|\^/| 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_y2 := proc(x)
> return(sin(c(x)));
> end;
exact_soln_y2 := proc(x) return sin(c(x)) end proc
> exact_soln_y2p := proc(x)
> return( cos(c(x)));
> end;
exact_soln_y2p := proc(x) return cos(c(x)) end proc
> exact_soln_y2pp := proc(x)
> return( neg( sin(c(x))));
> end;
exact_soln_y2pp := proc(x) return neg(sin(c(x))) end proc
> exact_soln_y1 := proc(x)
> return( cos(c(x)));
> end;
exact_soln_y1 := proc(x) return cos(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_3,
> array_const_0D0,
> array_const_1,
#END CONST
> array_y2_init,
> array_y1_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_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_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_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 (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 (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_3, array_const_0D0, array_const_1,
array_y2_init, array_y1_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_y2, array_x, array_y1,
array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_m1, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_y1_higher,
array_y1_higher_work, array_y1_higher_work2, array_y1_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_y2[1]) < min_size then
min_size := float_abs(array_y2[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
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 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_3,
> array_const_0D0,
> array_const_1,
#END CONST
> array_y2_init,
> array_y1_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_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_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_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;
> 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;
> 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_3, array_const_0D0, array_const_1,
array_y2_init, array_y1_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_y2, array_x, array_y1,
array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_m1, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_y1_higher,
array_y1_higher_work, array_y1_higher_work2, array_y1_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_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;
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;
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_3,
> array_const_0D0,
> array_const_1,
#END CONST
> array_y2_init,
> array_y1_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_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_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_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[1])) then # if number 5
> array_max_est_error[1] := c(est_tmp);
> fi;# end if 5
> ;
> 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[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_3, array_const_0D0, array_const_1,
array_y2_init, array_y1_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_y2, array_x, array_y1,
array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_m1, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_y1_higher,
array_y1_higher_work, array_y1_higher_work2, array_y1_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_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[1]) <= c(est_tmp) then
array_max_est_error[1] := c(est_tmp)
end if;
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[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_3,
> array_const_0D0,
> array_const_1,
#END CONST
> array_y2_init,
> array_y1_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_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_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_3, array_const_0D0, array_const_1,
array_y2_init, array_y1_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_y2, array_x, array_y1,
array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_m1, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_y1_higher,
array_y1_higher_work, array_y1_higher_work2, array_y1_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_3,
> array_const_0D0,
> array_const_1,
#END CONST
> array_y2_init,
> array_y1_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_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_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_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," ")
> ;
> ;
> 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," ")
> ;
> #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_3, array_const_0D0, array_const_1,
array_y2_init, array_y1_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_y2, array_x, array_y1,
array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_m1, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_y1_higher,
array_y1_higher_work, array_y1_higher_work2, array_y1_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_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, " ");
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, " ")
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_3,
> array_const_0D0,
> array_const_1,
#END CONST
> array_y2_init,
> array_y1_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_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_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_3, array_const_0D0, array_const_1,
array_y2_init, array_y1_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_y2, array_x, array_y1,
array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_m1, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_y1_higher,
array_y1_higher_work, array_y1_higher_work2, array_y1_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_3,
> array_const_0D0,
> array_const_1,
#END CONST
> array_y2_init,
> array_y1_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_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_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 - 3 - 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 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_y2_higher[1,last_no-1],array_y2_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_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 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_y1_higher[1,last_no-1],array_y1_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 - 3 - 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 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_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[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_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 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_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[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 - 3 - 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 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_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[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_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 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_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[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_3, array_const_0D0, array_const_1,
array_y2_init, array_y1_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_y2, array_x, array_y1,
array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_m1, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_y1_higher,
array_y1_higher_work, array_y1_higher_work2, array_y1_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 - 13;
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[1, 1] then
array_rad_test_poles[1, 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[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_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[2, 1] then
array_rad_test_poles[2, 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[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 - 13;
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[1, 2] then
array_rad_test_poles[1, 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[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_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[2, 2] then
array_rad_test_poles[2, 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[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 - 13;
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[1, 3] then
array_rad_test_poles[1, 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[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_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[2, 3] then
array_rad_test_poles[2, 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[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_3,
> array_const_0D0,
> array_const_1,
#END CONST
> array_y2_init,
> array_y1_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_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_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 cos 1 $eq_no = 1
> array_tmp1[1] := cos(array_x[1]);
> array_tmp1_g[1] := sin(array_x[1]);
> #emit pre neg FULL $eq_no = 1
> array_tmp2[1] := neg(array_tmp1[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y2_set_initial[1,4]) then # if number 1
> if (1 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp3[1]) * (expt((glob_h) , c(3))) * c(factorial_3(0,3));
> if (4 <= ATS_MAX_TERMS) then # if number 3
> array_y2[4] := temporary;
> array_y2_higher[1,4] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y2_higher[2,3] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y2_higher[3,2] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(1);
> array_y2_higher[4,1] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #emit pre neg FULL $eq_no = 2
> array_tmp5[1] := neg(array_y2[1]);
> #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5
> if ( not array_y1_set_initial[2,2]) then # if number 1
> if (1 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp5[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
> if (2 <= ATS_MAX_TERMS) then # if number 3
> array_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;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre cos ID_LINEAR iii = 2 $eq_no = 1
> array_tmp1[2] := neg(array_tmp1_g[1]) * array_x[2] / c(1);
> array_tmp1_g[2] := array_tmp1[1] * array_x[2] / c(1);
> #emit pre neg FULL $eq_no = 1
> array_tmp2[2] := neg(array_tmp1[2]);
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp3[2] := array_tmp2[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y2_set_initial[1,5]) then # if number 1
> if (2 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp3[2]) * (expt((glob_h) , c(3))) * c(factorial_3(1,4));
> if (5 <= ATS_MAX_TERMS) then # if number 3
> array_y2[5] := temporary;
> array_y2_higher[1,5] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y2_higher[2,4] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y2_higher[3,3] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y2_higher[4,2] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #emit pre neg FULL $eq_no = 2
> array_tmp5[2] := neg(array_y2[2]);
> #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5
> if ( not array_y1_set_initial[2,3]) then # if number 1
> if (2 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp5[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2));
> if (3 <= ATS_MAX_TERMS) then # if number 3
> array_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;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre cos ID_LINEAR iii = 3 $eq_no = 1
> array_tmp1[3] := neg(array_tmp1_g[2]) * array_x[2] / c(2);
> array_tmp1_g[3] := array_tmp1[2] * array_x[2] / c(2);
> #emit pre neg FULL $eq_no = 1
> array_tmp2[3] := neg(array_tmp1[3]);
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp3[3] := array_tmp2[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y2_set_initial[1,6]) then # if number 1
> if (3 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp3[3]) * (expt((glob_h) , c(3))) * c(factorial_3(2,5));
> if (6 <= ATS_MAX_TERMS) then # if number 3
> array_y2[6] := temporary;
> array_y2_higher[1,6] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y2_higher[2,5] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y2_higher[3,4] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y2_higher[4,3] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #emit pre neg FULL $eq_no = 2
> array_tmp5[3] := neg(array_y2[3]);
> #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5
> if ( not array_y1_set_initial[2,4]) then # if number 1
> if (3 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp5[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3));
> if (4 <= ATS_MAX_TERMS) then # if number 3
> array_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;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre cos ID_LINEAR iii = 4 $eq_no = 1
> array_tmp1[4] := neg(array_tmp1_g[3]) * array_x[2] / c(3);
> array_tmp1_g[4] := array_tmp1[3] * array_x[2] / c(3);
> #emit pre neg FULL $eq_no = 1
> array_tmp2[4] := neg(array_tmp1[4]);
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp3[4] := array_tmp2[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y2_set_initial[1,7]) then # if number 1
> if (4 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp3[4]) * (expt((glob_h) , c(3))) * c(factorial_3(3,6));
> if (7 <= ATS_MAX_TERMS) then # if number 3
> array_y2[7] := temporary;
> array_y2_higher[1,7] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(6);
> array_y2_higher[2,6] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y2_higher[3,5] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y2_higher[4,4] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #emit pre neg FULL $eq_no = 2
> array_tmp5[4] := neg(array_y2[4]);
> #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5
> if ( not array_y1_set_initial[2,5]) then # if number 1
> if (4 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp5[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4));
> if (5 <= ATS_MAX_TERMS) then # if number 3
> array_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;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre cos ID_LINEAR iii = 5 $eq_no = 1
> array_tmp1[5] := neg(array_tmp1_g[4]) * array_x[2] / c(4);
> array_tmp1_g[5] := array_tmp1[4] * array_x[2] / c(4);
> #emit pre neg FULL $eq_no = 1
> array_tmp2[5] := neg(array_tmp1[5]);
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp3[5] := array_tmp2[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y2_set_initial[1,8]) then # if number 1
> if (5 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp3[5]) * (expt((glob_h) , c(3))) * c(factorial_3(4,7));
> if (8 <= ATS_MAX_TERMS) then # if number 3
> array_y2[8] := temporary;
> array_y2_higher[1,8] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(7);
> array_y2_higher[2,7] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(6);
> array_y2_higher[3,6] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y2_higher[4,5] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #emit pre neg FULL $eq_no = 2
> array_tmp5[5] := neg(array_y2[5]);
> #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5
> if ( not array_y1_set_initial[2,6]) then # if number 1
> if (5 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp5[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5));
> if (6 <= ATS_MAX_TERMS) then # if number 3
> array_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;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= ATS_MAX_TERMS) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit cos LINEAR $eq_no = 1
> array_tmp1[kkk] := neg(array_tmp1_g[kkk - 1]) * array_x[2] / c(kkk - 1);
> array_tmp1_g[kkk] := array_tmp1[kkk - 1] * array_x[2] / c(kkk - 1);
> #emit neg FULL $eq_no = 1
> array_tmp2[kkk] := neg(array_tmp1[kkk]);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp3[kkk] := array_tmp2[kkk];
> #emit assign $eq_no = 1
> order_d := 3;
> if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1
> if ( not array_y2_set_initial[1,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;
> #emit neg FULL $eq_no = 2
> array_tmp5[kkk] := neg(array_y2[kkk]);
> #emit assign $eq_no = 2
> order_d := 1;
> if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1
> if ( not array_y1_set_initial[2,kkk + order_d]) then # if number 2
> temporary := c(array_tmp5[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
> array_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;
> 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_3, array_const_0D0, array_const_1,
array_y2_init, array_y1_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_y2, array_x, array_y1,
array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_m1, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_y1_higher,
array_y1_higher_work, array_y1_higher_work2, array_y1_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] := cos(array_x[1]);
array_tmp1_g[1] := sin(array_x[1]);
array_tmp2[1] := neg(array_tmp1[1]);
array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
if not array_y2_set_initial[1, 4] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp3[1])*expt(glob_h, c(3))*c(factorial_3(0, 3));
if 4 <= ATS_MAX_TERMS then
array_y2[4] := temporary;
array_y2_higher[1, 4] := temporary
end if;
temporary := c(temporary)*c(3)/c(glob_h);
array_y2_higher[2, 3] := c(temporary);
temporary := c(temporary)*c(2)/c(glob_h);
array_y2_higher[3, 2] := c(temporary);
temporary := c(temporary)*c(1)/c(glob_h);
array_y2_higher[4, 1] := c(temporary)
end if
end if;
kkk := 2;
array_tmp5[1] := neg(array_y2[1]);
if not array_y1_set_initial[2, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
if 2 <= ATS_MAX_TERMS then
array_y1[2] := temporary;
array_y1_higher[1, 2] := temporary
end if;
temporary := c(temporary)*c(1)/c(glob_h);
array_y1_higher[2, 1] := c(temporary)
end if
end if;
kkk := 2;
array_tmp1[2] := neg(array_tmp1_g[1])*array_x[2]/c(1);
array_tmp1_g[2] := array_tmp1[1]*array_x[2]/c(1);
array_tmp2[2] := neg(array_tmp1[2]);
array_tmp3[2] := array_tmp2[2];
if not array_y2_set_initial[1, 5] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp3[2])*expt(glob_h, c(3))*c(factorial_3(1, 4));
if 5 <= ATS_MAX_TERMS then
array_y2[5] := temporary;
array_y2_higher[1, 5] := temporary
end if;
temporary := c(temporary)*c(4)/c(glob_h);
array_y2_higher[2, 4] := c(temporary);
temporary := c(temporary)*c(3)/c(glob_h);
array_y2_higher[3, 3] := c(temporary);
temporary := c(temporary)*c(2)/c(glob_h);
array_y2_higher[4, 2] := c(temporary)
end if
end if;
kkk := 3;
array_tmp5[2] := neg(array_y2[2]);
if not array_y1_set_initial[2, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
if 3 <= ATS_MAX_TERMS then
array_y1[3] := temporary;
array_y1_higher[1, 3] := temporary
end if;
temporary := c(temporary)*c(2)/c(glob_h);
array_y1_higher[2, 2] := c(temporary)
end if
end if;
kkk := 3;
array_tmp1[3] := neg(array_tmp1_g[2])*array_x[2]/c(2);
array_tmp1_g[3] := array_tmp1[2]*array_x[2]/c(2);
array_tmp2[3] := neg(array_tmp1[3]);
array_tmp3[3] := array_tmp2[3];
if not array_y2_set_initial[1, 6] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp3[3])*expt(glob_h, c(3))*c(factorial_3(2, 5));
if 6 <= ATS_MAX_TERMS then
array_y2[6] := temporary;
array_y2_higher[1, 6] := temporary
end if;
temporary := c(temporary)*c(5)/c(glob_h);
array_y2_higher[2, 5] := c(temporary);
temporary := c(temporary)*c(4)/c(glob_h);
array_y2_higher[3, 4] := c(temporary);
temporary := c(temporary)*c(3)/c(glob_h);
array_y2_higher[4, 3] := c(temporary)
end if
end if;
kkk := 4;
array_tmp5[3] := neg(array_y2[3]);
if not array_y1_set_initial[2, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[3])*expt(glob_h, c(1))*c(factorial_3(2, 3));
if 4 <= ATS_MAX_TERMS then
array_y1[4] := temporary;
array_y1_higher[1, 4] := temporary
end if;
temporary := c(temporary)*c(3)/c(glob_h);
array_y1_higher[2, 3] := c(temporary)
end if
end if;
kkk := 4;
array_tmp1[4] := neg(array_tmp1_g[3])*array_x[2]/c(3);
array_tmp1_g[4] := array_tmp1[3]*array_x[2]/c(3);
array_tmp2[4] := neg(array_tmp1[4]);
array_tmp3[4] := array_tmp2[4];
if not array_y2_set_initial[1, 7] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp3[4])*expt(glob_h, c(3))*c(factorial_3(3, 6));
if 7 <= ATS_MAX_TERMS then
array_y2[7] := temporary;
array_y2_higher[1, 7] := temporary
end if;
temporary := c(temporary)*c(6)/c(glob_h);
array_y2_higher[2, 6] := c(temporary);
temporary := c(temporary)*c(5)/c(glob_h);
array_y2_higher[3, 5] := c(temporary);
temporary := c(temporary)*c(4)/c(glob_h);
array_y2_higher[4, 4] := c(temporary)
end if
end if;
kkk := 5;
array_tmp5[4] := neg(array_y2[4]);
if not array_y1_set_initial[2, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[4])*expt(glob_h, c(1))*c(factorial_3(3, 4));
if 5 <= ATS_MAX_TERMS then
array_y1[5] := temporary;
array_y1_higher[1, 5] := temporary
end if;
temporary := c(temporary)*c(4)/c(glob_h);
array_y1_higher[2, 4] := c(temporary)
end if
end if;
kkk := 5;
array_tmp1[5] := neg(array_tmp1_g[4])*array_x[2]/c(4);
array_tmp1_g[5] := array_tmp1[4]*array_x[2]/c(4);
array_tmp2[5] := neg(array_tmp1[5]);
array_tmp3[5] := array_tmp2[5];
if not array_y2_set_initial[1, 8] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp3[5])*expt(glob_h, c(3))*c(factorial_3(4, 7));
if 8 <= ATS_MAX_TERMS then
array_y2[8] := temporary;
array_y2_higher[1, 8] := temporary
end if;
temporary := c(temporary)*c(7)/c(glob_h);
array_y2_higher[2, 7] := c(temporary);
temporary := c(temporary)*c(6)/c(glob_h);
array_y2_higher[3, 6] := c(temporary);
temporary := c(temporary)*c(5)/c(glob_h);
array_y2_higher[4, 5] := c(temporary)
end if
end if;
kkk := 6;
array_tmp5[5] := neg(array_y2[5]);
if not array_y1_set_initial[2, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[5])*expt(glob_h, c(1))*c(factorial_3(4, 5));
if 6 <= ATS_MAX_TERMS then
array_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;
while kkk <= ATS_MAX_TERMS do
array_tmp1[kkk] := neg(array_tmp1_g[kkk - 1])*array_x[2]/c(kkk - 1)
;
array_tmp1_g[kkk] := array_tmp1[kkk - 1]*array_x[2]/c(kkk - 1);
array_tmp2[kkk] := neg(array_tmp1[kkk]);
array_tmp3[kkk] := array_tmp2[kkk];
order_d := 3;
if kkk + order_d <= ATS_MAX_TERMS then
if not array_y2_set_initial[1, 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;
array_tmp5[kkk] := neg(array_y2[kkk]);
order_d := 1;
if kkk + order_d <= ATS_MAX_TERMS then
if not array_y1_set_initial[2, kkk + order_d] then
temporary := c(array_tmp5[kkk])*expt(glob_h, c(order_d))*
c(factorial_3(kkk - 1, kkk + order_d - 1));
array_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;
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_3,
> array_const_0D0,
> array_const_1,
> #END CONST
> array_y2_init,
> array_y1_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_y2,
> array_x,
> array_y1,
> array_tmp0,
> array_tmp1_g,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> ATS_MAX_TERMS := 40;
> # before first input block
> #BEGIN FIRST INPUT BLOCK
> #BEGIN BLOCK 1
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=40;
> #END BLOCK 1
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> # before generate arrays
> array_y2_init:= Array(0..(40),[]);
> array_y1_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_y2:= Array(0..(40),[]);
> array_x:= Array(0..(40),[]);
> array_y1:= Array(0..(40),[]);
> array_tmp0:= Array(0..(40),[]);
> array_tmp1_g:= Array(0..(40),[]);
> array_tmp1:= Array(0..(40),[]);
> array_tmp2:= Array(0..(40),[]);
> array_tmp3:= Array(0..(40),[]);
> array_tmp4:= Array(0..(40),[]);
> array_tmp5:= Array(0..(40),[]);
> array_m1:= Array(0..(40),[]);
> array_y2_higher := Array(0..(4) ,(0..40+ 1),[]);
> array_y2_higher_work := Array(0..(4) ,(0..40+ 1),[]);
> array_y2_higher_work2 := Array(0..(4) ,(0..40+ 1),[]);
> array_y2_set_initial := Array(0..(3) ,(0..40+ 1),[]);
> 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_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_y2_init[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> 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_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_y2[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_y1[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_g[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp3[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp4[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp5[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_m1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=4) 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 <=4) 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 <=4) 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 <=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 <=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_y2);
> zero_ats_ar(array_x);
> zero_ats_ar(array_y1);
> zero_ats_ar(array_tmp0);
> zero_ats_ar(array_tmp1_g);
> zero_ats_ar(array_tmp1);
> zero_ats_ar(array_tmp2);
> zero_ats_ar(array_tmp3);
> zero_ats_ar(array_tmp4);
> zero_ats_ar(array_tmp5);
> zero_ats_ar(array_m1);
> zero_ats_ar(array_const_3);
> array_const_3[1] := c(3);
> zero_ats_ar(array_const_0D0);
> array_const_0D0[1] := c(0.0);
> zero_ats_ar(array_const_1);
> array_const_1[1] := c(1);
> 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_y2_set_initial[1,1] := true;
> array_y2_set_initial[1,2] := true;
> array_y2_set_initial[1,3] := true;
> array_y2_set_initial[1,4] := false;
> array_y2_set_initial[1,5] := false;
> array_y2_set_initial[1,6] := false;
> array_y2_set_initial[1,7] := false;
> array_y2_set_initial[1,8] := false;
> array_y2_set_initial[1,9] := false;
> array_y2_set_initial[1,10] := false;
> array_y2_set_initial[1,11] := false;
> array_y2_set_initial[1,12] := false;
> array_y2_set_initial[1,13] := false;
> array_y2_set_initial[1,14] := false;
> array_y2_set_initial[1,15] := false;
> array_y2_set_initial[1,16] := false;
> array_y2_set_initial[1,17] := false;
> array_y2_set_initial[1,18] := false;
> array_y2_set_initial[1,19] := false;
> array_y2_set_initial[1,20] := false;
> array_y2_set_initial[1,21] := false;
> array_y2_set_initial[1,22] := false;
> array_y2_set_initial[1,23] := false;
> array_y2_set_initial[1,24] := false;
> array_y2_set_initial[1,25] := false;
> array_y2_set_initial[1,26] := false;
> array_y2_set_initial[1,27] := false;
> array_y2_set_initial[1,28] := false;
> array_y2_set_initial[1,29] := false;
> array_y2_set_initial[1,30] := false;
> array_y2_set_initial[1,31] := false;
> array_y2_set_initial[1,32] := false;
> array_y2_set_initial[1,33] := false;
> array_y2_set_initial[1,34] := false;
> array_y2_set_initial[1,35] := false;
> array_y2_set_initial[1,36] := false;
> array_y2_set_initial[1,37] := false;
> array_y2_set_initial[1,38] := false;
> array_y2_set_initial[1,39] := false;
> array_y2_set_initial[1,40] := false;
> array_y1_set_initial[2,1] := true;
> array_y1_set_initial[2,2] := false;
> array_y1_set_initial[2,3] := false;
> array_y1_set_initial[2,4] := false;
> array_y1_set_initial[2,5] := false;
> array_y1_set_initial[2,6] := false;
> array_y1_set_initial[2,7] := false;
> array_y1_set_initial[2,8] := false;
> array_y1_set_initial[2,9] := false;
> array_y1_set_initial[2,10] := false;
> array_y1_set_initial[2,11] := false;
> array_y1_set_initial[2,12] := false;
> array_y1_set_initial[2,13] := false;
> array_y1_set_initial[2,14] := false;
> array_y1_set_initial[2,15] := false;
> array_y1_set_initial[2,16] := false;
> array_y1_set_initial[2,17] := false;
> array_y1_set_initial[2,18] := false;
> array_y1_set_initial[2,19] := false;
> array_y1_set_initial[2,20] := false;
> array_y1_set_initial[2,21] := false;
> array_y1_set_initial[2,22] := false;
> array_y1_set_initial[2,23] := false;
> array_y1_set_initial[2,24] := false;
> array_y1_set_initial[2,25] := false;
> array_y1_set_initial[2,26] := false;
> array_y1_set_initial[2,27] := false;
> array_y1_set_initial[2,28] := false;
> array_y1_set_initial[2,29] := false;
> array_y1_set_initial[2,30] := false;
> array_y1_set_initial[2,31] := false;
> array_y1_set_initial[2,32] := false;
> array_y1_set_initial[2,33] := false;
> array_y1_set_initial[2,34] := false;
> array_y1_set_initial[2,35] := false;
> array_y1_set_initial[2,36] := false;
> array_y1_set_initial[2,37] := false;
> array_y1_set_initial[2,38] := false;
> array_y1_set_initial[2,39] := false;
> array_y1_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/mtest4postcpx.cpx#################");
> omniout_str(ALWAYS,"diff ( y2 , x , 3 ) = neg ( cos ( x ) ) ; ");
> omniout_str(ALWAYS,"diff ( y1 , x , 1 ) = neg ( y2 ) ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=40;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := 0.1 + 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,"array_y2_init[1 + 1] := exact_soln_y2p(x_start);");
> omniout_str(ALWAYS,"array_y2_init[2 + 1] := exact_soln_y2pp(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_type_given_pole := 3;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=8;");
> omniout_str(ALWAYS,"glob_max_minutes:=(3.0);");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"glob_max_iter:=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_y2 := proc(x)");
> omniout_str(ALWAYS,"return(sin(c(x)));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2p := proc(x)");
> omniout_str(ALWAYS,"return( cos(c(x)));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2pp := proc(x)");
> omniout_str(ALWAYS,"return( neg( sin(c(x))));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y1 := proc(x)");
> omniout_str(ALWAYS,"return( cos(c(x)));");
> omniout_str(ALWAYS,"end;");
> 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 := 0.1 + 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);
> array_y2_init[1 + 1] := exact_soln_y2p(x_start);
> array_y2_init[2 + 1] := exact_soln_y2pp(x_start);
> glob_look_poles := true;
> glob_type_given_pole := 3;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=8;
> glob_max_minutes:=(3.0);
> glob_subiter_method:=3;
> glob_max_iter:=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_y2[term] := array_y2[term]* ratio;
> array_y2_higher[1,term] := array_y2_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> 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;
> 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 := 3;
> #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
> ;
> 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
> ;
> 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_y2[term] := array_y2[term]* ratio;
> array_y2_higher[1,term] := array_y2_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> 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;
> 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_y2[term] := array_y2[term]* ratio;
> array_y2_higher[1,term] := array_y2_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> 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;
> 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 <= 4) do # do number 2
> atomall();
> subiter := subiter + 1;
> od;# end do number 2;
> else
> subiter := 1;
> while (subiter <= 4 + 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_y2;
> order_diff := 4;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y2
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 4;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[4,iii] := array_y2_higher[4,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 := 4;
> 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 =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 3;
> calc_term := 2;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 3;
> 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 =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 3;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[3,iii] := array_y2_higher[3,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 3;
> calc_term := 1;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 3;
> #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 =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 2;
> calc_term := 3;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 2;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 2;
> calc_term := 2;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> 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 =1
> #BEFORE SUM SUBSERIES EQ =1
> 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 =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 4;
> #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 =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 1;
> calc_term := 4;
> #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 =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 3;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 1;
> calc_term := 3;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> 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 =1
> #BEFORE SUM SUBSERIES EQ =1
> 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 =1
> #BEFORE ADJUST SUBSERIES EQ =1
> 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 =1
> #BEFORE SUM SUBSERIES EQ =1
> 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 =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_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
> #Jump Series array_y1;
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =2
> #sum_and_adjust array_y1
> #BEFORE ADJUST SUBSERIES EQ =2
> 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 =2
> #BEFORE SUM SUBSERIES EQ =2
> 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 =2
> #BEFORE ADJUST SUBSERIES EQ =2
> 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 =2
> #BEFORE SUM SUBSERIES EQ =2
> 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 =2
> #BEFORE ADJUST SUBSERIES EQ =2
> 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 =2
> #BEFORE SUM SUBSERIES EQ =2
> 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 =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_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
> ;
> 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 ( y2 , x , 3 ) = neg ( cos ( x ) ) ; ");
> omniout_str(INFO,"diff ( y1 , x , 1 ) = neg ( y2 ) ; ");
> 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,"2017-11-26T15:23:59-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"mtest4")
> ;
> logitem_str(html_log_file,"diff ( y2 , x , 3 ) = neg ( cos ( x ) ) ; ")
> ;
> 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,"mtest4 diffeq.mxt")
> ;
> logitem_str(html_log_file,"mtest4 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 ( y1 , x , 1 ) = neg ( y2 ) ; ")
> ;
> 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_3, array_const_0D0, array_const_1,
array_y2_init, array_y1_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_y2, array_x, array_y1,
array_tmp0, array_tmp1_g, array_tmp1, array_tmp2, array_tmp3, array_tmp4,
array_tmp5, array_m1, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_y1_higher,
array_y1_higher_work, array_y1_higher_work2, array_y1_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
ATS_MAX_TERMS := 40;
Digits := 32;
max_terms := 40;
glob_html_log := true;
array_y2_init := Array(0 .. 40, []);
array_y1_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_y2 := Array(0 .. 40, []);
array_x := Array(0 .. 40, []);
array_y1 := Array(0 .. 40, []);
array_tmp0 := Array(0 .. 40, []);
array_tmp1_g := Array(0 .. 40, []);
array_tmp1 := Array(0 .. 40, []);
array_tmp2 := Array(0 .. 40, []);
array_tmp3 := Array(0 .. 40, []);
array_tmp4 := Array(0 .. 40, []);
array_tmp5 := Array(0 .. 40, []);
array_m1 := Array(0 .. 40, []);
array_y2_higher := Array(0 .. 4, 0 .. 41, []);
array_y2_higher_work := Array(0 .. 4, 0 .. 41, []);
array_y2_higher_work2 := Array(0 .. 4, 0 .. 41, []);
array_y2_set_initial := Array(0 .. 3, 0 .. 41, []);
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_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_y2_init[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 40 do array_y1_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_y2[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_y1[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_g[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 40 do array_tmp1[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp3[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp4[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp5[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_m1[term] := c(0.); term := term + 1 end do;
ord := 1;
while ord <= 4 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 <= 4 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 <= 4 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 <= 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 <= 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_y2);
zero_ats_ar(array_x);
zero_ats_ar(array_y1);
zero_ats_ar(array_tmp0);
zero_ats_ar(array_tmp1_g);
zero_ats_ar(array_tmp1);
zero_ats_ar(array_tmp2);
zero_ats_ar(array_tmp3);
zero_ats_ar(array_tmp4);
zero_ats_ar(array_tmp5);
zero_ats_ar(array_m1);
zero_ats_ar(array_const_3);
array_const_3[1] := c(3);
zero_ats_ar(array_const_0D0);
array_const_0D0[1] := c(0.);
zero_ats_ar(array_const_1);
array_const_1[1] := c(1);
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_y2_set_initial[1, 1] := true;
array_y2_set_initial[1, 2] := true;
array_y2_set_initial[1, 3] := true;
array_y2_set_initial[1, 4] := false;
array_y2_set_initial[1, 5] := false;
array_y2_set_initial[1, 6] := false;
array_y2_set_initial[1, 7] := false;
array_y2_set_initial[1, 8] := false;
array_y2_set_initial[1, 9] := false;
array_y2_set_initial[1, 10] := false;
array_y2_set_initial[1, 11] := false;
array_y2_set_initial[1, 12] := false;
array_y2_set_initial[1, 13] := false;
array_y2_set_initial[1, 14] := false;
array_y2_set_initial[1, 15] := false;
array_y2_set_initial[1, 16] := false;
array_y2_set_initial[1, 17] := false;
array_y2_set_initial[1, 18] := false;
array_y2_set_initial[1, 19] := false;
array_y2_set_initial[1, 20] := false;
array_y2_set_initial[1, 21] := false;
array_y2_set_initial[1, 22] := false;
array_y2_set_initial[1, 23] := false;
array_y2_set_initial[1, 24] := false;
array_y2_set_initial[1, 25] := false;
array_y2_set_initial[1, 26] := false;
array_y2_set_initial[1, 27] := false;
array_y2_set_initial[1, 28] := false;
array_y2_set_initial[1, 29] := false;
array_y2_set_initial[1, 30] := false;
array_y2_set_initial[1, 31] := false;
array_y2_set_initial[1, 32] := false;
array_y2_set_initial[1, 33] := false;
array_y2_set_initial[1, 34] := false;
array_y2_set_initial[1, 35] := false;
array_y2_set_initial[1, 36] := false;
array_y2_set_initial[1, 37] := false;
array_y2_set_initial[1, 38] := false;
array_y2_set_initial[1, 39] := false;
array_y2_set_initial[1, 40] := false;
array_y1_set_initial[2, 1] := true;
array_y1_set_initial[2, 2] := false;
array_y1_set_initial[2, 3] := false;
array_y1_set_initial[2, 4] := false;
array_y1_set_initial[2, 5] := false;
array_y1_set_initial[2, 6] := false;
array_y1_set_initial[2, 7] := false;
array_y1_set_initial[2, 8] := false;
array_y1_set_initial[2, 9] := false;
array_y1_set_initial[2, 10] := false;
array_y1_set_initial[2, 11] := false;
array_y1_set_initial[2, 12] := false;
array_y1_set_initial[2, 13] := false;
array_y1_set_initial[2, 14] := false;
array_y1_set_initial[2, 15] := false;
array_y1_set_initial[2, 16] := false;
array_y1_set_initial[2, 17] := false;
array_y1_set_initial[2, 18] := false;
array_y1_set_initial[2, 19] := false;
array_y1_set_initial[2, 20] := false;
array_y1_set_initial[2, 21] := false;
array_y1_set_initial[2, 22] := false;
array_y1_set_initial[2, 23] := false;
array_y1_set_initial[2, 24] := false;
array_y1_set_initial[2, 25] := false;
array_y1_set_initial[2, 26] := false;
array_y1_set_initial[2, 27] := false;
array_y1_set_initial[2, 28] := false;
array_y1_set_initial[2, 29] := false;
array_y1_set_initial[2, 30] := false;
array_y1_set_initial[2, 31] := false;
array_y1_set_initial[2, 32] := false;
array_y1_set_initial[2, 33] := false;
array_y1_set_initial[2, 34] := false;
array_y1_set_initial[2, 35] := false;
array_y1_set_initial[2, 36] := false;
array_y1_set_initial[2, 37] := false;
array_y1_set_initial[2, 38] := false;
array_y1_set_initial[2, 39] := false;
array_y1_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/mtest4postcpx.cpx#################");
omniout_str(ALWAYS,
"diff ( y2 , x , 3 ) = neg ( cos ( x ) ) ; ");
omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = neg ( y2 ) ; ")
;
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=40;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := 0.1 + 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, "array_y2_init[1 + 1] := exact_soln_y2p(x_start);")
;
omniout_str(ALWAYS, "array_y2_init[2 + 1] := exact_soln_y2pp(x_start);")
;
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_type_given_pole := 3;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=8;");
omniout_str(ALWAYS, "glob_max_minutes:=(3.0);");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "glob_max_iter:=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_y2 := proc(x)");
omniout_str(ALWAYS, "return(sin(c(x)));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2p := proc(x)");
omniout_str(ALWAYS, "return( cos(c(x)));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2pp := proc(x)");
omniout_str(ALWAYS, "return( neg( sin(c(x))));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y1 := proc(x)");
omniout_str(ALWAYS, "return( cos(c(x)));");
omniout_str(ALWAYS, "end;");
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,");
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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 := 0.1 + 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);
array_y2_init[2] := exact_soln_y2p(x_start);
array_y2_init[3] := exact_soln_y2pp(x_start);
glob_look_poles := true;
glob_type_given_pole := 3;
glob_desired_digits_correct := 8;
glob_max_minutes := 3.0;
glob_subiter_method := 3;
glob_max_iter := 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_y2[term] := array_y2[term]*ratio;
array_y2_higher[1, term] := array_y2_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
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;
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 := 3;
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;
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;
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_y2[term] := array_y2[term]*ratio;
array_y2_higher[1, term] := array_y2_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
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;
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_y2[term] := array_y2[term]*ratio;
array_y2_higher[1, term] :=
array_y2_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
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;
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 <= 4 do atomall(); subiter := subiter + 1
end do
else
subiter := 1;
while subiter <= 4 + 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 := 4;
ord := 4;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[4, iii] := array_y2_higher[4, 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 := 4;
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 := 3;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 3;
calc_term := 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 := 3;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[3, iii] := array_y2_higher[3, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 3;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 2;
calc_term := 3;
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 := 3;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 2;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 2;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[2, iii] := array_y2_higher[2, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 4;
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 := 4;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 3;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 3;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y2_higher_work[1, iii] := array_y2_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y2_higher_work[ord, iii];
iii := iii - 1
end do;
array_y2_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
term_no := ATS_MAX_TERMS;
while 1 <= term_no do
array_y2[term_no] := array_y2_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y2_higher[ord, term_no] :=
array_y2_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
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
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 ( y2 , x , 3 ) = neg ( cos ( x ) ) ; ");
omniout_str(INFO,
"diff ( y1 , x , 1 ) = neg ( y2 ) ; ");
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, "2017-11-26T15:23:59-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"mtest4");
logitem_str(html_log_file, "diff ( y2 , x , 3 ) = n\
eg ( cos ( x ) ) ; ");
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,
"mtest4 diffeq.mxt");
logitem_str(html_log_file, "mtest4 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 ( y1 , x , 1 ) = neg ( y2 ) ; ");
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=3.6MB, alloc=40.3MB, time=0.07
##############ECHO OF PROBLEM#################
##############temp/mtest4postcpx.cpx#################
diff ( y2 , x , 3 ) = neg ( cos ( x ) ) ;
diff ( y1 , x , 1 ) = neg ( y2 ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=40;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.1 + 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);
array_y2_init[1 + 1] := exact_soln_y2p(x_start);
array_y2_init[2 + 1] := exact_soln_y2pp(x_start);
glob_look_poles := true;
glob_type_given_pole := 3;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=8;
glob_max_minutes:=(3.0);
glob_subiter_method:=3;
glob_max_iter:=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_y2 := proc(x)
return(sin(c(x)));
end;
exact_soln_y2p := proc(x)
return( cos(c(x)));
end;
exact_soln_y2pp := proc(x)
return( neg( sin(c(x))));
end;
exact_soln_y1 := proc(x)
return( cos(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
memory used=53.1MB, alloc=40.3MB, time=0.67
x[1] = 0.1 0.1
h = 0.0001 0.005
y2[1] (numeric) = 0.100332999841 0.0996663334921
y2[1] (closed_form) = 0.100332999841 0.0996663334921
absolute error = 0
relative error = 0 %
Correct digits = 30
h = 0.0001 0.005
y1[1] (numeric) = 0.999983333337 -0.00999998888889
y1[1] (closed_form) = 0.999983333337 -0.00999998888889
absolute error = 0
relative error = 0 %
Correct digits = 30
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1768
Order of pole (three term test) = 33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1768
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=98.8MB, alloc=40.3MB, time=1.22
memory used=144.9MB, alloc=40.3MB, time=1.79
x[1] = 0.1001 0.105
h = 0.0001 0.003
y2[1] (numeric) = 0.100473841619 0.103666044323
y2[1] (closed_form) = 0.100484303074 0.104666466122
absolute error = 0.001
relative error = 0.6895 %
Correct digits = 2
h = 0.0001 0.003
y1[1] (numeric) = 1.0004816233 -0.0105121718948
y1[1] (closed_form) = 1.00048412347 -0.0105122476776
absolute error = 2.501e-06
relative error = 0.00025 %
Correct digits = 6
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.08713
Order of pole (three term test) = 33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.08713
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=190.6MB, alloc=40.3MB, time=2.36
memory used=236.8MB, alloc=40.3MB, time=2.93
x[1] = 0.1002 0.108
h = 0.001 0.001
y2[1] (numeric) = 0.100616375263 0.10766737703
y2[1] (closed_form) = 0.100616371804 0.107667312081
absolute error = 6.504e-08
relative error = 4.414e-05 %
Correct digits = 6
h = 0.001 0.001
y1[1] (numeric) = 1.00078856852 -0.0108243734538
y1[1] (closed_form) = 1.00079256889 -0.0108245151295
absolute error = 4.003e-06
relative error = 0.0003999 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.06949
Order of pole (three term test) = 33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.06949
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=282.6MB, alloc=40.3MB, time=3.50
x[1] = 0.1012 0.109
h = 0.001 0.003
y2[1] (numeric) = 0.10076060456 0.111670370011
y2[1] (closed_form) = 0.101628096885 0.108657179181
absolute error = 0.003136
relative error = 2.108 %
Correct digits = 2
h = 0.001 0.003
y1[1] (numeric) = 1.00079754891 -0.0110347305372
y1[1] (closed_form) = 1.00079960894 -0.0110337996083
absolute error = 2.261e-06
relative error = 0.0002259 %
Correct digits = 6
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.333
Order of pole (three term test) = 33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.333
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=328.5MB, alloc=40.3MB, time=4.05
memory used=374.6MB, alloc=40.3MB, time=4.62
x[1] = 0.1022 0.112
h = 0.0001 0.004
y2[1] (numeric) = 0.1009065357 0.115675029355
y2[1] (closed_form) = 0.102662734747 0.111648676907
absolute error = 0.004393
relative error = 2.896 %
Correct digits = 2
h = 0.0001 0.004
y1[1] (numeric) = 1.00103773316 -0.0114509033802
y1[1] (closed_form) = 1.00102792236 -0.0114503883919
absolute error = 9.824e-06
relative error = 0.0009814 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1921
Order of pole (three term test) = 33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1921
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=420.2MB, alloc=40.3MB, time=5.18
memory used=466.2MB, alloc=40.3MB, time=5.74
x[1] = 0.1023 0.116
h = 0.003 0.006
y2[1] (numeric) = 0.101054187418 0.11968137719
y2[1] (closed_form) = 0.102809505465 0.115652505773
absolute error = 0.004395
relative error = 2.84 %
Correct digits = 2
h = 0.003 0.006
y1[1] (numeric) = 1.00149834738 -0.0118665920569
y1[1] (closed_form) = 1.00147225055 -0.0118726973391
absolute error = 2.680e-05
relative error = 0.002676 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2598
Order of pole (three term test) = 33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2598
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=511.9MB, alloc=40.3MB, time=6.30
memory used=558.0MB, alloc=40.3MB, time=6.86
x[1] = 0.1053 0.122
h = 0.0001 0.005
y2[1] (numeric) = 0.101203617471 0.12368946749
y2[1] (closed_form) = 0.105888677761 0.121625440337
absolute error = 0.00512
relative error = 3.175 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.00192507279 -0.0128384203568
y1[1] (closed_form) = 1.00187103916 -0.0128547054021
absolute error = 5.643e-05
relative error = 0.005632 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1205
Order of pole (three term test) = 33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1205
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=603.6MB, alloc=40.3MB, time=7.42
x[1] = 0.1054 0.127
h = 0.0001 0.003
y2[1] (numeric) = 0.10135502708 0.127699365406
y2[1] (closed_form) = 0.106054523806 0.126634997662
absolute error = 0.004819
relative error = 2.917 %
Correct digits = 2
h = 0.0001 0.003
y1[1] (numeric) = 1.00254341618 -0.0133573855475
y1[1] (closed_form) = 1.00248109187 -0.0133969752478
absolute error = 7.384e-05
relative error = 0.007365 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.0994
Order of pole (three term test) = 33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.0994
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=649.4MB, alloc=40.3MB, time=7.98
memory used=695.7MB, alloc=40.3MB, time=8.55
x[1] = 0.1055 0.13
h = 0.001 0.001
y2[1] (numeric) = 0.101508472579 0.131711167183
y2[1] (closed_form) = 0.106195478058 0.129641643138
absolute error = 0.005124
relative error = 3.057 %
Correct digits = 2
h = 0.001 0.001
y1[1] (numeric) = 1.00292238834 -0.0136746507979
y1[1] (closed_form) = 1.00285489407 -0.0137281638158
absolute error = 8.613e-05
relative error = 0.008588 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.07919
Order of pole (three term test) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.07919
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=741.5MB, alloc=40.3MB, time=9.12
memory used=787.7MB, alloc=40.3MB, time=9.68
x[1] = 0.1065 0.131
h = 0.001 0.003
y2[1] (numeric) = 0.101663957884 0.135724911282
y2[1] (closed_form) = 0.107212191087 0.130630663334
absolute error = 0.007532
relative error = 4.457 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.00295452017 -0.0139099547201
y1[1] (closed_form) = 1.00287832643 -0.0139650037997
absolute error = 9.400e-05
relative error = 0.009372 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.379
Order of pole (three term test) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.379
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=833.4MB, alloc=40.3MB, time=10.25
memory used=879.5MB, alloc=40.3MB, time=10.81
x[1] = 0.1075 0.134
h = 0.0001 0.004
y2[1] (numeric) = 0.101821489214 0.139740603789
y2[1] (closed_form) = 0.108257789554 0.133625537144
absolute error = 0.008878
relative error = 5.162 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.00326597541 -0.0143529149717
y1[1] (closed_form) = 1.00316697577 -0.014420336423
absolute error = 0.0001198
relative error = 0.01194 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2183
Order of pole (three term test) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2183
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=925.1MB, alloc=40.3MB, time=11.37
x[1] = 0.1076 0.138
h = 0.003 0.006
y2[1] (numeric) = 0.101981085408 0.143758266824
y2[1] (closed_form) = 0.108416707526 0.137637798716
absolute error = 0.008881
relative error = 5.069 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.00382278237 -0.0147746943574
y1[1] (closed_form) = 1.00369866804 -0.014867247953
absolute error = 0.0001548
relative error = 0.01542 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2949
Order of pole (three term test) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2949
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=970.7MB, alloc=40.3MB, time=11.92
memory used=1016.7MB, alloc=40.3MB, time=12.48
x[1] = 0.1106 0.144
h = 0.0001 0.005
y2[1] (numeric) = 0.102142804514 0.147777954309
y2[1] (closed_form) = 0.111520997949 0.143615303875
absolute error = 0.01026
relative error = 5.643 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.00439120473 -0.0158243687342
y1[1] (closed_form) = 1.00421252288 -0.015948936748
absolute error = 0.0002178
relative error = 0.02169 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1361
Order of pole (three term test) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1361
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1062.3MB, alloc=40.3MB, time=13.04
memory used=1108.4MB, alloc=40.3MB, time=13.61
x[1] = 0.1107 0.149
h = 0.0001 0.003
y2[1] (numeric) = 0.102306848413 0.151799730948
y2[1] (closed_form) = 0.111702630738 0.148636531188
absolute error = 0.009914
relative error = 5.332 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.00512992559 -0.0163504707422
y1[1] (closed_form) = 1.00493198983 -0.0165216071589
absolute error = 0.0002617
relative error = 0.02603 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1122
Order of pole (three term test) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1122
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1154.2MB, alloc=40.3MB, time=14.17
memory used=1200.3MB, alloc=40.3MB, time=14.75
x[1] = 0.1108 0.152
h = 0.001 0.001
y2[1] (numeric) = 0.102473273868 0.15582369305
y2[1] (closed_form) = 0.111853235979 0.151650314108
absolute error = 0.01027
relative error = 5.448 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.00558112118 -0.0166730214823
y1[1] (closed_form) = 1.005371242 -0.0168719550168
absolute error = 0.0002892
relative error = 0.02876 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.08927
Order of pole (three term test) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.08927
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1246.2MB, alloc=40.3MB, time=15.31
x[1] = 0.1118 0.153
h = 0.001 0.003
y2[1] (numeric) = 0.102642084924 0.159849879162
y2[1] (closed_form) = 0.112875631156 0.152638701201
absolute error = 0.01252
relative error = 6.595 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.0056364003 -0.0169334155633
y1[1] (closed_form) = 1.00541102212 -0.0171364639514
absolute error = 0.0003034
relative error = 0.03017 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4269
Order of pole (three term test) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4269
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1291.8MB, alloc=40.3MB, time=15.87
memory used=1338.0MB, alloc=40.3MB, time=16.43
x[1] = 0.1128 0.156
h = 0.0001 0.004
y2[1] (numeric) = 0.102813287836 0.163878295364
y2[1] (closed_form) = 0.113933365397 0.155638072673
absolute error = 0.01384
relative error = 7.176 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.00601926452 -0.0174034619231
y1[1] (closed_form) = 1.00576003279 -0.0176308153291
absolute error = 0.0003448
relative error = 0.03428 %
Correct digits = 3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2455
Order of pole (three term test) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2455
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1383.8MB, alloc=40.3MB, time=17.00
memory used=1429.8MB, alloc=40.3MB, time=17.55
x[1] = 0.1129 0.16
h = 0.003 0.006
y2[1] (numeric) = 0.102986901561 0.167908963776
y2[1] (closed_form) = 0.114105438808 0.159660559171
absolute error = 0.01384
relative error = 7.055 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.00667254829 -0.0178316508402
y1[1] (closed_form) = 1.00637922732 -0.0181026571991
absolute error = 0.0003994
relative error = 0.03968 %
Correct digits = 3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3312
Order of pole (three term test) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3312
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1475.5MB, alloc=40.3MB, time=18.12
x[1] = 0.1159 0.166
h = 0.0001 0.005
y2[1] (numeric) = 0.103162984476 0.171941938279
y2[1] (closed_form) = 0.117237656736 0.165644636231
absolute error = 0.01542
relative error = 7.598 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.00738287564 -0.018959874983
y1[1] (closed_form) = 1.0070081304 -0.0192846397327
absolute error = 0.0004959
relative error = 0.04923 %
Correct digits = 3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1524
Order of pole (three term test) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1524
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1521.4MB, alloc=40.3MB, time=18.68
memory used=1567.4MB, alloc=40.3MB, time=19.24
x[1] = 0.116 0.171
h = 0.0001 0.003
y2[1] (numeric) = 0.103341739229 0.175977283111
y2[1] (closed_form) = 0.117436330118 0.170679780464
absolute error = 0.01506
relative error = 7.268 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.00824234747 -0.0194935315977
y1[1] (closed_form) = 1.00783720606 -0.0198881395948
absolute error = 0.0005656
relative error = 0.05611 %
Correct digits = 3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1254
Order of pole (three term test) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1254
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1611.4MB, alloc=40.3MB, time=19.77
memory used=1657.8MB, alloc=40.3MB, time=20.34
x[1] = 0.1161 0.174
h = 0.001 0.001
y2[1] (numeric) = 0.103523223061 0.180015094678
y2[1] (closed_form) = 0.11759735788 0.173702039755
absolute error = 0.01543
relative error = 7.354 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.00876599219 -0.0198216279562
y1[1] (closed_form) = 1.00834202675 -0.0202579089155
absolute error = 0.0006083
relative error = 0.06032 %
Correct digits = 3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.09967
Order of pole (three term test) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.09967
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1703.7MB, alloc=40.3MB, time=20.91
memory used=1749.8MB, alloc=40.3MB, time=21.48
x[1] = 0.1171 0.175
h = 0.001 0.003
y2[1] (numeric) = 0.103707440157 0.184055411627
y2[1] (closed_form) = 0.118626131847 0.174690005932
absolute error = 0.01761
relative error = 8.342 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.00884441213 -0.020107278104
y1[1] (closed_form) = 1.00839811108 -0.0205502166739
absolute error = 0.0006288
relative error = 0.06234 %
Correct digits = 3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4762
Order of pole (three term test) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4762
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1795.6MB, alloc=40.3MB, time=22.05
x[1] = 0.1181 0.178
h = 0.0001 0.004
y2[1] (numeric) = 0.103894396811 0.188098240036
y2[1] (closed_form) = 0.119697183615 0.177694995866
absolute error = 0.01892
relative error = 8.831 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.00929884129 -0.0206047567884
y1[1] (closed_form) = 1.00880752691 -0.0210838935875
absolute error = 0.0006863
relative error = 0.06801 %
Correct digits = 3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2735
Order of pole (three term test) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2735
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1841.5MB, alloc=40.3MB, time=22.60
memory used=1887.4MB, alloc=40.3MB, time=23.17
x[1] = 0.1182 0.182
h = 0.003 0.006
y2[1] (numeric) = 0.104084112113 0.192143602029
y2[1] (closed_form) = 0.119883429032 0.181729501103
absolute error = 0.01892
relative error = 8.692 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.01004892522 -0.0210397249553
y1[1] (closed_form) = 1.00951439597 -0.0215810253281
absolute error = 0.0007607
relative error = 0.07534 %
Correct digits = 3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3686
Order of pole (three term test) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3686
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=1933.1MB, alloc=40.3MB, time=23.73
memory used=1979.2MB, alloc=40.3MB, time=24.30
x[1] = 0.1212 0.188
h = 0.0001 0.005
y2[1] (numeric) = 0.104276644808 0.196191551456
y2[1] (closed_form) = 0.123046398106 0.187722147852
absolute error = 0.02059
relative error = 9.174 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.01090138897 -0.0222473078433
y1[1] (closed_form) = 1.01025835835 -0.0228639871644
absolute error = 0.0008909
relative error = 0.08817 %
Correct digits = 3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1691
Order of pole (three term test) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1691
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2024.9MB, alloc=40.3MB, time=24.85
memory used=2070.9MB, alloc=40.3MB, time=25.41
x[1] = 0.1213 0.193
h = 0.0001 0.003
y2[1] (numeric) = 0.104472198418 0.200242152073
y2[1] (closed_form) = 0.123263376946 0.192773458308
absolute error = 0.02022
relative error = 8.837 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.01188203468 -0.022789000333
y1[1] (closed_form) = 1.01119727997 -0.0234987849821
absolute error = 0.0009862
relative error = 0.09751 %
Correct digits = 3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1389
Order of pole (three term test) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1389
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2116.7MB, alloc=40.3MB, time=25.98
x[1] = 0.1214 0.196
h = 0.001 0.001
y2[1] (numeric) = 0.10467083071 0.204295500413
y2[1] (closed_form) = 0.12343560549 0.195805534333
absolute error = 0.0206
relative error = 8.898 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.01247838334 -0.0231229409658
y1[1] (closed_form) = 1.01176781311 -0.0238882620851
absolute error = 0.001044
relative error = 0.1032 %
Correct digits = 3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1104
Order of pole (three term test) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1104
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2162.7MB, alloc=40.3MB, time=26.55
memory used=2209.0MB, alloc=40.3MB, time=27.12
x[1] = 0.1224 0.197
h = 0.0001 0.004
y2[1] (numeric) = 0.104872546021 0.208351635239
y2[1] (closed_form) = 0.1244714577 0.196793290103
absolute error = 0.02275
relative error = 9.772 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.01257993525 -0.0234340357324
y1[1] (closed_form) = 1.01184015904 -0.0242085150168
absolute error = 0.001071
relative error = 0.1058 %
Correct digits = 3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6668
Order of pole (three term test) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6668
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2254.8MB, alloc=40.3MB, time=27.68
memory used=2300.9MB, alloc=40.3MB, time=28.24
x[1] = 0.1225 0.201
h = 0.003 0.006
y2[1] (numeric) = 0.105077347298 0.212410570452
y2[1] (closed_form) = 0.124670550712 0.200839764217
absolute error = 0.02275
relative error = 9.626 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.01341096125 -0.0238749725763
y1[1] (closed_form) = 1.01262296704 -0.0247266799437
absolute error = 0.00116
relative error = 0.1146 %
Correct digits = 3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4014
Order of pole (three term test) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4014
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2346.7MB, alloc=40.3MB, time=28.80
memory used=2392.8MB, alloc=40.3MB, time=29.36
x[1] = 0.1255 0.207
h = 0.0001 0.005
y2[1] (numeric) = 0.105285289505 0.216472356605
y2[1] (closed_form) = 0.127862128221 0.206841797121
absolute error = 0.02455
relative error = 10.09 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.01438206545 -0.0251493825366
y1[1] (closed_form) = 1.01346721491 -0.0260957947093
absolute error = 0.001316
relative error = 0.1298 %
Correct digits = 3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1838
Order of pole (three term test) = 33.03 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1838
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2438.5MB, alloc=40.3MB, time=29.92
x[1] = 0.1256 0.212
h = 0.0001 0.003
y2[1] (numeric) = 0.105496577006 0.220537057034
y2[1] (closed_form) = 0.128095656788 0.211909065234
absolute error = 0.02419
relative error = 9.769 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.01546404868 -0.0256981862325
y1[1] (closed_form) = 1.01450129208 -0.0267566252526
absolute error = 0.001431
relative error = 0.141 %
Correct digits = 3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1508
Order of pole (three term test) = 33.03 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1508
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2484.1MB, alloc=40.3MB, time=30.49
memory used=2530.4MB, alloc=40.3MB, time=31.06
x[1] = 0.1257 0.215
h = 0.001 0.001
y2[1] (numeric) = 0.105711268057 0.224604768409
y2[1] (closed_form) = 0.128278016733 0.214950812089
absolute error = 0.02454
relative error = 9.806 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.0161212003 -0.0260372542144
y1[1] (closed_form) = 1.01512876276 -0.0271625284212
absolute error = 0.0015
relative error = 0.1478 %
Correct digits = 3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1198
Order of pole (three term test) = 33.03 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1198
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2576.3MB, alloc=40.3MB, time=31.64
memory used=2622.5MB, alloc=40.3MB, time=32.20
x[1] = 0.1267 0.216
h = 0.001 0.003
y2[1] (numeric) = 0.105929367134 0.228675529614
y2[1] (closed_form) = 0.129320523304 0.215938649698
absolute error = 0.02663
relative error = 10.58 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.01624202016 -0.0263697141424
y1[1] (closed_form) = 1.01521540828 -0.0275067724077
absolute error = 0.001532
relative error = 0.1508 %
Correct digits = 3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5716
Order of pole (three term test) = 33.03 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5716
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2668.2MB, alloc=40.3MB, time=32.77
x[1] = 0.1277 0.219
h = 0.0001 0.004
y2[1] (numeric) = 0.106150880613 0.232749346724
y2[1] (closed_form) = 0.13041942861 0.218957267869
absolute error = 0.02791
relative error = 10.95 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.01682811687 -0.0269185458411
y1[1] (closed_form) = 1.01573788214 -0.0281138296284
absolute error = 0.001618
relative error = 0.1592 %
Correct digits = 3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3277
Order of pole (three term test) = 33.03 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3277
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2714.2MB, alloc=40.3MB, time=33.33
memory used=2760.2MB, alloc=40.3MB, time=33.89
x[1] = 0.1278 0.223
h = 0.003 0.006
y2[1] (numeric) = 0.106375827869 0.236826241888
y2[1] (closed_form) = 0.130634589116 0.223019117204
absolute error = 0.02791
relative error = 10.8 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.0177566407 -0.0273670768649
y1[1] (closed_form) = 1.01660878108 -0.0286580356999
absolute error = 0.001727
relative error = 0.1699 %
Correct digits = 3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4407
Order of pole (three term test) = 33.03 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4407
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2805.9MB, alloc=40.3MB, time=34.45
memory used=2852.1MB, alloc=40.3MB, time=35.01
x[1] = 0.1308 0.229
h = 0.0001 0.005
y2[1] (numeric) = 0.106604268437 0.240906268935
y2[1] (closed_form) = 0.13386219218 0.229033462834
absolute error = 0.02973
relative error = 11.21 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.01887036741 -0.0287226133327
y1[1] (closed_form) = 1.01756819591 -0.0301295987246
absolute error = 0.001917
relative error = 0.1883 %
Correct digits = 3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2013
Order of pole (three term test) = 33.03 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2013
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2897.9MB, alloc=40.3MB, time=35.57
memory used=2944.1MB, alloc=40.3MB, time=36.14
x[1] = 0.1309 0.234
h = 0.0001 0.003
y2[1] (numeric) = 0.106836407759 0.244989490687
y2[1] (closed_form) = 0.134116386021 0.234121106838
absolute error = 0.02937
relative error = 10.88 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.02007443346 -0.0292805082203
y1[1] (closed_form) = 1.01871268108 -0.0308227013598
absolute error = 0.002057
relative error = 0.2019 %
Correct digits = 3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1651
Order of pole (three term test) = 33.04 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1651
Order of pole (three term test) = 31.96 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=2989.9MB, alloc=40.3MB, time=36.70
x[1] = 0.131 0.237
h = 0.001 0.001
y2[1] (numeric) = 0.107072304708 0.249076003999
y2[1] (closed_form) = 0.13431139908 0.237175179306
absolute error = 0.02973
relative error = 10.91 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.02080483546 -0.0296260735958
y1[1] (closed_form) = 1.01940620362 -0.0312489074978
absolute error = 0.002142
relative error = 0.2101 %
Correct digits = 3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.131
Order of pole (three term test) = 33.04 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.131
Order of pole (three term test) = 31.96 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3035.9MB, alloc=40.3MB, time=37.27
memory used=3082.1MB, alloc=40.3MB, time=37.84
x[1] = 0.132 0.238
h = 0.001 0.003
y2[1] (numeric) = 0.10731196393 0.253165847901
y2[1] (closed_form) = 0.135362291695 0.238163201941
absolute error = 0.03181
relative error = 11.61 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.02094876429 -0.0299843860646
y1[1] (closed_form) = 1.01950903603 -0.0316214135167
absolute error = 0.00218
relative error = 0.2137 %
Correct digits = 3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6248
Order of pole (three term test) = 33.04 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6248
Order of pole (three term test) = 31.96 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3127.9MB, alloc=40.3MB, time=38.40
memory used=3174.0MB, alloc=40.3MB, time=38.97
x[1] = 0.133 0.241
h = 0.0001 0.004
y2[1] (numeric) = 0.107555391855 0.257259028472
y2[1] (closed_form) = 0.136477925424 0.241190657123
absolute error = 0.03309
relative error = 11.94 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.02160696741 -0.0305618983134
y1[1] (closed_form) = 1.02009214664 -0.0322688500487
absolute error = 0.002282
relative error = 0.2236 %
Correct digits = 3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3579
Order of pole (three term test) = 33.04 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3579
Order of pole (three term test) = 31.96 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3219.8MB, alloc=40.3MB, time=39.54
memory used=3265.8MB, alloc=40.3MB, time=40.10
x[1] = 0.1331 0.245
h = 0.003 0.006
y2[1] (numeric) = 0.107802608028 0.26135556788
y2[1] (closed_form) = 0.136710198818 0.245269683389
absolute error = 0.03308
relative error = 11.78 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.0226334276 -0.0310185437498
y1[1] (closed_form) = 1.02105140668 -0.0328395484898
absolute error = 0.002412
relative error = 0.2361 %
Correct digits = 3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4809
Order of pole (three term test) = 33.04 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4809
Order of pole (three term test) = 31.96 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3311.7MB, alloc=40.3MB, time=40.66
x[1] = 0.1361 0.251
h = 0.0001 0.005
y2[1] (numeric) = 0.108053672467 0.265455519955
y2[1] (closed_form) = 0.139976701625 0.251298331088
absolute error = 0.03492
relative error = 12.14 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.02389007571 -0.0324563263878
y1[1] (closed_form) = 1.02212608268 -0.0344144544453
absolute error = 0.002636
relative error = 0.2577 %
Correct digits = 3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2193
Order of pole (three term test) = 33.04 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2193
Order of pole (three term test) = 31.96 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3357.5MB, alloc=40.3MB, time=41.22
memory used=3403.5MB, alloc=40.3MB, time=41.79
x[1] = 0.1362 0.256
h = 0.0001 0.003
y2[1] (numeric) = 0.108308791796 0.269558946984
y2[1] (closed_form) = 0.140252863161 0.256408611272
absolute error = 0.03454
relative error = 11.82 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.02521679232 -0.03302398153
y1[1] (closed_form) = 1.023381336 -0.035140412088
absolute error = 0.002801
relative error = 0.2736 %
Correct digits = 3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1796
Order of pole (three term test) = 33.05 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1796
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3449.3MB, alloc=40.3MB, time=42.35
memory used=3495.5MB, alloc=40.3MB, time=42.92
x[1] = 0.1363 0.259
h = 0.001 0.001
y2[1] (numeric) = 0.108568025555 0.273665946037
y2[1] (closed_form) = 0.140461330509 0.259476356295
absolute error = 0.03491
relative error = 11.83 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.02602078496 -0.0333764569413
y1[1] (closed_form) = 1.02414112719 -0.0355872772541
absolute error = 0.002902
relative error = 0.2832 %
Correct digits = 3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1425
Order of pole (three term test) = 33.05 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1425
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3541.3MB, alloc=40.3MB, time=43.48
x[1] = 0.1373 0.26
h = 0.001 0.003
y2[1] (numeric) = 0.108831378574 0.277776556308
y2[1] (closed_form) = 0.141521318719 0.26046476933
absolute error = 0.03699
relative error = 12.48 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.02618780655 -0.0337608772499
y1[1] (closed_form) = 1.0242601065 -0.0359882391217
absolute error = 0.002946
relative error = 0.2874 %
Correct digits = 3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6793
Order of pole (three term test) = 33.05 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6793
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3587.3MB, alloc=40.3MB, time=44.04
memory used=3633.4MB, alloc=40.3MB, time=44.60
x[1] = 0.1383 0.263
h = 0.0001 0.004
y2[1] (numeric) = 0.109098857337 0.281890783878
y2[1] (closed_form) = 0.14265489557 0.263502181622
absolute error = 0.03826
relative error = 12.77 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.02691834188 -0.0343676049381
y1[1] (closed_form) = 1.02490396873 -0.0366764861378
absolute error = 0.003064
relative error = 0.2988 %
Correct digits = 3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3888
Order of pole (three term test) = 33.05 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3888
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3679.2MB, alloc=40.3MB, time=45.16
memory used=3725.3MB, alloc=40.3MB, time=45.72
x[1] = 0.1384 0.267
h = 0.003 0.006
y2[1] (numeric) = 0.109370481577 0.286008650942
y2[1] (closed_form) = 0.142905339051 0.267600190372
absolute error = 0.03826
relative error = 12.61 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.02804321609 -0.034832937173
y1[1] (closed_form) = 1.02595189411 -0.0372741608594
absolute error = 0.003215
relative error = 0.3131 %
Correct digits = 3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5221
Order of pole (three term test) = 33.05 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5221
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3771.0MB, alloc=40.3MB, time=46.30
memory used=3817.0MB, alloc=40.3MB, time=46.86
x[1] = 0.1414 0.273
h = 0.0001 0.005
y2[1] (numeric) = 0.109646311831 0.290130211342
y2[1] (closed_form) = 0.146213636862 0.273645126931
absolute error = 0.04011
relative error = 12.93 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.02944310671 -0.0363541927622
y1[1] (closed_form) = 1.02714195396 -0.0389533784147
absolute error = 0.003471
relative error = 0.3377 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2377
Order of pole (three term test) = 33.05 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2377
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3862.8MB, alloc=40.3MB, time=47.42
x[1] = 0.1415 0.278
h = 0.0001 0.003
y2[1] (numeric) = 0.109926556017 0.294255526809
y2[1] (closed_form) = 0.14651308381 0.278780308783
absolute error = 0.03972
relative error = 12.61 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.03089309086 -0.0369323423248
y1[1] (closed_form) = 1.02850837843 -0.0397128147928
absolute error = 0.003663
relative error = 0.3559 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1946
Order of pole (three term test) = 33.06 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1946
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=3908.8MB, alloc=40.3MB, time=47.98
memory used=3955.0MB, alloc=40.3MB, time=48.55
x[1] = 0.1416 0.281
h = 0.001 0.001
y2[1] (numeric) = 0.110211274391 0.298384694658
y2[1] (closed_form) = 0.146735815944 0.281863076396
absolute error = 0.04009
relative error = 12.62 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.03177104337 -0.0372921799297
y1[1] (closed_form) = 1.02933468047 -0.0401807199198
absolute error = 0.003779
relative error = 0.3668 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1542
Order of pole (three term test) = 33.06 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1542
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4000.9MB, alloc=40.3MB, time=49.11
memory used=4047.1MB, alloc=40.3MB, time=49.68
x[1] = 0.1426 0.282
h = 0.001 0.003
y2[1] (numeric) = 0.110500471975 0.302517754264
y2[1] (closed_form) = 0.147805613537 0.282852083264
absolute error = 0.04217
relative error = 13.21 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.03196113877 -0.0377029863293
y1[1] (closed_form) = 1.0294697674 -0.0406103481919
absolute error = 0.003829
relative error = 0.3716 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7352
Order of pole (three term test) = 33.06 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.7352
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4092.9MB, alloc=40.3MB, time=50.25
memory used=4139.1MB, alloc=40.3MB, time=50.81
x[1] = 0.1436 0.285
h = 0.0001 0.004
y2[1] (numeric) = 0.110794155317 0.306654711713
y2[1] (closed_form) = 0.148958358712 0.285900573122
absolute error = 0.04344
relative error = 13.48 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.03276424955 -0.0383395130542
y1[1] (closed_form) = 1.0301745143 -0.0413398696397
absolute error = 0.003963
relative error = 0.3844 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4206
Order of pole (three term test) = 33.06 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4206
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4184.9MB, alloc=40.3MB, time=51.37
x[1] = 0.1437 0.289
h = 0.003 0.006
y2[1] (numeric) = 0.111092344347 0.310795589231
y2[1] (closed_form) = 0.14922804219 0.290019374322
absolute error = 0.04343
relative error = 13.31 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.03398805455 -0.0388141570314
y1[1] (closed_form) = 1.0313114434 -0.04196503753
absolute error = 0.004134
relative error = 0.4005 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5644
Order of pole (three term test) = 33.06 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5644
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4230.6MB, alloc=40.3MB, time=51.93
memory used=4276.7MB, alloc=40.3MB, time=52.49
x[1] = 0.1467 0.295
h = 0.0001 0.005
y2[1] (numeric) = 0.111395100166 0.314940440682
y2[1] (closed_form) = 0.152581053121 0.296082584212
absolute error = 0.0453
relative error = 13.6 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.03553153064 -0.0404202200745
y1[1] (closed_form) = 1.03261703805 -0.0437496098217
absolute error = 0.004425
relative error = 0.4281 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2566
Order of pole (three term test) = 33.06 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2566
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4322.5MB, alloc=40.3MB, time=53.05
memory used=4368.5MB, alloc=40.3MB, time=53.62
x[1] = 0.1468 0.3
h = 0.0001 0.003
y2[1] (numeric) = 0.111702632091 0.319089327223
y2[1] (closed_form) = 0.152905119621 0.301244939142
absolute error = 0.0449
relative error = 13.29 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.03710544852 -0.0410096638462
y1[1] (closed_form) = 1.03409507953 -0.0445431898539
absolute error = 0.004642
relative error = 0.4485 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2099
Order of pole (three term test) = 33.07 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2099
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4414.2MB, alloc=40.3MB, time=54.18
x[1] = 0.1469 0.303
h = 0.001 0.001
y2[1] (numeric) = 0.112015001145 0.32324234644
y2[1] (closed_form) = 0.153142937046 0.304344082905
absolute error = 0.04526
relative error = 13.28 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.03805775914 -0.0413773556348
y1[1] (closed_form) = 1.03498816002 -0.0450325409788
absolute error = 0.004773
relative error = 0.4607 %
Correct digits = 2
memory used=4460.4MB, alloc=40.3MB, time=54.75
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1663
Order of pole (three term test) = 33.07 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1663
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4506.6MB, alloc=40.3MB, time=55.32
x[1] = 0.1479 0.304
h = 0.0001 0.004
y2[1] (numeric) = 0.112332212558 0.327399537911
y2[1] (closed_form) = 0.154223262421 0.305333885021
absolute error = 0.04735
relative error = 13.84 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.03827090654 -0.0418148494322
y1[1] (closed_form) = 1.03513931598 -0.0454910630373
absolute error = 0.004829
relative error = 0.4661 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.003
Order of pole (three term test) = 33.07 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.003
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4552.4MB, alloc=40.3MB, time=55.88
memory used=4598.4MB, alloc=40.3MB, time=56.44
x[1] = 0.148 0.308
h = 0.003 0.006
y2[1] (numeric) = 0.11265426963 0.331560915801
y2[1] (closed_form) = 0.154510097067 0.309472283621
absolute error = 0.04733
relative error = 13.68 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.03957757676 -0.042297768768
y1[1] (closed_form) = 1.03635349007 -0.04613926912
absolute error = 0.005015
relative error = 0.4834 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6016
Order of pole (three term test) = 33.07 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6016
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4644.1MB, alloc=40.3MB, time=57.00
memory used=4690.3MB, alloc=40.3MB, time=57.56
x[1] = 0.151 0.314
h = 0.0001 0.005
y2[1] (numeric) = 0.112981229683 0.335726530728
y2[1] (closed_form) = 0.157903701276 0.315553390472
absolute error = 0.04924
relative error = 13.96 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.04124098497 -0.0439756028663
y1[1] (closed_form) = 1.03775994886 -0.0480140405886
absolute error = 0.005332
relative error = 0.5132 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2733
Order of pole (three term test) = 33.07 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2733
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4736.0MB, alloc=40.3MB, time=58.12
x[1] = 0.1511 0.319
h = 0.0001 0.003
y2[1] (numeric) = 0.113313303331 0.339896443349
y2[1] (closed_form) = 0.158249680558 0.320741274242
absolute error = 0.04885
relative error = 13.66 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.04291872591 -0.0445751181572
y1[1] (closed_form) = 1.03933487464 -0.0488362369329
absolute error = 0.005568
relative error = 0.5351 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2234
Order of pole (three term test) = 33.08 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2234
Order of pole (three term test) = 31.92 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4781.9MB, alloc=40.3MB, time=58.68
memory used=4828.2MB, alloc=40.3MB, time=59.25
x[1] = 0.1512 0.322
h = 0.001 0.001
y2[1] (numeric) = 0.113650552294 0.344070751524
y2[1] (closed_form) = 0.158500930998 0.32385579414
absolute error = 0.0492
relative error = 13.64 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.04393332744 -0.0449497609687
y1[1] (closed_form) = 1.04028593203 -0.049343592276
absolute error = 0.00571
relative error = 0.5483 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1769
Order of pole (three term test) = 33.08 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1769
Order of pole (three term test) = 31.92 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4874.1MB, alloc=40.3MB, time=59.81
memory used=4920.4MB, alloc=40.3MB, time=60.39
x[1] = 0.1522 0.323
h = 0.001 0.003
y2[1] (numeric) = 0.113992981985 0.348249495016
y2[1] (closed_form) = 0.159590884709 0.324846577615
absolute error = 0.05125
relative error = 14.16 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.04416566586 -0.0454097420573
y1[1] (closed_form) = 1.04045123738 -0.0498269893422
absolute error = 0.005771
relative error = 0.5541 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.843
Order of pole (three term test) = 33.08 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.843
Order of pole (three term test) = 31.92 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=4966.3MB, alloc=40.3MB, time=60.96
memory used=5012.5MB, alloc=40.3MB, time=61.53
x[1] = 0.1532 0.326
h = 0.0001 0.004
y2[1] (numeric) = 0.114340599073 0.352432679919
y2[1] (closed_form) = 0.160782434477 0.327918927857
absolute error = 0.05251
relative error = 14.38 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.04510252166 -0.0461025818466
y1[1] (closed_form) = 1.04127019884 -0.0506339311263
absolute error = 0.005935
relative error = 0.5693 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4817
Order of pole (three term test) = 33.08 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4817
Order of pole (three term test) = 31.92 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5058.3MB, alloc=40.3MB, time=62.10
x[1] = 0.1533 0.33
h = 0.003 0.006
y2[1] (numeric) = 0.114693423901 0.356620328538
y2[1] (closed_form) = 0.161090515218 0.332081513707
absolute error = 0.05249
relative error = 14.22 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.04650917452 -0.0465961007672
y1[1] (closed_form) = 1.04257410438 -0.0513106760591
absolute error = 0.006141
relative error = 0.5883 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6459
Order of pole (three term test) = 33.08 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6459
Order of pole (three term test) = 31.92 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5104.0MB, alloc=40.3MB, time=62.65
memory used=5150.2MB, alloc=40.3MB, time=63.22
x[1] = 0.1563 0.336
h = 0.0001 0.005
y2[1] (numeric) = 0.115051518722 0.360812494811
y2[1] (closed_form) = 0.16453430587 0.338184616598
absolute error = 0.05441
relative error = 14.47 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.04831685465 -0.0483614810067
y1[1] (closed_form) = 1.04409646806 -0.0532929406906
absolute error = 0.006491
relative error = 0.6209 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2931
Order of pole (three term test) = 33.09 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2931
Order of pole (three term test) = 31.91 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5196.0MB, alloc=40.3MB, time=63.77
memory used=5242.1MB, alloc=40.3MB, time=64.34
x[1] = 0.1564 0.341
h = 0.0001 0.003
y2[1] (numeric) = 0.115415095757 0.365009238788
y2[1] (closed_form) = 0.164907407587 0.343403934662
absolute error = 0.054
relative error = 14.18 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.05011988377 -0.048973936283
y1[1] (closed_form) = 1.04578396391 -0.0541506224751
absolute error = 0.006753
relative error = 0.6448 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2394
Order of pole (three term test) = 33.09 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2394
Order of pole (three term test) = 31.91 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5287.9MB, alloc=40.3MB, time=64.90
x[1] = 0.1565 0.344
h = 0.001 0.001
y2[1] (numeric) = 0.115784217589 0.36921065866
y2[1] (closed_form) = 0.165175282845 0.346537370287
absolute error = 0.05435
relative error = 14.16 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.05120965252 -0.0493574448215
y1[1] (closed_form) = 1.046802371 -0.0546802431283
absolute error = 0.006911
relative error = 0.6593 %
Correct digits = 2
memory used=5334.2MB, alloc=40.3MB, time=65.47
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.1896
Order of pole (three term test) = 33.09 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.1896
Order of pole (three term test) = 31.91 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5380.1MB, alloc=40.3MB, time=66.04
x[1] = 0.1575 0.345
h = 0.001 0.003
y2[1] (numeric) = 0.116158889857 0.373416794419
y2[1] (closed_form) = 0.166277112327 0.347529326872
absolute error = 0.05641
relative error = 14.64 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.05146499476 -0.0498447292458
y1[1] (closed_form) = 1.04698367824 -0.0551930026442
absolute error = 0.006978
relative error = 0.6655 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9032
Order of pole (three term test) = 33.09 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.9032
Order of pole (three term test) = 31.91 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5425.9MB, alloc=44.3MB, time=66.60
memory used=5472.2MB, alloc=44.3MB, time=67.17
x[1] = 0.1585 0.348
h = 0.0001 0.004
y2[1] (numeric) = 0.116539119304 0.377627652168
y2[1] (closed_form) = 0.167491387414 0.350615979092
absolute error = 0.05767
relative error = 14.84 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.05247521171 -0.0505692966971
y1[1] (closed_form) = 1.04786401178 -0.0560427270402
absolute error = 0.007157
relative error = 0.682 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5159
Order of pole (three term test) = 33.1 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5159
Order of pole (three term test) = 31.91 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5518.1MB, alloc=44.3MB, time=67.73
memory used=5564.0MB, alloc=44.3MB, time=68.29
x[1] = 0.1586 0.352
h = 0.003 0.006
y2[1] (numeric) = 0.116924926513 0.381843254258
y2[1] (closed_form) = 0.1678218255 0.35480457816
absolute error = 0.05763
relative error = 14.68 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.05398247877 -0.0510741964326
y1[1] (closed_form) = 1.04925808543 -0.0567486234603
absolute error = 0.007384
relative error = 0.7027 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6914
Order of pole (three term test) = 33.1 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6914
Order of pole (three term test) = 31.9 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5609.8MB, alloc=44.3MB, time=68.85
x[1] = 0.1616 0.358
h = 0.0001 0.005
y2[1] (numeric) = 0.117316374414 0.38606365468
y2[1] (closed_form) = 0.171318796048 0.360931656483
absolute error = 0.05956
relative error = 14.91 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.05593483658 -0.0529287766195
y1[1] (closed_form) = 1.05089658578 -0.0588396400566
absolute error = 0.007767
relative error = 0.7379 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3135
Order of pole (three term test) = 33.1 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3135
Order of pole (three term test) = 31.9 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5655.7MB, alloc=44.3MB, time=69.41
memory used=5701.9MB, alloc=44.3MB, time=69.97
x[1] = 0.1617 0.363
h = 0.0001 0.003
y2[1] (numeric) = 0.117713676948 0.390288912847
y2[1] (closed_form) = 0.171720407544 0.366184701432
absolute error = 0.05914
relative error = 14.62 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.0578639645 -0.053555166872
y1[1] (closed_form) = 1.05269722104 -0.0597335918718
absolute error = 0.008054
relative error = 0.7639 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.256
Order of pole (three term test) = 33.1 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.256
Order of pole (three term test) = 31.9 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5747.7MB, alloc=44.3MB, time=70.54
memory used=5794.1MB, alloc=44.3MB, time=71.12
x[1] = 0.1618 0.366
h = 0.001 0.001
y2[1] (numeric) = 0.118116897607 0.394519127313
y2[1] (closed_form) = 0.172005760523 0.369338418916
absolute error = 0.05948
relative error = 14.6 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.05902938383 -0.0539481516137
y1[1] (closed_form) = 1.05378331863 -0.0602859568118
absolute error = 0.008227
relative error = 0.7795 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2026
Order of pole (three term test) = 33.11 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2026
Order of pole (three term test) = 31.89 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5839.9MB, alloc=44.3MB, time=71.68
memory used=5886.1MB, alloc=44.3MB, time=72.24
x[1] = 0.1628 0.367
h = 0.001 0.003
y2[1] (numeric) = 0.11852604227 0.398754338316
y2[1] (closed_form) = 0.173120199468 0.370331743901
absolute error = 0.06155
relative error = 15.06 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.05930769917 -0.054463108906
y1[1] (closed_form) = 1.05398059082 -0.0608283548403
absolute error = 0.0083
relative error = 0.7862 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.965
Order of pole (three term test) = 33.11 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.965
Order of pole (three term test) = 31.89 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5931.9MB, alloc=44.3MB, time=72.80
x[1] = 0.1638 0.37
h = 0.0001 0.004
y2[1] (numeric) = 0.118941117757 0.402994551969
y2[1] (closed_form) = 0.174358473351 0.373433822183
absolute error = 0.06281
relative error = 15.24 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.06039158817 -0.0552201821886
y1[1] (closed_form) = 1.05492249965 -0.0617214545662
absolute error = 0.008496
relative error = 0.804 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5511
Order of pole (three term test) = 33.11 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5511
Order of pole (three term test) = 31.89 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=5977.8MB, alloc=44.3MB, time=73.36
memory used=6023.8MB, alloc=44.3MB, time=73.92
x[1] = 0.1639 0.374
h = 0.003 0.006
y2[1] (numeric) = 0.119362144908 0.407239790674
y2[1] (closed_form) = 0.174712396291 0.377650267082
absolute error = 0.06276
relative error = 15.08 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.06200014006 -0.0557372984026
y1[1] (closed_form) = 1.05640721236 -0.0624571494307
absolute error = 0.008743
relative error = 0.8262 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7383
Order of pole (three term test) = 33.11 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.7383
Order of pole (three term test) = 31.89 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6069.5MB, alloc=44.3MB, time=74.48
memory used=6115.7MB, alloc=44.3MB, time=75.06
x[1] = 0.1669 0.38
h = 0.0001 0.005
y2[1] (numeric) = 0.119789187372 0.411490108486
y2[1] (closed_form) = 0.178265570028 0.383803298756
absolute error = 0.0647
relative error = 15.29 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.06409760174 -0.0576828429111
y1[1] (closed_form) = 1.05816210876 -0.0646582534612
absolute error = 0.009159
relative error = 0.8639 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3345
Order of pole (three term test) = 33.12 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3345
Order of pole (three term test) = 31.88 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6161.5MB, alloc=44.3MB, time=75.62
memory used=6207.5MB, alloc=44.3MB, time=76.18
x[1] = 0.167 0.385
h = 0.0001 0.003
y2[1] (numeric) = 0.120222460917 0.415745564157
y2[1] (closed_form) = 0.17869709951 0.389092371911
absolute error = 0.06426
relative error = 15.01 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.06615368823 -0.0583242311516
y1[1] (closed_form) = 1.0600764959 -0.0655893028202
absolute error = 0.009472
relative error = 0.8918 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.273
Order of pole (three term test) = 33.12 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.273
Order of pole (three term test) = 31.88 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6253.6MB, alloc=44.3MB, time=76.74
x[1] = 0.1671 0.388
h = 0.001 0.001
y2[1] (numeric) = 0.12066203 0.420006256633
y2[1] (closed_form) = 0.179000795811 0.392267742556
absolute error = 0.0646
relative error = 14.98 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.06739527047 -0.0587273438602
y1[1] (closed_form) = 1.06123065034 -0.0661649171799
absolute error = 0.00966
relative error = 0.9085 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.216
Order of pole (three term test) = 33.12 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.216
Order of pole (three term test) = 31.88 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6299.6MB, alloc=44.3MB, time=77.32
memory used=6345.7MB, alloc=44.3MB, time=77.88
x[1] = 0.1681 0.389
h = 0.001 0.003
y2[1] (numeric) = 0.121107900751 0.424272226418
y2[1] (closed_form) = 0.180128583978 0.393262628912
absolute error = 0.06667
relative error = 15.41 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.06769652483 -0.0592703671017
y1[1] (closed_form) = 1.06144385093 -0.06673724702
absolute error = 0.009739
relative error = 0.9157 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.029
Order of pole (three term test) = 33.12 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.029
Order of pole (three term test) = 31.88 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6391.5MB, alloc=44.3MB, time=78.44
memory used=6437.7MB, alloc=44.3MB, time=79.01
x[1] = 0.1691 0.392
h = 0.0001 0.004
y2[1] (numeric) = 0.121560080072 0.428543479634
y2[1] (closed_form) = 0.181392144673 0.396381258778
absolute error = 0.06793
relative error = 15.58 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.0688544136 -0.0600607749056
y1[1] (closed_form) = 1.06244755619 -0.0676743489303
absolute error = 0.009951
relative error = 0.9347 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5872
Order of pole (three term test) = 33.12 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5872
Order of pole (three term test) = 31.88 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6483.5MB, alloc=44.3MB, time=79.56
x[1] = 0.1692 0.396
h = 0.003 0.006
y2[1] (numeric) = 0.122018589072 0.43282003874
y2[1] (closed_form) = 0.18177069718 0.400627389341
absolute error = 0.06787
relative error = 15.43 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.07056495998 -0.0605909982628
y1[1] (closed_form) = 1.0640234133 -0.0684405239204
absolute error = 0.01022
relative error = 0.9583 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7864
Order of pole (three term test) = 33.13 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.7864
Order of pole (three term test) = 31.87 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6529.4MB, alloc=44.3MB, time=80.12
memory used=6575.6MB, alloc=44.3MB, time=80.69
x[1] = 0.1722 0.402
h = 0.0001 0.005
y2[1] (numeric) = 0.122483492164 0.437101957863
y2[1] (closed_form) = 0.185383129074 0.40680835101
absolute error = 0.06981
relative error = 15.62 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.07280797178 -0.0626293829044
y1[1] (closed_form) = 1.06589499251 -0.0707531281916
absolute error = 0.01067
relative error = 0.9986 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.356
Order of pole (three term test) = 33.13 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.356
Order of pole (three term test) = 31.87 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6621.4MB, alloc=44.3MB, time=81.25
memory used=6667.4MB, alloc=44.3MB, time=81.81
x[1] = 0.1723 0.407
h = 0.0001 0.003
y2[1] (numeric) = 0.122955007054 0.441389295074
y2[1] (closed_form) = 0.185846006791 0.41213576314
absolute error = 0.06936
relative error = 15.34 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.07499192577 -0.06328690089
y1[1] (closed_form) = 1.06792378719 -0.0717221460499
absolute error = 0.01101
relative error = 1.028 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2904
Order of pole (three term test) = 33.14 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2904
Order of pole (three term test) = 31.87 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6713.3MB, alloc=44.3MB, time=82.37
memory used=6759.5MB, alloc=44.3MB, time=82.94
x[1] = 0.1724 0.41
h = 0.001 0.001
y2[1] (numeric) = 0.123433199214 0.44568214974
y2[1] (closed_form) = 0.186168925429 0.415334163842
absolute error = 0.06969
relative error = 15.31 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.07631021219 -0.063700835055
y1[1] (closed_form) = 1.06914639045 -0.0723215414344
absolute error = 0.01121
relative error = 1.046 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2298
Order of pole (three term test) = 33.14 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2298
Order of pole (three term test) = 31.86 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6805.4MB, alloc=44.3MB, time=83.50
x[1] = 0.1734 0.411
h = 0.0001 0.004
y2[1] (numeric) = 0.12391807504 0.449980562647
y2[1] (closed_form) = 0.187310809027 0.416330802141
absolute error = 0.07177
relative error = 15.72 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.076634368 -0.0642723410277
y1[1] (closed_form) = 1.06937548317 -0.0729241137464
absolute error = 0.01129
relative error = 1.054 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.384
Order of pole (three term test) = 33.14 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.384
Order of pole (three term test) = 31.86 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6851.3MB, alloc=44.3MB, time=84.07
memory used=6897.3MB, alloc=44.3MB, time=84.63
x[1] = 0.1735 0.415
h = 0.003 0.006
y2[1] (numeric) = 0.1244096383 0.454284548362
y2[1] (closed_form) = 0.187711108747 0.420604276634
absolute error = 0.0717
relative error = 15.57 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.07843048003 -0.064814207433
y1[1] (closed_form) = 1.07103060008 -0.0737160031704
absolute error = 0.01158
relative error = 1.078 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.829
Order of pole (three term test) = 33.14 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.829
Order of pole (three term test) = 31.86 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=6943.0MB, alloc=44.3MB, time=85.18
memory used=6989.0MB, alloc=44.3MB, time=85.75
x[1] = 0.1765 0.421
h = 0.0001 0.005
y2[1] (numeric) = 0.124907949568 0.4585941578
y2[1] (closed_form) = 0.191376655253 0.426811617548
absolute error = 0.07368
relative error = 15.75 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.08079513866 -0.0669314734155
y1[1] (closed_form) = 1.0730042189 -0.076124378964
absolute error = 0.01205
relative error = 1.12 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3751
Order of pole (three term test) = 33.15 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3751
Order of pole (three term test) = 31.85 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7034.8MB, alloc=44.3MB, time=86.30
memory used=7080.9MB, alloc=44.3MB, time=86.87
x[1] = 0.1766 0.426
h = 0.0001 0.003
y2[1] (numeric) = 0.125413228317 0.462909448445
y2[1] (closed_form) = 0.191867185157 0.43217428577
absolute error = 0.07322
relative error = 15.48 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.08308637929 -0.0676033485648
y1[1] (closed_form) = 1.07513251711 -0.0771254355981
absolute error = 0.01241
relative error = 1.151 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3059
Order of pole (three term test) = 33.15 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3059
Order of pole (three term test) = 31.85 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7126.9MB, alloc=44.3MB, time=87.44
x[1] = 0.1767 0.429
h = 0.001 0.001
y2[1] (numeric) = 0.125925540932 0.467230520064
y2[1] (closed_form) = 0.192207067641 0.43539386063
absolute error = 0.07353
relative error = 15.45 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.08446902091 -0.0680268619091
y1[1] (closed_form) = 1.07641466469 -0.0777449248564
absolute error = 0.01262
relative error = 1.17 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.242
Order of pole (three term test) = 33.15 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.242
Order of pole (three term test) = 31.85 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7172.8MB, alloc=44.3MB, time=88.00
memory used=7218.9MB, alloc=44.3MB, time=88.57
x[1] = 0.1777 0.43
h = 0.001 0.003
y2[1] (numeric) = 0.126444894039 0.471557413702
y2[1] (closed_form) = 0.193361662958 0.436392337778
absolute error = 0.07559
relative error = 15.84 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.08481222976 -0.0686224400211
y1[1] (closed_form) = 1.07665777353 -0.0783736022804
absolute error = 0.01271
relative error = 1.178 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.152
Order of pole (three term test) = 33.15 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.152
Order of pole (three term test) = 31.85 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7264.7MB, alloc=44.3MB, time=89.13
memory used=7311.0MB, alloc=44.3MB, time=89.71
x[1] = 0.1787 0.433
h = 0.0001 0.004
y2[1] (numeric) = 0.126971294707 0.475890135501
y2[1] (closed_form) = 0.194675529064 0.439545105871
absolute error = 0.07684
relative error = 15.98 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.08610669212 -0.0694762858283
y1[1] (closed_form) = 1.07777766086 -0.0793936255503
absolute error = 0.01295
relative error = 1.198 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6574
Order of pole (three term test) = 33.16 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6574
Order of pole (three term test) = 31.85 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7356.8MB, alloc=44.3MB, time=90.28
x[1] = 0.1788 0.437
h = 0.003 0.006
y2[1] (numeric) = 0.127504764586 0.480228708049
y2[1] (closed_form) = 0.195102615291 0.44385172486
absolute error = 0.07676
relative error = 15.83 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.0880062041 -0.0700330414809
y1[1] (closed_form) = 1.07952496334 -0.0802173504665
absolute error = 0.01325
relative error = 1.224 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8799
Order of pole (three term test) = 33.16 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.8799
Order of pole (three term test) = 31.84 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7402.7MB, alloc=44.3MB, time=90.84
memory used=7448.7MB, alloc=44.3MB, time=91.41
x[1] = 0.1818 0.443
h = 0.0001 0.005
y2[1] (numeric) = 0.128045369614 0.48457318564
y2[1] (closed_form) = 0.19883317169 0.450090708459
absolute error = 0.07874
relative error = 16 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.09051728343 -0.0722468896194
y1[1] (closed_form) = 1.08161588983 -0.0827400595285
absolute error = 0.01376
relative error = 1.268 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3979
Order of pole (three term test) = 33.16 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3979
Order of pole (three term test) = 31.84 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7494.5MB, alloc=44.3MB, time=91.98
memory used=7540.6MB, alloc=44.3MB, time=92.54
x[1] = 0.1819 0.448
h = 0.0001 0.003
y2[1] (numeric) = 0.128593331418 0.488923625037
y2[1] (closed_form) = 0.199357746123 0.455496060783
absolute error = 0.07826
relative error = 15.74 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.09293819108 -0.0729371580719
y1[1] (closed_form) = 1.08385994262 -0.0837808138071
absolute error = 0.01414
relative error = 1.301 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3244
Order of pole (three term test) = 33.17 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3244
Order of pole (three term test) = 31.83 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7586.5MB, alloc=44.3MB, time=93.11
memory used=7632.8MB, alloc=44.3MB, time=93.70
x[1] = 0.182 0.451
h = 0.001 0.001
y2[1] (numeric) = 0.129148717498 0.493280126486
y2[1] (closed_form) = 0.199718508184 0.458741255002
absolute error = 0.07857
relative error = 15.7 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.09439860814 -0.0733728794248
y1[1] (closed_form) = 1.0852113438 -0.0844251395041
absolute error = 0.01437
relative error = 1.32 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2566
Order of pole (three term test) = 33.17 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2566
Order of pole (three term test) = 31.83 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7678.8MB, alloc=44.3MB, time=94.28
x[1] = 0.183 0.452
h = 0.001 0.003
y2[1] (numeric) = 0.129711534769 0.497642731345
y2[1] (closed_form) = 0.200888603742 0.459741841098
absolute error = 0.08064
relative error = 16.07 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.09476463955 -0.0739977698515
y1[1] (closed_form) = 1.0854702819 -0.085084684565
absolute error = 0.01447
relative error = 1.329 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.221
Order of pole (three term test) = 33.17 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.221
Order of pole (three term test) = 31.83 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7724.5MB, alloc=44.3MB, time=94.86
memory used=7770.8MB, alloc=44.3MB, time=95.45
x[1] = 0.184 0.455
h = 0.0001 0.004
y2[1] (numeric) = 0.130281790391 0.50201144577
y2[1] (closed_form) = 0.202231515819 0.462914406448
absolute error = 0.08189
relative error = 16.21 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.09613412325 -0.0748875845561
y1[1] (closed_form) = 1.08665270596 -0.0861506915662
absolute error = 0.01472
relative error = 1.351 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6967
Order of pole (three term test) = 33.17 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6967
Order of pole (three term test) = 31.83 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7816.6MB, alloc=44.3MB, time=96.03
memory used=7862.7MB, alloc=44.3MB, time=96.61
x[1] = 0.1841 0.459
h = 0.003 0.006
y2[1] (numeric) = 0.13085950633 0.50638629242
y2[1] (closed_form) = 0.202686587652 0.467256033816
absolute error = 0.08179
relative error = 16.06 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.09813785967 -0.0754602844955
y1[1] (closed_form) = 1.08849279854 -0.0870070350314
absolute error = 0.01505
relative error = 1.378 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9324
Order of pole (three term test) = 33.18 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.9324
Order of pole (three term test) = 31.82 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=7908.5MB, alloc=44.3MB, time=97.20
memory used=7954.6MB, alloc=44.3MB, time=97.79
x[1] = 0.1871 0.465
h = 0.0001 0.005
y2[1] (numeric) = 0.131444749406 0.510767325691
y2[1] (closed_form) = 0.206485309832 0.473528634562
absolute error = 0.08377
relative error = 16.22 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.10079586294 -0.0777729223184
y1[1] (closed_form) = 1.09070139764 -0.0896457151636
absolute error = 0.01558
relative error = 1.424 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4215
Order of pole (three term test) = 33.18 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4215
Order of pole (three term test) = 31.82 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8000.4MB, alloc=44.3MB, time=98.37
x[1] = 0.1872 0.47
h = 0.0001 0.003
y2[1] (numeric) = 0.132037743511 0.515154601593
y2[1] (closed_form) = 0.20704542858 0.478979013072
absolute error = 0.08328
relative error = 15.96 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.10334749108 -0.0784829213395
y1[1] (closed_form) = 1.0930619854 -0.0907271649432
absolute error = 0.01599
relative error = 1.458 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3435
Order of pole (three term test) = 33.19 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3435
Order of pole (three term test) = 31.81 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8046.1MB, alloc=44.3MB, time=98.95
memory used=8092.3MB, alloc=44.3MB, time=99.56
x[1] = 0.1873 0.473
h = 0.001 0.001
y2[1] (numeric) = 0.132638557314 0.519548220879
y2[1] (closed_form) = 0.207427991536 0.482251222072
absolute error = 0.08357
relative error = 15.92 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.10488630997 -0.0789316689226
y1[1] (closed_form) = 1.09448310605 -0.0913969360123
absolute error = 0.01624
relative error = 1.478 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2716
Order of pole (three term test) = 33.19 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2716
Order of pole (three term test) = 31.81 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8138.2MB, alloc=44.3MB, time=100.16
memory used=8184.4MB, alloc=44.3MB, time=100.75
x[1] = 0.1883 0.474
h = 0.001 0.003
y2[1] (numeric) = 0.133247198028 0.523948225239
y2[1] (closed_form) = 0.208614354164 0.483254100418
absolute error = 0.08565
relative error = 16.27 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.10527511544 -0.0795863588385
y1[1] (closed_form) = 1.09475783765 -0.0920877098006
absolute error = 0.01634
relative error = 1.487 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.293
Order of pole (three term test) = 33.19 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.293
Order of pole (three term test) = 31.81 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8230.3MB, alloc=44.3MB, time=101.35
x[1] = 0.1893 0.477
h = 0.0001 0.004
y2[1] (numeric) = 0.133863672916 0.528354620842
y2[1] (closed_form) = 0.209987664373 0.48644759628
absolute error = 0.0869
relative error = 16.4 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.10672001332 -0.0805131740738
y1[1] (closed_form) = 1.09600308892 -0.0932004623123
absolute error = 0.01661
relative error = 1.51 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7374
Order of pole (three term test) = 33.19 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.7374
Order of pole (three term test) = 31.81 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8276.5MB, alloc=44.3MB, time=101.94
memory used=8322.6MB, alloc=44.3MB, time=102.53
x[1] = 0.1894 0.481
h = 0.003 0.006
y2[1] (numeric) = 0.13448800427 0.532767430427
y2[1] (closed_form) = 0.210471941833 0.490826105342
absolute error = 0.08679
relative error = 16.25 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.10882883776 -0.0811029308553
y1[1] (closed_form) = 1.09793661082 -0.0940902438952
absolute error = 0.01695
relative error = 1.538 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9866
Order of pole (three term test) = 33.2 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.9866
Order of pole (three term test) = 31.8 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8368.4MB, alloc=44.3MB, time=103.12
memory used=8414.6MB, alloc=44.3MB, time=103.72
x[1] = 0.1924 0.487
h = 0.0001 0.005
y2[1] (numeric) = 0.135120259837 0.537186708497
y2[1] (closed_form) = 0.2143420246 0.497134297128
absolute error = 0.08877
relative error = 16.4 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.11163428655 -0.0835166812151
y1[1] (closed_form) = 1.10026327411 -0.0968466132164
absolute error = 0.01752
relative error = 1.586 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4458
Order of pole (three term test) = 33.2 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4458
Order of pole (three term test) = 31.8 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8460.5MB, alloc=44.3MB, time=104.30
memory used=8506.6MB, alloc=44.3MB, time=104.90
x[1] = 0.1925 0.492
h = 0.0001 0.003
y2[1] (numeric) = 0.135760665887 0.541612510283
y2[1] (closed_form) = 0.214939214161 0.502632056145
absolute error = 0.08825
relative error = 16.14 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.11431773788 -0.0842478200136
y1[1] (closed_form) = 1.10274122087 -0.0979698020854
absolute error = 0.01795
relative error = 1.622 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3632
Order of pole (three term test) = 33.21 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3632
Order of pole (three term test) = 31.79 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8552.5MB, alloc=44.3MB, time=105.49
x[1] = 0.1926 0.495
h = 0.001 0.001
y2[1] (numeric) = 0.136409292315 0.546044937078
y2[1] (closed_form) = 0.215344515567 0.50593268258
absolute error = 0.08854
relative error = 16.1 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.11593561395 -0.0847104557114
y1[1] (closed_form) = 1.10423255271 -0.0986656553211
absolute error = 0.01821
relative error = 1.643 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2872
Order of pole (three term test) = 33.21 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.2872
Order of pole (three term test) = 31.79 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8598.6MB, alloc=44.3MB, time=106.08
memory used=8644.8MB, alloc=44.3MB, time=106.67
x[1] = 0.1936 0.496
h = 0.001 0.003
y2[1] (numeric) = 0.137066146646 0.550484030918
y2[1] (closed_form) = 0.216547920043 0.506938033732
absolute error = 0.09063
relative error = 16.44 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.11634714085 -0.0853954566732
y1[1] (closed_form) = 1.10452304197 -0.0993880368486
absolute error = 0.01832
relative error = 1.652 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.367
Order of pole (three term test) = 33.21 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.367
Order of pole (three term test) = 31.79 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8690.8MB, alloc=44.3MB, time=107.25
memory used=8737.1MB, alloc=44.3MB, time=107.83
x[1] = 0.1946 0.499
h = 0.0001 0.004
y2[1] (numeric) = 0.137731236246 0.554929797988
y2[1] (closed_form) = 0.217952999288 0.510153595812
absolute error = 0.09187
relative error = 16.56 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.11786786192 -0.086360357044
y1[1] (closed_form) = 1.10583142866 -0.100548332615
absolute error = 0.01861
relative error = 1.676 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7794
Order of pole (three term test) = 33.21 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.7794
Order of pole (three term test) = 31.79 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8782.8MB, alloc=44.3MB, time=108.40
memory used=8829.0MB, alloc=44.3MB, time=108.98
x[1] = 0.1947 0.503
h = 0.003 0.006
y2[1] (numeric) = 0.138404583754 0.559382261112
y2[1] (closed_form) = 0.218467724315 0.514570869889
absolute error = 0.09175
relative error = 16.41 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.12008267707 -0.0869683414753
y1[1] (closed_form) = 1.10785905392 -0.101472408919
absolute error = 0.01897
relative error = 1.705 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.043
Order of pole (three term test) = 33.22 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.043
Order of pole (three term test) = 31.78 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8874.9MB, alloc=44.3MB, time=109.55
x[1] = 0.1977 0.509
h = 0.0001 0.005
y2[1] (numeric) = 0.139086257884 0.563841474908
y2[1] (closed_form) = 0.222412403309 0.520916626191
absolute error = 0.09373
relative error = 16.55 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.12303611074 -0.089485643691
y1[1] (closed_form) = 1.11030419934 -0.10434826674
absolute error = 0.01957
relative error = 1.755 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4709
Order of pole (three term test) = 33.22 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4709
Order of pole (three term test) = 31.78 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=8920.7MB, alloc=44.3MB, time=110.12
memory used=8966.9MB, alloc=44.3MB, time=110.70
x[1] = 0.1978 0.514
h = 0.0001 0.003
y2[1] (numeric) = 0.139776487402 0.568307493802
y2[1] (closed_form) = 0.22304821813 0.526464132994
absolute error = 0.09319
relative error = 16.3 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.12585253724 -0.0902394043546
y1[1] (closed_form) = 1.1129003729 -0.105514284687
absolute error = 0.02003
relative error = 1.791 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3836
Order of pole (three term test) = 33.23 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3836
Order of pole (three term test) = 31.77 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9012.8MB, alloc=44.3MB, time=111.28
memory used=9059.2MB, alloc=44.3MB, time=111.87
x[1] = 0.1979 0.517
h = 0.001 0.001
y2[1] (numeric) = 0.140475343484 0.572780419655
y2[1] (closed_form) = 0.223477212537 0.529794587172
absolute error = 0.09347
relative error = 16.26 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.12755015486 -0.0907168342807
y1[1] (closed_form) = 1.11446243357 -0.106236885149
absolute error = 0.0203
relative error = 1.813 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3033
Order of pole (three term test) = 33.23 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3033
Order of pole (three term test) = 31.77 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9105.2MB, alloc=44.3MB, time=112.45
x[1] = 0.1989 0.518
h = 0.0001 0.004
y2[1] (numeric) = 0.141182833979 0.577260294867
y2[1] (closed_form) = 0.224698441986 0.530802588836
absolute error = 0.09557
relative error = 16.58 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.12798434627 -0.0914326824276
y1[1] (closed_form) = 1.11476864446 -0.106991271513
absolute error = 0.02041
relative error = 1.823 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.826
Order of pole (three term test) = 33.23 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.826
Order of pole (three term test) = 31.77 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9151.3MB, alloc=44.3MB, time=113.02
memory used=9197.5MB, alloc=44.3MB, time=113.58
x[1] = 0.199 0.522
h = 0.003 0.006
y2[1] (numeric) = 0.141898963244 0.581747134546
y2[1] (closed_form) = 0.225239894755 0.535255129962
absolute error = 0.09543
relative error = 16.43 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.13028820478 -0.0920567934542
y1[1] (closed_form) = 1.11687826023 -0.107944449662
absolute error = 0.02079
relative error = 1.853 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.092
Order of pole (three term test) = 33.24 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.092
Order of pole (three term test) = 31.77 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9243.2MB, alloc=44.3MB, time=114.14
memory used=9289.4MB, alloc=44.3MB, time=114.71
x[1] = 0.202 0.528
h = 0.0001 0.005
y2[1] (numeric) = 0.14262379604 0.586240990122
y2[1] (closed_form) = 0.22925092786 0.541635742479
absolute error = 0.09744
relative error = 16.57 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.1333653837 -0.0946623377507
y1[1] (closed_form) = 1.11942719981 -0.110923244089
absolute error = 0.02142
relative error = 1.904 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4932
Order of pole (three term test) = 33.24 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4932
Order of pole (three term test) = 31.76 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9335.1MB, alloc=44.3MB, time=115.27
memory used=9381.4MB, alloc=44.3MB, time=115.84
x[1] = 0.2021 0.533
h = 0.0001 0.003
y2[1] (numeric) = 0.143357563384 0.590741915326
y2[1] (closed_form) = 0.229920625823 0.547228462435
absolute error = 0.09688
relative error = 16.32 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.136293539 -0.0954361364859
y1[1] (closed_form) = 1.12212639623 -0.112125613455
absolute error = 0.02189
relative error = 1.941 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4018
Order of pole (three term test) = 33.25 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4018
Order of pole (three term test) = 31.75 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9427.4MB, alloc=44.3MB, time=116.41
x[1] = 0.2022 0.536
h = 0.001 0.001
y2[1] (numeric) = 0.144100337588 0.595250012549
y2[1] (closed_form) = 0.230370413973 0.550586024862
absolute error = 0.09715
relative error = 16.28 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.13805815227 -0.0959266206205
y1[1] (closed_form) = 1.12375010223 -0.112870940099
absolute error = 0.02218
relative error = 1.964 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3176
Order of pole (three term test) = 33.25 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3176
Order of pole (three term test) = 31.75 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9473.3MB, alloc=44.3MB, time=116.98
memory used=9519.6MB, alloc=44.3MB, time=117.56
x[1] = 0.2032 0.537
h = 0.001 0.003
y2[1] (numeric) = 0.144852126788 0.599765324524
y2[1] (closed_form) = 0.231607585939 0.551596673241
absolute error = 0.09923
relative error = 16.59 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.13851118386 -0.0966686031683
y1[1] (closed_form) = 1.12407020471 -0.113653020395
absolute error = 0.02229
relative error = 1.973 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.511
Order of pole (three term test) = 33.25 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.511
Order of pole (three term test) = 31.75 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9565.6MB, alloc=44.3MB, time=118.12
memory used=9611.8MB, alloc=44.3MB, time=118.70
x[1] = 0.2042 0.54
h = 0.0001 0.004
y2[1] (numeric) = 0.14561293856 0.60428785747
y2[1] (closed_form) = 0.233075201639 0.554856745278
absolute error = 0.1005
relative error = 16.69 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.14017203005 -0.0977063244968
y1[1] (closed_form) = 1.12549754312 -0.114903269739
absolute error = 0.02261
relative error = 1.998 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8615
Order of pole (three term test) = 33.25 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.8615
Order of pole (three term test) = 31.75 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9657.7MB, alloc=44.3MB, time=119.26
memory used=9703.8MB, alloc=44.3MB, time=119.83
x[1] = 0.2043 0.544
h = 0.003 0.006
y2[1] (numeric) = 0.146382796223 0.608817634383
y2[1] (closed_form) = 0.233649451978 0.55935159987
absolute error = 0.1003
relative error = 16.55 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.14258363889 -0.0983509681619
y1[1] (closed_form) = 1.1277026207 -0.115892427998
absolute error = 0.023
relative error = 2.029 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.152
Order of pole (three term test) = 33.26 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.152
Order of pole (three term test) = 31.74 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9749.7MB, alloc=44.3MB, time=120.40
x[1] = 0.2073 0.55
h = 0.0001 0.005
y2[1] (numeric) = 0.147161770409 0.613354710138
y2[1] (closed_form) = 0.237741193909 0.565773488247
absolute error = 0.1023
relative error = 16.67 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.14580983773 -0.101064853932
y1[1] (closed_form) = 1.1303709133 -0.118994272584
absolute error = 0.02366
relative error = 2.082 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.52
Order of pole (three term test) = 33.26 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.52
Order of pole (three term test) = 31.74 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9795.6MB, alloc=44.3MB, time=120.98
memory used=9841.6MB, alloc=44.3MB, time=121.54
x[1] = 0.2074 0.555
h = 0.0001 0.003
y2[1] (numeric) = 0.147950094852 0.617899137615
y2[1] (closed_form) = 0.238452459722 0.571420417242
absolute error = 0.1017
relative error = 16.43 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.14887321375 -0.101864192303
y1[1] (closed_form) = 1.13319008261 -0.120241613581
absolute error = 0.02416
relative error = 2.12 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4235
Order of pole (three term test) = 33.27 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4235
Order of pole (three term test) = 31.73 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9887.5MB, alloc=44.3MB, time=122.12
memory used=9933.9MB, alloc=44.3MB, time=122.70
x[1] = 0.2075 0.558
h = 0.001 0.001
y2[1] (numeric) = 0.148747843251 0.622451019829
y2[1] (closed_form) = 0.238927747891 0.574810465358
absolute error = 0.102
relative error = 16.38 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.15071890229 -0.102371254299
y1[1] (closed_form) = 1.13488555869 -0.121014994772
absolute error = 0.02446
relative error = 2.143 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3347
Order of pole (three term test) = 33.27 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3347
Order of pole (three term test) = 31.73 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=9979.8MB, alloc=44.3MB, time=123.28
x[1] = 0.2085 0.559
h = 0.001 0.003
y2[1] (numeric) = 0.149555024093 0.627010399911
y2[1] (closed_form) = 0.240184223593 0.575824096575
absolute error = 0.1041
relative error = 16.68 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.15119448173 -0.103145135031
y1[1] (closed_form) = 1.13522132013 -0.121829867983
absolute error = 0.02458
relative error = 2.153 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.593
Order of pole (three term test) = 33.28 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.593
Order of pole (three term test) = 31.73 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10025.7MB, alloc=44.3MB, time=123.84
memory used=10072.0MB, alloc=44.3MB, time=124.42
x[1] = 0.2095 0.562
h = 0.0001 0.004
y2[1] (numeric) = 0.15037164507 0.631577284099
y2[1] (closed_form) = 0.241687628014 0.579109516289
absolute error = 0.1053
relative error = 16.78 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.15293239883 -0.104224315888
y1[1] (closed_form) = 1.13671278427 -0.123130140954
absolute error = 0.02491
relative error = 2.179 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9078
Order of pole (three term test) = 33.28 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.9078
Order of pole (three term test) = 31.72 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10117.8MB, alloc=44.3MB, time=124.98
memory used=10163.9MB, alloc=44.3MB, time=125.55
x[1] = 0.2096 0.566
h = 0.003 0.006
y2[1] (numeric) = 0.151197729893 0.636151695487
y2[1] (closed_form) = 0.242295986016 0.583648599727
absolute error = 0.1051
relative error = 16.64 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.15545277588 -0.104890837866
y1[1] (closed_form) = 1.13901409833 -0.124156244567
absolute error = 0.02533
relative error = 2.21 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.214
Order of pole (three term test) = 33.28 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.214
Order of pole (three term test) = 31.72 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10209.7MB, alloc=44.3MB, time=126.12
memory used=10256.0MB, alloc=44.3MB, time=126.70
x[1] = 0.2126 0.572
h = 0.0001 0.005
y2[1] (numeric) = 0.152033350288 0.640733689093
y2[1] (closed_form) = 0.246471799989 0.590113737583
absolute error = 0.1071
relative error = 16.75 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.15882858403 -0.107715852456
y1[1] (closed_form) = 1.14180223707 -0.127383175806
absolute error = 0.02601
relative error = 2.264 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5477
Order of pole (three term test) = 33.29 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5477
Order of pole (three term test) = 31.71 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10301.7MB, alloc=44.3MB, time=127.27
x[1] = 0.2127 0.577
h = 0.0001 0.003
y2[1] (numeric) = 0.152878742825 0.645323316908
y2[1] (closed_form) = 0.247226274899 0.595817284301
absolute error = 0.1065
relative error = 16.52 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.16202847782 -0.108542431376
y1[1] (closed_form) = 1.1447423737 -0.128676714606
absolute error = 0.02654
relative error = 2.304 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.446
Order of pole (three term test) = 33.3 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.446
Order of pole (three term test) = 31.71 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10347.6MB, alloc=44.3MB, time=127.83
memory used=10394.0MB, alloc=44.3MB, time=128.40
x[1] = 0.2128 0.58
h = 0.001 0.001
y2[1] (numeric) = 0.153733982642 0.649920682601
y2[1] (closed_form) = 0.247728070401 0.59924125286
absolute error = 0.1068
relative error = 16.47 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.16395601132 -0.109067110136
y1[1] (closed_form) = 1.14651021251 -0.129478898361
absolute error = 0.02685
relative error = 2.327 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3525
Order of pole (three term test) = 33.3 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3525
Order of pole (three term test) = 31.7 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10440.1MB, alloc=44.3MB, time=128.98
memory used=10486.5MB, alloc=44.3MB, time=129.56
x[1] = 0.2138 0.581
h = 0.001 0.003
y2[1] (numeric) = 0.154599078594 0.654525829718
y2[1] (closed_form) = 0.249004659092 0.60025803602
absolute error = 0.1089
relative error = 16.76 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.16445406822 -0.109873498453
y1[1] (closed_form) = 1.14686159593 -0.130327014312
absolute error = 0.02698
relative error = 2.337 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.677
Order of pole (three term test) = 33.3 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.677
Order of pole (three term test) = 31.7 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10532.5MB, alloc=44.3MB, time=130.12
x[1] = 0.2148 0.584
h = 0.0001 0.004
y2[1] (numeric) = 0.155474038495 0.659138764516
y2[1] (closed_form) = 0.250545303887 0.603569950688
absolute error = 0.1101
relative error = 16.85 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.16626952743 -0.110995437307
y1[1] (closed_form) = 1.14841756257 -0.131678251571
absolute error = 0.02732
relative error = 2.364 %
Correct digits = 2
memory used=10578.6MB, alloc=44.3MB, time=130.70
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9558
Order of pole (three term test) = 33.3 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.9558
Order of pole (three term test) = 31.7 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10624.7MB, alloc=44.3MB, time=131.26
x[1] = 0.2149 0.588
h = 0.003 0.006
y2[1] (numeric) = 0.156358886461 0.663759510195
y2[1] (closed_form) = 0.251189105511 0.608155190564
absolute error = 0.1099
relative error = 16.71 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.1688997298 -0.111685244706
y1[1] (closed_form) = 1.150815923 -0.132742305069
absolute error = 0.02776
relative error = 2.396 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.278
Order of pole (three term test) = 33.31 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.278
Order of pole (three term test) = 31.69 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10670.5MB, alloc=44.3MB, time=131.83
memory used=10716.7MB, alloc=44.3MB, time=132.41
x[1] = 0.2179 0.594
h = 0.0001 0.005
y2[1] (numeric) = 0.15725369536 0.668388121923
y2[1] (closed_form) = 0.25545240316 0.61466555163
absolute error = 0.1119
relative error = 16.82 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.1724257524 -0.114624296889
y1[1] (closed_form) = 1.15372442649 -0.136096444436
absolute error = 0.02847
relative error = 2.451 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5765
Order of pole (three term test) = 33.31 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5765
Order of pole (three term test) = 31.69 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10762.6MB, alloc=44.3MB, time=132.98
memory used=10808.8MB, alloc=44.3MB, time=133.55
x[1] = 0.218 0.599
h = 0.0001 0.003
y2[1] (numeric) = 0.158158704716 0.673024650768
y2[1] (closed_form) = 0.256251761317 0.62042814049
absolute error = 0.1113
relative error = 16.58 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.17576351048 -0.115479894183
y1[1] (closed_form) = 1.15678656924 -0.137437456484
absolute error = 0.02902
relative error = 2.491 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4693
Order of pole (three term test) = 33.32 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4693
Order of pole (three term test) = 31.68 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10854.8MB, alloc=44.3MB, time=134.13
x[1] = 0.2181 0.602
h = 0.001 0.001
y2[1] (numeric) = 0.159073991169 0.677669201086
y2[1] (closed_form) = 0.256781091462 0.623887473529
absolute error = 0.1115
relative error = 16.53 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.17777368769 -0.116023275281
y1[1] (closed_form) = 1.15862738968 -0.138269220829
absolute error = 0.02935
relative error = 2.515 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3709
Order of pole (three term test) = 33.32 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.3709
Order of pole (three term test) = 31.68 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10900.8MB, alloc=44.3MB, time=134.70
memory used=10947.1MB, alloc=44.3MB, time=135.28
x[1] = 0.2191 0.603
h = 0.001 0.003
y2[1] (numeric) = 0.15999956395 0.682321816855
y2[1] (closed_form) = 0.2580786123 0.624907574485
absolute error = 0.1136
relative error = 16.81 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.17829414661 -0.116862806038
y1[1] (closed_form) = 1.1589943575 -0.139151048143
absolute error = 0.02948
relative error = 2.526 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.765
Order of pole (three term test) = 33.33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.765
Order of pole (three term test) = 31.68 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=10993.1MB, alloc=44.3MB, time=135.85
memory used=11039.3MB, alloc=44.3MB, time=136.43
x[1] = 0.2201 0.606
h = 0.0001 0.004
y2[1] (numeric) = 0.160935431003 0.686982504353
y2[1] (closed_form) = 0.259657972281 0.628247134777
absolute error = 0.1149
relative error = 16.9 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.18018763443 -0.118028857442
y1[1] (closed_form) = 1.16061522089 -0.140554228629
absolute error = 0.02984
relative error = 2.552 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.006
Order of pole (three term test) = 33.33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.006
Order of pole (three term test) = 31.67 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11085.1MB, alloc=44.3MB, time=137.00
memory used=11131.3MB, alloc=44.3MB, time=137.57
x[1] = 0.2202 0.61
h = 0.003 0.006
y2[1] (numeric) = 0.161881616866 0.691651286888
y2[1] (closed_form) = 0.26033858041 0.632880471461
absolute error = 0.1147
relative error = 16.76 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.18292875854 -0.118743419716
y1[1] (closed_form) = 1.16311147303 -0.141657276478
absolute error = 0.03029
relative error = 2.586 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.344
Order of pole (three term test) = 33.33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.344
Order of pole (three term test) = 31.67 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11177.0MB, alloc=44.3MB, time=138.14
x[1] = 0.2232 0.616
h = 0.0001 0.005
y2[1] (numeric) = 0.162838195594 0.696328219787
y2[1] (closed_form) = 0.264692823802 0.639438029682
absolute error = 0.1167
relative error = 16.86 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.18660561588 -0.121799541115
y1[1] (closed_form) = 1.16614088506 -0.145140831516
absolute error = 0.03104
relative error = 2.642 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6063
Order of pole (three term test) = 33.34 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6063
Order of pole (three term test) = 31.66 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11222.8MB, alloc=44.3MB, time=138.71
memory used=11269.1MB, alloc=44.3MB, time=139.29
x[1] = 0.2233 0.621
h = 0.0001 0.003
y2[1] (numeric) = 0.163805409788 0.701013353166
y2[1] (closed_form) = 0.26553877359 0.645262101556
absolute error = 0.116
relative error = 16.63 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.19008263429 -0.122686012678
y1[1] (closed_form) = 1.16932611729 -0.146530642357
absolute error = 0.03161
relative error = 2.683 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4936
Order of pole (three term test) = 33.35 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4936
Order of pole (three term test) = 31.66 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11314.9MB, alloc=44.3MB, time=139.86
memory used=11361.3MB, alloc=44.3MB, time=140.44
x[1] = 0.2234 0.624
h = 0.001 0.001
y2[1] (numeric) = 0.164783337644 0.705706792093
y2[1] (closed_form) = 0.266096686488 0.648758252816
absolute error = 0.1162
relative error = 16.57 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.19217628307 -0.123249229057
y1[1] (closed_form) = 1.17124056466 -0.147392795823
absolute error = 0.03196
relative error = 2.707 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.39
Order of pole (three term test) = 33.35 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.39
Order of pole (three term test) = 31.65 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11407.2MB, alloc=44.3MB, time=141.02
x[1] = 0.2244 0.625
h = 0.0001 0.004
y2[1] (numeric) = 0.16577198879 0.710408580999
y2[1] (closed_form) = 0.267415968948 0.649781834048
absolute error = 0.1184
relative error = 16.84 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.19271906329 -0.124122562817
y1[1] (closed_form) = 1.17162307852 -0.14830882213
absolute error = 0.03209
relative error = 2.718 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.348
Order of pole (three term test) = 33.35 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.348
Order of pole (three term test) = 31.65 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11453.6MB, alloc=44.3MB, time=141.59
memory used=11499.5MB, alloc=44.3MB, time=142.16
x[1] = 0.2245 0.629
h = 0.003 0.006
y2[1] (numeric) = 0.166771368298 0.715118735668
y2[1] (closed_form) = 0.268128766968 0.654458595881
absolute error = 0.1181
relative error = 16.7 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.19555348805 -0.124858922249
y1[1] (closed_form) = 1.17420477878 -0.149445121938
absolute error = 0.03256
relative error = 2.751 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.404
Order of pole (three term test) = 33.36 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.404
Order of pole (three term test) = 31.65 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11545.2MB, alloc=44.3MB, time=142.72
memory used=11591.3MB, alloc=44.3MB, time=143.30
x[1] = 0.2275 0.635
h = 0.0001 0.005
y2[1] (numeric) = 0.167781546097 0.719837308249
y2[1] (closed_form) = 0.272563511543 0.661059501194
absolute error = 0.1201
relative error = 16.8 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.19935652532 -0.128015007489
y1[1] (closed_form) = 1.17734029839 -0.153040458423
absolute error = 0.03333
relative error = 2.807 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6329
Order of pole (three term test) = 33.36 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6329
Order of pole (three term test) = 31.64 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11637.2MB, alloc=44.3MB, time=143.86
memory used=11683.4MB, alloc=44.3MB, time=144.44
x[1] = 0.2276 0.64
h = 0.0001 0.003
y2[1] (numeric) = 0.168802767536 0.724564348038
y2[1] (closed_form) = 0.273450188741 0.666939046621
absolute error = 0.1195
relative error = 16.57 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.20295069679 -0.128928683655
y1[1] (closed_form) = 1.18063298733 -0.154471889345
absolute error = 0.03392
relative error = 2.849 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5151
Order of pole (three term test) = 33.37 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5151
Order of pole (three term test) = 31.63 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11729.3MB, alloc=44.3MB, time=145.01
x[1] = 0.2277 0.643
h = 0.001 0.001
y2[1] (numeric) = 0.169835112198 0.729299960762
y2[1] (closed_form) = 0.274033098173 0.670468419478
absolute error = 0.1197
relative error = 16.52 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.2051145593 -0.129509330835
y1[1] (closed_form) = 1.18261172293 -0.155359983885
absolute error = 0.03427
relative error = 2.873 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.407
Order of pole (three term test) = 33.38 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.407
Order of pole (three term test) = 31.63 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11775.3MB, alloc=44.3MB, time=145.58
memory used=11821.6MB, alloc=44.3MB, time=146.16
x[1] = 0.2287 0.644
h = 0.001 0.003
y2[1] (numeric) = 0.170878590052 0.734044191257
y2[1] (closed_form) = 0.275371740691 0.671495396738
absolute error = 0.1218
relative error = 16.78 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.20567587474 -0.130411358116
y1[1] (closed_form) = 1.18300800258 -0.156305668146
absolute error = 0.03441
relative error = 2.884 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.937
Order of pole (three term test) = 33.38 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.937
Order of pole (three term test) = 31.63 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11867.6MB, alloc=44.3MB, time=146.73
memory used=11913.7MB, alloc=44.3MB, time=147.31
x[1] = 0.2297 0.647
h = 0.0001 0.004
y2[1] (numeric) = 0.171933209294 0.738797045846
y2[1] (closed_form) = 0.277026787269 0.674889977815
absolute error = 0.123
relative error = 16.86 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.20771372946 -0.131661992926
y1[1] (closed_form) = 1.18475138096 -0.157807456753
absolute error = 0.0348
relative error = 2.911 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.103
Order of pole (three term test) = 33.38 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.103
Order of pole (three term test) = 31.62 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=11959.5MB, alloc=44.3MB, time=147.88
memory used=12005.5MB, alloc=44.3MB, time=148.44
x[1] = 0.2298 0.651
h = 0.003 0.006
y2[1] (numeric) = 0.172998995289 0.743558548054
y2[1] (closed_form) = 0.277778979651 0.679618500022
absolute error = 0.1227
relative error = 16.72 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.21066119124 -0.132425971317
y1[1] (closed_form) = 1.18743265414 -0.158984791963
absolute error = 0.03528
relative error = 2.945 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.475
Order of pole (three term test) = 33.39 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.475
Order of pole (three term test) = 31.62 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12051.4MB, alloc=44.3MB, time=149.01
x[1] = 0.2328 0.657
h = 0.0001 0.005
y2[1] (numeric) = 0.174076024428 0.748328753544
y2[1] (closed_form) = 0.282311229771 0.686270319178
absolute error = 0.1248
relative error = 16.81 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.2146162391 -0.135705019465
y1[1] (closed_form) = 1.19069018914 -0.162713877657
absolute error = 0.03608
relative error = 3.002 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6648
Order of pole (three term test) = 33.39 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6648
Order of pole (three term test) = 31.61 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12097.3MB, alloc=44.3MB, time=149.58
memory used=12143.6MB, alloc=44.3MB, time=150.15
x[1] = 0.2329 0.662
h = 0.0001 0.003
y2[1] (numeric) = 0.175164545367 0.753107710607
y2[1] (closed_form) = 0.283247743675 0.692215957118
absolute error = 0.1241
relative error = 16.59 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.21835236466 -0.136653187822
y1[1] (closed_form) = 1.19410811989 -0.164196696031
absolute error = 0.03669
relative error = 3.044 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5411
Order of pole (three term test) = 33.4 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5411
Order of pole (three term test) = 31.6 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12189.4MB, alloc=44.3MB, time=150.72
memory used=12235.8MB, alloc=44.3MB, time=151.30
x[1] = 0.233 0.665
h = 0.001 0.001
y2[1] (numeric) = 0.176264639362 0.757895525736
y2[1] (closed_form) = 0.283861226714 0.695784893628
absolute error = 0.1242
relative error = 16.53 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.22060129593 -0.137255878792
y1[1] (closed_form) = 1.19616176422 -0.165116758738
absolute error = 0.03706
relative error = 3.069 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4275
Order of pole (three term test) = 33.41 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4275
Order of pole (three term test) = 31.6 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12281.7MB, alloc=44.3MB, time=151.88
x[1] = 0.234 0.666
h = 0.001 0.003
y2[1] (numeric) = 0.177376316802 0.762692244256
y2[1] (closed_form) = 0.285223201365 0.696815654319
absolute error = 0.1264
relative error = 16.78 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.22118476956 -0.138192991447
y1[1] (closed_form) = 1.19657352245 -0.166097601157
absolute error = 0.03721
relative error = 3.08 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.034
Order of pole (three term test) = 33.41 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.034
Order of pole (three term test) = 31.6 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12327.9MB, alloc=44.3MB, time=152.45
memory used=12374.0MB, alloc=44.3MB, time=153.02
x[1] = 0.235 0.669
h = 0.0001 0.004
y2[1] (numeric) = 0.178499586027 0.767497872511
y2[1] (closed_form) = 0.286921304717 0.700241211747
absolute error = 0.1276
relative error = 16.86 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.22330211552 -0.139491896716
y1[1] (closed_form) = 1.19838303506 -0.167654344407
absolute error = 0.0376
relative error = 3.108 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.159
Order of pole (three term test) = 33.41 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.159
Order of pole (three term test) = 31.59 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12419.8MB, alloc=44.3MB, time=153.59
memory used=12465.9MB, alloc=44.3MB, time=154.16
x[1] = 0.2351 0.673
h = 0.003 0.006
y2[1] (numeric) = 0.179634472873 0.77231243415
y2[1] (closed_form) = 0.287714337178 0.705023474745
absolute error = 0.1273
relative error = 16.72 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.22636382654 -0.140285151398
y1[1] (closed_form) = 1.20116482903 -0.168873877114
absolute error = 0.03811
relative error = 3.142 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.549
Order of pole (three term test) = 33.42 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.549
Order of pole (three term test) = 31.59 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12511.6MB, alloc=44.3MB, time=154.72
memory used=12557.8MB, alloc=44.3MB, time=155.30
x[1] = 0.2381 0.679
h = 0.0001 0.005
y2[1] (numeric) = 0.180781055051 0.777135985018
y2[1] (closed_form) = 0.292347710522 0.711728183458
absolute error = 0.1293
relative error = 16.81 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.23047154696 -0.143690562449
y1[1] (closed_form) = 1.20454499492 -0.172739171907
absolute error = 0.03894
relative error = 3.2 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.698
Order of pole (three term test) = 33.42 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.698
Order of pole (three term test) = 31.58 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12603.7MB, alloc=44.3MB, time=155.87
x[1] = 0.2382 0.684
h = 0.0001 0.003
y2[1] (numeric) = 0.181939584649 0.781968572353
y2[1] (closed_form) = 0.293335874739 0.717742406252
absolute error = 0.1286
relative error = 16.58 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.23435116863 -0.144675314192
y1[1] (closed_form) = 1.20808937996 -0.174274850906
absolute error = 0.03957
relative error = 3.242 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5681
Order of pole (three term test) = 33.43 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5681
Order of pole (three term test) = 31.57 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12649.6MB, alloc=44.3MB, time=156.43
memory used=12696.0MB, alloc=44.3MB, time=157.02
x[1] = 0.2383 0.687
h = 0.001 0.001
y2[1] (numeric) = 0.183110144654 0.786810303449
y2[1] (closed_form) = 0.293981043423 0.7213523905
absolute error = 0.1288
relative error = 16.53 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.23668608226 -0.145301324644
y1[1] (closed_form) = 1.21021865477 -0.175227780203
absolute error = 0.03995
relative error = 3.267 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4488
Order of pole (three term test) = 33.44 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4488
Order of pole (three term test) = 31.57 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12742.1MB, alloc=44.3MB, time=157.58
memory used=12788.3MB, alloc=44.3MB, time=158.17
x[1] = 0.2393 0.688
h = 0.001 0.003
y2[1] (numeric) = 0.184292745892 0.791661224132
y2[1] (closed_form) = 0.295367211555 0.722387086932
absolute error = 0.1309
relative error = 16.77 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.23729161682 -0.146274260083
y1[1] (closed_form) = 1.21064585055 -0.176244323998
absolute error = 0.0401
relative error = 3.278 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.135
Order of pole (three term test) = 33.44 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.135
Order of pole (three term test) = 31.57 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12834.2MB, alloc=44.3MB, time=158.74
memory used=12880.6MB, alloc=44.3MB, time=159.34
x[1] = 0.2403 0.691
h = 0.0001 0.004
y2[1] (numeric) = 0.185487396852 0.796521340773
y2[1] (closed_form) = 0.297109944786 0.725844786474
absolute error = 0.1321
relative error = 16.85 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.2394889993 -0.147623017798
y1[1] (closed_form) = 1.21252195933 -0.177857153656
absolute error = 0.04051
relative error = 3.306 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.216
Order of pole (three term test) = 33.44 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.216
Order of pole (three term test) = 31.56 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12926.4MB, alloc=44.3MB, time=159.93
x[1] = 0.2404 0.695
h = 0.003 0.006
y2[1] (numeric) = 0.186694123857 0.801390677147
y2[1] (closed_form) = 0.297945294196 0.730682785655
absolute error = 0.1318
relative error = 16.71 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.24266621128 -0.148447272334
y1[1] (closed_form) = 1.21540525796 -0.179120088638
absolute error = 0.04104
relative error = 3.34 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.625
Order of pole (three term test) = 33.45 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.625
Order of pole (three term test) = 31.56 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=12972.1MB, alloc=44.3MB, time=160.48
memory used=13018.4MB, alloc=44.3MB, time=161.05
x[1] = 0.2434 0.701
h = 0.0001 0.005
y2[1] (numeric) = 0.18791300599 0.806269289288
y2[1] (closed_form) = 0.30268346688 0.73744236017
absolute error = 0.1338
relative error = 16.79 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.24692727891 -0.151982575209
y1[1] (closed_form) = 1.21890869438 -0.18312414312
absolute error = 0.04189
relative error = 3.399 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7325
Order of pole (three term test) = 33.46 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.7325
Order of pole (three term test) = 31.55 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13064.2MB, alloc=44.3MB, time=161.61
memory used=13110.4MB, alloc=44.3MB, time=162.18
x[1] = 0.2435 0.706
h = 0.0001 0.003
y2[1] (numeric) = 0.189144298892 0.811157223345
y2[1] (closed_form) = 0.30372513456 0.743527679381
absolute error = 0.1331
relative error = 16.57 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.25095198852 -0.153006084517
y1[1] (closed_form) = 1.22258079154 -0.184714209508
absolute error = 0.04255
relative error = 3.441 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5961
Order of pole (three term test) = 33.46 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5961
Order of pole (three term test) = 31.54 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13156.4MB, alloc=44.3MB, time=162.74
x[1] = 0.2436 0.709
h = 0.001 0.001
y2[1] (numeric) = 0.190388087348 0.816054587443
y2[1] (closed_form) = 0.30440312495 0.747180206777
absolute error = 0.1332
relative error = 16.51 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.25337382736 -0.153656740482
y1[1] (closed_form) = 1.22478644535 -0.185700936442
absolute error = 0.04294
relative error = 3.467 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4709
Order of pole (three term test) = 33.47 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4709
Order of pole (three term test) = 31.54 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13202.6MB, alloc=44.3MB, time=163.31
memory used=13248.9MB, alloc=44.3MB, time=163.88
x[1] = 0.2446 0.71
h = 0.001 0.003
y2[1] (numeric) = 0.191644382635 0.820961427927
y2[1] (closed_form) = 0.305814359858 0.748218987413
absolute error = 0.1354
relative error = 16.75 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.25400131938 -0.154666262893
y1[1] (closed_form) = 1.22522903638 -0.186753744708
absolute error = 0.0431
relative error = 3.477 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.24
Order of pole (three term test) = 33.47 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.24
Order of pole (three term test) = 31.54 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13294.9MB, alloc=44.3MB, time=164.44
memory used=13341.1MB, alloc=44.3MB, time=165.02
x[1] = 0.2456 0.713
h = 0.0001 0.004
y2[1] (numeric) = 0.192913193397 0.825877751195
y2[1] (closed_form) = 0.307603323916 0.751709999076
absolute error = 0.1366
relative error = 16.82 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.25627929803 -0.156066514924
y1[1] (closed_form) = 1.22717222056 -0.188423833642
absolute error = 0.04352
relative error = 3.505 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.276
Order of pole (three term test) = 33.47 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.276
Order of pole (three term test) = 31.53 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13386.8MB, alloc=44.3MB, time=165.58
memory used=13433.0MB, alloc=44.3MB, time=166.15
x[1] = 0.2457 0.717
h = 0.003 0.006
y2[1] (numeric) = 0.194194546461 0.830803581153
y2[1] (closed_form) = 0.308482499437 0.756605745377
absolute error = 0.1363
relative error = 16.68 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.25957330224 -0.156923560206
y1[1] (closed_form) = 1.23015804386 -0.189731419135
absolute error = 0.04406
relative error = 3.54 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.705
Order of pole (three term test) = 33.48 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.705
Order of pole (three term test) = 31.53 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13478.8MB, alloc=44.3MB, time=166.72
x[1] = 0.2487 0.723
h = 0.0001 0.005
y2[1] (numeric) = 0.195488522329 0.835738974033
y2[1] (closed_form) = 0.313329208155 0.763422162512
absolute error = 0.1383
relative error = 16.75 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.2639884037 -0.160592414475
y1[1] (closed_form) = 1.2337854143 -0.19387687591
absolute error = 0.04495
relative error = 3.599 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7683
Order of pole (three term test) = 33.49 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.7683
Order of pole (three term test) = 31.52 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13524.7MB, alloc=44.3MB, time=167.29
memory used=13570.9MB, alloc=44.3MB, time=167.86
x[1] = 0.2488 0.728
h = 0.0001 0.003
y2[1] (numeric) = 0.196795380326 0.840683974855
y2[1] (closed_form) = 0.314426273422 0.769581109641
absolute error = 0.1375
relative error = 16.53 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.26815984296 -0.1616569399
y1[1] (closed_form) = 1.23758652693 -0.195522911033
absolute error = 0.04562
relative error = 3.641 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6252
Order of pole (three term test) = 33.5 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6252
Order of pole (three term test) = 31.51 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13616.9MB, alloc=44.3MB, time=168.45
memory used=13663.2MB, alloc=44.3MB, time=169.04
x[1] = 0.2489 0.731
h = 0.001 0.001
y2[1] (numeric) = 0.198115207097 0.845638692601
y2[1] (closed_form) = 0.315138246463 0.773277687335
absolute error = 0.1376
relative error = 16.48 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.2706695791 -0.162333618589
y1[1] (closed_form) = 1.23986933524 -0.196544399873
absolute error = 0.04603
relative error = 3.667 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4939
Order of pole (three term test) = 33.5 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.4939
Order of pole (three term test) = 31.51 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13709.1MB, alloc=44.3MB, time=169.67
memory used=13755.4MB, alloc=44.3MB, time=170.30
x[1] = 0.2499 0.732
h = 0.0001 0.004
y2[1] (numeric) = 0.199448014388 0.850603174161
y2[1] (closed_form) = 0.316575433823 0.774320696654
absolute error = 0.1398
relative error = 16.71 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.27131891869 -0.163380519237
y1[1] (closed_form) = 1.24032727777 -0.197634055829
absolute error = 0.04619
relative error = 3.678 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.973
Order of pole (three term test) = 33.5 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.973
Order of pole (three term test) = 31.5 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13801.3MB, alloc=44.3MB, time=171.18
x[1] = 0.25 0.736
h = 0.003 0.006
y2[1] (numeric) = 0.200793808129 0.855577436139
y2[1] (closed_form) = 0.317492846624 0.779268319478
absolute error = 0.1394
relative error = 16.57 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.27471126466 -0.1642663075
y1[1] (closed_form) = 1.24340274838 -0.198979869842
absolute error = 0.04675
relative error = 3.712 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.776
Order of pole (three term test) = 33.51 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.776
Order of pole (three term test) = 31.5 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13847.1MB, alloc=44.3MB, time=171.74
memory used=13893.3MB, alloc=44.3MB, time=172.32
x[1] = 0.253 0.742
h = 0.0001 0.005
y2[1] (numeric) = 0.20215266446 0.860561531584
y2[1] (closed_form) = 0.322435310466 0.786136602907
absolute error = 0.1414
relative error = 16.65 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.27925526023 -0.16804934631
y1[1] (closed_form) = 1.24713907531 -0.203247740885
absolute error = 0.04765
relative error = 3.771 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8004
Order of pole (three term test) = 33.52 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.8004
Order of pole (three term test) = 31.49 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=13939.1MB, alloc=44.3MB, time=172.89
memory used=13985.3MB, alloc=44.3MB, time=173.47
x[1] = 0.2531 0.747
h = 0.0001 0.003
y2[1] (numeric) = 0.203524845982 0.865555504548
y2[1] (closed_form) = 0.323580690774 0.792361660785
absolute error = 0.1406
relative error = 16.43 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.28355026492 -0.169149840272
y1[1] (closed_form) = 1.25105301216 -0.204941701948
absolute error = 0.04834
relative error = 3.813 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6513
Order of pole (three term test) = 33.53 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6513
Order of pole (three term test) = 31.48 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14031.2MB, alloc=44.3MB, time=174.05
x[1] = 0.2532 0.75
h = 0.001 0.001
y2[1] (numeric) = 0.204910440986 0.8705594648
y2[1] (closed_form) = 0.324322314868 0.796097795764
absolute error = 0.1407
relative error = 16.37 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.28613401321 -0.169849295512
y1[1] (closed_form) = 1.25340330449 -0.205992978524
absolute error = 0.04876
relative error = 3.839 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5144
Order of pole (three term test) = 33.53 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5144
Order of pole (three term test) = 31.48 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14077.4MB, alloc=44.3MB, time=174.63
memory used=14123.7MB, alloc=44.3MB, time=175.20
x[1] = 0.2542 0.751
h = 0.001 0.003
y2[1] (numeric) = 0.206309461625 0.875573459712
y2[1] (closed_form) = 0.325782507598 0.797144881281
absolute error = 0.1429
relative error = 16.6 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.28680147 -0.17092796997
y1[1] (closed_form) = 1.2538748736 -0.207114652195
absolute error = 0.04892
relative error = 3.85 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.447
Order of pole (three term test) = 33.53 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.447
Order of pole (three term test) = 31.47 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14169.5MB, alloc=44.3MB, time=175.77
memory used=14215.7MB, alloc=44.3MB, time=176.34
x[1] = 0.2552 0.754
h = 0.0001 0.004
y2[1] (numeric) = 0.207721916842 0.880597495732
y2[1] (closed_form) = 0.327661427051 0.800701605346
absolute error = 0.1441
relative error = 16.66 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.28922870936 -0.172427098316
y1[1] (closed_form) = 1.25594492087 -0.208893739119
absolute error = 0.04937
relative error = 3.878 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.394
Order of pole (three term test) = 33.54 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.394
Order of pole (three term test) = 31.47 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14261.7MB, alloc=44.3MB, time=176.91
memory used=14307.8MB, alloc=44.3MB, time=177.48
x[1] = 0.2553 0.758
h = 0.0001 0.004
y2[1] (numeric) = 0.209147834449 0.885631597031
y2[1] (closed_form) = 0.328625539666 0.805710779413
absolute error = 0.1437
relative error = 16.52 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.2927403208 -0.173349144698
y1[1] (closed_form) = 1.25912492715 -0.210286631604
absolute error = 0.04994
relative error = 3.912 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.111
Order of pole (three term test) = 33.55 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.111
Order of pole (three term test) = 31.46 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14353.6MB, alloc=44.3MB, time=178.05
x[1] = 0.2554 0.762
h = 0.003 0.006
y2[1] (numeric) = 0.210587236713 0.890675832576
y2[1] (closed_form) = 0.329595551581 0.810732573911
absolute error = 0.1434
relative error = 16.38 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.29627194563 -0.174277425629
y1[1] (closed_form) = 1.26232489863 -0.211683893879
absolute error = 0.05051
relative error = 3.947 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.878
Order of pole (three term test) = 33.55 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.878
Order of pole (three term test) = 31.46 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14399.3MB, alloc=44.3MB, time=178.61
memory used=14445.6MB, alloc=44.3MB, time=179.20
x[1] = 0.2584 0.768
h = 0.0001 0.005
y2[1] (numeric) = 0.212040204328 0.895730269475
y2[1] (closed_form) = 0.334671736815 0.817676484628
absolute error = 0.1454
relative error = 16.45 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.30099722109 -0.178224907702
y1[1] (closed_form) = 1.26621372943 -0.216119287686
absolute error = 0.05144
relative error = 4.004 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8461
Order of pole (three term test) = 33.56 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.8461
Order of pole (three term test) = 31.45 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14491.6MB, alloc=44.3MB, time=179.77
memory used=14537.7MB, alloc=44.3MB, time=180.35
x[1] = 0.2585 0.773
h = 0.0001 0.003
y2[1] (numeric) = 0.213507004563 0.900794950535
y2[1] (closed_form) = 0.335883551278 0.823996016976
absolute error = 0.1445
relative error = 16.24 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.30546725261 -0.179378596104
y1[1] (closed_form) = 1.27028437459 -0.21787775553
absolute error = 0.05215
relative error = 4.047 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6883
Order of pole (three term test) = 33.57 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6883
Order of pole (three term test) = 31.44 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14583.6MB, alloc=44.3MB, time=180.92
memory used=14630.1MB, alloc=44.3MB, time=181.51
x[1] = 0.2586 0.776
h = 0.001 0.001
y2[1] (numeric) = 0.214987728002 0.905869986676
y2[1] (closed_form) = 0.336665971527 0.827788691023
absolute error = 0.1446
relative error = 16.18 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.30815582279 -0.18011166788
y1[1] (closed_form) = 1.2727284224 -0.21896916811
absolute error = 0.05258
relative error = 4.072 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5437
Order of pole (three term test) = 33.58 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5437
Order of pole (three term test) = 31.43 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14676.1MB, alloc=44.3MB, time=182.08
x[1] = 0.2596 0.777
h = 0.001 0.003
y2[1] (numeric) = 0.216482387364 0.910955425965
y2[1] (closed_form) = 0.338158497258 0.828842113114
absolute error = 0.1468
relative error = 16.4 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.30884850074 -0.181235813615
y1[1] (closed_form) = 1.27321932576 -0.220134895664
absolute error = 0.05275
relative error = 4.082 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.586
Order of pole (three term test) = 33.58 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.586
Order of pole (three term test) = 31.43 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14722.0MB, alloc=44.3MB, time=182.66
memory used=14768.2MB, alloc=44.3MB, time=183.23
x[1] = 0.2606 0.78
h = 0.0001 0.004
y2[1] (numeric) = 0.21799099179 0.916051274889
y2[1] (closed_form) = 0.340095966612 0.832443939954
absolute error = 0.148
relative error = 16.46 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.31137177266 -0.182801022677
y1[1] (closed_form) = 1.2753721271 -0.221982918078
absolute error = 0.05321
relative error = 4.11 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.473
Order of pole (three term test) = 33.58 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.473
Order of pole (three term test) = 31.43 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14814.0MB, alloc=44.3MB, time=183.79
memory used=14860.1MB, alloc=44.3MB, time=184.36
x[1] = 0.2607 0.784
h = 0.003 0.006
y2[1] (numeric) = 0.219513569742 0.921157557812
y2[1] (closed_form) = 0.34111449093 0.837529762931
absolute error = 0.1476
relative error = 16.32 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.31502431172 -0.183767887492
y1[1] (closed_form) = 1.27867800967 -0.223428835531
absolute error = 0.0538
relative error = 4.144 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.968
Order of pole (three term test) = 33.59 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.968
Order of pole (three term test) = 31.42 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14906.0MB, alloc=44.3MB, time=184.93
x[1] = 0.2637 0.79
h = 0.0001 0.005
y2[1] (numeric) = 0.221050206328 0.926274331681
y2[1] (closed_form) = 0.346310843919 0.844536711474
absolute error = 0.1496
relative error = 16.39 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.31990576002 -0.187860716932
y1[1] (closed_form) = 1.28269307582 -0.228014188885
absolute error = 0.05475
relative error = 4.202 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8865
Order of pole (three term test) = 33.6 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.8865
Order of pole (three term test) = 31.41 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=14952.1MB, alloc=44.3MB, time=185.51
memory used=14998.1MB, alloc=44.3MB, time=186.08
x[1] = 0.2638 0.795
h = 0.0001 0.003
y2[1] (numeric) = 0.222601172899 0.931401638049
y2[1] (closed_form) = 0.347583939952 0.850937781192
absolute error = 0.1486
relative error = 16.17 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.32452776309 -0.189062723087
y1[1] (closed_form) = 1.2868970587 -0.22983369543
absolute error = 0.05548
relative error = 4.244 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7212
Order of pole (three term test) = 33.61 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.7212
Order of pole (three term test) = 31.4 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15044.1MB, alloc=44.3MB, time=186.65
memory used=15090.4MB, alloc=44.3MB, time=187.23
x[1] = 0.2639 0.798
h = 0.001 0.001
y2[1] (numeric) = 0.224166562098 0.936539588784
y2[1] (closed_form) = 0.348403950026 0.85477921536
absolute error = 0.1487
relative error = 16.11 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.32730733399 -0.189826268054
y1[1] (closed_form) = 1.28942083297 -0.230962962143
absolute error = 0.05593
relative error = 4.269 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5697
Order of pole (three term test) = 33.61 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5697
Order of pole (three term test) = 31.4 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15136.3MB, alloc=44.3MB, time=187.80
memory used=15182.7MB, alloc=44.3MB, time=188.37
x[1] = 0.2649 0.799
h = 0.001 0.003
y2[1] (numeric) = 0.225746387162 0.941688232554
y2[1] (closed_form) = 0.349925188953 0.85583732432
absolute error = 0.151
relative error = 16.33 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.32802149174 -0.190990336344
y1[1] (closed_form) = 1.28992697687 -0.232167434898
absolute error = 0.0561
relative error = 4.28 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.71
Order of pole (three term test) = 33.62 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.71
Order of pole (three term test) = 31.4 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15228.6MB, alloc=44.3MB, time=188.93
x[1] = 0.2659 0.802
h = 0.0001 0.004
y2[1] (numeric) = 0.227340657407 0.946847575874
y2[1] (closed_form) = 0.351915591737 0.859477314253
absolute error = 0.1522
relative error = 16.38 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.33062775046 -0.192614230309
y1[1] (closed_form) = 1.29214902791 -0.234077851003
absolute error = 0.05657
relative error = 4.308 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.543
Order of pole (three term test) = 33.62 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.543
Order of pole (three term test) = 31.39 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15274.5MB, alloc=44.3MB, time=189.50
memory used=15320.6MB, alloc=44.3MB, time=190.06
x[1] = 0.266 0.806
h = 0.003 0.006
y2[1] (numeric) = 0.228949401874 0.95201764326
y2[1] (closed_form) = 0.352984278931 0.864629246913
absolute error = 0.1517
relative error = 16.25 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.33440266293 -0.19362174877
y1[1] (closed_form) = 1.29556199159 -0.235573853852
absolute error = 0.05717
relative error = 4.342 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.062
Order of pole (three term test) = 33.63 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.062
Order of pole (three term test) = 31.38 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15366.5MB, alloc=44.3MB, time=190.63
memory used=15412.7MB, alloc=44.3MB, time=191.23
x[1] = 0.269 0.812
h = 0.0001 0.005
y2[1] (numeric) = 0.230572707297 0.957198491883
y2[1] (closed_form) = 0.358304802955 0.871701216028
absolute error = 0.1537
relative error = 16.31 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.33944102645 -0.197864129253
y1[1] (closed_form) = 1.29970405426 -0.240312193705
absolute error = 0.05815
relative error = 4.399 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9287
Order of pole (three term test) = 33.64 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.9287
Order of pole (three term test) = 31.37 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15458.5MB, alloc=44.3MB, time=191.78
memory used=15504.7MB, alloc=44.3MB, time=192.35
x[1] = 0.2691 0.817
h = 0.0001 0.003
y2[1] (numeric) = 0.232210849239 0.962390162005
y2[1] (closed_form) = 0.359641253834 0.878186444601
absolute error = 0.1527
relative error = 16.1 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.3442168545 -0.199117061271
y1[1] (closed_form) = 1.30404286723 -0.242194548948
absolute error = 0.0589
relative error = 4.441 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7555
Order of pole (three term test) = 33.65 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.7555
Order of pole (three term test) = 31.36 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15550.7MB, alloc=44.3MB, time=192.91
x[1] = 0.2692 0.82
h = 0.001 0.001
y2[1] (numeric) = 0.23386392247 0.967592766476
y2[1] (closed_form) = 0.360500123486 0.882078199046
absolute error = 0.1528
relative error = 16.04 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.34708852253 -0.199912668748
y1[1] (closed_form) = 1.30664725523 -0.243362773241
absolute error = 0.05936
relative error = 4.466 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5967
Order of pole (three term test) = 33.65 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.5967
Order of pole (three term test) = 31.36 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15596.7MB, alloc=44.3MB, time=193.48
memory used=15643.0MB, alloc=44.3MB, time=194.04
x[1] = 0.2702 0.821
h = 0.001 0.003
y2[1] (numeric) = 0.235531940762 0.972806354579
y2[1] (closed_form) = 0.362051015947 0.883141122511
absolute error = 0.1551
relative error = 16.25 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.34782402449 -0.201117564079
y1[1] (closed_form) = 1.30716858953 -0.244606658384
absolute error = 0.05953
relative error = 4.477 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.838
Order of pole (three term test) = 33.65 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.838
Order of pole (three term test) = 31.36 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15688.9MB, alloc=44.3MB, time=194.60
memory used=15735.3MB, alloc=44.3MB, time=195.17
x[1] = 0.2712 0.824
h = 0.0001 0.004
y2[1] (numeric) = 0.237214913614 0.97803093286
y2[1] (closed_form) = 0.364096108541 0.886820470894
absolute error = 0.1563
relative error = 16.3 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.35051390549 -0.202802098346
y1[1] (closed_form) = 1.30946045781 -0.246580857406
absolute error = 0.06002
relative error = 4.504 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.616
Order of pole (three term test) = 33.66 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.616
Order of pole (three term test) = 31.35 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15781.1MB, alloc=44.3MB, time=195.73
x[1] = 0.2713 0.828
h = 0.003 0.006
y2[1] (numeric) = 0.238912870664 0.983266525989
y2[1] (closed_form) = 0.36521664737 0.892040612884
absolute error = 0.1558
relative error = 16.16 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.35441269047 -0.203852413696
y1[1] (closed_form) = 1.31298170976 -0.248128423675
absolute error = 0.06064
relative error = 4.538 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.159
Order of pole (three term test) = 33.67 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.159
Order of pole (three term test) = 31.34 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15827.1MB, alloc=44.3MB, time=196.28
memory used=15873.2MB, alloc=44.3MB, time=196.84
x[1] = 0.2743 0.834
h = 0.0001 0.005
y2[1] (numeric) = 0.240625900323 0.988513191372
y2[1] (closed_form) = 0.370665417487 0.899179586003
absolute error = 0.1578
relative error = 16.22 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.35960871972 -0.208248689208
y1[1] (closed_form) = 1.31725155233 -0.253022876346
absolute error = 0.06163
relative error = 4.595 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9726
Order of pole (three term test) = 33.68 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.9726
Order of pole (three term test) = 31.34 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=15919.1MB, alloc=44.3MB, time=197.40
memory used=15965.2MB, alloc=44.3MB, time=197.96
x[1] = 0.2744 0.839
h = 0.0001 0.003
y2[1] (numeric) = 0.242354282502 0.993770967931
y2[1] (closed_form) = 0.372067345001 0.90575161851
absolute error = 0.1568
relative error = 16.01 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.36454027659 -0.20955524735
y1[1] (closed_form) = 1.32172673455 -0.254969950384
absolute error = 0.06241
relative error = 4.637 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7911
Order of pole (three term test) = 33.69 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.7911
Order of pole (three term test) = 31.33 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16011.0MB, alloc=44.3MB, time=198.53
memory used=16057.5MB, alloc=44.3MB, time=199.10
x[1] = 0.2745 0.842
h = 0.001 0.001
y2[1] (numeric) = 0.24409811417 0.999039969526
y2[1] (closed_form) = 0.372966373433 0.909695267268
absolute error = 0.1568
relative error = 15.95 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.36750516769 -0.210384562533
y1[1] (closed_form) = 1.32441265124 -0.256178272267
absolute error = 0.06288
relative error = 4.661 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6249
Order of pole (three term test) = 33.7 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6249
Order of pole (three term test) = 31.32 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16103.5MB, alloc=44.3MB, time=199.66
x[1] = 0.2755 0.843
h = 0.001 0.003
y2[1] (numeric) = 0.245857409649 1.00432024608
y2[1] (closed_form) = 0.374547874408 0.910763128154
absolute error = 0.1591
relative error = 16.16 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.36826187038 -0.211631218174
y1[1] (closed_form) = 1.32494912353 -0.257462258499
absolute error = 0.06306
relative error = 4.672 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.972
Order of pole (three term test) = 33.7 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.972
Order of pole (three term test) = 31.32 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16149.5MB, alloc=44.3MB, time=200.22
memory used=16195.7MB, alloc=44.3MB, time=200.79
x[1] = 0.2765 0.846
h = 0.0001 0.004
y2[1] (numeric) = 0.247632178628 1.00961180416
y2[1] (closed_form) = 0.376649447306 0.914483035533
absolute error = 0.1603
relative error = 16.21 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.37103602213 -0.213378413769
y1[1] (closed_form) = 1.32731139356 -0.259501675023
absolute error = 0.06355
relative error = 4.699 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.692
Order of pole (three term test) = 33.7 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.692
Order of pole (three term test) = 31.31 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16241.6MB, alloc=44.3MB, time=201.34
memory used=16287.9MB, alloc=44.3MB, time=201.91
x[1] = 0.2766 0.85
h = 0.003 0.006
y2[1] (numeric) = 0.24942245136 1.01491466861
y2[1] (closed_form) = 0.37782356608 0.919773505505
absolute error = 0.1598
relative error = 16.07 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.3750602187 -0.214473744085
y1[1] (closed_form) = 1.33094217826 -0.261102331502
absolute error = 0.06419
relative error = 4.733 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.261
Order of pole (three term test) = 33.71 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.261
Order of pole (three term test) = 31.3 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16333.8MB, alloc=44.3MB, time=202.47
x[1] = 0.2796 0.856
h = 0.0001 0.005
y2[1] (numeric) = 0.251228317989 1.02022889706
y2[1] (closed_form) = 0.383404731443 0.9269814667
absolute error = 0.1618
relative error = 16.13 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.38041467148 -0.219028401031
y1[1] (closed_form) = 1.33534060599 -0.266156124286
absolute error = 0.06521
relative error = 4.789 %
Correct digits = 1
memory used=16379.9MB, alloc=44.3MB, time=203.04
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.018
Order of pole (three term test) = 33.72 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.018
Order of pole (three term test) = 31.3 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16425.8MB, alloc=44.3MB, time=203.60
x[1] = 0.2797 0.861
h = 0.0001 0.003
y2[1] (numeric) = 0.253050062909 1.02555452705
y2[1] (closed_form) = 0.384874307477 0.933642972525
absolute error = 0.1607
relative error = 15.91 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.38550391149 -0.220391379408
y1[1] (closed_form) = 1.3399537437 -0.268169848527
absolute error = 0.06601
relative error = 4.831 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8283
Order of pole (three term test) = 33.73 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.8283
Order of pole (three term test) = 31.28 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16471.7MB, alloc=44.3MB, time=204.16
memory used=16518.0MB, alloc=44.3MB, time=204.73
x[1] = 0.2798 0.864
h = 0.001 0.001
y2[1] (numeric) = 0.254887785358 1.03089167348
y2[1] (closed_form) = 0.385814824307 0.937640103926
absolute error = 0.1607
relative error = 15.85 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.38856318114 -0.221256104397
y1[1] (closed_form) = 1.34272213184 -0.269419445304
absolute error = 0.06649
relative error = 4.855 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6542
Order of pole (three term test) = 33.74 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6542
Order of pole (three term test) = 31.28 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16564.1MB, alloc=44.3MB, time=205.30
memory used=16610.4MB, alloc=44.3MB, time=205.86
x[1] = 0.2808 0.865
h = 0.0001 0.004
y2[1] (numeric) = 0.256741500229 1.03624038694
y2[1] (closed_form) = 0.387427903882 0.938713020261
absolute error = 0.1631
relative error = 16.06 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.38934093289 -0.222545482773
y1[1] (closed_form) = 1.34327368726 -0.270744243139
absolute error = 0.06667
relative error = 4.866 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.937
Order of pole (three term test) = 33.74 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.937
Order of pole (three term test) = 31.28 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16656.3MB, alloc=44.3MB, time=206.42
x[1] = 0.2809 0.869
h = 0.003 0.006
y2[1] (numeric) = 0.25861121473 1.04160068524
y2[1] (closed_form) = 0.388648685156 0.944066404719
absolute error = 0.1626
relative error = 15.92 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.39347084367 -0.223680074824
y1[1] (closed_form) = 1.34700043743 -0.272390532846
absolute error = 0.06732
relative error = 4.899 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.352
Order of pole (three term test) = 33.75 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.352
Order of pole (three term test) = 31.27 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16702.0MB, alloc=44.3MB, time=206.97
memory used=16748.2MB, alloc=44.3MB, time=207.54
x[1] = 0.2839 0.875
h = 0.0001 0.005
y2[1] (numeric) = 0.260497014252 1.04697262285
y2[1] (closed_form) = 0.394346338814 0.951336983551
absolute error = 0.1645
relative error = 15.97 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.39895789948 -0.228370248446
y1[1] (closed_form) = 1.35151216048 -0.277582597783
absolute error = 0.06836
relative error = 4.955 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.059
Order of pole (three term test) = 33.76 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.059
Order of pole (three term test) = 31.26 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16794.1MB, alloc=44.3MB, time=208.09
memory used=16840.3MB, alloc=44.3MB, time=208.66
x[1] = 0.284 0.88
h = 0.0001 0.003
y2[1] (numeric) = 0.262399187171 1.05235623609
y2[1] (closed_form) = 0.395874813522 0.958078503676
absolute error = 0.1634
relative error = 15.76 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.40418007206 -0.229782448438
y1[1] (closed_form) = 1.35624617846 -0.279653616731
absolute error = 0.06917
relative error = 4.995 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8616
Order of pole (three term test) = 33.77 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.8616
Order of pole (three term test) = 31.25 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16886.2MB, alloc=44.3MB, time=209.22
memory used=16932.6MB, alloc=44.3MB, time=209.79
x[1] = 0.2841 0.883
h = 0.001 0.001
y2[1] (numeric) = 0.264317834721 1.05775164082
y2[1] (closed_form) = 0.396851467737 0.96212347061
absolute error = 0.1634
relative error = 15.7 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.40731889521 -0.230678025144
y1[1] (closed_form) = 1.35908684304 -0.280938715146
absolute error = 0.06966
relative error = 5.019 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6805
Order of pole (three term test) = 33.78 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.6805
Order of pole (three term test) = 31.24 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=16978.5MB, alloc=44.3MB, time=210.35
x[1] = 0.2851 0.884
h = 0.001 0.003
y2[1] (numeric) = 0.266252972294 1.0631588882
y2[1] (closed_form) = 0.398492455778 0.96320122134
absolute error = 0.1658
relative error = 15.9 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.40811406546 -0.232003763451
y1[1] (closed_form) = 1.35965183365 -0.28229904936
absolute error = 0.06984
relative error = 5.03 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.237
Order of pole (three term test) = 33.78 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.237
Order of pole (three term test) = 31.24 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17024.6MB, alloc=44.3MB, time=210.92
memory used=17070.9MB, alloc=44.3MB, time=211.48
x[1] = 0.2861 0.887
h = 0.0001 0.004
y2[1] (numeric) = 0.268204609941 1.06857798487
y2[1] (closed_form) = 0.400703495076 0.967000537974
absolute error = 0.167
relative error = 15.95 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.41104444039 -0.233871313144
y1[1] (closed_form) = 1.36214753773 -0.284462941475
absolute error = 0.07036
relative error = 5.056 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.843
Order of pole (three term test) = 33.78 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.843
Order of pole (three term test) = 31.24 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17116.8MB, alloc=44.3MB, time=212.04
memory used=17163.0MB, alloc=44.3MB, time=212.60
x[1] = 0.2862 0.891
h = 0.003 0.006
y2[1] (numeric) = 0.270172779115 1.07400895598
y2[1] (closed_form) = 0.401981156144 0.972428267003
absolute error = 0.1664
relative error = 15.81 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.41530269157 -0.235055191655
y1[1] (closed_form) = 1.36598625611 -0.286165279694
absolute error = 0.07102
relative error = 5.089 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.462
Order of pole (three term test) = 33.79 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.462
Order of pole (three term test) = 31.23 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17208.8MB, alloc=44.3MB, time=213.16
x[1] = 0.2892 0.897
h = 0.0001 0.005
y2[1] (numeric) = 0.272157573325 1.07945185963
y2[1] (closed_form) = 0.407819107306 0.979771578895
absolute error = 0.1683
relative error = 15.86 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.42094957671 -0.239912362565
y1[1] (closed_form) = 1.37062816088 -0.291522954273
absolute error = 0.07208
relative error = 5.144 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.109
Order of pole (three term test) = 33.8 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.109
Order of pole (three term test) = 31.22 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17255.0MB, alloc=44.3MB, time=213.72
memory used=17301.0MB, alloc=44.3MB, time=214.28
x[1] = 0.2893 0.902
h = 0.0001 0.003
y2[1] (numeric) = 0.274159285697 1.08490673073
y2[1] (closed_form) = 0.409419378271 0.986607633921
absolute error = 0.1672
relative error = 15.65 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.42633315247 -0.241386365457
y1[1] (closed_form) = 1.37550323701 -0.293664364581
absolute error = 0.07292
relative error = 5.184 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9018
Order of pole (three term test) = 33.82 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.9018
Order of pole (three term test) = 31.2 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17346.9MB, alloc=44.3MB, time=214.84
memory used=17393.3MB, alloc=44.3MB, time=215.41
x[1] = 0.2894 0.905
h = 0.001 0.001
y2[1] (numeric) = 0.276178019869 1.09037368621
y2[1] (closed_form) = 0.410440059948 0.990709095211
absolute error = 0.1672
relative error = 15.59 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.42956855334 -0.242320631077
y1[1] (closed_form) = 1.37842821701 -0.294993018434
absolute error = 0.07341
relative error = 5.208 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7122
Order of pole (three term test) = 33.82 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.7122
Order of pole (three term test) = 31.2 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17439.2MB, alloc=44.3MB, time=215.97
memory used=17485.4MB, alloc=44.3MB, time=216.54
x[1] = 0.2904 0.906
h = 0.001 0.003
y2[1] (numeric) = 0.278213791837 1.09585277792
y2[1] (closed_form) = 0.412114472254 0.991792119412
absolute error = 0.1696
relative error = 15.79 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.43038447108 -0.243690937783
y1[1] (closed_form) = 1.37900819058 -0.29639554621
absolute error = 0.0736
relative error = 5.218 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.387
Order of pole (three term test) = 33.82 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.387
Order of pole (three term test) = 31.2 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17531.4MB, alloc=44.3MB, time=217.10
x[1] = 0.2914 0.909
h = 0.0001 0.004
y2[1] (numeric) = 0.280266611859 1.10134401254
y2[1] (closed_form) = 0.414387297787 0.995635482114
absolute error = 0.1708
relative error = 15.84 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.43340102445 -0.245627251506
y1[1] (closed_form) = 1.38157608051 -0.298629009893
absolute error = 0.07413
relative error = 5.244 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.929
Order of pole (three term test) = 33.83 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.929
Order of pole (three term test) = 31.19 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17577.3MB, alloc=44.3MB, time=217.66
memory used=17623.5MB, alloc=44.3MB, time=218.22
x[1] = 0.2915 0.913
h = 0.003 0.006
y2[1] (numeric) = 0.28233651206 1.10684741538
y2[1] (closed_form) = 0.415723687005 1.00113973237
absolute error = 0.1702
relative error = 15.7 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.43778927322 -0.246862861525
y1[1] (closed_form) = 1.38552812024 -0.300389068015
absolute error = 0.07481
relative error = 5.277 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.577
Order of pole (three term test) = 33.84 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.577
Order of pole (three term test) = 31.18 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17669.3MB, alloc=44.3MB, time=218.78
memory used=17715.5MB, alloc=44.3MB, time=219.34
x[1] = 0.2945 0.919
h = 0.0001 0.005
y2[1] (numeric) = 0.284423587839 1.11236304482
y2[1] (closed_form) = 0.421706309917 1.00855776379
absolute error = 0.1721
relative error = 15.74 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.44359676267 -0.251891945794
y1[1] (closed_form) = 1.39030107357 -0.305915877496
absolute error = 0.07589
relative error = 5.331 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.16
Order of pole (three term test) = 33.85 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.16
Order of pole (three term test) = 31.17 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17761.4MB, alloc=44.3MB, time=219.90
memory used=17807.5MB, alloc=44.3MB, time=220.46
x[1] = 0.2946 0.924
h = 0.0001 0.003
y2[1] (numeric) = 0.286528137207 1.11789093421
y2[1] (closed_form) = 0.423380701027 1.01549109722
absolute error = 0.1709
relative error = 15.54 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.44914384504 -0.253430830386
y1[1] (closed_form) = 1.39531893111 -0.308129792437
absolute error = 0.07674
relative error = 5.37 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9436
Order of pole (three term test) = 33.86 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.9436
Order of pole (three term test) = 31.16 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17853.6MB, alloc=44.3MB, time=221.03
x[1] = 0.2947 0.927
h = 0.001 0.001
y2[1] (numeric) = 0.288650266282 1.12343120161
y2[1] (closed_form) = 0.424446832053 1.01965068477
absolute error = 0.1709
relative error = 15.47 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.45247706637 -0.254405659596
y1[1] (closed_form) = 1.39832925022 -0.309503289647
absolute error = 0.07725
relative error = 5.394 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7452
Order of pole (three term test) = 33.87 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.7452
Order of pole (three term test) = 31.15 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17899.5MB, alloc=44.3MB, time=221.59
memory used=17945.9MB, alloc=44.3MB, time=222.16
x[1] = 0.2957 0.928
h = 0.001 0.003
y2[1] (numeric) = 0.290789991682 1.1289838996
y2[1] (closed_form) = 0.426155684606 1.02073908572
absolute error = 0.1733
relative error = 15.67 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.45331355422 -0.255821584773
y1[1] (closed_form) = 1.39892414409 -0.310948785691
absolute error = 0.07744
relative error = 5.404 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.545
Order of pole (three term test) = 33.87 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.545
Order of pole (three term test) = 31.15 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=17991.8MB, alloc=44.3MB, time=222.72
memory used=18038.0MB, alloc=44.3MB, time=223.28
x[1] = 0.2967 0.931
h = 0.0001 0.004
y2[1] (numeric) = 0.292947323878 1.13454903488
y2[1] (closed_form) = 0.428492228947 1.0246277167
absolute error = 0.1745
relative error = 15.71 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.45641698332 -0.257828951772
y1[1] (closed_form) = 1.40156486972 -0.313253438106
absolute error = 0.07798
relative error = 5.43 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.018
Order of pole (three term test) = 33.88 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.018
Order of pole (three term test) = 31.15 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18083.8MB, alloc=44.3MB, time=223.84
x[1] = 0.2968 0.935
h = 0.003 0.006
y2[1] (numeric) = 0.295122295688 1.14012663294
y2[1] (closed_form) = 0.429889239295 1.03021068602
absolute error = 0.1739
relative error = 15.58 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.46093692716 -0.259118818805
y1[1] (closed_form) = 1.40563162216 -0.315072940267
absolute error = 0.07867
relative error = 5.462 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.696
Order of pole (three term test) = 33.89 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.696
Order of pole (three term test) = 31.14 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18129.7MB, alloc=44.3MB, time=224.39
memory used=18175.7MB, alloc=44.3MB, time=224.95
x[1] = 0.2998 0.941
h = 0.0001 0.005
y2[1] (numeric) = 0.297315004459 1.14571675242
y2[1] (closed_form) = 0.436020991588 1.03770542376
absolute error = 0.1758
relative error = 15.62 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.46690579957 -0.264324883708
y1[1] (closed_form) = 1.41053651121 -0.320772517585
absolute error = 0.07977
relative error = 5.515 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.214
Order of pole (three term test) = 33.9 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.214
Order of pole (three term test) = 31.13 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18221.6MB, alloc=44.3MB, time=225.51
memory used=18267.8MB, alloc=44.3MB, time=226.07
x[1] = 0.2999 0.946
h = 0.0001 0.003
y2[1] (numeric) = 0.299525753231 1.15131942507
y2[1] (closed_form) = 0.437771883213 1.04473880616
absolute error = 0.1746
relative error = 15.41 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.47261854287 -0.265931829752
y1[1] (closed_form) = 1.41569892158 -0.323061116788
absolute error = 0.08064
relative error = 5.554 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9873
Order of pole (three term test) = 33.91 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.9873
Order of pole (three term test) = 31.11 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18313.7MB, alloc=44.3MB, time=226.63
memory used=18360.1MB, alloc=44.3MB, time=227.20
x[1] = 0.3 0.949
h = 0.001 0.001
y2[1] (numeric) = 0.301754650675 1.15693477013
y2[1] (closed_form) = 0.438884919749 1.04895816779
absolute error = 0.1745
relative error = 15.35 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.47605085712 -0.266949158421
y1[1] (closed_form) = 1.41879563195 -0.324480785622
absolute error = 0.08117
relative error = 5.577 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7797
Order of pole (three term test) = 33.92 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.7797
Order of pole (three term test) = 31.11 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18405.9MB, alloc=44.3MB, time=227.77
x[1] = 0.301 0.95
h = 0.001 0.003
y2[1] (numeric) = 0.304001714055 1.16256284089
y2[1] (closed_form) = 0.44062924549 1.05005204317
absolute error = 0.177
relative error = 15.54 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.4769077282 -0.268411782834
y1[1] (closed_form) = 1.41940538022 -0.325970047709
absolute error = 0.08136
relative error = 5.587 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.708
Order of pole (three term test) = 33.92 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.708
Order of pole (three term test) = 31.11 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18451.9MB, alloc=44.3MB, time=228.33
memory used=18498.1MB, alloc=44.3MB, time=228.89
x[1] = 0.302 0.953
h = 0.0001 0.004
y2[1] (numeric) = 0.306266954057 1.16820364409
y2[1] (closed_form) = 0.44303148082 1.05398717043
absolute error = 0.1782
relative error = 15.58 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.48009874192 -0.270492563469
y1[1] (closed_form) = 1.42211960806 -0.328347555463
absolute error = 0.08191
relative error = 5.612 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.111
Order of pole (three term test) = 33.93 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.111
Order of pole (three term test) = 31.1 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18543.9MB, alloc=44.3MB, time=229.45
memory used=18590.0MB, alloc=44.3MB, time=230.01
x[1] = 0.3021 0.957
h = 0.003 0.006
y2[1] (numeric) = 0.308550404216 1.1738572054
y2[1] (closed_form) = 0.444491051273 1.05965107841
absolute error = 0.1775
relative error = 15.45 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.48475211864 -0.271839295046
y1[1] (closed_form) = 1.42630250298 -0.330228279655
absolute error = 0.08262
relative error = 5.643 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.82
Order of pole (three term test) = 33.94 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.82
Order of pole (three term test) = 31.09 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18635.8MB, alloc=44.3MB, time=230.56
memory used=18682.1MB, alloc=44.3MB, time=231.13
x[1] = 0.3051 0.963
h = 0.0001 0.005
y2[1] (numeric) = 0.310852163884 1.17952358372
y2[1] (closed_form) = 0.450776476458 1.06722450947
absolute error = 0.1794
relative error = 15.49 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.49088315536 -0.277227561497
y1[1] (closed_form) = 1.43134023474 -0.336104367285
absolute error = 0.08374
relative error = 5.695 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.27
Order of pole (three term test) = 33.95 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.27
Order of pole (three term test) = 31.08 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18728.0MB, alloc=44.3MB, time=231.68
x[1] = 0.3052 0.968
h = 0.0001 0.003
y2[1] (numeric) = 0.313172541276 1.18520280917
y2[1] (closed_form) = 0.452606307179 1.07436073918
absolute error = 0.1781
relative error = 15.28 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.49676376489 -0.278905851677
y1[1] (closed_form) = 1.43664901787 -0.338469898138
absolute error = 0.08463
relative error = 5.734 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.033
Order of pole (three term test) = 33.96 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.033
Order of pole (three term test) = 31.07 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18773.8MB, alloc=44.3MB, time=232.24
memory used=18820.2MB, alloc=44.3MB, time=232.81
x[1] = 0.3053 0.971
h = 0.001 0.001
y2[1] (numeric) = 0.315511647693 1.19089500216
y2[1] (closed_form) = 0.453767740715 1.07864153901
absolute error = 0.1781
relative error = 15.22 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.5002964743 -0.279967678057
y1[1] (closed_form) = 1.43983320027 -0.339937108066
absolute error = 0.08516
relative error = 5.756 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8157
Order of pole (three term test) = 33.97 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.8157
Order of pole (three term test) = 31.06 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18866.3MB, alloc=44.3MB, time=233.38
memory used=18912.7MB, alloc=44.3MB, time=233.94
x[1] = 0.3063 0.972
h = 0.0001 0.004
y2[1] (numeric) = 0.317869501064 1.19660021674
y2[1] (closed_form) = 0.455548590031 1.07974098074
absolute error = 0.1806
relative error = 15.41 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.50117353181 -0.281478113593
y1[1] (closed_form) = 1.44045773362 -0.341470957387
absolute error = 0.08536
relative error = 5.766 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.908
Order of pole (three term test) = 33.97 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.908
Order of pole (three term test) = 31.06 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=18958.5MB, alloc=44.3MB, time=234.50
x[1] = 0.3064 0.976
h = 0.003 0.006
y2[1] (numeric) = 0.320246109823 1.2023184719
y2[1] (closed_form) = 0.457062598435 1.08547712996
absolute error = 0.1799
relative error = 15.28 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.50593945921 -0.282874284385
y1[1] (closed_form) = 1.4447425337 -0.343404437807
absolute error = 0.08608
relative error = 5.796 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.932
Order of pole (three term test) = 33.98 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.932
Order of pole (three term test) = 31.05 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19004.5MB, alloc=44.3MB, time=235.05
memory used=19050.7MB, alloc=44.3MB, time=235.62
x[1] = 0.3094 0.982
h = 0.0001 0.005
y2[1] (numeric) = 0.322641568185 1.20804982331
y2[1] (closed_form) = 0.463483036279 1.09312179461
absolute error = 0.1818
relative error = 15.31 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.51220623077 -0.288418487084
y1[1] (closed_form) = 1.44989751851 -0.349433944067
absolute error = 0.08721
relative error = 5.847 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.32
Order of pole (three term test) = 34 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.32
Order of pole (three term test) = 31.04 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19096.6MB, alloc=44.3MB, time=236.18
memory used=19142.7MB, alloc=44.3MB, time=236.74
x[1] = 0.3095 0.987
h = 0.0001 0.003
y2[1] (numeric) = 0.325056188949 1.21379429968
y2[1] (closed_form) = 0.46538154263 1.10034979538
absolute error = 0.1804
relative error = 15.1 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.51822845086 -0.29015881555
y1[1] (closed_form) = 1.45533474314 -0.351865773576
absolute error = 0.08811
relative error = 5.885 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.074
Order of pole (three term test) = 34.01 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.074
Order of pole (three term test) = 31.02 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19188.6MB, alloc=44.3MB, time=237.30
memory used=19235.0MB, alloc=44.3MB, time=237.87
x[1] = 0.3096 0.99
h = 0.001 0.001
y2[1] (numeric) = 0.327490085728 1.2195520225
y2[1] (closed_form) = 0.466585097655 1.10468542586
absolute error = 0.1804
relative error = 15.04 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.52184583987 -0.291259297345
y1[1] (closed_form) = 1.45859569527 -0.353373974005
absolute error = 0.08865
relative error = 5.907 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8479
Order of pole (three term test) = 34.02 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.8479
Order of pole (three term test) = 31.01 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19281.0MB, alloc=44.3MB, time=238.43
x[1] = 0.3106 0.991
h = 0.001 0.003
y2[1] (numeric) = 0.329943277032 1.22532304648
y2[1] (closed_form) = 0.468398172378 1.10579018039
absolute error = 0.1829
relative error = 15.23 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.52273956122 -0.292810448844
y1[1] (closed_form) = 1.4592334417 -0.354946703337
absolute error = 0.08885
relative error = 5.916 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.033
Order of pole (three term test) = 34.02 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.033
Order of pole (three term test) = 31.01 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19326.9MB, alloc=44.3MB, time=238.99
memory used=19373.1MB, alloc=44.3MB, time=239.56
x[1] = 0.3116 0.994
h = 0.0001 0.004
y2[1] (numeric) = 0.332415773969 1.23110737843
y2[1] (closed_form) = 0.470927444286 1.10981595482
absolute error = 0.1841
relative error = 15.27 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.52609302562 -0.295032196693
y1[1] (closed_form) = 1.46208718745 -0.357463491725
absolute error = 0.08941
relative error = 5.94 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.296
Order of pole (three term test) = 34.03 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.296
Order of pole (three term test) = 31.01 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19419.1MB, alloc=44.3MB, time=240.12
memory used=19465.2MB, alloc=44.3MB, time=240.68
x[1] = 0.3117 0.998
h = 0.003 0.006
y2[1] (numeric) = 0.334907611457 1.23690504439
y2[1] (closed_form) = 0.472507720945 1.11563725712
absolute error = 0.1834
relative error = 15.14 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.53099568 -0.296490237521
y1[1] (closed_form) = 1.46649091638 -0.35946163176
absolute error = 0.09015
relative error = 5.97 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.067
Order of pole (three term test) = 34.04 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.067
Order of pole (three term test) = 31 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19511.0MB, alloc=44.3MB, time=241.24
memory used=19557.2MB, alloc=44.3MB, time=241.80
x[1] = 0.3147 1.004
h = 0.0001 0.005
y2[1] (numeric) = 0.337418892736 1.24271610375
y2[1] (closed_form) = 0.479090499715 1.12336436903
absolute error = 0.1852
relative error = 15.17 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.53742605189 -0.302226635606
y1[1] (closed_form) = 1.47178053067 -0.365674899012
absolute error = 0.0913
relative error = 6.02 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.381
Order of pole (three term test) = 34.05 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.381
Order of pole (three term test) = 30.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19603.1MB, alloc=44.3MB, time=242.36
x[1] = 0.3148 1.009
h = 0.0001 0.003
y2[1] (numeric) = 0.339949936065 1.24854058352
y2[1] (closed_form) = 0.481072609644 1.13070053128
absolute error = 0.1839
relative error = 14.96 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.54362031971 -0.304044612126
y1[1] (closed_form) = 1.47736767334 -0.368188004331
absolute error = 0.09222
relative error = 6.057 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.123
Order of pole (three term test) = 34.06 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.123
Order of pole (three term test) = 30.97 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19648.9MB, alloc=44.3MB, time=242.92
memory used=19695.3MB, alloc=44.3MB, time=243.49
x[1] = 0.3149 1.012
h = 0.001 0.001
y2[1] (numeric) = 0.342500857835 1.2543786064
y2[1] (closed_form) = 0.482327414374 1.13510076014
absolute error = 0.1838
relative error = 14.9 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.54734057273 -0.30519342919
y1[1] (closed_form) = 1.48071820284 -0.369746393097
absolute error = 0.09277
relative error = 6.078 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8868
Order of pole (three term test) = 34.07 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.8868
Order of pole (three term test) = 30.96 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19741.2MB, alloc=44.3MB, time=244.05
memory used=19787.5MB, alloc=44.3MB, time=244.62
x[1] = 0.3159 1.013
h = 0.001 0.003
y2[1] (numeric) = 0.345071677261 1.2602302279
y2[1] (closed_form) = 0.484179014441 1.13621124901
absolute error = 0.1864
relative error = 15.09 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.5482540914 -0.306794517083
y1[1] (closed_form) = 1.4813706059 -0.371365302207
absolute error = 0.09297
relative error = 6.087 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.218
Order of pole (three term test) = 34.07 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.218
Order of pole (three term test) = 30.96 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19833.5MB, alloc=44.3MB, time=245.18
x[1] = 0.3169 1.016
h = 0.0001 0.004
y2[1] (numeric) = 0.347662405686 1.26609545487
y2[1] (closed_form) = 0.486779833842 1.14028709067
absolute error = 0.1876
relative error = 15.13 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.55169721114 -0.309096774933
y1[1] (closed_form) = 1.48429987333 -0.373959986455
absolute error = 0.09354
relative error = 6.111 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.401
Order of pole (three term test) = 34.08 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.401
Order of pole (three term test) = 30.96 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19879.6MB, alloc=44.3MB, time=245.74
memory used=19925.7MB, alloc=44.3MB, time=246.30
x[1] = 0.317 1.02
h = 0.003 0.006
y2[1] (numeric) = 0.350273078806 1.27197431354
y2[1] (closed_form) = 0.48842845687 1.14619583156
absolute error = 0.1868
relative error = 15 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.55673844952 -0.310619542622
y1[1] (closed_form) = 1.48882407287 -0.37602472413
absolute error = 0.09429
relative error = 6.14 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.208
Order of pole (three term test) = 34.09 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.208
Order of pole (three term test) = 30.95 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=19971.5MB, alloc=44.3MB, time=246.85
memory used=20017.7MB, alloc=44.3MB, time=247.42
x[1] = 0.32 1.026
h = 0.0001 0.005
y2[1] (numeric) = 0.352903802036 1.27786686357
y2[1] (closed_form) = 0.495178379905 1.15400737847
absolute error = 0.1886
relative error = 15.02 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.56333320593 -0.316553821502
y1[1] (closed_form) = 1.49424927924 -0.382425818777
absolute error = 0.09546
relative error = 6.189 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.444
Order of pole (three term test) = 34.11 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.444
Order of pole (three term test) = 30.93 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20063.6MB, alloc=44.3MB, time=247.98
memory used=20109.8MB, alloc=44.3MB, time=248.54
x[1] = 0.3201 1.031
h = 0.0001 0.003
y2[1] (numeric) = 0.35555489924 1.28377313016
y2[1] (closed_form) = 0.497246708025 1.16145458467
absolute error = 0.1872
relative error = 14.82 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.56970187741 -0.31845304161
y1[1] (closed_form) = 1.49998830116 -0.385022648709
absolute error = 0.09639
relative error = 6.224 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.174
Order of pole (three term test) = 34.12 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.174
Order of pole (three term test) = 30.92 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20155.9MB, alloc=44.3MB, time=249.10
x[1] = 0.3202 1.034
h = 0.001 0.001
y2[1] (numeric) = 0.358226489668 1.28969323727
y2[1] (closed_form) = 0.498554360765 1.16592112543
absolute error = 0.1871
relative error = 14.76 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.57352638459 -0.319652381769
y1[1] (closed_form) = 1.50342957217 -0.386632717719
absolute error = 0.09695
relative error = 6.246 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9274
Order of pole (three term test) = 34.13 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.9274
Order of pole (three term test) = 30.91 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20201.9MB, alloc=44.3MB, time=249.68
memory used=20248.2MB, alloc=44.3MB, time=250.25
x[1] = 0.3212 1.035
h = 0.001 0.003
y2[1] (numeric) = 0.360918593261 1.29562724124
y2[1] (closed_form) = 0.500445589348 1.1670374231
absolute error = 0.1897
relative error = 14.94 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.57445947284 -0.321304611682
y1[1] (closed_form) = 1.50409655175 -0.388298696857
absolute error = 0.09716
relative error = 6.254 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.411
Order of pole (three term test) = 34.13 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.411
Order of pole (three term test) = 30.91 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20294.2MB, alloc=44.3MB, time=250.81
memory used=20340.4MB, alloc=44.3MB, time=251.38
x[1] = 0.3222 1.038
h = 0.0001 0.004
y2[1] (numeric) = 0.363631221603 1.30157514894
y2[1] (closed_form) = 0.503120092573 1.1711645837
absolute error = 0.191
relative error = 14.98 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.57799299975 -0.323690031305
y1[1] (closed_form) = 1.50710207125 -0.390973143098
absolute error = 0.09774
relative error = 6.277 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.511
Order of pole (three term test) = 34.14 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.511
Order of pole (three term test) = 30.9 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20386.2MB, alloc=44.3MB, time=251.93
x[1] = 0.3223 1.042
h = 0.003 0.006
y2[1] (numeric) = 0.366364411192 1.30753698679
y2[1] (closed_form) = 0.504839191638 1.17716307263
absolute error = 0.1902
relative error = 14.85 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.58317471976 -0.325280471201
y1[1] (closed_form) = 1.51174832255 -0.393106474897
absolute error = 0.0985
relative error = 6.306 %
Correct digits = 1
memory used=20432.3MB, alloc=44.3MB, time=252.49
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.354
Order of pole (three term test) = 34.15 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.354
Order of pole (three term test) = 30.89 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20478.3MB, alloc=44.3MB, time=253.05
x[1] = 0.3253 1.048
h = 0.0001 0.005
y2[1] (numeric) = 0.369118269681 1.31351281473
y2[1] (closed_form) = 0.511761158173 1.18506104181
absolute error = 0.192
relative error = 14.87 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.58993464336 -0.331418480032
y1[1] (closed_form) = 1.51731010164 -0.399699580598
absolute error = 0.09968
relative error = 6.353 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.51
Order of pole (three term test) = 34.16 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.51
Order of pole (three term test) = 30.88 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20524.2MB, alloc=44.3MB, time=253.61
memory used=20570.2MB, alloc=44.3MB, time=254.17
x[1] = 0.3254 1.053
h = 0.0001 0.003
y2[1] (numeric) = 0.371893126689 1.3195026561
y2[1] (closed_form) = 0.513918384301 1.19262220492
absolute error = 0.1904
relative error = 14.67 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.59648012578 -0.333402650388
y1[1] (closed_form) = 1.52320301373 -0.402382657538
absolute error = 0.1006
relative error = 6.388 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.228
Order of pole (three term test) = 34.18 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.228
Order of pole (three term test) = 30.87 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20616.2MB, alloc=44.3MB, time=254.73
memory used=20662.5MB, alloc=44.3MB, time=255.30
x[1] = 0.3255 1.056
h = 0.001 0.001
y2[1] (numeric) = 0.374689104412 1.32550663614
y2[1] (closed_form) = 0.515280522917 1.19715678901
absolute error = 0.1904
relative error = 14.61 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.60041030723 -0.334654768797
y1[1] (closed_form) = 1.52673621971 -0.404045943426
absolute error = 0.1012
relative error = 6.408 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9698
Order of pole (three term test) = 34.19 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 0.9698
Order of pole (three term test) = 30.86 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20708.5MB, alloc=44.3MB, time=255.86
x[1] = 0.3265 1.057
h = 0.001 0.003
y2[1] (numeric) = 0.377506223536 1.33152481202
y2[1] (closed_form) = 0.517212502611 1.19827896336
absolute error = 0.1931
relative error = 14.79 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.60136272587 -0.33635937924
y1[1] (closed_form) = 1.52741769136 -0.405759907701
absolute error = 0.1014
relative error = 6.417 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.612
Order of pole (three term test) = 34.19 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.612
Order of pole (three term test) = 30.86 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20754.5MB, alloc=44.3MB, time=256.42
memory used=20800.9MB, alloc=44.3MB, time=257.00
x[1] = 0.3275 1.06
h = 0.0001 0.004
y2[1] (numeric) = 0.380344495897 1.33755719065
y2[1] (closed_form) = 0.519962871554 1.20245870083
absolute error = 0.1943
relative error = 14.83 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.60498742173 -0.338830689844
y1[1] (closed_form) = 1.53050020949 -0.408516036216
absolute error = 0.102
relative error = 6.439 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.626
Order of pole (three term test) = 34.2 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.626
Order of pole (three term test) = 30.85 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20846.8MB, alloc=44.3MB, time=257.55
memory used=20892.8MB, alloc=44.3MB, time=258.12
x[1] = 0.3276 1.064
h = 0.003 0.006
y2[1] (numeric) = 0.383203958814 1.34360379866
y2[1] (closed_form) = 0.521754629387 1.20854927172
absolute error = 0.1935
relative error = 14.7 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.61031156171 -0.340491837614
y1[1] (closed_form) = 1.53527013335 -0.410720018362
absolute error = 0.1028
relative error = 6.467 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.507
Order of pole (three term test) = 34.21 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.507
Order of pole (three term test) = 30.84 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=20938.6MB, alloc=44.3MB, time=258.68
memory used=20984.8MB, alloc=44.3MB, time=259.25
x[1] = 0.3306 1.07
h = 0.0001 0.005
y2[1] (numeric) = 0.386084722241 1.34966469626
y2[1] (closed_form) = 0.528853637249 1.21653564971
absolute error = 0.1952
relative error = 14.72 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.61723743239 -0.346839592094
y1[1] (closed_form) = 1.54096948326 -0.417509438169
absolute error = 0.104
relative error = 6.513 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.579
Order of pole (three term test) = 34.22 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.579
Order of pole (three term test) = 30.83 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21030.7MB, alloc=44.3MB, time=259.81
x[1] = 0.3307 1.075
h = 0.0001 0.003
y2[1] (numeric) = 0.388987121711 1.35573990483
y2[1] (closed_form) = 0.531102508312 1.22421371394
absolute error = 0.1936
relative error = 14.51 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.62396218449 -0.348912532757
y1[1] (closed_form) = 1.5470183465 -0.420281359725
absolute error = 0.1049
relative error = 6.547 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.284
Order of pole (three term test) = 34.24 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.284
Order of pole (three term test) = 30.81 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21076.7MB, alloc=44.3MB, time=260.36
memory used=21123.1MB, alloc=44.3MB, time=260.94
x[1] = 0.3308 1.078
h = 0.001 0.001
y2[1] (numeric) = 0.391911282448 1.36182955097
y2[1] (closed_form) = 0.532520811379 1.22881809111
absolute error = 0.1936
relative error = 14.45 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.62799949032 -0.350219753271
y1[1] (closed_form) = 1.55064471041 -0.421999444826
absolute error = 0.1055
relative error = 6.567 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.014
Order of pole (three term test) = 34.25 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.014
Order of pole (three term test) = 30.8 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21168.9MB, alloc=44.3MB, time=261.50
memory used=21215.3MB, alloc=44.3MB, time=262.07
x[1] = 0.3318 1.079
h = 0.0001 0.004
y2[1] (numeric) = 0.394857225907 1.36793369267
y2[1] (closed_form) = 0.534494684729 1.2299462032
absolute error = 0.1963
relative error = 14.64 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.62897098829 -0.351978016123
y1[1] (closed_form) = 1.5513405851 -0.423762334605
absolute error = 0.1057
relative error = 6.575 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.102
Order of pole (three term test) = 34.25 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.102
Order of pole (three term test) = 30.8 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21261.1MB, alloc=44.3MB, time=262.63
x[1] = 0.3319 1.083
h = 0.003 0.006
y2[1] (numeric) = 0.397824961944 1.37405235027
y2[1] (closed_form) = 0.536349639149 1.23611882512
absolute error = 0.1955
relative error = 14.51 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.6344153216 -0.353700472412
y1[1] (closed_form) = 1.55621916659 -0.426027323161
absolute error = 0.1065
relative error = 6.602 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.645
Order of pole (three term test) = 34.27 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.645
Order of pole (three term test) = 30.79 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21307.1MB, alloc=44.3MB, time=263.18
memory used=21353.2MB, alloc=44.3MB, time=263.75
x[1] = 0.3349 1.089
h = 0.0001 0.005
y2[1] (numeric) = 0.400814594918 1.38018558071
y2[1] (closed_form) = 0.543604032401 1.2441850843
absolute error = 0.1972
relative error = 14.52 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.64148007429 -0.360227733303
y1[1] (closed_form) = 1.5620401556 -0.432987606916
absolute error = 0.1077
relative error = 6.646 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.641
Order of pole (three term test) = 34.28 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.641
Order of pole (three term test) = 30.78 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21399.0MB, alloc=44.3MB, time=264.30
memory used=21445.2MB, alloc=44.3MB, time=264.87
x[1] = 0.335 1.094
h = 0.0001 0.003
y2[1] (numeric) = 0.403826465589 1.38633340372
y2[1] (closed_form) = 0.545932599855 1.2519672926
absolute error = 0.1956
relative error = 14.32 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.64835613378 -0.362377652472
y1[1] (closed_form) = 1.56822604706 -0.435836249668
absolute error = 0.1087
relative error = 6.679 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.334
Order of pole (three term test) = 34.3 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.334
Order of pole (three term test) = 30.76 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21491.2MB, alloc=44.3MB, time=265.43
memory used=21537.6MB, alloc=44.3MB, time=266.00
x[1] = 0.3351 1.097
h = 0.001 0.001
y2[1] (numeric) = 0.406860701842 1.39249594708
y2[1] (closed_form) = 0.547399763428 1.25663385777
absolute error = 0.1955
relative error = 14.26 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.65248383994 -0.363732618972
y1[1] (closed_form) = 1.57193427948 -0.437601676763
absolute error = 0.1093
relative error = 6.698 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.054
Order of pole (three term test) = 34.31 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.054
Order of pole (three term test) = 30.75 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21583.7MB, alloc=44.3MB, time=266.56
x[1] = 0.3361 1.098
h = 0.001 0.003
y2[1] (numeric) = 0.409917325803 1.39867326955
y2[1] (closed_form) = 0.549410556397 1.25776764231
absolute error = 0.1983
relative error = 14.45 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.65347103617 -0.365536589497
y1[1] (closed_form) = 1.57264307537 -0.439407282554
absolute error = 0.1095
relative error = 6.706 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.011
Order of pole (three term test) = 34.31 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.011
Order of pole (three term test) = 30.75 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21629.6MB, alloc=44.3MB, time=267.13
memory used=21675.8MB, alloc=44.3MB, time=267.69
x[1] = 0.3371 1.101
h = 0.0001 0.004
y2[1] (numeric) = 0.412996349793 1.40486537814
y2[1] (closed_form) = 0.552307400403 1.2620495499
absolute error = 0.1995
relative error = 14.48 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.65726488547 -0.368172722497
y1[1] (closed_form) = 1.57587194149 -0.44231976453
absolute error = 0.1101
relative error = 6.727 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.853
Order of pole (three term test) = 34.32 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.853
Order of pole (three term test) = 30.74 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21721.7MB, alloc=44.3MB, time=268.25
memory used=21767.9MB, alloc=44.3MB, time=268.82
x[1] = 0.3372 1.105
h = 0.003 0.006
y2[1] (numeric) = 0.416097812718 1.41107229985
y2[1] (closed_form) = 0.55423919315 1.26831869129
absolute error = 0.1986
relative error = 14.35 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.66285530136 -0.369971700096
y1[1] (closed_form) = 1.58087734412 -0.444659372678
absolute error = 0.1109
relative error = 6.753 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.811
Order of pole (three term test) = 34.33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.811
Order of pole (three term test) = 30.73 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21813.7MB, alloc=44.3MB, time=269.38
memory used=21859.9MB, alloc=44.3MB, time=269.94
x[1] = 0.3402 1.111
h = 0.0001 0.005
y2[1] (numeric) = 0.419221828986 1.41729409544
y2[1] (closed_form) = 0.561680175729 1.27647711538
absolute error = 0.2003
relative error = 14.36 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.67008741933 -0.376720193533
y1[1] (closed_form) = 1.58683786057 -0.451824290492
absolute error = 0.1121
relative error = 6.796 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.715
Order of pole (three term test) = 34.34 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.715
Order of pole (three term test) = 30.72 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21905.8MB, alloc=44.3MB, time=270.50
x[1] = 0.3403 1.116
h = 0.0001 0.003
y2[1] (numeric) = 0.422368745578 1.42353078258
y2[1] (closed_form) = 0.564105648802 1.28438182348
absolute error = 0.1986
relative error = 14.16 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.67714739596 -0.378966201503
y1[1] (closed_form) = 1.59318370566 -0.454766791343
absolute error = 0.1131
relative error = 6.827 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.395
Order of pole (three term test) = 34.36 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.395
Order of pole (three term test) = 30.7 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=21951.6MB, alloc=44.3MB, time=271.06
memory used=21998.1MB, alloc=44.3MB, time=271.63
x[1] = 0.3404 1.119
h = 0.001 0.001
y2[1] (numeric) = 0.425538693567 1.42978249042
y2[1] (closed_form) = 0.565632191275 1.28912150893
absolute error = 0.1985
relative error = 14.1 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.68138496692 -0.380380722438
y1[1] (closed_form) = 1.59698747101 -0.456590071714
absolute error = 0.1137
relative error = 6.846 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.102
Order of pole (three term test) = 34.37 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.102
Order of pole (three term test) = 30.69 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22044.1MB, alloc=44.3MB, time=272.20
memory used=22090.5MB, alloc=44.3MB, time=272.76
x[1] = 0.3414 1.12
h = 0.001 0.003
y2[1] (numeric) = 0.428731695895 1.43604927864
y2[1] (closed_form) = 0.567687058319 1.29026134001
absolute error = 0.2014
relative error = 14.29 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.68239074827 -0.382240770339
y1[1] (closed_form) = 1.59771050312 -0.458446422643
absolute error = 0.1139
relative error = 6.854 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.239
Order of pole (three term test) = 34.37 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.239
Order of pole (three term test) = 30.69 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22136.3MB, alloc=44.3MB, time=273.32
x[1] = 0.3424 1.123
h = 0.0001 0.004
y2[1] (numeric) = 0.431947765152 1.44233115427
y2[1] (closed_form) = 0.570666257927 1.29459948589
absolute error = 0.2027
relative error = 14.32 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.68627797734 -0.384970972718
y1[1] (closed_form) = 1.60101861699 -0.461446379376
absolute error = 0.1145
relative error = 6.874 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.983
Order of pole (three term test) = 34.38 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.983
Order of pole (three term test) = 30.69 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22182.4MB, alloc=44.3MB, time=273.88
memory used=22228.3MB, alloc=44.3MB, time=274.44
x[1] = 0.3425 1.127
h = 0.003 0.006
y2[1] (numeric) = 0.435186941134 1.44862814451
y2[1] (closed_form) = 0.572677231824 1.30096755446
absolute error = 0.2018
relative error = 14.19 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.69201653435 -0.38684978226
y1[1] (closed_form) = 1.60615257722 -0.463862841145
absolute error = 0.1153
relative error = 6.899 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.984
Order of pole (three term test) = 34.4 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.984
Order of pole (three term test) = 30.67 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22274.2MB, alloc=44.3MB, time=275.00
memory used=22320.4MB, alloc=44.3MB, time=275.56
x[1] = 0.3455 1.133
h = 0.0001 0.005
y2[1] (numeric) = 0.438449340737 1.45494031043
y2[1] (closed_form) = 0.580310098932 1.30922012769
absolute error = 0.2034
relative error = 14.2 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.69941678355 -0.393826028296
y1[1] (closed_form) = 1.61225366766 -0.471237049766
absolute error = 0.1166
relative error = 6.94 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.793
Order of pole (three term test) = 34.41 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.793
Order of pole (three term test) = 30.66 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22366.3MB, alloc=44.3MB, time=276.12
memory used=22412.4MB, alloc=44.3MB, time=276.68
x[1] = 0.3456 1.138
h = 0.0001 0.003
y2[1] (numeric) = 0.441735317314 1.46126766752
y2[1] (closed_form) = 0.582835426971 1.31725037387
absolute error = 0.2016
relative error = 14 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.70666328811 -0.396172290344
y1[1] (closed_form) = 1.61876167334 -0.474276230234
absolute error = 0.1176
relative error = 6.971 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.458
Order of pole (three term test) = 34.43 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.458
Order of pole (three term test) = 30.64 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22458.5MB, alloc=44.3MB, time=277.24
x[1] = 0.3457 1.141
h = 0.001 0.001
y2[1] (numeric) = 0.445045005219 1.46761034638
y2[1] (closed_form) = 0.584423149707 1.3220649845
absolute error = 0.2015
relative error = 13.94 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.71101226247 -0.397648898668
y1[1] (closed_form) = 1.62266228062 -0.476159082261
absolute error = 0.1182
relative error = 6.989 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.152
Order of pole (three term test) = 34.44 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.152
Order of pole (three term test) = 30.63 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22504.6MB, alloc=44.3MB, time=277.80
memory used=22551.0MB, alloc=44.3MB, time=278.38
x[1] = 0.3467 1.142
h = 0.001 0.003
y2[1] (numeric) = 0.448378428231 1.47396840757
y2[1] (closed_form) = 0.586523293517 1.32321090258
absolute error = 0.2045
relative error = 14.13 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.71203634082 -0.399566396501
y1[1] (closed_form) = 1.62339944566 -0.478067193304
absolute error = 0.1184
relative error = 6.996 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.477
Order of pole (three term test) = 34.44 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.477
Order of pole (three term test) = 30.63 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22596.9MB, alloc=44.3MB, time=278.94
memory used=22643.2MB, alloc=44.3MB, time=279.51
x[1] = 0.3477 1.145
h = 0.0001 0.004
y2[1] (numeric) = 0.451735599218 1.48034185818
y2[1] (closed_form) = 0.589587218744 1.32760656979
absolute error = 0.2057
relative error = 14.16 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.71601774734 -0.402393715451
y1[1] (closed_form) = 1.6267876159 -0.481156764054
absolute error = 0.119
relative error = 7.016 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.118
Order of pole (three term test) = 34.45 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.118
Order of pole (three term test) = 30.63 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22689.1MB, alloc=44.3MB, time=280.07
memory used=22735.2MB, alloc=44.3MB, time=280.63
x[1] = 0.3478 1.149
h = 0.003 0.006
y2[1] (numeric) = 0.455116558891 1.48673072561
y2[1] (closed_form) = 0.591679775785 1.33407599991
absolute error = 0.2048
relative error = 14.03 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.72190654495 -0.404355765331
y1[1] (closed_form) = 1.63205191084 -0.483652378496
absolute error = 0.1198
relative error = 7.04 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.165
Order of pole (three term test) = 34.47 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.165
Order of pole (three term test) = 30.61 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22781.0MB, alloc=44.3MB, time=281.18
x[1] = 0.3508 1.155
h = 0.0001 0.005
y2[1] (numeric) = 0.458521426701 1.49313507121
y2[1] (closed_form) = 0.599509932068 1.3424247047
absolute error = 0.2064
relative error = 14.04 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.72947568364 -0.411566462071
y1[1] (closed_form) = 1.63829463711 -0.491240662874
absolute error = 0.1211
relative error = 7.08 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.875
Order of pole (three term test) = 34.48 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.875
Order of pole (three term test) = 30.6 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22826.9MB, alloc=44.3MB, time=281.74
memory used=22873.1MB, alloc=44.3MB, time=282.30
x[1] = 0.3509 1.16
h = 0.0001 0.003
y2[1] (numeric) = 0.461950562537 1.49955490827
y2[1] (closed_form) = 0.602138139222 1.35058356117
absolute error = 0.2046
relative error = 13.83 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.73691137872 -0.414017266256
y1[1] (closed_form) = 1.64496706174 -0.494379426373
absolute error = 0.1221
relative error = 7.109 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.525
Order of pole (three term test) = 34.5 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.525
Order of pole (three term test) = 30.58 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=22919.0MB, alloc=44.3MB, time=282.87
memory used=22965.3MB, alloc=44.3MB, time=283.44
x[1] = 0.351 1.163
h = 0.001 0.001
y2[1] (numeric) = 0.465404104125 1.5059903688
y2[1] (closed_form) = 0.603788888954 1.3554749218
absolute error = 0.2045
relative error = 13.78 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.74137332518 -0.415558569284
y1[1] (closed_form) = 1.64896585022 -0.496323618183
absolute error = 0.1227
relative error = 7.127 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.204
Order of pole (three term test) = 34.51 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.204
Order of pole (three term test) = 30.57 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23011.4MB, alloc=44.3MB, time=284.00
x[1] = 0.352 1.164
h = 0.001 0.003
y2[1] (numeric) = 0.468882076108 1.51244151432
y2[1] (closed_form) = 0.605935534281 1.35662695953
absolute error = 0.2075
relative error = 13.97 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.74241539876 -0.417534924972
y1[1] (closed_form) = 1.64971703927 -0.49828453121
absolute error = 0.1229
relative error = 7.134 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.725
Order of pole (three term test) = 34.51 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.725
Order of pole (three term test) = 30.57 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23057.5MB, alloc=44.3MB, time=284.56
memory used=23103.6MB, alloc=44.3MB, time=285.13
x[1] = 0.353 1.167
h = 0.0001 0.004
y2[1] (numeric) = 0.47238449164 1.51890835194
y2[1] (closed_form) = 0.609086607187 1.36108143761
absolute error = 0.2088
relative error = 14 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.74649178839 -0.420462492333
y1[1] (closed_form) = 1.65318609007 -0.501465914766
absolute error = 0.1236
relative error = 7.152 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.26
Order of pole (three term test) = 34.52 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.26
Order of pole (three term test) = 30.56 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23149.4MB, alloc=44.3MB, time=285.68
memory used=23195.4MB, alloc=44.3MB, time=286.24
x[1] = 0.3531 1.171
h = 0.003 0.006
y2[1] (numeric) = 0.475911392368 1.5253909093
y2[1] (closed_form) = 0.611263210204 1.3676546908
absolute error = 0.2078
relative error = 13.87 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.75253296707 -0.422511290764
y1[1] (closed_form) = 1.65858253782 -0.504043047413
absolute error = 0.1244
relative error = 7.176 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.354
Order of pole (three term test) = 34.54 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.354
Order of pole (three term test) = 30.55 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23241.3MB, alloc=44.3MB, time=286.80
memory used=23287.6MB, alloc=44.3MB, time=287.37
x[1] = 0.3561 1.177
h = 0.0001 0.005
y2[1] (numeric) = 0.47946290037 1.531889248
y2[1] (closed_form) = 0.619296172672 1.37610150738
absolute error = 0.2093
relative error = 13.87 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.76027174441 -0.42996331754
y1[1] (closed_form) = 1.6649679764 -0.511850323136
absolute error = 0.1257
relative error = 7.214 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.96
Order of pole (three term test) = 34.55 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.96
Order of pole (three term test) = 30.54 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23333.5MB, alloc=44.3MB, time=287.93
x[1] = 0.3562 1.182
h = 0.0001 0.003
y2[1] (numeric) = 0.483039382239 1.53840337906
y2[1] (closed_form) = 0.622030359993 1.38439208101
absolute error = 0.2075
relative error = 13.67 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.76789934447 -0.432523077293
y1[1] (closed_form) = 1.67180713007 -0.515091656827
absolute error = 0.1267
relative error = 7.242 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.594
Order of pole (three term test) = 34.57 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.594
Order of pole (three term test) = 30.52 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23379.3MB, alloc=44.3MB, time=288.48
memory used=23425.6MB, alloc=44.3MB, time=289.05
x[1] = 0.3563 1.185
h = 0.001 0.001
y2[1] (numeric) = 0.486640979165 1.54493343593
y2[1] (closed_form) = 0.623746030085 1.38936203674
absolute error = 0.2074
relative error = 13.62 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.77247586189 -0.434131758259
y1[1] (closed_form) = 1.67590546946 -0.51709900741
absolute error = 0.1273
relative error = 7.259 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.258
Order of pole (three term test) = 34.58 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.258
Order of pole (three term test) = 30.51 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23471.8MB, alloc=44.3MB, time=289.62
memory used=23518.2MB, alloc=44.3MB, time=290.18
x[1] = 0.3573 1.186
h = 0.0001 0.004
y2[1] (numeric) = 0.490267716679 1.55147948112
y2[1] (closed_form) = 0.62594042431 1.39052021872
absolute error = 0.2105
relative error = 13.8 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.77353561477 -0.436168415637
y1[1] (closed_form) = 1.67667056769 -0.519113791637
absolute error = 0.1275
relative error = 7.266 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.573
Order of pole (three term test) = 34.59 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.573
Order of pole (three term test) = 30.51 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23564.0MB, alloc=44.3MB, time=290.74
x[1] = 0.3574 1.19
h = 0.003 0.006
y2[1] (numeric) = 0.493919606278 1.55804153641
y2[1] (closed_form) = 0.628190114011 1.3971858739
absolute error = 0.2095
relative error = 13.68 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.7797054423 -0.438292257812
y1[1] (closed_form) = 1.68218326618 -0.521761434123
absolute error = 0.1284
relative error = 7.288 %
Correct digits = 1
memory used=23610.1MB, alloc=44.3MB, time=291.30
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.523
Order of pole (three term test) = 34.6 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.523
Order of pole (three term test) = 30.49 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23655.9MB, alloc=44.3MB, time=291.86
x[1] = 0.3604 1.196
h = 0.0001 0.005
y2[1] (numeric) = 0.497596763902 1.56461966012
y2[1] (closed_form) = 0.636400950389 1.40572123301
absolute error = 0.211
relative error = 13.67 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.78758614966 -0.445950781975
y1[1] (closed_form) = 1.68869511025 -0.529759530445
absolute error = 0.1296
relative error = 7.324 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.036
Order of pole (three term test) = 34.62 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.036
Order of pole (three term test) = 30.48 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23701.8MB, alloc=44.3MB, time=292.42
memory used=23747.9MB, alloc=44.3MB, time=292.98
x[1] = 0.3605 1.201
h = 0.0001 0.003
y2[1] (numeric) = 0.501299562065 1.57121386129
y2[1] (closed_form) = 0.639227285397 1.41412901341
absolute error = 0.209
relative error = 13.47 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.79537578214 -0.4486048036
y1[1] (closed_form) = 1.69568094018 -0.53308958603
absolute error = 0.1307
relative error = 7.352 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.656
Order of pole (three term test) = 34.64 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.656
Order of pole (three term test) = 30.46 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23793.7MB, alloc=44.3MB, time=293.54
memory used=23840.1MB, alloc=44.3MB, time=294.11
x[1] = 0.3606 1.204
h = 0.001 0.001
y2[1] (numeric) = 0.505028145 1.5778242747
y2[1] (closed_form) = 0.64099942297 1.41916891938
absolute error = 0.2089
relative error = 13.42 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.80004901911 -0.450271740481
y1[1] (closed_form) = 1.69986687271 -0.535151589235
absolute error = 0.1313
relative error = 7.368 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.307
Order of pole (three term test) = 34.65 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.307
Order of pole (three term test) = 30.45 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23886.1MB, alloc=44.3MB, time=294.68
x[1] = 0.3616 1.205
h = 0.001 0.003
y2[1] (numeric) = 0.508782539012 1.5844509637
y2[1] (closed_form) = 0.643235860989 1.42033299292
absolute error = 0.2122
relative error = 13.61 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.80112325218 -0.452359779934
y1[1] (closed_form) = 1.70064450637 -0.537213457703
absolute error = 0.1315
relative error = 7.374 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.218
Order of pole (three term test) = 34.65 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.218
Order of pole (three term test) = 30.45 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=23932.1MB, alloc=44.3MB, time=295.24
memory used=23978.3MB, alloc=44.3MB, time=295.80
x[1] = 0.3626 1.208
h = 0.0001 0.004
y2[1] (numeric) = 0.512562757807 1.59109393547
y2[1] (closed_form) = 0.646554988799 1.42490146738
absolute error = 0.2135
relative error = 13.64 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.80537589496 -0.455479562511
y1[1] (closed_form) = 1.7042674619 -0.540570757159
absolute error = 0.1321
relative error = 7.391 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.54
Order of pole (three term test) = 34.66 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.54
Order of pole (three term test) = 30.44 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24024.3MB, alloc=44.3MB, time=296.36
memory used=24070.4MB, alloc=44.3MB, time=296.92
x[1] = 0.3627 1.212
h = 0.003 0.006
y2[1] (numeric) = 0.516368844846 1.59775321805
y2[1] (closed_form) = 0.648893444868 1.43167563134
absolute error = 0.2125
relative error = 13.52 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.81170213745 -0.457696859307
y1[1] (closed_form) = 1.70991583633 -0.543304478862
absolute error = 0.133
relative error = 7.413 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.728
Order of pole (three term test) = 34.68 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.728
Order of pole (three term test) = 30.43 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24116.2MB, alloc=44.3MB, time=297.48
memory used=24162.4MB, alloc=44.3MB, time=298.05
x[1] = 0.3657 1.218
h = 0.0001 0.005
y2[1] (numeric) = 0.520200927274 1.60442887362
y2[1] (closed_form) = 0.657317639105 1.44031284887
absolute error = 0.2139
relative error = 13.51 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.81975382743 -0.465609824578
y1[1] (closed_form) = 1.71657249485 -0.551531056354
absolute error = 0.1343
relative error = 7.447 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.128
Order of pole (three term test) = 34.69 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.128
Order of pole (three term test) = 30.42 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24208.2MB, alloc=44.3MB, time=298.60
x[1] = 0.3658 1.223
h = 0.0001 0.003
y2[1] (numeric) = 0.524059384639 1.61112090879
y2[1] (closed_form) = 0.660255898618 1.44885826136
absolute error = 0.2118
relative error = 13.31 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.82774048225 -0.468381241672
y1[1] (closed_form) = 1.72372952933 -0.554969440997
absolute error = 0.1353
relative error = 7.474 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.731
Order of pole (three term test) = 34.72 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.731
Order of pole (three term test) = 30.4 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24254.1MB, alloc=44.3MB, time=299.16
memory used=24300.5MB, alloc=44.3MB, time=299.73
x[1] = 0.3659 1.226
h = 0.001 0.001
y2[1] (numeric) = 0.527944364819 1.61782945986
y2[1] (closed_form) = 0.662096585669 1.45398027503
absolute error = 0.2118
relative error = 13.25 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.83253130369 -0.470120688041
y1[1] (closed_form) = 1.7280176664 -0.557098109841
absolute error = 0.136
relative error = 7.489 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.367
Order of pole (three term test) = 34.73 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.367
Order of pole (three term test) = 30.39 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24346.4MB, alloc=44.3MB, time=300.30
memory used=24392.7MB, alloc=44.3MB, time=300.87
x[1] = 0.3669 1.227
h = 0.001 0.003
y2[1] (numeric) = 0.531855895057 1.62455459118
y2[1] (closed_form) = 0.664383155816 1.45515053172
absolute error = 0.2151
relative error = 13.45 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.83362259642 -0.472271776601
y1[1] (closed_form) = 1.72880899229 -0.559215914983
absolute error = 0.1362
relative error = 7.495 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.499
Order of pole (three term test) = 34.73 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.499
Order of pole (three term test) = 30.39 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24438.7MB, alloc=44.3MB, time=301.43
x[1] = 0.3679 1.23
h = 0.0001 0.004
y2[1] (numeric) = 0.535793989366 1.63129630996
y2[1] (closed_form) = 0.667796644713 1.459781573
absolute error = 0.2164
relative error = 13.48 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.83797254589 -0.47550116885
y1[1] (closed_form) = 1.7325152998 -0.56267164658
absolute error = 0.1368
relative error = 7.511 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.7
Order of pole (three term test) = 34.74 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.7
Order of pole (three term test) = 30.38 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24484.9MB, alloc=44.3MB, time=302.00
memory used=24530.9MB, alloc=44.3MB, time=302.56
x[1] = 0.368 1.234
h = 0.003 0.006
y2[1] (numeric) = 0.53975869222 1.63805464449
y2[1] (closed_form) = 0.670226513161 1.46666678888
absolute error = 0.2154
relative error = 13.36 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.84445746484 -0.477815732745
y1[1] (closed_form) = 1.73830128785 -0.565494011167
absolute error = 0.1377
relative error = 7.532 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.942
Order of pole (three term test) = 34.76 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.942
Order of pole (three term test) = 30.36 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24576.7MB, alloc=44.3MB, time=303.11
memory used=24623.0MB, alloc=44.3MB, time=303.68
x[1] = 0.371 1.24
h = 0.0001 0.005
y2[1] (numeric) = 0.543750133592 1.6448296572
y2[1] (closed_form) = 0.67886992039 1.47540783806
absolute error = 0.2167
relative error = 13.34 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.8526808529 -0.485990568043
y1[1] (closed_form) = 1.74510387715 -0.573954372964
absolute error = 0.139
relative error = 7.564 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.224
Order of pole (three term test) = 34.77 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.224
Order of pole (three term test) = 30.35 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24668.8MB, alloc=44.3MB, time=304.24
memory used=24714.9MB, alloc=44.3MB, time=304.80
x[1] = 0.3711 1.245
h = 0.0001 0.003
y2[1] (numeric) = 0.547768700229 1.65162135219
y2[1] (closed_form) = 0.681923436971 1.48409409343
absolute error = 0.2146
relative error = 13.14 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.86086739773 -0.488884176186
y1[1] (closed_form) = 1.75243457734 -0.577504323451
absolute error = 0.14
relative error = 7.59 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.809
Order of pole (three term test) = 34.8 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.809
Order of pole (three term test) = 30.33 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24760.8MB, alloc=44.3MB, time=305.36
x[1] = 0.3712 1.248
h = 0.001 0.001
y2[1] (numeric) = 0.551814543751 1.65842986729
y2[1] (closed_form) = 0.683834707255 1.48930012076
absolute error = 0.2146
relative error = 13.09 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.86577749141 -0.490699046648
y1[1] (closed_form) = 1.75682637758 -0.579701628512
absolute error = 0.1407
relative error = 7.605 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.428
Order of pole (three term test) = 34.81 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.428
Order of pole (three term test) = 30.32 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24806.8MB, alloc=44.3MB, time=305.93
memory used=24853.1MB, alloc=44.3MB, time=306.50
x[1] = 0.3722 1.249
h = 0.001 0.003
y2[1] (numeric) = 0.555887692366 1.66525526788
y2[1] (closed_form) = 0.686172724953 1.49047656089
absolute error = 0.218
relative error = 13.29 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.86688548373 -0.49291473665
y1[1] (closed_form) = 1.75763126256 -0.581876520435
absolute error = 0.1409
relative error = 7.61 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.793
Order of pole (three term test) = 34.81 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.793
Order of pole (three term test) = 30.32 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24899.2MB, alloc=44.3MB, time=307.06
memory used=24945.4MB, alloc=44.3MB, time=307.62
x[1] = 0.3732 1.252
h = 0.0001 0.004
y2[1] (numeric) = 0.559988160404 1.67209756121
y2[1] (closed_form) = 0.689683211266 1.4951714843
absolute error = 0.2194
relative error = 13.32 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.8713335731 -0.496257218601
y1[1] (closed_form) = 1.76142180591 -0.585433124095
absolute error = 0.1415
relative error = 7.625 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.867
Order of pole (three term test) = 34.82 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.867
Order of pole (three term test) = 30.31 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=24991.2MB, alloc=44.3MB, time=308.18
memory used=25037.3MB, alloc=44.3MB, time=308.74
x[1] = 0.3733 1.256
h = 0.003 0.006
y2[1] (numeric) = 0.564115993377 1.67895677579
y2[1] (closed_form) = 0.69220720568 1.50217032453
absolute error = 0.2183
relative error = 13.2 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.87797947114 -0.498672970354
y1[1] (closed_form) = 1.76734738731 -0.588346767742
absolute error = 0.1424
relative error = 7.645 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.165
Order of pole (three term test) = 34.84 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.165
Order of pole (three term test) = 30.29 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25083.3MB, alloc=44.3MB, time=309.30
x[1] = 0.3763 1.262
h = 0.0001 0.005
y2[1] (numeric) = 0.568271324163 1.68583297434
y2[1] (closed_form) = 0.701075805196 1.51101717482
absolute error = 0.2195
relative error = 13.18 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.88637525785 -0.507117298842
y1[1] (closed_form) = 1.77429703575 -0.597046357601
absolute error = 0.1437
relative error = 7.676 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.325
Order of pole (three term test) = 34.86 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.325
Order of pole (three term test) = 30.28 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25129.1MB, alloc=44.3MB, time=309.86
memory used=25175.3MB, alloc=44.3MB, time=310.42
x[1] = 0.3764 1.267
h = 0.0001 0.003
y2[1] (numeric) = 0.572454546879 1.69272615833
y2[1] (closed_form) = 0.704247996801 1.51984752119
absolute error = 0.2174
relative error = 12.98 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.89476461252 -0.510138029662
y1[1] (closed_form) = 1.78180391598 -0.600711202083
absolute error = 0.1448
relative error = 7.7 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.891
Order of pole (three term test) = 34.88 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.891
Order of pole (three term test) = 30.26 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25221.2MB, alloc=44.3MB, time=310.99
memory used=25267.5MB, alloc=44.3MB, time=311.57
x[1] = 0.3765 1.27
h = 0.001 0.001
y2[1] (numeric) = 0.576665816994 1.69963646718
y2[1] (closed_form) = 0.706231935846 1.52513948999
absolute error = 0.2173
relative error = 12.93 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.89979569638 -0.512031321179
y1[1] (closed_form) = 1.78630086924 -0.602979169409
absolute error = 0.1454
relative error = 7.714 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.493
Order of pole (three term test) = 34.89 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.493
Order of pole (three term test) = 30.25 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25313.5MB, alloc=44.3MB, time=312.15
x[1] = 0.3775 1.271
h = 0.001 0.003
y2[1] (numeric) = 0.580905163708 1.70656396729
y2[1] (closed_form) = 0.708622741419 1.52632210466
absolute error = 0.2209
relative error = 13.13 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.90092001201 -0.514313203113
y1[1] (closed_form) = 1.78711917307 -0.605212327408
absolute error = 0.1456
relative error = 7.719 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.1
Order of pole (three term test) = 34.89 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.1
Order of pole (three term test) = 30.25 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25359.7MB, alloc=44.3MB, time=312.72
memory used=25405.8MB, alloc=44.3MB, time=313.29
x[1] = 0.3785 1.274
h = 0.0001 0.004
y2[1] (numeric) = 0.585172601674 1.71350866598
y2[1] (closed_form) = 0.712232920598 1.53108223201
absolute error = 0.2223
relative error = 13.17 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.90546708012 -0.517772347616
y1[1] (closed_form) = 1.79099485099 -0.608872308692
absolute error = 0.1463
relative error = 7.734 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.042
Order of pole (three term test) = 34.91 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.042
Order of pole (three term test) = 30.24 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25451.6MB, alloc=44.3MB, time=313.86
memory used=25497.7MB, alloc=44.3MB, time=314.43
x[1] = 0.3786 1.278
h = 0.003 0.006
y2[1] (numeric) = 0.589468177473 1.72047059196
y2[1] (closed_form) = 0.714853823977 1.53819729889
absolute error = 0.2212
relative error = 13.04 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.91227630108 -0.520293318606
y1[1] (closed_form) = 1.79706204783 -0.611879941745
absolute error = 0.1472
relative error = 7.753 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.398
Order of pole (three term test) = 34.92 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.398
Order of pole (three term test) = 30.23 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25543.5MB, alloc=44.3MB, time=315.00
memory used=25589.8MB, alloc=44.3MB, time=315.57
x[1] = 0.3816 1.284
h = 0.0001 0.005
y2[1] (numeric) = 0.593792026959 1.72744980824
y2[1] (closed_form) = 0.723953722418 1.54715191543
absolute error = 0.2224
relative error = 13.02 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.92084517045 -0.529014961264
y1[1] (closed_form) = 1.80415989502 -0.620824346788
absolute error = 0.1485
relative error = 7.782 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.43
Order of pole (three term test) = 34.94 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.43
Order of pole (three term test) = 30.21 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25635.7MB, alloc=44.3MB, time=316.13
x[1] = 0.3817 1.289
h = 0.0001 0.003
y2[1] (numeric) = 0.598144551804 1.73444631358
y2[1] (closed_form) = 0.727248094715 1.55612963896
absolute error = 0.2201
relative error = 12.82 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.92944030694 -0.532167885372
y1[1] (closed_form) = 1.81184552312 -0.624607506889
absolute error = 0.1496
relative error = 7.805 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.976
Order of pole (three term test) = 34.97 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.976
Order of pole (three term test) = 30.19 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25681.5MB, alloc=44.3MB, time=316.70
memory used=25727.9MB, alloc=44.3MB, time=317.28
x[1] = 0.3818 1.292
h = 0.001 0.001
y2[1] (numeric) = 0.602525911424 1.74146024899
y2[1] (closed_form) = 0.729306841226 1.56150949926
absolute error = 0.2201
relative error = 12.77 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.93459412913 -0.534142679035
y1[1] (closed_form) = 1.81644915075 -0.626948219266
absolute error = 0.1502
relative error = 7.818 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.56
Order of pole (three term test) = 34.98 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.56
Order of pole (three term test) = 30.18 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25773.9MB, alloc=44.3MB, time=317.85
memory used=25820.4MB, alloc=44.3MB, time=318.44
x[1] = 0.3828 1.293
h = 0.0001 0.004
y2[1] (numeric) = 0.606936136044 1.74849168196
y2[1] (closed_form) = 0.731751800502 1.56269827007
absolute error = 0.2238
relative error = 12.97 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.93573437502 -0.53649238216
y1[1] (closed_form) = 1.8172807257 -0.629240852333
absolute error = 0.1504
relative error = 7.823 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.389
Order of pole (three term test) = 34.98 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 9.389
Order of pole (three term test) = 30.18 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25866.2MB, alloc=44.3MB, time=319.01
memory used=25912.3MB, alloc=44.3MB, time=319.58
x[1] = 0.3829 1.297
h = 0.003 0.006
y2[1] (numeric) = 0.61137523904 1.75554063594
y2[1] (closed_form) = 0.734456975581 1.56991668882
absolute error = 0.2227
relative error = 12.85 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.94268151847 -0.539104196748
y1[1] (closed_form) = 1.82347263713 -0.632329896104
absolute error = 0.1513
relative error = 7.841 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.608
Order of pole (three term test) = 35 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.608
Order of pole (three term test) = 30.16 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=25958.1MB, alloc=44.3MB, time=320.16
x[1] = 0.3859 1.303
h = 0.0001 0.005
y2[1] (numeric) = 0.615843349509 1.76260717061
y2[1] (closed_form) = 0.743759642602 1.57896849362
absolute error = 0.2238
relative error = 12.82 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.95139513253 -0.548063055227
y1[1] (closed_form) = 1.83070197896 -0.641487831439
absolute error = 0.1526
relative error = 7.868 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.524
Order of pole (three term test) = 35.02 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.524
Order of pole (three term test) = 30.15 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26004.0MB, alloc=44.3MB, time=320.73
memory used=26050.1MB, alloc=44.3MB, time=321.31
x[1] = 0.386 1.308
h = 0.0001 0.003
y2[1] (numeric) = 0.620340875791 1.76969128239
y2[1] (closed_form) = 0.747160250377 1.58807724939
absolute error = 0.2215
relative error = 12.62 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.96016406234 -0.551330118256
y1[1] (closed_form) = 1.83854503131 -0.645373474713
absolute error = 0.1537
relative error = 7.89 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.053
Order of pole (three term test) = 35.04 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.053
Order of pole (three term test) = 30.13 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26096.0MB, alloc=44.3MB, time=321.89
memory used=26142.3MB, alloc=44.3MB, time=322.48
x[1] = 0.3861 1.311
h = 0.001 0.001
y2[1] (numeric) = 0.624867980766 1.77679311371
y2[1] (closed_form) = 0.749284063937 1.59353526936
absolute error = 0.2215
relative error = 12.58 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 1.9654215243 -0.553375248212
y1[1] (closed_form) = 1.84324262448 -0.647777219775
absolute error = 0.1544
relative error = 7.903 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.621
Order of pole (three term test) = 35.06 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.621
Order of pole (three term test) = 30.12 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26188.3MB, alloc=44.3MB, time=323.07
x[1] = 0.3871 1.312
h = 0.001 0.003
y2[1] (numeric) = 0.629424695547 1.78391273305
y2[1] (closed_form) = 0.751776677715 1.59472998465
absolute error = 0.2253
relative error = 12.78 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 1.96657473187 -0.555782743523
y1[1] (closed_form) = 1.84408622712 -0.650121882632
absolute error = 0.1546
relative error = 7.907 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.708
Order of pole (three term test) = 35.06 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.708
Order of pole (three term test) = 30.12 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26234.4MB, alloc=44.3MB, time=323.64
memory used=26280.5MB, alloc=44.3MB, time=324.22
x[1] = 0.3881 1.315
h = 0.0001 0.004
y2[1] (numeric) = 0.634011035412 1.79105014777
y2[1] (closed_form) = 0.755578930836 1.59961624775
absolute error = 0.2268
relative error = 12.82 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 1.97130545635 -0.559465369665
y1[1] (closed_form) = 1.8481240679 -0.65398008457
absolute error = 0.1553
relative error = 7.92 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.388
Order of pole (three term test) = 35.07 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.388
Order of pole (three term test) = 30.11 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26326.3MB, alloc=44.3MB, time=324.80
memory used=26372.4MB, alloc=44.3MB, time=325.38
x[1] = 0.3882 1.319
h = 0.003 0.006
y2[1] (numeric) = 0.638627048998 1.79820538705
y2[1] (closed_form) = 0.758386352731 1.60695585189
absolute error = 0.2257
relative error = 12.7 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 1.9784203298 -0.562190098562
y1[1] (closed_form) = 1.85446150561 -0.657168339072
absolute error = 0.1562
relative error = 7.937 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.861
Order of pole (three term test) = 35.09 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.861
Order of pole (three term test) = 30.09 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26418.1MB, alloc=44.3MB, time=325.95
memory used=26464.4MB, alloc=44.3MB, time=326.53
x[1] = 0.3912 1.325
h = 0.0001 0.005
y2[1] (numeric) = 0.643272877904 1.80537851441
y2[1] (closed_form) = 0.767932008526 1.61611914291
absolute error = 0.2266
relative error = 12.67 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 1.98730823018 -0.571441154716
y1[1] (closed_form) = 1.86184126469 -0.666581863328
absolute error = 0.1575
relative error = 7.962 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.638
Order of pole (three term test) = 35.11 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.638
Order of pole (three term test) = 30.08 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26510.2MB, alloc=44.3MB, time=327.10
x[1] = 0.3913 1.33
h = 0.0001 0.003
y2[1] (numeric) = 0.647948938382 1.81256952343
y2[1] (closed_form) = 0.77146152156 1.62538153844
absolute error = 0.2243
relative error = 12.46 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 1.99628853197 -0.574850093858
y1[1] (closed_form) = 1.86986803033 -0.670592413166
absolute error = 0.1586
relative error = 7.983 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.145
Order of pole (three term test) = 35.14 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.145
Order of pole (three term test) = 30.06 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26556.0MB, alloc=44.3MB, time=327.68
memory used=26602.4MB, alloc=44.3MB, time=328.26
x[1] = 0.3914 1.333
h = 0.001 0.001
y2[1] (numeric) = 0.652655397456 1.81977855821
y2[1] (closed_form) = 0.773664244789 1.63093116603
absolute error = 0.2243
relative error = 12.43 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.0016720196 -0.57698261001
y1[1] (closed_form) = 1.87467523962 -0.673072915352
absolute error = 0.1593
relative error = 7.995 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.694
Order of pole (three term test) = 35.15 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.694
Order of pole (three term test) = 30.04 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26648.4MB, alloc=44.3MB, time=328.85
memory used=26694.7MB, alloc=44.3MB, time=329.44
x[1] = 0.3924 1.334
h = 0.001 0.003
y2[1] (numeric) = 0.65739228732 1.82700568832
y2[1] (closed_form) = 0.776213624275 1.63213199384
absolute error = 0.2282
relative error = 12.63 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.00284038891 -0.579461021931
y1[1] (closed_form) = 1.87553183267 -0.675479385724
absolute error = 0.1595
relative error = 7.999 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.056
Order of pole (three term test) = 35.15 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.056
Order of pole (three term test) = 30.05 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26740.6MB, alloc=44.3MB, time=330.02
memory used=26786.8MB, alloc=44.3MB, time=330.60
x[1] = 0.3934 1.337
h = 0.0001 0.004
y2[1] (numeric) = 0.662159623597 1.83425092116
y2[1] (closed_form) = 0.780123605677 1.63708731254
absolute error = 0.2298
relative error = 12.67 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.00767249588 -0.583270968976
y1[1] (closed_form) = 1.87965749225 -0.679448496513
absolute error = 0.1601
relative error = 8.011 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.586
Order of pole (three term test) = 35.16 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.586
Order of pole (three term test) = 30.04 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26832.6MB, alloc=44.3MB, time=331.18
x[1] = 0.3935 1.341
h = 0.003 0.006
y2[1] (numeric) = 0.666957456074 1.84151428615
y2[1] (closed_form) = 0.783036266083 1.64455079361
absolute error = 0.2286
relative error = 12.55 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.01495756464 -0.58611298107
y1[1] (closed_form) = 1.88614260204 -0.682738893345
absolute error = 0.161
relative error = 8.028 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.125
Order of pole (three term test) = 35.19 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.125
Order of pole (three term test) = 30.02 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26878.5MB, alloc=44.3MB, time=331.75
memory used=26924.7MB, alloc=44.3MB, time=332.33
x[1] = 0.3965 1.347
h = 0.0001 0.005
y2[1] (numeric) = 0.671785929551 1.84879584709
y2[1] (closed_form) = 0.792831399776 1.6538275224
absolute error = 0.2295
relative error = 12.51 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.02402037858 -0.595664656457
y1[1] (closed_form) = 1.89367394757 -0.692414019454
absolute error = 0.1623
relative error = 8.051 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.757
Order of pole (three term test) = 35.2 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.757
Order of pole (three term test) = 30.01 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=26970.6MB, alloc=44.3MB, time=332.91
memory used=27016.8MB, alloc=44.3MB, time=333.49
x[1] = 0.3966 1.352
h = 0.0001 0.003
y2[1] (numeric) = 0.676645468366 1.85609559455
y2[1] (closed_form) = 0.796493587409 1.66324695748
absolute error = 0.2271
relative error = 12.31 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.03321517828 -0.599220966372
y1[1] (closed_form) = 1.90188715077 -0.696553176342
absolute error = 0.1635
relative error = 8.071 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.242
Order of pole (three term test) = 35.23 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.242
Order of pole (three term test) = 29.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=27062.9MB, alloc=44.3MB, time=334.07
x[1] = 0.3967 1.355
h = 0.001 0.001
y2[1] (numeric) = 0.6815362438 1.86341367432
y2[1] (closed_form) = 0.798777518849 1.66889020918
absolute error = 0.2271
relative error = 12.28 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.03872652876 -0.601444206435
y1[1] (closed_form) = 1.9068055894 -0.699112687696
absolute error = 0.1641
relative error = 8.082 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.77
Order of pole (three term test) = 35.25 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.77
Order of pole (three term test) = 29.97 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=27109.1MB, alloc=44.3MB, time=334.65
memory used=27155.2MB, alloc=44.3MB, time=335.24
x[1] = 0.3977 1.356
h = 0.001 0.003
y2[1] (numeric) = 0.686458289152 1.87075015711
y2[1] (closed_form) = 0.801385106419 1.67009710244
absolute error = 0.2312
relative error = 12.48 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.03990961448 -0.603995281477
y1[1] (closed_form) = 1.90767500216 -0.701582262519
absolute error = 0.1643
relative error = 8.085 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.419
Order of pole (three term test) = 35.25 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.419
Order of pole (three term test) = 29.97 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=27201.1MB, alloc=44.3MB, time=335.82
memory used=27247.5MB, alloc=44.3MB, time=336.40
x[1] = 0.3987 1.359
h = 0.0001 0.004
y2[1] (numeric) = 0.691411620406 1.87810505036
y2[1] (closed_form) = 0.805405754419 1.67512282409
absolute error = 0.2328
relative error = 12.53 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.04484396034 -0.607936504584
y1[1] (closed_form) = 1.91188943585 -0.705665053945
absolute error = 0.165
relative error = 8.097 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.793
Order of pole (three term test) = 35.26 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.793
Order of pole (three term test) = 29.96 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=27293.3MB, alloc=44.3MB, time=336.97
memory used=27339.6MB, alloc=44.3MB, time=337.56
x[1] = 0.3988 1.363
h = 0.003 0.006
y2[1] (numeric) = 0.696396288525 1.88547838372
y2[1] (closed_form) = 0.808426721899 1.68271290559
absolute error = 0.2317
relative error = 12.41 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.05230173091 -0.610900288964
y1[1] (closed_form) = 1.91852440707 -0.709060605717
absolute error = 0.1659
relative error = 8.112 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.402
Order of pole (three term test) = 35.28 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.402
Order of pole (three term test) = 29.95 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=27385.4MB, alloc=44.3MB, time=338.13
x[1] = 0.4018 1.369
h = 0.0001 0.005
y2[1] (numeric) = 0.701412441592 1.89287022126
y2[1] (closed_form) = 0.818477962814 1.69210501722
absolute error = 0.2324
relative error = 12.36 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.06154006231 -0.620761217591
y1[1] (closed_form) = 1.92620851635 -0.719003501232
absolute error = 0.1672
relative error = 8.134 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.881
Order of pole (three term test) = 35.3 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.881
Order of pole (three term test) = 29.94 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=27431.2MB, alloc=44.3MB, time=338.71
memory used=27477.3MB, alloc=44.3MB, time=339.30
x[1] = 0.4019 1.374
h = 0.0001 0.003
y2[1] (numeric) = 0.70646051222 1.90028055046
y2[1] (closed_form) = 0.8222766915 1.70168493229
absolute error = 0.2299
relative error = 12.16 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.07095253813 -0.624470544004
y1[1] (closed_form) = 1.93461093635 -0.723275067769
absolute error = 0.1684
relative error = 8.152 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.343
Order of pole (three term test) = 35.33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.343
Order of pole (three term test) = 29.91 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=27523.2MB, alloc=44.3MB, time=339.87
memory used=27569.5MB, alloc=44.3MB, time=340.46
x[1] = 0.402 1.377
h = 0.001 0.001
y2[1] (numeric) = 0.711540676061 1.90770951881
y2[1] (closed_form) = 0.824644188553 1.70742384834
absolute error = 0.23
relative error = 12.13 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.07659361877 -0.626787937104
y1[1] (closed_form) = 1.93964224984 -0.725915902298
absolute error = 0.1691
relative error = 8.163 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.85
Order of pole (three term test) = 35.35 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.85
Order of pole (three term test) = 29.9 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=27615.6MB, alloc=44.3MB, time=341.05
x[1] = 0.403 1.378
h = 0.001 0.003
y2[1] (numeric) = 0.716652967552 1.91515719818
y2[1] (closed_form) = 0.827311454534 1.70863674915
absolute error = 0.2343
relative error = 12.34 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.07779095642 -0.629413463047
y1[1] (closed_form) = 1.94052430274 -0.728449910272
absolute error = 0.1693
relative error = 8.166 %
Correct digits = 1
memory used=27661.9MB, alloc=44.3MB, time=341.62
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.799
Order of pole (three term test) = 35.35 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.799
Order of pole (three term test) = 29.9 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=27707.8MB, alloc=44.3MB, time=342.20
x[1] = 0.404 1.381
h = 0.0001 0.004
y2[1] (numeric) = 0.721797403044 1.92262359606
y2[1] (closed_form) = 0.831445774326 1.71373422742
absolute error = 0.2359
relative error = 12.39 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.08282840043 -0.633490019398
y1[1] (closed_form) = 1.94482847982 -0.732649226652
absolute error = 0.1699
relative error = 8.177 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.009
Order of pole (three term test) = 35.36 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.009
Order of pole (three term test) = 29.89 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=27753.8MB, alloc=44.3MB, time=342.77
memory used=27799.9MB, alloc=44.3MB, time=343.35
x[1] = 0.4041 1.385
h = 0.003 0.006
y2[1] (numeric) = 0.726974034709 1.93010874233
y2[1] (closed_form) = 0.834578196349 1.72145366529
absolute error = 0.2348
relative error = 12.27 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.09046142054 -0.636580187992
y1[1] (closed_form) = 1.9516155456 -0.736153028866
absolute error = 0.1709
relative error = 8.191 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.69
Order of pole (three term test) = 35.38 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.69
Order of pole (three term test) = 29.87 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=27845.9MB, alloc=44.3MB, time=343.93
memory used=27892.1MB, alloc=44.3MB, time=344.52
x[1] = 0.4071 1.391
h = 0.0001 0.005
y2[1] (numeric) = 0.732183013991 1.93761270131
y2[1] (closed_form) = 0.844892317481 1.73096309771
absolute error = 0.2354
relative error = 12.22 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.09987584804 -0.646759220323
y1[1] (closed_form) = 1.95945360313 -0.74637001905
absolute error = 0.1722
relative error = 8.211 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.011
Order of pole (three term test) = 35.4 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.011
Order of pole (three term test) = 29.86 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=27938.0MB, alloc=44.3MB, time=345.09
x[1] = 0.4072 1.396
h = 0.0001 0.003
y2[1] (numeric) = 0.737424781979 1.9451354573
y2[1] (closed_form) = 0.848831553353 1.74070697454
absolute error = 0.2328
relative error = 12.02 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.10950923046 -0.650627363344
y1[1] (closed_form) = 1.96804807459 -0.750777902335
absolute error = 0.1733
relative error = 8.229 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.448
Order of pole (three term test) = 35.43 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.448
Order of pole (three term test) = 29.84 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=27984.0MB, alloc=44.3MB, time=345.67
memory used=28030.3MB, alloc=44.3MB, time=346.27
x[1] = 0.4073 1.399
h = 0.001 0.001
y2[1] (numeric) = 0.742699518805 1.95267715951
y2[1] (closed_form) = 0.851285033834 1.7465436193
absolute error = 0.233
relative error = 11.99 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.1152819387 -0.653042432019
y1[1] (closed_form) = 1.97319394093 -0.753502437447
absolute error = 0.174
relative error = 8.239 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.934
Order of pole (three term test) = 35.45 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.934
Order of pole (three term test) = 29.82 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=28076.2MB, alloc=44.3MB, time=346.85
memory used=28122.5MB, alloc=44.3MB, time=347.44
x[1] = 0.4083 1.4
h = 0.003 0.006
y2[1] (numeric) = 0.748007260079 1.96023788101
y2[1] (closed_form) = 0.854013477162 1.74776245861
absolute error = 0.2375
relative error = 12.21 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.116493044 -0.655744238592
y1[1] (closed_form) = 1.97408844515 -0.756102239592
absolute error = 0.1742
relative error = 8.241 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 19.51
Order of pole (three term test) = 35.45 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 19.51
Order of pole (three term test) = 29.82 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=28168.4MB, alloc=44.3MB, time=348.02
memory used=28214.7MB, alloc=44.3MB, time=348.61
x[1] = 0.4113 1.406
h = 0.0001 0.005
y2[1] (numeric) = 0.753348116241 1.96781760698
y2[1] (closed_form) = 0.864515449485 1.75734688534
absolute error = 0.238
relative error = 12.15 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.12602517624 -0.66614036655
y1[1] (closed_form) = 1.98202599317 -0.766515443146
absolute error = 0.1755
relative error = 8.26 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.103
Order of pole (three term test) = 35.47 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.103
Order of pole (three term test) = 29.81 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=28260.5MB, alloc=44.3MB, time=349.19
x[1] = 0.4114 1.411
h = 0.0001 0.003
y2[1] (numeric) = 0.758722524405 1.97541629795
y2[1] (closed_form) = 0.868557928547 1.76720192988
absolute error = 0.2354
relative error = 11.96 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.13580764983 -0.670117690649
y1[1] (closed_form) = 1.99075069374 -0.771024343915
absolute error = 0.1767
relative error = 8.277 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.523
Order of pole (three term test) = 35.5 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.523
Order of pole (three term test) = 29.79 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=28306.4MB, alloc=44.3MB, time=349.77
memory used=28352.8MB, alloc=44.3MB, time=350.36
x[1] = 0.4115 1.414
h = 0.001 0.001
y2[1] (numeric) = 0.76413066767 1.98303410421
y2[1] (closed_form) = 0.871074515334 1.77310477112
absolute error = 0.2356
relative error = 11.93 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.14166917826 -0.672599884357
y1[1] (closed_form) = 1.9959741684 -0.773810805567
absolute error = 0.1774
relative error = 8.287 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.992
Order of pole (three term test) = 35.52 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 1.992
Order of pole (three term test) = 29.78 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=28398.9MB, alloc=44.3MB, time=350.95
memory used=28445.3MB, alloc=44.3MB, time=351.54
x[1] = 0.4125 1.415
h = 0.001 0.003
y2[1] (numeric) = 0.769572582503 1.99067109963
y2[1] (closed_form) = 0.87384607382 1.77432606248
absolute error = 0.2402
relative error = 12.14 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.14288918045 -0.67535358417
y1[1] (closed_form) = 1.99687542396 -0.776456981128
absolute error = 0.1776
relative error = 8.289 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.475
Order of pole (three term test) = 35.52 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 9.475
Order of pole (three term test) = 29.78 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=28491.3MB, alloc=44.3MB, time=352.13
x[1] = 0.4135 1.418
h = 0.0001 0.004
y2[1] (numeric) = 0.775048285894 1.99832729175
y2[1] (closed_form) = 0.878181149541 1.77954471017
absolute error = 0.2419
relative error = 12.19 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.14810036562 -0.679665004615
y1[1] (closed_form) = 2.00133021574 -0.780861952185
absolute error = 0.1783
relative error = 8.299 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.394
Order of pole (three term test) = 35.53 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.394
Order of pole (three term test) = 29.77 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=28537.5MB, alloc=44.3MB, time=352.71
memory used=28583.4MB, alloc=44.3MB, time=353.28
x[1] = 0.4136 1.422
h = 0.003 0.006
y2[1] (numeric) = 0.78055783213 2.00600271083
y2[1] (closed_form) = 0.881512473173 1.78748584172
absolute error = 0.2407
relative error = 12.08 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.15603123918 -0.682976421899
y1[1] (closed_form) = 2.00837628302 -0.784559685562
absolute error = 0.1792
relative error = 8.312 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.205
Order of pole (three term test) = 35.56 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.205
Order of pole (three term test) = 29.75 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=28629.2MB, alloc=44.3MB, time=353.85
memory used=28675.4MB, alloc=44.3MB, time=354.43
x[1] = 0.4166 1.428
h = 0.0001 0.005
y2[1] (numeric) = 0.786101378533 2.0136974215
y2[1] (closed_form) = 0.892289141898 1.79719066332
absolute error = 0.2411
relative error = 12.02 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.16574034968 -0.693705927801
y1[1] (closed_form) = 2.016469624 -0.795258056813
absolute error = 0.1805
relative error = 8.329 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.242
Order of pole (three term test) = 35.58 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.242
Order of pole (three term test) = 29.74 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=28721.3MB, alloc=44.3MB, time=355.00
memory used=28767.5MB, alloc=44.3MB, time=355.77
x[1] = 0.4167 1.433
h = 0.0001 0.003
y2[1] (numeric) = 0.791679380853 2.02141140221
y2[1] (closed_form) = 0.896479145988 1.8072155364
absolute error = 0.2385
relative error = 11.82 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.17574922494 -0.697852120562
y1[1] (closed_form) = 2.02539118289 -0.799910187411
absolute error = 0.1817
relative error = 8.345 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.637
Order of pole (three term test) = 35.61 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.637
Order of pole (three term test) = 29.71 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=28813.5MB, alloc=44.3MB, time=356.37
x[1] = 0.4168 1.436
h = 0.001 0.001
y2[1] (numeric) = 0.797292027098 2.02914480502
y2[1] (closed_form) = 0.89908599201 1.81321958215
absolute error = 0.2387
relative error = 11.79 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.18174560609 -0.700438096654
y1[1] (closed_form) = 2.03073205346 -0.802784554454
absolute error = 0.1824
relative error = 8.354 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.082
Order of pole (three term test) = 35.63 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.082
Order of pole (three term test) = 29.7 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=28859.6MB, alloc=44.3MB, time=356.95
memory used=28906.0MB, alloc=44.3MB, time=357.53
x[1] = 0.4178 1.437
h = 0.001 0.003
y2[1] (numeric) = 0.802939354967 2.03689770504
y2[1] (closed_form) = 0.901921322246 1.81444662962
absolute error = 0.2435
relative error = 12.02 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.18297851292 -0.703271229084
y1[1] (closed_form) = 2.03164538336 -0.805498891064
absolute error = 0.1826
relative error = 8.356 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.902
Order of pole (three term test) = 35.63 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 9.902
Order of pole (three term test) = 29.7 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=28951.9MB, alloc=44.3MB, time=358.12
memory used=28998.1MB, alloc=44.3MB, time=358.71
x[1] = 0.4188 1.44
h = 0.0001 0.004
y2[1] (numeric) = 0.80862138184 2.04467010983
y2[1] (closed_form) = 0.906378526557 1.8197406215
absolute error = 0.2453
relative error = 12.06 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.18829508229 -0.707729343791
y1[1] (closed_form) = 2.03619251354 -0.81002842917
absolute error = 0.1833
relative error = 8.365 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.637
Order of pole (three term test) = 35.64 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.637
Order of pole (three term test) = 29.69 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=29043.9MB, alloc=44.3MB, time=359.30
memory used=29090.1MB, alloc=44.3MB, time=359.90
x[1] = 0.4189 1.444
h = 0.003 0.006
y2[1] (numeric) = 0.814338163298 2.0524620499
y2[1] (closed_form) = 0.909830244181 1.82781859604
absolute error = 0.2441
relative error = 11.96 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.1964081924 -0.71118010773
y1[1] (closed_form) = 2.04339681219 -0.813843219109
absolute error = 0.1843
relative error = 8.377 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.529
Order of pole (three term test) = 35.67 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.529
Order of pole (three term test) = 29.67 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=29135.9MB, alloc=44.3MB, time=360.48
x[1] = 0.4219 1.45
h = 0.0001 0.005
y2[1] (numeric) = 0.820089860256 2.06027359012
y2[1] (closed_form) = 0.920888785975 1.83764572385
absolute error = 0.2444
relative error = 11.89 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.20629475628 -0.722252472795
y1[1] (closed_form) = 2.05164714102 -0.8248335232
absolute error = 0.1856
relative error = 8.392 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.388
Order of pole (three term test) = 35.69 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.388
Order of pole (three term test) = 29.66 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=29181.9MB, alloc=44.3MB, time=361.08
memory used=29228.0MB, alloc=44.3MB, time=361.68
x[1] = 0.422 1.455
h = 0.0001 0.003
y2[1] (numeric) = 0.825876937469 2.06810470543
y2[1] (closed_form) = 0.925230563389 1.84784401885
absolute error = 0.2416
relative error = 11.69 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.21653339579 -0.726573793737
y1[1] (closed_form) = 2.06076854081 -0.829633085305
absolute error = 0.1868
relative error = 8.407 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.755
Order of pole (three term test) = 35.72 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.755
Order of pole (three term test) = 29.64 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=29273.9MB, alloc=44.3MB, time=362.28
memory used=29320.3MB, alloc=44.3MB, time=362.88
x[1] = 0.4221 1.458
h = 0.001 0.001
y2[1] (numeric) = 0.83169958775 2.07595554969
y2[1] (closed_form) = 0.927930257415 1.85395139853
absolute error = 0.242
relative error = 11.67 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.2226666027 -0.729267352472
y1[1] (closed_form) = 2.06622857195 -0.832597913813
absolute error = 0.1875
relative error = 8.416 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.176
Order of pole (three term test) = 35.74 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.176
Order of pole (three term test) = 29.62 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=29366.3MB, alloc=44.3MB, time=363.47
x[1] = 0.4231 1.459
h = 0.001 0.003
y2[1] (numeric) = 0.837557850063 2.08382619926
y2[1] (closed_form) = 0.930830938263 1.85518410029
absolute error = 0.2469
relative error = 11.9 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.22391186617 -0.732181867446
y1[1] (closed_form) = 2.06715375957 -0.835381862006
absolute error = 0.1877
relative error = 8.418 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.35
Order of pole (three term test) = 35.74 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 10.35
Order of pole (three term test) = 29.63 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=29412.3MB, alloc=44.3MB, time=364.06
memory used=29458.6MB, alloc=44.3MB, time=364.66
x[1] = 0.4241 1.462
h = 0.0001 0.004
y2[1] (numeric) = 0.843451742187 2.09171666174
y2[1] (closed_form) = 0.935413537957 1.86055481053
absolute error = 0.2488
relative error = 11.95 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.22933467369 -0.7367911427
y1[1] (closed_form) = 2.07179424493 -0.840039092751
absolute error = 0.1884
relative error = 8.425 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.891
Order of pole (three term test) = 35.76 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.891
Order of pole (three term test) = 29.62 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=29504.6MB, alloc=44.3MB, time=365.24
memory used=29550.7MB, alloc=44.3MB, time=365.83
x[1] = 0.4242 1.466
h = 0.003 0.006
y2[1] (numeric) = 0.849381321029 2.09962696788
y2[1] (closed_form) = 0.938989107219 1.86877250597
absolute error = 0.2476
relative error = 11.84 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.23763271296 -0.740386363936
y1[1] (closed_form) = 2.07915916988 -0.843974358672
absolute error = 0.1893
relative error = 8.437 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.868
Order of pole (three term test) = 35.78 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.868
Order of pole (three term test) = 29.6 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=29596.5MB, alloc=44.3MB, time=366.42
memory used=29642.8MB, alloc=44.3MB, time=367.02
x[1] = 0.4272 1.472
h = 0.0001 0.005
y2[1] (numeric) = 0.855346751185 2.10755718279
y2[1] (closed_form) = 0.950336855782 1.87872384136
absolute error = 0.2478
relative error = 11.77 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.24769717238 -0.751811301366
y1[1] (closed_form) = 2.08756768493 -0.855263530456
absolute error = 0.1906
relative error = 8.45 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.541
Order of pole (three term test) = 35.8 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.541
Order of pole (three term test) = 29.59 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=29688.8MB, alloc=44.3MB, time=367.61
x[1] = 0.4273 1.477
h = 0.0001 0.003
y2[1] (numeric) = 0.861348506625 2.11550727778
y2[1] (closed_form) = 0.954834764458 1.88909919533
absolute error = 0.2449
relative error = 11.57 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.25816899077 -0.756314177369
y1[1] (closed_form) = 2.09689196493 -0.860214839571
absolute error = 0.1918
relative error = 8.465 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.879
Order of pole (three term test) = 35.84 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.879
Order of pole (three term test) = 29.56 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=29734.7MB, alloc=44.3MB, time=368.19
memory used=29781.0MB, alloc=44.3MB, time=368.78
x[1] = 0.4274 1.48
h = 0.001 0.001
y2[1] (numeric) = 0.867386785087 2.12347740852
y2[1] (closed_form) = 0.957629961691 1.89531206382
absolute error = 0.2454
relative error = 11.55 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.26444102631 -0.759119220235
y1[1] (closed_form) = 2.10247295456 -0.863272754653
absolute error = 0.1926
relative error = 8.473 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.274
Order of pole (three term test) = 35.86 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.274
Order of pole (three term test) = 29.55 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=29827.0MB, alloc=44.3MB, time=369.36
memory used=29873.4MB, alloc=44.3MB, time=369.94
x[1] = 0.4284 1.481
h = 0.0001 0.004
y2[1] (numeric) = 0.873461626835 2.13146765266
y2[1] (closed_form) = 0.960597603125 1.8965503054
absolute error = 0.2506
relative error = 11.79 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.26569807601 -0.762117112247
y1[1] (closed_form) = 2.10340977243 -0.866127799464
absolute error = 0.1928
relative error = 8.474 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.68
Order of pole (three term test) = 35.86 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 13.68
Order of pole (three term test) = 29.55 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=29919.2MB, alloc=44.3MB, time=370.51
memory used=29965.4MB, alloc=44.3MB, time=371.09
x[1] = 0.4285 1.485
h = 0.003 0.006
y2[1] (numeric) = 0.879573049256 2.13947803699
y2[1] (closed_form) = 0.964280904814 1.90489213211
absolute error = 0.2494
relative error = 11.68 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.27415230923 -0.765836716515
y1[1] (closed_form) = 2.11091640365 -0.870167622718
absolute error = 0.1937
relative error = 8.485 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.173
Order of pole (three term test) = 35.89 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.173
Order of pole (three term test) = 29.53 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=30011.2MB, alloc=44.3MB, time=371.66
x[1] = 0.4315 1.491
h = 0.0001 0.005
y2[1] (numeric) = 0.885721208864 2.14750862324
y2[1] (closed_form) = 0.975882078065 1.91495546245
absolute error = 0.2494
relative error = 11.6 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.28436532698 -0.777563055749
y1[1] (closed_form) = 2.11946571737 -0.881717831422
absolute error = 0.195
relative error = 8.496 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.678
Order of pole (three term test) = 35.91 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.678
Order of pole (three term test) = 29.52 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=30057.0MB, alloc=44.3MB, time=372.23
memory used=30103.2MB, alloc=44.3MB, time=372.80
x[1] = 0.4316 1.496
h = 0.0001 0.003
y2[1] (numeric) = 0.891906587753 2.15555937958
y2[1] (closed_form) = 0.980515785944 1.92548810173
absolute error = 0.2465
relative error = 11.41 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.29503410748 -0.7822222629
y1[1] (closed_form) = 2.12896898703 -0.886800836883
absolute error = 0.1963
relative error = 8.509 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.991
Order of pole (three term test) = 35.94 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.991
Order of pole (three term test) = 29.5 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=30149.1MB, alloc=44.3MB, time=373.38
memory used=30195.4MB, alloc=44.3MB, time=373.95
x[1] = 0.4317 1.499
h = 0.001 0.001
y2[1] (numeric) = 0.898129387983 2.16363046334
y2[1] (closed_form) = 0.983394075357 1.93179469868
absolute error = 0.247
relative error = 11.4 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.30142338566 -0.785123266822
y1[1] (closed_form) = 2.13465671163 -0.88993956318
absolute error = 0.197
relative error = 8.517 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.362
Order of pole (three term test) = 35.97 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.362
Order of pole (three term test) = 29.48 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=30241.4MB, alloc=44.3MB, time=374.53
x[1] = 0.4327 1.5
h = 0.001 0.003
y2[1] (numeric) = 0.904389650948 2.17172195331
y2[1] (closed_form) = 0.986420603841 1.93303843142
absolute error = 0.2524
relative error = 11.63 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.30268980377 -0.788192197727
y1[1] (closed_form) = 2.13560422134 -0.892856886926
absolute error = 0.1972
relative error = 8.518 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.23
Order of pole (three term test) = 35.97 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 11.23
Order of pole (three term test) = 29.48 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=30287.6MB, alloc=44.3MB, time=375.09
memory used=30333.8MB, alloc=44.3MB, time=375.67
x[1] = 0.4337 1.503
h = 0.0001 0.004
y2[1] (numeric) = 0.910687395203 2.17983385715
y2[1] (closed_form) = 0.991244535463 1.93855716263
absolute error = 0.2544
relative error = 11.68 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.30830959698 -0.793090580123
y1[1] (closed_form) = 2.1404227814 -0.897759176755
absolute error = 0.1978
relative error = 8.524 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.394
Order of pole (three term test) = 35.98 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.394
Order of pole (three term test) = 29.48 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=30379.7MB, alloc=44.3MB, time=376.24
memory used=30425.8MB, alloc=44.3MB, time=376.80
x[1] = 0.4338 1.507
h = 0.003 0.006
y2[1] (numeric) = 0.917022680203 2.18796620609
y2[1] (closed_form) = 0.995058326154 1.94704420219
absolute error = 0.2532
relative error = 11.58 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.31695380509 -0.796964377581
y1[1] (closed_form) = 2.14809465904 -0.901926056482
absolute error = 0.1988
relative error = 8.534 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.541
Order of pole (three term test) = 36.01 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.541
Order of pole (three term test) = 29.46 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=30471.6MB, alloc=44.3MB, time=377.36
memory used=30517.9MB, alloc=44.3MB, time=377.94
x[1] = 0.4368 1.513
h = 0.0001 0.005
y2[1] (numeric) = 0.923395677637 2.19611906567
y2[1] (closed_form) = 1.00696276114 1.95723534058
absolute error = 0.2531
relative error = 11.5 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.32734543261 -0.809061736466
y1[1] (closed_form) = 2.15680448203 -0.913788486239
absolute error = 0.2001
relative error = 8.544 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.844
Order of pole (three term test) = 36.03 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.844
Order of pole (three term test) = 29.45 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=30563.6MB, alloc=44.3MB, time=378.50
x[1] = 0.4369 1.518
h = 0.0001 0.003
y2[1] (numeric) = 0.929806879221 2.20429240025
y2[1] (closed_form) = 1.01176096637 1.96795198011
absolute error = 0.2501
relative error = 11.3 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.33825379291 -0.813914747276
y1[1] (closed_form) = 2.16651649436 -0.919031543195
absolute error = 0.2014
relative error = 8.556 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.126
Order of pole (three term test) = 36.07 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.126
Order of pole (three term test) = 29.42 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=30609.5MB, alloc=44.3MB, time=379.06
memory used=30655.8MB, alloc=44.3MB, time=379.64
x[1] = 0.437 1.521
h = 0.001 0.001
y2[1] (numeric) = 0.936256492181 2.21248636903
y2[1] (closed_form) = 1.014739856 1.97436817816
absolute error = 0.2507
relative error = 11.29 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.34478565304 -0.816934671488
y1[1] (closed_form) = 2.17232864536 -0.922268407721
absolute error = 0.2021
relative error = 8.563 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.468
Order of pole (three term test) = 36.09 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.468
Order of pole (three term test) = 29.41 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=30701.7MB, alloc=44.3MB, time=380.21
memory used=30748.0MB, alloc=44.3MB, time=380.79
x[1] = 0.438 1.522
h = 0.001 0.003
y2[1] (numeric) = 0.94274455928 2.22070105211
y2[1] (closed_form) = 1.01783642784 1.97561722263
absolute error = 0.2563
relative error = 11.53 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.34606274771 -0.820090760792
y1[1] (closed_form) = 2.17328735042 -0.925259688404
absolute error = 0.2023
relative error = 8.563 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.74
Order of pole (three term test) = 36.09 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 11.74
Order of pole (three term test) = 29.41 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=30793.9MB, alloc=44.3MB, time=381.36
x[1] = 0.439 1.525
h = 0.0001 0.004
y2[1] (numeric) = 0.9492710995 2.22893645722
y2[1] (closed_form) = 1.02279550466 1.98121667646
absolute error = 0.2584
relative error = 11.59 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.35179119417 -0.825153591683
y1[1] (closed_form) = 2.17820228454 -0.930299047435
absolute error = 0.2029
relative error = 8.569 %
Correct digits = 1
memory used=30840.2MB, alloc=44.3MB, time=381.92
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.682
Order of pole (three term test) = 36.11 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.682
Order of pole (three term test) = 29.4 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=30886.0MB, alloc=44.3MB, time=382.49
x[1] = 0.4391 1.529
h = 0.003 0.006
y2[1] (numeric) = 0.95583617372 2.2371926158
y2[1] (closed_form) = 1.02674350247 1.98985190887
absolute error = 0.2573
relative error = 11.49 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.36062819034 -0.829187099654
y1[1] (closed_form) = 2.1860419346 -0.934596672629
absolute error = 0.2039
relative error = 8.578 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.925
Order of pole (three term test) = 36.14 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.925
Order of pole (three term test) = 29.38 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=30931.8MB, alloc=44.3MB, time=383.05
memory used=30978.1MB, alloc=44.3MB, time=383.62
x[1] = 0.4421 1.535
h = 0.0001 0.005
y2[1] (numeric) = 0.962439957573 2.24546959361
y2[1] (closed_form) = 1.03895900344 2.00017272536
absolute error = 0.257
relative error = 11.4 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.37119876211 -0.841665896687
y1[1] (closed_form) = 2.19491347133 -0.946778763074
absolute error = 0.2052
relative error = 8.586 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.017
Order of pole (three term test) = 36.16 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.017
Order of pole (three term test) = 29.37 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=31024.0MB, alloc=44.3MB, time=384.19
memory used=31070.2MB, alloc=44.3MB, time=384.76
x[1] = 0.4422 1.54
h = 0.0001 0.003
y2[1] (numeric) = 0.969082952597 2.25376735103
y2[1] (closed_form) = 1.04392639296 2.01107713205
absolute error = 0.254
relative error = 11.21 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.38235026997 -0.846719649231
y1[1] (closed_form) = 2.20483743149 -0.952186526969
absolute error = 0.2065
relative error = 8.597 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.266
Order of pole (three term test) = 36.2 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.266
Order of pole (three term test) = 29.35 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=31116.1MB, alloc=44.3MB, time=385.33
x[1] = 0.4423 1.543
h = 0.001 0.001
y2[1] (numeric) = 0.975765371315 2.26208604913
y2[1] (closed_form) = 1.04700873732 2.01760516178
absolute error = 0.2546
relative error = 11.2 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.38902680273 -0.849862704347
y1[1] (closed_form) = 2.21077590389 -0.955524360982
absolute error = 0.2072
relative error = 8.604 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.579
Order of pole (three term test) = 36.22 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.579
Order of pole (three term test) = 29.33 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=31162.2MB, alloc=44.3MB, time=385.90
memory used=31208.5MB, alloc=44.3MB, time=386.47
x[1] = 0.4433 1.544
h = 0.001 0.003
y2[1] (numeric) = 0.982487257896 2.27042576939
y2[1] (closed_form) = 1.05017705561 2.01885936525
absolute error = 0.2605
relative error = 11.45 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.39031393387 -0.853108081529
y1[1] (closed_form) = 2.21174554377 -0.95859118598
absolute error = 0.2074
relative error = 8.604 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.27
Order of pole (three term test) = 36.22 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 12.27
Order of pole (three term test) = 29.34 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=31254.4MB, alloc=44.3MB, time=387.04
memory used=31300.5MB, alloc=44.3MB, time=387.61
x[1] = 0.4443 1.547
h = 0.0001 0.004
y2[1] (numeric) = 0.989248631761 2.27878651957
y2[1] (closed_form) = 1.05527484447 2.02454093809
absolute error = 0.2627
relative error = 11.51 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.39615188239 -0.858340279877
y1[1] (closed_form) = 2.21675791752 -0.963771058023
absolute error = 0.2081
relative error = 8.608 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.983
Order of pole (three term test) = 36.24 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.983
Order of pole (three term test) = 29.33 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=31346.4MB, alloc=44.3MB, time=388.18
memory used=31392.5MB, alloc=44.3MB, time=388.76
x[1] = 0.4444 1.551
h = 0.003 0.006
y2[1] (numeric) = 0.996049555248 2.28716833134
y2[1] (closed_form) = 1.05936086328 2.0333273796
absolute error = 0.2616
relative error = 11.41 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.40518452048 -0.862539160622
y1[1] (closed_form) = 2.224767912 -0.968203216414
absolute error = 0.2091
relative error = 8.617 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.326
Order of pole (three term test) = 36.27 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 9.326
Order of pole (three term test) = 29.31 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=31438.4MB, alloc=44.3MB, time=389.32
x[1] = 0.4474 1.557
h = 0.0001 0.005
y2[1] (numeric) = 1.00289020803 2.29557127067
y2[1] (closed_form) = 1.07189540655 2.0437797308
absolute error = 0.2611
relative error = 11.31 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.41593432908 -0.875410064052
y1[1] (closed_form) = 2.23380236612 -0.98071259064
absolute error = 0.2104
relative error = 8.624 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.197
Order of pole (three term test) = 36.29 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.197
Order of pole (three term test) = 29.3 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=31484.2MB, alloc=44.3MB, time=389.90
memory used=31530.4MB, alloc=44.3MB, time=390.46
x[1] = 0.4475 1.562
h = 0.0001 0.003
y2[1] (numeric) = 1.00977110168 2.3039952938
y2[1] (closed_form) = 1.0770367882 2.05487571776
absolute error = 0.258
relative error = 11.12 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.42733260396 -0.880671678642
y1[1] (closed_form) = 2.24394153748 -0.98628984144
absolute error = 0.2116
relative error = 8.634 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.413
Order of pole (three term test) = 36.33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.413
Order of pole (three term test) = 29.27 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=31576.4MB, alloc=44.3MB, time=391.05
memory used=31622.9MB, alloc=44.3MB, time=391.63
x[1] = 0.4476 1.565
h = 0.001 0.001
y2[1] (numeric) = 1.01669245416 2.31244056373
y2[1] (closed_form) = 1.08022551506 2.06151783657
absolute error = 0.2588
relative error = 11.12 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.43415592957 -0.883942185468
y1[1] (closed_form) = 2.25000826033 -0.98973155169
absolute error = 0.2124
relative error = 8.64 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.695
Order of pole (three term test) = 36.36 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.695
Order of pole (three term test) = 29.26 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=31668.9MB, alloc=44.3MB, time=392.20
x[1] = 0.4486 1.566
h = 0.001 0.003
y2[1] (numeric) = 1.02365431109 2.32090716334
y2[1] (closed_form) = 1.08346731681 2.06277703198
absolute error = 0.265
relative error = 11.37 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.43545243165 -0.88727902756
y1[1] (closed_form) = 2.25098856187 -0.992875545377
absolute error = 0.2126
relative error = 8.639 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.82
Order of pole (three term test) = 36.36 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 12.82
Order of pole (three term test) = 29.26 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=31715.2MB, alloc=44.3MB, time=392.77
memory used=31761.1MB, alloc=44.3MB, time=393.33
x[1] = 0.4496 1.569
h = 0.0001 0.004
y2[1] (numeric) = 1.03065669233 2.32939510038
y2[1] (closed_form) = 1.08870746695 2.06854212527
absolute error = 0.2672
relative error = 11.43 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.44140072759 -0.892685633281
y1[1] (closed_form) = 2.25609945247 -0.998199461027
absolute error = 0.2132
relative error = 8.643 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.297
Order of pole (three term test) = 36.37 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.297
Order of pole (three term test) = 29.26 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=31807.0MB, alloc=44.3MB, time=393.89
memory used=31853.2MB, alloc=44.3MB, time=394.46
x[1] = 0.4497 1.573
h = 0.003 0.006
y2[1] (numeric) = 1.03769966171 2.3379044068
y2[1] (closed_form) = 1.09293541882 2.07748282889
absolute error = 0.2662
relative error = 11.34 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.45063190199 -0.897055697244
y1[1] (closed_form) = 2.26428240963 -1.00277004141
absolute error = 0.2142
relative error = 8.652 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.746
Order of pole (three term test) = 36.41 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 9.746
Order of pole (three term test) = 29.23 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=31899.0MB, alloc=44.3MB, time=395.02
memory used=31945.2MB, alloc=44.3MB, time=395.58
x[1] = 0.4527 1.579
h = 0.0001 0.005
y2[1] (numeric) = 1.04478340304 2.34643514873
y2[1] (closed_form) = 1.10579715686 2.08806855701
absolute error = 0.2655
relative error = 11.24 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.46156119561 -0.910329629908
y1[1] (closed_form) = 2.27348098276 -1.01561450972
absolute error = 0.2155
relative error = 8.656 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.386
Order of pole (three term test) = 36.43 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.386
Order of pole (three term test) = 29.23 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=31991.0MB, alloc=44.3MB, time=396.14
x[1] = 0.4528 1.584
h = 0.0001 0.003
y2[1] (numeric) = 1.05190843818 2.35498727817
y2[1] (closed_form) = 1.11111746249 2.09935998408
absolute error = 0.2624
relative error = 11.05 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.47320990849 -0.915806413177
y1[1] (closed_form) = 2.2838386873 -1.02136615485
absolute error = 0.2168
relative error = 8.666 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.567
Order of pole (three term test) = 36.47 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.567
Order of pole (three term test) = 29.2 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=32037.0MB, alloc=44.3MB, time=396.70
memory used=32083.3MB, alloc=44.3MB, time=397.28
x[1] = 0.4529 1.587
h = 0.001 0.001
y2[1] (numeric) = 1.05907499063 2.36356096004
y2[1] (closed_form) = 1.11441557471 2.1061184766
absolute error = 0.2633
relative error = 11.05 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.48018217662 -0.919208805164
y1[1] (closed_form) = 2.29003562387 -1.02491472537
absolute error = 0.2176
relative error = 8.671 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.817
Order of pole (three term test) = 36.5 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.817
Order of pole (three term test) = 29.19 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=32129.3MB, alloc=44.3MB, time=397.84
memory used=32175.7MB, alloc=44.3MB, time=398.42
x[1] = 0.4539 1.588
h = 0.0001 0.004
y2[1] (numeric) = 1.0662831075 2.37215627863
y2[1] (closed_form) = 1.1177326316 2.10738248198
absolute error = 0.2697
relative error = 11.31 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.48148735785 -0.922639337565
y1[1] (closed_form) = 2.29102630078 -1.02813754978
absolute error = 0.2177
relative error = 8.67 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.95
Order of pole (three term test) = 36.5 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 16.95
Order of pole (three term test) = 29.19 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=32221.7MB, alloc=44.3MB, time=398.98
memory used=32267.9MB, alloc=44.3MB, time=399.54
x[1] = 0.454 1.592
h = 0.003 0.006
y2[1] (numeric) = 1.0735328089 2.38077326291
y2[1] (closed_form) = 1.12208407645 2.11646019845
absolute error = 0.2687
relative error = 11.22 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.49088621925 -0.927156601823
y1[1] (closed_form) = 2.29936198451 -1.03282836853
absolute error = 0.2187
relative error = 8.678 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.12
Order of pole (three term test) = 36.53 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 10.12
Order of pole (three term test) = 29.17 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=32313.7MB, alloc=44.3MB, time=400.10
x[1] = 0.457 1.598
h = 0.0001 0.005
y2[1] (numeric) = 1.08082426967 2.38941197558
y2[1] (closed_form) = 1.13523250029 2.12716622938
absolute error = 0.2678
relative error = 11.11 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.50196523901 -0.940774924485
y1[1] (closed_form) = 2.30870690732 -1.0459657003
absolute error = 0.22
relative error = 8.681 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.556
Order of pole (three term test) = 36.56 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.556
Order of pole (three term test) = 29.17 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=32359.5MB, alloc=44.3MB, time=400.66
memory used=32405.8MB, alloc=44.3MB, time=401.22
x[1] = 0.4571 1.603
h = 0.0001 0.003
y2[1] (numeric) = 1.08815802069 2.39807236496
y2[1] (closed_form) = 1.14070847248 2.13863122546
absolute error = 0.2647
relative error = 10.92 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.51382549204 -0.946436736553
y1[1] (closed_form) = 2.31925758243 -1.05186882944
absolute error = 0.2213
relative error = 8.69 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.705
Order of pole (three term test) = 36.6 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.705
Order of pole (three term test) = 29.14 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=32451.7MB, alloc=44.3MB, time=401.79
memory used=32498.1MB, alloc=44.3MB, time=402.36
x[1] = 0.4572 1.606
h = 0.001 0.001
y2[1] (numeric) = 1.09553429037 2.40675459774
y2[1] (closed_form) = 1.14410177957 2.14549309219
absolute error = 0.2657
relative error = 10.93 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.52092354274 -0.949952505547
y1[1] (closed_form) = 2.32556952384 -1.05551024799
absolute error = 0.222
relative error = 8.695 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.926
Order of pole (three term test) = 36.62 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 2.926
Order of pole (three term test) = 29.12 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=32544.2MB, alloc=44.3MB, time=402.93
x[1] = 0.4582 1.607
h = 0.001 0.003
y2[1] (numeric) = 1.1029531271 2.41545875945
y2[1] (closed_form) = 1.14748500526 2.14676200624
absolute error = 0.2724
relative error = 11.19 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.52223540743 -0.953462850558
y1[1] (closed_form) = 2.32656985855 -1.05880216876
absolute error = 0.2222
relative error = 8.693 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.91
Order of pole (three term test) = 36.62 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 13.91
Order of pole (three term test) = 29.13 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=32590.3MB, alloc=44.3MB, time=403.50
memory used=32636.5MB, alloc=44.3MB, time=404.06
x[1] = 0.4592 1.61
h = 0.0001 0.004
y2[1] (numeric) = 1.11041455162 2.42418485794
y2[1] (closed_form) = 1.15299902511 2.15268806063
absolute error = 0.2748
relative error = 11.25 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.52838818709 -0.959202711403
y1[1] (closed_form) = 2.3318687909 -1.06440261346
absolute error = 0.2229
relative error = 8.696 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.92
Order of pole (three term test) = 36.64 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.92
Order of pole (three term test) = 29.12 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=32682.4MB, alloc=44.3MB, time=404.62
memory used=32728.4MB, alloc=44.3MB, time=405.18
x[1] = 0.4593 1.614
h = 0.003 0.006
y2[1] (numeric) = 1.11791863065 2.4329329256
y2[1] (closed_form) = 1.15749991496 2.16192586907
absolute error = 0.2739
relative error = 11.17 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.53799099901 -0.963902219242
y1[1] (closed_form) = 2.34038248279 -1.06923933502
absolute error = 0.2239
relative error = 8.703 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.58
Order of pole (three term test) = 36.68 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 10.58
Order of pole (three term test) = 29.1 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=32774.3MB, alloc=44.3MB, time=405.75
memory used=32820.5MB, alloc=44.3MB, time=406.32
x[1] = 0.4623 1.62
h = 0.0001 0.005
y2[1] (numeric) = 1.12546555594 2.44170302892
y2[1] (closed_form) = 1.17099116495 2.17276876495
absolute error = 0.2728
relative error = 11.05 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.54924983037 -0.977944298679
y1[1] (closed_form) = 2.34989384914 -1.08272679133
absolute error = 0.2252
relative error = 8.705 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.761
Order of pole (three term test) = 36.7 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.761
Order of pole (three term test) = 29.1 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=32866.3MB, alloc=44.3MB, time=406.88
x[1] = 0.4624 1.625
h = 0.0001 0.003
y2[1] (numeric) = 1.1330558691 2.45049511172
y2[1] (closed_form) = 1.17665553172 2.18443657237
absolute error = 0.2696
relative error = 10.87 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.56136739083 -0.983835193813
y1[1] (closed_form) = 2.36066945821 -1.08881375477
absolute error = 0.2265
relative error = 8.712 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.872
Order of pole (three term test) = 36.75 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.872
Order of pole (three term test) = 29.07 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=32912.3MB, alloc=44.3MB, time=407.44
memory used=32958.5MB, alloc=44.3MB, time=408.00
x[1] = 0.4625 1.628
h = 0.001 0.001
y2[1] (numeric) = 1.14068980438 2.45930934266
y2[1] (closed_form) = 1.18016399027 2.19141917551
absolute error = 0.2708
relative error = 10.88 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.56861840504 -0.987491291446
y1[1] (closed_form) = 2.36711539622 -1.0925677737
absolute error = 0.2273
relative error = 8.717 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.057
Order of pole (three term test) = 36.78 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.057
Order of pole (three term test) = 29.05 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=33004.6MB, alloc=44.3MB, time=408.58
memory used=33051.0MB, alloc=44.3MB, time=409.14
x[1] = 0.4635 1.629
h = 0.001 0.003
y2[1] (numeric) = 1.14836741172 2.46814580875
y2[1] (closed_form) = 1.18362586529 2.19269254182
absolute error = 0.2777
relative error = 11.14 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.5699376058 -0.991099542136
y1[1] (closed_form) = 2.36812555771 -1.09594172432
absolute error = 0.2274
relative error = 8.715 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 14.54
Order of pole (three term test) = 36.78 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 14.54
Order of pole (three term test) = 29.06 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=33097.0MB, alloc=44.3MB, time=409.71
memory used=33143.3MB, alloc=44.3MB, time=410.28
x[1] = 0.4645 1.632
h = 0.0001 0.004
y2[1] (numeric) = 1.15608871235 2.47700451786
y2[1] (closed_form) = 1.18929314216 2.19870619901
absolute error = 0.2803
relative error = 11.21 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.57620310131 -0.997028788701
y1[1] (closed_form) = 2.37352619559 -1.10169679566
absolute error = 0.2281
relative error = 8.717 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.277
Order of pole (three term test) = 36.79 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.277
Order of pole (three term test) = 29.05 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=33189.2MB, alloc=44.3MB, time=410.84
x[1] = 0.4646 1.636
h = 0.003 0.006
y2[1] (numeric) = 1.16385377456 2.48588550263
y2[1] (closed_form) = 1.19394768349 2.20810726147
absolute error = 0.2794
relative error = 11.13 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.58601287714 -1.00191680339
y1[1] (closed_form) = 2.38222064922 -1.10668361076
absolute error = 0.2291
relative error = 8.724 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.05
Order of pole (three term test) = 36.83 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 11.05
Order of pole (three term test) = 29.03 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=33235.0MB, alloc=44.3MB, time=411.40
memory used=33281.3MB, alloc=44.3MB, time=411.97
x[1] = 0.4676 1.642
h = 0.0001 0.005
y2[1] (numeric) = 1.17166279457 2.49478882968
y2[1] (closed_form) = 1.20779043935 2.21908881943
absolute error = 0.2781
relative error = 11.01 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.59745162519 -1.01639433691
y1[1] (closed_form) = 2.39189965004 -1.12052955906
absolute error = 0.2304
relative error = 8.724 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.975
Order of pole (three term test) = 36.86 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.975
Order of pole (three term test) = 29.03 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=33327.1MB, alloc=44.3MB, time=412.52
memory used=33373.2MB, alloc=44.3MB, time=413.09
x[1] = 0.4677 1.647
h = 0.0001 0.003
y2[1] (numeric) = 1.1795163249 2.50371443816
y2[1] (closed_form) = 1.21364850434 2.23096343677
absolute error = 0.2749
relative error = 10.82 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.60983031547 -1.02252219106
y1[1] (closed_form) = 2.40290368634 -1.12680564505
absolute error = 0.2317
relative error = 8.731 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.046
Order of pole (three term test) = 36.9 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.046
Order of pole (three term test) = 29.01 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=33419.2MB, alloc=44.3MB, time=413.66
x[1] = 0.4678 1.65
h = 0.001 0.001
y2[1] (numeric) = 1.18741460577 2.51266249875
y2[1] (closed_form) = 1.21727534242 2.23806914163
absolute error = 0.2762
relative error = 10.84 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.61723652907 -1.02632339492
y1[1] (closed_form) = 2.40948568428 -1.13067547922
absolute error = 0.2325
relative error = 8.735 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.195
Order of pole (three term test) = 36.93 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.195
Order of pole (three term test) = 28.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=33465.3MB, alloc=44.3MB, time=414.22
memory used=33511.7MB, alloc=44.3MB, time=414.79
x[1] = 0.4688 1.651
h = 0.001 0.003
y2[1] (numeric) = 1.19535768873 2.52163309992
y2[1] (closed_form) = 1.22081774208 2.23934673338
absolute error = 0.2834
relative error = 11.11 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.61856229258 -1.03003192325
y1[1] (closed_form) = 2.41050534625 -1.13413323353
absolute error = 0.2326
relative error = 8.733 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 15.19
Order of pole (three term test) = 36.93 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 15.19
Order of pole (three term test) = 29 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=33557.6MB, alloc=44.3MB, time=415.35
memory used=33603.9MB, alloc=44.3MB, time=415.92
x[1] = 0.4698 1.654
h = 0.0001 0.004
y2[1] (numeric) = 1.2033455955 2.5306262496
y2[1] (closed_form) = 1.2266422623 2.24544941343
absolute error = 0.2861
relative error = 11.18 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.62494132806 -1.03615609476
y1[1] (closed_form) = 2.41600880976 -1.14004681492
absolute error = 0.2333
relative error = 8.734 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.649
Order of pole (three term test) = 36.95 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.649
Order of pole (three term test) = 28.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=33649.7MB, alloc=44.3MB, time=416.49
memory used=33695.8MB, alloc=44.3MB, time=417.05
x[1] = 0.4699 1.658
h = 0.003 0.006
y2[1] (numeric) = 1.21137839602 2.53964198064
y2[1] (closed_form) = 1.23145476971 2.25501693053
absolute error = 0.2853
relative error = 11.11 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.63496112115 -1.04123904099
y1[1] (closed_form) = 2.4248868261 -1.14518802485
absolute error = 0.2344
relative error = 8.74 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.55
Order of pole (three term test) = 36.99 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 11.55
Order of pole (three term test) = 28.97 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=33741.6MB, alloc=44.3MB, time=417.61
x[1] = 0.4729 1.664
h = 0.0001 0.005
y2[1] (numeric) = 1.21945629103 2.54868035982
y2[1] (closed_form) = 1.24565790377 2.26613892894
absolute error = 0.2838
relative error = 10.97 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.64657983618 -1.05616400022
y1[1] (closed_form) = 2.43473464515 -1.15940103514
absolute error = 0.2357
relative error = 8.739 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.199
Order of pole (three term test) = 37.02 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.199
Order of pole (three term test) = 28.97 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=33787.6MB, alloc=44.3MB, time=418.17
memory used=33833.7MB, alloc=44.3MB, time=418.73
x[1] = 0.473 1.669
h = 0.0001 0.003
y2[1] (numeric) = 1.22757984421 2.55774132143
y2[1] (closed_form) = 1.25171510718 2.27822440391
absolute error = 0.2806
relative error = 10.79 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.65922352953 -1.06253689236
y1[1] (closed_form) = 2.44597066198 -1.16587167142
absolute error = 0.237
relative error = 8.746 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.228
Order of pole (three term test) = 37.06 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.228
Order of pole (three term test) = 28.94 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=33879.6MB, alloc=44.3MB, time=419.29
memory used=33926.0MB, alloc=44.3MB, time=419.87
x[1] = 0.4731 1.672
h = 0.001 0.001
y2[1] (numeric) = 1.23574930191 2.56682503817
y2[1] (closed_form) = 1.25546363553 2.28545560429
absolute error = 0.2821
relative error = 10.82 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.66678720728 -1.06648810272
y1[1] (closed_form) = 2.45269081822 -1.16986062021
absolute error = 0.2377
relative error = 8.749 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.338
Order of pole (three term test) = 37.09 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.338
Order of pole (three term test) = 28.93 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=33972.0MB, alloc=44.3MB, time=420.44
x[1] = 0.4741 1.673
h = 0.001 0.003
y2[1] (numeric) = 1.24396471734 2.57593160007
y2[1] (closed_form) = 1.25908847285 2.28673717781
absolute error = 0.2896
relative error = 11.09 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.66811873052 -1.07029933231
y1[1] (closed_form) = 2.45371963914 -1.17340399249
absolute error = 0.2379
relative error = 8.747 %
Correct digits = 1
memory used=34018.3MB, alloc=44.3MB, time=421.01
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 15.88
Order of pole (three term test) = 37.09 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 15.88
Order of pole (three term test) = 28.93 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=34064.3MB, alloc=44.3MB, time=421.57
x[1] = 0.4751 1.676
h = 0.0001 0.004
y2[1] (numeric) = 1.25222611273 2.58506101504
y2[1] (closed_form) = 1.26507431519 2.29293030469
absolute error = 0.2924
relative error = 11.17 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.67461212215 -1.07662410146
y1[1] (closed_form) = 2.45932705827 -1.17948006356
absolute error = 0.2386
relative error = 8.748 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.038
Order of pole (three term test) = 37.11 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 9.038
Order of pole (three term test) = 28.93 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=34110.1MB, alloc=44.3MB, time=422.13
memory used=34156.2MB, alloc=44.3MB, time=422.69
x[1] = 0.4752 1.68
h = 0.003 0.006
y2[1] (numeric) = 1.26053355967 2.59421331621
y2[1] (closed_form) = 1.27004921414 2.30266751613
absolute error = 0.2917
relative error = 11.09 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.68484502556 -1.08190856896
y1[1] (closed_form) = 2.46839148601 -1.18478008284
absolute error = 0.2397
relative error = 8.753 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.07
Order of pole (three term test) = 37.15 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 12.07
Order of pole (three term test) = 28.91 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=34201.9MB, alloc=44.3MB, time=423.26
memory used=34248.2MB, alloc=44.3MB, time=423.83
x[1] = 0.4782 1.686
h = 0.0001 0.005
y2[1] (numeric) = 1.26888726356 2.60338857044
y2[1] (closed_form) = 1.28462179578 2.31393171334
absolute error = 0.2899
relative error = 10.95 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.69664370017 -1.09729320527
y1[1] (closed_form) = 2.47840929841 -1.19936893184
absolute error = 0.2409
relative error = 8.75 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.433
Order of pole (three term test) = 37.18 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.433
Order of pole (three term test) = 28.91 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=34294.2MB, alloc=44.3MB, time=424.39
x[1] = 0.4783 1.691
h = 0.0001 0.003
y2[1] (numeric) = 1.27728779949 2.61258670704
y2[1] (closed_form) = 1.29088371777 2.32623214333
absolute error = 0.2867
relative error = 10.78 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.70955632044 -1.1039194219
y1[1] (closed_form) = 2.48988090945 -1.20603968896
absolute error = 0.2423
relative error = 8.756 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.418
Order of pole (three term test) = 37.23 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.418
Order of pole (three term test) = 28.89 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=34340.1MB, alloc=44.3MB, time=424.95
memory used=34386.5MB, alloc=44.3MB, time=425.52
x[1] = 0.4784 1.694
h = 0.001 0.001
y2[1] (numeric) = 1.28573542007 2.62180790076
y2[1] (closed_form) = 1.29475733186 2.33359126187
absolute error = 0.2884
relative error = 10.81 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.7172797558 -1.10802566449
y1[1] (closed_form) = 2.49674135757 -1.21015113829
absolute error = 0.243
relative error = 8.759 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.489
Order of pole (three term test) = 37.26 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.489
Order of pole (three term test) = 28.87 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=34432.6MB, alloc=44.3MB, time=426.09
memory used=34479.1MB, alloc=44.3MB, time=426.66
x[1] = 0.4794 1.695
h = 0.0001 0.004
y2[1] (numeric) = 1.29423018021 2.63105224317
y2[1] (closed_form) = 1.29846655837 2.3348765561
absolute error = 0.2962
relative error = 11.09 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.71861620508 -1.1119420715
y1[1] (closed_form) = 2.49777898014 -1.21378198397
absolute error = 0.2432
relative error = 8.757 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 20.99
Order of pole (three term test) = 37.26 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 20.99
Order of pole (three term test) = 28.88 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=34525.0MB, alloc=44.3MB, time=427.22
memory used=34571.1MB, alloc=44.3MB, time=427.78
x[1] = 0.4795 1.699
h = 0.003 0.006
y2[1] (numeric) = 1.30277210313 2.6403197656
y2[1] (closed_form) = 1.30358279433 2.34476446742
absolute error = 0.2956
relative error = 11.02 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.72902909163 -1.11739962875
y1[1] (closed_form) = 2.50700814778 -1.21922005686
absolute error = 0.2443
relative error = 8.762 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.54
Order of pole (three term test) = 37.3 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 12.54
Order of pole (three term test) = 28.86 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=34617.0MB, alloc=44.3MB, time=428.34
x[1] = 0.4825 1.705
h = 0.0001 0.005
y2[1] (numeric) = 1.31136138419 2.64961053149
y2[1] (closed_form) = 1.31847907848 2.35615700801
absolute error = 0.2935
relative error = 10.87 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.7409776826 -1.13317689503
y1[1] (closed_form) = 2.51717784127 -1.23413756062
absolute error = 0.2455
relative error = 8.758 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.643
Order of pole (three term test) = 37.33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.643
Order of pole (three term test) = 28.86 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=34662.8MB, alloc=44.3MB, time=428.90
memory used=34709.1MB, alloc=44.3MB, time=429.47
x[1] = 0.4826 1.71
h = 0.0001 0.003
y2[1] (numeric) = 1.31999860857 2.65892446582
y2[1] (closed_form) = 1.3249191654 2.3686483153
absolute error = 0.2903
relative error = 10.7 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.75411744282 -1.14002070152
y1[1] (closed_form) = 2.52885766091 -1.24098228127
absolute error = 0.2469
relative error = 8.763 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.589
Order of pole (three term test) = 37.39 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.589
Order of pole (three term test) = 28.84 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=34755.1MB, alloc=44.3MB, time=430.03
memory used=34801.5MB, alloc=44.3MB, time=430.60
x[1] = 0.4827 1.713
h = 0.001 0.001
y2[1] (numeric) = 1.32868403436 2.66826174519
y2[1] (closed_form) = 1.32890167083 2.37612105044
absolute error = 0.2921
relative error = 10.73 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.76197578255 -1.14426007253
y1[1] (closed_form) = 2.5358421189 -1.24520024748
absolute error = 0.2476
relative error = 8.766 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.624
Order of pole (three term test) = 37.42 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.624
Order of pole (three term test) = 28.82 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=34847.5MB, alloc=44.3MB, time=431.17
x[1] = 0.4837 1.714
h = 0.001 0.003
y2[1] (numeric) = 1.33741771798 2.67762246256
y2[1] (closed_form) = 1.33268508975 2.37741036215
absolute error = 0.3002
relative error = 11.02 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.76331567585 -1.14826605954
y1[1] (closed_form) = 2.53688809184 -1.24890780639
absolute error = 0.2478
relative error = 8.763 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.23
Order of pole (three term test) = 37.42 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 17.23
Order of pole (three term test) = 28.83 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=34893.8MB, alloc=44.3MB, time=431.73
memory used=34939.9MB, alloc=44.3MB, time=432.30
x[1] = 0.4847 1.717
h = 0.0001 0.004
y2[1] (numeric) = 1.3461996826 2.68700662588
y2[1] (closed_form) = 1.33898117898 2.3837776324
absolute error = 0.3033
relative error = 11.09 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.77002080894 -1.15497378615
y1[1] (closed_form) = 2.54269404002 -1.25529589263
absolute error = 0.2485
relative error = 8.763 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.81
Order of pole (three term test) = 37.44 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 9.81
Order of pole (three term test) = 28.83 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=34985.7MB, alloc=44.3MB, time=432.86
memory used=35031.9MB, alloc=44.3MB, time=433.42
x[1] = 0.4848 1.721
h = 0.003 0.006
y2[1] (numeric) = 1.35503000307 2.69641426875
y2[1] (closed_form) = 1.34426830603 2.39384142778
absolute error = 0.3028
relative error = 11.03 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.78065258181 -1.16064540024
y1[1] (closed_form) = 2.55211510349 -1.26090126446
absolute error = 0.2496
relative error = 8.767 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.1
Order of pole (three term test) = 37.48 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 13.1
Order of pole (three term test) = 28.8 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=35077.8MB, alloc=44.3MB, time=433.98
memory used=35123.9MB, alloc=44.3MB, time=434.55
x[1] = 0.4878 1.727
h = 0.0001 0.005
y2[1] (numeric) = 1.36390889368 2.70584545825
y2[1] (closed_form) = 1.35955143354 2.40537949502
absolute error = 0.3005
relative error = 10.88 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.79278095311 -1.17690557621
y1[1] (closed_form) = 2.56245705931 -1.27621148959
absolute error = 0.2508
relative error = 8.762 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.897
Order of pole (three term test) = 37.51 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.897
Order of pole (three term test) = 28.81 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=35169.8MB, alloc=44.3MB, time=435.11
x[1] = 0.4879 1.732
h = 0.0001 0.003
y2[1] (numeric) = 1.37283695149 2.71530011409
y2[1] (closed_form) = 1.36620695678 2.4180935864
absolute error = 0.2973
relative error = 10.7 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.80619697036 -1.18401847734
y1[1] (closed_form) = 2.57437942985 -1.28326704353
absolute error = 0.2522
relative error = 8.767 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.795
Order of pole (three term test) = 37.57 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.795
Order of pole (three term test) = 28.79 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=35215.7MB, alloc=44.3MB, time=435.67
memory used=35261.9MB, alloc=44.3MB, time=436.24
x[1] = 0.488 1.735
h = 0.001 0.001
y2[1] (numeric) = 1.38181444117 2.72477841495
y2[1] (closed_form) = 1.3703210693 2.42569886843
absolute error = 0.2993
relative error = 10.74 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.81421935006 -1.18842244579
y1[1] (closed_form) = 2.58150828701 -1.28761402158
absolute error = 0.253
relative error = 8.769 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.787
Order of pole (three term test) = 37.6 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.787
Order of pole (three term test) = 28.77 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=35307.9MB, alloc=44.3MB, time=436.81
memory used=35354.3MB, alloc=44.3MB, time=437.38
x[1] = 0.489 1.736
h = 0.001 0.003
y2[1] (numeric) = 1.39084142091 2.7342804554
y2[1] (closed_form) = 1.37419261774 2.42699139108
absolute error = 0.3077
relative error = 11.03 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.81556255371 -1.19253829705
y1[1] (closed_form) = 2.58256237593 -1.29141262338
absolute error = 0.2531
relative error = 8.766 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 18.01
Order of pole (three term test) = 37.6 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 18.01
Order of pole (three term test) = 28.78 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=35400.2MB, alloc=44.3MB, time=437.94
memory used=35446.5MB, alloc=44.3MB, time=438.51
x[1] = 0.49 1.739
h = 0.0001 0.004
y2[1] (numeric) = 1.39991791443 2.74380624342
y2[1] (closed_form) = 1.3806622108 2.43345325312
absolute error = 0.3109
relative error = 11.11 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.82238430228 -1.19946346504
y1[1] (closed_form) = 2.58847561482 -1.29797512061
absolute error = 0.2538
relative error = 8.765 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.25
Order of pole (three term test) = 37.62 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 10.25
Order of pole (three term test) = 28.78 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=35492.4MB, alloc=44.3MB, time=439.07
x[1] = 0.4901 1.743
h = 0.003 0.006
y2[1] (numeric) = 1.40904399838 2.75335581284
y2[1] (closed_form) = 1.38612498653 2.44369628781
absolute error = 0.3105
relative error = 11.05 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.83323817077 -1.20535623022
y1[1] (closed_form) = 2.59809156211 -1.30375254414
absolute error = 0.2549
relative error = 8.769 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.69
Order of pole (three term test) = 37.66 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 13.69
Order of pole (three term test) = 28.76 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=35538.1MB, alloc=44.3MB, time=439.62
memory used=35584.4MB, alloc=44.3MB, time=440.19
x[1] = 0.4931 1.749
h = 0.0001 0.005
y2[1] (numeric) = 1.418219892 2.76292923078
y2[1] (closed_form) = 1.40180461621 2.45538157787
absolute error = 0.308
relative error = 10.89 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.84554613069 -1.22211241846
y1[1] (closed_form) = 2.60860692478 -1.31946488285
absolute error = 0.2562
relative error = 8.763 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.162
Order of pole (three term test) = 37.7 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.162
Order of pole (three term test) = 28.77 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=35630.2MB, alloc=44.3MB, time=440.75
memory used=35676.4MB, alloc=44.3MB, time=441.32
x[1] = 0.4932 1.754
h = 0.0001 0.003
y2[1] (numeric) = 1.42744620446 2.77252641149
y2[1] (closed_form) = 1.40868157531 2.46832269779
absolute error = 0.3048
relative error = 10.72 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.85924247699 -1.22950333519
y1[1] (closed_form) = 2.62077563643 -1.32673726738
absolute error = 0.2575
relative error = 8.767 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.011
Order of pole (three term test) = 37.75 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.011
Order of pole (three term test) = 28.75 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=35722.3MB, alloc=44.3MB, time=441.88
x[1] = 0.4933 1.757
h = 0.001 0.001
y2[1] (numeric) = 1.43672320719 2.78214753576
y2[1] (closed_form) = 1.41293094433 2.47606303465
absolute error = 0.307
relative error = 10.77 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.86743127386 -1.23407731012
y1[1] (closed_form) = 2.62805112917 -1.33121690173
absolute error = 0.2583
relative error = 8.769 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.957
Order of pole (three term test) = 37.79 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 3.957
Order of pole (three term test) = 28.73 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=35768.5MB, alloc=44.3MB, time=442.45
memory used=35814.6MB, alloc=44.3MB, time=443.02
x[1] = 0.4943 1.758
h = 0.001 0.003
y2[1] (numeric) = 1.44605096019 2.79179269978
y2[1] (closed_form) = 1.41689268886 2.47735845462
absolute error = 0.3158
relative error = 11.06 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.86877685912 -1.23830566109
y1[1] (closed_form) = 2.62911292875 -1.33510852412
absolute error = 0.2585
relative error = 8.766 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 18.82
Order of pole (three term test) = 37.79 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 18.82
Order of pole (three term test) = 28.74 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=35860.5MB, alloc=44.3MB, time=443.58
memory used=35906.7MB, alloc=44.3MB, time=444.14
x[1] = 0.4953 1.761
h = 0.0001 0.004
y2[1] (numeric) = 1.45542948774 2.80146191155
y2[1] (closed_form) = 1.42354024241 2.48391634574
absolute error = 0.3191
relative error = 11.15 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.87571599903 -1.24545449436
y1[1] (closed_form) = 2.63513462384 -1.34184980341
absolute error = 0.2592
relative error = 8.764 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.71
Order of pole (three term test) = 37.81 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 10.71
Order of pole (three term test) = 28.74 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=35952.6MB, alloc=44.3MB, time=444.71
memory used=35998.8MB, alloc=44.3MB, time=445.28
x[1] = 0.4954 1.765
h = 0.003 0.006
y2[1] (numeric) = 1.46485886832 2.81115520514
y2[1] (closed_form) = 1.42918354627 2.49434201576
absolute error = 0.3188
relative error = 11.09 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.88679521123 -1.25157568476
y1[1] (closed_form) = 2.64494849169 -1.34780415531
absolute error = 0.2603
relative error = 8.768 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 14.31
Order of pole (three term test) = 37.86 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 14.31
Order of pole (three term test) = 28.72 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=36044.7MB, alloc=44.3MB, time=445.84
x[1] = 0.4984 1.771
h = 0.0001 0.005
y2[1] (numeric) = 1.47433932626 2.82087264771
y2[1] (closed_form) = 1.44526955204 2.50617619947
absolute error = 0.316
relative error = 10.92 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.89928249829 -1.26884128941
y1[1] (closed_form) = 2.65563839101 -1.36392822358
absolute error = 0.2615
relative error = 8.761 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.439
Order of pole (three term test) = 37.89 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.439
Order of pole (three term test) = 28.74 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=36090.5MB, alloc=44.3MB, time=446.39
memory used=36136.7MB, alloc=44.3MB, time=446.96
x[1] = 0.4985 1.776
h = 0.0001 0.003
y2[1] (numeric) = 1.4838714831 2.83061414784
y2[1] (closed_form) = 1.45237410047 2.51934864425
absolute error = 0.3129
relative error = 10.76 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.91326329512 -1.27651936895
y1[1] (closed_form) = 2.6680572957 -1.37142359231
absolute error = 0.2629
relative error = 8.765 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.236
Order of pole (three term test) = 37.95 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.236
Order of pole (three term test) = 28.71 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=36182.5MB, alloc=44.3MB, time=447.52
memory used=36228.8MB, alloc=44.3MB, time=448.09
x[1] = 0.4986 1.779
h = 0.001 0.001
y2[1] (numeric) = 1.49345561717 2.84037988845
y2[1] (closed_form) = 1.45676246856 2.5272265739
absolute error = 0.3153
relative error = 10.81 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.92162091418 -1.28126889609
y1[1] (closed_form) = 2.67548169637 -1.3760396221
absolute error = 0.2638
relative error = 8.767 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.135
Order of pole (three term test) = 37.99 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.135
Order of pole (three term test) = 28.7 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=36274.8MB, alloc=44.3MB, time=448.66
x[1] = 0.4996 1.78
h = 0.001 0.003
y2[1] (numeric) = 1.50309179034 2.85016996738
y2[1] (closed_form) = 1.46081651754 2.52852455786
absolute error = 0.3244
relative error = 11.11 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 2.92296791771 -1.28561243835
y1[1] (closed_form) = 2.67655078311 -1.38002628698
absolute error = 0.2639
relative error = 8.763 %
Correct digits = 1
memory used=36321.3MB, alloc=44.3MB, time=449.24
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 19.66
Order of pole (three term test) = 37.98 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 19.66
Order of pole (three term test) = 28.71 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=36367.2MB, alloc=44.3MB, time=449.80
x[1] = 0.5006 1.783
h = 0.0001 0.004
y2[1] (numeric) = 1.51278002748 2.85998439268
y2[1] (closed_form) = 1.46764659177 2.53517991762
absolute error = 0.3279
relative error = 11.19 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.93002521159 -1.29299130821
y1[1] (closed_form) = 2.68268210764 -1.3869508262
absolute error = 0.2646
relative error = 8.761 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.19
Order of pole (three term test) = 38.01 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 11.19
Order of pole (three term test) = 28.71 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=36413.2MB, alloc=44.3MB, time=450.36
memory used=36459.4MB, alloc=44.3MB, time=450.92
x[1] = 0.5007 1.787
h = 0.003 0.006
y2[1] (numeric) = 1.52252040893 2.86982319862
y2[1] (closed_form) = 1.47347542812 2.54579166015
absolute error = 0.3277
relative error = 11.14 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.94133305404 -1.29934838186
y1[1] (closed_form) = 2.69269698176 -1.39308710997
absolute error = 0.2657
relative error = 8.765 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 14.95
Order of pole (three term test) = 38.06 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 14.95
Order of pole (three term test) = 28.69 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=36505.3MB, alloc=44.3MB, time=451.49
memory used=36551.6MB, alloc=44.3MB, time=452.06
x[1] = 0.5037 1.793
h = 0.0001 0.005
y2[1] (numeric) = 1.53231316423 2.87968645239
y2[1] (closed_form) = 1.48997790389 2.55777638144
absolute error = 0.3247
relative error = 10.97 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 2.95399933361 -1.31713711462
y1[1] (closed_form) = 2.70356253107 -1.40963275221
absolute error = 0.267
relative error = 8.756 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.728
Order of pole (three term test) = 38.09 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.728
Order of pole (three term test) = 28.71 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=36597.4MB, alloc=44.3MB, time=452.62
x[1] = 0.5038 1.798
h = 0.0001 0.003
y2[1] (numeric) = 1.54215892754 2.88957405671
y2[1] (closed_form) = 1.49731635283 2.5711844998
absolute error = 0.3215
relative error = 10.81 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 2.96826875155 -1.32511173549
y1[1] (closed_form) = 2.71623554282 -1.41735741875
absolute error = 0.2684
relative error = 8.76 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.472
Order of pole (three term test) = 38.15 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.472
Order of pole (three term test) = 28.68 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=36643.5MB, alloc=44.3MB, time=453.18
memory used=36689.7MB, alloc=44.3MB, time=453.76
x[1] = 0.5039 1.801
h = 0.001 0.001
y2[1] (numeric) = 1.55205798427 2.89948619665
y2[1] (closed_form) = 1.50184755801 2.57920259052
absolute error = 0.3242
relative error = 10.86 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 2.97679762538 -1.33004250033
y1[1] (closed_form) = 2.72381115982 -1.42211368003
absolute error = 0.2692
relative error = 8.762 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.321
Order of pole (three term test) = 38.19 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.321
Order of pole (three term test) = 28.67 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=36735.8MB, alloc=44.3MB, time=454.33
memory used=36782.1MB, alloc=44.3MB, time=454.90
x[1] = 0.5049 1.802
h = 0.0001 0.004
y2[1] (numeric) = 1.56201039822 2.90942297176
y2[1] (closed_form) = 1.50599606249 2.58050278477
absolute error = 0.3337
relative error = 11.17 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 2.97814504817 -1.33450398261
y1[1] (closed_form) = 2.72488709138 -1.42619745435
absolute error = 0.2693
relative error = 8.758 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26
Order of pole (three term test) = 38.19 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 26
Order of pole (three term test) = 28.68 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=36828.0MB, alloc=44.3MB, time=455.46
memory used=36874.1MB, alloc=44.3MB, time=456.02
x[1] = 0.505 1.806
h = 0.003 0.006
y2[1] (numeric) = 1.57201619613 2.91938441596
y2[1] (closed_form) = 1.51198643104 2.59127977001
absolute error = 0.3336
relative error = 11.12 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 2.98964595382 -1.34106345815
y1[1] (closed_form) = 2.7350797442 -1.4324919994
absolute error = 0.2705
relative error = 8.761 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 15.53
Order of pole (three term test) = 38.24 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 15.53
Order of pole (three term test) = 28.66 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=36920.1MB, alloc=44.3MB, time=456.58
x[1] = 0.508 1.812
h = 0.0001 0.005
y2[1] (numeric) = 1.58207559638 2.92937059302
y2[1] (closed_form) = 1.52885382557 2.60340049252
absolute error = 0.3303
relative error = 10.94 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 3.0024610823 -1.35929883292
y1[1] (closed_form) = 2.74610255054 -1.44940646943
absolute error = 0.2717
relative error = 8.751 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.989
Order of pole (three term test) = 38.28 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.989
Order of pole (three term test) = 28.69 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=36965.9MB, alloc=44.3MB, time=457.14
memory used=37012.1MB, alloc=44.3MB, time=457.70
x[1] = 0.5081 1.817
h = 0.0001 0.003
y2[1] (numeric) = 1.5921892443 2.93938140058
y2[1] (closed_form) = 1.53639590654 2.61701788508
absolute error = 0.3272
relative error = 10.78 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.0169742392 -1.36752790972
y1[1] (closed_form) = 2.7590003078 -1.45733059711
absolute error = 0.2732
relative error = 8.754 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.683
Order of pole (three term test) = 38.34 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.683
Order of pole (three term test) = 28.66 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=37058.1MB, alloc=44.3MB, time=458.27
memory used=37104.6MB, alloc=44.3MB, time=458.85
x[1] = 0.5082 1.82
h = 0.001 0.001
y2[1] (numeric) = 1.60235743148 2.94941702565
y2[1] (closed_form) = 1.54105149735 2.62516046725
absolute error = 0.33
relative error = 10.84 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.02564770374 -1.3726141558
y1[1] (closed_form) = 2.76670969743 -1.46220887309
absolute error = 0.274
relative error = 8.756 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.488
Order of pole (three term test) = 38.38 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.488
Order of pole (three term test) = 28.65 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=37150.6MB, alloc=44.3MB, time=459.41
x[1] = 0.5092 1.821
h = 0.001 0.003
y2[1] (numeric) = 1.61258022342 2.9594775693
y2[1] (closed_form) = 1.54528304152 2.62646342561
absolute error = 0.3397
relative error = 11.15 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 3.02699468469 -1.3771760653
y1[1] (closed_form) = 2.7677923428 -1.46637785212
absolute error = 0.2741
relative error = 8.752 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 21.34
Order of pole (three term test) = 38.38 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 21.34
Order of pole (three term test) = 28.66 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=37196.9MB, alloc=44.3MB, time=459.98
memory used=37242.9MB, alloc=44.3MB, time=460.54
x[1] = 0.5102 1.824
h = 0.0001 0.004
y2[1] (numeric) = 1.62285764607 2.96956303958
y2[1] (closed_form) = 1.55246404434 2.63330629674
absolute error = 0.3435
relative error = 11.24 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 3.03427052499 -1.38499372666
y1[1] (closed_form) = 2.77413312325 -1.47365434959
absolute error = 0.2748
relative error = 8.749 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.15
Order of pole (three term test) = 38.4 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 12.15
Order of pole (three term test) = 28.67 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=37288.9MB, alloc=44.3MB, time=461.10
memory used=37335.1MB, alloc=44.3MB, time=461.67
x[1] = 0.5103 1.828
h = 0.003 0.006
y2[1] (numeric) = 1.63318978338 2.97967347122
y2[1] (closed_form) = 1.55864955826 2.64427592448
absolute error = 0.3436
relative error = 11.19 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 3.04600618775 -1.39180326488
y1[1] (closed_form) = 2.78453271859 -1.48014044657
absolute error = 0.276
relative error = 8.752 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.23
Order of pole (three term test) = 38.46 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 16.23
Order of pole (three term test) = 28.65 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=37380.8MB, alloc=44.3MB, time=462.22
memory used=37427.1MB, alloc=44.3MB, time=462.79
x[1] = 0.5133 1.834
h = 0.0001 0.005
y2[1] (numeric) = 1.64357687488 2.98980893144
y2[1] (closed_form) = 1.57595278916 2.65655029309
absolute error = 0.3401
relative error = 11.01 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 3.05899948631 -1.41058775459
y1[1] (closed_form) = 2.79573332059 -1.49749542029
absolute error = 0.2772
relative error = 8.742 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.303
Order of pole (three term test) = 38.5 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.303
Order of pole (three term test) = 28.68 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=37473.0MB, alloc=44.3MB, time=463.36
x[1] = 0.5134 1.839
h = 0.0001 0.003
y2[1] (numeric) = 1.65401957905 2.99996931171
y2[1] (closed_form) = 1.5837408941 2.67041167214
absolute error = 0.337
relative error = 10.85 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.07380904215 -1.41913121116
y1[1] (closed_form) = 2.80889271409 -1.5056609845
absolute error = 0.2787
relative error = 8.745 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.939
Order of pole (three term test) = 38.56 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.939
Order of pole (three term test) = 28.65 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=37519.0MB, alloc=44.3MB, time=463.92
memory used=37565.2MB, alloc=44.3MB, time=464.49
x[1] = 0.5135 1.842
h = 0.001 0.001
y2[1] (numeric) = 1.66451819487 3.01015480125
y2[1] (closed_form) = 1.58854669439 2.67869932449
absolute error = 0.3401
relative error = 10.92 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.0826582956 -1.42440950983
y1[1] (closed_form) = 2.81675776056 -1.51068686727
absolute error = 0.2795
relative error = 8.746 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.69
Order of pole (three term test) = 38.6 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.69
Order of pole (three term test) = 28.64 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=37611.2MB, alloc=44.3MB, time=465.10
memory used=37657.4MB, alloc=44.3MB, time=465.67
x[1] = 0.5145 1.843
h = 0.001 0.003
y2[1] (numeric) = 1.67507278988 3.02036550284
y2[1] (closed_form) = 1.59287681815 2.68000380539
absolute error = 0.3501
relative error = 11.23 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 3.08400376283 -1.4290945587
y1[1] (closed_form) = 2.81784640109 -1.51495693041
absolute error = 0.2797
relative error = 8.741 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.3
Order of pole (three term test) = 38.6 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 22.3
Order of pole (three term test) = 28.66 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=37703.3MB, alloc=44.3MB, time=466.24
memory used=37749.6MB, alloc=44.3MB, time=466.80
x[1] = 0.5155 1.846
h = 0.0001 0.004
y2[1] (numeric) = 1.68568339062 3.03060142457
y2[1] (closed_form) = 1.60025396363 2.68694833093
absolute error = 0.3541
relative error = 11.32 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 3.09139983349 -1.43716116033
y1[1] (closed_form) = 2.82430026333 -1.52243009444
absolute error = 0.2804
relative error = 8.739 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.7
Order of pole (three term test) = 38.63 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 12.7
Order of pole (three term test) = 28.66 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=37795.4MB, alloc=44.3MB, time=467.36
x[1] = 0.5156 1.85
h = 0.003 0.006
y2[1] (numeric) = 1.69635008308 3.04086260137
y2[1] (closed_form) = 1.60664000133 2.69811415991
absolute error = 0.3543
relative error = 11.28 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 3.1033736519 -1.44422878155
y1[1] (closed_form) = 2.83491002992 -1.52911312588
absolute error = 0.2816
relative error = 8.741 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.96
Order of pole (three term test) = 38.68 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 16.96
Order of pole (three term test) = 28.64 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=37841.1MB, alloc=44.3MB, time=467.92
memory used=37887.3MB, alloc=44.3MB, time=468.48
x[1] = 0.5186 1.856
h = 0.0001 0.005
y2[1] (numeric) = 1.70707311231 3.05114910043
y2[1] (closed_form) = 1.62438982014 2.71054373536
absolute error = 0.3505
relative error = 11.09 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 3.11654455375 -1.46357703404
y1[1] (closed_form) = 2.84628948669 -1.54691912799
absolute error = 0.2828
relative error = 8.73 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.632
Order of pole (three term test) = 38.72 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.632
Order of pole (three term test) = 28.68 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=37933.3MB, alloc=44.3MB, time=469.05
memory used=37979.5MB, alloc=44.3MB, time=469.61
x[1] = 0.5187 1.861
h = 0.0001 0.003
y2[1] (numeric) = 1.7178531502 3.06146080681
y2[1] (closed_form) = 1.63243073254 2.72465360429
absolute error = 0.3475
relative error = 10.94 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.13165482215 -1.47244495614
y1[1] (closed_form) = 2.85971461176 -1.5553329206
absolute error = 0.2843
relative error = 8.733 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.206
Order of pole (three term test) = 38.79 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.206
Order of pole (three term test) = 28.66 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=38025.5MB, alloc=44.3MB, time=470.18
x[1] = 0.5188 1.864
h = 0.001 0.001
y2[1] (numeric) = 1.72869050333 3.07179791189
y2[1] (closed_form) = 1.63739086621 2.73308898455
absolute error = 0.3508
relative error = 11.01 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.14068237716 -1.47792142
y1[1] (closed_form) = 2.86773772881 -1.56051053584
absolute error = 0.2852
relative error = 8.734 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.901
Order of pole (three term test) = 38.83 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 4.901
Order of pole (three term test) = 28.65 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=38071.8MB, alloc=44.3MB, time=470.75
memory used=38117.9MB, alloc=44.3MB, time=471.32
x[1] = 0.5198 1.865
h = 0.001 0.003
y2[1] (numeric) = 1.73958524131 3.08216052027
y2[1] (closed_form) = 1.641821848 2.73439457288
absolute error = 0.3612
relative error = 11.33 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 3.14202522116 -1.48273253018
y1[1] (closed_form) = 2.86883186496 -1.5648838838
absolute error = 0.2853
relative error = 8.73 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.31
Order of pole (three term test) = 38.83 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 23.31
Order of pole (three term test) = 28.66 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=38163.9MB, alloc=44.3MB, time=471.88
memory used=38210.2MB, alloc=44.3MB, time=472.44
x[1] = 0.5208 1.868
h = 0.0001 0.004
y2[1] (numeric) = 1.7505373913 3.09254864003
y2[1] (closed_form) = 1.64940011912 2.74144219853
absolute error = 0.3654
relative error = 11.42 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 3.14954222199 -1.49105505222
y1[1] (closed_form) = 2.87540000859 -1.57255862673
absolute error = 0.286
relative error = 8.727 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.27
Order of pole (three term test) = 38.86 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 13.27
Order of pole (three term test) = 28.67 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=38256.0MB, alloc=44.3MB, time=473.00
memory used=38302.1MB, alloc=44.3MB, time=473.57
x[1] = 0.5209 1.872
h = 0.003 0.006
y2[1] (numeric) = 1.76154704135 3.10296230634
y2[1] (closed_form) = 1.65599219623 2.75280783015
absolute error = 0.3657
relative error = 11.38 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 3.16175763161 -1.49838897723
y1[1] (closed_form) = 2.88622322507 -1.57944411397
absolute error = 0.2872
relative error = 8.729 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.72
Order of pole (three term test) = 38.92 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 17.72
Order of pole (three term test) = 28.65 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=38348.1MB, alloc=44.3MB, time=474.13
x[1] = 0.5239 1.878
h = 0.0001 0.005
y2[1] (numeric) = 1.77261444218 3.11340158628
y2[1] (closed_form) = 1.67419959429 2.7653941398
absolute error = 0.3617
relative error = 11.19 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 3.17510548281 -1.5183159721
y1[1] (closed_form) = 2.89778257209 -1.59771191652
absolute error = 0.2885
relative error = 8.717 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.975
Order of pole (three term test) = 38.96 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.975
Order of pole (three term test) = 28.69 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=38394.0MB, alloc=44.3MB, time=474.69
memory used=38440.3MB, alloc=44.3MB, time=475.25
x[1] = 0.524 1.883
h = 0.0001 0.003
y2[1] (numeric) = 1.78374027938 3.1238663583
y2[1] (closed_form) = 1.68250027086 2.77975705634
absolute error = 0.3587
relative error = 11.04 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.19052082478 -1.52751869764
y1[1] (closed_form) = 2.91147758729 -1.60638090454
absolute error = 0.29
relative error = 8.72 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.485
Order of pole (three term test) = 39.03 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.485
Order of pole (three term test) = 28.67 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=38486.3MB, alloc=44.3MB, time=475.82
memory used=38532.6MB, alloc=44.3MB, time=476.39
x[1] = 0.5241 1.886
h = 0.001 0.001
y2[1] (numeric) = 1.79492486728 3.134356816
y2[1] (closed_form) = 1.68761896662 2.78834285361
absolute error = 0.3623
relative error = 11.12 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.19972922033 -1.5331995916
y1[1] (closed_form) = 2.91966122533 -1.61171448399
absolute error = 0.2909
relative error = 8.722 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.121
Order of pole (three term test) = 39.08 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.121
Order of pole (three term test) = 28.66 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=38578.6MB, alloc=44.3MB, time=476.95
x[1] = 0.5251 1.887
h = 0.001 0.003
y2[1] (numeric) = 1.80616827764 3.1448730658
y2[1] (closed_form) = 1.69215313111 2.78964911122
absolute error = 0.3731
relative error = 11.43 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 3.20106829145 -1.53813974606
y1[1] (closed_form) = 2.92076033601 -1.61619336584
absolute error = 0.291
relative error = 8.717 %
Correct digits = 1
memory used=38625.0MB, alloc=44.3MB, time=477.52
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.35
Order of pole (three term test) = 39.08 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 24.35
Order of pole (three term test) = 28.68 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=38670.9MB, alloc=44.3MB, time=478.08
x[1] = 0.5261 1.89
h = 0.0001 0.004
y2[1] (numeric) = 1.81747053825 3.15541511577
y2[1] (closed_form) = 1.69993762662 2.79680128276
absolute error = 0.3774
relative error = 11.53 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 3.20870690277 -1.54672533151
y1[1] (closed_form) = 2.9274439657 -1.62407471858
absolute error = 0.2917
relative error = 8.713 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.86
Order of pole (three term test) = 39.11 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 13.86
Order of pole (three term test) = 28.69 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=38716.9MB, alloc=44.3MB, time=478.64
memory used=38763.0MB, alloc=44.3MB, time=479.21
x[1] = 0.5262 1.894
h = 0.003 0.006
y2[1] (numeric) = 1.82883173927 3.16598300129
y2[1] (closed_form) = 1.70674139927 2.8083703615
absolute error = 0.3779
relative error = 11.5 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 3.22116737575 -1.55433398608
y1[1] (closed_form) = 2.9384839608 -1.63116832502
absolute error = 0.2929
relative error = 8.716 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 18.52
Order of pole (three term test) = 39.17 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 18.52
Order of pole (three term test) = 28.68 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=38808.9MB, alloc=44.3MB, time=479.76
memory used=38855.2MB, alloc=44.3MB, time=480.34
x[1] = 0.5292 1.9
h = 0.0001 0.005
y2[1] (numeric) = 1.8402521372 3.17657678935
y2[1] (closed_form) = 1.7254176131 2.82111489744
absolute error = 0.3736
relative error = 11.3 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 3.23469143128 -1.57485504118
y1[1] (closed_form) = 2.95022420787 -1.64990895256
absolute error = 0.2942
relative error = 8.704 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.333
Order of pole (three term test) = 39.21 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.333
Order of pole (three term test) = 28.72 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=38901.2MB, alloc=44.3MB, time=480.90
x[1] = 0.5293 1.905
h = 0.0001 0.003
y2[1] (numeric) = 1.85173243164 3.18719635156
y2[1] (closed_form) = 1.733985188 2.8357354741
absolute error = 0.3707
relative error = 11.15 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.25041625464 -1.58440316598
y1[1] (closed_form) = 2.96419333531 -1.65884028232
absolute error = 0.2957
relative error = 8.707 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.777
Order of pole (three term test) = 39.29 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.777
Order of pole (three term test) = 28.7 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=38947.2MB, alloc=44.3MB, time=481.46
memory used=38993.4MB, alloc=44.3MB, time=482.04
x[1] = 0.5294 1.908
h = 0.001 0.001
y2[1] (numeric) = 1.86327294487 3.19784188374
y2[1] (closed_form) = 1.73926678195 2.84447440907
absolute error = 0.3745
relative error = 11.23 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.25980805571 -1.59029491067
y1[1] (closed_form) = 2.97253998156 -1.66433416623
absolute error = 0.2967
relative error = 8.708 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.351
Order of pole (three term test) = 39.33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.351
Order of pole (three term test) = 28.69 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=39039.5MB, alloc=44.3MB, time=482.60
memory used=39085.8MB, alloc=44.3MB, time=483.17
x[1] = 0.5304 1.909
h = 0.0001 0.004
y2[1] (numeric) = 1.87487375081 3.20851349416
y2[1] (closed_form) = 1.74390650101 2.84578087407
absolute error = 0.3857
relative error = 11.55 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 3.2611421629 -1.59536715451
y1[1] (closed_form) = 2.97364352332 -1.66892088033
absolute error = 0.2968
relative error = 8.703 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 32.2
Order of pole (three term test) = 39.33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 32.2
Order of pole (three term test) = 28.71 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=39131.6MB, alloc=44.3MB, time=483.73
memory used=39177.8MB, alloc=44.3MB, time=484.30
x[1] = 0.5305 1.913
h = 0.003 0.006
y2[1] (numeric) = 1.8865348802 3.21921121954
y2[1] (closed_form) = 1.75089464989 2.85753064089
absolute error = 0.3863
relative error = 11.53 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 3.27380953368 -1.60321133767
y1[1] (closed_form) = 2.98487539181 -1.67619563777
absolute error = 0.298
relative error = 8.705 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 19.23
Order of pole (three term test) = 39.39 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 19.23
Order of pole (three term test) = 28.7 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=39223.8MB, alloc=44.3MB, time=484.86
x[1] = 0.5335 1.919
h = 0.0001 0.005
y2[1] (numeric) = 1.89825657714 3.22993512347
y2[1] (closed_form) = 1.76998168555 2.87041831057
absolute error = 0.3817
relative error = 11.32 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 3.2874797877 -1.62423939458
y1[1] (closed_form) = 2.99677795485 -1.6953501114
absolute error = 0.2993
relative error = 8.692 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.656
Order of pole (three term test) = 39.44 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.656
Order of pole (three term test) = 28.75 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=39269.6MB, alloc=44.3MB, time=485.42
memory used=39315.8MB, alloc=44.3MB, time=485.99
x[1] = 0.5336 1.924
h = 0.0001 0.003
y2[1] (numeric) = 1.91003955355 3.24068507163
y2[1] (closed_form) = 1.77878170411 2.88526770653
absolute error = 0.3789
relative error = 11.18 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.30346591302 -1.63408364006
y1[1] (closed_form) = 3.01098970289 -1.70450978391
absolute error = 0.3008
relative error = 8.695 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.039
Order of pole (three term test) = 39.52 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.039
Order of pole (three term test) = 28.74 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=39361.8MB, alloc=44.3MB, time=486.56
memory used=39408.1MB, alloc=44.3MB, time=487.13
x[1] = 0.5337 1.927
h = 0.001 0.001
y2[1] (numeric) = 1.92188413865 3.25146126186
y2[1] (closed_form) = 1.78420520264 2.89414267305
absolute error = 0.3829
relative error = 11.26 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.31301253026 -1.64015611728
y1[1] (closed_form) = 3.01948066303 -1.71014323015
absolute error = 0.3018
relative error = 8.696 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.559
Order of pole (three term test) = 39.56 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.559
Order of pole (three term test) = 28.73 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=39454.1MB, alloc=44.3MB, time=487.69
x[1] = 0.5347 1.928
h = 0.001 0.003
y2[1] (numeric) = 1.93379040832 3.26226380408
y2[1] (closed_form) = 1.78893772112 2.8954502247
absolute error = 0.3944
relative error = 11.59 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 3.31434155847 -1.64534080975
y1[1] (closed_form) = 3.0205888888 -1.71482459787
absolute error = 0.3019
relative error = 8.691 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.43
Order of pole (three term test) = 39.56 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 26.43
Order of pole (three term test) = 28.75 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=39500.5MB, alloc=44.3MB, time=488.26
memory used=39546.5MB, alloc=44.3MB, time=488.83
x[1] = 0.5357 1.931
h = 0.0001 0.004
y2[1] (numeric) = 1.94575839158 3.27309270637
y2[1] (closed_form) = 1.79711864415 2.90280338338
absolute error = 0.399
relative error = 11.69 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 3.32220481739 -1.65442779357
y1[1] (closed_form) = 3.02749324057 -1.72310280025
absolute error = 0.3026
relative error = 8.687 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 15.05
Order of pole (three term test) = 39.6 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 15.05
Order of pole (three term test) = 28.76 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=39592.5MB, alloc=44.3MB, time=489.39
memory used=39638.7MB, alloc=44.3MB, time=489.95
x[1] = 0.5358 1.935
h = 0.003 0.006
y2[1] (numeric) = 1.95778818263 3.28394800452
y2[1] (closed_form) = 1.80432935455 2.91476356601
absolute error = 0.3998
relative error = 11.66 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 3.33512371318 -1.66256271791
y1[1] (closed_form) = 3.0389482873 -1.73059656385
absolute error = 0.3039
relative error = 8.69 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 20.1
Order of pole (three term test) = 39.66 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 20.1
Order of pole (three term test) = 28.75 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=39684.5MB, alloc=44.3MB, time=490.51
memory used=39730.8MB, alloc=44.3MB, time=491.09
x[1] = 0.5388 1.941
h = 0.0001 0.005
y2[1] (numeric) = 1.96988004913 3.29482976531
y2[1] (closed_form) = 1.82390676918 2.9278122789
absolute error = 0.395
relative error = 11.45 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 3.34896854656 -1.68421385145
y1[1] (closed_form) = 3.0510336924 -1.75024505552
absolute error = 0.3052
relative error = 8.676 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.045
Order of pole (three term test) = 39.71 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 9.045
Order of pole (three term test) = 28.81 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=39776.7MB, alloc=44.3MB, time=491.65
x[1] = 0.5389 1.946
h = 0.0001 0.003
y2[1] (numeric) = 1.98203471755 3.30573784721
y2[1] (closed_form) = 1.83298739173 2.94292815528
absolute error = 0.3922
relative error = 11.31 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.36527235938 -1.69442364026
y1[1] (closed_form) = 3.06552766938 -1.75968080709
absolute error = 0.3068
relative error = 8.679 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.356
Order of pole (three term test) = 39.79 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.356
Order of pole (three term test) = 28.8 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=39822.7MB, alloc=44.3MB, time=492.21
memory used=39869.1MB, alloc=44.3MB, time=492.78
x[1] = 0.539 1.949
h = 0.001 0.001
y2[1] (numeric) = 1.99425252543 3.31667245033
y2[1] (closed_form) = 1.83858211836 2.95196146174
absolute error = 0.3965
relative error = 11.4 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.37500715434 -1.70071917562
y1[1] (closed_form) = 3.07418641914 -1.76548290105
absolute error = 0.3077
relative error = 8.68 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.809
Order of pole (three term test) = 39.84 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 5.809
Order of pole (three term test) = 28.79 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=39915.1MB, alloc=44.3MB, time=493.35
memory used=39961.5MB, alloc=44.3MB, time=493.92
x[1] = 0.54 1.95
h = 0.001 0.003
y2[1] (numeric) = 2.00653355094 3.32763368647
y2[1] (closed_form) = 1.84342474007 2.95326832507
absolute error = 0.4084
relative error = 11.73 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 3.37632891742 -1.70604171423
y1[1] (closed_form) = 3.0752980314 -1.77027651919
absolute error = 0.3078
relative error = 8.674 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.62
Order of pole (three term test) = 39.84 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 27.62
Order of pole (three term test) = 28.81 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=40007.4MB, alloc=44.3MB, time=494.48
memory used=40053.7MB, alloc=44.3MB, time=495.05
x[1] = 0.541 1.953
h = 0.0001 0.004
y2[1] (numeric) = 2.01887782379 3.33862156373
y2[1] (closed_form) = 1.85182711982 2.96073022699
absolute error = 0.4132
relative error = 11.83 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 3.38431559322 -1.71541294088
y1[1] (closed_form) = 3.08232140286 -1.77877638708
absolute error = 0.3086
relative error = 8.671 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 15.72
Order of pole (three term test) = 39.87 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 15.72
Order of pole (three term test) = 28.83 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=40099.4MB, alloc=44.3MB, time=495.60
x[1] = 0.5411 1.957
h = 0.003 0.006
y2[1] (numeric) = 2.03128544043 3.34963611809
y2[1] (closed_form) = 1.85926646858 2.97290459669
absolute error = 0.4141
relative error = 11.81 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 3.39748959204 -1.72384765893
y1[1] (closed_form) = 3.09400310278 -1.78649524493
absolute error = 0.3099
relative error = 8.674 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 21
Order of pole (three term test) = 39.94 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 21
Order of pole (three term test) = 28.82 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=40145.3MB, alloc=44.3MB, time=496.16
memory used=40191.4MB, alloc=44.3MB, time=496.73
x[1] = 0.5441 1.963
h = 0.0001 0.005
y2[1] (numeric) = 2.0437566747 3.36067741614
y2[1] (closed_form) = 1.87934623117 2.98611573619
absolute error = 0.4091
relative error = 11.59 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 3.41150797213 -1.74613821693
y1[1] (closed_form) = 3.10627227759 -1.80664953138
absolute error = 0.3112
relative error = 8.66 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.452
Order of pole (three term test) = 39.99 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 9.452
Order of pole (three term test) = 28.88 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=40237.3MB, alloc=44.3MB, time=497.29
memory used=40283.4MB, alloc=44.3MB, time=497.85
x[1] = 0.5442 1.968
h = 0.0001 0.003
y2[1] (numeric) = 2.0562922679 3.37174530887
y2[1] (closed_form) = 1.88871512307 3.00150286692
absolute error = 0.4064
relative error = 11.46 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.42813401593 -1.75672493328
y1[1] (closed_form) = 3.12105289106 -1.81636904422
absolute error = 0.3128
relative error = 8.663 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.686
Order of pole (three term test) = 40.08 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.686
Order of pole (three term test) = 28.88 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=40329.4MB, alloc=44.3MB, time=498.42
x[1] = 0.5443 1.971
h = 0.001 0.001
y2[1] (numeric) = 2.06889256608 3.38283999864
y2[1] (closed_form) = 1.89448573528 3.01069732701
absolute error = 0.411
relative error = 11.55 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.43805962847 -1.76325042338
y1[1] (closed_form) = 3.12988202499 -1.8223444506
absolute error = 0.3138
relative error = 8.664 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.07
Order of pole (three term test) = 40.13 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.07
Order of pole (three term test) = 28.87 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=40375.5MB, alloc=44.3MB, time=498.99
memory used=40421.7MB, alloc=44.3MB, time=499.56
x[1] = 0.5453 1.972
h = 0.001 0.003
y2[1] (numeric) = 2.08155764979 3.39396159922
y2[1] (closed_form) = 1.89944097289 3.01200296845
absolute error = 0.4232
relative error = 11.88 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 3.43937280731 -1.76871404164
y1[1] (closed_form) = 3.1309964126 -1.82725276392
absolute error = 0.3139
relative error = 8.658 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.87
Order of pole (three term test) = 40.13 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 28.87
Order of pole (three term test) = 28.9 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=40467.6MB, alloc=44.3MB, time=500.12
memory used=40514.0MB, alloc=44.3MB, time=500.69
x[1] = 0.5463 1.975
h = 0.0001 0.004
y2[1] (numeric) = 2.09428754941 3.40511011868
y2[1] (closed_form) = 1.90807038043 3.01957505609
absolute error = 0.4282
relative error = 11.99 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 3.44748349097 -1.77837732684
y1[1] (closed_form) = 3.13814002356 -1.83597981057
absolute error = 0.3147
relative error = 8.655 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.43
Order of pole (three term test) = 40.17 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 16.43
Order of pole (three term test) = 28.92 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=40559.8MB, alloc=44.3MB, time=501.25
memory used=40605.9MB, alloc=44.3MB, time=501.81
x[1] = 0.5464 1.979
h = 0.003 0.006
y2[1] (numeric) = 2.10708236371 3.41628559319
y2[1] (closed_form) = 1.91574459861 3.03196742845
absolute error = 0.4293
relative error = 11.97 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 3.46091620543 -1.78712111457
y1[1] (closed_form) = 3.15005190244 -1.84393000626
absolute error = 0.316
relative error = 8.658 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 21.95
Order of pole (three term test) = 40.24 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 21.95
Order of pole (three term test) = 28.91 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=40651.7MB, alloc=44.3MB, time=502.37
x[1] = 0.5494 1.985
h = 0.0001 0.005
y2[1] (numeric) = 2.11994237285 3.42748808913
y2[1] (closed_form) = 1.93633894504 3.04534233485
absolute error = 0.424
relative error = 11.75 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 3.4751069923 -1.81006780979
y1[1] (closed_form) = 3.16250574041 -1.86460213767
absolute error = 0.3173
relative error = 8.643 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.877
Order of pole (three term test) = 40.29 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 9.877
Order of pole (three term test) = 28.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=40697.6MB, alloc=44.3MB, time=502.94
memory used=40743.9MB, alloc=44.3MB, time=503.50
x[1] = 0.5495 1.99
h = 0.0001 0.003
y2[1] (numeric) = 2.13286833325 3.43871744975
y2[1] (closed_form) = 1.94600396634 3.06100555027
absolute error = 0.4214
relative error = 11.62 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.49205985494 -1.82104311902
y1[1] (closed_form) = 3.17757746242 -1.87461329023
absolute error = 0.319
relative error = 8.647 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.032
Order of pole (three term test) = 40.38 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.032
Order of pole (three term test) = 28.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=40789.7MB, alloc=44.3MB, time=504.06
memory used=40836.1MB, alloc=44.3MB, time=504.63
x[1] = 0.5496 1.993
h = 0.001 0.001
y2[1] (numeric) = 2.14586059969 3.44997387971
y2[1] (closed_form) = 1.95195523939 3.07036401017
absolute error = 0.4263
relative error = 11.72 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.50217894925 -1.82780563017
y1[1] (closed_form) = 3.18657961237 -1.88076679246
absolute error = 0.32
relative error = 8.648 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.343
Order of pole (three term test) = 40.43 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.343
Order of pole (three term test) = 28.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=40882.1MB, alloc=44.3MB, time=505.20
memory used=40928.5MB, alloc=44.3MB, time=505.79
x[1] = 0.5506 1.994
h = 0.001 0.003
y2[1] (numeric) = 2.15891925514 3.46125749473
y2[1] (closed_form) = 1.95702565659 3.07166786934
absolute error = 0.4388
relative error = 12.05 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 3.50348217828 -1.83341362798
y1[1] (closed_form) = 3.1876961387 -1.88579229866
absolute error = 0.3201
relative error = 8.643 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.16
Order of pole (three term test) = 40.43 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 30.16
Order of pole (three term test) = 29 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=40974.4MB, alloc=44.3MB, time=506.34
x[1] = 0.5516 1.997
h = 0.0001 0.004
y2[1] (numeric) = 2.1720443307 3.47256830288
y2[1] (closed_form) = 1.96588779222 3.07935158244
absolute error = 0.444
relative error = 12.15 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 3.51171743392 -1.84337696738
y1[1] (closed_form) = 3.19496121079 -1.89475216896
absolute error = 0.3209
relative error = 8.639 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.17
Order of pole (three term test) = 40.47 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 17.17
Order of pole (three term test) = 29.03 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=41020.3MB, alloc=44.3MB, time=506.90
memory used=41066.5MB, alloc=44.3MB, time=507.47
x[1] = 0.5517 2.001
h = 0.003 0.006
y2[1] (numeric) = 2.18523592748 3.48390634052
y2[1] (closed_form) = 1.97380326878 3.09196581766
absolute error = 0.4453
relative error = 12.14 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 3.52541251065 -1.8524393292
y1[1] (closed_form) = 3.2071068454 -1.90294010523
absolute error = 0.3223
relative error = 8.642 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.93
Order of pole (three term test) = 40.55 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 22.93
Order of pole (three term test) = 29.03 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=41112.3MB, alloc=44.3MB, time=508.02
memory used=41158.5MB, alloc=44.3MB, time=508.59
x[1] = 0.5547 2.007
h = 0.0001 0.005
y2[1] (numeric) = 2.19849433213 3.49527167376
y2[1] (closed_form) = 1.99492470776 3.10550578593
absolute error = 0.4397
relative error = 11.91 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 3.5397744525 -1.87605924661
y1[1] (closed_form) = 3.21974620341 -1.92414241094
absolute error = 0.3236
relative error = 8.628 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.32
Order of pole (three term test) = 40.6 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 10.32
Order of pole (three term test) = 29.1 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=41204.4MB, alloc=44.3MB, time=509.15
x[1] = 0.5548 2.012
h = 0.0001 0.003
y2[1] (numeric) = 2.2118203165 3.50666413789
y2[1] (closed_form) = 2.00489391789 3.12144997321
absolute error = 0.4373
relative error = 11.79 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.55705876553 -1.88743510153
y1[1] (closed_form) = 3.23511357073 -1.93445328254
absolute error = 0.3254
relative error = 8.632 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.393
Order of pole (three term test) = 40.7 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.393
Order of pole (three term test) = 29.1 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=41250.5MB, alloc=44.3MB, time=509.72
memory used=41296.7MB, alloc=44.3MB, time=510.29
x[1] = 0.5549 2.015
h = 0.001 0.001
y2[1] (numeric) = 2.22521424429 3.51808393985
y2[1] (closed_form) = 2.01103074767 3.13097531169
absolute error = 0.4424
relative error = 11.89 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.56737402963 -1.89444187355
y1[1] (closed_form) = 3.24429140587 -1.94078978559
absolute error = 0.3264
relative error = 8.634 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.628
Order of pole (three term test) = 40.75 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.628
Order of pole (three term test) = 29.11 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=41342.8MB, alloc=44.3MB, time=510.86
memory used=41389.1MB, alloc=44.3MB, time=511.43
x[1] = 0.5559 2.016
h = 0.0001 0.004
y2[1] (numeric) = 2.23867620096 3.52953119736
y2[1] (closed_form) = 2.01621896027 3.13227680055
absolute error = 0.4553
relative error = 12.22 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 3.56866589536 -1.90019761838
y1[1] (closed_form) = 3.24540940793 -1.94593503632
absolute error = 0.3265
relative error = 8.628 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 39.88
Order of pole (three term test) = 40.75 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 39.88
Order of pole (three term test) = 29.13 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=41435.1MB, alloc=44.3MB, time=512.00
memory used=41481.3MB, alloc=44.3MB, time=512.56
x[1] = 0.556 2.02
h = 0.003 0.006
y2[1] (numeric) = 2.25220622177 3.5410059502
y2[1] (closed_form) = 2.02434463728 3.14508811377
absolute error = 0.4568
relative error = 12.21 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 3.58258241691 -1.90953288715
y1[1] (closed_form) = 3.25776209368 -1.95433001975
absolute error = 0.3279
relative error = 8.631 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.82
Order of pole (three term test) = 40.83 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 23.82
Order of pole (three term test) = 29.14 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=41527.0MB, alloc=44.3MB, time=513.12
x[1] = 0.559 2.026
h = 0.0001 0.005
y2[1] (numeric) = 2.26580457953 3.55250826112
y2[1] (closed_form) = 2.04592802297 3.1587776491
absolute error = 0.451
relative error = 11.98 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 3.5970859468 -1.93372714965
y1[1] (closed_form) = 3.27056831816 -1.97599654921
absolute error = 0.3292
relative error = 8.616 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.72
Order of pole (three term test) = 40.89 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 10.72
Order of pole (three term test) = 29.22 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=41572.8MB, alloc=44.3MB, time=513.68
memory used=41619.1MB, alloc=44.3MB, time=514.25
x[1] = 0.5591 2.031
h = 0.0001 0.003
y2[1] (numeric) = 2.2794720597 3.5640379585
y2[1] (closed_form) = 2.05616225107 3.17497140266
absolute error = 0.4486
relative error = 11.86 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.61465003766 -1.94544613941
y1[1] (closed_form) = 3.28619755461 -1.98656843903
absolute error = 0.331
relative error = 8.62 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.718
Order of pole (three term test) = 40.99 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.718
Order of pole (three term test) = 29.23 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=41664.9MB, alloc=44.3MB, time=514.82
memory used=41711.3MB, alloc=44.3MB, time=515.39
x[1] = 0.5592 2.034
h = 0.001 0.001
y2[1] (numeric) = 2.29320903379 3.57559525136
y2[1] (closed_form) = 2.06246078148 3.18464500699
absolute error = 0.454
relative error = 11.96 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.62513084707 -1.95266212509
y1[1] (closed_form) = 3.2955310414 -1.99306434906
absolute error = 0.3321
relative error = 8.622 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.885
Order of pole (three term test) = 41.05 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 6.885
Order of pole (three term test) = 29.23 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=41757.4MB, alloc=44.3MB, time=515.95
x[1] = 0.5602 2.035
h = 0.001 0.003
y2[1] (numeric) = 2.30701558946 3.58718025922
y2[1] (closed_form) = 2.06775256195 3.18594540945
absolute error = 0.4672
relative error = 12.3 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 3.62641212601 -1.95854361705
y1[1] (closed_form) = 3.29665123082 -1.99831475075
absolute error = 0.3322
relative error = 8.616 %
Correct digits = 1
memory used=41803.8MB, alloc=44.3MB, time=516.52
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 32.74
Order of pole (three term test) = 41.05 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 32.74
Order of pole (three term test) = 29.26 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=41849.8MB, alloc=44.3MB, time=517.09
x[1] = 0.5612 2.038
h = 0.0001 0.004
y2[1] (numeric) = 2.32089175916 3.59879299014
y2[1] (closed_form) = 2.07706200658 3.19384359015
absolute error = 0.4727
relative error = 12.41 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 3.63487713108 -1.96907844497
y1[1] (closed_form) = 3.30414850674 -2.00772185709
absolute error = 0.333
relative error = 8.612 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 18.64
Order of pole (three term test) = 41.09 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 18.64
Order of pole (three term test) = 29.29 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=41895.7MB, alloc=44.3MB, time=517.64
memory used=41941.9MB, alloc=44.3MB, time=518.21
x[1] = 0.5613 2.042
h = 0.003 0.006
y2[1] (numeric) = 2.33483764854 3.61043348082
y2[1] (closed_form) = 2.08544121655 3.20688414955
absolute error = 0.4744
relative error = 12.4 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 3.64906278886 -1.97875034162
y1[1] (closed_form) = 3.31674182085 -2.01636688756
absolute error = 0.3344
relative error = 8.616 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.89
Order of pole (three term test) = 41.17 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 24.89
Order of pole (three term test) = 29.3 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=41987.7MB, alloc=44.3MB, time=518.76
memory used=42033.9MB, alloc=44.3MB, time=519.34
x[1] = 0.5643 2.048
h = 0.0001 0.005
y2[1] (numeric) = 2.34885355667 3.62210179687
y2[1] (closed_form) = 2.10757570324 3.2207411846
absolute error = 0.4683
relative error = 12.17 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 3.66373486162 -2.00365017602
y1[1] (closed_form) = 3.3297352089 -2.03858728735
absolute error = 0.3358
relative error = 8.601 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.2
Order of pole (three term test) = 41.23 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 11.2
Order of pole (three term test) = 29.39 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=42079.7MB, alloc=44.3MB, time=519.89
x[1] = 0.5644 2.053
h = 0.0001 0.003
y2[1] (numeric) = 2.36294028508 3.63379775825
y2[1] (closed_form) = 2.11812960437 3.2372252581
absolute error = 0.466
relative error = 12.05 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.68163900987 -2.01579242574
y1[1] (closed_form) = 3.34566880747 -2.04947442494
absolute error = 0.3377
relative error = 8.606 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.11
Order of pole (three term test) = 41.33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 9.11
Order of pole (three term test) = 29.4 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=42125.8MB, alloc=44.3MB, time=520.46
memory used=42172.0MB, alloc=44.3MB, time=521.03
x[1] = 0.5645 2.056
h = 0.001 0.001
y2[1] (numeric) = 2.37709821462 3.6455215763
y2[1] (closed_form) = 2.12462309739 3.24707124707
absolute error = 0.4717
relative error = 12.16 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.69232098055 -2.02326643141
y1[1] (closed_form) = 3.3551831078 -2.05616276333
absolute error = 0.3387
relative error = 8.608 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.194
Order of pole (three term test) = 41.4 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.194
Order of pole (three term test) = 29.41 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=42217.9MB, alloc=44.3MB, time=521.59
memory used=42264.2MB, alloc=44.3MB, time=522.16
x[1] = 0.5655 2.057
h = 0.001 0.003
y2[1] (numeric) = 2.39132743555 3.65727337261
y2[1] (closed_form) = 2.13003769077 3.24836814098
absolute error = 0.4853
relative error = 12.49 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 3.69358816881 -2.02930203343
y1[1] (closed_form) = 3.35630349799 -2.06153781323
absolute error = 0.3388
relative error = 8.602 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 34.21
Order of pole (three term test) = 41.4 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 34.21
Order of pole (three term test) = 29.44 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=42310.1MB, alloc=44.3MB, time=522.72
memory used=42356.4MB, alloc=44.3MB, time=523.29
x[1] = 0.5665 2.06
h = 0.0001 0.004
y2[1] (numeric) = 2.40562798109 3.66905315521
y2[1] (closed_form) = 2.13959689371 3.25638211815
absolute error = 0.491
relative error = 12.6 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 3.70217917984 -2.04016060965
y1[1] (closed_form) = 3.36392580584 -2.07119462999
absolute error = 0.3397
relative error = 8.598 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 19.48
Order of pole (three term test) = 41.44 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 19.48
Order of pole (three term test) = 29.48 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=42402.2MB, alloc=44.3MB, time=523.85
x[1] = 0.5666 2.064
h = 0.003 0.006
y2[1] (numeric) = 2.41999995939 3.68086096098
y2[1] (closed_form) = 2.1482364982 3.26965591504
absolute error = 0.4929
relative error = 12.6 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 3.71663771791 -2.05017933717
y1[1] (closed_form) = 3.37676347372 -2.08009658595
absolute error = 0.3412
relative error = 8.603 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.01
Order of pole (three term test) = 41.52 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 26.01
Order of pole (three term test) = 29.49 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=42448.0MB, alloc=44.3MB, time=524.41
memory used=42494.2MB, alloc=44.3MB, time=524.98
x[1] = 0.5696 2.07
h = 0.0001 0.005
y2[1] (numeric) = 2.43444367644 3.69269685515
y2[1] (closed_form) = 2.17093540923 3.2836816054
absolute error = 0.4865
relative error = 12.36 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 3.73147672995 -2.07580296174
y1[1] (closed_form) = 3.38994476712 -2.10288401714
absolute error = 0.3426
relative error = 8.588 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.71
Order of pole (three term test) = 41.59 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 11.71
Order of pole (three term test) = 29.59 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=42540.1MB, alloc=44.3MB, time=525.54
memory used=42586.3MB, alloc=44.3MB, time=526.10
x[1] = 0.5697 2.075
h = 0.0001 0.003
y2[1] (numeric) = 2.4489599501 3.70456064897
y2[1] (closed_form) = 2.18181763952 3.30046105296
absolute error = 0.4844
relative error = 12.24 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.74972569248 -2.0883813031
y1[1] (closed_form) = 3.40618745323 -2.1140950822
absolute error = 0.3445
relative error = 8.593 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.52
Order of pole (three term test) = 41.7 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 9.52
Order of pole (three term test) = 29.61 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=42632.3MB, alloc=44.3MB, time=526.66
x[1] = 0.5698 2.078
h = 0.001 0.001
y2[1] (numeric) = 2.46354917077 3.7164525561
y2[1] (closed_form) = 2.18851135195 3.31048240117
absolute error = 0.4904
relative error = 12.36 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.76061158039 -2.09612109895
y1[1] (closed_form) = 3.41588534504 -2.12098111721
absolute error = 0.3456
relative error = 8.596 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.518
Order of pole (three term test) = 41.76 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.518
Order of pole (three term test) = 29.62 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=42678.5MB, alloc=44.3MB, time=527.23
memory used=42724.7MB, alloc=44.3MB, time=527.80
x[1] = 0.5708 2.079
h = 0.001 0.003
y2[1] (numeric) = 2.47821143141 3.72837270022
y2[1] (closed_form) = 2.19405152932 3.31177511504
absolute error = 0.5043
relative error = 12.69 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 3.76186311645 -2.10231438344
y1[1] (closed_form) = 3.41700519327 -2.12648352722
absolute error = 0.3457
relative error = 8.59 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 35.75
Order of pole (three term test) = 41.76 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 35.75
Order of pole (three term test) = 29.65 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=42770.7MB, alloc=44.3MB, time=528.36
memory used=42816.9MB, alloc=44.3MB, time=528.92
x[1] = 0.5718 2.082
h = 0.0001 0.004
y2[1] (numeric) = 2.49294676601 3.74032108934
y2[1] (closed_form) = 2.20386671783 3.31990631307
absolute error = 0.5102
relative error = 12.8 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 3.77058057707 -2.11350544699
y1[1] (closed_form) = 3.42475375608 -2.13639623483
absolute error = 0.3466
relative error = 8.586 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 20.35
Order of pole (three term test) = 41.81 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 20.35
Order of pole (three term test) = 29.69 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=42862.8MB, alloc=44.3MB, time=529.49
memory used=42909.0MB, alloc=44.3MB, time=530.05
x[1] = 0.5719 2.086
h = 0.003 0.006
y2[1] (numeric) = 2.50775528529 3.7522977605
y2[1] (closed_form) = 2.21277375154 3.33341738436
absolute error = 0.5123
relative error = 12.8 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 3.78531577083 -2.12388145738
y1[1] (closed_form) = 3.43783955463 -2.14556216886
absolute error = 0.3482
relative error = 8.591 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.18
Order of pole (three term test) = 41.9 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 27.18
Order of pole (three term test) = 29.71 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=42954.8MB, alloc=44.3MB, time=530.61
x[1] = 0.5749 2.092
h = 0.0001 0.005
y2[1] (numeric) = 2.5226373023 3.76430277853
y2[1] (closed_form) = 2.23605070687 3.34761283087
absolute error = 0.5057
relative error = 12.56 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 3.80031998792 -2.15024749195
y1[1] (closed_form) = 3.45120944861 -2.16893009487
absolute error = 0.3496
relative error = 8.577 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.23
Order of pole (three term test) = 41.97 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 12.23
Order of pole (three term test) = 29.82 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=43000.8MB, alloc=44.3MB, time=531.17
memory used=43046.8MB, alloc=44.3MB, time=531.74
x[1] = 0.575 2.097
h = 0.0001 0.003
y2[1] (numeric) = 2.53759365157 3.77633594566
y2[1] (closed_form) = 2.24727014106 3.36469276468
absolute error = 0.5037
relative error = 12.45 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.81891856205 -2.16327506994
y1[1] (closed_form) = 3.46776601303 -2.18047398685
absolute error = 0.3516
relative error = 8.583 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.948
Order of pole (three term test) = 42.08 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 9.948
Order of pole (three term test) = 29.84 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=43092.6MB, alloc=44.3MB, time=532.30
memory used=43138.9MB, alloc=44.3MB, time=532.88
x[1] = 0.5751 2.1
h = 0.001 0.001
y2[1] (numeric) = 2.55262473327 3.78839747789
y2[1] (closed_form) = 2.25416946186 3.37489248002
absolute error = 0.51
relative error = 12.57 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.83001114478 -2.17128861525
y1[1] (closed_form) = 3.47765031187 -2.18756311972
absolute error = 0.3527
relative error = 8.586 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.856
Order of pole (three term test) = 42.15 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 7.856
Order of pole (three term test) = 29.86 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=43184.9MB, alloc=44.3MB, time=533.44
memory used=43231.2MB, alloc=44.3MB, time=534.01
x[1] = 0.5761 2.101
h = 0.001 0.003
y2[1] (numeric) = 2.56773064314 3.80048750104
y2[1] (closed_form) = 2.25983805061 3.37618031115
absolute error = 0.5242
relative error = 12.9 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 3.83124541344 -2.17764322681
y1[1] (closed_form) = 3.47876884545 -2.19319565968
absolute error = 0.3528
relative error = 8.579 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.36
Order of pole (three term test) = 42.15 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 37.36
Order of pole (three term test) = 29.9 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=43277.1MB, alloc=44.3MB, time=534.57
x[1] = 0.5771 2.104
h = 0.0001 0.004
y2[1] (numeric) = 2.58291141595 3.8126060231
y2[1] (closed_form) = 2.269915596 3.38443014816
absolute error = 0.5304
relative error = 13.01 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 3.84008973181 -2.18917571556
y1[1] (closed_form) = 3.48664488415 -2.20337058466
absolute error = 0.3537
relative error = 8.576 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 21.27
Order of pole (three term test) = 42.2 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 21.27
Order of pole (three term test) = 29.94 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=43323.0MB, alloc=44.3MB, time=535.14
memory used=43369.2MB, alloc=44.3MB, time=535.71
x[1] = 0.5772 2.108
h = 0.003 0.006
y2[1] (numeric) = 2.59816716507 3.82475308123
y2[1] (closed_form) = 2.27909727085 3.39818257659
absolute error = 0.5327
relative error = 13.02 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 3.85510538718 -2.19991971543
y1[1] (closed_form) = 3.49998264181 -2.21280772757
absolute error = 0.3554
relative error = 8.582 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.41
Order of pole (three term test) = 42.29 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 28.41
Order of pole (three term test) = 29.96 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=43415.1MB, alloc=44.3MB, time=536.26
memory used=43461.3MB, alloc=44.3MB, time=536.83
x[1] = 0.5802 2.114
h = 0.0001 0.005
y2[1] (numeric) = 2.61349821072 3.83692873983
y2[1] (closed_form) = 2.30296619363 3.41254882267
absolute error = 0.5259
relative error = 12.77 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 3.87027293927 -2.22704718931
y1[1] (closed_form) = 3.51354178219 -2.23676992047
absolute error = 0.3569
relative error = 8.568 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.78
Order of pole (three term test) = 42.37 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 12.78
Order of pole (three term test) = 30.09 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=43507.0MB, alloc=44.3MB, time=537.40
x[1] = 0.5803 2.119
h = 0.0001 0.003
y2[1] (numeric) = 2.62890540447 3.84913279185
y2[1] (closed_form) = 2.31453193025 3.4299344133
absolute error = 0.524
relative error = 12.66 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.8892259617 -2.24053746934
y1[1] (closed_form) = 3.53041708123 -2.24865576378
absolute error = 0.3589
relative error = 8.574 %
Correct digits = 1
memory used=43553.1MB, alloc=44.3MB, time=537.96
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.4
Order of pole (three term test) = 42.49 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 10.4
Order of pole (three term test) = 30.12 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=43599.3MB, alloc=44.3MB, time=538.53
x[1] = 0.5804 2.122
h = 0.001 0.001
y2[1] (numeric) = 2.64438915651 3.8613654556
y2[1] (closed_form) = 2.32164238373 3.440315537
absolute error = 0.5305
relative error = 12.78 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.9005280378 -2.24883291669
y1[1] (closed_form) = 3.54049064025 -2.25595353178
absolute error = 0.3601
relative error = 8.578 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.209
Order of pole (three term test) = 42.56 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.209
Order of pole (three term test) = 30.14 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=43645.3MB, alloc=44.3MB, time=539.10
memory used=43691.7MB, alloc=44.3MB, time=539.66
x[1] = 0.5814 2.123
h = 0.0001 0.004
y2[1] (numeric) = 2.6599495654 3.87362685908
y2[1] (closed_form) = 2.32744226864 3.44159775053
absolute error = 0.5452
relative error = 13.12 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 3.90174336859 -2.25535257343
y1[1] (closed_form) = 3.54160705553 -2.26171903056
absolute error = 0.3602
relative error = 8.572 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49.4
Order of pole (three term test) = 42.56 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 49.4
Order of pole (three term test) = 30.18 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=43737.6MB, alloc=44.3MB, time=540.22
memory used=43783.8MB, alloc=44.3MB, time=540.79
x[1] = 0.5815 2.127
h = 0.003 0.006
y2[1] (numeric) = 2.67558667151 3.88591704533
y2[1] (closed_form) = 2.33686331695 3.45556462738
absolute error = 0.5477
relative error = 13.13 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 3.91699567061 -2.26641159727
y1[1] (closed_form) = 3.55516814758 -2.27139248606
absolute error = 0.3619
relative error = 8.577 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.51
Order of pole (three term test) = 42.66 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 29.51
Order of pole (three term test) = 30.2 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=43829.6MB, alloc=44.3MB, time=541.35
x[1] = 0.5845 2.133
h = 0.0001 0.005
y2[1] (numeric) = 2.69130077965 3.8982360755
y2[1] (closed_form) = 2.36125112078 3.47008596468
absolute error = 0.5406
relative error = 12.88 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 3.93229780379 -2.29418844341
y1[1] (closed_form) = 3.56889797026 -2.29587520898
absolute error = 0.3634
relative error = 8.564 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.28
Order of pole (three term test) = 42.73 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 13.28
Order of pole (three term test) = 30.34 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=43875.4MB, alloc=44.3MB, time=541.91
memory used=43921.6MB, alloc=44.3MB, time=542.48
x[1] = 0.5846 2.138
h = 0.0001 0.003
y2[1] (numeric) = 2.70709275636 3.91058373446
y2[1] (closed_form) = 2.3731186778 3.48774311659
absolute error = 0.5388
relative error = 12.77 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 3.95154992234 -2.30807483543
y1[1] (closed_form) = 3.58605578976 -2.30805899813
absolute error = 0.3655
relative error = 8.57 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.8
Order of pole (three term test) = 42.86 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 10.8
Order of pole (three term test) = 30.37 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=43967.6MB, alloc=44.3MB, time=543.04
memory used=44014.0MB, alloc=44.3MB, time=543.62
x[1] = 0.5847 2.141
h = 0.001 0.001
y2[1] (numeric) = 2.72296302062 3.92296024267
y2[1] (closed_form) = 2.38041318584 3.49828545858
absolute error = 0.5456
relative error = 12.89 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 3.96302872893 -2.31661157647
y1[1] (closed_form) = 3.59629714873 -2.31553859124
absolute error = 0.3667
relative error = 8.574 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.527
Order of pole (three term test) = 42.93 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.527
Order of pole (three term test) = 30.4 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=44060.2MB, alloc=44.3MB, time=544.18
x[1] = 0.5857 2.142
h = 0.001 0.003
y2[1] (numeric) = 2.73891167346 3.93536573006
y2[1] (closed_form) = 2.38632852029 3.49956383476
absolute error = 0.5606
relative error = 13.23 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 3.96422695869 -2.32327166785
y1[1] (closed_form) = 3.5974127035 -2.32142088655
absolute error = 0.3668
relative error = 8.568 %
Correct digits = 1
memory used=44106.6MB, alloc=44.3MB, time=544.75
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 40.55
Order of pole (three term test) = 42.93 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 40.55
Order of pole (three term test) = 30.44 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=44152.6MB, alloc=44.3MB, time=545.32
x[1] = 0.5867 2.145
h = 0.0001 0.004
y2[1] (numeric) = 2.75493875116 3.94780020457
y2[1] (closed_form) = 2.39691026223 3.50804149198
absolute error = 0.5671
relative error = 13.35 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 3.97330478167 -2.33545400442
y1[1] (closed_form) = 3.60553249203 -2.33209953621
absolute error = 0.3678
relative error = 8.565 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.08
Order of pole (three term test) = 42.99 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 23.08
Order of pole (three term test) = 30.49 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=44198.5MB, alloc=44.3MB, time=545.88
memory used=44244.6MB, alloc=44.3MB, time=546.44
x[1] = 0.5868 2.149
h = 0.003 0.006
y2[1] (numeric) = 2.77104437216 3.96026370364
y2[1] (closed_form) = 2.40661980788 3.52225753658
absolute error = 0.5698
relative error = 13.36 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 3.98884460128 -2.34690134741
y1[1] (closed_form) = 3.61935289583 -2.34205809711
absolute error = 0.3695
relative error = 8.572 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.83
Order of pole (three term test) = 43.09 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 30.83
Order of pole (three term test) = 30.53 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=44290.4MB, alloc=44.3MB, time=547.00
memory used=44336.6MB, alloc=44.3MB, time=547.57
x[1] = 0.5898 2.155
h = 0.0001 0.005
y2[1] (numeric) = 2.78722887055 3.97275629079
y2[1] (closed_form) = 2.43162630562 3.53695162734
absolute error = 0.5625
relative error = 13.1 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 4.00430625675 -2.37547565024
y1[1] (closed_form) = 3.63327319814 -2.36716155095
absolute error = 0.3711
relative error = 8.558 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.88
Order of pole (three term test) = 43.17 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 13.88
Order of pole (three term test) = 30.68 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=44382.5MB, alloc=44.3MB, time=548.13
x[1] = 0.5899 2.16
h = 0.0001 0.003
y2[1] (numeric) = 2.80349313056 3.98527774112
y2[1] (closed_form) = 2.44385764621 3.55492432831
absolute error = 0.5608
relative error = 13 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 4.02392179435 -2.38985032334
y1[1] (closed_form) = 3.65075907846 -2.37970482705
absolute error = 0.3733
relative error = 8.566 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.28
Order of pole (three term test) = 43.3 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 11.28
Order of pole (three term test) = 30.72 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=44428.5MB, alloc=44.3MB, time=548.69
memory used=44474.7MB, alloc=44.3MB, time=549.26
x[1] = 0.59 2.163
h = 0.001 0.001
y2[1] (numeric) = 2.81983758161 3.99782827743
y2[1] (closed_form) = 2.45137390054 3.5656538966
absolute error = 0.5679
relative error = 13.13 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 4.03561528021 -2.3986844544
y1[1] (closed_form) = 3.66119517679 -2.38740369699
absolute error = 0.3746
relative error = 8.57 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.911
Order of pole (three term test) = 43.38 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 8.911
Order of pole (three term test) = 30.75 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=44520.8MB, alloc=44.3MB, time=549.82
memory used=44567.2MB, alloc=44.3MB, time=550.39
x[1] = 0.591 2.164
h = 0.001 0.003
y2[1] (numeric) = 2.83626232774 4.01040803189
y2[1] (closed_form) = 2.45742606549 3.56692523469
absolute error = 0.5833
relative error = 13.47 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 4.03679135267 -2.40551661338
y1[1] (closed_form) = 3.66230706737 -2.39342438636
absolute error = 0.3747
relative error = 8.564 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 42.37
Order of pole (three term test) = 43.38 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 42.37
Order of pole (three term test) = 30.79 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=44613.0MB, alloc=44.3MB, time=550.96
memory used=44659.3MB, alloc=44.3MB, time=551.53
x[1] = 0.592 2.167
h = 0.0001 0.004
y2[1] (numeric) = 2.85276740606 4.02301701239
y2[1] (closed_form) = 2.46828919926 3.57552562754
absolute error = 0.59
relative error = 13.58 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 4.04599697476 -2.41806684797
y1[1] (closed_form) = 3.67055788601 -2.40438417325
absolute error = 0.3757
relative error = 8.562 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.12
Order of pole (three term test) = 43.44 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 24.12
Order of pole (three term test) = 30.86 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=44705.3MB, alloc=44.3MB, time=552.09
x[1] = 0.5921 2.171
h = 0.003 0.006
y2[1] (numeric) = 2.8693529378 4.0356552565
y2[1] (closed_form) = 2.47829498449 3.58999505687
absolute error = 0.5929
relative error = 13.59 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 4.06182820417 -2.42991399519
y1[1] (closed_form) = 3.68464158009 -2.41463560306
absolute error = 0.3775
relative error = 8.569 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 32.22
Order of pole (three term test) = 43.55 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 32.22
Order of pole (three term test) = 30.89 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=44751.1MB, alloc=44.3MB, time=552.64
memory used=44797.4MB, alloc=44.3MB, time=553.22
x[1] = 0.5951 2.177
h = 0.0001 0.005
y2[1] (numeric) = 2.88601926474 4.04832282715
y2[1] (closed_form) = 2.5039350041 3.60486276852
absolute error = 0.5854
relative error = 13.34 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 4.07744708583 -2.45930603101
y1[1] (closed_form) = 3.69875285405 -2.44037447951
absolute error = 0.3792
relative error = 8.557 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 14.5
Order of pole (three term test) = 43.63 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 14.5
Order of pole (three term test) = 31.06 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=44843.2MB, alloc=44.3MB, time=553.78
memory used=44889.6MB, alloc=44.3MB, time=554.35
x[1] = 0.5952 2.182
h = 0.0001 0.003
y2[1] (numeric) = 2.90276728911 4.06101948931
y2[1] (closed_form) = 2.51653989636 3.62315636013
absolute error = 0.5839
relative error = 13.24 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 4.09743099083 -2.47418343009
y1[1] (closed_form) = 3.7165718421 -2.45328703935
absolute error = 0.3814
relative error = 8.565 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.79
Order of pole (three term test) = 43.77 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 11.79
Order of pole (three term test) = 31.11 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=44935.6MB, alloc=44.3MB, time=554.92
x[1] = 0.5953 2.185
h = 0.001 0.001
y2[1] (numeric) = 2.91959745106 4.0737454681
y2[1] (closed_form) = 2.52428382614 3.63407629366
absolute error = 0.5913
relative error = 13.36 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 4.10934201336 -2.48332369465
y1[1] (closed_form) = 3.72720564232 -2.46121113009
absolute error = 0.3828
relative error = 8.57 %
Correct digits = 1
memory used=44981.9MB, alloc=44.3MB, time=555.49
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.311
Order of pole (three term test) = 43.86 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 9.311
Order of pole (three term test) = 31.14 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=45028.1MB, alloc=44.3MB, time=556.06
x[1] = 0.5963 2.186
h = 0.001 0.003
y2[1] (numeric) = 2.93650985765 4.08650089798
y2[1] (closed_form) = 2.53047587741 3.63533976182
absolute error = 0.607
relative error = 13.7 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 4.11049408729 -2.49033186218
y1[1] (closed_form) = 3.72831297152 -2.46737321779
absolute error = 0.3829
relative error = 8.564 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 44.28
Order of pole (three term test) = 43.86 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 44.28
Order of pole (three term test) = 31.19 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=45074.0MB, alloc=44.3MB, time=556.62
memory used=45120.2MB, alloc=44.3MB, time=557.19
x[1] = 0.5973 2.189
h = 0.0001 0.004
y2[1] (numeric) = 2.95350454686 4.09928578679
y2[1] (closed_form) = 2.54162736153 3.64406427794
absolute error = 0.6139
relative error = 13.82 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 4.11982775961 -2.50325975409
y1[1] (closed_form) = 3.736696026 -2.47862106298
absolute error = 0.3839
relative error = 8.562 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.21
Order of pole (three term test) = 43.92 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 25.21
Order of pole (three term test) = 31.26 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=45166.1MB, alloc=44.3MB, time=557.75
memory used=45212.2MB, alloc=44.3MB, time=558.32
x[1] = 0.5974 2.193
h = 0.003 0.006
y2[1] (numeric) = 2.97058164281 4.11210017222
y2[1] (closed_form) = 2.55193732273 3.65879135542
absolute error = 0.6171
relative error = 13.83 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 4.13595431805 -2.51551846802
y1[1] (closed_form) = 3.75104704061 -2.48917332011
absolute error = 0.3858
relative error = 8.57 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 33.67
Order of pole (three term test) = 44.03 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 33.67
Order of pole (three term test) = 31.31 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=45258.0MB, alloc=44.3MB, time=558.88
x[1] = 0.6004 2.199
h = 0.0001 0.005
y2[1] (numeric) = 2.98774149511 4.12494411654
y2[1] (closed_form) = 2.57822602149 3.67383348676
absolute error = 0.6093
relative error = 13.57 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 4.1517279723 -2.54574895491
y1[1] (closed_form) = 3.76534971711 -2.51556264512
absolute error = 0.3876
relative error = 8.558 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 15.15
Order of pole (three term test) = 44.12 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 15.15
Order of pole (three term test) = 31.49 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=45304.0MB, alloc=44.3MB, time=559.44
memory used=45350.3MB, alloc=44.3MB, time=560.01
x[1] = 0.6005 2.204
h = 0.0001 0.003
y2[1] (numeric) = 3.00498502437 4.13781737429
y2[1] (closed_form) = 2.59121447866 3.69245336982
absolute error = 0.6079
relative error = 13.48 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 4.17208522816 -2.56114387404
y1[1] (closed_form) = 3.78350692552 -2.52885453152
absolute error = 0.3899
relative error = 8.568 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.32
Order of pole (three term test) = 44.27 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 12.32
Order of pole (three term test) = 31.55 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=45396.1MB, alloc=44.3MB, time=560.58
memory used=45442.4MB, alloc=44.3MB, time=561.15
x[1] = 0.6006 2.207
h = 0.001 0.001
y2[1] (numeric) = 3.02231268167 4.15072017292
y2[1] (closed_form) = 2.59919216125 3.7035668412
absolute error = 0.6156
relative error = 13.61 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 4.18421666288 -2.57059922618
y1[1] (closed_form) = 3.7943414278 -2.53700993584
absolute error = 0.3913
relative error = 8.573 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.73
Order of pole (three term test) = 44.36 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 9.73
Order of pole (three term test) = 31.59 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=45488.4MB, alloc=44.3MB, time=561.72
memory used=45534.7MB, alloc=44.3MB, time=562.29
x[1] = 0.6016 2.208
h = 0.001 0.003
y2[1] (numeric) = 3.03972457723 4.1636526492
y2[1] (closed_form) = 2.6055272166 3.70482157139
absolute error = 0.6317
relative error = 13.95 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 4.18534283521 -2.57778742172
y1[1] (closed_form) = 3.79544326336 -2.54331648955
absolute error = 0.3914
relative error = 8.567 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 46.27
Order of pole (three term test) = 44.36 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 46.27
Order of pole (three term test) = 31.64 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=45580.7MB, alloc=44.3MB, time=562.85
x[1] = 0.6026 2.211
h = 0.0001 0.004
y2[1] (numeric) = 3.0572207499 4.17661481092
y2[1] (closed_form) = 2.61697417 3.71367158775
absolute error = 0.6389
relative error = 14.06 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 4.19480476335 -2.59110294989
y1[1] (closed_form) = 3.8039597525 -2.55485947626
absolute error = 0.3925
relative error = 8.566 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.34
Order of pole (three term test) = 44.42 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 26.34
Order of pole (three term test) = 31.71 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=45626.6MB, alloc=44.3MB, time=563.42
memory used=45672.7MB, alloc=44.3MB, time=563.98
x[1] = 0.6027 2.215
h = 0.003 0.006
y2[1] (numeric) = 3.07480132673 4.18960669587
y2[1] (closed_form) = 2.62759644233 3.72866062332
absolute error = 0.6422
relative error = 14.08 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 4.21123059603 -2.60378527671
y1[1] (closed_form) = 3.81858216963 -2.56572071865
absolute error = 0.3945
relative error = 8.575 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 35.18
Order of pole (three term test) = 44.54 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 35.18
Order of pole (three term test) = 31.77 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=45718.5MB, alloc=44.3MB, time=564.54
memory used=45764.8MB, alloc=44.3MB, time=565.11
x[1] = 0.6057 2.221
h = 0.0001 0.005
y2[1] (numeric) = 3.09246666537 4.20262836562
y2[1] (closed_form) = 2.65454931394 3.74387790143
absolute error = 0.6342
relative error = 13.82 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 4.22715640571 -2.63487538326
y1[1] (closed_form) = 3.83307661513 -2.59277585934
absolute error = 0.3963
relative error = 8.564 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 15.83
Order of pole (three term test) = 44.64 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 15.83
Order of pole (three term test) = 31.96 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=45810.7MB, alloc=44.3MB, time=565.67
x[1] = 0.6058 2.226
h = 0.0001 0.003
y2[1] (numeric) = 3.11021770514 4.21567956394
y2[1] (closed_form) = 2.66793160025 3.76282953601
absolute error = 0.633
relative error = 13.72 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 4.2478920297 -2.65080297349
y1[1] (closed_form) = 3.85157722229 -2.60645736697
absolute error = 0.3988
relative error = 8.575 %
Correct digits = 1
memory used=45856.8MB, alloc=44.3MB, time=566.23
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.88
Order of pole (three term test) = 44.79 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 12.88
Order of pole (three term test) = 32.03 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=45902.9MB, alloc=44.3MB, time=566.80
x[1] = 0.6059 2.229
h = 0.001 0.001
y2[1] (numeric) = 3.12805490835 4.2287605206
y2[1] (closed_form) = 2.67614926471 3.77413975159
absolute error = 0.641
relative error = 13.85 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 4.26024676945 -2.6605825826
y1[1] (closed_form) = 3.86261546433 -2.61485032989
absolute error = 0.4003
relative error = 8.581 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.17
Order of pole (three term test) = 44.88 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 10.17
Order of pole (three term test) = 32.08 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=45949.0MB, alloc=44.3MB, time=567.37
memory used=45995.4MB, alloc=44.3MB, time=567.94
x[1] = 0.6069 2.23
h = 0.0001 0.004
y2[1] (numeric) = 3.14597838842 4.24187137475
y2[1] (closed_form) = 2.68263050506 3.77538483842
absolute error = 0.6575
relative error = 14.2 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 4.26134507345 -2.66795490551
y1[1] (closed_form) = 3.86371083781 -2.62130448189
absolute error = 0.4004
relative error = 8.575 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 61.18
Order of pole (three term test) = 44.89 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 61.18
Order of pole (three term test) = 32.13 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=46041.3MB, alloc=44.3MB, time=568.50
memory used=46087.5MB, alloc=44.3MB, time=569.07
x[1] = 0.607 2.234
h = 0.003 0.006
y2[1] (numeric) = 3.16398819151 4.25501217291
y2[1] (closed_form) = 2.69352508289 3.79060670154
absolute error = 0.6611
relative error = 14.22 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 4.27802333293 -2.68099965381
y1[1] (closed_form) = 3.87857399405 -2.63243507682
absolute error = 0.4024
relative error = 8.584 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 36.54
Order of pole (three term test) = 45.01 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 36.54
Order of pole (three term test) = 32.19 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=46133.4MB, alloc=44.3MB, time=569.63
x[1] = 0.61 2.24
h = 0.0001 0.005
y2[1] (numeric) = 3.18208465806 4.2681829736
y2[1] (closed_form) = 2.72106022476 3.80598343431
absolute error = 0.6528
relative error = 13.95 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 4.29407381595 -2.71282261405
y1[1] (closed_form) = 3.89324193641 -2.66007361175
absolute error = 0.4043
relative error = 8.574 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.45
Order of pole (three term test) = 45.12 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 16.45
Order of pole (three term test) = 32.4 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=46179.4MB, alloc=44.3MB, time=570.19
memory used=46225.7MB, alloc=44.3MB, time=570.76
x[1] = 0.6101 2.245
h = 0.0001 0.003
y2[1] (numeric) = 3.20026874389 4.28138351119
y2[1] (closed_form) = 2.73478587995 3.82522990964
absolute error = 0.6517
relative error = 13.86 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 4.31512860281 -2.72920593898
y1[1] (closed_form) = 3.91204713947 -2.67409475692
absolute error = 0.4068
relative error = 8.585 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.37
Order of pole (three term test) = 45.28 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 13.37
Order of pole (three term test) = 32.48 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=46271.6MB, alloc=44.3MB, time=571.32
memory used=46318.0MB, alloc=44.3MB, time=571.90
x[1] = 0.6102 2.248
h = 0.001 0.001
y2[1] (numeric) = 3.21854092115 4.29461401761
y2[1] (closed_form) = 2.74321282313 3.83671503191
absolute error = 0.66
relative error = 13.99 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 4.32767165183 -2.73926293106
y1[1] (closed_form) = 3.92326614897 -2.68269484522
absolute error = 0.4083
relative error = 8.592 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.56
Order of pole (three term test) = 45.37 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 10.56
Order of pole (three term test) = 32.53 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=46364.0MB, alloc=44.3MB, time=572.46
memory used=46410.3MB, alloc=44.3MB, time=573.04
x[1] = 0.6112 2.249
h = 0.001 0.003
y2[1] (numeric) = 3.23690130607 4.30787463408
y2[1] (closed_form) = 2.74982262126 3.8379528578
absolute error = 0.6768
relative error = 14.34 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 4.32874517989 -2.74679188664
y1[1] (closed_form) = 3.92435696629 -2.6892786967
absolute error = 0.4085
relative error = 8.586 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.23
Order of pole (three term test) = 45.38 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 50.23
Order of pole (three term test) = 32.59 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=46456.2MB, alloc=44.3MB, time=573.60
x[1] = 0.6122 2.252
h = 0.0001 0.004
y2[1] (numeric) = 3.2553499392 4.32116536829
y2[1] (closed_form) = 2.76183735255 3.84704375246
absolute error = 0.6844
relative error = 14.45 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 4.3384426141 -2.76084475892
y1[1] (closed_form) = 3.93312863143 -2.70138867251
absolute error = 0.4097
relative error = 8.585 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.59
Order of pole (three term test) = 45.45 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 28.59
Order of pole (three term test) = 32.68 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=46502.0MB, alloc=44.3MB, time=574.16
memory used=46548.1MB, alloc=44.3MB, time=574.72
x[1] = 0.6123 2.256
h = 0.003 0.006
y2[1] (numeric) = 3.27388695323 4.33448625819
y2[1] (closed_form) = 2.77305987175 3.86253582025
absolute error = 0.6882
relative error = 14.47 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 4.35542744616 -2.77433598555
y1[1] (closed_form) = 3.9482710263 -2.71284392966
absolute error = 0.4118
relative error = 8.596 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.19
Order of pole (three term test) = 45.58 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 38.19
Order of pole (three term test) = 32.75 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=46593.9MB, alloc=44.3MB, time=575.28
memory used=46640.1MB, alloc=44.3MB, time=575.84
x[1] = 0.6153 2.262
h = 0.0001 0.005
y2[1] (numeric) = 3.29251272122 4.34783736406
y2[1] (closed_form) = 2.80128893047 3.87808904471
absolute error = 0.6797
relative error = 14.21 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 4.3716248248 -2.80705861787
y1[1] (closed_form) = 3.96313142925 -2.74117780503
absolute error = 0.4138
relative error = 8.587 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.19
Order of pole (three term test) = 45.69 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 17.19
Order of pole (three term test) = 32.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=46686.1MB, alloc=44.3MB, time=576.41
x[1] = 0.6154 2.267
h = 0.0001 0.003
y2[1] (numeric) = 3.31122821846 4.36121840891
y2[1] (closed_form) = 2.81542813586 3.89767771929
absolute error = 0.6787
relative error = 14.12 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 4.39306726543 -2.82400338523
y1[1] (closed_form) = 3.98228997162 -2.75560835439
absolute error = 0.4164
relative error = 8.599 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.98
Order of pole (three term test) = 45.86 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 13.98
Order of pole (three term test) = 33.07 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=46732.2MB, alloc=44.3MB, time=576.97
memory used=46778.5MB, alloc=44.3MB, time=577.54
x[1] = 0.6155 2.27
h = 0.001 0.001
y2[1] (numeric) = 3.3300339288 4.374629627
y2[1] (closed_form) = 2.82410702873 3.90936572043
absolute error = 0.6873
relative error = 14.25 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 4.40583896756 -2.83440204803
y1[1] (closed_form) = 3.9937185519 -2.76445800211
absolute error = 0.418
relative error = 8.606 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.04
Order of pole (three term test) = 45.96 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 11.04
Order of pole (three term test) = 33.13 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=46824.6MB, alloc=44.3MB, time=578.11
memory used=46870.9MB, alloc=44.3MB, time=578.68
x[1] = 0.6165 2.271
h = 0.001 0.003
y2[1] (numeric) = 3.34892997186 4.38807116199
y2[1] (closed_form) = 2.83086911506 3.91059215462
absolute error = 0.7045
relative error = 14.59 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 4.40688084101 -2.84212287031
y1[1] (closed_form) = 3.99480104389 -2.77119546894
absolute error = 0.4181
relative error = 8.6 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 52.48
Order of pole (three term test) = 45.96 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 52.48
Order of pole (three term test) = 33.19 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=46916.8MB, alloc=44.3MB, time=579.25
memory used=46963.1MB, alloc=44.3MB, time=579.81
x[1] = 0.6175 2.274
h = 0.0001 0.004
y2[1] (numeric) = 3.36791638911 4.40154302148
y2[1] (closed_form) = 2.84320058341 3.91981251202
absolute error = 0.7123
relative error = 14.71 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 4.41670683906 -2.85659292181
y1[1] (closed_form) = 4.00370961631 -2.78362176308
absolute error = 0.4194
relative error = 8.601 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.88
Order of pole (three term test) = 46.04 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 29.88
Order of pole (three term test) = 33.28 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=47009.0MB, alloc=44.3MB, time=580.37
x[1] = 0.6176 2.278
h = 0.003 0.006
y2[1] (numeric) = 3.38699331639 4.4150452435
y2[1] (closed_form) = 2.85475977361 3.93557923036
absolute error = 0.7164
relative error = 14.73 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 4.43400226071 -2.87054354018
y1[1] (closed_form) = 4.01913548201 -2.79541043664
absolute error = 0.4216
relative error = 8.612 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 39.91
Order of pole (three term test) = 46.18 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 39.91
Order of pole (three term test) = 33.36 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=47054.8MB, alloc=44.3MB, time=580.93
memory used=47101.1MB, alloc=44.3MB, time=581.50
x[1] = 0.6206 2.284
h = 0.0001 0.005
y2[1] (numeric) = 3.4061611353 4.42857788746
y2[1] (closed_form) = 2.88369924671 3.95130945406
absolute error = 0.7076
relative error = 14.47 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 4.45034340614 -2.90418838498
y1[1] (closed_form) = 4.0341885128 -2.82445603622
absolute error = 0.4237
relative error = 8.604 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.96
Order of pole (three term test) = 46.29 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 17.96
Order of pole (three term test) = 33.61 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=47147.0MB, alloc=44.3MB, time=582.06
memory used=47193.3MB, alloc=44.3MB, time=582.62
x[1] = 0.6207 2.289
h = 0.0001 0.003
y2[1] (numeric) = 3.42542084091 4.44214066462
y2[1] (closed_form) = 2.89826301712 3.9712459613
absolute error = 0.7069
relative error = 14.38 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 4.47217861161 -2.92171083717
y1[1] (closed_form) = 4.05370576382 -2.83930703709
absolute error = 0.4265
relative error = 8.618 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 14.6
Order of pole (three term test) = 46.47 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 14.6
Order of pole (three term test) = 33.71 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=47239.3MB, alloc=44.3MB, time=583.19
x[1] = 0.6208 2.292
h = 0.001 0.001
y2[1] (numeric) = 3.44477292909 4.45573381156
y2[1] (closed_form) = 2.90720054244 3.98314014607
absolute error = 0.7158
relative error = 14.52 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 4.48518190678 -2.93246099817
y1[1] (closed_form) = 4.06534706154 -2.84841294434
absolute error = 0.4282
relative error = 8.626 %
Correct digits = 1
memory used=47285.8MB, alloc=44.3MB, time=583.76
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.53
Order of pole (three term test) = 46.58 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 11.53
Order of pole (three term test) = 33.78 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=47331.8MB, alloc=44.3MB, time=584.33
x[1] = 0.6218 2.293
h = 0.001 0.003
y2[1] (numeric) = 3.46421752289 4.46935747439
y2[1] (closed_form) = 2.914118286 3.98435417068
absolute error = 0.7334
relative error = 14.86 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 4.48618996237 -2.94037802879
y1[1] (closed_form) = 4.06642015043 -2.85530735073
absolute error = 0.4283
relative error = 8.62 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 54.84
Order of pole (three term test) = 46.58 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 54.84
Order of pole (three term test) = 33.84 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=47377.7MB, alloc=44.3MB, time=584.90
memory used=47424.0MB, alloc=44.3MB, time=585.46
x[1] = 0.6228 2.296
h = 0.0001 0.004
y2[1] (numeric) = 3.48375466475 4.48301166066
y2[1] (closed_form) = 2.92677426394 3.99370531867
absolute error = 0.7414
relative error = 14.97 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 4.49614453006 -2.95527614594
y1[1] (closed_form) = 4.07546679373 -2.86805770628
absolute error = 0.4296
relative error = 8.621 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.22
Order of pole (three term test) = 46.66 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 31.22
Order of pole (three term test) = 33.95 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=47470.0MB, alloc=44.3MB, time=586.02
memory used=47516.1MB, alloc=44.3MB, time=586.59
x[1] = 0.6229 2.3
h = 0.003 0.006
y2[1] (numeric) = 3.50338449372 4.49669640843
y2[1] (closed_form) = 2.93867907232 4.00975118017
absolute error = 0.7457
relative error = 15 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 4.5137545798 -2.96969937848
y1[1] (closed_form) = 4.09118041393 -2.88018876856
absolute error = 0.432
relative error = 8.633 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 41.7
Order of pole (three term test) = 46.81 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 41.7
Order of pole (three term test) = 34.04 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=47562.0MB, alloc=44.3MB, time=587.16
x[1] = 0.6259 2.306
h = 0.0001 0.005
y2[1] (numeric) = 3.52310740011 4.51041177619
y2[1] (closed_form) = 2.96834582255 4.02565882568
absolute error = 0.7367
relative error = 14.73 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 4.53023617468 -3.00428946204
y1[1] (closed_form) = 4.10642616163 -2.90996284553
absolute error = 0.4342
relative error = 8.627 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 18.77
Order of pole (three term test) = 46.94 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 18.77
Order of pole (three term test) = 34.3 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=47608.0MB, alloc=44.3MB, time=587.72
memory used=47654.2MB, alloc=44.3MB, time=588.28
x[1] = 0.626 2.311
h = 0.0001 0.003
y2[1] (numeric) = 3.5429243992 4.52415746308
y2[1] (closed_form) = 2.98334544747 4.04594885855
absolute error = 0.7361
relative error = 14.64 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 4.55246928432 -3.0224062304
y1[1] (closed_form) = 4.12630755614 -2.9252456206
absolute error = 0.4371
relative error = 8.642 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 15.26
Order of pole (three term test) = 47.12 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 15.26
Order of pole (three term test) = 34.42 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=47700.1MB, alloc=44.3MB, time=588.84
memory used=47746.6MB, alloc=44.3MB, time=589.42
x[1] = 0.6261 2.314
h = 0.001 0.001
y2[1] (numeric) = 3.56283599911 4.53793370801
y2[1] (closed_form) = 2.992548454 4.0580525654
absolute error = 0.7453
relative error = 14.78 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 4.56570712618 -3.03351795162
y1[1] (closed_form) = 4.13816475517 -2.93461465391
absolute error = 0.4388
relative error = 8.65 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.05
Order of pole (three term test) = 47.24 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 12.05
Order of pole (three term test) = 34.49 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=47792.5MB, alloc=44.3MB, time=589.98
memory used=47838.8MB, alloc=44.3MB, time=590.56
x[1] = 0.6271 2.315
h = 0.001 0.003
y2[1] (numeric) = 3.58284232645 4.55174065957
y2[1] (closed_form) = 2.99962529186 4.05925312059
absolute error = 0.7633
relative error = 15.12 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 4.56667912953 -3.04163561751
y1[1] (closed_form) = 4.13922732232 -2.94166939345
absolute error = 0.439
relative error = 8.645 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 57.31
Order of pole (three term test) = 47.24 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 57.31
Order of pole (three term test) = 34.56 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=47884.6MB, alloc=44.3MB, time=591.12
x[1] = 0.6281 2.318
h = 0.0001 0.004
y2[1] (numeric) = 3.60294342465 4.56557832523
y2[1] (closed_form) = 3.01261373041 4.06873637096
absolute error = 0.7716
relative error = 15.24 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 4.57676221536 -3.05697292937
y1[1] (closed_form) = 4.14841318746 -2.95475173342
absolute error = 0.4404
relative error = 8.647 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 32.63
Order of pole (three term test) = 47.32 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 32.63
Order of pole (three term test) = 34.67 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=47930.6MB, alloc=44.3MB, time=591.68
memory used=47976.8MB, alloc=44.3MB, time=592.25
x[1] = 0.6282 2.322
h = 0.003 0.006
y2[1] (numeric) = 3.62313943601 4.57944674309
y2[1] (closed_form) = 3.02487332681 4.08506591489
absolute error = 0.7761
relative error = 15.27 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 4.59469095187 -3.07188231441
y1[1] (closed_form) = 4.16441889718 -2.96723437995
absolute error = 0.4428
relative error = 8.66 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 43.58
Order of pole (three term test) = 47.48 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 43.58
Order of pole (three term test) = 34.77 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=48022.7MB, alloc=44.3MB, time=592.81
memory used=48068.9MB, alloc=44.3MB, time=593.37
x[1] = 0.6312 2.328
h = 0.0001 0.005
y2[1] (numeric) = 3.64343075978 4.59334597066
y2[1] (closed_form) = 3.05528458987 4.10115131606
absolute error = 0.7669
relative error = 15 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 4.61130948335 -3.10744115851
y1[1] (closed_form) = 4.17985736882 -2.99775406456
absolute error = 0.4452
relative error = 8.655 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 19.61
Order of pole (three term test) = 47.61 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 19.61
Order of pole (three term test) = 35.06 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=48114.7MB, alloc=44.3MB, time=593.94
x[1] = 0.6313 2.333
h = 0.0001 0.003
y2[1] (numeric) = 3.66381843182 4.60727569457
y2[1] (closed_form) = 3.07073163997 4.12180062707
absolute error = 0.7664
relative error = 14.91 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 4.63394566313 -3.12616927202
y1[1] (closed_form) = 4.20010840701 -3.01348021829
absolute error = 0.4482
relative error = 8.671 %
Correct digits = 1
memory used=48160.9MB, alloc=44.3MB, time=594.50
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 15.95
Order of pole (three term test) = 47.81 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 15.95
Order of pole (three term test) = 35.19 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=48207.0MB, alloc=44.3MB, time=595.07
x[1] = 0.6314 2.336
h = 0.001 0.001
y2[1] (numeric) = 3.68430297278 4.62123615605
y2[1] (closed_form) = 3.08020714636 4.13411722804
absolute error = 0.776
relative error = 15.05 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 4.64742101793 -3.13765285522
y1[1] (closed_form) = 4.21218472829 -3.02311941454
absolute error = 0.4501
relative error = 8.68 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.59
Order of pole (three term test) = 47.93 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 12.59
Order of pole (three term test) = 35.27 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=48253.1MB, alloc=44.3MB, time=595.64
memory used=48299.3MB, alloc=44.3MB, time=596.20
x[1] = 0.6324 2.337
h = 0.0001 0.004
y2[1] (numeric) = 3.70488451295 4.63522750623
y2[1] (closed_form) = 3.08744658502 4.13530321073
absolute error = 0.7945
relative error = 15.39 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 4.64835466153 -3.14597567013
y1[1] (closed_form) = 4.21323561284 -3.03033795145
absolute error = 0.4502
relative error = 8.675 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 75.78
Order of pole (three term test) = 47.94 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 75.78
Order of pole (three term test) = 35.34 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=48345.2MB, alloc=44.3MB, time=596.77
memory used=48391.4MB, alloc=44.3MB, time=597.33
x[1] = 0.6325 2.341
h = 0.003 0.006
y2[1] (numeric) = 3.72556310504 4.64924979542
y2[1] (closed_form) = 3.10001563431 4.15188498863
absolute error = 0.7992
relative error = 15.42 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 4.66655208422 -3.1613007566
y1[1] (closed_form) = 4.22950059531 -3.04312721717
absolute error = 0.4527
relative error = 8.689 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 45.26
Order of pole (three term test) = 48.1 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 45.26
Order of pole (three term test) = 35.45 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=48437.2MB, alloc=44.3MB, time=597.90
x[1] = 0.6355 2.347
h = 0.0001 0.005
y2[1] (numeric) = 3.74633912909 4.66330307825
y2[1] (closed_form) = 3.13107972055 4.1681327478
absolute error = 0.7898
relative error = 15.15 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 4.68328189857 -3.19768523594
y1[1] (closed_form) = 4.24511406388 -3.07430041286
absolute error = 0.4552
relative error = 8.685 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 20.37
Order of pole (three term test) = 48.24 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 20.37
Order of pole (three term test) = 35.75 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=48483.1MB, alloc=44.3MB, time=598.46
memory used=48529.2MB, alloc=44.3MB, time=599.02
x[1] = 0.6356 2.352
h = 0.0001 0.003
y2[1] (numeric) = 3.7672136391 4.67738703048
y2[1] (closed_form) = 3.1469170103 4.18910148795
absolute error = 0.7894
relative error = 15.07 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 4.70625793422 -3.21693611092
y1[1] (closed_form) = 4.26569320812 -3.09041323113
absolute error = 0.4584
relative error = 8.702 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.57
Order of pole (three term test) = 48.45 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 16.57
Order of pole (three term test) = 35.89 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=48575.1MB, alloc=44.3MB, time=599.58
memory used=48621.5MB, alloc=44.3MB, time=600.16
x[1] = 0.6357 2.355
h = 0.001 0.001
y2[1] (numeric) = 3.78818716674 4.69150189546
y2[1] (closed_form) = 3.15663023723 4.20160742994
absolute error = 0.7993
relative error = 15.21 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 4.71993349064 -3.22873763153
y1[1] (closed_form) = 4.27796408543 -3.10028807943
absolute error = 0.4603
relative error = 8.712 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.08
Order of pole (three term test) = 48.57 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 13.08
Order of pole (three term test) = 35.98 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=48667.5MB, alloc=44.3MB, time=600.72
memory used=48713.7MB, alloc=44.3MB, time=601.29
x[1] = 0.6367 2.356
h = 0.001 0.003
y2[1] (numeric) = 3.80925984549 4.70564782658
y2[1] (closed_form) = 3.16401269139 4.20278194686
absolute error = 0.8181
relative error = 15.55 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 4.72083334767 -3.23723491905
y1[1] (closed_form) = 4.27900595988 -3.10765059541
absolute error = 0.4604
relative error = 8.707 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 62.21
Order of pole (three term test) = 48.58 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 62.21
Order of pole (three term test) = 36.06 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=48759.7MB, alloc=44.3MB, time=601.85
x[1] = 0.6377 2.359
h = 0.0001 0.004
y2[1] (numeric) = 3.83043172061 4.71982483115
y2[1] (closed_form) = 3.17763994142 4.21251863259
absolute error = 0.8267
relative error = 15.67 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 4.73115171138 -3.25340716532
y1[1] (closed_form) = 4.28845808499 -3.12137071078
absolute error = 0.462
relative error = 8.71 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 35.41
Order of pole (three term test) = 48.67 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 35.41
Order of pole (three term test) = 36.19 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=48805.5MB, alloc=44.3MB, time=602.41
memory used=48851.6MB, alloc=44.3MB, time=602.98
x[1] = 0.6378 2.363
h = 0.003 0.006
y2[1] (numeric) = 3.85170294073 4.73403294732
y2[1] (closed_form) = 3.19058139701 4.2293927791
absolute error = 0.8317
relative error = 15.7 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 4.74967531063 -3.26924409412
y1[1] (closed_form) = 4.30502347555 -3.13452923039
absolute error = 0.4646
relative error = 8.725 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 47.3
Order of pole (three term test) = 48.84 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 47.3
Order of pole (three term test) = 36.31 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=48897.4MB, alloc=44.3MB, time=603.54
memory used=48943.7MB, alloc=44.3MB, time=604.10
x[1] = 0.6408 2.369
h = 0.0001 0.005
y2[1] (numeric) = 3.87307392222 4.74827223073
y2[1] (closed_form) = 3.22242308632 4.24581888182
absolute error = 0.8221
relative error = 15.42 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 4.76653507045 -3.30664182459
y1[1] (closed_form) = 4.3208296641 -3.16648094202
absolute error = 0.4672
relative error = 8.722 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 21.29
Order of pole (three term test) = 49 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 21.29
Order of pole (three term test) = 36.63 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=48989.6MB, alloc=44.3MB, time=604.66
x[1] = 0.6409 2.374
h = 0.0001 0.003
y2[1] (numeric) = 3.89454574045 4.76254234395
y2[1] (closed_form) = 3.23873003246 4.2671579084
absolute error = 0.8219
relative error = 15.34 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 4.78992371388 -3.32653637205
y1[1] (closed_form) = 4.34178900616 -3.18305943739
absolute error = 0.4705
relative error = 8.74 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.31
Order of pole (three term test) = 49.21 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 17.31
Order of pole (three term test) = 36.79 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=49035.7MB, alloc=44.3MB, time=605.22
memory used=49081.8MB, alloc=44.3MB, time=605.79
x[1] = 0.641 2.377
h = 0.001 0.001
y2[1] (numeric) = 3.91611894022 4.77684353264
y2[1] (closed_form) = 3.24872924415 4.27988319678
absolute error = 0.8321
relative error = 15.49 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 4.80384225251 -3.33872931273
y1[1] (closed_form) = 4.354285186 -3.19321797012
absolute error = 0.4725
relative error = 8.751 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.67
Order of pole (three term test) = 49.35 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 13.67
Order of pole (three term test) = 36.89 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=49127.7MB, alloc=44.3MB, time=606.35
memory used=49174.0MB, alloc=44.3MB, time=606.92
x[1] = 0.642 2.378
h = 0.001 0.003
y2[1] (numeric) = 3.9377936588 4.7911759528
y2[1] (closed_form) = 3.25628102758 4.28104101275
absolute error = 0.8513
relative error = 15.83 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 4.80469931181 -3.34744026771
y1[1] (closed_form) = 4.35531314422 -3.20075093719
absolute error = 0.4727
relative error = 8.746 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 65.01
Order of pole (three term test) = 49.35 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 65.01
Order of pole (three term test) = 36.97 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=49219.9MB, alloc=44.3MB, time=607.48
memory used=49266.2MB, alloc=44.3MB, time=608.05
x[1] = 0.643 2.381
h = 0.0001 0.004
y2[1] (numeric) = 3.95956994253 4.80553961164
y2[1] (closed_form) = 3.27026449028 4.29091355576
absolute error = 0.8602
relative error = 15.94 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 4.81514570401 -3.36408464288
y1[1] (closed_form) = 4.36490780396 -3.21482671857
absolute error = 0.4743
relative error = 8.75 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.01
Order of pole (three term test) = 49.45 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 37.01
Order of pole (three term test) = 37.11 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=49312.1MB, alloc=44.3MB, time=608.61
x[1] = 0.6431 2.385
h = 0.003 0.006
y2[1] (numeric) = 3.98144794349 4.81993454728
y2[1] (closed_form) = 3.28358818782 4.30808474599
absolute error = 0.8654
relative error = 15.98 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 4.83399959183 -3.38044791816
y1[1] (closed_form) = 4.38177808635 -3.22836435468
absolute error = 0.4771
relative error = 8.766 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49.43
Order of pole (three term test) = 49.63 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 49.43
Order of pole (three term test) = 37.24 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=49358.0MB, alloc=44.3MB, time=609.16
memory used=49404.2MB, alloc=44.3MB, time=609.73
x[1] = 0.6461 2.391
h = 0.0001 0.005
y2[1] (numeric) = 4.00342808758 4.83436081419
y2[1] (closed_form) = 3.3162258284 4.32468925527
absolute error = 0.8556
relative error = 15.7 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 4.85098517397 -3.41888393018
y1[1] (closed_form) = 4.39777674958 -3.26111283605
absolute error = 0.4799
relative error = 8.765 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.24
Order of pole (three term test) = 49.8 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 22.24
Order of pole (three term test) = 37.59 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=49450.1MB, alloc=44.3MB, time=610.28
memory used=49496.3MB, alloc=44.3MB, time=610.85
x[1] = 0.6462 2.396
h = 0.0001 0.003
y2[1] (numeric) = 4.02551147189 4.84881806133
y2[1] (closed_form) = 3.33301484229 4.34640449415
absolute error = 0.8556
relative error = 15.62 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 4.87479166211 -3.43944039458
y1[1] (closed_form) = 4.41912197889 -3.27816945511
absolute error = 0.4834
relative error = 8.785 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 18.09
Order of pole (three term test) = 50.03 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 18.09
Order of pole (three term test) = 37.76 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=49542.2MB, alloc=44.3MB, time=611.42
memory used=49588.6MB, alloc=44.3MB, time=611.99
x[1] = 0.6463 2.399
h = 0.001 0.001
y2[1] (numeric) = 4.04769865463 4.86330653663
y2[1] (closed_form) = 3.34330756538 4.35935259868
absolute error = 0.8661
relative error = 15.77 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 4.88895618153 -3.45203578976
y1[1] (closed_form) = 4.43184678939 -3.28861921811
absolute error = 0.4854
relative error = 8.796 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 14.28
Order of pole (three term test) = 50.16 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 14.28
Order of pole (three term test) = 37.87 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=49634.5MB, alloc=44.3MB, time=612.55
x[1] = 0.6473 2.4
h = 0.001 0.003
y2[1] (numeric) = 4.06998977702 4.87782639872
y2[1] (closed_form) = 3.35103239112 4.36049248037
absolute error = 0.8857
relative error = 16.11 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 4.88976790983 -3.46096518917
y1[1] (closed_form) = 4.43285954324 -3.29632631046
absolute error = 0.4857
relative error = 8.792 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 67.93
Order of pole (three term test) = 50.17 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 67.93
Order of pole (three term test) = 37.95 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=49680.4MB, alloc=44.3MB, time=613.11
memory used=49726.8MB, alloc=44.3MB, time=613.68
x[1] = 0.6483 2.403
h = 0.0001 0.004
y2[1] (numeric) = 4.09238488642 4.89237765472
y2[1] (closed_form) = 3.36538074432 4.37050212057
absolute error = 0.8949
relative error = 16.22 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 4.9003420294 -3.47809382456
y1[1] (closed_form) = 4.4425978293 -3.31076641297
absolute error = 0.4874
relative error = 8.796 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.67
Order of pole (three term test) = 50.28 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 38.67
Order of pole (three term test) = 38.11 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=49772.6MB, alloc=44.3MB, time=614.24
memory used=49818.7MB, alloc=44.3MB, time=614.80
x[1] = 0.6484 2.407
h = 0.003 0.006
y2[1] (numeric) = 4.11488413852 4.90696034271
y2[1] (closed_form) = 3.37909676302 4.38797507595
absolute error = 0.9004
relative error = 16.26 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 4.91953033231 -3.4949982945
y1[1] (closed_form) = 4.45977753786 -3.32469327214
absolute error = 0.4903
relative error = 8.814 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 51.65
Order of pole (three term test) = 50.47 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 51.65
Order of pole (three term test) = 38.25 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=49864.7MB, alloc=44.3MB, time=615.36
x[1] = 0.6514 2.413
h = 0.0001 0.005
y2[1] (numeric) = 4.1374879689 4.92157451591
y2[1] (closed_form) = 3.41254910758 4.40475795047
absolute error = 0.8903
relative error = 15.98 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 4.93663738936 -3.53449815273
y1[1] (closed_form) = 4.47596833239 -3.3582571852
absolute error = 0.4932
relative error = 8.814 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.24
Order of pole (three term test) = 50.64 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 23.24
Order of pole (three term test) = 38.62 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=49910.7MB, alloc=44.3MB, time=615.92
memory used=49956.7MB, alloc=44.3MB, time=616.48
x[1] = 0.6515 2.418
h = 0.0001 0.003
y2[1] (numeric) = 4.1601974968 4.93621980924
y2[1] (closed_form) = 3.42983290809 4.42685538664
absolute error = 0.8904
relative error = 15.9 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 4.9608669788 -3.55573521164
y1[1] (closed_form) = 4.49770520283 -3.37580468256
absolute error = 0.4969
relative error = 8.836 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 18.9
Order of pole (three term test) = 50.89 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 18.9
Order of pole (three term test) = 38.81 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=50002.5MB, alloc=44.3MB, time=617.04
memory used=50048.8MB, alloc=44.3MB, time=617.62
x[1] = 0.6516 2.421
h = 0.001 0.001
y2[1] (numeric) = 4.18301329418 4.95089647289
y2[1] (closed_form) = 3.44042685499 4.44002981021
absolute error = 0.9013
relative error = 16.05 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 4.97528048569 -3.56874435678
y1[1] (closed_form) = 4.51066200847 -3.38655340776
absolute error = 0.4991
relative error = 8.848 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 14.93
Order of pole (three term test) = 51.03 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 14.93
Order of pole (three term test) = 38.93 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=50094.9MB, alloc=44.3MB, time=618.18
memory used=50141.2MB, alloc=44.3MB, time=618.76
x[1] = 0.6526 2.422
h = 0.001 0.003
y2[1] (numeric) = 4.20593550626 4.96560466818
y2[1] (closed_form) = 3.44832851081 4.44115047575
absolute error = 0.9214
relative error = 16.39 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 4.9760442681 -3.57789707026
y1[1] (closed_form) = 4.51165822224 -3.39443837542
absolute error = 0.4993
relative error = 8.844 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 70.99
Order of pole (three term test) = 51.04 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 70.99
Order of pole (three term test) = 39.02 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=50187.1MB, alloc=44.3MB, time=619.32
x[1] = 0.6536 2.425
h = 0.0001 0.004
y2[1] (numeric) = 4.22896418151 4.98034440211
y2[1] (closed_form) = 3.46305063068 4.45129843048
absolute error = 0.9309
relative error = 16.51 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 4.98674574286 -3.59552236506
y1[1] (closed_form) = 4.52154120685 -3.40925165377
absolute error = 0.5011
relative error = 8.849 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 40.41
Order of pole (three term test) = 51.16 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 40.41
Order of pole (three term test) = 39.18 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=50233.0MB, alloc=44.3MB, time=619.88
memory used=50279.1MB, alloc=44.3MB, time=620.45
x[1] = 0.6537 2.429
h = 0.003 0.006
y2[1] (numeric) = 4.25209947925 4.9951157127
y2[1] (closed_form) = 3.47716929898 4.46907791851
absolute error = 0.9366
relative error = 16.54 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 5.00627260024 -3.61298322955
y1[1] (closed_form) = 4.53903492619 -3.42357809219
absolute error = 0.5042
relative error = 8.868 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 53.97
Order of pole (three term test) = 51.35 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 53.97
Order of pole (three term test) = 39.34 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=50325.0MB, alloc=44.3MB, time=621.01
memory used=50371.2MB, alloc=44.3MB, time=621.57
x[1] = 0.6567 2.435
h = 0.0001 0.005
y2[1] (numeric) = 4.27534184497 5.00991865186
y2[1] (closed_form) = 3.51145551328 4.48603900829
absolute error = 0.9263
relative error = 16.26 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 5.02349655254 -3.65357304341
y1[1] (closed_form) = 4.55541740609 -3.45797651547
absolute error = 0.5073
relative error = 8.87 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.29
Order of pole (three term test) = 51.54 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 24.29
Order of pole (three term test) = 39.73 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=50417.0MB, alloc=44.3MB, time=622.14
memory used=50463.2MB, alloc=44.3MB, time=622.70
x[1] = 0.6568 2.44
h = 0.0001 0.003
y2[1] (numeric) = 4.29869242052 5.02475284003
y2[1] (closed_form) = 3.529247134 4.50852468558
absolute error = 0.9266
relative error = 16.18 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 5.04815451742 -3.67550981712
y1[1] (closed_form) = 4.5775517356 -3.47602796084
absolute error = 0.5111
relative error = 8.893 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 19.75
Order of pole (three term test) = 51.8 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 19.75
Order of pole (three term test) = 39.94 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=50509.3MB, alloc=44.3MB, time=623.27
x[1] = 0.6569 2.443
h = 0.001 0.001
y2[1] (numeric) = 4.32215179188 5.03961852964
y2[1] (closed_form) = 3.54015020724 4.52192896401
absolute error = 0.9378
relative error = 16.33 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 5.06282002527 -3.68894427452
y1[1] (closed_form) = 4.59074393688 -3.48708357059
absolute error = 0.5134
relative error = 8.906 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 15.6
Order of pole (three term test) = 51.95 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 15.6
Order of pole (three term test) = 40.06 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=50555.3MB, alloc=44.3MB, time=623.83
memory used=50601.7MB, alloc=44.3MB, time=624.40
x[1] = 0.6579 2.444
h = 0.0001 0.004
y2[1] (numeric) = 4.3457201084 5.05451588474
y2[1] (closed_form) = 3.54823255705 4.52302908153
absolute error = 0.9584
relative error = 16.67 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 5.06353316296 -3.69832526596
y1[1] (closed_form) = 4.59172222586 -3.49515024083
absolute error = 0.5137
relative error = 8.902 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 93.86
Order of pole (three term test) = 51.97 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 93.86
Order of pole (three term test) = 40.16 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=50647.7MB, alloc=44.3MB, time=624.96
memory used=50693.6MB, alloc=44.3MB, time=625.52
x[1] = 0.658 2.448
h = 0.003 0.006
y2[1] (numeric) = 4.36939743018 5.06944495967
y2[1] (closed_form) = 3.56270254849 4.54108124387
absolute error = 0.9643
relative error = 16.71 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 5.08334531908 -3.71626166245
y1[1] (closed_form) = 4.60949487706 -3.50982529582
absolute error = 0.5169
relative error = 8.921 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 56.06
Order of pole (three term test) = 52.17 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 56.06
Order of pole (three term test) = 40.33 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=50739.5MB, alloc=44.3MB, time=626.08
x[1] = 0.661 2.454
h = 0.0001 0.005
y2[1] (numeric) = 4.39318418131 5.08440580371
y2[1] (closed_form) = 3.59772008088 4.55820578055
absolute error = 0.9538
relative error = 16.42 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 5.10066301068 -3.75778012055
y1[1] (closed_form) = 4.62605217232 -3.54495536553
absolute error = 0.5201
relative error = 8.925 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.23
Order of pole (three term test) = 52.37 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 25.23
Order of pole (three term test) = 40.74 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=50785.6MB, alloc=44.3MB, time=626.64
memory used=50831.6MB, alloc=44.3MB, time=627.21
x[1] = 0.6611 2.459
h = 0.0001 0.003
y2[1] (numeric) = 4.41708152355 5.09939802472
y2[1] (closed_form) = 3.61595477519 4.58103679374
absolute error = 0.9542
relative error = 16.35 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 5.12568199479 -3.78031492848
y1[1] (closed_form) = 4.64853954973 -3.56344647442
absolute error = 0.5241
relative error = 8.948 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 20.52
Order of pole (three term test) = 52.64 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 20.52
Order of pole (three term test) = 40.96 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=50877.6MB, alloc=44.3MB, time=627.77
memory used=50924.1MB, alloc=44.3MB, time=628.34
x[1] = 0.6612 2.462
h = 0.001 0.001
y2[1] (numeric) = 4.4410900552 5.11442187721
y2[1] (closed_form) = 3.62712761469 4.59464559397
absolute error = 0.9658
relative error = 16.5 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 5.14055980905 -3.79411284875
y1[1] (closed_form) = 4.66194090971 -3.57476987297
absolute error = 0.5265
relative error = 8.962 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.2
Order of pole (three term test) = 52.8 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 16.2
Order of pole (three term test) = 41.1 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=50970.0MB, alloc=44.3MB, time=628.90
memory used=51016.3MB, alloc=44.3MB, time=629.48
x[1] = 0.6622 2.463
h = 0.001 0.003
y2[1] (numeric) = 4.46520992922 5.12947752765
y2[1] (closed_form) = 3.63536892048 4.59572913514
absolute error = 0.9867
relative error = 16.84 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 5.14122861539 -3.80368793652
y1[1] (closed_form) = 4.66290485018 -3.58299630844
absolute error = 0.5268
relative error = 8.958 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 77.05
Order of pole (three term test) = 52.82 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 77.05
Order of pole (three term test) = 41.2 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=51062.3MB, alloc=44.3MB, time=630.04
x[1] = 0.6632 2.466
h = 0.0001 0.004
y2[1] (numeric) = 4.48944119617 5.14456498283
y2[1] (closed_form) = 3.65080917389 4.60614232864
absolute error = 0.9966
relative error = 16.96 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 5.15216235493 -3.82225690395
y1[1] (closed_form) = 4.67306456932 -3.59852649588
absolute error = 0.5288
relative error = 8.965 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 43.86
Order of pole (three term test) = 52.94 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 43.86
Order of pole (three term test) = 41.38 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=51108.2MB, alloc=44.3MB, time=630.60
memory used=51154.2MB, alloc=44.3MB, time=631.17
x[1] = 0.6633 2.47
h = 0.003 0.006
y2[1] (numeric) = 4.51378402238 5.15968428066
y2[1] (closed_form) = 3.6657016591 4.62451014697
absolute error = 1.003
relative error = 16.99 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 5.17232068249 -3.84077852936
y1[1] (closed_form) = 4.69116002563 -3.61362102885
absolute error = 0.5321
relative error = 8.986 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 58.58
Order of pole (three term test) = 53.16 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 58.58
Order of pole (three term test) = 41.57 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=51200.1MB, alloc=44.3MB, time=631.73
memory used=51246.5MB, alloc=44.3MB, time=632.30
x[1] = 0.6663 2.476
h = 0.0001 0.005
y2[1] (numeric) = 4.53823887237 5.17483547047
y2[1] (closed_form) = 3.70158985853 4.64181255524
absolute error = 0.992
relative error = 16.71 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 5.18974621971 -3.88343631345
y1[1] (closed_form) = 4.70790812678 -3.64962225621
absolute error = 0.5356
relative error = 8.991 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.37
Order of pole (three term test) = 53.38 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 26.37
Order of pole (three term test) = 42 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=51292.3MB, alloc=44.3MB, time=632.85
x[1] = 0.6664 2.481
h = 0.0001 0.003
y2[1] (numeric) = 4.56280693134 5.1900181449
y2[1] (closed_form) = 3.72035741483 4.66504337581
absolute error = 0.9926
relative error = 16.64 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 5.21520328927 -3.90670712303
y1[1] (closed_form) = 4.73080412314 -3.66864242567
absolute error = 0.5397
relative error = 9.016 %
Correct digits = 1
memory used=51338.5MB, alloc=44.3MB, time=633.42
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 21.44
Order of pole (three term test) = 53.66 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 21.44
Order of pole (three term test) = 42.25 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=51384.6MB, alloc=44.3MB, time=633.98
x[1] = 0.6665 2.484
h = 0.001 0.001
y2[1] (numeric) = 4.58748881228 5.20523256067
y2[1] (closed_form) = 3.73185456364 4.67888879678
absolute error = 1.005
relative error = 16.79 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 5.23033864352 -3.92095230043
y1[1] (closed_form) = 4.74444740117 -3.68028793084
absolute error = 0.5422
relative error = 9.03 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.93
Order of pole (three term test) = 53.83 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 16.93
Order of pole (three term test) = 42.39 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=51430.5MB, alloc=44.3MB, time=634.54
memory used=51476.9MB, alloc=44.3MB, time=635.12
x[1] = 0.6675 2.485
h = 0.001 0.003
y2[1] (numeric) = 4.61228467247 5.22047888705
y2[1] (closed_form) = 3.74028397821 4.67994922159
absolute error = 1.026
relative error = 17.12 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 5.23095161934 -3.93076503074
y1[1] (closed_form) = 4.74539075231 -3.68870341896
absolute error = 0.5426
relative error = 9.027 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 80.52
Order of pole (three term test) = 53.85 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 80.52
Order of pole (three term test) = 42.5 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=51522.8MB, alloc=44.3MB, time=635.68
memory used=51569.1MB, alloc=44.3MB, time=636.25
x[1] = 0.6685 2.488
h = 0.0001 0.004
y2[1] (numeric) = 4.63719456361 5.23575713067
y2[1] (closed_form) = 3.75612451186 4.69050418762
absolute error = 1.036
relative error = 17.24 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 5.24201123528 -3.94986733642
y1[1] (closed_form) = 4.75569822927 -3.70463324263
absolute error = 0.5446
relative error = 9.035 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 45.84
Order of pole (three term test) = 53.98 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 45.84
Order of pole (three term test) = 42.69 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=51615.0MB, alloc=44.3MB, time=636.81
x[1] = 0.6686 2.492
h = 0.003 0.006
y2[1] (numeric) = 4.66221865594 5.25106732936
y2[1] (closed_form) = 3.77145056436 4.70919256305
absolute error = 1.043
relative error = 17.28 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 5.26251990381 -3.96899046571
y1[1] (closed_form) = 4.7741212205 -3.7201583557
absolute error = 0.5481
relative error = 9.056 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 61.22
Order of pole (three term test) = 54.21 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 61.22
Order of pole (three term test) = 42.9 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=51660.7MB, alloc=44.3MB, time=637.37
memory used=51706.9MB, alloc=44.3MB, time=637.94
x[1] = 0.6716 2.498
h = 0.0001 0.005
y2[1] (numeric) = 4.68735742449 5.26640953087
y2[1] (closed_form) = 3.80822982829 4.7266723617
absolute error = 1.032
relative error = 17 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 5.2800479832 -4.01281534367
y1[1] (closed_form) = 4.79105936726 -3.75705106045
absolute error = 0.5518
relative error = 9.064 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.55
Order of pole (three term test) = 54.44 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 27.55
Order of pole (three term test) = 43.36 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=51752.7MB, alloc=44.3MB, time=638.50
memory used=51798.8MB, alloc=44.3MB, time=639.07
x[1] = 0.6717 2.503
h = 0.0001 0.003
y2[1] (numeric) = 4.71261207834 5.28178331209
y2[1] (closed_form) = 3.82754422098 4.7503092042
absolute error = 1.032
relative error = 16.92 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 5.30594845462 -4.03684262833
y1[1] (closed_form) = 4.81436998555 -3.77661430197
absolute error = 0.5562
relative error = 9.09 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.4
Order of pole (three term test) = 54.74 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 22.4
Order of pole (three term test) = 43.62 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=51844.8MB, alloc=44.3MB, time=639.64
memory used=51891.1MB, alloc=44.3MB, time=640.21
x[1] = 0.6718 2.506
h = 0.001 0.001
y2[1] (numeric) = 4.73798324545 5.29718893192
y2[1] (closed_form) = 3.8393741499 4.76439487701
absolute error = 1.045
relative error = 17.07 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 5.3213443762 -4.0515474405
y1[1] (closed_form) = 4.82825868595 -3.78859040506
absolute error = 0.5588
relative error = 9.105 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.69
Order of pole (three term test) = 54.92 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 17.69
Order of pole (three term test) = 43.78 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=51937.2MB, alloc=44.3MB, time=640.78
x[1] = 0.6728 2.507
h = 0.001 0.003
y2[1] (numeric) = 4.76347108753 5.31262656246
y2[1] (closed_form) = 3.84799576374 4.76543070305
absolute error = 1.067
relative error = 17.41 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 5.32189856384 -4.06160306303
y1[1] (closed_form) = 4.82917991522 -3.79719900265
absolute error = 0.5592
relative error = 9.102 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 84.14
Order of pole (three term test) = 54.94 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 84.14
Order of pole (three term test) = 43.88 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=51983.2MB, alloc=44.3MB, time=641.34
memory used=52029.4MB, alloc=44.3MB, time=641.91
x[1] = 0.6738 2.51
h = 0.0001 0.004
y2[1] (numeric) = 4.7890756575 5.32809621021
y2[1] (closed_form) = 3.86424626128 4.77612855955
absolute error = 1.077
relative error = 17.53 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 5.33308337636 -4.08125221266
y1[1] (closed_form) = 4.8396361343 -3.8135381292
absolute error = 0.5614
relative error = 9.111 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 47.9
Order of pole (three term test) = 55.08 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 47.9
Order of pole (three term test) = 44.09 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=52075.2MB, alloc=44.3MB, time=642.47
memory used=52121.4MB, alloc=44.3MB, time=643.04
x[1] = 0.6739 2.514
h = 0.003 0.006
y2[1] (numeric) = 4.81479712953 5.34359791284
y2[1] (closed_form) = 3.88001722702 4.79514243824
absolute error = 1.084
relative error = 17.57 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 5.35394656122 -4.10099350367
y1[1] (closed_form) = 4.85839143919 -3.8295051972
absolute error = 0.565
relative error = 9.134 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 63.97
Order of pole (three term test) = 55.32 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 63.97
Order of pole (three term test) = 44.31 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=52167.2MB, alloc=44.3MB, time=643.60
x[1] = 0.6769 2.52
h = 0.0001 0.005
y2[1] (numeric) = 4.84063598945 5.35913171649
y2[1] (closed_form) = 3.91770840057 4.81279901914
absolute error = 1.073
relative error = 17.28 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 5.371571614 -4.14601383051
y1[1] (closed_form) = 4.87551875 -3.86731014983
absolute error = 0.569
relative error = 9.143 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.79
Order of pole (three term test) = 55.57 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 28.79
Order of pole (three term test) = 44.8 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=52213.3MB, alloc=44.3MB, time=644.16
memory used=52259.3MB, alloc=44.3MB, time=644.72
x[1] = 0.677 2.525
h = 0.0001 0.003
y2[1] (numeric) = 4.86659347061 5.37469718179
y2[1] (closed_form) = 3.93758394804 4.83684815568
absolute error = 1.073
relative error = 17.21 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 5.39792081255 -4.17081854573
y1[1] (closed_form) = 4.89925005558 -3.88743081918
absolute error = 0.5736
relative error = 9.171 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.41
Order of pole (three term test) = 55.88 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 23.41
Order of pole (three term test) = 45.08 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=52305.2MB, alloc=44.3MB, time=645.28
memory used=52351.4MB, alloc=44.3MB, time=645.85
x[1] = 0.6771 2.528
h = 0.001 0.001
y2[1] (numeric) = 4.89267021634 5.39029456979
y2[1] (closed_form) = 3.94975533565 4.85117774336
absolute error = 1.086
relative error = 17.36 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 5.41358032997 -4.18599566073
y1[1] (closed_form) = 4.91338771749 -3.89974621946
absolute error = 0.5763
relative error = 9.187 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 18.49
Order of pole (three term test) = 56.07 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 18.49
Order of pole (three term test) = 45.25 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=52397.5MB, alloc=44.3MB, time=646.42
memory used=52443.9MB, alloc=44.3MB, time=646.99
x[1] = 0.6781 2.529
h = 0.001 0.003
y2[1] (numeric) = 4.91886639289 5.40592405549
y2[1] (closed_form) = 3.95857332111 4.85218743216
absolute error = 1.109
relative error = 17.7 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 5.41407267826 -4.19629952572
y1[1] (closed_form) = 4.91428523721 -3.90855206623
absolute error = 0.5767
relative error = 9.184 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 87.92
Order of pole (three term test) = 56.09 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 87.92
Order of pole (three term test) = 45.36 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=52489.9MB, alloc=44.3MB, time=647.55
x[1] = 0.6791 2.532
h = 0.0001 0.004
y2[1] (numeric) = 4.94518205438 5.42158564522
y2[1] (closed_form) = 3.97524368644 4.86302926663
absolute error = 1.119
relative error = 17.82 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 5.42538192053 -4.21650932068
y1[1] (closed_form) = 4.92489115507 -3.92531038362
absolute error = 0.579
relative error = 9.194 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.05
Order of pole (three term test) = 56.24 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 50.05
Order of pole (three term test) = 45.59 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=52535.8MB, alloc=44.3MB, time=648.11
memory used=52581.9MB, alloc=44.3MB, time=648.68
x[1] = 0.6792 2.536
h = 0.003 0.006
y2[1] (numeric) = 4.97161737905 5.4372793765
y2[1] (closed_form) = 3.99147119016 4.88237363938
absolute error = 1.126
relative error = 17.86 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 5.44660380085 -4.2368858226
y1[1] (closed_form) = 4.94398360079 -3.94173106036
absolute error = 0.5829
relative error = 9.218 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 66.85
Order of pole (three term test) = 56.5 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 66.85
Order of pole (three term test) = 45.82 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=52627.7MB, alloc=44.3MB, time=649.24
memory used=52673.9MB, alloc=44.3MB, time=649.80
x[1] = 0.6822 2.542
h = 0.0001 0.005
y2[1] (numeric) = 4.99817286372 5.4530052937
y2[1] (closed_form) = 4.03009557541 4.9002062623
absolute error = 1.115
relative error = 17.57 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 5.46431998372 -4.28313055197
y1[1] (closed_form) = 4.9612990676 -3.9804694914
absolute error = 0.5871
relative error = 9.229 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.09
Order of pole (three term test) = 56.76 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 30.09
Order of pole (three term test) = 46.34 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=52719.8MB, alloc=44.3MB, time=650.37
memory used=52766.0MB, alloc=44.3MB, time=650.93
x[1] = 0.6823 2.547
h = 0.0001 0.003
y2[1] (numeric) = 5.02484976652 5.46876294078
y2[1] (closed_form) = 4.05054694806 4.9246740221
absolute error = 1.116
relative error = 17.5 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 5.49112324095 -4.30873414591
y1[1] (closed_form) = 4.9854571876 -4.00116229662
absolute error = 0.5919
relative error = 9.259 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.47
Order of pole (three term test) = 57.1 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 24.47
Order of pole (three term test) = 46.64 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=52812.0MB, alloc=44.3MB, time=651.50
x[1] = 0.6824 2.55
h = 0.001 0.001
y2[1] (numeric) = 5.05164874644 5.48455258088
y2[1] (closed_form) = 4.06306868549 4.93925121926
absolute error = 1.129
relative error = 17.65 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 5.50704938229 -4.32439652863
y1[1] (closed_form) = 4.99984738453 -4.01382590613
absolute error = 0.5947
relative error = 9.276 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 19.32
Order of pole (three term test) = 57.3 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 19.32
Order of pole (three term test) = 46.82 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=52858.0MB, alloc=44.3MB, time=652.06
memory used=52904.3MB, alloc=44.3MB, time=652.63
x[1] = 0.6834 2.551
h = 0.0001 0.004
y2[1] (numeric) = 5.07856997444 5.50037439192
y2[1] (closed_form) = 4.07208729836 4.94023317466
absolute error = 1.152
relative error = 17.99 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 5.50747674393 -4.33495408861
y1[1] (closed_form) = 5.00071955024 -4.02283322617
absolute error = 0.5952
relative error = 9.273 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 116.3
Order of pole (three term test) = 57.32 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 116.3
Order of pole (three term test) = 46.94 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=52950.1MB, alloc=44.3MB, time=653.19
memory used=52996.3MB, alloc=44.3MB, time=653.76
x[1] = 0.6835 2.555
h = 0.003 0.006
y2[1] (numeric) = 5.10561351895 5.51622843253
y2[1] (closed_form) = 4.08871328253 4.95987168794
absolute error = 1.159
relative error = 18.03 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 5.52900073065 -4.35587324466
y1[1] (closed_form) = 5.02011169522 -4.03964980887
absolute error = 0.5991
relative error = 9.298 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 69.44
Order of pole (three term test) = 57.59 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 69.44
Order of pole (three term test) = 47.19 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=53042.2MB, alloc=44.3MB, time=654.32
x[1] = 0.6865 2.561
h = 0.0001 0.005
y2[1] (numeric) = 5.13277985294 5.53211474486
y2[1] (closed_form) = 4.12815627694 4.97786661488
absolute error = 1.147
relative error = 17.74 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 5.54678818497 -4.40316086984
y1[1] (closed_form) = 5.03759968511 -4.07920688354
absolute error = 0.6035
relative error = 9.31 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.25
Order of pole (three term test) = 57.87 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 31.25
Order of pole (three term test) = 47.73 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=53088.3MB, alloc=44.3MB, time=654.88
memory used=53134.5MB, alloc=44.3MB, time=655.44
x[1] = 0.6866 2.566
h = 0.0001 0.003
y2[1] (numeric) = 5.16007025633 5.54803285827
y2[1] (closed_form) = 4.14911023287 5.00270692683
absolute error = 1.149
relative error = 17.67 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 5.57397389924 -4.42944695034
y1[1] (closed_form) = 5.0621372063 -4.10039903231
absolute error = 0.6085
relative error = 9.34 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.41
Order of pole (three term test) = 58.22 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 25.41
Order of pole (three term test) = 48.05 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=53180.3MB, alloc=44.3MB, time=656.00
memory used=53226.8MB, alloc=44.3MB, time=656.57
x[1] = 0.6867 2.569
h = 0.001 0.001
y2[1] (numeric) = 5.18748540194 5.56398303792
y2[1] (closed_form) = 4.16193781543 5.01750456186
absolute error = 1.162
relative error = 17.83 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 5.59012453829 -4.44552385313
y1[1] (closed_form) = 5.07675196083 -4.11336660451
absolute error = 0.6115
relative error = 9.358 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 20.07
Order of pole (three term test) = 58.42 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 20.07
Order of pole (three term test) = 48.24 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=53272.9MB, alloc=44.3MB, time=657.14
memory used=53319.4MB, alloc=44.3MB, time=657.71
x[1] = 0.6877 2.57
h = 0.001 0.003
y2[1] (numeric) = 5.21502546476 5.57996546432
y2[1] (closed_form) = 4.17113295182 5.01846378221
absolute error = 1.185
relative error = 18.16 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 5.59049526483 -4.45629706972
y1[1] (closed_form) = 5.07760341115 -4.12255112393
absolute error = 0.6119
relative error = 9.356 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 95.44
Order of pole (three term test) = 58.45 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 95.44
Order of pole (three term test) = 48.36 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=53365.3MB, alloc=44.3MB, time=658.27
x[1] = 0.6887 2.573
h = 0.0001 0.004
y2[1] (numeric) = 5.24269050122 5.59598014352
y2[1] (closed_form) = 4.18860998293 5.02958159913
absolute error = 1.197
relative error = 18.28 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 5.60203032762 -4.47757158252
y1[1] (closed_form) = 5.08849560928 -4.14011474387
absolute error = 0.6145
relative error = 9.367 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 54.33
Order of pole (three term test) = 58.62 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 54.33
Order of pole (three term test) = 48.61 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=53411.3MB, alloc=44.3MB, time=658.83
memory used=53457.4MB, alloc=44.3MB, time=659.39
x[1] = 0.6888 2.577
h = 0.003 0.006
y2[1] (numeric) = 5.27048069738 5.61202711271
y2[1] (closed_form) = 4.20571483943 5.04956015707
absolute error = 1.204
relative error = 18.32 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 5.62392067382 -4.49915828325
y1[1] (closed_form) = 5.1082341514 -4.15740732624
absolute error = 0.6186
relative error = 9.393 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 72.56
Order of pole (three term test) = 58.9 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 72.56
Order of pole (three term test) = 48.88 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=53503.3MB, alloc=44.3MB, time=659.95
memory used=53549.4MB, alloc=44.3MB, time=660.52
x[1] = 0.6918 2.583
h = 0.0001 0.005
y2[1] (numeric) = 5.29839657118 5.62810641293
y2[1] (closed_form) = 4.24613194566 5.06772964592
absolute error = 1.192
relative error = 18.03 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 5.64178777404 -4.54772504417
y1[1] (closed_form) = 5.12590833246 -4.19793865708
absolute error = 0.6233
relative error = 9.407 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 32.66
Order of pole (three term test) = 59.2 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 32.66
Order of pole (three term test) = 49.45 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=53595.3MB, alloc=44.3MB, time=661.08
memory used=53641.5MB, alloc=44.3MB, time=661.64
x[1] = 0.6919 2.588
h = 0.0001 0.003
y2[1] (numeric) = 5.32643942826 5.64421755597
y2[1] (closed_form) = 4.26768991294 5.09300069347
absolute error = 1.194
relative error = 17.96 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 5.66943732993 -4.57485069699
y1[1] (closed_form) = 5.15088441702 -4.21973120078
absolute error = 0.6285
relative error = 9.439 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.56
Order of pole (three term test) = 59.57 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 26.56
Order of pole (three term test) = 49.79 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=53687.4MB, alloc=44.3MB, time=662.21
x[1] = 0.692 2.591
h = 0.001 0.001
y2[1] (numeric) = 5.35460995779 5.66036080902
y2[1] (closed_form) = 4.28088492741 5.10805300755
absolute error = 1.207
relative error = 18.12 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 5.68586013801 -4.59143746777
y1[1] (closed_form) = 5.16575855835 -4.23306410499
absolute error = 0.6316
relative error = 9.457 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 20.97
Order of pole (three term test) = 59.79 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 20.97
Order of pole (three term test) = 50 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=53733.4MB, alloc=44.3MB, time=662.78
memory used=53779.7MB, alloc=44.3MB, time=663.35
x[1] = 0.693 2.592
h = 0.001 0.003
y2[1] (numeric) = 5.38290833968 5.67653635562
y2[1] (closed_form) = 4.29028885844 5.10898141798
absolute error = 1.231
relative error = 18.46 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 5.68615983541 -4.60247466215
y1[1] (closed_form) = 5.16658149024 -4.24245820896
absolute error = 0.6321
relative error = 9.455 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 99.73
Order of pole (three term test) = 59.82 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 99.73
Order of pole (three term test) = 50.12 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=53825.6MB, alloc=44.3MB, time=663.91
memory used=53871.9MB, alloc=44.3MB, time=664.48
x[1] = 0.694 2.595
h = 0.0001 0.004
y2[1] (numeric) = 5.41133463162 5.69274420161
y2[1] (closed_form) = 4.30821533779 5.12024626641
absolute error = 1.243
relative error = 18.57 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 5.69781663735 -4.6243506322
y1[1] (closed_form) = 5.17762608131 -4.26047056157
absolute error = 0.6348
relative error = 9.468 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 56.77
Order of pole (three term test) = 59.99 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 56.77
Order of pole (three term test) = 50.39 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=53917.7MB, alloc=44.3MB, time=665.05
x[1] = 0.6941 2.599
h = 0.003 0.006
y2[1] (numeric) = 5.43988902402 5.70898438397
y2[1] (closed_form) = 4.32581152448 5.14056998853
absolute error = 1.251
relative error = 18.62 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 5.7200775236 -4.64662312293
y1[1] (closed_form) = 5.19771598689 -4.27825163107
absolute error = 0.6392
relative error = 9.495 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 75.83
Order of pole (three term test) = 60.3 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 75.83
Order of pole (three term test) = 50.67 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=53963.5MB, alloc=44.3MB, time=665.60
memory used=54009.8MB, alloc=44.3MB, time=666.17
x[1] = 0.6971 2.605
h = 0.0001 0.005
y2[1] (numeric) = 5.46857204648 5.72525694171
y2[1] (closed_form) = 4.36722540705 5.15891289718
absolute error = 1.238
relative error = 18.32 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 5.73801757224 -4.69649979547
y1[1] (closed_form) = 5.21557496455 -4.31977981918
absolute error = 0.6441
relative error = 9.511 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 34.13
Order of pole (three term test) = 60.61 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 34.13
Order of pole (three term test) = 51.27 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=54055.8MB, alloc=44.3MB, time=666.73
memory used=54102.0MB, alloc=44.3MB, time=667.33
x[1] = 0.6972 2.61
h = 0.0001 0.003
y2[1] (numeric) = 5.49738503079 5.74156136843
y2[1] (closed_form) = 4.38940310811 5.18462117427
absolute error = 1.24
relative error = 18.25 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 5.76613630795 -4.72448797446
y1[1] (closed_form) = 5.24099591723 -4.34218851839
absolute error = 0.6496
relative error = 9.544 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.75
Order of pole (three term test) = 61 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 27.75
Order of pole (three term test) = 51.64 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=54148.0MB, alloc=44.3MB, time=667.89
memory used=54194.3MB, alloc=44.3MB, time=668.46
x[1] = 0.6973 2.613
h = 0.001 0.001
y2[1] (numeric) = 5.52632868285 5.75789793336
y2[1] (closed_form) = 4.40297508086 5.19993195279
absolute error = 1.254
relative error = 18.41 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 5.78283430424 -4.74159848502
y1[1] (closed_form) = 5.25613311736 -4.3558963023
absolute error = 0.6528
relative error = 9.563 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 21.91
Order of pole (three term test) = 61.23 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 21.91
Order of pole (three term test) = 51.86 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=54240.4MB, alloc=44.3MB, time=669.03
x[1] = 0.6983 2.614
h = 0.001 0.003
y2[1] (numeric) = 5.55540318761 5.77426682306
y2[1] (closed_form) = 4.41259231051 5.20082778343
absolute error = 1.279
relative error = 18.75 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 5.78305952889 -4.75290541973
y1[1] (closed_form) = 5.25692571513 -4.36550446573
absolute error = 0.6534
relative error = 9.562 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 104.2
Order of pole (three term test) = 61.26 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 104.2
Order of pole (three term test) = 51.99 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=54286.4MB, alloc=44.3MB, time=669.60
memory used=54332.6MB, alloc=44.3MB, time=670.16
x[1] = 0.6993 2.617
h = 0.0001 0.004
y2[1] (numeric) = 5.58460860406 5.79066804319
y2[1] (closed_form) = 4.43097903838 5.21224061848
absolute error = 1.291
relative error = 18.86 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 5.79483692813 -4.77539786941
y1[1] (closed_form) = 5.26812353383 -4.38397633904
absolute error = 0.6562
relative error = 9.575 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 59.33
Order of pole (three term test) = 61.45 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 59.33
Order of pole (three term test) = 52.27 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=54378.5MB, alloc=44.3MB, time=670.72
memory used=54424.7MB, alloc=44.3MB, time=671.29
x[1] = 0.6994 2.621
h = 0.003 0.006
y2[1] (numeric) = 5.61394512701 5.80710163046
y2[1] (closed_form) = 4.4490793176 5.23291466709
absolute error = 1.299
relative error = 18.91 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 5.81747253006 -4.79837482134
y1[1] (closed_form) = 5.28856981546 -4.4022586878
absolute error = 0.6608
relative error = 9.603 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 79.24
Order of pole (three term test) = 61.77 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 79.24
Order of pole (three term test) = 52.57 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=54470.4MB, alloc=44.3MB, time=671.85
x[1] = 0.7024 2.627
h = 0.0001 0.005
y2[1] (numeric) = 5.64341329804 5.82356762176
y2[1] (closed_form) = 4.49151313593 5.25142970004
absolute error = 1.286
relative error = 18.61 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 5.8354785172 -4.84959282631
y1[1] (closed_form) = 5.30661204693 -4.44480683185
absolute error = 0.666
relative error = 9.621 %
Correct digits = 1
memory used=54516.6MB, alloc=44.3MB, time=672.42
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 35.66
Order of pole (three term test) = 62.11 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 35.66
Order of pole (three term test) = 53.2 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=54562.6MB, alloc=44.3MB, time=673.00
x[1] = 0.7025 2.632
h = 0.0001 0.003
y2[1] (numeric) = 5.67301447551 5.84006549197
y2[1] (closed_form) = 4.51432667772 5.27758175544
absolute error = 1.288
relative error = 18.55 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 5.86407176641 -4.87846702151
y1[1] (closed_form) = 5.33248423162 -4.46784783182
absolute error = 0.6717
relative error = 9.655 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29
Order of pole (three term test) = 62.52 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 29
Order of pole (three term test) = 53.59 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=54608.5MB, alloc=44.3MB, time=673.55
memory used=54654.9MB, alloc=44.3MB, time=674.13
x[1] = 0.7026 2.635
h = 0.001 0.001
y2[1] (numeric) = 5.7027493825 5.85659551229
y2[1] (closed_form) = 4.52828536726 5.29315481371
absolute error = 1.303
relative error = 18.7 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 5.88104796276 -4.89611546661
y1[1] (closed_form) = 5.34788819504 -4.48194027538
absolute error = 0.6751
relative error = 9.676 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.9
Order of pole (three term test) = 62.76 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 22.9
Order of pole (three term test) = 53.83 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=54700.9MB, alloc=44.3MB, time=674.70
memory used=54747.2MB, alloc=44.3MB, time=675.28
x[1] = 0.7036 2.636
h = 0.001 0.003
y2[1] (numeric) = 5.73261820907 5.87315787237
y2[1] (closed_form) = 4.53812048918 5.29401623007
absolute error = 1.327
relative error = 19.04 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 5.88119516413 -4.90769801324
y1[1] (closed_form) = 5.34864857927 -4.49176706371
absolute error = 0.6757
relative error = 9.675 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 108.9
Order of pole (three term test) = 62.8 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 108.9
Order of pole (three term test) = 53.97 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=54793.1MB, alloc=44.3MB, time=675.84
x[1] = 0.7046 2.639
h = 0.0001 0.004
y2[1] (numeric) = 5.76262101556 5.88975257766
y2[1] (closed_form) = 4.55697851016 5.30557796701
absolute error = 1.34
relative error = 19.16 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 5.89309191328 -4.93082229109
y1[1] (closed_form) = 5.36000042297 -4.510709491
absolute error = 0.6787
relative error = 9.689 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 61.99
Order of pole (three term test) = 63 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 61.99
Order of pole (three term test) = 54.26 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=54839.0MB, alloc=44.3MB, time=676.40
memory used=54885.1MB, alloc=44.3MB, time=676.96
x[1] = 0.7047 2.643
h = 0.003 0.006
y2[1] (numeric) = 5.79275800131 5.90637966459
y2[1] (closed_form) = 4.5755959558 5.32660754657
absolute error = 1.348
relative error = 19.2 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 5.9161063991 -4.95452281069
y1[1] (closed_form) = 5.3808081388 -4.52950622277
absolute error = 0.6835
relative error = 9.718 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 82.8
Order of pole (three term test) = 63.33 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 82.8
Order of pole (three term test) = 54.58 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=54930.8MB, alloc=44.3MB, time=677.52
memory used=54977.2MB, alloc=44.3MB, time=678.09
x[1] = 0.7077 2.649
h = 0.0001 0.005
y2[1] (numeric) = 5.82302972008 5.92303916779
y2[1] (closed_form) = 4.61907337448 5.34529324893
absolute error = 1.335
relative error = 18.9 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 5.93417099181 -5.00711422638
y1[1] (closed_form) = 5.39903192696 -4.57309792921
absolute error = 0.689
relative error = 9.738 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.26
Order of pole (three term test) = 63.7 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 37.26
Order of pole (three term test) = 55.24 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=55023.0MB, alloc=44.3MB, time=678.65
memory used=55069.1MB, alloc=44.3MB, time=679.21
x[1] = 0.7078 2.654
h = 0.0001 0.003
y2[1] (numeric) = 5.85343755734 5.93973054289
y2[1] (closed_form) = 4.64253925732 5.37189568543
absolute error = 1.337
relative error = 18.84 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 5.96324408056 -5.03689847586
y1[1] (closed_form) = 5.42536176581 -4.5967877687
absolute error = 0.695
relative error = 9.774 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.3
Order of pole (three term test) = 64.13 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 30.3
Order of pole (three term test) = 55.66 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=55115.1MB, alloc=44.3MB, time=679.78
x[1] = 0.7079 2.657
h = 0.001 0.001
y2[1] (numeric) = 5.8839822537 5.95645406301
y2[1] (closed_form) = 4.65689465966 5.38773486814
absolute error = 1.352
relative error = 18.99 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 5.98050147955 -5.05509938029
y1[1] (closed_form) = 5.44103622892 -4.61127488947
absolute error = 0.6986
relative error = 9.795 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.93
Order of pole (three term test) = 64.39 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 23.93
Order of pole (three term test) = 55.91 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=55161.1MB, alloc=44.3MB, time=680.34
memory used=55207.4MB, alloc=44.3MB, time=680.91
x[1] = 0.7089 2.658
h = 0.0001 0.004
y2[1] (numeric) = 5.9146640045 5.97320992092
y2[1] (closed_form) = 4.66695235879 5.38855996923
absolute error = 1.378
relative error = 19.33 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 5.98056699714 -5.06696352129
y1[1] (closed_form) = 5.44176245451 -4.62132496028
absolute error = 0.6992
relative error = 9.794 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 144
Order of pole (three term test) = 64.42 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 144
Order of pole (three term test) = 56.05 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=55253.1MB, alloc=44.3MB, time=681.48
memory used=55299.2MB, alloc=44.3MB, time=682.04
x[1] = 0.709 2.662
h = 0.003 0.006
y2[1] (numeric) = 5.94548288759 5.98999817981
y2[1] (closed_form) = 4.6860213562 5.40990615561
absolute error = 1.387
relative error = 19.37 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 6.0039003963 -5.09128192946
y1[1] (closed_form) = 5.4628917112 -4.64057080396
absolute error = 0.7042
relative error = 9.824 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 86.01
Order of pole (three term test) = 64.77 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 86.01
Order of pole (three term test) = 56.39 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=55344.9MB, alloc=44.3MB, time=682.60
x[1] = 0.712 2.668
h = 0.0001 0.005
y2[1] (numeric) = 5.97643943014 6.00681887254
y2[1] (closed_form) = 4.73041440826 5.42875029776
absolute error = 1.374
relative error = 19.08 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 6.02200798251 -5.14504284479
y1[1] (closed_form) = 5.48128311905 -4.68507794062
absolute error = 0.7099
relative error = 9.845 %
Correct digits = 1
memory used=55390.9MB, alloc=44.3MB, time=683.16
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.71
Order of pole (three term test) = 65.16 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 38.71
Order of pole (three term test) = 57.08 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=55437.0MB, alloc=44.3MB, time=683.74
x[1] = 0.7121 2.673
h = 0.0001 0.003
y2[1] (numeric) = 6.00753504155 6.02367143792
y2[1] (closed_form) = 4.75444985165 5.45575378092
absolute error = 1.376
relative error = 19.01 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 6.05148499743 -5.17560424706
y1[1] (closed_form) = 5.50802008238 -4.70933427373
absolute error = 0.7161
relative error = 9.881 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.48
Order of pole (three term test) = 65.61 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 31.48
Order of pole (three term test) = 57.52 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=55482.9MB, alloc=44.3MB, time=684.30
memory used=55529.3MB, alloc=44.3MB, time=684.87
x[1] = 0.7122 2.676
h = 0.001 0.001
y2[1] (numeric) = 6.03877047779 6.04055615092
y2[1] (closed_form) = 4.76915168808 5.47183002762
absolute error = 1.391
relative error = 19.17 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 6.06897901662 -5.19427688145
y1[1] (closed_form) = 5.52393526683 -4.72416604332
absolute error = 0.7198
relative error = 9.903 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.86
Order of pole (three term test) = 65.88 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 24.86
Order of pole (three term test) = 57.79 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=55575.3MB, alloc=44.3MB, time=685.43
memory used=55621.6MB, alloc=44.3MB, time=686.00
x[1] = 0.7132 2.677
h = 0.001 0.003
y2[1] (numeric) = 6.07014593883 6.05747320712
y2[1] (closed_form) = 4.77940526148 5.47262502427
absolute error = 1.417
relative error = 19.5 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 6.06897358207 -5.20638033997
y1[1] (closed_form) = 5.52463321759 -4.73441254921
absolute error = 0.7205
relative error = 9.902 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 118.2
Order of pole (three term test) = 65.92 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 118.2
Order of pole (three term test) = 57.93 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=55667.5MB, alloc=44.3MB, time=686.56
x[1] = 0.7142 2.68
h = 0.0001 0.004
y2[1] (numeric) = 6.10166148758 6.07442261154
y2[1] (closed_form) = 4.79916870601 5.48447205971
absolute error = 1.43
relative error = 19.62 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 6.08108552568 -5.23070396128
y1[1] (closed_form) = 5.53627957839 -4.75425893965
absolute error = 0.7237
relative error = 9.918 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 67.29
Order of pole (three term test) = 66.14 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 67.29
Order of pole (three term test) = 58.26 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=55713.3MB, alloc=44.3MB, time=687.12
memory used=55759.4MB, alloc=44.3MB, time=687.68
x[1] = 0.7143 2.684
h = 0.003 0.006
y2[1] (numeric) = 6.13331733204 6.09140440009
y2[1] (closed_form) = 4.81877998797 5.50618373601
absolute error = 1.439
relative error = 19.67 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 6.1048054211 -5.25578216319
y1[1] (closed_form) = 5.55777996522 -4.77404434203
absolute error = 0.7289
relative error = 9.949 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 89.88
Order of pole (three term test) = 66.51 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 89.88
Order of pole (three term test) = 58.62 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=55805.2MB, alloc=44.3MB, time=688.24
memory used=55851.4MB, alloc=44.3MB, time=688.81
x[1] = 0.7173 2.69
h = 0.0001 0.005
y2[1] (numeric) = 6.1651140494 6.10841860307
y2[1] (closed_form) = 4.86426207717 5.5251956914
absolute error = 1.426
relative error = 19.37 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 6.12295726238 -5.31097711303
y1[1] (closed_form) = 5.57634963541 -4.81964037906
absolute error = 0.735
relative error = 9.972 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 40.45
Order of pole (three term test) = 66.92 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 40.45
Order of pole (three term test) = 59.34 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=55897.2MB, alloc=44.3MB, time=689.36
memory used=55943.5MB, alloc=44.3MB, time=689.93
x[1] = 0.7174 2.695
h = 0.0001 0.003
y2[1] (numeric) = 6.19705307716 6.12546463904
y2[1] (closed_form) = 4.88898156298 5.55266219087
absolute error = 1.428
relative error = 19.3 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 6.15292385004 -5.34249416523
y1[1] (closed_form) = 5.60355656335 -4.84457732686
absolute error = 0.7414
relative error = 10.01 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 32.89
Order of pole (three term test) = 67.4 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 32.89
Order of pole (three term test) = 59.8 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=55989.4MB, alloc=44.3MB, time=690.50
x[1] = 0.7175 2.698
h = 0.001 0.001
y2[1] (numeric) = 6.22913518962 6.14254278479
y2[1] (closed_form) = 4.90409931665 5.56901191832
absolute error = 1.444
relative error = 19.46 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 6.17070454489 -5.36174681192
y1[1] (closed_form) = 5.6197494091 -4.85982301965
absolute error = 0.7453
relative error = 10.03 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.97
Order of pole (three term test) = 67.68 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 25.97
Order of pole (three term test) = 60.09 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=56035.3MB, alloc=44.3MB, time=691.06
memory used=56081.6MB, alloc=44.3MB, time=691.63
x[1] = 0.7185 2.699
h = 0.001 0.003
y2[1] (numeric) = 6.26136059225 6.15965323912
y2[1] (closed_form) = 4.91458445834 5.56976693711
absolute error = 1.47
relative error = 19.79 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 6.17061040426 -5.37414314318
y1[1] (closed_form) = 5.62040945839 -4.87030175086
absolute error = 0.746
relative error = 10.03 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 123.5
Order of pole (three term test) = 67.73 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 123.5
Order of pole (three term test) = 60.24 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=56127.7MB, alloc=44.3MB, time=692.19
memory used=56173.9MB, alloc=44.3MB, time=692.76
x[1] = 0.7195 2.702
h = 0.0001 0.004
y2[1] (numeric) = 6.29372934938 6.17679600682
y2[1] (closed_form) = 4.93485217969 5.5817653948
absolute error = 1.483
relative error = 19.91 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 6.18283753704 -5.39914396417
y1[1] (closed_form) = 5.63221204088 -4.89065165251
absolute error = 0.7495
relative error = 10.05 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 70.32
Order of pole (three term test) = 67.97 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 70.32
Order of pole (three term test) = 60.58 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=56219.8MB, alloc=44.3MB, time=693.32
x[1] = 0.7196 2.706
h = 0.003 0.006
y2[1] (numeric) = 6.32624167384 6.19397112339
y2[1] (closed_form) = 4.95501975098 5.60384788617
absolute error = 1.493
relative error = 19.96 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 6.20694806313 -5.4250023964
y1[1] (closed_form) = 5.65408874605 -4.91099064848
absolute error = 0.7549
relative error = 10.08 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 93.92
Order of pole (three term test) = 68.35 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 93.92
Order of pole (three term test) = 60.96 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=56265.8MB, alloc=44.3MB, time=693.88
memory used=56311.9MB, alloc=44.3MB, time=694.44
x[1] = 0.7226 2.712
h = 0.0001 0.005
y2[1] (numeric) = 6.35889815576 6.2111786166
y2[1] (closed_form) = 5.00161604755 5.62302571555
absolute error = 1.479
relative error = 19.66 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 6.2251358228 -5.48166546005
y1[1] (closed_form) = 5.67283451111 -4.95770070494
absolute error = 0.7613
relative error = 10.1 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 42.27
Order of pole (three term test) = 68.79 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 42.27
Order of pole (three term test) = 61.72 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=56357.8MB, alloc=44.3MB, time=695.00
memory used=56404.1MB, alloc=44.3MB, time=695.57
x[1] = 0.7227 2.717
h = 0.0001 0.003
y2[1] (numeric) = 6.39170026122 6.22841788404
y2[1] (closed_form) = 5.02703725163 5.65096198892
absolute error = 1.482
relative error = 19.59 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 6.25559727209 -5.51416387475
y1[1] (closed_form) = 5.70051799219 -4.98333598188
absolute error = 0.768
relative error = 10.14 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 34.37
Order of pole (three term test) = 69.29 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 34.37
Order of pole (three term test) = 62.21 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=56450.2MB, alloc=44.3MB, time=696.14
memory used=56496.6MB, alloc=44.3MB, time=696.71
x[1] = 0.7228 2.72
h = 0.001 0.001
y2[1] (numeric) = 6.42464878322 6.24568920431
y2[1] (closed_form) = 5.04258162813 5.6675891256
absolute error = 1.498
relative error = 19.75 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 6.27366760844 -5.53401206676
y1[1] (closed_form) = 5.71699232636 -4.99900632519
absolute error = 0.7721
relative error = 10.17 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.14
Order of pole (three term test) = 69.59 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 27.14
Order of pole (three term test) = 62.51 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=56542.5MB, alloc=44.3MB, time=697.28
x[1] = 0.7238 2.721
h = 0.001 0.003
y2[1] (numeric) = 6.45774393291 6.26299277943
y2[1] (closed_form) = 5.05330329461 5.66830206545
absolute error = 1.525
relative error = 20.08 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 6.27348076261 -5.5467075892
y1[1] (closed_form) = 5.71761233128 -5.00972221315
absolute error = 0.7729
relative error = 10.17 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 129.1
Order of pole (three term test) = 69.64 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 129.1
Order of pole (three term test) = 62.67 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=56588.4MB, alloc=44.3MB, time=697.84
memory used=56634.7MB, alloc=44.3MB, time=698.41
x[1] = 0.7248 2.724
h = 0.0001 0.004
y2[1] (numeric) = 6.49098577607 6.28032861396
y2[1] (closed_form) = 5.07408733153 5.68045268896
absolute error = 1.539
relative error = 20.2 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 6.28582138401 -5.57240230508
y1[1] (closed_form) = 5.72957177056 -5.03058765657
absolute error = 0.7765
relative error = 10.18 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 73.48
Order of pole (three term test) = 69.89 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 73.48
Order of pole (three term test) = 63.03 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=56680.7MB, alloc=44.3MB, time=698.97
memory used=56726.7MB, alloc=44.3MB, time=699.53
x[1] = 0.7249 2.728
h = 0.003 0.006
y2[1] (numeric) = 6.52437453044 6.29769674299
y2[1] (closed_form) = 5.09482553705 5.70291135989
absolute error = 1.548
relative error = 20.25 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 6.31032665713 -5.59906187766
y1[1] (closed_form) = 5.75183002475 -5.05149462117
absolute error = 0.7821
relative error = 10.22 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 98.15
Order of pole (three term test) = 70.3 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 98.15
Order of pole (three term test) = 63.43 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=56772.6MB, alloc=44.3MB, time=700.09
memory used=56818.9MB, alloc=44.3MB, time=700.66
x[1] = 0.7279 2.734
h = 0.0001 0.005
y2[1] (numeric) = 6.55791079937 6.31509719158
y2[1] (closed_form) = 5.14256175792 5.72225293979
absolute error = 1.534
relative error = 19.95 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 6.32854163201 -5.65722784244
y1[1] (closed_form) = 5.77074953768 -5.09934436508
absolute error = 0.7889
relative error = 10.24 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 44.17
Order of pole (three term test) = 70.77 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 44.17
Order of pole (three term test) = 64.22 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=56864.7MB, alloc=44.3MB, time=701.22
x[1] = 0.728 2.739
h = 0.0001 0.003
y2[1] (numeric) = 6.59159607807 6.33252933578
y2[1] (closed_form) = 5.1687027856 5.75066579516
absolute error = 1.537
relative error = 19.88 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 6.35950321101 -5.69073392838
y1[1] (closed_form) = 5.79891621483 -5.12569611516
absolute error = 0.7959
relative error = 10.28 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 35.92
Order of pole (three term test) = 71.29 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 35.92
Order of pole (three term test) = 64.74 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=56910.6MB, alloc=44.3MB, time=701.78
memory used=56957.0MB, alloc=44.3MB, time=702.35
x[1] = 0.7281 2.742
h = 0.001 0.001
y2[1] (numeric) = 6.62543117866 6.34999345589
y2[1] (closed_form) = 5.1846847497 5.76757429654
absolute error = 1.554
relative error = 20.04 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 6.37786613705 -5.71119355764
y1[1] (closed_form) = 5.81567589384 -5.14180209556
absolute error = 0.8002
relative error = 10.31 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.36
Order of pole (three term test) = 71.61 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 28.36
Order of pole (three term test) = 65.06 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=57003.0MB, alloc=44.3MB, time=702.91
memory used=57049.2MB, alloc=44.3MB, time=703.49
x[1] = 0.7291 2.743
h = 0.001 0.003
y2[1] (numeric) = 6.65941631809 6.36748975726
y2[1] (closed_form) = 5.19564799549 5.768242982
absolute error = 1.582
relative error = 20.37 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 6.37758246474 -5.72419470781
y1[1] (closed_form) = 5.81625363793 -5.15276017047
absolute error = 0.801
relative error = 10.31 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 134.9
Order of pole (three term test) = 71.66 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 134.9
Order of pole (three term test) = 65.23 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=57095.0MB, alloc=44.3MB, time=704.05
x[1] = 0.7301 2.746
h = 0.0001 0.004
y2[1] (numeric) = 6.69355156364 6.38501824415
y2[1] (closed_form) = 5.21696065765 5.78054646388
absolute error = 1.596
relative error = 20.49 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 6.39003474727 -5.7506003734
y1[1] (closed_form) = 5.8283705204 -5.17415345786
absolute error = 0.8048
relative error = 10.33 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 76.79
Order of pole (three term test) = 71.93 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 76.79
Order of pole (three term test) = 65.6 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=57141.0MB, alloc=44.3MB, time=704.60
memory used=57187.2MB, alloc=44.3MB, time=705.17
x[1] = 0.7302 2.75
h = 0.003 0.006
y2[1] (numeric) = 6.72783713805 6.40257895123
y2[1] (closed_form) = 5.23828419016 5.80338671727
absolute error = 1.606
relative error = 20.54 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 6.4149388627 -5.77808248023
y1[1] (closed_form) = 5.85101559577 -5.19564311407
absolute error = 0.8107
relative error = 10.36 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 102.6
Order of pole (three term test) = 72.36 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 102.6
Order of pole (three term test) = 66.03 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=57233.0MB, alloc=44.3MB, time=705.73
memory used=57279.2MB, alloc=44.3MB, time=706.29
x[1] = 0.7332 2.756
h = 0.0001 0.005
y2[1] (numeric) = 6.76227365821 6.42017190073
y2[1] (closed_form) = 5.28718661017 5.82288973302
absolute error = 1.591
relative error = 20.23 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 6.43317197104 -5.83778685509
y1[1] (closed_form) = 5.87010632302 -5.24465877359
absolute error = 0.8178
relative error = 10.39 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 46.16
Order of pole (three term test) = 72.86 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 46.16
Order of pole (three term test) = 66.86 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=57325.1MB, alloc=44.3MB, time=706.85
memory used=57371.4MB, alloc=44.3MB, time=707.42
x[1] = 0.7333 2.761
h = 0.0001 0.003
y2[1] (numeric) = 6.79686264896 6.43779644649
y2[1] (closed_form) = 5.31406600613 5.8517860279
absolute error = 1.594
relative error = 20.17 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 6.46463892319 -5.87232753024
y1[1] (closed_form) = 5.89876289237 -5.27174558012
absolute error = 0.8252
relative error = 10.43 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.53
Order of pole (three term test) = 73.41 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 37.53
Order of pole (three term test) = 67.41 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=57417.3MB, alloc=44.3MB, time=707.98
x[1] = 0.7334 2.764
h = 0.001 0.001
y2[1] (numeric) = 6.83160494198 6.4554528705
y2[1] (closed_form) = 5.33049678774 5.86897987568
absolute error = 1.612
relative error = 20.33 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 6.48329736705 -5.89341485546
y1[1] (closed_form) = 5.91581180114 -5.28829844935
absolute error = 0.8296
relative error = 10.45 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.64
Order of pole (three term test) = 73.74 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 29.64
Order of pole (three term test) = 67.74 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=57463.5MB, alloc=44.3MB, time=708.56
memory used=57509.7MB, alloc=44.3MB, time=709.13
x[1] = 0.7344 2.765
h = 0.0001 0.004
y2[1] (numeric) = 6.86650076019 6.47314138144
y2[1] (closed_form) = 5.34170676718 5.8696020548
absolute error = 1.64
relative error = 20.66 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 6.48291262145 -5.90672818996
y1[1] (closed_form) = 5.91634499219 -5.299503842
absolute error = 0.8305
relative error = 10.46 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 178.4
Order of pole (three term test) = 73.8 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 178.4
Order of pole (three term test) = 67.92 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=57555.6MB, alloc=44.3MB, time=709.69
memory used=57601.8MB, alloc=44.3MB, time=710.26
x[1] = 0.7345 2.769
h = 0.003 0.006
y2[1] (numeric) = 6.90155019201 6.49086204726
y2[1] (closed_form) = 5.36354153305 5.89278233398
absolute error = 1.65
relative error = 20.71 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 6.50815221628 -5.93491244053
y1[1] (closed_form) = 5.93933446939 -5.32150242698
absolute error = 0.8366
relative error = 10.49 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 106.5
Order of pole (three term test) = 74.25 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 106.5
Order of pole (three term test) = 68.37 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=57647.7MB, alloc=44.3MB, time=710.82
memory used=57693.9MB, alloc=44.3MB, time=711.39
x[1] = 0.7375 2.775
h = 0.0001 0.005
y2[1] (numeric) = 6.93675382474 6.50861488903
y2[1] (closed_form) = 5.41346737115 5.91243663179
absolute error = 1.636
relative error = 20.41 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 6.5263932139 -5.99592648255
y1[1] (closed_form) = 5.95858471973 -5.3715411118
absolute error = 0.844
relative error = 10.52 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 47.94
Order of pole (three term test) = 74.78 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 47.94
Order of pole (three term test) = 69.22 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=57739.9MB, alloc=44.3MB, time=711.94
x[1] = 0.7376 2.78
h = 0.0001 0.003
y2[1] (numeric) = 6.97211320935 6.52639924126
y2[1] (closed_form) = 5.44099165205 5.94176368786
absolute error = 1.639
relative error = 20.34 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 6.55828529403 -6.03135033544
y1[1] (closed_form) = 5.98767743931 -5.39926990921
absolute error = 0.8515
relative error = 10.56 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.99
Order of pole (three term test) = 75.36 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 38.99
Order of pole (three term test) = 69.8 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=57785.7MB, alloc=44.3MB, time=712.50
memory used=57832.0MB, alloc=44.3MB, time=713.07
x[1] = 0.7377 2.783
h = 0.001 0.001
y2[1] (numeric) = 7.00762919471 6.54421538754
y2[1] (closed_form) = 5.45781449624 5.95921189356
absolute error = 1.657
relative error = 20.5 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 6.57719222217 -6.05297344032
y1[1] (closed_form) = 6.00498395025 -5.41621315365
absolute error = 0.8561
relative error = 10.59 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.79
Order of pole (three term test) = 75.7 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 30.79
Order of pole (three term test) = 70.15 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=57877.9MB, alloc=44.3MB, time=713.64
memory used=57924.2MB, alloc=44.3MB, time=714.20
x[1] = 0.7387 2.784
h = 0.001 0.003
y2[1] (numeric) = 7.04330200893 6.56206353953
y2[1] (closed_form) = 5.46924165275 5.95979520273
absolute error = 1.685
relative error = 20.84 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 6.57671990644 -6.06655202965
y1[1] (closed_form) = 6.00547992763 -5.42763618519
absolute error = 0.857
relative error = 10.59 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 146.4
Order of pole (three term test) = 75.77 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 146.4
Order of pole (three term test) = 70.33 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=57970.2MB, alloc=44.3MB, time=714.77
x[1] = 0.7397 2.787
h = 0.0001 0.004
y2[1] (numeric) = 7.07913172215 6.57994370098
y2[1] (closed_form) = 5.49156983992 5.97239143227
absolute error = 1.7
relative error = 20.95 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 6.58937170552 -6.09430664195
y1[1] (closed_form) = 6.01789780476 -5.4500434746
absolute error = 0.8612
relative error = 10.61 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 83.35
Order of pole (three term test) = 76.07 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 83.35
Order of pole (three term test) = 70.74 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=58016.2MB, alloc=44.3MB, time=715.38
memory used=58062.4MB, alloc=44.3MB, time=715.94
x[1] = 0.7398 2.791
h = 0.003 0.006
y2[1] (numeric) = 7.11511856675 6.59785590572
y2[1] (closed_form) = 5.51401816056 5.99596363155
absolute error = 1.71
relative error = 21 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 6.61501758281 -6.12335397981
y1[1] (closed_form) = 6.04128420583 -5.47265303667
absolute error = 0.8675
relative error = 10.64 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 111.3
Order of pole (three term test) = 76.54 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 111.3
Order of pole (three term test) = 71.22 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=58108.3MB, alloc=44.3MB, time=716.50
memory used=58154.6MB, alloc=44.3MB, time=717.07
x[1] = 0.7428 2.797
h = 0.0001 0.005
y2[1] (numeric) = 7.15126318556 6.61580017051
y2[1] (closed_form) = 5.56516064664 6.01577485375
absolute error = 1.696
relative error = 20.69 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 6.6332590022 -6.18597352199
y1[1] (closed_form) = 6.06070076316 -5.52390800724
absolute error = 0.8753
relative error = 10.67 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.1
Order of pole (three term test) = 77.1 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 50.1
Order of pole (three term test) = 72.11 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=58200.4MB, alloc=44.3MB, time=717.63
memory used=58246.7MB, alloc=44.3MB, time=718.19
x[1] = 0.7429 2.802
h = 0.0001 0.003
y2[1] (numeric) = 7.18756716032 6.63377580653
y2[1] (closed_form) = 5.593458924 6.04559847064
absolute error = 1.699
relative error = 20.63 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 6.66566598888 -6.22248300975
y1[1] (closed_form) = 6.09029620623 -5.55240756302
absolute error = 0.8832
relative error = 10.72 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 40.74
Order of pole (three term test) = 77.7 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 40.74
Order of pole (three term test) = 72.73 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=58292.7MB, alloc=44.3MB, time=718.76
x[1] = 0.743 2.805
h = 0.001 0.001
y2[1] (numeric) = 7.22403136029 6.65178309893
y2[1] (closed_form) = 5.61075216025 6.06333964027
absolute error = 1.717
relative error = 20.79 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 6.68487374069 -6.24476464511
y1[1] (closed_form) = 6.10789939053 -5.56981931263
absolute error = 0.8879
relative error = 10.74 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 32.17
Order of pole (three term test) = 78.07 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 32.17
Order of pole (three term test) = 73.1 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=58338.6MB, alloc=44.3MB, time=719.33
memory used=58385.0MB, alloc=44.3MB, time=719.90
x[1] = 0.744 2.806
h = 0.001 0.003
y2[1] (numeric) = 7.26065601985 6.66982226279
y2[1] (closed_form) = 5.62243594247 6.0638721057
absolute error = 1.747
relative error = 21.12 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 6.6842922104 -6.25866777545
y1[1] (closed_form) = 6.1083464043 -5.58149951248
absolute error = 0.889
relative error = 10.74 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 153
Order of pole (three term test) = 78.14 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 153
Order of pole (three term test) = 73.28 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=58430.9MB, alloc=44.3MB, time=720.47
memory used=58477.4MB, alloc=44.3MB, time=721.04
x[1] = 0.745 2.809
h = 0.0001 0.004
y2[1] (numeric) = 7.29744121068 6.68789330154
y2[1] (closed_form) = 5.64532951202 6.0766230277
absolute error = 1.762
relative error = 21.24 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 6.69704974055 -6.28718373626
y1[1] (closed_form) = 6.12092326737 -5.60447138662
absolute error = 0.8933
relative error = 10.76 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 87.1
Order of pole (three term test) = 78.46 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 87.1
Order of pole (three term test) = 73.71 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=58523.2MB, alloc=44.3MB, time=721.60
x[1] = 0.7451 2.813
h = 0.003 0.006
y2[1] (numeric) = 7.33438717052 6.70599624847
y2[1] (closed_form) = 5.66840711958 6.10059265885
absolute error = 1.773
relative error = 21.29 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 6.7231059189 -6.31711703359
y1[1] (closed_form) = 6.14471198176 -5.62770768812
absolute error = 0.8999
relative error = 10.8 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 116.3
Order of pole (three term test) = 78.95 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 116.3
Order of pole (three term test) = 74.21 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=58569.3MB, alloc=44.3MB, time=722.18
memory used=58615.3MB, alloc=44.3MB, time=722.75
x[1] = 0.7481 2.819
h = 0.0001 0.005
y2[1] (numeric) = 7.37149455656 6.72413111713
y2[1] (closed_form) = 5.72079419099 6.12055791047
absolute error = 1.758
relative error = 20.98 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 6.74133750318 -6.38137978083
y1[1] (closed_form) = 6.16429174495 -5.68020684104
absolute error = 0.9081
relative error = 10.83 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 52.35
Order of pole (three term test) = 79.55 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 52.35
Order of pole (three term test) = 75.15 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=58661.2MB, alloc=44.3MB, time=723.31
memory used=58707.4MB, alloc=44.3MB, time=723.87
x[1] = 0.7482 2.824
h = 0.0001 0.003
y2[1] (numeric) = 7.40876498174 6.74229719459
y2[1] (closed_form) = 5.74988632203 6.1508850858
absolute error = 1.761
relative error = 20.92 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 6.77426454934 -6.41900368265
y1[1] (closed_form) = 6.19439675816 -5.70949705097
absolute error = 0.9163
relative error = 10.88 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 42.57
Order of pole (three term test) = 80.19 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 42.57
Order of pole (three term test) = 75.79 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=58753.3MB, alloc=44.3MB, time=724.44
memory used=58799.6MB, alloc=44.3MB, time=725.01
x[1] = 0.7483 2.827
h = 0.001 0.001
y2[1] (numeric) = 7.44619933621 6.76049476749
y2[1] (closed_form) = 5.76766197228 6.16892327487
absolute error = 1.78
relative error = 21.07 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 6.79377598252 -6.44196122743
y1[1] (closed_form) = 6.21230058077 -5.72738934953
absolute error = 0.9213
relative error = 10.9 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 33.62
Order of pole (three term test) = 80.57 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 33.62
Order of pole (three term test) = 76.19 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=58845.7MB, alloc=44.3MB, time=725.57
x[1] = 0.7493 2.828
h = 0.001 0.003
y2[1] (numeric) = 7.48379786074 6.77872405437
y2[1] (closed_form) = 5.7796078313 6.16940241445
absolute error = 1.81
relative error = 21.41 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 6.79308060437 -6.45619581911
y1[1] (closed_form) = 6.2126961107 -5.73933214721
absolute error = 0.9224
relative error = 10.91 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 159.9
Order of pole (three term test) = 80.65 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 159.9
Order of pole (three term test) = 76.38 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=58891.6MB, alloc=44.3MB, time=726.13
memory used=58937.8MB, alloc=44.3MB, time=726.70
x[1] = 0.7503 2.831
h = 0.0001 0.004
y2[1] (numeric) = 7.52156062863 6.79698505833
y2[1] (closed_form) = 5.80308019466 6.18230850318
absolute error = 1.825
relative error = 21.52 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 6.80594149456 -6.48549166768
y1[1] (closed_form) = 6.22543233635 -5.76288201264
absolute error = 0.9269
relative error = 10.93 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 91.02
Order of pole (three term test) = 80.98 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 91.02
Order of pole (three term test) = 76.83 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=58983.7MB, alloc=44.3MB, time=727.26
memory used=59029.7MB, alloc=44.3MB, time=727.82
x[1] = 0.7504 2.835
h = 0.003 0.006
y2[1] (numeric) = 7.55948788306 6.81527781207
y2[1] (closed_form) = 5.8268032009 6.20668111238
absolute error = 1.836
relative error = 21.57 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 6.83241195863 -6.51633432269
y1[1] (closed_form) = 6.24962879076 -5.78676119548
absolute error = 0.9338
relative error = 10.96 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 121.6
Order of pole (three term test) = 81.51 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 121.6
Order of pole (three term test) = 77.36 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=59075.5MB, alloc=44.3MB, time=728.38
memory used=59121.7MB, alloc=44.3MB, time=728.95
x[1] = 0.7534 2.841
h = 0.0001 0.005
y2[1] (numeric) = 7.59758029587 6.83360232579
y2[1] (closed_form) = 5.88046339835 6.22679727845
absolute error = 1.821
relative error = 21.26 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 6.85062302258 -6.58227875662
y1[1] (closed_form) = 6.26936844293 -5.84053303266
absolute error = 0.9424
relative error = 11 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 54.71
Order of pole (three term test) = 82.14 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 54.71
Order of pole (three term test) = 78.33 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=59167.7MB, alloc=44.3MB, time=729.51
x[1] = 0.7535 2.846
h = 0.0001 0.003
y2[1] (numeric) = 7.63583951182 6.85195786177
y2[1] (closed_form) = 5.91036971968 6.25763505427
absolute error = 1.825
relative error = 21.2 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 6.88407524052 -6.62104651413
y1[1] (closed_form) = 6.29998992085 -5.87063427183
absolute error = 0.9509
relative error = 11.04 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 44.49
Order of pole (three term test) = 82.81 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 44.49
Order of pole (three term test) = 79.01 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=59213.4MB, alloc=44.3MB, time=730.07
memory used=59259.8MB, alloc=44.3MB, time=730.65
x[1] = 0.7536 2.849
h = 0.001 0.001
y2[1] (numeric) = 7.67426644238 6.87034470802
y2[1] (closed_form) = 5.92864009507 6.2759743412
absolute error = 1.844
relative error = 21.36 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 6.90389318261 -6.64469774595
y1[1] (closed_form) = 6.31819837173 -5.88901945234
absolute error = 0.9561
relative error = 11.07 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 35.13
Order of pole (three term test) = 83.21 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 35.13
Order of pole (three term test) = 79.43 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=59305.7MB, alloc=44.3MB, time=731.22
memory used=59352.0MB, alloc=44.3MB, time=731.79
x[1] = 0.7546 2.85
h = 0.001 0.003
y2[1] (numeric) = 7.71286133489 6.8887630866
y2[1] (closed_form) = 5.94085358901 6.27639758741
absolute error = 1.875
relative error = 21.69 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 6.90307918398 -6.65927084711
y1[1] (closed_form) = 6.31853981289 -5.90123038509
absolute error = 0.9572
relative error = 11.07 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 167.1
Order of pole (three term test) = 83.29 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 167.1
Order of pole (three term test) = 79.62 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=59397.8MB, alloc=44.3MB, time=732.35
x[1] = 0.7556 2.853
h = 0.0001 0.004
y2[1] (numeric) = 7.75162426428 6.90721300028
y2[1] (closed_form) = 5.9649184577 6.28945925286
absolute error = 1.89
relative error = 21.81 %
Correct digits = 1
h = 0.0001 0.004
y1[1] (numeric) = 6.91604091145 -6.6893655189
y1[1] (closed_form) = 6.3314357156 -5.92537194904
absolute error = 0.962
relative error = 11.09 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 95.11
Order of pole (three term test) = 83.65 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 95.11
Order of pole (three term test) = 80.09 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=59444.0MB, alloc=44.3MB, time=732.92
memory used=59490.1MB, alloc=44.3MB, time=733.48
x[1] = 0.7557 2.857
h = 0.003 0.006
y2[1] (numeric) = 7.79055547933 6.92569448112
y2[1] (closed_form) = 5.9893033626 6.31424041951
absolute error = 1.902
relative error = 21.86 %
Correct digits = 1
h = 0.003 0.006
y1[1] (numeric) = 6.94292960826 -6.72114146734
y1[1] (closed_form) = 6.3560453727 -5.94991054332
absolute error = 0.9691
relative error = 11.13 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 127
Order of pole (three term test) = 84.2 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 127
Order of pole (three term test) = 80.65 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=59535.8MB, alloc=44.3MB, time=734.03
memory used=59582.1MB, alloc=44.3MB, time=734.60
x[1] = 0.7587 2.863
h = 0.0001 0.005
y2[1] (numeric) = 7.82965566681 6.94420753582
y2[1] (closed_form) = 6.04426584244 6.33450415695
absolute error = 1.887
relative error = 21.55 %
Correct digits = 1
h = 0.0001 0.005
y1[1] (numeric) = 6.96110902446 -6.78880686112
y1[1] (closed_form) = 6.37594137307 -6.0049841842
absolute error = 0.9782
relative error = 11.17 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 57.17
Order of pole (three term test) = 84.87 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 57.17
Order of pole (three term test) = 81.67 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=59628.0MB, alloc=44.3MB, time=735.16
memory used=59674.2MB, alloc=44.3MB, time=735.72
x[1] = 0.7588 2.868
h = 0.0001 0.003
y2[1] (numeric) = 7.86892650387 6.96275140111
y2[1] (closed_form) = 6.07500718095 6.36585961822
absolute error = 1.891
relative error = 21.49 %
Correct digits = 1
h = 0.0001 0.003
y1[1] (numeric) = 6.99509148128 -6.82874859287
y1[1] (closed_form) = 6.40708625658 -6.03591731793
absolute error = 0.9871
relative error = 11.21 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 46.49
Order of pole (three term test) = 85.58 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 46.49
Order of pole (three term test) = 82.39 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=59720.2MB, alloc=44.3MB, time=736.29
x[1] = 0.7589 2.871
h = 0.001 0.001
y2[1] (numeric) = 7.90836892382 6.98132636635
y2[1] (closed_form) = 6.09378488842 6.38450410333
absolute error = 1.91
relative error = 21.64 %
Correct digits = 1
h = 0.001 0.001
y1[1] (numeric) = 7.01521872677 -6.85311169669
y1[1] (closed_form) = 6.42560334963 -6.05480800915
absolute error = 0.9924
relative error = 11.24 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 36.71
Order of pole (three term test) = 86 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 36.71
Order of pole (three term test) = 82.82 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=59766.2MB, alloc=44.3MB, time=736.86
memory used=59812.6MB, alloc=44.3MB, time=737.43
x[1] = 0.7599 2.872
h = 0.001 0.003
y2[1] (numeric) = 7.94798318069 6.99993265714
y2[1] (closed_form) = 6.1062716844 6.38486880073
absolute error = 1.942
relative error = 21.98 %
Correct digits = 1
h = 0.001 0.003
y1[1] (numeric) = 7.01428119194 -6.86803048532
y1[1] (closed_form) = 6.42588800987 -6.06729272384
absolute error = 0.9937
relative error = 11.24 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 174.6
Order of pole (three term test) = 86.09 0
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
Radius of convergence (three term test) for eq 2 = 174.6
Order of pole (three term test) = 83.03 0
NO COMPLEX POLE (six term test) for Equation 2
memory used=59859.2MB, alloc=44.3MB, time=738.01
memory used=59907.0MB, alloc=44.3MB, time=738.68
Finished!
Maximum Time Reached before Solution Completed!
diff ( y2 , x , 3 ) = neg ( cos ( x ) ) ;
diff ( y1 , x , 1 ) = neg ( y2 ) ;
Iterations = 754
Total Elapsed Time = 12 Minutes 18 Seconds
Expected Time Remaining = 0 Seconds
Optimized Time Remaining = 0 Seconds
Expected Total Time = 12 Minutes 18 Seconds
> quit
memory used=59909.2MB, alloc=44.3MB, time=738.71