809974397 -0.429065116378
y1[1] (closed_form) = 2.84363383971 -2.01294159496
absolute error = 2.372
relative error = 68.08 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.09870381384 2.72743052118
absolute error = 3.243
relative error = 94.24 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=15750.4MB, alloc=44.3MB, time=216.45
x[1] = 0.6388 1.941
h = 0.0001 0.005
y1[1] (numeric) = 1.07808977395 -0.430557607663
y1[1] (closed_form) = 2.85370438793 -2.0337946236
absolute error = 2.392
relative error = 68.27 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.11938995023 2.73845246879
absolute error = 3.264
relative error = 94.27 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=15800.1MB, alloc=44.3MB, time=217.13
x[1] = 0.6389 1.946
h = 0.0001 0.003
y1[1] (numeric) = 1.07856065802 -0.431565742199
y1[1] (closed_form) = 2.86721940582 -2.0446923053
absolute error = 2.409
relative error = 68.4 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.12987219074 2.75255082544
absolute error = 3.282
relative error = 94.3 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.639 1.949
h = 0.001 0.001
y1[1] (numeric) = 1.07883520192 -0.432174549724
y1[1] (closed_form) = 2.87527635722 -2.05136723881
absolute error = 2.418
relative error = 68.47 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.1363033996 2.76095976013
absolute error = 3.293
relative error = 94.32 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=15849.7MB, alloc=44.3MB, time=217.79
x[1] = 0.64 1.95
h = 0.001 0.003
y1[1] (numeric) = 1.0787337085 -0.432472383313
y1[1] (closed_form) = 2.87589896058 -2.05626737746
absolute error = 2.422
relative error = 68.51 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.14123280443 2.7617815313
absolute error = 3.296
relative error = 94.32 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.641 1.953
h = 0.0001 0.004
y1[1] (numeric) = 1.07882855525 -0.433169543914
y1[1] (closed_form) = 2.88204840617 -2.06546972857
absolute error = 2.432
relative error = 68.6 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.15029437445 2.76835758395
absolute error = 3.307
relative error = 94.34 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=15899.4MB, alloc=44.3MB, time=218.45
x[1] = 0.6411 1.957
h = 0.003 0.006
y1[1] (numeric) = 1.07920126923 -0.433978014944
y1[1] (closed_form) = 2.89292905064 -2.07436543321
absolute error = 2.446
relative error = 68.7 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.15886278147 2.77970053256
absolute error = 3.321
relative error = 94.36 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=15948.8MB, alloc=44.3MB, time=219.11
x[1] = 0.6441 1.963
h = 0.0001 0.005
y1[1] (numeric) = 1.07919129922 -0.435470506229
y1[1] (closed_form) = 2.90313229937 -2.09573794536
absolute error = 2.466
relative error = 68.88 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.18006710252 2.79083360011
absolute error = 3.343
relative error = 94.38 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6442 1.968
h = 0.0001 0.003
y1[1] (numeric) = 1.07966218329 -0.436478640765
y1[1] (closed_form) = 2.91690374285 -2.10694505096
absolute error = 2.483
relative error = 69.01 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.19086478813 2.8051735271
absolute error = 3.36
relative error = 94.41 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=15998.3MB, alloc=44.3MB, time=219.77
x[1] = 0.6443 1.971
h = 0.001 0.001
y1[1] (numeric) = 1.07993672719 -0.43708744829
y1[1] (closed_form) = 2.92511266795 -2.11380851956
absolute error = 2.493
relative error = 69.08 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.19748801392 2.81372550796
absolute error = 3.371
relative error = 94.43 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=16048.0MB, alloc=44.3MB, time=220.43
x[1] = 0.6453 1.972
h = 0.001 0.003
y1[1] (numeric) = 1.07983523377 -0.437385281879
y1[1] (closed_form) = 2.92572678997 -2.1188226584
absolute error = 2.497
relative error = 69.12 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.2025297491 2.81453461294
absolute error = 3.375
relative error = 94.43 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6463 1.975
h = 0.0001 0.004
y1[1] (numeric) = 1.07993008051 -0.43808244248
y1[1] (closed_form) = 2.93197320939 -2.12826205355
absolute error = 2.507
relative error = 69.21 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.21182921664 2.82119762079
absolute error = 3.386
relative error = 94.45 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=16097.6MB, alloc=44.3MB, time=221.09
x[1] = 0.6464 1.979
h = 0.003 0.006
y1[1] (numeric) = 1.0803027945 -0.43889091351
y1[1] (closed_form) = 2.94305943507 -2.13740970426
absolute error = 2.521
relative error = 69.31 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.22065429926 2.83273438771
absolute error = 3.4
relative error = 94.47 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=16147.0MB, alloc=44.3MB, time=221.75
x[1] = 0.6494 1.985
h = 0.0001 0.005
y1[1] (numeric) = 1.08029282449 -0.440383404795
y1[1] (closed_form) = 2.95339505175 -2.15931382371
absolute error = 2.542
relative error = 69.49 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.24238906894 2.84397870578
absolute error = 3.422
relative error = 94.5 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6495 1.99
h = 0.0001 0.003
y1[1] (numeric) = 1.08076370856 -0.441391539331
y1[1] (closed_form) = 2.96742658584 -2.17083867453
absolute error = 2.559
relative error = 69.61 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.25351046689 2.8585642228
absolute error = 3.441
relative error = 94.52 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=16196.5MB, alloc=44.3MB, time=222.40
x[1] = 0.6496 1.993
h = 0.001 0.001
y1[1] (numeric) = 1.08103825246 -0.442000346856
y1[1] (closed_form) = 2.97578962661 -2.1778957219
absolute error = 2.57
relative error = 69.68 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.26033072375 2.86726160423
absolute error = 3.452
relative error = 94.54 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6506 1.994
h = 0.001 0.003
y1[1] (numeric) = 1.08093675903 -0.442298180445
y1[1] (closed_form) = 2.97639437788 -2.18302629022
absolute error = 2.573
relative error = 69.72 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.26548727662 2.86805723608
absolute error = 3.455
relative error = 94.54 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=16246.2MB, alloc=44.3MB, time=223.06
x[1] = 0.6516 1.997
h = 0.0001 0.004
y1[1] (numeric) = 1.08103160578 -0.442995341046
y1[1] (closed_form) = 2.98273841759 -2.19270848981
absolute error = 2.584
relative error = 69.81 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.27503043545 2.87480806816
absolute error = 3.467
relative error = 94.56 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=16295.8MB, alloc=44.3MB, time=223.72
x[1] = 0.6517 2.001
h = 0.003 0.006
y1[1] (numeric) = 1.08140431977 -0.443803812076
y1[1] (closed_form) = 2.99403314555 -2.20211484271
absolute error = 2.598
relative error = 69.9 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.2841189078 2.88654185509
absolute error = 3.481
relative error = 94.58 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6547 2.007
h = 0.0001 0.005
y1[1] (numeric) = 1.08139434975 -0.445296303361
y1[1] (closed_form) = 3.004500734 -2.2245629665
absolute error = 2.62
relative error = 70.08 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.30639665786 2.89789748129
absolute error = 3.504
relative error = 94.6 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=16345.5MB, alloc=44.3MB, time=224.38
x[1] = 0.6548 2.012
h = 0.0001 0.003
y1[1] (numeric) = 1.08186523382 -0.446304437897
y1[1] (closed_form) = 3.01879606819 -2.23641408938
absolute error = 2.637
relative error = 70.2 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.31785024025 2.91273264451
absolute error = 3.523
relative error = 94.63 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=16395.2MB, alloc=44.3MB, time=225.05
x[1] = 0.6549 2.015
h = 0.001 0.001
y1[1] (numeric) = 1.08213977772 -0.446913245422
y1[1] (closed_form) = 3.02731539169 -2.2436698834
absolute error = 2.648
relative error = 70.27 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.32487266608 2.92157780122
absolute error = 3.534
relative error = 94.65 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6559 2.016
h = 0.0001 0.004
y1[1] (numeric) = 1.0820382843 -0.447211079011
y1[1] (closed_form) = 3.02790985141 -2.24891936138
absolute error = 2.652
relative error = 70.31 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.33014657319 2.9223591201
absolute error = 3.538
relative error = 94.65 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=16444.8MB, alloc=44.3MB, time=225.70
x[1] = 0.656 2.02
h = 0.003 0.006
y1[1] (numeric) = 1.08241099829 -0.448019550042
y1[1] (closed_form) = 3.03938961108 -2.25855140203
absolute error = 2.666
relative error = 70.41 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.33946486648 2.93426833024
absolute error = 3.553
relative error = 94.67 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=16494.3MB, alloc=44.3MB, time=226.36
x[1] = 0.659 2.026
h = 0.0001 0.005
y1[1] (numeric) = 1.08240102827 -0.449512041327
y1[1] (closed_form) = 3.04997711465 -2.28147636217
absolute error = 2.688
relative error = 70.58 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.36221891429 2.94572643125
absolute error = 3.576
relative error = 94.7 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6591 2.031
h = 0.0001 0.003
y1[1] (numeric) = 1.08287191234 -0.450520175863
y1[1] (closed_form) = 3.06450655206 -2.29361211432
absolute error = 2.706
relative error = 70.7 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.37396233396 2.96078385562
absolute error = 3.595
relative error = 94.72 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=16543.8MB, alloc=44.3MB, time=227.02
x[1] = 0.6592 2.034
h = 0.001 0.001
y1[1] (numeric) = 1.08314645624 -0.451128983388
y1[1] (closed_form) = 3.07316460649 -2.30104132084
absolute error = 2.717
relative error = 70.77 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.38116119183 2.96976062332
absolute error = 3.606
relative error = 94.74 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6602 2.035
h = 0.001 0.003
y1[1] (numeric) = 1.08304496282 -0.451426816977
y1[1] (closed_form) = 3.07375090309 -2.30639531601
absolute error = 2.721
relative error = 70.81 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.38653836777 2.97053036365
absolute error = 3.61
relative error = 94.74 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=16593.5MB, alloc=44.3MB, time=227.68
x[1] = 0.6612 2.038
h = 0.0001 0.004
y1[1] (numeric) = 1.08313980957 -0.452123977577
y1[1] (closed_form) = 3.0802813302 -2.31654392836
absolute error = 2.732
relative error = 70.89 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.39654978262 2.97744994277
absolute error = 3.622
relative error = 94.76 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=16643.0MB, alloc=44.3MB, time=228.33
x[1] = 0.6613 2.042
h = 0.003 0.006
y1[1] (numeric) = 1.08351252355 -0.452932448608
y1[1] (closed_form) = 3.09197520503 -2.32644765329
absolute error = 2.747
relative error = 70.98 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.40614436502 2.98956229076
absolute error = 3.637
relative error = 94.78 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6643 2.048
h = 0.0001 0.005
y1[1] (numeric) = 1.08350255354 -0.454424939893
y1[1] (closed_form) = 3.10269391883 -2.34994043879
absolute error = 2.769
relative error = 71.16 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.4294654458 3.00113175993
absolute error = 3.66
relative error = 94.8 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=16692.5MB, alloc=44.3MB, time=228.99
x[1] = 0.6644 2.053
h = 0.0001 0.003
y1[1] (numeric) = 1.08397343761 -0.455433074429
y1[1] (closed_form) = 3.11749428376 -2.36241884741
absolute error = 2.788
relative error = 71.27 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.44155732697 3.01644658158
absolute error = 3.68
relative error = 94.83 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=16742.0MB, alloc=44.3MB, time=229.65
x[1] = 0.6645 2.056
h = 0.001 0.001
y1[1] (numeric) = 1.08424798151 -0.456041881954
y1[1] (closed_form) = 3.12631278463 -2.37005673069
absolute error = 2.799
relative error = 71.34 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.44896822468 3.02557566194
absolute error = 3.692
relative error = 94.84 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6655 2.057
h = 0.001 0.003
y1[1] (numeric) = 1.08414648809 -0.456339715543
y1[1] (closed_form) = 3.12688702018 -2.37553440108
absolute error = 2.803
relative error = 71.38 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.45446762002 3.02632946719
absolute error = 3.696
relative error = 94.85 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=16791.4MB, alloc=44.3MB, time=230.31
x[1] = 0.6665 2.06
h = 0.0001 0.004
y1[1] (numeric) = 1.08424133484 -0.457036876143
y1[1] (closed_form) = 3.13351692035 -2.3859430367
absolute error = 2.814
relative error = 71.46 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.4647400278 3.03333933485
absolute error = 3.708
relative error = 94.86 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=16841.0MB, alloc=44.3MB, time=230.96
x[1] = 0.6666 2.064
h = 0.003 0.006
y1[1] (numeric) = 1.08461404882 -0.457845347174
y1[1] (closed_form) = 3.14542793213 -2.39612568846
absolute error = 2.829
relative error = 71.55 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.47461809851 3.04565810536
absolute error = 3.723
relative error = 94.88 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6696 2.07
h = 0.0001 0.005
y1[1] (numeric) = 1.08460407881 -0.459337838459
y1[1] (closed_form) = 3.15627726413 -2.42019951
absolute error = 2.853
relative error = 71.72 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.49851954307 3.05733877857
absolute error = 3.747
relative error = 94.9 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=16890.5MB, alloc=44.3MB, time=231.62
x[1] = 0.6697 2.075
h = 0.0001 0.003
y1[1] (numeric) = 1.08507496288 -0.460345972995
y1[1] (closed_form) = 3.17135239422 -2.43302971601
absolute error = 2.871
relative error = 71.83 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.5109689704 3.07291515986
absolute error = 3.767
relative error = 94.93 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6698 2.078
h = 0.001 0.001
y1[1] (numeric) = 1.08534950678 -0.46095478052
y1[1] (closed_form) = 3.18033358079 -2.44088181496
absolute error = 2.883
relative error = 71.9 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.51859741581 3.08219898667
absolute error = 3.779
relative error = 94.94 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=16940.2MB, alloc=44.3MB, time=232.28
x[1] = 0.6708 2.079
h = 0.001 0.003
y1[1] (numeric) = 1.08524801336 -0.461252614109
y1[1] (closed_form) = 3.18089473961 -2.44648579188
absolute error = 2.887
relative error = 71.93 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.52422171366 3.08293591796
absolute error = 3.783
relative error = 94.95 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=16989.8MB, alloc=44.3MB, time=232.94
x[1] = 0.6718 2.082
h = 0.0001 0.004
y1[1] (numeric) = 1.0853428601 -0.461949774709
y1[1] (closed_form) = 3.18762470808 -2.45716074252
absolute error = 2.898
relative error = 72.01 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.5347614326 3.0900368744
absolute error = 3.795
relative error = 94.96 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6719 2.086
h = 0.003 0.006
y1[1] (numeric) = 1.08571557409 -0.46275824574
y1[1] (closed_form) = 3.19975591253 -2.46762974147
absolute error = 2.914
relative error = 72.1 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.54493036822 3.10256538011
absolute error = 3.811
relative error = 94.98 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=17039.4MB, alloc=44.3MB, time=233.60
x[1] = 0.6749 2.092
h = 0.0001 0.005
y1[1] (numeric) = 1.08570560407 -0.464250737025
y1[1] (closed_form) = 3.21073519475 -2.49229810511
absolute error = 2.937
relative error = 72.27 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.56942579793 3.11435700861
absolute error = 3.836
relative error = 95 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=17088.9MB, alloc=44.3MB, time=234.26
x[1] = 0.675 2.097
h = 0.0001 0.003
y1[1] (numeric) = 1.08617648814 -0.465258871561
y1[1] (closed_form) = 3.22608897087 -2.50548947387
absolute error = 2.957
relative error = 72.38 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.58224208007 3.13019914772
absolute error = 3.856
relative error = 95.03 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6751 2.1
h = 0.001 0.001
y1[1] (numeric) = 1.08645103204 -0.465867679086
y1[1] (closed_form) = 3.23523510661 -2.51356146302
absolute error = 2.968
relative error = 72.45 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.59009371633 3.13964017461
absolute error = 3.868
relative error = 95.04 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=17138.6MB, alloc=44.3MB, time=234.92
x[1] = 0.6761 2.101
h = 0.001 0.003
y1[1] (numeric) = 1.08634953862 -0.466165512675
y1[1] (closed_form) = 3.2357821376 -2.51929443233
absolute error = 2.972
relative error = 72.48 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.59584565278 3.14035925625
absolute error = 3.873
relative error = 95.05 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=17188.2MB, alloc=44.3MB, time=235.58
x[1] = 0.6771 2.104
h = 0.0001 0.004
y1[1] (numeric) = 1.08644438537 -0.466862673275
y1[1] (closed_form) = 3.24261275313 -2.53024213448
absolute error = 2.984
relative error = 72.56 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.60665914427 3.14755208091
absolute error = 3.885
relative error = 95.06 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6772 2.108
h = 0.003 0.006
y1[1] (numeric) = 1.08681709935 -0.467671144306
y1[1] (closed_form) = 3.25496723959 -2.5410050829
absolute error = 3
relative error = 72.65 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.61712650291 3.16029366225
absolute error = 3.901
relative error = 95.08 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=17237.7MB, alloc=44.3MB, time=236.24
x[1] = 0.6802 2.114
h = 0.0001 0.005
y1[1] (numeric) = 1.08680712934 -0.469163635591
y1[1] (closed_form) = 3.26607572463 -2.56628179607
absolute error = 3.024
relative error = 72.81 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.6422298358 3.17219590936
absolute error = 3.926
relative error = 95.1 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6803 2.119
h = 0.0001 0.003
y1[1] (numeric) = 1.08727801341 -0.470171770127
y1[1] (closed_form) = 3.28171207045 -2.57984392259
absolute error = 3.044
relative error = 72.92 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.65542251067 3.18830804011
absolute error = 3.947
relative error = 95.13 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=17287.3MB, alloc=44.3MB, time=236.90
x[1] = 0.6804 2.122
h = 0.001 0.001
y1[1] (numeric) = 1.08755255731 -0.470780577652
y1[1] (closed_form) = 3.29102544278 -2.58814161519
absolute error = 3.056
relative error = 72.99 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.66350311932 3.19790874031
absolute error = 3.96
relative error = 95.14 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=17336.9MB, alloc=44.3MB, time=237.55
x[1] = 0.6814 2.123
h = 0.0001 0.004
y1[1] (numeric) = 1.08745106389 -0.471078411241
y1[1] (closed_form) = 3.29155725831 -2.59400631826
absolute error = 3.06
relative error = 73.02 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.66938548452 3.19860895868
absolute error = 3.964
relative error = 95.14 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6815 2.127
h = 0.003 0.006
y1[1] (numeric) = 1.08782377787 -0.471886882271
y1[1] (closed_form) = 3.30411006594 -2.6050258078
absolute error = 3.076
relative error = 73.11 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.68011331698 3.2115403252
absolute error = 3.981
relative error = 95.16 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=17386.4MB, alloc=44.3MB, time=238.21
x[1] = 0.6845 2.133
h = 0.0001 0.005
y1[1] (numeric) = 1.08781380786 -0.473379373556
y1[1] (closed_form) = 3.31533657891 -2.63083593381
absolute error = 3.101
relative error = 73.27 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.70574997848 3.22354492242
absolute error = 4.006
relative error = 95.19 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=17436.1MB, alloc=44.3MB, time=238.87
x[1] = 0.6846 2.138
h = 0.0001 0.003
y1[1] (numeric) = 1.08828469193 -0.474387508092
y1[1] (closed_form) = 3.33122390201 -2.64472162856
absolute error = 3.121
relative error = 73.38 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.71927117089 3.23989751282
absolute error = 4.027
relative error = 95.21 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6847 2.141
h = 0.001 0.001
y1[1] (numeric) = 1.08855923583 -0.474996315617
y1[1] (closed_form) = 3.34068586119 -2.65321633288
absolute error = 3.133
relative error = 73.44 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.72755166663 3.24964047368
absolute error = 4.04
relative error = 95.23 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=17485.8MB, alloc=44.3MB, time=239.53
x[1] = 0.6857 2.142
h = 0.001 0.003
y1[1] (numeric) = 1.08845774241 -0.475294149207
y1[1] (closed_form) = 3.34120529479 -2.65919686588
absolute error = 3.138
relative error = 73.48 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.73354881869 3.25032521366
absolute error = 4.044
relative error = 95.23 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=17535.4MB, alloc=44.3MB, time=240.19
x[1] = 0.6867 2.145
h = 0.0001 0.004
y1[1] (numeric) = 1.08855258916 -0.475991309807
y1[1] (closed_form) = 3.34822810674 -2.67066852026
absolute error = 3.15
relative error = 73.55 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.74488832222 3.25769443183
absolute error = 4.057
relative error = 95.24 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6868 2.149
h = 0.003 0.006
y1[1] (numeric) = 1.08892530314 -0.476799780837
y1[1] (closed_form) = 3.36101012897 -2.68199656613
absolute error = 3.166
relative error = 73.64 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.75592909872 3.27084525826
absolute error = 4.074
relative error = 95.26 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=17584.8MB, alloc=44.3MB, time=240.84
x[1] = 0.6898 2.155
h = 0.0001 0.005
y1[1] (numeric) = 1.08891533313 -0.478292272122
y1[1] (closed_form) = 3.37236440364 -2.70844156856
absolute error = 3.192
relative error = 73.79 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.78220037947 3.28295977621
absolute error = 4.1
relative error = 95.28 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6899 2.16
h = 0.0001 0.003
y1[1] (numeric) = 1.0893862172 -0.479300406658
y1[1] (closed_form) = 3.38854183088 -2.72271645667
absolute error = 3.212
relative error = 73.9 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.79611628948 3.29959045042
absolute error = 4.122
relative error = 95.31 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=17634.6MB, alloc=44.3MB, time=241.52
x[1] = 0.69 2.163
h = 0.001 0.001
y1[1] (numeric) = 1.0896607611 -0.479909214183
y1[1] (closed_form) = 3.39817541883 -2.73144803379
absolute error = 3.225
relative error = 73.96 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.8046368652 3.30949781107
absolute error = 4.135
relative error = 95.32 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=17684.0MB, alloc=44.3MB, time=242.18
x[1] = 0.691 2.164
h = 0.001 0.003
y1[1] (numeric) = 1.08955926768 -0.480207047773
y1[1] (closed_form) = 3.39867754629 -2.73756556681
absolute error = 3.229
relative error = 73.99 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.81076979837 3.31016173178
absolute error = 4.139
relative error = 95.32 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.692 2.167
h = 0.0001 0.004
y1[1] (numeric) = 1.08965411442 -0.480904208373
y1[1] (closed_form) = 3.40580264144 -2.74932920702
absolute error = 3.242
relative error = 74.07 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.82240236914 3.31762500551
absolute error = 4.153
relative error = 95.33 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=17733.6MB, alloc=44.3MB, time=242.83
x[1] = 0.6921 2.171
h = 0.003 0.006
y1[1] (numeric) = 1.09002682841 -0.481712679403
y1[1] (closed_form) = 3.41881706399 -2.76097395494
absolute error = 3.259
relative error = 74.15 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.83376419042 3.3309987127
absolute error = 4.17
relative error = 95.35 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=17783.1MB, alloc=44.3MB, time=243.49
x[1] = 0.6951 2.177
h = 0.0001 0.005
y1[1] (numeric) = 1.09001685839 -0.483205170688
y1[1] (closed_form) = 3.43029810959 -2.78806853868
absolute error = 3.285
relative error = 74.31 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.86068489341 3.34322254774
absolute error = 4.197
relative error = 95.38 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6952 2.182
h = 0.0001 0.003
y1[1] (numeric) = 1.09048774246 -0.484213305224
y1[1] (closed_form) = 3.44676968746 -2.80274290125
absolute error = 3.306
relative error = 74.41 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.87500574417 3.36013564263
absolute error = 4.219
relative error = 95.4 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=17832.7MB, alloc=44.3MB, time=244.15
x[1] = 0.6953 2.185
h = 0.001 0.001
y1[1] (numeric) = 1.09076228636 -0.484822112749
y1[1] (closed_form) = 3.45657726001 -2.81171757882
absolute error = 3.318
relative error = 74.47 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.88377259517 3.37020993292
absolute error = 4.232
relative error = 95.41 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=17882.2MB, alloc=44.3MB, time=244.81
x[1] = 0.6963 2.186
h = 0.001 0.003
y1[1] (numeric) = 1.09066079294 -0.485119946339
y1[1] (closed_form) = 3.45706088354 -2.81797501809
absolute error = 3.323
relative error = 74.5 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.89004426043 3.37085190674
absolute error = 4.237
relative error = 95.42 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6973 2.189
h = 0.0001 0.004
y1[1] (numeric) = 1.09075563969 -0.485817106939
y1[1] (closed_form) = 3.4642887669 -2.83003766916
absolute error = 3.336
relative error = 74.58 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.90197694255 3.3784099258
absolute error = 4.25
relative error = 95.43 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=17931.6MB, alloc=44.3MB, time=245.46
x[1] = 0.6974 2.193
h = 0.003 0.006
y1[1] (numeric) = 1.09112835367 -0.486625577969
y1[1] (closed_form) = 3.47753880757 -2.84200746342
absolute error = 3.353
relative error = 74.66 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.91366810771 3.39200996135
absolute error = 4.268
relative error = 95.45 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7004 2.199
h = 0.0001 0.005
y1[1] (numeric) = 1.09111838366 -0.488118069254
y1[1] (closed_form) = 3.48914553964 -2.86976665909
absolute error = 3.38
relative error = 74.81 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.94125335754 3.40434240822
absolute error = 4.295
relative error = 95.47 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=17981.1MB, alloc=44.3MB, time=246.12
x[1] = 0.7005 2.204
h = 0.0001 0.003
y1[1] (numeric) = 1.09158926773 -0.48912620379
y1[1] (closed_form) = 3.50591535558 -2.88485102796
absolute error = 3.401
relative error = 74.91 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.95598962268 3.42154229498
absolute error = 4.318
relative error = 95.49 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=18030.7MB, alloc=44.3MB, time=246.78
x[1] = 0.7006 2.207
h = 0.001 0.001
y1[1] (numeric) = 1.09186381163 -0.489735011315
y1[1] (closed_form) = 3.51589929116 -2.89407518505
absolute error = 3.414
relative error = 74.97 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.96500909546 3.43178606341
absolute error = 4.331
relative error = 95.5 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7016 2.208
h = 0.001 0.003
y1[1] (numeric) = 1.09176231821 -0.490032844905
y1[1] (closed_form) = 3.51636317192 -2.90047549626
absolute error = 3.419
relative error = 75 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.97142250193 3.43240492037
absolute error = 4.336
relative error = 95.51 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=18080.3MB, alloc=44.3MB, time=247.44
x[1] = 0.7026 2.211
h = 0.0001 0.004
y1[1] (numeric) = 1.09185716496 -0.490730005505
y1[1] (closed_form) = 3.52369432562 -2.91284434349
absolute error = 3.432
relative error = 75.08 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.98366249845 3.44005834772
absolute error = 4.35
relative error = 95.52 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=18129.7MB, alloc=44.3MB, time=248.10
x[1] = 0.7027 2.215
h = 0.003 0.006
y1[1] (numeric) = 1.09222987894 -0.491538476536
y1[1] (closed_form) = 3.53718323384 -2.92514773154
absolute error = 3.45
relative error = 75.16 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 2.99569150953 3.45388818561
absolute error = 4.368
relative error = 95.54 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7057 2.221
h = 0.0001 0.005
y1[1] (numeric) = 1.09221990893 -0.49303096782
y1[1] (closed_form) = 3.54891447021 -2.95358690209
absolute error = 3.477
relative error = 75.31 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.02395675907 3.46632843357
absolute error = 4.396
relative error = 95.56 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=18179.2MB, alloc=44.3MB, time=248.76
x[1] = 0.7058 2.226
h = 0.0001 0.003
y1[1] (numeric) = 1.092690793 -0.494039102356
y1[1] (closed_form) = 3.56598665203 -2.96909206559
absolute error = 3.499
relative error = 75.41 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.03911916851 3.48381951727
absolute error = 4.419
relative error = 95.58 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=18228.9MB, alloc=44.3MB, time=249.42
x[1] = 0.7059 2.229
h = 0.001 0.001
y1[1] (numeric) = 1.0929653369 -0.494647909881
y1[1] (closed_form) = 3.57614935132 -2.97857223612
absolute error = 3.512
relative error = 75.47 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.04839776429 3.49423533072
absolute error = 4.433
relative error = 95.59 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7069 2.23
h = 0.0001 0.004
y1[1] (numeric) = 1.09286384348 -0.494945743471
y1[1] (closed_form) = 3.57659220813 -2.98511844552
absolute error = 3.517
relative error = 75.5 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.05495598031 3.49482985725
absolute error = 4.437
relative error = 95.59 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=18278.2MB, alloc=44.3MB, time=250.07
x[1] = 0.707 2.234
h = 0.003 0.006
y1[1] (numeric) = 1.09323655746 -0.495754214501
y1[1] (closed_form) = 3.59029346757 -2.99771308444
absolute error = 3.535
relative error = 75.58 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.0672799703 3.50886446915
absolute error = 4.456
relative error = 95.61 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.71 2.24
h = 0.0001 0.005
y1[1] (numeric) = 1.09322658745 -0.497246705786
y1[1] (closed_form) = 3.60213920402 -3.02674865359
absolute error = 3.563
relative error = 75.72 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.09614190196 3.52140513292
absolute error = 4.484
relative error = 95.63 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=18327.7MB, alloc=44.3MB, time=250.73
x[1] = 0.7101 2.245
h = 0.0001 0.003
y1[1] (numeric) = 1.09369747152 -0.498254840322
y1[1] (closed_form) = 3.61948018034 -3.04262119282
absolute error = 3.585
relative error = 75.82 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.11167637371 3.53915567722
absolute error = 4.508
relative error = 95.66 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=18377.3MB, alloc=44.3MB, time=251.39
x[1] = 0.7102 2.248
h = 0.001 0.001
y1[1] (numeric) = 1.09397201542 -0.498863647847
y1[1] (closed_form) = 3.629801851 -3.0523249155
absolute error = 3.599
relative error = 75.88 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.12118124933 3.54972484552
absolute error = 4.522
relative error = 95.67 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7112 2.249
h = 0.001 0.003
y1[1] (numeric) = 1.093870522 -0.499161481436
y1[1] (closed_form) = 3.63022734005 -3.05899945153
absolute error = 3.604
relative error = 75.91 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.12786692601 3.55029919905
absolute error = 4.527
relative error = 95.67 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=18426.9MB, alloc=44.3MB, time=252.05
x[1] = 0.7122 2.252
h = 0.0001 0.004
y1[1] (numeric) = 1.09396536874 -0.499858642037
y1[1] (closed_form) = 3.63775571172 -3.07195650298
absolute error = 3.618
relative error = 75.98 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.140697339 3.55813569684
absolute error = 4.541
relative error = 95.68 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=18476.4MB, alloc=44.3MB, time=252.71
x[1] = 0.7123 2.256
h = 0.003 0.006
y1[1] (numeric) = 1.09433808273 -0.500667113067
y1[1] (closed_form) = 3.65170207525 -3.08490115762
absolute error = 3.636
relative error = 76.06 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.15337550936 3.57240675136
absolute error = 4.56
relative error = 95.7 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7153 2.262
h = 0.0001 0.005
y1[1] (numeric) = 1.09432811271 -0.502159604352
y1[1] (closed_form) = 3.66367003471 -3.11464621317
absolute error = 3.664
relative error = 76.2 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.18294710516 3.58505360689
absolute error = 4.589
relative error = 95.72 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=18525.9MB, alloc=44.3MB, time=253.37
x[1] = 0.7154 2.267
h = 0.0001 0.003
y1[1] (numeric) = 1.09479899678 -0.503167738888
y1[1] (closed_form) = 3.68132129898 -3.1309602742
absolute error = 3.687
relative error = 76.3 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.19892833616 3.60310376864
absolute error = 4.613
relative error = 95.74 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=18575.5MB, alloc=44.3MB, time=254.03
x[1] = 0.7155 2.27
h = 0.001 0.001
y1[1] (numeric) = 1.09507354069 -0.503776546413
y1[1] (closed_form) = 3.69182634043 -3.14093256362
absolute error = 3.701
relative error = 76.35 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.20870482494 3.6138498879
absolute error = 4.628
relative error = 95.75 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7165 2.271
h = 0.001 0.003
y1[1] (numeric) = 1.09497204726 -0.504074380002
y1[1] (closed_form) = 3.69222834229 -3.1477588103
absolute error = 3.706
relative error = 76.38 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.21554119788 3.61439757069
absolute error = 4.632
relative error = 95.76 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=18625.1MB, alloc=44.3MB, time=254.69
x[1] = 0.7175 2.274
h = 0.0001 0.004
y1[1] (numeric) = 1.09506689401 -0.504771540603
y1[1] (closed_form) = 3.69986131634 -3.16104352451
absolute error = 3.72
relative error = 76.45 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.22870043347 3.6223313053
absolute error = 4.647
relative error = 95.77 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7176 2.278
h = 0.003 0.006
y1[1] (numeric) = 1.09543960799 -0.505580011633
y1[1] (closed_form) = 3.71405612351 -3.17434734917
absolute error = 3.739
relative error = 76.53 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.24174189274 3.63684235217
absolute error = 4.667
relative error = 95.78 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=18674.5MB, alloc=44.3MB, time=255.34
x[1] = 0.7206 2.284
h = 0.0001 0.005
y1[1] (numeric) = 1.09542963798 -0.507072502918
y1[1] (closed_form) = 3.72614482537 -3.20481824371
absolute error = 3.768
relative error = 76.67 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.27203958452 3.64959426883
absolute error = 4.696
relative error = 95.8 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=18724.0MB, alloc=44.3MB, time=256.00
x[1] = 0.7207 2.289
h = 0.0001 0.003
y1[1] (numeric) = 1.09590052205 -0.508080637454
y1[1] (closed_form) = 3.74411062047 -3.22158538107
absolute error = 3.792
relative error = 76.76 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.28847907059 3.66794855041
absolute error = 4.721
relative error = 95.83 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7208 2.292
h = 0.001 0.001
y1[1] (numeric) = 1.09617506595 -0.508689444979
y1[1] (closed_form) = 3.7548014965 -3.23183323381
absolute error = 3.806
relative error = 76.82 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.29853413604 3.67887423997
absolute error = 4.735
relative error = 95.84 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=18773.6MB, alloc=44.3MB, time=256.66
x[1] = 0.7218 2.293
h = 0.001 0.003
y1[1] (numeric) = 1.09607357253 -0.508987278568
y1[1] (closed_form) = 3.75517860244 -3.23881439712
absolute error = 3.811
relative error = 76.85 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.30552444982 3.67939390737
absolute error = 4.74
relative error = 95.84 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=18823.1MB, alloc=44.3MB, time=257.32
x[1] = 0.7228 2.296
h = 0.0001 0.004
y1[1] (numeric) = 1.09616841928 -0.509684439169
y1[1] (closed_form) = 3.76291656069 -3.25243461104
absolute error = 3.825
relative error = 76.91 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.3190203579 3.68742542701
absolute error = 4.755
relative error = 95.85 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7229 2.3
h = 0.003 0.006
y1[1] (numeric) = 1.09654113326 -0.510492910199
y1[1] (closed_form) = 3.77736318055 -3.26610698172
absolute error = 3.845
relative error = 76.99 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.33243443621 3.70218004064
absolute error = 4.775
relative error = 95.87 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=18872.5MB, alloc=44.3MB, time=257.98
x[1] = 0.7259 2.306
h = 0.0001 0.005
y1[1] (numeric) = 1.09653116325 -0.511985401484
y1[1] (closed_form) = 3.78957102997 -3.29732042692
absolute error = 3.874
relative error = 77.13 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.36347501135 3.71503576636
absolute error = 4.805
relative error = 95.89 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=18922.1MB, alloc=44.3MB, time=258.63
x[1] = 0.726 2.311
h = 0.0001 0.003
y1[1] (numeric) = 1.09700204732 -0.51299353602
y1[1] (closed_form) = 3.80785563652 -3.31455247509
absolute error = 3.898
relative error = 77.22 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.38038452816 3.73369870192
absolute error = 4.831
relative error = 95.91 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7261 2.314
h = 0.001 0.001
y1[1] (numeric) = 1.09727659122 -0.513602343545
y1[1] (closed_form) = 3.81873483136 -3.32508305667
absolute error = 3.913
relative error = 77.28 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.39072530268 3.74480659804
absolute error = 4.846
relative error = 95.92 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=18971.6MB, alloc=44.3MB, time=259.29
x[1] = 0.7271 2.315
h = 0.001 0.003
y1[1] (numeric) = 1.0971750978 -0.513900177134
y1[1] (closed_form) = 3.81908558519 -3.33222240742
absolute error = 3.918
relative error = 77.3 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.39787286554 3.74529685671
absolute error = 4.851
relative error = 95.92 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7281 2.318
h = 0.0001 0.004
y1[1] (numeric) = 1.09726994454 -0.514597337735
y1[1] (closed_form) = 3.82692887907 -3.34618613546
absolute error = 3.933
relative error = 77.37 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.4117134723 3.75342667564
absolute error = 4.866
relative error = 95.93 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=19021.3MB, alloc=44.3MB, time=259.95
x[1] = 0.7282 2.322
h = 0.003 0.006
y1[1] (numeric) = 1.09764265853 -0.515405808765
y1[1] (closed_form) = 3.84163070952 -3.36023665491
absolute error = 3.953
relative error = 77.44 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.42550972647 3.76842845461
absolute error = 4.886
relative error = 95.95 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=19070.8MB, alloc=44.3MB, time=260.61
x[1] = 0.7312 2.328
h = 0.0001 0.005
y1[1] (numeric) = 1.09763268851 -0.51689830005
y1[1] (closed_form) = 3.85395599281 -3.39220972878
absolute error = 3.983
relative error = 77.58 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.45731033525 3.78138661138
absolute error = 4.917
relative error = 95.97 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7313 2.333
h = 0.0001 0.003
y1[1] (numeric) = 1.09810357258 -0.517906434586
y1[1] (closed_form) = 3.87256372837 -3.40991880852
absolute error = 4.008
relative error = 77.67 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.47470194478 3.80036276619
absolute error = 4.943
relative error = 95.99 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=19120.4MB, alloc=44.3MB, time=261.27
x[1] = 0.7314 2.336
h = 0.001 0.001
y1[1] (numeric) = 1.09837811649 -0.518515242111
y1[1] (closed_form) = 3.88363374616 -3.42073945729
absolute error = 4.023
relative error = 77.72 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.48533573352 3.81165552156
absolute error = 4.958
relative error = 96 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=19170.1MB, alloc=44.3MB, time=261.93
x[1] = 0.7324 2.337
h = 0.0001 0.004
y1[1] (numeric) = 1.09827662306 -0.5188130757
y1[1] (closed_form) = 3.88395664278 -3.42804033229
absolute error = 4.028
relative error = 77.75 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.49264391854 3.81211492808
absolute error = 4.964
relative error = 96 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7325 2.341
h = 0.003 0.006
y1[1] (numeric) = 1.09864933705 -0.519621546731
y1[1] (closed_form) = 3.89888555695 -3.4424211205
absolute error = 4.048
relative error = 77.82 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.50677396371 3.82733707006
absolute error = 4.984
relative error = 96.02 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=19219.6MB, alloc=44.3MB, time=262.59
x[1] = 0.7355 2.347
h = 0.0001 0.005
y1[1] (numeric) = 1.09863936704 -0.521114038015
y1[1] (closed_form) = 3.91131978934 -3.47506064936
absolute error = 4.079
relative error = 77.96 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.53924160482 3.84039153148
absolute error = 5.016
relative error = 96.04 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=19269.2MB, alloc=44.3MB, time=263.25
x[1] = 0.7356 2.352
h = 0.0001 0.003
y1[1] (numeric) = 1.0991102511 -0.522122172551
y1[1] (closed_form) = 3.93021503283 -3.49318635163
absolute error = 4.104
relative error = 78.05 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.55705426037 3.85964691757
absolute error = 5.042
relative error = 96.06 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7357 2.355
h = 0.001 0.001
y1[1] (numeric) = 1.09938479501 -0.522730980076
y1[1] (closed_form) = 3.94145490224 -3.50426037774
absolute error = 4.119
relative error = 78.1 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.56794400523 3.87110454209
absolute error = 5.058
relative error = 96.07 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=19318.8MB, alloc=44.3MB, time=263.91
x[1] = 0.7367 2.356
h = 0.001 0.003
y1[1] (numeric) = 1.09928330158 -0.523028813666
y1[1] (closed_form) = 3.94175455604 -3.51170336784
absolute error = 4.125
relative error = 78.13 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.57539359175 3.87153816619
absolute error = 5.063
relative error = 96.07 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7377 2.359
h = 0.0001 0.004
y1[1] (numeric) = 1.09937814833 -0.523725974266
y1[1] (closed_form) = 3.94979900496 -3.52632698638
absolute error = 4.14
relative error = 78.19 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.58989640024 3.87985648306
absolute error = 5.079
relative error = 96.08 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=19368.3MB, alloc=44.3MB, time=264.56
x[1] = 0.7378 2.363
h = 0.003 0.006
y1[1] (numeric) = 1.09975086232 -0.524534445297
y1[1] (closed_form) = 3.96498964784 -3.5411043719
absolute error = 4.16
relative error = 78.26 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.60442698199 3.89533266915
absolute error = 5.1
relative error = 96.1 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=19417.8MB, alloc=44.3MB, time=265.22
x[1] = 0.7408 2.369
h = 0.0001 0.005
y1[1] (numeric) = 1.0997408923 -0.526026936581
y1[1] (closed_form) = 3.97753800665 -3.57453633202
absolute error = 4.192
relative error = 78.39 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.63768758129 3.90848686124
absolute error = 5.132
relative error = 96.12 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7409 2.374
h = 0.0001 0.003
y1[1] (numeric) = 1.10021177637 -0.527035071117
y1[1] (closed_form) = 3.99676466115 -3.59316235189
absolute error = 4.218
relative error = 78.48 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.65600550335 3.92806419373
absolute error = 5.159
relative error = 96.14 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=19467.4MB, alloc=44.3MB, time=265.88
x[1] = 0.741 2.377
h = 0.001 0.001
y1[1] (numeric) = 1.10048632027 -0.527643878642
y1[1] (closed_form) = 4.00820015667 -3.6045405433
absolute error = 4.233
relative error = 78.53 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.66720229697 3.93971174765
absolute error = 5.175
relative error = 96.15 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=19517.1MB, alloc=44.3MB, time=266.54
x[1] = 0.742 2.378
h = 0.001 0.003
y1[1] (numeric) = 1.10038482685 -0.527941712232
y1[1] (closed_form) = 4.00846905904 -3.61215146563
absolute error = 4.239
relative error = 78.56 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.67481897751 3.94011173752
absolute error = 5.18
relative error = 96.15 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.743 2.381
h = 0.0001 0.004
y1[1] (numeric) = 1.1004796736 -0.528638872832
y1[1] (closed_form) = 4.01661976859 -3.62714253643
absolute error = 4.255
relative error = 78.62 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.68969044881 3.94852972558
absolute error = 5.197
relative error = 96.16 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=19566.6MB, alloc=44.3MB, time=267.19
x[1] = 0.7431 2.385
h = 0.003 0.006
y1[1] (numeric) = 1.10085238758 -0.529447343863
y1[1] (closed_form) = 4.03207561959 -3.64232679934
absolute error = 4.276
relative error = 78.69 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.70463180129 3.96426362292
absolute error = 5.218
relative error = 96.18 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=19616.0MB, alloc=44.3MB, time=267.85
x[1] = 0.7461 2.391
h = 0.0001 0.005
y1[1] (numeric) = 1.10084241757 -0.530939835147
y1[1] (closed_form) = 4.04473602897 -3.6765693596
absolute error = 4.308
relative error = 78.82 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.73870359082 3.97751578603
absolute error = 5.251
relative error = 96.2 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7462 2.396
h = 0.0001 0.003
y1[1] (numeric) = 1.10131330164 -0.531947969683
y1[1] (closed_form) = 4.06429851642 -3.69570867311
absolute error = 4.335
relative error = 78.91 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.75753969674 3.99741971861
absolute error = 5.279
relative error = 96.21 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=19665.7MB, alloc=44.3MB, time=268.51
x[1] = 0.7463 2.399
h = 0.001 0.001
y1[1] (numeric) = 1.10158784554 -0.532556777208
y1[1] (closed_form) = 4.07593219817 -3.70739888433
absolute error = 4.35
relative error = 78.96 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.7690513604 4.00925990101
absolute error = 5.295
relative error = 96.23 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7473 2.4
h = 0.001 0.003
y1[1] (numeric) = 1.10148635212 -0.532854610798
y1[1] (closed_form) = 4.07616869672 -3.71518127161
absolute error = 4.356
relative error = 78.98 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.77683870086 4.00962466268
absolute error = 5.301
relative error = 96.23 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=19715.3MB, alloc=44.3MB, time=269.17
x[1] = 0.7483 2.403
h = 0.0001 0.004
y1[1] (numeric) = 1.10158119886 -0.533551771398
y1[1] (closed_form) = 4.08442588679 -3.73054853033
absolute error = 4.372
relative error = 79.04 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.79208757843 4.0181426916
absolute error = 5.317
relative error = 96.24 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=19764.7MB, alloc=44.3MB, time=269.83
x[1] = 0.7484 2.407
h = 0.003 0.006
y1[1] (numeric) = 1.10195391285 -0.534360242429
y1[1] (closed_form) = 4.10015045135 -3.74615019805
absolute error = 4.394
relative error = 79.11 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.80745018317 4.03413798905
absolute error = 5.339
relative error = 96.25 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7514 2.413
h = 0.0001 0.005
y1[1] (numeric) = 1.10194394284 -0.535852733713
y1[1] (closed_form) = 4.1129206975 -3.78122192305
absolute error = 4.427
relative error = 79.24 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.84235178768 4.04748621898
absolute error = 5.373
relative error = 96.27 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=19814.4MB, alloc=44.3MB, time=270.49
x[1] = 0.7515 2.418
h = 0.0001 0.003
y1[1] (numeric) = 1.1024148269 -0.536860868249
y1[1] (closed_form) = 4.13282347327 -3.80088781856
absolute error = 4.454
relative error = 79.32 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.86171930723 4.0677214334
absolute error = 5.401
relative error = 96.29 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=19863.9MB, alloc=44.3MB, time=271.15
x[1] = 0.7516 2.421
h = 0.001 0.001
y1[1] (numeric) = 1.10268937081 -0.537469675774
y1[1] (closed_form) = 4.14465791893 -3.81289809262
absolute error = 4.47
relative error = 79.37 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.8735538507 4.07975695777
absolute error = 5.418
relative error = 96.3 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7526 2.422
h = 0.001 0.003
y1[1] (numeric) = 1.10258787738 -0.537767509364
y1[1] (closed_form) = 4.14486030649 -3.82085554816
absolute error = 4.476
relative error = 79.4 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.88151548658 4.08008484139
absolute error = 5.423
relative error = 96.3 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=19913.5MB, alloc=44.3MB, time=271.81
x[1] = 0.7536 2.425
h = 0.0001 0.004
y1[1] (numeric) = 1.10268272413 -0.538464669964
y1[1] (closed_form) = 4.15322415781 -3.83660792681
absolute error = 4.493
relative error = 79.46 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.89715070929 4.08870323842
absolute error = 5.44
relative error = 96.31 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=19963.1MB, alloc=44.3MB, time=272.46
x[1] = 0.7537 2.429
h = 0.003 0.006
y1[1] (numeric) = 1.10305543812 -0.539273140995
y1[1] (closed_form) = 4.16922096653 -3.85263777975
absolute error = 4.514
relative error = 79.52 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.91294530083 4.10496364577
absolute error = 5.463
relative error = 96.33 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7567 2.435
h = 0.0001 0.005
y1[1] (numeric) = 1.1030454681 -0.540765632279
y1[1] (closed_form) = 4.18209869235 -3.88855763774
absolute error = 4.548
relative error = 79.65 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.9486957458 4.11840588862
absolute error = 5.497
relative error = 96.35 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=20012.7MB, alloc=44.3MB, time=273.15
x[1] = 0.7568 2.44
h = 0.0001 0.003
y1[1] (numeric) = 1.10351635217 -0.541773766815
y1[1] (closed_form) = 4.20234624412 -3.90876372305
absolute error = 4.576
relative error = 79.73 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.96860822827 4.13897709372
absolute error = 5.526
relative error = 96.36 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7569 2.443
h = 0.001 0.001
y1[1] (numeric) = 1.10379089607 -0.54238257434
y1[1] (closed_form) = 4.21438404829 -3.92110229572
absolute error = 4.593
relative error = 79.78 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.98077385409 4.1512106873
absolute error = 5.543
relative error = 96.37 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=20062.3MB, alloc=44.3MB, time=273.81
x[1] = 0.7579 2.444
h = 0.0001 0.004
y1[1] (numeric) = 1.10368940265 -0.54268040793
y1[1] (closed_form) = 4.21455056131 -3.9292384947
absolute error = 4.599
relative error = 79.81 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 3.98891349174 4.15149998556
absolute error = 5.549
relative error = 96.38 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=20111.9MB, alloc=44.3MB, time=274.47
x[1] = 0.758 2.448
h = 0.003 0.006
y1[1] (numeric) = 1.10406211664 -0.54348887896
y1[1] (closed_form) = 4.23078983459 -3.94564244459
absolute error = 4.621
relative error = 79.87 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.00508549799 4.1679969014
absolute error = 5.572
relative error = 96.39 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.761 2.454
h = 0.0001 0.005
y1[1] (numeric) = 1.10405214662 -0.544981370245
y1[1] (closed_form) = 4.24376849244 -3.98230661128
absolute error = 4.655
relative error = 79.99 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.04158105993 4.18152873184
absolute error = 5.607
relative error = 96.41 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=20161.5MB, alloc=44.3MB, time=275.12
x[1] = 0.7611 2.459
h = 0.0001 0.003
y1[1] (numeric) = 1.10452303069 -0.545989504781
y1[1] (closed_form) = 4.26432309479 -4.00298463969
absolute error = 4.683
relative error = 80.08 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.06196964844 4.20239965448
absolute error = 5.636
relative error = 96.43 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=20211.0MB, alloc=44.3MB, time=275.78
x[1] = 0.7612 2.462
h = 0.001 0.001
y1[1] (numeric) = 1.10479757459 -0.546598312306
y1[1] (closed_form) = 4.27654208106 -4.01561008144
absolute error = 4.7
relative error = 80.13 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.07442457383 4.21481001383
absolute error = 5.653
relative error = 96.44 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7622 2.463
h = 0.001 0.003
y1[1] (numeric) = 1.10469608117 -0.546896145895
y1[1] (closed_form) = 4.27667844812 -4.02390359262
absolute error = 4.706
relative error = 80.15 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.08272094089 4.21506686865
absolute error = 5.659
relative error = 96.44 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=20260.7MB, alloc=44.3MB, time=276.44
x[1] = 0.7632 2.466
h = 0.0001 0.004
y1[1] (numeric) = 1.10479092792 -0.547593306496
y1[1] (closed_form) = 4.28524595773 -4.04039577849
absolute error = 4.724
relative error = 80.21 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.09909833683 4.22387760788
absolute error = 5.677
relative error = 96.45 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=20310.3MB, alloc=44.3MB, time=277.11
x[1] = 0.7633 2.47
h = 0.003 0.006
y1[1] (numeric) = 1.1051636419 -0.548401777526
y1[1] (closed_form) = 4.30176424445 -4.05724862373
absolute error = 4.747
relative error = 80.27 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.11572295287 4.24064672483
absolute error = 5.7
relative error = 96.46 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7663 2.476
h = 0.0001 0.005
y1[1] (numeric) = 1.10515367189 -0.549894268811
y1[1] (closed_form) = 4.31484583329 -4.09479735344
absolute error = 4.782
relative error = 80.39 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.15310388095 4.25426856759
absolute error = 5.736
relative error = 96.48 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=20359.9MB, alloc=44.3MB, time=277.77
x[1] = 0.7664 2.481
h = 0.0001 0.003
y1[1] (numeric) = 1.10562455596 -0.550902403347
y1[1] (closed_form) = 4.33575381577 -4.11604171347
absolute error = 4.811
relative error = 80.47 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.17406346318 4.27548448233
absolute error = 5.766
relative error = 96.5 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7665 2.484
h = 0.001 0.001
y1[1] (numeric) = 1.10589909986 -0.551511210872
y1[1] (closed_form) = 4.34818113459 -4.1290112753
absolute error = 4.828
relative error = 80.52 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.18686522919 4.28809812329
absolute error = 5.784
relative error = 96.51 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=20409.5MB, alloc=44.3MB, time=278.43
x[1] = 0.7675 2.485
h = 0.001 0.003
y1[1] (numeric) = 1.10579760644 -0.551809044461
y1[1] (closed_form) = 4.34827823564 -4.13749058687
absolute error = 4.834
relative error = 80.54 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.19534670977 4.28831310346
absolute error = 5.79
relative error = 96.51 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=20459.0MB, alloc=44.3MB, time=279.08
x[1] = 0.7685 2.488
h = 0.0001 0.004
y1[1] (numeric) = 1.10589245318 -0.552506205062
y1[1] (closed_form) = 4.35695280356 -4.15439456609
absolute error = 4.852
relative error = 80.6 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.21213713737 4.2972250099
absolute error = 5.808
relative error = 96.52 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7686 2.492
h = 0.003 0.006
y1[1] (numeric) = 1.10626516717 -0.553314676092
y1[1] (closed_form) = 4.37375370439 -4.17170784264
absolute error = 4.875
relative error = 80.66 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.2292258536 4.31427009622
absolute error = 5.832
relative error = 96.53 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=20508.4MB, alloc=44.3MB, time=279.74
x[1] = 0.7716 2.498
h = 0.0001 0.005
y1[1] (numeric) = 1.10625519716 -0.554807167377
y1[1] (closed_form) = 4.38693543138 -4.21016130555
absolute error = 4.912
relative error = 80.78 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.26751236748 4.32797944392
absolute error = 5.868
relative error = 96.55 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=20558.0MB, alloc=44.3MB, time=280.40
x[1] = 0.7717 2.503
h = 0.0001 0.003
y1[1] (numeric) = 1.10672608123 -0.555815301913
y1[1] (closed_form) = 4.40820137187 -4.23198655909
absolute error = 4.941
relative error = 80.86 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.28905744732 4.34954513542
absolute error = 5.899
relative error = 96.57 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7718 2.506
h = 0.001 0.001
y1[1] (numeric) = 1.10700062513 -0.556424109438
y1[1] (closed_form) = 4.42083966439 -4.24530905239
absolute error = 4.959
relative error = 80.9 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.30221483229 4.36236482324
absolute error = 5.917
relative error = 96.58 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=20607.6MB, alloc=44.3MB, time=281.06
x[1] = 0.7728 2.507
h = 0.001 0.003
y1[1] (numeric) = 1.1068991317 -0.556721943027
y1[1] (closed_form) = 4.42089556618 -4.25397805291
absolute error = 4.965
relative error = 80.93 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.31088534343 4.36253604875
absolute error = 5.923
relative error = 96.58 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=20657.1MB, alloc=44.3MB, time=281.72
x[1] = 0.7738 2.51
h = 0.0001 0.004
y1[1] (numeric) = 1.10699397845 -0.557419103628
y1[1] (closed_form) = 4.42967720503 -4.27130355544
absolute error = 4.983
relative error = 80.98 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.32809853624 4.3715492697
absolute error = 5.942
relative error = 96.59 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7739 2.514
h = 0.003 0.006
y1[1] (numeric) = 1.10736669244 -0.558227574658
y1[1] (closed_form) = 4.44676434213 -4.28908907509
absolute error = 5.007
relative error = 81.04 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.34566311902 4.38887411125
absolute error = 5.967
relative error = 96.6 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=20706.7MB, alloc=44.3MB, time=282.38
x[1] = 0.7769 2.52
h = 0.0001 0.005
y1[1] (numeric) = 1.10735672242 -0.559720065943
y1[1] (closed_form) = 4.46004324909 -4.32846787721
absolute error = 5.044
relative error = 81.16 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.38487587165 4.4026682852
absolute error = 6.004
relative error = 96.62 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.777 2.525
h = 0.0001 0.003
y1[1] (numeric) = 1.10782760649 -0.560728200479
y1[1] (closed_form) = 4.48167175317 -4.35088893449
absolute error = 5.074
relative error = 81.24 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.40702130149 4.42458856106
absolute error = 6.035
relative error = 96.64 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=20756.2MB, alloc=44.3MB, time=283.04
x[1] = 0.7771 2.528
h = 0.001 0.001
y1[1] (numeric) = 1.10810215039 -0.561337008004
y1[1] (closed_form) = 4.49452367445 -4.36457338078
absolute error = 5.092
relative error = 81.28 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.42054329395 4.437617072
absolute error = 6.054
relative error = 96.65 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=20805.9MB, alloc=44.3MB, time=283.70
x[1] = 0.7781 2.529
h = 0.001 0.003
y1[1] (numeric) = 1.10800065697 -0.561634841593
y1[1] (closed_form) = 4.4945363807 -4.37343603567
absolute error = 5.099
relative error = 81.31 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.42940682867 4.4377425988
absolute error = 6.06
relative error = 96.65 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7791 2.532
h = 0.0001 0.004
y1[1] (numeric) = 1.10809550372 -0.562332002194
y1[1] (closed_form) = 4.50342505361 -4.39119300865
absolute error = 5.117
relative error = 81.36 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.44705273663 4.44685722917
absolute error = 6.079
relative error = 96.66 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=20855.6MB, alloc=44.3MB, time=284.36
x[1] = 0.7792 2.536
h = 0.003 0.006
y1[1] (numeric) = 1.1084682177 -0.563140473224
y1[1] (closed_form) = 4.52080206949 -4.40946286523
absolute error = 5.142
relative error = 81.42 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.4651052345 4.46446562837
absolute error = 6.104
relative error = 96.67 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=20905.1MB, alloc=44.3MB, time=285.02
x[1] = 0.7822 2.542
h = 0.0001 0.005
y1[1] (numeric) = 1.10845824769 -0.564632964509
y1[1] (closed_form) = 4.53417502675 -4.44978805715
absolute error = 5.18
relative error = 81.53 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.50526532093 4.47834177253
absolute error = 6.142
relative error = 96.69 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7823 2.547
h = 0.0001 0.003
y1[1] (numeric) = 1.10892913176 -0.565641099045
y1[1] (closed_form) = 4.55617072636 -4.47282018459
absolute error = 5.211
relative error = 81.61 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.52802630956 4.500621462
absolute error = 6.174
relative error = 96.7 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=20954.8MB, alloc=44.3MB, time=285.68
x[1] = 0.7824 2.55
h = 0.001 0.001
y1[1] (numeric) = 1.10920367566 -0.56624990657
y1[1] (closed_form) = 4.56923894442 -4.48687582019
absolute error = 5.229
relative error = 81.65 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.54192211298 4.51386158248
absolute error = 6.193
relative error = 96.71 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=21004.4MB, alloc=44.3MB, time=286.34
x[1] = 0.7834 2.551
h = 0.0001 0.004
y1[1] (numeric) = 1.10910218224 -0.566547740159
y1[1] (closed_form) = 4.569206394 -4.49593617312
absolute error = 5.236
relative error = 81.68 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.55098274163 4.51393940066
absolute error = 6.199
relative error = 96.72 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7835 2.555
h = 0.003 0.006
y1[1] (numeric) = 1.10947489622 -0.56735621119
y1[1] (closed_form) = 4.58684183022 -4.51462932283
absolute error = 5.261
relative error = 81.74 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.56946164922 4.53180094627
absolute error = 6.225
relative error = 96.73 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=21054.0MB, alloc=44.3MB, time=287.00
x[1] = 0.7865 2.561
h = 0.0001 0.005
y1[1] (numeric) = 1.10946492621 -0.568848702475
y1[1] (closed_form) = 4.60030472411 -4.55578527193
absolute error = 5.299
relative error = 81.85 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.61045347874 4.54575685561
absolute error = 6.264
relative error = 96.75 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7866 2.566
h = 0.0001 0.003
y1[1] (numeric) = 1.10993581028 -0.569856837011
y1[1] (closed_form) = 4.62262775489 -4.57935144144
absolute error = 5.331
relative error = 81.92 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.63375241674 4.56835738485
absolute error = 6.296
relative error = 96.76 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=21103.6MB, alloc=44.3MB, time=287.66
x[1] = 0.7867 2.569
h = 0.001 0.001
y1[1] (numeric) = 1.11021035418 -0.570465644535
y1[1] (closed_form) = 4.63588887513 -4.59373152826
absolute error = 5.349
relative error = 81.97 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.6479749557 4.5817864963
absolute error = 6.316
relative error = 96.77 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=21153.3MB, alloc=44.3MB, time=288.32
x[1] = 0.7877 2.57
h = 0.001 0.003
y1[1] (numeric) = 1.11010886076 -0.570763478125
y1[1] (closed_form) = 4.63581808986 -4.60296592558
absolute error = 5.356
relative error = 81.99 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.65720915791 4.58182400259
absolute error = 6.322
relative error = 96.77 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7887 2.573
h = 0.0001 0.004
y1[1] (numeric) = 1.1102037075 -0.571460638725
y1[1] (closed_form) = 4.64491108064 -4.62155173022
absolute error = 5.376
relative error = 82.04 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.675686282 4.59113284055
absolute error = 6.342
relative error = 96.78 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=21202.7MB, alloc=44.3MB, time=288.98
x[1] = 0.7888 2.577
h = 0.003 0.006
y1[1] (numeric) = 1.11057642149 -0.572269109756
y1[1] (closed_form) = 4.662843376 -4.64075244941
absolute error = 5.401
relative error = 82.1 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.69467625157 4.60928521134
absolute error = 6.368
relative error = 96.79 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=21252.3MB, alloc=44.3MB, time=289.64
x[1] = 0.7918 2.583
h = 0.0001 0.005
y1[1] (numeric) = 1.11056645148 -0.573761601041
y1[1] (closed_form) = 4.67639428196 -4.68289521457
absolute error = 5.441
relative error = 82.21 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.7366559145 4.62331754718
absolute error = 6.408
relative error = 96.81 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7919 2.588
h = 0.0001 0.003
y1[1] (numeric) = 1.11103733555 -0.574769735577
y1[1] (closed_form) = 4.6990933846 -4.70710178134
absolute error = 5.473
relative error = 82.28 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.76059962959 4.64628672066
absolute error = 6.441
relative error = 96.83 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=21301.9MB, alloc=44.3MB, time=290.30
x[1] = 0.792 2.591
h = 0.001 0.001
y1[1] (numeric) = 1.11131187945 -0.575378543101
y1[1] (closed_form) = 4.71257591381 -4.72187080051
absolute error = 5.492
relative error = 82.33 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.7752136603 4.65993276648
absolute error = 6.461
relative error = 96.84 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=21351.6MB, alloc=44.3MB, time=290.96
x[1] = 0.793 2.592
h = 0.001 0.003
y1[1] (numeric) = 1.11121038603 -0.575676376691
y1[1] (closed_form) = 4.71245590789 -4.73131065948
absolute error = 5.499
relative error = 82.35 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.78465276695 4.65991869324
absolute error = 6.468
relative error = 96.84 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.794 2.595
h = 0.0001 0.004
y1[1] (numeric) = 1.11130523277 -0.576373537291
y1[1] (closed_form) = 4.72165566033 -4.75035763365
absolute error = 5.519
relative error = 82.4 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.80359230784 4.66932902964
absolute error = 6.488
relative error = 96.85 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=21401.2MB, alloc=44.3MB, time=291.62
x[1] = 0.7941 2.599
h = 0.003 0.006
y1[1] (numeric) = 1.11167794676 -0.577182008322
y1[1] (closed_form) = 4.73988851263 -4.77007885849
absolute error = 5.545
relative error = 82.45 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.8231062308 4.68777607288
absolute error = 6.515
relative error = 96.86 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7971 2.605
h = 0.0001 0.005
y1[1] (numeric) = 1.11166797674 -0.578674499607
y1[1] (closed_form) = 4.7535237804 -4.81323081388
absolute error = 5.585
relative error = 82.56 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.86609613921 4.70188144249
absolute error = 6.555
relative error = 96.88 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=21450.8MB, alloc=44.3MB, time=292.28
x[1] = 0.7972 2.61
h = 0.0001 0.003
y1[1] (numeric) = 1.11213886081 -0.579682634143
y1[1] (closed_form) = 4.77660365853 -4.83809410807
absolute error = 5.618
relative error = 82.63 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.8907009047 4.72522414828
absolute error = 6.589
relative error = 96.89 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=21500.4MB, alloc=44.3MB, time=292.94
x[1] = 0.7973 2.613
h = 0.001 0.001
y1[1] (numeric) = 1.11241340471 -0.580291441667
y1[1] (closed_form) = 4.7903102993 -4.85326193749
absolute error = 5.638
relative error = 82.68 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.90571627253 4.73908994177
absolute error = 6.609
relative error = 96.9 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7983 2.614
h = 0.001 0.003
y1[1] (numeric) = 1.11231191129 -0.580589275257
y1[1] (closed_form) = 4.79013881649 -4.86291153396
absolute error = 5.645
relative error = 82.7 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.91536458383 4.7390220812
absolute error = 6.616
relative error = 96.9 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=21549.9MB, alloc=44.3MB, time=293.60
x[1] = 0.7993 2.617
h = 0.0001 0.004
y1[1] (numeric) = 1.11240675804 -0.581286435857
y1[1] (closed_form) = 4.79944508287 -4.88243050716
absolute error = 5.665
relative error = 82.75 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.93477737115 4.7485337894
absolute error = 6.637
relative error = 96.91 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=21599.4MB, alloc=44.3MB, time=294.26
x[1] = 0.7994 2.621
h = 0.003 0.006
y1[1] (numeric) = 1.11277947202 -0.582094906888
y1[1] (closed_form) = 4.81798220554 -4.90268548123
absolute error = 5.692
relative error = 82.8 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.95482844652 4.76727936453
absolute error = 6.664
relative error = 96.92 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8024 2.627
h = 0.0001 0.005
y1[1] (numeric) = 1.11276950201 -0.583587398173
y1[1] (closed_form) = 4.83169798794 -4.94686948078
absolute error = 5.733
relative error = 82.91 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 4.99885149012 4.78145417285
absolute error = 6.706
relative error = 96.94 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=21649.0MB, alloc=44.3MB, time=294.93
x[1] = 0.8025 2.632
h = 0.0001 0.003
y1[1] (numeric) = 1.11324038608 -0.584595532709
y1[1] (closed_form) = 4.85516336565 -4.97240622076
absolute error = 5.767
relative error = 82.98 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 5.02413396781 4.80517531515
absolute error = 6.74
relative error = 96.95 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=21698.6MB, alloc=44.3MB, time=295.59
x[1] = 0.8026 2.635
h = 0.001 0.001
y1[1] (numeric) = 1.11351492998 -0.585204340233
y1[1] (closed_form) = 4.86909682974 -4.98798297243
absolute error = 5.787
relative error = 83.02 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 5.03956075235 4.8192636762
absolute error = 6.761
relative error = 96.96 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8036 2.636
h = 0.001 0.003
y1[1] (numeric) = 1.11341343656 -0.585502173823
y1[1] (closed_form) = 4.86887154139 -4.99784666588
absolute error = 5.794
relative error = 83.04 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 5.04942265138 4.81913974721
absolute error = 6.768
relative error = 96.96 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=21748.2MB, alloc=44.3MB, time=296.25
x[1] = 0.8046 2.639
h = 0.0001 0.004
y1[1] (numeric) = 1.1135082833 -0.586199334423
y1[1] (closed_form) = 4.87828401249 -5.01784870764
absolute error = 5.815
relative error = 83.09 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 5.06931975414 4.8287526364
absolute error = 6.789
relative error = 96.97 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8047 2.643
h = 0.003 0.006
y1[1] (numeric) = 1.11388099729 -0.587007805454
y1[1] (closed_form) = 4.8971291332 -5.03865098882
absolute error = 5.842
relative error = 83.15 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 5.08992149547 4.8478006137
absolute error = 6.817
relative error = 96.98 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=21797.7MB, alloc=44.3MB, time=296.91
x[1] = 0.8077 2.649
h = 0.0001 0.005
y1[1] (numeric) = 1.11387102728 -0.588500296739
y1[1] (closed_form) = 4.91092137908 -5.0838903758
absolute error = 5.884
relative error = 83.25 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 5.13500105118 4.86204105638
absolute error = 6.859
relative error = 97 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=21847.3MB, alloc=44.3MB, time=297.57
x[1] = 0.8078 2.654
h = 0.0001 0.003
y1[1] (numeric) = 1.11434191135 -0.589508431275
y1[1] (closed_form) = 4.93477699914 -5.11011767691
absolute error = 5.919
relative error = 83.32 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 5.16097830013 4.88614555389
absolute error = 6.895
relative error = 97.01 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8079 2.657
h = 0.001 0.001
y1[1] (numeric) = 1.11461645525 -0.590117238799
y1[1] (closed_form) = 4.94894000637 -5.12611370214
absolute error = 5.939
relative error = 83.36 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 5.17682682046 4.9004593079
absolute error = 6.916
relative error = 97.02 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=21896.8MB, alloc=44.3MB, time=298.23
x[1] = 0.8089 2.658
h = 0.0001 0.004
y1[1] (numeric) = 1.11451496183 -0.590415072389
y1[1] (closed_form) = 4.94865850938 -5.13619593711
absolute error = 5.947
relative error = 83.38 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 5.18690677457 4.90027695402
absolute error = 6.923
relative error = 97.03 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=21946.2MB, alloc=44.3MB, time=298.88
x[1] = 0.809 2.662
h = 0.003 0.006
y1[1] (numeric) = 1.11488767581 -0.591223543419
y1[1] (closed_form) = 4.96777848464 -5.15747669446
absolute error = 5.975
relative error = 83.43 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 5.2079899123 4.91959512004
absolute error = 6.952
relative error = 97.04 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.812 2.668
h = 0.0001 0.005
y1[1] (numeric) = 1.1148777058 -0.592716034704
y1[1] (closed_form) = 4.98164610199 -5.20364275591
absolute error = 6.018
relative error = 83.53 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 5.25399726109 4.93390182046
absolute error = 6.995
relative error = 97.05 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=21995.8MB, alloc=44.3MB, time=299.54
x[1] = 0.8121 2.673
h = 0.0001 0.003
y1[1] (numeric) = 1.11534858987 -0.59372416924
y1[1] (closed_form) = 5.00584995144 -5.23047375838
absolute error = 6.053
relative error = 83.6 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 5.28058186978 4.95834880607
absolute error = 7.031
relative error = 97.07 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=22045.3MB, alloc=44.3MB, time=300.20
x[1] = 0.8122 2.676
h = 0.001 0.001
y1[1] (numeric) = 1.11562313377 -0.594332976765
y1[1] (closed_form) = 5.0202178917 -5.24683637754
absolute error = 6.074
relative error = 83.64 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 5.2967991255 4.97286403226
absolute error = 7.053
relative error = 97.08 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8132 2.677
h = 0.001 0.003
y1[1] (numeric) = 1.11552164035 -0.594630810354
y1[1] (closed_form) = 5.01988870634 -5.25711106081
absolute error = 6.081
relative error = 83.66 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 5.30707115256 4.97263211355
absolute error = 7.06
relative error = 97.08 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=22094.9MB, alloc=44.3MB, time=300.86
x[1] = 0.8142 2.68
h = 0.0001 0.004
y1[1] (numeric) = 1.11561648709 -0.595327970955
y1[1] (closed_form) = 5.02950383166 -5.27804103198
absolute error = 6.103
relative error = 83.71 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 5.32789855818 4.98243863019
absolute error = 7.082
relative error = 97.09 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8143 2.684
h = 0.003 0.006
y1[1] (numeric) = 1.11598920108 -0.596136441985
y1[1] (closed_form) = 5.04893894482 -5.29989514059
absolute error = 6.131
relative error = 83.76 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 5.34955832249 5.00206659423
absolute error = 7.111
relative error = 97.1 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=22144.3MB, alloc=44.3MB, time=301.52
x[1] = 0.8173 2.69
h = 0.0001 0.005
y1[1] (numeric) = 1.11597923106 -0.59762893327
y1[1] (closed_form) = 5.06287521165 -5.34716141582
absolute error = 6.175
relative error = 83.86 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 5.39666706431 5.01643156087
absolute error = 7.155
relative error = 97.11 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=22193.9MB, alloc=44.3MB, time=302.18
x[1] = 0.8174 2.695
h = 0.0001 0.003
y1[1] (numeric) = 1.11645011513 -0.598637067806
y1[1] (closed_form) = 5.08747838755 -5.37471585724
absolute error = 6.211
relative error = 83.93 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 5.42397921622 5.04127130155
absolute error = 7.192
relative error = 97.13 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8175 2.698
h = 0.001 0.001
y1[1] (numeric) = 1.11672465903 -0.599245875331
y1[1] (closed_form) = 5.10208107952 -5.39151763422
absolute error = 6.233
relative error = 83.97 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 5.44063803121 5.05601731886
absolute error = 7.214
relative error = 97.13 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=22243.5MB, alloc=44.3MB, time=302.84
x[1] = 0.8185 2.699
h = 0.001 0.003
y1[1] (numeric) = 1.11662316561 -0.59954370892
y1[1] (closed_form) = 5.10169106379 -5.40201939152
absolute error = 6.241
relative error = 83.99 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 5.45113668585 5.05572243817
absolute error = 7.222
relative error = 97.14 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=22293.1MB, alloc=44.3MB, time=303.50
x[1] = 0.8195 2.702
h = 0.0001 0.004
y1[1] (numeric) = 1.11671801236 -0.600240869521
y1[1] (closed_form) = 5.11141128666 -5.42346547546
absolute error = 6.263
relative error = 84.03 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 5.47248144514 5.06562935333
absolute error = 7.244
relative error = 97.14 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8196 2.706
h = 0.003 0.006
y1[1] (numeric) = 1.11709072634 -0.601049340551
y1[1] (closed_form) = 5.13116530188 -5.44590743172
absolute error = 6.292
relative error = 84.09 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 5.49473228881 5.08557101277
absolute error = 7.274
relative error = 97.16 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=22342.6MB, alloc=44.3MB, time=304.15
x[1] = 0.8226 2.712
h = 0.0001 0.005
y1[1] (numeric) = 1.11708075633 -0.602541831836
y1[1] (closed_form) = 5.1451655487 -5.49429872069
absolute error = 6.337
relative error = 84.18 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 5.54296725175 5.09998980836
absolute error = 7.319
relative error = 97.17 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=22392.3MB, alloc=44.3MB, time=304.81
x[1] = 0.8227 2.717
h = 0.0001 0.003
y1[1] (numeric) = 1.1175516404 -0.603549966372
y1[1] (closed_form) = 5.17017284203 -5.52259490165
absolute error = 6.373
relative error = 84.25 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 5.5710251922 5.12522725943
absolute error = 7.357
relative error = 97.18 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8228 2.72
h = 0.001 0.001
y1[1] (numeric) = 1.1178261843 -0.604158773897
y1[1] (closed_form) = 5.18501302493 -5.53984690238
absolute error = 6.396
relative error = 84.29 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 5.58813660063 5.14020690578
absolute error = 7.38
relative error = 97.19 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=22442.0MB, alloc=44.3MB, time=305.47
x[1] = 0.8238 2.721
h = 0.001 0.003
y1[1] (numeric) = 1.11772469088 -0.604456607486
y1[1] (closed_form) = 5.18455955181 -5.55058043075
absolute error = 6.403
relative error = 84.31 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 5.59886660064 5.13984648019
absolute error = 7.387
relative error = 97.19 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8248 2.724
h = 0.0001 0.004
y1[1] (numeric) = 1.11781953763 -0.605153768087
y1[1] (closed_form) = 5.19438430229 -5.57255467213
absolute error = 6.426
relative error = 84.35 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 5.62074075564 5.14985333268
absolute error = 7.41
relative error = 97.2 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=22491.6MB, alloc=44.3MB, time=306.13
x[1] = 0.8249 2.728
h = 0.003 0.006
y1[1] (numeric) = 1.11819225161 -0.605962239117
y1[1] (closed_form) = 5.21446099201 -5.59559931484
absolute error = 6.456
relative error = 84.4 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 5.64359747407 5.1701125901
absolute error = 7.44
relative error = 97.21 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=22541.1MB, alloc=44.3MB, time=306.79
x[1] = 0.8279 2.734
h = 0.0001 0.005
y1[1] (numeric) = 1.1181822816 -0.607454730402
y1[1] (closed_form) = 5.22852031616 -5.64514094534
absolute error = 6.502
relative error = 84.5 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 5.69298401229 5.18458053924
absolute error = 7.487
relative error = 97.23 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.828 2.739
h = 0.0001 0.003
y1[1] (numeric) = 1.11865316567 -0.608462864938
y1[1] (closed_form) = 5.25393652914 -5.67419759885
absolute error = 6.539
relative error = 84.56 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 5.72180641933 5.21022066343
absolute error = 7.525
relative error = 97.24 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=22590.7MB, alloc=44.3MB, time=307.45
x[1] = 0.8281 2.742
h = 0.001 0.001
y1[1] (numeric) = 1.11892770957 -0.609071672463
y1[1] (closed_form) = 5.26901694548 -5.6919111499
absolute error = 6.562
relative error = 84.6 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 5.7393817162 5.22543677769
absolute error = 7.548
relative error = 97.25 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=22640.3MB, alloc=44.3MB, time=308.11
x[1] = 0.8291 2.743
h = 0.001 0.003
y1[1] (numeric) = 1.11882621615 -0.609369506052
y1[1] (closed_form) = 5.26849730497 -5.70288123724
absolute error = 6.57
relative error = 84.62 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 5.75034786959 5.22500814045
absolute error = 7.556
relative error = 97.25 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8301 2.746
h = 0.0001 0.004
y1[1] (numeric) = 1.11892106289 -0.610066666653
y1[1] (closed_form) = 5.27842593761 -5.72539594593
absolute error = 6.593
relative error = 84.66 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 5.77276372699 5.23511439119
absolute error = 7.579
relative error = 97.26 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=22689.8MB, alloc=44.3MB, time=308.77
x[1] = 0.8302 2.75
h = 0.003 0.006
y1[1] (numeric) = 1.11929377688 -0.610875137683
y1[1] (closed_form) = 5.29882908083 -5.7490584639
absolute error = 6.623
relative error = 84.71 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 5.7962414659 5.25569515265
absolute error = 7.611
relative error = 97.27 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=22739.4MB, alloc=44.3MB, time=309.43
x[1] = 0.8332 2.756
h = 0.0001 0.005
y1[1] (numeric) = 1.11928380686 -0.612367628968
y1[1] (closed_form) = 5.31294233828 -5.79977630198
absolute error = 6.671
relative error = 84.81 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 5.84680547002 5.27020733379
absolute error = 7.658
relative error = 97.28 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8333 2.761
h = 0.0001 0.003
y1[1] (numeric) = 1.11975469093 -0.613375763504
y1[1] (closed_form) = 5.33877228222 -5.82961260316
absolute error = 6.709
relative error = 84.87 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 5.87641146419 5.29625509912
absolute error = 7.697
relative error = 97.3 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=22789.0MB, alloc=44.3MB, time=310.09
x[1] = 0.8334 2.764
h = 0.001 0.001
y1[1] (numeric) = 1.12002923483 -0.613984571029
y1[1] (closed_form) = 5.35409567639 -5.84779929756
absolute error = 6.732
relative error = 84.91 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 5.89446221115 5.31171051979
absolute error = 7.721
relative error = 97.31 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8344 2.765
h = 0.0001 0.004
y1[1] (numeric) = 1.11992774141 -0.614282404618
y1[1] (closed_form) = 5.35350707316 -5.85901082419
absolute error = 6.74
relative error = 84.93 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 5.90566941767 5.31121091797
absolute error = 7.729
relative error = 97.31 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=22838.5MB, alloc=44.3MB, time=310.75
x[1] = 0.8345 2.769
h = 0.003 0.006
y1[1] (numeric) = 1.1203004554 -0.615090875649
y1[1] (closed_form) = 5.37420185945 -5.88321367434
absolute error = 6.771
relative error = 84.98 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 5.92969021871 5.33207919841
absolute error = 7.761
relative error = 97.32 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=22887.9MB, alloc=44.3MB, time=311.41
x[1] = 0.8375 2.775
h = 0.0001 0.005
y1[1] (numeric) = 1.12029048538 -0.616583366934
y1[1] (closed_form) = 5.38837167173 -5.93496452987
absolute error = 6.819
relative error = 85.07 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 5.98128845384 5.34663977373
absolute error = 7.809
relative error = 97.33 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8376 2.78
h = 0.0001 0.003
y1[1] (numeric) = 1.12076136945 -0.61759150147
y1[1] (closed_form) = 5.41457120588 -5.96548261899
absolute error = 6.858
relative error = 85.13 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 6.01157965358 5.37305205608
absolute error = 7.849
relative error = 97.35 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=22937.4MB, alloc=44.3MB, time=312.06
x[1] = 0.8377 2.783
h = 0.001 0.001
y1[1] (numeric) = 1.12103591335 -0.618200308995
y1[1] (closed_form) = 5.43011177435 -5.98408313177
absolute error = 6.882
relative error = 85.17 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 6.03004622173 5.38872159145
absolute error = 7.873
relative error = 97.35 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=22987.0MB, alloc=44.3MB, time=312.73
x[1] = 0.8387 2.784
h = 0.001 0.003
y1[1] (numeric) = 1.12093441993 -0.618498142584
y1[1] (closed_form) = 5.42946446183 -5.99550732948
absolute error = 6.89
relative error = 85.18 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 6.04146580517 5.38816158624
absolute error = 7.881
relative error = 97.35 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8397 2.787
h = 0.0001 0.004
y1[1] (numeric) = 1.12102926668 -0.619195303184
y1[1] (closed_form) = 5.43959120208 -6.01906020041
absolute error = 6.914
relative error = 85.23 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 6.06492216352 5.39845789084
absolute error = 7.905
relative error = 97.36 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=23036.6MB, alloc=44.3MB, time=313.39
x[1] = 0.8398 2.791
h = 0.003 0.006
y1[1] (numeric) = 1.12140198066 -0.620003774215
y1[1] (closed_form) = 5.46061967601 -6.04391010203
absolute error = 6.946
relative error = 85.28 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 6.08959308038 5.41965513748
absolute error = 7.938
relative error = 97.37 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=23086.0MB, alloc=44.3MB, time=314.04
x[1] = 0.8428 2.797
h = 0.0001 0.005
y1[1] (numeric) = 1.12139201065 -0.6214962655
y1[1] (closed_form) = 5.4748335023 -6.09688683325
absolute error = 6.995
relative error = 85.37 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 6.14241848831 5.43425042725
absolute error = 7.987
relative error = 97.39 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8429 2.802
h = 0.0001 0.003
y1[1] (numeric) = 1.12186289472 -0.622504400036
y1[1] (closed_form) = 5.50145597772 -6.12822140352
absolute error = 7.035
relative error = 85.43 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 6.17353000635 5.46107984225
absolute error = 8.028
relative error = 97.4 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=23135.6MB, alloc=44.3MB, time=314.70
x[1] = 0.843 2.805
h = 0.001 0.001
y1[1] (numeric) = 1.12213743862 -0.623113207561
y1[1] (closed_form) = 5.51724477656 -6.14731732849
absolute error = 7.059
relative error = 85.46 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 6.19249423448 5.47699410547
absolute error = 8.053
relative error = 97.41 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.844 2.806
h = 0.001 0.003
y1[1] (numeric) = 1.1220359452 -0.62341104115
y1[1] (closed_form) = 5.51652312522 -6.15899233383
absolute error = 7.068
relative error = 85.48 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 6.20416427337 5.47635783654
absolute error = 8.061
relative error = 97.41 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=23185.3MB, alloc=44.3MB, time=315.36
x[1] = 0.845 2.809
h = 0.0001 0.004
y1[1] (numeric) = 1.12213079195 -0.62410820175
y1[1] (closed_form) = 5.5267516131 -6.1831224124
absolute error = 7.092
relative error = 85.52 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 6.22819906164 5.48675169636
absolute error = 8.086
relative error = 97.42 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=23234.8MB, alloc=44.3MB, time=316.02
x[1] = 0.8451 2.813
h = 0.003 0.006
y1[1] (numeric) = 1.12250350593 -0.624916672781
y1[1] (closed_form) = 5.54811756659 -6.20863559935
absolute error = 7.125
relative error = 85.57 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 6.25353628592 5.50828181982
absolute error = 8.119
relative error = 97.43 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8481 2.819
h = 0.0001 0.005
y1[1] (numeric) = 1.12249353592 -0.626409164066
y1[1] (closed_form) = 5.56236953219 -6.26286567447
absolute error = 7.175
relative error = 85.66 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 6.30761635484 5.52290615854
absolute error = 8.169
relative error = 97.44 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=23284.4MB, alloc=44.3MB, time=316.68
x[1] = 0.8482 2.824
h = 0.0001 0.003
y1[1] (numeric) = 1.12296441999 -0.627417298602
y1[1] (closed_form) = 5.58941977889 -6.29503722088
absolute error = 7.216
relative error = 85.72 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 6.33956863273 5.55015768259
absolute error = 8.211
relative error = 97.45 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=23334.0MB, alloc=44.3MB, time=317.34
x[1] = 0.8483 2.827
h = 0.001 0.001
y1[1] (numeric) = 1.12323896389 -0.628026106127
y1[1] (closed_form) = 5.60545955307 -6.31464094651
absolute error = 7.241
relative error = 85.75 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 6.35904287855 5.56631950654
absolute error = 8.236
relative error = 97.46 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8493 2.828
h = 0.001 0.003
y1[1] (numeric) = 1.12313747047 -0.628323939716
y1[1] (closed_form) = 5.60466051108 -6.32657191409
absolute error = 7.249
relative error = 85.77 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 6.37096854513 5.56560396213
absolute error = 8.245
relative error = 97.46 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=23383.7MB, alloc=44.3MB, time=318.00
x[1] = 0.8503 2.831
h = 0.0001 0.004
y1[1] (numeric) = 1.12323231721 -0.629021100317
y1[1] (closed_form) = 5.61498978241 -6.35129258722
absolute error = 7.275
relative error = 85.81 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 6.39559514537 5.57609451064
absolute error = 8.27
relative error = 97.47 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=23433.2MB, alloc=44.3MB, time=318.66
x[1] = 0.8504 2.835
h = 0.003 0.006
y1[1] (numeric) = 1.1236050312 -0.629829571347
y1[1] (closed_form) = 5.63669700657 -6.37748567446
absolute error = 7.308
relative error = 85.86 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 6.4216152501 5.5979614179
absolute error = 8.304
relative error = 97.48 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8534 2.841
h = 0.0001 0.005
y1[1] (numeric) = 1.12359506118 -0.631322062632
y1[1] (closed_form) = 5.65098096186 -6.43299714202
absolute error = 7.359
relative error = 85.95 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 6.476978047 5.61260886071
absolute error = 8.355
relative error = 97.49 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=23482.7MB, alloc=44.3MB, time=319.32
x[1] = 0.8535 2.846
h = 0.0001 0.003
y1[1] (numeric) = 1.12406594525 -0.632330197168
y1[1] (closed_form) = 5.67846380969 -6.4660266409
absolute error = 7.401
relative error = 86 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 6.50979200805 5.64028746655
absolute error = 8.398
relative error = 97.5 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8536 2.849
h = 0.001 0.001
y1[1] (numeric) = 1.12434048915 -0.632939004693
y1[1] (closed_form) = 5.69475730016 -6.48615084575
absolute error = 7.426
relative error = 86.04 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 6.52978891953 5.65669967804
absolute error = 8.424
relative error = 97.51 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=23532.4MB, alloc=44.3MB, time=319.98
x[1] = 0.8546 2.85
h = 0.001 0.003
y1[1] (numeric) = 1.12423899573 -0.633236838282
y1[1] (closed_form) = 5.69387772071 -6.49834302882
absolute error = 7.435
relative error = 86.06 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 6.54197548411 5.65590175065
absolute error = 8.433
relative error = 97.51 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=23581.9MB, alloc=44.3MB, time=320.64
x[1] = 0.8556 2.853
h = 0.0001 0.004
y1[1] (numeric) = 1.12433384248 -0.633933998883
y1[1] (closed_form) = 5.70430671956 -6.52366797619
absolute error = 7.461
relative error = 86.1 %
Correct digits = 0
h = 0.0001 0.004
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 6.56720757073 5.66648802736
absolute error = 8.459
relative error = 97.52 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8557 2.857
h = 0.003 0.006
y1[1] (numeric) = 1.12470655646 -0.634742469913
y1[1] (closed_form) = 5.72635900251 -6.55055796825
absolute error = 7.495
relative error = 86.14 %
Correct digits = 0
h = 0.003 0.006
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 6.59392751882 5.6886956197
absolute error = 8.494
relative error = 97.53 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=23631.5MB, alloc=44.3MB, time=321.29
x[1] = 0.8587 2.863
h = 0.0001 0.005
y1[1] (numeric) = 1.12469658645 -0.636234961198
y1[1] (closed_form) = 5.7406685136 -6.60737946846
absolute error = 7.547
relative error = 86.23 %
Correct digits = 0
h = 0.0001 0.005
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 6.65060170089 5.70335993312
absolute error = 8.546
relative error = 97.54 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=23681.1MB, alloc=44.3MB, time=321.95
x[1] = 0.8588 2.868
h = 0.0001 0.003
y1[1] (numeric) = 1.12516747052 -0.637243095734
y1[1] (closed_form) = 5.76858878956 -6.6412883882
absolute error = 7.59
relative error = 86.28 %
Correct digits = 0
h = 0.0001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 6.68429876088 5.73147058725
absolute error = 8.59
relative error = 97.55 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8589 2.871
h = 0.001 0.001
y1[1] (numeric) = 1.12544201442 -0.637851903259
y1[1] (closed_form) = 5.78513873158 -6.66194604729
absolute error = 7.616
relative error = 86.32 %
Correct digits = 0
h = 0.001 0.001
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 6.7048312827 5.74813600536
absolute error = 8.616
relative error = 97.56 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=23730.8MB, alloc=44.3MB, time=322.62
x[1] = 0.8599 2.872
h = 0.001 0.003
y1[1] (numeric) = 1.125340521 -0.638149736848
y1[1] (closed_form) = 5.78417537021 -6.6744047994
absolute error = 7.625
relative error = 86.33 %
Correct digits = 0
h = 0.001 0.003
y2[1] (numeric) = 0.199663505514 0.0981700839054
y2[1] (closed_form) = 6.71728411532 5.74725248906
absolute error = 8.625
relative error = 97.56 %
Correct digits = 0
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO 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=23780.6MB, alloc=44.3MB, time=323.29
Finished!
Maximum Time Reached before Solution Completed!
diff ( y1 , x , 1 ) = neg ( y2 ) ;
diff ( y2 , x , 1 ) = y1 ;
Iterations = 754
Total Elapsed Time = 5 Minutes 23 Seconds
Expected Time Remaining = 0 Seconds
Optimized Time Remaining = 0 Seconds
Expected Total Time = 5 Minutes 23 Seconds
> quit
memory used=23781.4MB, alloc=44.3MB, time=323.30