|\^/| Maple 2016 (X86 64 LINUX)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2016
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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#BEGIN OUTFILE1
# before write maple top matter
# before write_ats library and user def block
#BEGIN ATS LIBRARY BLOCK
# Begin Function number 2
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s\n",str);
> fi;# end if 1;
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
# End Function number 2
# Begin Function number 3
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s",str);
> fi;# end if 1;
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
# End Function number 3
# Begin Function number 4
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> print(label,str);
> fi;# end if 1;
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
# End Function number 4
# Begin Function number 5
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 5
# Begin Function number 6
> omniout_complex := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> if vallen = 4 then
> printf("%-30s = %-20.4g %-20g %s \n",prelabel,Re(value), Im(value), postlabel);
> else
> printf("%-30s = %-20.12g %-20.12g %s \n",prelabel,Re(value),Im(value), postlabel);
> fi;# end if 0;
> fi;# end if -1;
> end;
omniout_complex := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then printf("%-30s = %-20.4g %-20g %s \n", prelabel,
Re(value), Im(value), postlabel)
else printf("%-30s = %-20.12g %-20.12g %s \n", prelabel, Re(value),
Im(value), postlabel)
end if
end if
end proc
# End Function number 6
# Begin Function number 7
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number -1
> if vallen = 5 then # if number 0
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;# end if 0;
> fi;# end if -1;
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 7
# Begin Function number 8
> logitem_time := proc(fd,secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> fprintf(fd,"| ");
> if (secs_in >= 0) then # if number -1
> years_int := int_trunc(secs_in / glob_sec_in_year);
> sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
> days_int := int_trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := sec_temp mod int_trunc(glob_sec_in_day) ;
> hours_int := int_trunc(sec_temp / glob_sec_in_hour);
> sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
> minutes_int := int_trunc(sec_temp / glob_sec_in_minute);
> sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
> if (years_int > 0) then # if number 0
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 1
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 2
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 3
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 3
> else
> fprintf(fd," 0.0 Seconds");
> fi;# end if 2
> fprintf(fd," | \n");
> end;
logitem_time := proc(fd, secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
fprintf(fd, "");
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, " 0.0 Seconds")
end if;
fprintf(fd, " | \n")
end proc
# End Function number 8
# Begin Function number 9
> omniout_timestr := proc(secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> if (secs_in >= 0) then # if number 2
> years_int := int_trunc(secs_in / glob_sec_in_year);
> sec_temp := (int_trunc(secs_in) mod int_trunc(glob_sec_in_year));
> days_int := int_trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_day)) ;
> hours_int := int_trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_hour));
> minutes_int := int_trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod int_trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 3
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 4
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 5
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 6
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 6
> else
> printf(" 0.0 Seconds\n");
> fi;# end if 5
> end;
omniout_timestr := proc(secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" 0.0 Seconds\n")
end if
end proc
# End Function number 9
# Begin Function number 10
> zero_ats_ar := proc(arr_a)
> global ATS_MAX_TERMS;
> local iii;
> iii := 1;
> while (iii <= ATS_MAX_TERMS) do # do number 1
> arr_a [iii] := glob__0;
> iii := iii + 1;
> od;# end do number 1
> end;
zero_ats_ar := proc(arr_a)
local iii;
global ATS_MAX_TERMS;
iii := 1;
while iii <= ATS_MAX_TERMS do arr_a[iii] := glob__0; iii := iii + 1
end do
end proc
# End Function number 10
# Begin Function number 11
> ats := proc(mmm_ats,arr_a,arr_b,jjj_ats)
> global ATS_MAX_TERMS;
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := glob__0;
> if (jjj_ats <= mmm_ats) then # if number 5
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> if ((lll_ats <= ATS_MAX_TERMS and (iii_ats <= ATS_MAX_TERMS) )) then # if number 6
> ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]);
> fi;# end if 6;
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 5;
> ret_ats;
> end;
ats := proc(mmm_ats, arr_a, arr_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
global ATS_MAX_TERMS;
ret_ats := glob__0;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
if lll_ats <= ATS_MAX_TERMS and iii_ats <= ATS_MAX_TERMS then
ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats])
end if;
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
# End Function number 11
# Begin Function number 12
> att := proc(mmm_att,arr_aa,arr_bb,jjj_att)
> global ATS_MAX_TERMS;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := glob__0;
> if (jjj_att < mmm_att) then # if number 5
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while ((iii_att < mmm_att) and (iii_att <= ATS_MAX_TERMS) ) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if ((lll_att <= ATS_MAX_TERMS and (iii_att <= ATS_MAX_TERMS) )) then # if number 6
> ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att);
> fi;# end if 6;
> iii_att := iii_att + 1;
> od;# end do number 1;
> ret_att := ret_att / c(mmm_att) ;
> fi;# end if 5;
> ret_att;
> end;
att := proc(mmm_att, arr_aa, arr_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global ATS_MAX_TERMS;
ret_att := glob__0;
if jjj_att < mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att < mmm_att and iii_att <= ATS_MAX_TERMS do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= ATS_MAX_TERMS and iii_att <= ATS_MAX_TERMS then
ret_att :=
ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])*c(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/c(mmm_att)
end if;
ret_att
end proc
# End Function number 12
# Begin Function number 13
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
# End Function number 13
# Begin Function number 14
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
# End Function number 14
# Begin Function number 15
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
# End Function number 15
# Begin Function number 16
> logitem_good_digits := proc(file,rel_error)
> global glob_small_float,glob_prec;
> local good_digits;
> fprintf(file,"");
> fprintf(file,"%d",glob_min_good_digits);
> fprintf(file," | ");
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float, glob_prec;
fprintf(file, "");
fprintf(file, "%d", glob_min_good_digits);
fprintf(file, " | ")
end proc
# End Function number 16
# Begin Function number 17
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
# End Function number 17
# Begin Function number 18
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
# End Function number 18
# Begin Function number 19
> logitem_complex := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g + %g I",Re(x),Im(x));
> fprintf(file," | ");
> end;
logitem_complex := proc(file, x)
fprintf(file, "");
fprintf(file, "%g + %g I", Re(x), Im(x));
fprintf(file, " | ")
end proc
# End Function number 19
# Begin Function number 20
> logitem_h_reason := proc(file)
> global glob_h_reason;
> fprintf(file,"");
> if (glob_h_reason = 1) then # if number 5
> fprintf(file,"Max H");
> elif
> (glob_h_reason = 2) then # if number 6
> fprintf(file,"Display Interval");
> elif
> (glob_h_reason = 3) then # if number 7
> fprintf(file,"Optimal");
> elif
> (glob_h_reason = 4) then # if number 8
> fprintf(file,"Pole Accuracy");
> elif
> (glob_h_reason = 5) then # if number 9
> fprintf(file,"Min H (Pole)");
> elif
> (glob_h_reason = 6) then # if number 10
> fprintf(file,"Pole");
> elif
> (glob_h_reason = 7) then # if number 11
> fprintf(file,"Opt Iter");
> else
> fprintf(file,"Impossible");
> fi;# end if 11
> fprintf(file," | ");
> end;
logitem_h_reason := proc(file)
global glob_h_reason;
fprintf(file, "");
if glob_h_reason = 1 then fprintf(file, "Max H")
elif glob_h_reason = 2 then fprintf(file, "Display Interval")
elif glob_h_reason = 3 then fprintf(file, "Optimal")
elif glob_h_reason = 4 then fprintf(file, "Pole Accuracy")
elif glob_h_reason = 5 then fprintf(file, "Min H (Pole)")
elif glob_h_reason = 6 then fprintf(file, "Pole")
elif glob_h_reason = 7 then fprintf(file, "Opt Iter")
else fprintf(file, "Impossible")
end if;
fprintf(file, " | ")
end proc
# End Function number 20
# Begin Function number 21
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
# End Function number 21
# Begin Function number 22
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file) fprintf(file, "\n") end proc
# End Function number 22
# Begin Function number 23
> chk_data := proc()
> global glob_max_iter,ALWAYS, ATS_MAX_TERMS;
> local errflag;
> errflag := false;
> if (glob_max_iter < 2) then # if number 11
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 11;
> if (errflag) then # if number 11
> quit;
> fi;# end if 11
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, ATS_MAX_TERMS;
errflag := false;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
# End Function number 23
# Begin Function number 24
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := c(clock_sec2);
> sub1 := c(t_end2-t_start2);
> sub2 := c(t2-t_start2);
> if (sub1 = glob__0) then # if number 11
> sec_left := glob__0;
> else
> if (sub2 > glob__0) then # if number 12
> rrr := (sub1/sub2);
> sec_left := rrr * c(ms2) - c(ms2);
> else
> sec_left := glob__0;
> fi;# end if 12
> fi;# end if 11;
> sec_left;
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := c(clock_sec2);
sub1 := c(t_end2 - t_start2);
sub2 := c(t2 - t_start2);
if sub1 = glob__0 then sec_left := glob__0
else
if glob__0 < sub2 then
rrr := sub1/sub2; sec_left := rrr*c(ms2) - c(ms2)
else sec_left := glob__0
end if
end if;
sec_left
end proc
# End Function number 24
# Begin Function number 25
> comp_percent := proc(t_end2,t_start2, t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub2 > glob_small_float) then # if number 11
> rrr := (glob__100*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 11;
> rrr;
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < sub2 then rrr := glob__100*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
# End Function number 25
# Begin Function number 26
> comp_rad_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 11
> ret := float_abs(term1 * glob_h / term2);
> else
> ret := glob_larger_float;
> fi;# end if 11;
> ret;
> #BOTTOM TWO TERM RADIUS ANALYSIS
> end;
comp_rad_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := float_abs(term1*glob_h/term2)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 26
# Begin Function number 27
> comp_ord_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM ORDER ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 11
> ret := glob__1 + float_abs(term2) * c(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(c(last_no));
> else
> ret := glob_larger_float;
> fi;# end if 11;
> ret;
> #BOTTOM TWO TERM ORDER ANALYSIS
> end;
comp_ord_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := glob__1 + float_abs(term2)*
c(last_no)*ln(float_abs(term1*glob_h/term2))/ln(c(last_no))
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 27
# Begin Function number 28
> c := proc(in_val)
> #To Force Conversion when needed
> local ret;
> ret := evalc(in_val);
> ret;
> #End Conversion
> end;
c := proc(in_val) local ret; ret := evalc(in_val); ret end proc
# End Function number 28
# Begin Function number 29
> comp_rad_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret,temp;
> temp := float_abs(term2*term2*c(last_no)+glob__m2*term2*term2-term1*term3*c(last_no)+term1*term3);
> if (float_abs(temp) > glob__0) then # if number 11
> ret := float_abs((term2*glob_h*term1)/(temp));
> else
> ret := glob_larger_float;
> fi;# end if 11;
> ret;
> #BOTTOM THREE TERM RADIUS ANALYSIS
> end;
comp_rad_from_three_terms := proc(term1, term2, term3, last_no)
local ret, temp;
global glob_h, glob_larger_float;
temp := float_abs(term2*term2*c(last_no) + glob__m2*term2*term2
- term1*term3*c(last_no) + term1*term3);
if glob__0 < float_abs(temp) then
ret := float_abs(term2*glob_h*term1/temp)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 29
# Begin Function number 30
> comp_ord_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM ORDER ANALYSIS
> local ret;
> ret := float_abs((glob__4*term1*term3*c(last_no)-glob__3*term1*term3-glob__4*term2*term2*c(last_no)+glob__4*term2*term2+term2*term2*c(last_no*last_no)-term1*term3*c(last_no*last_no))/(term2*term2*c(last_no)-glob__2*term2*term2-term1*term3*c(last_no)+term1*term3));
> ret;
> #TOP THREE TERM ORDER ANALYSIS
> end;
comp_ord_from_three_terms := proc(term1, term2, term3, last_no)
local ret;
ret := float_abs((glob__4*term1*term3*c(last_no) - glob__3*term1*term3
- glob__4*term2*term2*c(last_no) + glob__4*term2*term2
+ term2*term2*c(last_no*last_no) - term1*term3*c(last_no*last_no))
/(term2*term2*c(last_no) - glob__2*term2*term2
- term1*term3*c(last_no) + term1*term3));
ret
end proc
# End Function number 30
# Begin Function number 31
> comp_rad_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> #TOP SIX TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float,glob_six_term_ord_save;
> local ret,rm0,rm1,rm2,rm3,rm4,nr1,nr2,dr1,dr2,ds2,rad_c,ord_no,ds1,rcs;
> if ((term5 <> glob__0) and (term4 <> glob__0) and (term3 <> glob__0) and (term2 <> glob__0) and (term1 <> glob__0)) then # if number 11
> rm0 := term6/term5;
> rm1 := term5/term4;
> rm2 := term4/term3;
> rm3 := term3/term2;
> rm4 := term2/term1;
> nr1 := c(last_no-1)*rm0 - glob__2*c(last_no-2)*rm1 + c(last_no-3)*rm2;
> nr2 := c(last_no-2)*rm1 - glob__2*c(last_no-3)*rm2 + c(last_no-4)*rm3;
> dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
> dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
> ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
> ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
> if ((float_abs(nr1 * dr2 - nr2 * dr1) = glob__0) or (float_abs(dr1) = glob__0)) then # if number 12
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> else
> if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0) then # if number 13
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) -c(last_no)/glob__2;
> if (float_abs(rcs) <> glob__0) then # if number 14
> if (rcs > glob__0) then # if number 15
> rad_c := float_abs( sqrt(rcs) * float_abs(glob_h));
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 15
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 14
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 13
> fi;# end if 12
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 11;
> glob_six_term_ord_save := ord_no;
> rad_c;
> #BOTTOM SIX TERM RADIUS ANALYSIS
> end;
comp_rad_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
local ret, rm0, rm1, rm2, rm3, rm4, nr1, nr2, dr1, dr2, ds2, rad_c, ord_no,
ds1, rcs;
global glob_h, glob_larger_float, glob_six_term_ord_save;
if term5 <> glob__0 and term4 <> glob__0 and term3 <> glob__0 and
term2 <> glob__0 and term1 <> glob__0 then
rm0 := term6/term5;
rm1 := term5/term4;
rm2 := term4/term3;
rm3 := term3/term2;
rm4 := term2/term1;
nr1 := c(last_no - 1)*rm0 - glob__2*c(last_no - 2)*rm1
+ c(last_no - 3)*rm2;
nr2 := c(last_no - 2)*rm1 - glob__2*c(last_no - 3)*rm2
+ c(last_no - 4)*rm3;
dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
if
float_abs(nr1*dr2 - nr2*dr1) = glob__0 or float_abs(dr1) = glob__0
then rad_c := glob_larger_float; ord_no := glob_larger_float
else
if glob__0 < float_abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no :=
(rcs*nr1 - ds1)/(glob__2*dr1) - c(last_no)/glob__2;
if float_abs(rcs) <> glob__0 then
if glob__0 < rcs then
rad_c := float_abs(sqrt(rcs)*float_abs(glob_h))
else
rad_c := glob_larger_float;
ord_no := glob_larger_float
end if
else
rad_c := glob_larger_float; ord_no := glob_larger_float
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if;
glob_six_term_ord_save := ord_no;
rad_c
end proc
# End Function number 31
# Begin Function number 32
> comp_ord_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> global glob_six_term_ord_save;
> #TOP SIX TERM ORDER ANALYSIS
> #TOP SAVED FROM SIX TERM RADIUS ANALYSIS
> glob_six_term_ord_save;
> #BOTTOM SIX TERM ORDER ANALYSIS
> end;
comp_ord_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
global glob_six_term_ord_save;
glob_six_term_ord_save
end proc
# End Function number 32
# Begin Function number 33
> factorial_2 := proc(nnn)
> ret := nnn!;
> ret;;
> end;
Warning, `ret` is implicitly declared local to procedure `factorial_2`
factorial_2 := proc(nnn) local ret; ret := nnn!; ret end proc
# End Function number 33
# Begin Function number 34
> factorial_1 := proc(nnn)
> global ATS_MAX_TERMS,array_fact_1;
> local ret;
> if (nnn <= ATS_MAX_TERMS) then # if number 11
> if (array_fact_1[nnn] = 0) then # if number 12
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 12;
> else
> ret := factorial_2(nnn);
> fi;# end if 11;
> ret;
> end;
factorial_1 := proc(nnn)
local ret;
global ATS_MAX_TERMS, array_fact_1;
if nnn <= ATS_MAX_TERMS then
if array_fact_1[nnn] = 0 then
ret := factorial_2(nnn); array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := factorial_2(nnn)
end if;
ret
end proc
# End Function number 34
# Begin Function number 35
> factorial_3 := proc(mmm,nnn)
> global ATS_MAX_TERMS,array_fact_2;
> local ret;
> if ((nnn <= ATS_MAX_TERMS) and (mmm <= ATS_MAX_TERMS)) then # if number 11
> if (array_fact_2[mmm,nnn] = 0) then # if number 12
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 12;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 11;
> ret;
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global ATS_MAX_TERMS, array_fact_2;
if nnn <= ATS_MAX_TERMS and mmm <= ATS_MAX_TERMS then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := factorial_2(mmm)/factorial_2(nnn)
end if;
ret
end proc
# End Function number 35
# Begin Function number 36
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
# End Function number 36
# Begin Function number 37
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
# End Function number 37
# Begin Function number 38
> float_abs := proc(x)
> abs(x);
> end;
float_abs := proc(x) abs(x) end proc
# End Function number 38
# Begin Function number 39
> expt := proc(x,y)
> x^y;
> end;
expt := proc(x, y) x^y end proc
# End Function number 39
# Begin Function number 40
> neg := proc(x)
> -x;
> end;
neg := proc(x) -x end proc
# End Function number 40
# Begin Function number 41
> int_trunc := proc(x)
> trunc(x);
> end;
int_trunc := proc(x) trunc(x) end proc
# End Function number 41
# Begin Function number 42
> estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer)
> local desired_abs_gbl_error,range,estimated_steps,step_error;
> global glob_desired_digits_correct,ALWAYS,ATS_MAX_TERMS;
> omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
> desired_abs_gbl_error := expt(glob__10,c( -glob_desired_digits_correct)) * c(float_abs(c(estimated_answer)));
> omniout_float(ALWAYS,"estimated_h",32,estimated_h,32,"");
> omniout_float(ALWAYS,"estimated_answer",32,estimated_answer,32,"");
> omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,"");
> range := (x_end - x_start);
> omniout_float(ALWAYS,"range",32,range,32,"");
> estimated_steps := range / estimated_h;
> omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,"");
> step_error := (c(float_abs(desired_abs_gbl_error) /sqrt(c( estimated_steps))/c(ATS_MAX_TERMS)));
> omniout_float(ALWAYS,"step_error",32,step_error,32,"");
> (step_error);;
> end;
estimated_needed_step_error := proc(
x_start, x_end, estimated_h, estimated_answer)
local desired_abs_gbl_error, range, estimated_steps, step_error;
global glob_desired_digits_correct, ALWAYS, ATS_MAX_TERMS;
omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, "");
desired_abs_gbl_error :=
expt(glob__10, c(-glob_desired_digits_correct))*
c(float_abs(c(estimated_answer)));
omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, "");
omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, "")
;
omniout_float(ALWAYS, "desired_abs_gbl_error", 32,
desired_abs_gbl_error, 32, "");
range := x_end - x_start;
omniout_float(ALWAYS, "range", 32, range, 32, "");
estimated_steps := range/estimated_h;
omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, "");
step_error := c(float_abs(desired_abs_gbl_error)/(
sqrt(c(estimated_steps))*c(ATS_MAX_TERMS)));
omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
step_error
end proc
# End Function number 42
#END ATS LIBRARY BLOCK
#BEGIN USER FUNCTION BLOCK
#BEGIN BLOCK 3
#BEGIN USER DEF BLOCK
> exact_soln_y1 := proc(x)
> return(neg(cos(c(x))));
> end;
exact_soln_y1 := proc(x) return neg(cos(c(x))) end proc
> exact_soln_y2 := proc(x)
> return(neg(sin(c(x))));
> end;
exact_soln_y2 := proc(x) return neg(sin(c(x))) end proc
> exact_soln_y2p := proc(x)
> return(neg(cos(c(x))));
> end;
exact_soln_y2p := proc(x) return neg(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_1,
> array_const_0D0,
> array_const_2,
#END CONST
> array_y1_init,
> array_y2_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local min_size;
> min_size := glob_estimated_size_answer;
> if (float_abs(array_y1[1]) < min_size) then # if number 5
> min_size := float_abs(array_y1[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 5;
> if (float_abs(array_y2[1]) < min_size) then # if number 5
> min_size := float_abs(array_y2[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 5;
> if (min_size < glob__1) then # if number 5
> min_size := glob__1;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 5;
> min_size;
> end;
est_size_answer := proc()
local min_size;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2,
array_y1_init, array_y2_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y1, array_x, array_y2,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
min_size := glob_estimated_size_answer;
if float_abs(array_y1[1]) < min_size then
min_size := float_abs(array_y1[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if float_abs(array_y2[1]) < min_size then
min_size := float_abs(array_y2[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if min_size < glob__1 then
min_size := glob__1;
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
min_size
end proc
# End Function number 4
# Begin Function number 5
> test_suggested_h := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2,
#END CONST
> array_y1_init,
> array_y2_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> max_estimated_step_error := glob__small;
> no_terms := ATS_MAX_TERMS;
> hn_div_ho := glob__0_5;
> hn_div_ho_2 := glob__0_25;
> hn_div_ho_3 := glob__0_125;
> omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,"");
> omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,"");
> omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,"");
> est_tmp := float_abs(array_y1[no_terms-3] + array_y1[no_terms - 2] * hn_div_ho + array_y1[no_terms - 1] * hn_div_ho_2 + array_y1[no_terms] * hn_div_ho_3);
> if (est_tmp >= max_estimated_step_error) then # if number 5
> max_estimated_step_error := est_tmp;
> fi;# end if 5;
> est_tmp := float_abs(array_y2[no_terms-3] + array_y2[no_terms - 2] * hn_div_ho + array_y2[no_terms - 1] * hn_div_ho_2 + array_y2[no_terms] * hn_div_ho_3);
> if (est_tmp >= max_estimated_step_error) then # if number 5
> max_estimated_step_error := est_tmp;
> fi;# end if 5;
> omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,"");
> max_estimated_step_error;
> end;
test_suggested_h := proc()
local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3,
no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2,
array_y1_init, array_y2_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y1, array_x, array_y2,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
max_estimated_step_error := glob__small;
no_terms := ATS_MAX_TERMS;
hn_div_ho := glob__0_5;
hn_div_ho_2 := glob__0_25;
hn_div_ho_3 := glob__0_125;
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, "");
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, "");
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, "");
est_tmp := float_abs(array_y1[no_terms - 3]
+ array_y1[no_terms - 2]*hn_div_ho
+ array_y1[no_terms - 1]*hn_div_ho_2
+ array_y1[no_terms]*hn_div_ho_3);
if max_estimated_step_error <= est_tmp then
max_estimated_step_error := est_tmp
end if;
est_tmp := float_abs(array_y2[no_terms - 3]
+ array_y2[no_terms - 2]*hn_div_ho
+ array_y2[no_terms - 1]*hn_div_ho_2
+ array_y2[no_terms]*hn_div_ho_3);
if max_estimated_step_error <= est_tmp then
max_estimated_step_error := est_tmp
end if;
omniout_float(ALWAYS, "max_estimated_step_error", 32,
max_estimated_step_error, 32, "");
max_estimated_step_error
end proc
# End Function number 5
# Begin Function number 6
> track_estimated_error := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2,
#END CONST
> array_y1_init,
> array_y2_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> no_terms := ATS_MAX_TERMS;
> hn_div_ho := glob__0_5;
> hn_div_ho_2 := glob__0_25;
> hn_div_ho_3 := glob__0_125;
> est_tmp := c(float_abs(array_y1[no_terms-3])) + c(float_abs(array_y1[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y1[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y1[no_terms])) * c(hn_div_ho_3);
> if (glob_prec * c(float_abs(array_y1[1])) > c(est_tmp)) then # if number 5
> est_tmp := c(glob_prec) * c(float_abs(array_y1[1]));
> fi;# end if 5;
> if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 5
> array_max_est_error[1] := c(est_tmp);
> fi;# end if 5
> ;
> est_tmp := c(float_abs(array_y2[no_terms-3])) + c(float_abs(array_y2[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y2[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y2[no_terms])) * c(hn_div_ho_3);
> if (glob_prec * c(float_abs(array_y2[1])) > c(est_tmp)) then # if number 5
> est_tmp := c(glob_prec) * c(float_abs(array_y2[1]));
> fi;# end if 5;
> if (c(est_tmp) >= c(array_max_est_error[2])) then # if number 5
> array_max_est_error[2] := c(est_tmp);
> fi;# end if 5
> ;
> end;
track_estimated_error := proc()
local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2,
array_y1_init, array_y2_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y1, array_x, array_y2,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
no_terms := ATS_MAX_TERMS;
hn_div_ho := glob__0_5;
hn_div_ho_2 := glob__0_25;
hn_div_ho_3 := glob__0_125;
est_tmp := c(float_abs(array_y1[no_terms - 3]))
+ c(float_abs(array_y1[no_terms - 2]))*c(hn_div_ho)
+ c(float_abs(array_y1[no_terms - 1]))*c(hn_div_ho_2)
+ c(float_abs(array_y1[no_terms]))*c(hn_div_ho_3);
if c(est_tmp) < glob_prec*c(float_abs(array_y1[1])) then
est_tmp := c(glob_prec)*c(float_abs(array_y1[1]))
end if;
if c(array_max_est_error[1]) <= c(est_tmp) then
array_max_est_error[1] := c(est_tmp)
end if;
est_tmp := c(float_abs(array_y2[no_terms - 3]))
+ c(float_abs(array_y2[no_terms - 2]))*c(hn_div_ho)
+ c(float_abs(array_y2[no_terms - 1]))*c(hn_div_ho_2)
+ c(float_abs(array_y2[no_terms]))*c(hn_div_ho_3);
if c(est_tmp) < glob_prec*c(float_abs(array_y2[1])) then
est_tmp := c(glob_prec)*c(float_abs(array_y2[1]))
end if;
if c(array_max_est_error[2]) <= c(est_tmp) then
array_max_est_error[2] := c(est_tmp)
end if
end proc
# End Function number 6
# Begin Function number 7
> reached_interval := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2,
#END CONST
> array_y1_init,
> array_y2_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local ret;
> if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 5
> ret := true;
> else
> ret := false;
> fi;# end if 5;
> return(ret);
> end;
reached_interval := proc()
local ret;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2,
array_y1_init, array_y2_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y1, array_x, array_y2,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
if glob_check_sign*glob_next_display - glob_h/glob__10 <=
glob_check_sign*array_x[1] then ret := true
else ret := false
end if;
return ret
end proc
# End Function number 7
# Begin Function number 8
> display_alot := proc(iter)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2,
#END CONST
> array_y1_init,
> array_y2_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err;
> #TOP DISPLAY ALOT
> ind_var := array_x[1];
> omniout_complex(ALWAYS,"x[1] ",33,ind_var,20," ");
> term_no := 1;
> numeric_val := array_y1[term_no];
> omniout_complex(ALWAYS,"h ",33,glob_h,20," ");
> omniout_complex(ALWAYS,"y1[1] (numeric) ",33,numeric_val,20," ");
> closed_form_val_y := evalf(exact_soln_y1(ind_var));
> omniout_complex(ALWAYS,"y1[1] (closed_form) ",33,closed_form_val_y,20," ");
> abserr := float_abs(numeric_val - closed_form_val_y);
> if (float_abs(closed_form_val_y) > 0.0) then # if number 5
> relerr := abserr/float_abs(closed_form_val_y);
> if (float_abs(c(relerr)) > 0.0) then # if number 6
> glob_good_digits := round(-log10(relerr));
> else
> relerr := 0.0 ;
> glob_good_digits := Digits - 2;
> fi;# end if 6;
> else
> ;
> relerr := glob__m1 ;
> glob_good_digits := -16;
> fi;# end if 5;
> if (glob_good_digits < glob_min_good_digits) then # if number 5
> glob_min_good_digits := glob_good_digits;
> fi;# end if 5;
> omniout_float(ALWAYS,"absolute error ",4,abserr,4," ");
> omniout_float(ALWAYS,"relative error ",4,relerr * glob__100 ,4,"%");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> ;
> term_no := 1;
> numeric_val := array_y2[term_no];
> omniout_complex(ALWAYS,"h ",33,glob_h,20," ");
> omniout_complex(ALWAYS,"y2[1] (numeric) ",33,numeric_val,20," ");
> closed_form_val_y := evalf(exact_soln_y2(ind_var));
> omniout_complex(ALWAYS,"y2[1] (closed_form) ",33,closed_form_val_y,20," ");
> abserr := float_abs(numeric_val - closed_form_val_y);
> if (float_abs(closed_form_val_y) > 0.0) then # if number 5
> relerr := abserr/float_abs(closed_form_val_y);
> if (float_abs(c(relerr)) > 0.0) then # if number 6
> glob_good_digits := round(-log10(relerr));
> else
> relerr := 0.0 ;
> glob_good_digits := Digits - 2;
> fi;# end if 6;
> else
> ;
> relerr := glob__m1 ;
> glob_good_digits := -16;
> fi;# end if 5;
> if (glob_good_digits < glob_min_good_digits) then # if number 5
> glob_min_good_digits := glob_good_digits;
> fi;# end if 5;
> omniout_float(ALWAYS,"absolute error ",4,abserr,4," ");
> omniout_float(ALWAYS,"relative error ",4,relerr * glob__100 ,4,"%");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> #BOTTOM DISPLAY ALOT
> end;
display_alot := proc(iter)
local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no,
est_rel_err;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2,
array_y1_init, array_y2_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y1, array_x, array_y2,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
ind_var := array_x[1];
omniout_complex(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
term_no := 1;
numeric_val := array_y1[term_no];
omniout_complex(ALWAYS, "h ", 33, glob_h,
20, " ");
omniout_complex(ALWAYS, "y1[1] (numeric) ", 33,
numeric_val, 20, " ");
closed_form_val_y := evalf(exact_soln_y1(ind_var));
omniout_complex(ALWAYS, "y1[1] (closed_form) ", 33,
closed_form_val_y, 20, " ");
abserr := float_abs(numeric_val - closed_form_val_y);
if 0. < float_abs(closed_form_val_y) then
relerr := abserr/float_abs(closed_form_val_y);
if 0. < float_abs(c(relerr)) then
glob_good_digits := round(-log10(relerr))
else relerr := 0.; glob_good_digits := Digits - 2
end if
else relerr := glob__m1; glob_good_digits := -16
end if;
if glob_good_digits < glob_min_good_digits then
glob_min_good_digits := glob_good_digits
end if;
omniout_float(ALWAYS, "absolute error ", 4, abserr, 4,
" ");
omniout_float(ALWAYS, "relative error ", 4,
relerr*glob__100, 4, "%");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ");
term_no := 1;
numeric_val := array_y2[term_no];
omniout_complex(ALWAYS, "h ", 33, glob_h,
20, " ");
omniout_complex(ALWAYS, "y2[1] (numeric) ", 33,
numeric_val, 20, " ");
closed_form_val_y := evalf(exact_soln_y2(ind_var));
omniout_complex(ALWAYS, "y2[1] (closed_form) ", 33,
closed_form_val_y, 20, " ");
abserr := float_abs(numeric_val - closed_form_val_y);
if 0. < float_abs(closed_form_val_y) then
relerr := abserr/float_abs(closed_form_val_y);
if 0. < float_abs(c(relerr)) then
glob_good_digits := round(-log10(relerr))
else relerr := 0.; glob_good_digits := Digits - 2
end if
else relerr := glob__m1; glob_good_digits := -16
end if;
if glob_good_digits < glob_min_good_digits then
glob_min_good_digits := glob_good_digits
end if;
omniout_float(ALWAYS, "absolute error ", 4, abserr, 4,
" ");
omniout_float(ALWAYS, "relative error ", 4,
relerr*glob__100, 4, "%");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ")
end proc
# End Function number 8
# Begin Function number 9
> prog_report := proc(x_start,x_end)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2,
#END CONST
> array_y1_init,
> array_y2_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := (clock_sec1) - (glob_orig_start_sec);
> glob_clock_sec := (clock_sec1) - (glob_clock_start_sec);
> left_sec := (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1);
> expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h) ,( clock_sec1) - (glob_orig_start_sec));
> opt_clock_sec := ( clock_sec1) - (glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec));
> glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
> percent_done := comp_percent((x_end),(x_start),(array_x[1]) + (glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr((total_clock_sec));
> if (c(percent_done) < glob__100) then # if number 5
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr((expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr((glob_optimal_expect_sec));
> omniout_str_noeol(INFO,"Expected Total Time ");
> omniout_timestr((glob_total_exp_sec));
> fi;# end if 5;
> #BOTTOM PROGRESS REPORT
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2,
array_y1_init, array_y2_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y1, array_x, array_y2,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec := clock_sec1 - glob_orig_start_sec;
glob_clock_sec := clock_sec1 - glob_clock_start_sec;
left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1;
expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h,
clock_sec1 - glob_orig_start_sec);
opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec;
glob_optimal_expect_sec :=
comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec)
;
glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h);
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(total_clock_sec);
if c(percent_done) < glob__100 then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(expect_sec);
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(glob_optimal_expect_sec);
omniout_str_noeol(INFO, "Expected Total Time ");
omniout_timestr(glob_total_exp_sec)
end if
end proc
# End Function number 9
# Begin Function number 10
> check_for_pole := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2,
#END CONST
> array_y1_init,
> array_y2_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad, last_no;
> #TOP CHECK FOR POLE
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,1] := glob_larger_float;
> array_ord_test_poles[1,1] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_ratio(array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 5
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 5;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 6
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 7
> found_sing := 0;
> fi;# end if 7;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 7
> if (rad_c < array_rad_test_poles[1,1]) then # if number 8
> array_rad_test_poles[1,1] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_ratio(array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
> array_rad_test_poles[1,1] := rad_c;
> array_ord_test_poles[1,1] := tmp_ord;
> fi;# end if 8;
> fi;# end if 7;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[2,1] := glob_larger_float;
> array_ord_test_poles[2,1] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 2 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_ratio(array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 7
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 7;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 8
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 9
> found_sing := 0;
> fi;# end if 9;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 9
> if (rad_c < array_rad_test_poles[2,1]) then # if number 10
> array_rad_test_poles[2,1] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_ratio(array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
> array_rad_test_poles[2,1] := rad_c;
> array_ord_test_poles[2,1] := tmp_ord;
> fi;# end if 10;
> fi;# end if 9;
> #BOTTOM general radius test2
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,2] := glob_larger_float;
> array_ord_test_poles[1,2] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_three_terms(array_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 9
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 9;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 9
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 10
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 11
> found_sing := 0;
> fi;# end if 11;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 11
> if (rad_c < array_rad_test_poles[1,2]) then # if number 12
> array_rad_test_poles[1,2] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_three_terms(array_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
> array_rad_test_poles[1,2] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 13
> glob_min_pole_est := rad_c;
> fi;# end if 13;
> array_ord_test_poles[1,2] := tmp_ord;
> fi;# end if 12;
> fi;# end if 11;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[2,2] := glob_larger_float;
> array_ord_test_poles[2,2] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 2 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_three_terms(array_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 11
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 11;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 11
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 12
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 13
> found_sing := 0;
> fi;# end if 13;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 13
> if (rad_c < array_rad_test_poles[2,2]) then # if number 14
> array_rad_test_poles[2,2] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_three_terms(array_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
> array_rad_test_poles[2,2] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 15
> glob_min_pole_est := rad_c;
> fi;# end if 15;
> array_ord_test_poles[2,2] := tmp_ord;
> fi;# end if 14;
> fi;# end if 13;
> #BOTTOM general radius test2
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,3] := glob_larger_float;
> array_ord_test_poles[1,3] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_six_terms(array_y1_higher[1,last_no-5],array_y1_higher[1,last_no-4],array_y1_higher[1,last_no-3],array_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 13
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 13;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 13
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 14
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 15
> found_sing := 0;
> fi;# end if 15;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 15
> if (rad_c < array_rad_test_poles[1,3]) then # if number 16
> array_rad_test_poles[1,3] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_six_terms(array_y1_higher[1,last_no-5],array_y1_higher[1,last_no-4],array_y1_higher[1,last_no-3],array_y1_higher[1,last_no-2],array_y1_higher[1,last_no-1],array_y1_higher[1,last_no],last_no);
> array_rad_test_poles[1,3] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 17
> glob_min_pole_est := rad_c;
> fi;# end if 17;
> array_ord_test_poles[1,3] := tmp_ord;
> fi;# end if 16;
> fi;# end if 15;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[2,3] := glob_larger_float;
> array_ord_test_poles[2,3] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 2 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_six_terms(array_y2_higher[1,last_no-5],array_y2_higher[1,last_no-4],array_y2_higher[1,last_no-3],array_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 15
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 15;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 15
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 16
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 17
> found_sing := 0;
> fi;# end if 17;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 17
> if (rad_c < array_rad_test_poles[2,3]) then # if number 18
> array_rad_test_poles[2,3] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_six_terms(array_y2_higher[1,last_no-5],array_y2_higher[1,last_no-4],array_y2_higher[1,last_no-3],array_y2_higher[1,last_no-2],array_y2_higher[1,last_no-1],array_y2_higher[1,last_no],last_no);
> array_rad_test_poles[2,3] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 19
> glob_min_pole_est := rad_c;
> fi;# end if 19;
> array_ord_test_poles[2,3] := tmp_ord;
> fi;# end if 18;
> fi;# end if 17;
> #BOTTOM general radius test2
> ;
> if (true) then # if number 17
> display_poles();
> fi;# end if 17
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2,
term3, part1, part2, part3, part4, part5, part6, part7, part8, part9,
part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4,
found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio,
prev_tmp_rad, last_no;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2,
array_y1_init, array_y2_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y1, array_x, array_y2,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 1] := glob_larger_float;
array_ord_test_poles[1, 1] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do
tmp_rad := comp_rad_from_ratio(array_y1_higher[1, last_no - 1],
array_y1_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 1] then
array_rad_test_poles[1, 1] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_ratio(array_y1_higher[1, last_no - 1],
array_y1_higher[1, last_no], last_no);
array_rad_test_poles[1, 1] := rad_c;
array_ord_test_poles[1, 1] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[2, 1] := glob_larger_float;
array_ord_test_poles[2, 1] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 12;
cnt := 0;
while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do
tmp_rad := comp_rad_from_ratio(array_y2_higher[1, last_no - 1],
array_y2_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[2, 1] then
array_rad_test_poles[2, 1] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_ratio(array_y2_higher[1, last_no - 1],
array_y2_higher[1, last_no], last_no);
array_rad_test_poles[2, 1] := rad_c;
array_ord_test_poles[2, 1] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 2] := glob_larger_float;
array_ord_test_poles[1, 2] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do
tmp_rad := comp_rad_from_three_terms(
array_y1_higher[1, last_no - 2],
array_y1_higher[1, last_no - 1], array_y1_higher[1, last_no],
last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 2] then
array_rad_test_poles[1, 2] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_three_terms(
array_y1_higher[1, last_no - 2],
array_y1_higher[1, last_no - 1],
array_y1_higher[1, last_no], last_no);
array_rad_test_poles[1, 2] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 2] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[2, 2] := glob_larger_float;
array_ord_test_poles[2, 2] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 12;
cnt := 0;
while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do
tmp_rad := comp_rad_from_three_terms(
array_y2_higher[1, last_no - 2],
array_y2_higher[1, last_no - 1], array_y2_higher[1, last_no],
last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[2, 2] then
array_rad_test_poles[2, 2] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_three_terms(
array_y2_higher[1, last_no - 2],
array_y2_higher[1, last_no - 1],
array_y2_higher[1, last_no], last_no);
array_rad_test_poles[2, 2] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[2, 2] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 3] := glob_larger_float;
array_ord_test_poles[1, 3] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do
tmp_rad := comp_rad_from_six_terms(array_y1_higher[1, last_no - 5],
array_y1_higher[1, last_no - 4],
array_y1_higher[1, last_no - 3],
array_y1_higher[1, last_no - 2],
array_y1_higher[1, last_no - 1], array_y1_higher[1, last_no],
last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 3] then
array_rad_test_poles[1, 3] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_six_terms(
array_y1_higher[1, last_no - 5],
array_y1_higher[1, last_no - 4],
array_y1_higher[1, last_no - 3],
array_y1_higher[1, last_no - 2],
array_y1_higher[1, last_no - 1],
array_y1_higher[1, last_no], last_no);
array_rad_test_poles[1, 3] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 3] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[2, 3] := glob_larger_float;
array_ord_test_poles[2, 3] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 12;
cnt := 0;
while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do
tmp_rad := comp_rad_from_six_terms(array_y2_higher[1, last_no - 5],
array_y2_higher[1, last_no - 4],
array_y2_higher[1, last_no - 3],
array_y2_higher[1, last_no - 2],
array_y2_higher[1, last_no - 1], array_y2_higher[1, last_no],
last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[2, 3] then
array_rad_test_poles[2, 3] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_six_terms(
array_y2_higher[1, last_no - 5],
array_y2_higher[1, last_no - 4],
array_y2_higher[1, last_no - 3],
array_y2_higher[1, last_no - 2],
array_y2_higher[1, last_no - 1],
array_y2_higher[1, last_no], last_no);
array_rad_test_poles[2, 3] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[2, 3] := tmp_ord
end if
end if;
display_poles()
end proc
# End Function number 10
# Begin Function number 11
> atomall := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2,
#END CONST
> array_y1_init,
> array_y2_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> # before write maple main top matter
> # before generate constants assign
> # before generate globals assign
> #END OUTFILE1
> #BEGIN OUTFILE2
> #END OUTFILE2
> #BEGIN ATOMHDR1
> #emit pre neg FULL $eq_no = 1
> array_tmp1[1] := neg(array_y2[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y1_set_initial[1,2]) then # if number 1
> if (1 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
> if (2 <= ATS_MAX_TERMS) then # if number 3
> array_y1[2] := temporary;
> array_y1_higher[1,2] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(1);
> array_y1_higher[2,1] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #emit pre diff $eq_no = 2 i = 1 order_d = 1
> array_tmp4[1] := array_y1_higher[2,1];
> #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5
> if ( not array_y2_set_initial[2,3]) then # if number 1
> if (1 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp4[1]) * (expt((glob_h) , c(2))) * c(factorial_3(0,2));
> if (3 <= ATS_MAX_TERMS) then # if number 3
> array_y2[3] := temporary;
> array_y2_higher[1,3] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y2_higher[2,2] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(1);
> array_y2_higher[3,1] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre neg FULL $eq_no = 1
> array_tmp1[2] := neg(array_y2[2]);
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y1_set_initial[1,3]) then # if number 1
> if (2 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2));
> if (3 <= ATS_MAX_TERMS) then # if number 3
> array_y1[3] := temporary;
> array_y1_higher[1,3] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y1_higher[2,2] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #emit pre diff $eq_no = 2 i = 2 order_d = 1
> array_tmp4[2] := array_y1_higher[2,2];
> #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5
> if ( not array_y2_set_initial[2,4]) then # if number 1
> if (2 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp4[2]) * (expt((glob_h) , c(2))) * c(factorial_3(1,3));
> 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);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre neg FULL $eq_no = 1
> array_tmp1[3] := neg(array_y2[3]);
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp2[3] := array_tmp1[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y1_set_initial[1,4]) then # if number 1
> if (3 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3));
> if (4 <= ATS_MAX_TERMS) then # if number 3
> array_y1[4] := temporary;
> array_y1_higher[1,4] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y1_higher[2,3] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #emit pre diff $eq_no = 2 i = 3 order_d = 1
> array_tmp4[3] := array_y1_higher[2,3];
> #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5
> if ( not array_y2_set_initial[2,5]) then # if number 1
> if (3 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp4[3]) * (expt((glob_h) , c(2))) * c(factorial_3(2,4));
> 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);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre neg FULL $eq_no = 1
> array_tmp1[4] := neg(array_y2[4]);
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp2[4] := array_tmp1[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y1_set_initial[1,5]) then # if number 1
> if (4 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4));
> if (5 <= ATS_MAX_TERMS) then # if number 3
> array_y1[5] := temporary;
> array_y1_higher[1,5] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y1_higher[2,4] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #emit pre diff $eq_no = 2 i = 4 order_d = 1
> array_tmp4[4] := array_y1_higher[2,4];
> #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5
> if ( not array_y2_set_initial[2,6]) then # if number 1
> if (4 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp4[4]) * (expt((glob_h) , c(2))) * c(factorial_3(3,5));
> 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);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre neg FULL $eq_no = 1
> array_tmp1[5] := neg(array_y2[5]);
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp2[5] := array_tmp1[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y1_set_initial[1,6]) then # if number 1
> if (5 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp2[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5));
> if (6 <= ATS_MAX_TERMS) then # if number 3
> array_y1[6] := temporary;
> array_y1_higher[1,6] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y1_higher[2,5] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #emit pre diff $eq_no = 2 i = 5 order_d = 1
> array_tmp4[5] := array_y1_higher[2,5];
> #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5
> if ( not array_y2_set_initial[2,7]) then # if number 1
> if (5 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp4[5]) * (expt((glob_h) , c(2))) * c(factorial_3(4,6));
> 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);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= ATS_MAX_TERMS) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit neg FULL $eq_no = 1
> array_tmp1[kkk] := neg(array_y2[kkk]);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp2[kkk] := array_tmp1[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1
> if ( not array_y1_set_initial[1,kkk + order_d]) then # if number 2
> temporary := c(array_tmp2[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
> array_y1[kkk + order_d] := c(temporary);
> array_y1_higher[1,kkk + order_d] := c(temporary);
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := c(temporary) / c(glob_h) * c(adj2);
> else
> temporary := c(temporary);
> fi;# end if 4;
> array_y1_higher[adj3,term] := c(temporary);
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 1
> fi;# end if 2
> fi;# end if 1;
> #emit diff $eq_no = 2
> if (kkk <= ATS_MAX_TERMS) then # if number 1
> array_tmp4[kkk] := array_y1_higher[2,kkk];
> fi;# end if 1;
> #emit assign $eq_no = 2
> order_d := 2;
> if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1
> if ( not array_y2_set_initial[2,kkk + order_d]) then # if number 2
> temporary := c(array_tmp4[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
> array_y2[kkk + order_d] := c(temporary);
> array_y2_higher[1,kkk + order_d] := c(temporary);
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := c(temporary) / c(glob_h) * c(adj2);
> else
> temporary := c(temporary);
> fi;# end if 4;
> array_y2_higher[adj3,term] := c(temporary);
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 1
> fi;# end if 2
> fi;# end if 1;
> kkk := kkk + 1;
> od;# end do number 1;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2,
array_y1_init, array_y2_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y1, array_x, array_y2,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
array_tmp1[1] := neg(array_y2[1]);
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
if not array_y1_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
if 2 <= ATS_MAX_TERMS then
array_y1[2] := temporary;
array_y1_higher[1, 2] := temporary
end if;
temporary := c(temporary)*c(1)/c(glob_h);
array_y1_higher[2, 1] := c(temporary)
end if
end if;
kkk := 2;
array_tmp4[1] := array_y1_higher[2, 1];
if not array_y2_set_initial[2, 3] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[1])*expt(glob_h, c(2))*c(factorial_3(0, 2));
if 3 <= ATS_MAX_TERMS then
array_y2[3] := temporary;
array_y2_higher[1, 3] := temporary
end if;
temporary := c(temporary)*c(2)/c(glob_h);
array_y2_higher[2, 2] := c(temporary);
temporary := c(temporary)*c(1)/c(glob_h);
array_y2_higher[3, 1] := c(temporary)
end if
end if;
kkk := 2;
array_tmp1[2] := neg(array_y2[2]);
array_tmp2[2] := array_tmp1[2];
if not array_y1_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
if 3 <= ATS_MAX_TERMS then
array_y1[3] := temporary;
array_y1_higher[1, 3] := temporary
end if;
temporary := c(temporary)*c(2)/c(glob_h);
array_y1_higher[2, 2] := c(temporary)
end if
end if;
kkk := 3;
array_tmp4[2] := array_y1_higher[2, 2];
if not array_y2_set_initial[2, 4] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[2])*expt(glob_h, c(2))*c(factorial_3(1, 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)
end if
end if;
kkk := 3;
array_tmp1[3] := neg(array_y2[3]);
array_tmp2[3] := array_tmp1[3];
if not array_y1_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[3])*expt(glob_h, c(1))*c(factorial_3(2, 3));
if 4 <= ATS_MAX_TERMS then
array_y1[4] := temporary;
array_y1_higher[1, 4] := temporary
end if;
temporary := c(temporary)*c(3)/c(glob_h);
array_y1_higher[2, 3] := c(temporary)
end if
end if;
kkk := 4;
array_tmp4[3] := array_y1_higher[2, 3];
if not array_y2_set_initial[2, 5] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[3])*expt(glob_h, c(2))*c(factorial_3(2, 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)
end if
end if;
kkk := 4;
array_tmp1[4] := neg(array_y2[4]);
array_tmp2[4] := array_tmp1[4];
if not array_y1_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[4])*expt(glob_h, c(1))*c(factorial_3(3, 4));
if 5 <= ATS_MAX_TERMS then
array_y1[5] := temporary;
array_y1_higher[1, 5] := temporary
end if;
temporary := c(temporary)*c(4)/c(glob_h);
array_y1_higher[2, 4] := c(temporary)
end if
end if;
kkk := 5;
array_tmp4[4] := array_y1_higher[2, 4];
if not array_y2_set_initial[2, 6] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[4])*expt(glob_h, c(2))*c(factorial_3(3, 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)
end if
end if;
kkk := 5;
array_tmp1[5] := neg(array_y2[5]);
array_tmp2[5] := array_tmp1[5];
if not array_y1_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp2[5])*expt(glob_h, c(1))*c(factorial_3(4, 5));
if 6 <= ATS_MAX_TERMS then
array_y1[6] := temporary;
array_y1_higher[1, 6] := temporary
end if;
temporary := c(temporary)*c(5)/c(glob_h);
array_y1_higher[2, 5] := c(temporary)
end if
end if;
kkk := 6;
array_tmp4[5] := array_y1_higher[2, 5];
if not array_y2_set_initial[2, 7] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[5])*expt(glob_h, c(2))*c(factorial_3(4, 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)
end if
end if;
kkk := 6;
while kkk <= ATS_MAX_TERMS do
array_tmp1[kkk] := neg(array_y2[kkk]);
array_tmp2[kkk] := array_tmp1[kkk];
order_d := 1;
if kkk + order_d <= ATS_MAX_TERMS then
if not array_y1_set_initial[1, kkk + order_d] then
temporary := c(array_tmp2[kkk])*expt(glob_h, c(order_d))*
c(factorial_3(kkk - 1, kkk + order_d - 1));
array_y1[kkk + order_d] := c(temporary);
array_y1_higher[1, kkk + order_d] := c(temporary);
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while
1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1
do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := c(temporary)*c(adj2)/c(glob_h)
else temporary := c(temporary)
end if;
array_y1_higher[adj3, term] := c(temporary)
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
if kkk <= ATS_MAX_TERMS then
array_tmp4[kkk] := array_y1_higher[2, kkk]
end if;
order_d := 2;
if kkk + order_d <= ATS_MAX_TERMS then
if not array_y2_set_initial[2, kkk + order_d] then
temporary := c(array_tmp4[kkk])*expt(glob_h, c(order_d))*
c(factorial_3(kkk - 1, kkk + order_d - 1));
array_y2[kkk + order_d] := c(temporary);
array_y2_higher[1, kkk + order_d] := c(temporary);
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while
1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1
do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := c(temporary)*c(adj2)/c(glob_h)
else temporary := c(temporary)
end if;
array_y2_higher[adj3, term] := c(temporary)
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
# End Function number 12
#END OUTFILE5
# Begin Function number 12
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it;
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2,
> #END CONST
> array_y1_init,
> array_y2_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y1,
> array_x,
> array_y2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y1_higher,
> array_y1_higher_work,
> array_y1_higher_work2,
> array_y1_set_initial,
> array_y2_higher,
> array_y2_higher_work,
> array_y2_higher_work2,
> array_y2_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> ATS_MAX_TERMS := 30;
> # before first input block
> #BEGIN FIRST INPUT BLOCK
> #BEGIN BLOCK 1
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=30;
> #END BLOCK 1
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> # before generate arrays
> array_y1_init:= Array(0..(30),[]);
> array_y2_init:= Array(0..(30),[]);
> array_norms:= Array(0..(30),[]);
> array_fact_1:= Array(0..(30),[]);
> array_1st_rel_error:= Array(0..(3),[]);
> array_last_rel_error:= Array(0..(3),[]);
> array_est_rel_error:= Array(0..(3),[]);
> array_max_est_error:= Array(0..(3),[]);
> array_type_pole:= Array(0..(3),[]);
> array_type_real_pole:= Array(0..(3),[]);
> array_type_complex_pole:= Array(0..(3),[]);
> array_est_digits:= Array(0..(3),[]);
> array_y1:= Array(0..(30),[]);
> array_x:= Array(0..(30),[]);
> array_y2:= Array(0..(30),[]);
> array_tmp0:= Array(0..(30),[]);
> array_tmp1:= Array(0..(30),[]);
> array_tmp2:= Array(0..(30),[]);
> array_tmp3:= Array(0..(30),[]);
> array_tmp4:= Array(0..(30),[]);
> array_m1:= Array(0..(30),[]);
> array_y1_higher := Array(0..(2) ,(0..30+ 1),[]);
> array_y1_higher_work := Array(0..(2) ,(0..30+ 1),[]);
> array_y1_higher_work2 := Array(0..(2) ,(0..30+ 1),[]);
> array_y1_set_initial := Array(0..(3) ,(0..30+ 1),[]);
> array_y2_higher := Array(0..(3) ,(0..30+ 1),[]);
> array_y2_higher_work := Array(0..(3) ,(0..30+ 1),[]);
> array_y2_higher_work2 := Array(0..(3) ,(0..30+ 1),[]);
> array_y2_set_initial := Array(0..(3) ,(0..30+ 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..(30) ,(0..30+ 1),[]);
> # before generate constants
> # before generate globals definition
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> # before generate const definition
> # before arrays initialized
> term := 1;
> while (term <= 30) do # do number 1
> array_y1_init[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_y2_init[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_norms[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_fact_1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 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 <= 30) do # do number 1
> array_y1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_x[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_y2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp0[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp3[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp4[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_m1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_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 <= 30) 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 <= 30) 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 <= 30) 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 <= 30) 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 <=3) do # do number 1
> term := 1;
> while (term <= 30) 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 <=3) do # do number 1
> term := 1;
> while (term <= 30) 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 <= 30) do # do number 2
> array_y2_set_initial[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_rad_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_ord_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_rad_test_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_ord_test_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=30) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_fact_2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> # before symbols initialized
> #BEGIN SYMBOLS INITIALIZATED
> zero_ats_ar(array_y1);
> zero_ats_ar(array_x);
> zero_ats_ar(array_y2);
> zero_ats_ar(array_tmp0);
> zero_ats_ar(array_tmp1);
> zero_ats_ar(array_tmp2);
> zero_ats_ar(array_tmp3);
> zero_ats_ar(array_tmp4);
> zero_ats_ar(array_m1);
> zero_ats_ar(array_const_1);
> array_const_1[1] := c(1);
> zero_ats_ar(array_const_0D0);
> array_const_0D0[1] := c(0.0);
> zero_ats_ar(array_const_2);
> array_const_2[1] := c(2);
> zero_ats_ar(array_m1);
> array_m1[1] := glob__m1;
> #END SYMBOLS INITIALIZATED
> # before generate factorials init
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= ATS_MAX_TERMS) do # do number 1
> jjjf := 0;
> while (jjjf <= ATS_MAX_TERMS) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Table
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> glob_yes_pole := 4;
> glob_no_pole := 3;
> glob_not_given := 0;
> glob_no_sing_tests := 4;
> glob_ratio_test := 1;
> glob_three_term_test := 2;
> glob_six_term_test := 3;
> glob_log_10 := log(c(10.0));
> MAX_UNCHANGED := 10;
> glob__small := c(0.1e-50);
> glob_small_float := c(0.1e-50);
> glob_smallish_float := c(0.1e-60);
> glob_large_float := c(1.0e100);
> glob_larger_float := c(1.1e100);
> glob__m2 := c(-2);
> glob__m1 := c(-1);
> glob__0 := c(0);
> glob__1 := c(1);
> glob__2 := c(2);
> glob__3 := c(3);
> glob__4 := c(4);
> glob__5 := c(5);
> glob__8 := c(8);
> glob__10 := c(10);
> glob__100 := c(100);
> glob__pi := c(0.0);
> glob__0_5 := c(0.5);
> glob__0_8 := c(0.8);
> glob__m0_8 := c(-0.8);
> glob__0_25 := c(0.25);
> glob__0_125 := c(0.125);
> glob_h := 0.1;
> glob_nxt := 1;
> glob_prec := c(1.0e-16);
> glob_check_sign := c(1.0);
> glob_desired_digits_correct := c(8.0);
> glob_max_estimated_step_error := c(0.0);
> glob_ratio_of_radius := c(0.1);
> glob_percent_done := c(0.0);
> glob_total_exp_sec := c(0.1);
> glob_optimal_expect_sec := c(0.1);
> glob_estimated_size_answer := c(100.0);
> glob_almost_1 := c(0.9990);
> glob_clock_sec := c(0.0);
> glob_clock_start_sec := c(0.0);
> glob_disp_incr := c(0.1);
> glob_diff_rc_fm := c(0.1);
> glob_diff_rc_fmm1 := c(0.1);
> glob_diff_rc_fmm2 := c(0.1);
> glob_diff_ord_fm := c(0.1);
> glob_diff_ord_fmm1 := c(0.1);
> glob_diff_ord_fmm2 := c(0.1);
> glob_six_term_ord_save := c(0.1);
> glob_guess_error_rc := c(0.1);
> glob_guess_error_ord := c(0.1);
> glob_least_given_sing := c(9.9e200);
> glob_least_ratio_sing := c(9.9e200);
> glob_least_3_sing := c(9.9e100);
> glob_least_6_sing := c(9.9e100);
> glob_last_good_h := c(0.1);
> glob_max_h := c(0.1);
> glob_min_h := c(0.000001);
> glob_display_interval := c(0.1);
> glob_abserr := c(0.1e-10);
> glob_relerr := c(0.1e-10);
> glob_min_pole_est := c(0.1e+10);
> glob_max_rel_trunc_err := c(0.1e-10);
> glob_max_trunc_err := c(0.1e-10);
> glob_max_hours := c(0.0);
> glob_optimal_clock_start_sec := c(0.0);
> glob_optimal_start := c(0.0);
> glob_upper_ratio_limit := c(1.0001);
> glob_lower_ratio_limit := c(0.9999);
> glob_max_sec := c(10000.0);
> glob_orig_start_sec := c(0.0);
> glob_normmax := c(0.0);
> glob_max_minutes := c(0.0);
> glob_next_display := c(0.0);
> glob_est_digits := 1;
> glob_subiter_method := 3;
> glob_html_log := true;
> glob_min_good_digits := 99999;
> glob_good_digits := 0;
> glob_min_apfp_est_good_digits := 99999;
> glob_apfp_est_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> glob_h_reason := 0;
> glob_sec_in_minute := 60 ;
> glob_min_in_hour := 60;
> glob_hours_in_day := 24;
> glob_days_in_year := 365;
> glob_sec_in_hour := 3600;
> glob_sec_in_day := 86400;
> glob_sec_in_year := 31536000;
> glob_not_yet_finished := true;
> glob_initial_pass := true;
> glob_not_yet_start_msg := true;
> glob_reached_optimal_h := false;
> glob_optimal_done := false;
> glob_type_given_pole := 0;
> glob_optimize := false;
> glob_look_poles := false;
> glob_dump_closed_form := false;
> glob_max_iter := 10000;
> glob_no_eqs := 0;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_start := 0;
> glob_iter := 0;
> # before generate set diff initial
> array_y1_set_initial[1,1] := true;
> array_y1_set_initial[1,2] := false;
> array_y1_set_initial[1,3] := false;
> array_y1_set_initial[1,4] := false;
> array_y1_set_initial[1,5] := false;
> array_y1_set_initial[1,6] := false;
> array_y1_set_initial[1,7] := false;
> array_y1_set_initial[1,8] := false;
> array_y1_set_initial[1,9] := false;
> array_y1_set_initial[1,10] := false;
> array_y1_set_initial[1,11] := false;
> array_y1_set_initial[1,12] := false;
> array_y1_set_initial[1,13] := false;
> array_y1_set_initial[1,14] := false;
> array_y1_set_initial[1,15] := false;
> array_y1_set_initial[1,16] := false;
> array_y1_set_initial[1,17] := false;
> array_y1_set_initial[1,18] := false;
> array_y1_set_initial[1,19] := false;
> array_y1_set_initial[1,20] := false;
> array_y1_set_initial[1,21] := false;
> array_y1_set_initial[1,22] := false;
> array_y1_set_initial[1,23] := false;
> array_y1_set_initial[1,24] := false;
> array_y1_set_initial[1,25] := false;
> array_y1_set_initial[1,26] := false;
> array_y1_set_initial[1,27] := false;
> array_y1_set_initial[1,28] := false;
> array_y1_set_initial[1,29] := false;
> array_y1_set_initial[1,30] := false;
> array_y2_set_initial[2,1] := true;
> array_y2_set_initial[2,2] := true;
> array_y2_set_initial[2,3] := false;
> array_y2_set_initial[2,4] := false;
> array_y2_set_initial[2,5] := false;
> array_y2_set_initial[2,6] := false;
> array_y2_set_initial[2,7] := false;
> array_y2_set_initial[2,8] := false;
> array_y2_set_initial[2,9] := false;
> array_y2_set_initial[2,10] := false;
> array_y2_set_initial[2,11] := false;
> array_y2_set_initial[2,12] := false;
> array_y2_set_initial[2,13] := false;
> array_y2_set_initial[2,14] := false;
> array_y2_set_initial[2,15] := false;
> array_y2_set_initial[2,16] := false;
> array_y2_set_initial[2,17] := false;
> array_y2_set_initial[2,18] := false;
> array_y2_set_initial[2,19] := false;
> array_y2_set_initial[2,20] := false;
> array_y2_set_initial[2,21] := false;
> array_y2_set_initial[2,22] := false;
> array_y2_set_initial[2,23] := false;
> array_y2_set_initial[2,24] := false;
> array_y2_set_initial[2,25] := false;
> array_y2_set_initial[2,26] := false;
> array_y2_set_initial[2,27] := false;
> array_y2_set_initial[2,28] := false;
> array_y2_set_initial[2,29] := false;
> array_y2_set_initial[2,30] := false;
> # before generate init omniout const
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> ATS_MAX_TERMS := 30;
> glob_iolevel := INFO;
> # set default block
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> glob_display_flag := true;
> glob_no_eqs := 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/mtest5postcpx.cpx#################");
> omniout_str(ALWAYS,"diff ( y1 , x , 1 ) = neg ( y2 ) ; ");
> omniout_str(ALWAYS,"diff ( y2 , x , 2 ) = diff ( y1 , x , 1 ) ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := 0.5 + 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,"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_y1 := proc(x)");
> omniout_str(ALWAYS,"return(neg(cos(c(x))));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2 := proc(x)");
> omniout_str(ALWAYS,"return(neg(sin(c(x))));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_y2p := proc(x)");
> omniout_str(ALWAYS,"return(neg(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 := 0.5 + 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);
> glob_look_poles := true;
> glob_type_given_pole := 3;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=8;
> glob_max_minutes:=(3.0);
> glob_subiter_method:=3;
> glob_max_iter:=10000;
> glob_upper_ratio_limit:=c(1.000001);
> glob_lower_ratio_limit:=c(0.999999);
> glob_look_poles:=true;
> glob_h:=c(0.001);
> glob_display_interval:=c(0.01);
> #END OVERRIDE BLOCK
> #END BLOCK 2
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_sec := (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours);
> # after second input block
> found_h := true;
> glob_h := next_delta();
> #START ADJUST ALL SERIES
> if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 17
> h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius;
> omniout_str(ALWAYS,"SETTING H FOR POLE");
> glob_h_reason := 6;
> if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 18
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> h_new := glob_min_h;
> glob_h_reason := 5;
> fi;# end if 18;
> term := 1;
> ratio := c(1.0);
> while (term <= ATS_MAX_TERMS) do # do number 1
> array_y1[term] := array_y1[term]* ratio;
> array_y1_higher[1,term] := array_y1_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> array_y2[term] := array_y2[term]* ratio;
> array_y2_higher[1,term] := array_y2_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / float_abs(glob_h);
> term := term + 1;
> od;# end do number 1;
> glob_h := h_new;
> fi;# end if 17;
> #BOTTOM ADJUST ALL SERIES
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 17
> html_log_file := fopen("entry.html",WRITE,TEXT);
> fi;# end if 17;
> #BEGIN SOLUTION CODE
> found_h := true;
> if (found_h) then # if number 17
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := c(x_start);
> array_x[2] := c(glob_h);
> glob_next_display := c(x_start);
> glob_min_pole_est := glob_larger_float;
> glob_least_given_sing := glob_larger_float;
> glob_least_ratio_sing := glob_larger_float;
> glob_least_3_sing := glob_larger_float;
> glob_least_6_sing := glob_larger_float;
> order_diff := 1;
> #Start Series array_y1
> term_no := 1;
> while (term_no <= order_diff) do # do number 1
> array_y1[term_no] := array_y1_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1));
> term_no := term_no + 1;
> od;# end do number 1;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 1
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 2
> it := term_no + r_order - 1;
> if (term_no < ATS_MAX_TERMS) then # if number 18
> array_y1_higher[r_order,term_no] := array_y1_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 18;
> term_no := term_no + 1;
> od;# end do number 2;
> r_order := r_order + 1;
> od;# end do number 1
> ;
> order_diff := 2;
> #Start Series array_y2
> term_no := 1;
> while (term_no <= order_diff) do # do number 1
> array_y2[term_no] := array_y2_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1));
> term_no := term_no + 1;
> od;# end do number 1;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 1
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 2
> it := term_no + r_order - 1;
> if (term_no < ATS_MAX_TERMS) then # if number 18
> array_y2_higher[r_order,term_no] := array_y2_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 18;
> term_no := term_no + 1;
> od;# end do number 2;
> r_order := r_order + 1;
> od;# end do number 1
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> glob_clock_sec := elapsed_time_seconds();
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> found_h := true;
> glob_h := next_delta();
> #START ADJUST ALL SERIES
> if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 18
> h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius;
> omniout_str(ALWAYS,"SETTING H FOR POLE");
> glob_h_reason := 6;
> if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 19
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> h_new := glob_min_h;
> glob_h_reason := 5;
> fi;# end if 19;
> term := 1;
> ratio := c(1.0);
> while (term <= ATS_MAX_TERMS) do # do number 1
> array_y1[term] := array_y1[term]* ratio;
> array_y1_higher[1,term] := array_y1_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> array_y2[term] := array_y2[term]* ratio;
> array_y2_higher[1,term] := array_y2_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / float_abs(glob_h);
> term := term + 1;
> od;# end do number 1;
> glob_h := h_new;
> fi;# end if 18;
> #BOTTOM ADJUST ALL SERIES
> #END OPTIMIZE CODE
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_iter < glob_max_iter) and ((glob_iter < 10) or ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0))))) do # do number 1
> #left paren 0001C
> if (true) then # if number 18
> omniout_str(INFO," ");
> fi;# end if 18;
> found_h := true;
> glob_h := next_delta();
> #START ADJUST ALL SERIES
> if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 18
> h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius;
> omniout_str(ALWAYS,"SETTING H FOR POLE");
> glob_h_reason := 6;
> if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 19
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> h_new := glob_min_h;
> glob_h_reason := 5;
> fi;# end if 19;
> term := 1;
> ratio := c(1.0);
> while (term <= ATS_MAX_TERMS) do # do number 2
> array_y1[term] := array_y1[term]* ratio;
> array_y1_higher[1,term] := array_y1_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> array_y2[term] := array_y2[term]* ratio;
> array_y2_higher[1,term] := array_y2_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / float_abs(glob_h);
> term := term + 1;
> od;# end do number 2;
> glob_h := h_new;
> fi;# end if 18;
> #BOTTOM ADJUST ALL SERIES
> #END OPTIMIZE CODE
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> if (glob_subiter_method = 1 ) then # if number 18
> atomall();
> elif
> (glob_subiter_method = 2 ) then # if number 19
> subiter := 1;
> while (subiter <= 3) do # do number 2
> atomall();
> subiter := subiter + 1;
> od;# end do number 2;
> else
> subiter := 1;
> while (subiter <= 3 + ATS_MAX_TERMS) do # do number 2
> atomall();
> subiter := subiter + 1;
> od;# end do number 2;
> fi;# end if 19;
> if ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0))) then # if number 19
> display_alot(current_iter);
> fi;# end if 19;
> if ((glob_look_poles) and ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0)))) then # if number 19
> check_for_pole();
> fi;# end if 19;
> if (true) then # if number 19
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 19;
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y1;
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y1
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y1_higher_work[2,iii] := array_y1_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y1
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y1
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y1
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y1
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y1_higher_work[1,iii] := array_y1_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y1
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y1_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := ATS_MAX_TERMS;
> while (term_no >= 1) do # do number 2
> array_y1[term_no] := array_y1_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 3
> array_y1_higher[ord,term_no] := array_y1_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 3;
> term_no := term_no - 1;
> od;# end do number 2;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> #Jump Series array_y2;
> order_diff := 3;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =2
> #sum_and_adjust array_y2
> #BEFORE ADJUST SUBSERIES EQ =2
> 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 =2
> #BEFORE SUM SUBSERIES EQ =2
> 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 =2
> #BEFORE ADJUST SUBSERIES EQ =2
> 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 =2
> #BEFORE SUM SUBSERIES EQ =2
> 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 =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[2,iii] := array_y2_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := glob__0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 1;
> calc_term := 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 =2
> #BEFORE SUM SUBSERIES EQ =2
> 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 =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := glob__0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y2_higher_work[1,iii] := array_y2_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =2
> #BEFORE SUM SUBSERIES EQ =2
> temp_sum := glob__0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y2_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =2
> #END SUM AND ADJUST EQ =2
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := ATS_MAX_TERMS;
> while (term_no >= 1) do # do number 2
> array_y2[term_no] := array_y2_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 3
> array_y2_higher[ord,term_no] := array_y2_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 3;
> term_no := term_no - 1;
> od;# end do number 2;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> ;
> od;# end do number 1;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 19
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 19;
> if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec )) then # if number 19
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 19;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y1 , x , 1 ) = neg ( y2 ) ; ");
> omniout_str(INFO,"diff ( y2 , x , 2 ) = diff ( y1 , x , 1 ) ; ");
> 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,"2017-11-26T15:36:18-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"mtest5")
> ;
> logitem_str(html_log_file,"diff ( y1 , x , 1 ) = neg ( y2 ) ; ")
> ;
> logitem_complex(html_log_file,x_start)
> ;
> logitem_complex(html_log_file,x_end)
> ;
> logitem_complex(html_log_file,array_x[1])
> ;
> logitem_complex(html_log_file,glob_h)
> ;
> logitem_h_reason(html_log_file)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> glob_desired_digits_correct := 0.0;
> logitem_float(html_log_file,glob_desired_digits_correct)
> ;
> if (array_est_digits[1] <> -16) then # if number 20
> logitem_integer(html_log_file,array_est_digits[1])
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 20;
> if (glob_min_good_digits <> -16) then # if number 20
> logitem_integer(html_log_file,glob_min_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 20;
> if (glob_good_digits <> -16) then # if number 20
> logitem_integer(html_log_file,glob_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 20;
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> logitem_integer(html_log_file,ATS_MAX_TERMS)
> ;
> if (glob_type_given_pole = 0) then # if number 20
> logitem_str(html_log_file,"Not Given")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 4) then # if number 21
> logitem_str(html_log_file,"No Solution")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 5) then # if number 22
> logitem_str(html_log_file,"Some Pole")
> ;
> logitem_str(html_log_file,"????")
> ;
> elif
> (glob_type_given_pole = 3) then # if number 23
> logitem_str(html_log_file,"No Pole")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 1) then # if number 24
> logitem_str(html_log_file,"Real Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> elif
> (glob_type_given_pole = 2) then # if number 25
> logitem_str(html_log_file,"Complex Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> fi;# end if 25;
> if (glob_least_ratio_sing < glob_large_float) then # if number 25
> glob_least_ratio_sing := 0;
> logitem_float(html_log_file,glob_least_ratio_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 25;
> if (glob_least_3_sing < glob_large_float) then # if number 25
> logitem_float(html_log_file,glob_least_3_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 25;
> if (glob_least_6_sing < glob_large_float) then # if number 25
> glob_least_6_sing := 0.0;
> logitem_float(html_log_file,glob_least_6_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 25;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_time(html_log_file,(glob_clock_sec))
> ;
> if (c(glob_percent_done) < glob__100) then # if number 25
> logitem_time(html_log_file,(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 25;
> log_revs(html_log_file," 309 | ")
> ;
> logitem_str(html_log_file,"mtest5 diffeq.mxt")
> ;
> logitem_str(html_log_file,"mtest5 maple results")
> ;
> logitem_str(html_log_file,"Poor Accuracy - Not sure of algorithm for multiple equations")
> ;
> logend(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logitem_str(html_log_file,"diff ( y2 , x , 2 ) = diff ( y1 , x , 1 ) ; ")
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> ;
> glob_desired_digits_correct := 0.0;
> logditto(html_log_file)
> ;
> if (array_est_digits[2] <> -16) then # if number 25
> logitem_integer(html_log_file,array_est_digits[2])
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 25;
> if (glob_min_good_digits <> -16) then # if number 25
> logitem_integer(html_log_file,glob_min_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 25;
> if (glob_good_digits <> -16) then # if number 25
> logitem_integer(html_log_file,glob_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 25;
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> logditto(html_log_file)
> ;
> if (glob_type_given_pole = 0) then # if number 25
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> elif
> (glob_type_given_pole = 4) then # if number 26
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> elif
> (glob_type_given_pole = 5) then # if number 27
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> elif
> (glob_type_given_pole = 3) then # if number 28
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> elif
> (glob_type_given_pole = 1) then # if number 29
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> elif
> (glob_type_given_pole = 2) then # if number 30
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> fi;# end if 30;
> if (glob_least_ratio_sing < glob_large_float) then # if number 30
> glob_least_ratio_sing := 0;
> logditto(html_log_file)
> ;
> else
> logditto(html_log_file)
> ;
> fi;# end if 30;
> if (glob_least_3_sing < glob_large_float) then # if number 30
> logditto(html_log_file)
> ;
> else
> logditto(html_log_file)
> ;
> fi;# end if 30;
> if (glob_least_6_sing < glob_large_float) then # if number 30
> glob_least_6_sing := 0.0;
> logditto(html_log_file)
> ;
> else
> logditto(html_log_file)
> ;
> fi;# end if 30;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> if (c(glob_percent_done) < glob__100) then # if number 30
> logditto(html_log_file)
> ;
> 0;
> else
> logditto(html_log_file)
> ;
> 0;
> fi;# end if 30;
> logditto(html_log_file);
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logditto(html_log_file)
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 29;
> if (glob_html_log) then # if number 29
> fclose(html_log_file);
> fi;# end if 29
> ;
> ;;
> end;
> # End Function number 12
> #END OUTFILEMAIN
> end;
Warning, `h_new` is implicitly declared local to procedure `main`
Warning, `ratio` is implicitly declared local to procedure `main`
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max,
term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order,
sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it,
last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err,
estimated_step_error, min_value, est_answer, found_h, repeat_it, h_new,
ratio;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2,
array_y1_init, array_y2_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y1, array_x, array_y2,
array_tmp0, array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_m1,
array_y1_higher, array_y1_higher_work, array_y1_higher_work2,
array_y1_set_initial, array_y2_higher, array_y2_higher_work,
array_y2_higher_work2, array_y2_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
ATS_MAX_TERMS := 30;
Digits := 32;
max_terms := 30;
glob_html_log := true;
array_y1_init := Array(0 .. 30, []);
array_y2_init := Array(0 .. 30, []);
array_norms := Array(0 .. 30, []);
array_fact_1 := Array(0 .. 30, []);
array_1st_rel_error := Array(0 .. 3, []);
array_last_rel_error := Array(0 .. 3, []);
array_est_rel_error := Array(0 .. 3, []);
array_max_est_error := Array(0 .. 3, []);
array_type_pole := Array(0 .. 3, []);
array_type_real_pole := Array(0 .. 3, []);
array_type_complex_pole := Array(0 .. 3, []);
array_est_digits := Array(0 .. 3, []);
array_y1 := Array(0 .. 30, []);
array_x := Array(0 .. 30, []);
array_y2 := Array(0 .. 30, []);
array_tmp0 := Array(0 .. 30, []);
array_tmp1 := Array(0 .. 30, []);
array_tmp2 := Array(0 .. 30, []);
array_tmp3 := Array(0 .. 30, []);
array_tmp4 := Array(0 .. 30, []);
array_m1 := Array(0 .. 30, []);
array_y1_higher := Array(0 .. 2, 0 .. 31, []);
array_y1_higher_work := Array(0 .. 2, 0 .. 31, []);
array_y1_higher_work2 := Array(0 .. 2, 0 .. 31, []);
array_y1_set_initial := Array(0 .. 3, 0 .. 31, []);
array_y2_higher := Array(0 .. 3, 0 .. 31, []);
array_y2_higher_work := Array(0 .. 3, 0 .. 31, []);
array_y2_higher_work2 := Array(0 .. 3, 0 .. 31, []);
array_y2_set_initial := Array(0 .. 3, 0 .. 31, []);
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 .. 30, 0 .. 31, []);
term := 1;
while term <= 30 do array_y1_init[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 30 do array_y2_init[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 30 do array_norms[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 30 do array_fact_1[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 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 <= 30 do array_y1[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_x[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_y2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp0[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp1[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp3[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp4[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_m1[term] := c(0.); term := term + 1 end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 do
array_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 <= 30 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 <= 30 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 <= 30 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 <= 30 do
array_y2_higher[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 30 do
array_y2_higher_work[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 30 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 <= 30 do
array_y2_set_initial[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 3 do
array_given_rad_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 3 do
array_given_ord_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 4 do
array_rad_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 4 do
array_ord_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 30 do
term := 1;
while term <= 30 do
array_fact_2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
zero_ats_ar(array_y1);
zero_ats_ar(array_x);
zero_ats_ar(array_y2);
zero_ats_ar(array_tmp0);
zero_ats_ar(array_tmp1);
zero_ats_ar(array_tmp2);
zero_ats_ar(array_tmp3);
zero_ats_ar(array_tmp4);
zero_ats_ar(array_m1);
zero_ats_ar(array_const_1);
array_const_1[1] := c(1);
zero_ats_ar(array_const_0D0);
array_const_0D0[1] := c(0.);
zero_ats_ar(array_const_2);
array_const_2[1] := c(2);
zero_ats_ar(array_m1);
array_m1[1] := glob__m1;
iiif := 0;
while iiif <= ATS_MAX_TERMS do
jjjf := 0;
while jjjf <= ATS_MAX_TERMS do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
glob_yes_pole := 4;
glob_no_pole := 3;
glob_not_given := 0;
glob_no_sing_tests := 4;
glob_ratio_test := 1;
glob_three_term_test := 2;
glob_six_term_test := 3;
glob_log_10 := log(c(10.0));
MAX_UNCHANGED := 10;
glob__small := c(0.1*10^(-50));
glob_small_float := c(0.1*10^(-50));
glob_smallish_float := c(0.1*10^(-60));
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob__m2 := c(-2);
glob__m1 := c(-1);
glob__0 := c(0);
glob__1 := c(1);
glob__2 := c(2);
glob__3 := c(3);
glob__4 := c(4);
glob__5 := c(5);
glob__8 := c(8);
glob__10 := c(10);
glob__100 := c(100);
glob__pi := c(0.);
glob__0_5 := c(0.5);
glob__0_8 := c(0.8);
glob__m0_8 := c(-0.8);
glob__0_25 := c(0.25);
glob__0_125 := c(0.125);
glob_h := 0.1;
glob_nxt := 1;
glob_prec := c(0.10*10^(-15));
glob_check_sign := c(1.0);
glob_desired_digits_correct := c(8.0);
glob_max_estimated_step_error := c(0.);
glob_ratio_of_radius := c(0.1);
glob_percent_done := c(0.);
glob_total_exp_sec := c(0.1);
glob_optimal_expect_sec := c(0.1);
glob_estimated_size_answer := c(100.0);
glob_almost_1 := c(0.9990);
glob_clock_sec := c(0.);
glob_clock_start_sec := c(0.);
glob_disp_incr := c(0.1);
glob_diff_rc_fm := c(0.1);
glob_diff_rc_fmm1 := c(0.1);
glob_diff_rc_fmm2 := c(0.1);
glob_diff_ord_fm := c(0.1);
glob_diff_ord_fmm1 := c(0.1);
glob_diff_ord_fmm2 := c(0.1);
glob_six_term_ord_save := c(0.1);
glob_guess_error_rc := c(0.1);
glob_guess_error_ord := c(0.1);
glob_least_given_sing := c(0.99*10^201);
glob_least_ratio_sing := c(0.99*10^201);
glob_least_3_sing := c(0.99*10^101);
glob_least_6_sing := c(0.99*10^101);
glob_last_good_h := c(0.1);
glob_max_h := c(0.1);
glob_min_h := c(0.1*10^(-5));
glob_display_interval := c(0.1);
glob_abserr := c(0.1*10^(-10));
glob_relerr := c(0.1*10^(-10));
glob_min_pole_est := c(0.1*10^10);
glob_max_rel_trunc_err := c(0.1*10^(-10));
glob_max_trunc_err := c(0.1*10^(-10));
glob_max_hours := c(0.);
glob_optimal_clock_start_sec := c(0.);
glob_optimal_start := c(0.);
glob_upper_ratio_limit := c(1.0001);
glob_lower_ratio_limit := c(0.9999);
glob_max_sec := c(10000.0);
glob_orig_start_sec := c(0.);
glob_normmax := c(0.);
glob_max_minutes := c(0.);
glob_next_display := c(0.);
glob_est_digits := 1;
glob_subiter_method := 3;
glob_html_log := true;
glob_min_good_digits := 99999;
glob_good_digits := 0;
glob_min_apfp_est_good_digits := 99999;
glob_apfp_est_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
glob_h_reason := 0;
glob_sec_in_minute := 60;
glob_min_in_hour := 60;
glob_hours_in_day := 24;
glob_days_in_year := 365;
glob_sec_in_hour := 3600;
glob_sec_in_day := 86400;
glob_sec_in_year := 31536000;
glob_not_yet_finished := true;
glob_initial_pass := true;
glob_not_yet_start_msg := true;
glob_reached_optimal_h := false;
glob_optimal_done := false;
glob_type_given_pole := 0;
glob_optimize := false;
glob_look_poles := false;
glob_dump_closed_form := false;
glob_max_iter := 10000;
glob_no_eqs := 0;
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_start := 0;
glob_iter := 0;
array_y1_set_initial[1, 1] := true;
array_y1_set_initial[1, 2] := false;
array_y1_set_initial[1, 3] := false;
array_y1_set_initial[1, 4] := false;
array_y1_set_initial[1, 5] := false;
array_y1_set_initial[1, 6] := false;
array_y1_set_initial[1, 7] := false;
array_y1_set_initial[1, 8] := false;
array_y1_set_initial[1, 9] := false;
array_y1_set_initial[1, 10] := false;
array_y1_set_initial[1, 11] := false;
array_y1_set_initial[1, 12] := false;
array_y1_set_initial[1, 13] := false;
array_y1_set_initial[1, 14] := false;
array_y1_set_initial[1, 15] := false;
array_y1_set_initial[1, 16] := false;
array_y1_set_initial[1, 17] := false;
array_y1_set_initial[1, 18] := false;
array_y1_set_initial[1, 19] := false;
array_y1_set_initial[1, 20] := false;
array_y1_set_initial[1, 21] := false;
array_y1_set_initial[1, 22] := false;
array_y1_set_initial[1, 23] := false;
array_y1_set_initial[1, 24] := false;
array_y1_set_initial[1, 25] := false;
array_y1_set_initial[1, 26] := false;
array_y1_set_initial[1, 27] := false;
array_y1_set_initial[1, 28] := false;
array_y1_set_initial[1, 29] := false;
array_y1_set_initial[1, 30] := false;
array_y2_set_initial[2, 1] := true;
array_y2_set_initial[2, 2] := true;
array_y2_set_initial[2, 3] := false;
array_y2_set_initial[2, 4] := false;
array_y2_set_initial[2, 5] := false;
array_y2_set_initial[2, 6] := false;
array_y2_set_initial[2, 7] := false;
array_y2_set_initial[2, 8] := false;
array_y2_set_initial[2, 9] := false;
array_y2_set_initial[2, 10] := false;
array_y2_set_initial[2, 11] := false;
array_y2_set_initial[2, 12] := false;
array_y2_set_initial[2, 13] := false;
array_y2_set_initial[2, 14] := false;
array_y2_set_initial[2, 15] := false;
array_y2_set_initial[2, 16] := false;
array_y2_set_initial[2, 17] := false;
array_y2_set_initial[2, 18] := false;
array_y2_set_initial[2, 19] := false;
array_y2_set_initial[2, 20] := false;
array_y2_set_initial[2, 21] := false;
array_y2_set_initial[2, 22] := false;
array_y2_set_initial[2, 23] := false;
array_y2_set_initial[2, 24] := false;
array_y2_set_initial[2, 25] := false;
array_y2_set_initial[2, 26] := false;
array_y2_set_initial[2, 27] := false;
array_y2_set_initial[2, 28] := false;
array_y2_set_initial[2, 29] := false;
array_y2_set_initial[2, 30] := false;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
ATS_MAX_TERMS := 30;
glob_iolevel := INFO;
glob_orig_start_sec := elapsed_time_seconds();
glob_display_flag := true;
glob_no_eqs := 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/mtest5postcpx.cpx#################");
omniout_str(ALWAYS, "diff ( y1 , x , 1 ) = neg ( y2 ) ; ")
;
omniout_str(ALWAYS,
"diff ( y2 , x , 2 ) = diff ( y1 , x , 1 ) ; ");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := 0.5 + 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, "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_y1 := proc(x)");
omniout_str(ALWAYS, "return(neg(cos(c(x))));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2 := proc(x)");
omniout_str(ALWAYS, "return(neg(sin(c(x))));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_y2p := proc(x)");
omniout_str(ALWAYS, "return(neg(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,");
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omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 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(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob_almost_1 := c(0.99);
x_start := 0.5 + 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);
glob_look_poles := true;
glob_type_given_pole := 3;
glob_desired_digits_correct := 8;
glob_max_minutes := 3.0;
glob_subiter_method := 3;
glob_max_iter := 10000;
glob_upper_ratio_limit := c(1.000001);
glob_lower_ratio_limit := c(0.999999);
glob_look_poles := true;
glob_h := c(0.001);
glob_display_interval := c(0.01);
glob_last_good_h := glob_h;
glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours;
found_h := true;
glob_h := next_delta();
if
float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h)
then
h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius;
omniout_str(ALWAYS, "SETTING H FOR POLE");
glob_h_reason := 6;
if glob_check_sign*h_new < glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
h_new := glob_min_h;
glob_h_reason := 5
end if;
term := 1;
ratio := c(1.0);
while term <= ATS_MAX_TERMS do
array_y1[term] := array_y1[term]*ratio;
array_y1_higher[1, term] := array_y1_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
array_y2[term] := array_y2[term]*ratio;
array_y2_higher[1, term] := array_y2_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/float_abs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT)
end if;
found_h := true;
if found_h then
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := c(x_start);
array_x[2] := c(glob_h);
glob_next_display := c(x_start);
glob_min_pole_est := glob_larger_float;
glob_least_given_sing := glob_larger_float;
glob_least_ratio_sing := glob_larger_float;
glob_least_3_sing := glob_larger_float;
glob_least_6_sing := glob_larger_float;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y1[term_no] := array_y1_init[term_no]*
expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1));
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
if term_no < ATS_MAX_TERMS then
array_y1_higher[r_order, term_no] := array_y1_init[it]*
expt(glob_h, c(term_no - 1))/
c(factorial_1(term_no - 1))
end if;
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
order_diff := 2;
term_no := 1;
while term_no <= order_diff do
array_y2[term_no] := array_y2_init[term_no]*
expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1));
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
if term_no < ATS_MAX_TERMS then
array_y2_higher[r_order, term_no] := array_y2_init[it]*
expt(glob_h, c(term_no - 1))/
c(factorial_1(term_no - 1))
end if;
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
glob_clock_sec := elapsed_time_seconds();
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
found_h := true;
glob_h := next_delta();
if float_abs(glob_min_pole_est)*glob_ratio_of_radius <
float_abs(glob_h) then
h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius
;
omniout_str(ALWAYS, "SETTING H FOR POLE");
glob_h_reason := 6;
if glob_check_sign*h_new < glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
h_new := glob_min_h;
glob_h_reason := 5
end if;
term := 1;
ratio := c(1.0);
while term <= ATS_MAX_TERMS do
array_y1[term] := array_y1[term]*ratio;
array_y1_higher[1, term] := array_y1_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
array_y2[term] := array_y2[term]*ratio;
array_y2_higher[1, term] := array_y2_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/float_abs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_iter < glob_max_iter and
(glob_iter < 10 or not (Re(glob_h) = 0. and Im(glob_h) = 0.)) do
omniout_str(INFO, " ");
found_h := true;
glob_h := next_delta();
if float_abs(glob_min_pole_est)*glob_ratio_of_radius <
float_abs(glob_h) then
h_new :=
glob_check_sign*glob_min_pole_est*glob_ratio_of_radius;
omniout_str(ALWAYS, "SETTING H FOR POLE");
glob_h_reason := 6;
if glob_check_sign*h_new < glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
h_new := glob_min_h;
glob_h_reason := 5
end if;
term := 1;
ratio := c(1.0);
while term <= ATS_MAX_TERMS do
array_y1[term] := array_y1[term]*ratio;
array_y1_higher[1, term] :=
array_y1_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
array_y2[term] := array_y2[term]*ratio;
array_y2_higher[1, term] :=
array_y2_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/float_abs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
if glob_subiter_method = 1 then atomall()
elif glob_subiter_method = 2 then
subiter := 1;
while subiter <= 3 do atomall(); subiter := subiter + 1
end do
else
subiter := 1;
while subiter <= 3 + ATS_MAX_TERMS do
atomall(); subiter := subiter + 1
end do
end if;
if not (Re(glob_h) = 0. and Im(glob_h) = 0.) then
display_alot(current_iter)
end if;
if
glob_look_poles and not (Re(glob_h) = 0. and Im(glob_h) = 0.)
then check_for_pole()
end if;
glob_next_display := glob_next_display + glob_display_interval;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y1_higher_work[2, iii] := array_y1_higher[2, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y1_higher_work[1, iii] := array_y1_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y1_higher_work[ord, iii];
iii := iii - 1
end do;
array_y1_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
term_no := ATS_MAX_TERMS;
while 1 <= term_no do
array_y1[term_no] := array_y1_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y1_higher[ord, term_no] :=
array_y1_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do;
order_diff := 3;
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 := 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 := 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
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if glob_max_sec <= elapsed_time_seconds() - glob_orig_start_sec
then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO,
"diff ( y1 , x , 1 ) = neg ( y2 ) ; ");
omniout_str(INFO,
"diff ( y2 , x , 2 ) = diff ( y1 , x , 1 ) ; ")
;
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, "2017-11-26T15:36:18-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"mtest5");
logitem_str(html_log_file,
"diff ( y1 , x , 1 ) = neg ( y2 ) ; ");
logitem_complex(html_log_file, x_start);
logitem_complex(html_log_file, x_end);
logitem_complex(html_log_file, array_x[1]);
logitem_complex(html_log_file, glob_h);
logitem_h_reason(html_log_file);
logitem_integer(html_log_file, Digits);
glob_desired_digits_correct := 0.;
logitem_float(html_log_file, glob_desired_digits_correct);
if array_est_digits[1] <> -16 then
logitem_integer(html_log_file, array_est_digits[1])
else logitem_str(html_log_file, "Unknown")
end if;
if glob_min_good_digits <> -16 then
logitem_integer(html_log_file, glob_min_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
if glob_good_digits <> -16 then
logitem_integer(html_log_file, glob_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
logitem_integer(html_log_file, ATS_MAX_TERMS);
if glob_type_given_pole = 0 then
logitem_str(html_log_file, "Not Given");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 4 then
logitem_str(html_log_file, "No Solution");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 5 then
logitem_str(html_log_file, "Some Pole");
logitem_str(html_log_file, "????")
elif glob_type_given_pole = 3 then
logitem_str(html_log_file, "No Pole");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 1 then
logitem_str(html_log_file, "Real Sing");
logitem_float(html_log_file, glob_least_given_sing)
elif glob_type_given_pole = 2 then
logitem_str(html_log_file, "Complex Sing");
logitem_float(html_log_file, glob_least_given_sing)
end if;
if glob_least_ratio_sing < glob_large_float then
glob_least_ratio_sing := 0;
logitem_float(html_log_file, glob_least_ratio_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_3_sing < glob_large_float then
logitem_float(html_log_file, glob_least_3_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_6_sing < glob_large_float then
glob_least_6_sing := 0.;
logitem_float(html_log_file, glob_least_6_sing)
else logitem_str(html_log_file, "NONE")
end if;
logitem_integer(html_log_file, glob_iter);
logitem_time(html_log_file, glob_clock_sec);
if c(glob_percent_done) < glob__100 then
logitem_time(html_log_file, glob_total_exp_sec); 0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 309 | ");
logitem_str(html_log_file,
"mtest5 diffeq.mxt");
logitem_str(html_log_file, "mtest5 maple results");
logitem_str(html_log_file, "Poor Accuracy - Not sure of algor\
ithm for multiple equations");
logend(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logitem_str(html_log_file, "diff ( y2 , x , 2 ) = d\
iff ( y1 , x , 1 ) ; ");
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
glob_desired_digits_correct := 0.;
logditto(html_log_file);
if array_est_digits[2] <> -16 then
logitem_integer(html_log_file, array_est_digits[2])
else logitem_str(html_log_file, "Unknown")
end if;
if glob_min_good_digits <> -16 then
logitem_integer(html_log_file, glob_min_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
if glob_good_digits <> -16 then
logitem_integer(html_log_file, glob_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
logditto(html_log_file);
if glob_type_given_pole = 0 then
logditto(html_log_file); logditto(html_log_file)
elif glob_type_given_pole = 4 then
logditto(html_log_file); logditto(html_log_file)
elif glob_type_given_pole = 5 then
logditto(html_log_file); logditto(html_log_file)
elif glob_type_given_pole = 3 then
logditto(html_log_file); logditto(html_log_file)
elif glob_type_given_pole = 1 then
logditto(html_log_file); logditto(html_log_file)
elif glob_type_given_pole = 2 then
logditto(html_log_file); logditto(html_log_file)
end if;
if glob_least_ratio_sing < glob_large_float then
glob_least_ratio_sing := 0; logditto(html_log_file)
else logditto(html_log_file)
end if;
if glob_least_3_sing < glob_large_float then
logditto(html_log_file)
else logditto(html_log_file)
end if;
if glob_least_6_sing < glob_large_float then
glob_least_6_sing := 0.; logditto(html_log_file)
else logditto(html_log_file)
end if;
logditto(html_log_file);
logditto(html_log_file);
if c(glob_percent_done) < glob__100 then
logditto(html_log_file); 0
else logditto(html_log_file); 0
end if;
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end if
end proc
# End Function number 12
> main();
memory used=4.0MB, alloc=40.3MB, time=0.08
##############ECHO OF PROBLEM#################
##############temp/mtest5postcpx.cpx#################
diff ( y1 , x , 1 ) = neg ( y2 ) ;
diff ( y2 , x , 2 ) = diff ( y1 , x , 1 ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.5 + 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);
glob_look_poles := true;
glob_type_given_pole := 3;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=8;
glob_max_minutes:=(3.0);
glob_subiter_method:=3;
glob_max_iter:=10000;
glob_upper_ratio_limit:=c(1.000001);
glob_lower_ratio_limit:=c(0.999999);
glob_look_poles:=true;
glob_h:=c(0.001);
glob_display_interval:=c(0.01);
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y1 := proc(x)
return(neg(cos(c(x))));
end;
exact_soln_y2 := proc(x)
return(neg(sin(c(x))));
end;
exact_soln_y2p := proc(x)
return(neg(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
x[1] = 0.5 0.1
h = 0.0001 0.005
y1[1] (numeric) = -0.881974132513 0.0480224980785
y1[1] (closed_form) = -0.881974132513 0.0480224980785
absolute error = 0
relative error = 0 %
Correct digits = 30
h = 0.0001 0.005
y2[1] (numeric) = -0.48182466457 -0.0879045930986
y2[1] (closed_form) = -0.48182466457 -0.0879045930986
absolute error = 0
relative error = 0 %
Correct digits = 30
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=55.6MB, alloc=40.3MB, time=0.74
x[1] = 0.5001 0.105
h = 0.0001 0.003
y1[1] (numeric) = -0.882374267978 0.0504412988723
y1[1] (closed_form) = -0.882376470517 0.0504414630278
absolute error = 2.209e-06
relative error = 0.0002499 %
Correct digits = 6
h = 0.0001 0.003
y2[1] (numeric) = -0.482111018094 -0.0914285594627
y2[1] (closed_form) = -0.482159040939 -0.0923105372607
absolute error = 0.0008833
relative error = 0.1799 %
Correct digits = 3
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5002 0.108
h = 0.001 0.001
y1[1] (numeric) = -0.882605615411 0.0518973918614
y1[1] (closed_form) = -0.882609137575 0.0518976648562
absolute error = 3.533e-06
relative error = 0.0003996 %
Correct digits = 5
h = 0.001 0.001
y2[1] (numeric) = -0.482405634827 -0.0949536841305
y2[1] (closed_form) = -0.482400798598 -0.0949528967489
absolute error = 4.900e-06
relative error = 0.0009966 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=104.0MB, alloc=40.3MB, time=1.37
x[1] = 0.5012 0.109
h = 0.001 0.003
y1[1] (numeric) = -0.882219777562 0.0524766621587
y1[1] (closed_form) = -0.882221637583 0.0524759010315
absolute error = 2.010e-06
relative error = 0.0002274 %
Correct digits = 6
h = 0.001 0.003
y2[1] (numeric) = -0.482702543792 -0.0984786031364
y2[1] (closed_form) = -0.48333540063 -0.0957831255093
absolute error = 0.002769
relative error = 0.5619 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5022 0.112
h = 0.0001 0.004
y1[1] (numeric) = -0.882037647185 0.0540254579997
y1[1] (closed_form) = -0.882029021211 0.0540245487961
absolute error = 8.674e-06
relative error = 0.0009815 %
Correct digits = 5
h = 0.0001 0.004
y2[1] (numeric) = -0.483001780229 -0.102001989746
y2[1] (closed_form) = -0.484377274643 -0.0983762500648
absolute error = 0.003878
relative error = 0.7846 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=152.5MB, alloc=40.3MB, time=2.00
x[1] = 0.5023 0.116
h = 0.003 0.006
y1[1] (numeric) = -0.882404385284 0.0559684496031
y1[1] (closed_form) = -0.882381119365 0.0559726854948
absolute error = 2.365e-05
relative error = 0.002675 %
Correct digits = 5
h = 0.003 0.006
y2[1] (numeric) = -0.483307154434 -0.105524962614
y2[1] (closed_form) = -0.484685488973 -0.10189956581
absolute error = 0.003879
relative error = 0.7831 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5053 0.122
h = 0.0001 0.005
y1[1] (numeric) = -0.881597697549 0.0591910902934
y1[1] (closed_form) = -0.88154934183 0.0592031450938
absolute error = 4.984e-05
relative error = 0.00564 %
Correct digits = 4
h = 0.0001 0.005
y2[1] (numeric) = -0.483624880227 -0.1090413155
y2[1] (closed_form) = -0.487676890069 -0.107018590904
absolute error = 0.004529
relative error = 0.9071 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=201.0MB, alloc=40.3MB, time=2.63
x[1] = 0.5054 0.127
h = 0.0001 0.003
y1[1] (numeric) = -0.882103299776 0.0616211199713
y1[1] (closed_form) = -0.882046654093 0.061653422206
absolute error = 6.521e-05
relative error = 0.007375 %
Correct digits = 4
h = 0.0001 0.003
y2[1] (numeric) = -0.483957174544 -0.112551556542
y2[1] (closed_form) = -0.488067210107 -0.111421528929
absolute error = 0.004263
relative error = 0.8514 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=249.4MB, alloc=40.3MB, time=3.26
x[1] = 0.5055 0.13
h = 0.001 0.001
y1[1] (numeric) = -0.882397809185 0.0630849320355
y1[1] (closed_form) = -0.882336058546 0.0631293099751
absolute error = 7.604e-05
relative error = 0.008596 %
Correct digits = 4
h = 0.001 0.001
y2[1] (numeric) = -0.484297780213 -0.11606331333
y2[1] (closed_form) = -0.488342603003 -0.114061861897
absolute error = 0.004513
relative error = 0.8999 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5065 0.131
h = 0.001 0.003
y1[1] (numeric) = -0.882031159174 0.0636872204789
y1[1] (closed_form) = -0.881961714474 0.0637325966513
absolute error = 8.296e-05
relative error = 0.009381 %
Correct digits = 4
h = 0.001 0.003
y2[1] (numeric) = -0.48464071399 -0.119574956893
y2[1] (closed_form) = -0.489288182706 -0.114880579988
absolute error = 0.006606
relative error = 1.314 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=297.9MB, alloc=40.3MB, time=3.90
x[1] = 0.5075 0.134
h = 0.0001 0.004
y1[1] (numeric) = -0.881910336804 0.0652629897117
y1[1] (closed_form) = -0.881820402906 0.0653182445642
absolute error = 0.0001056
relative error = 0.01194 %
Correct digits = 4
h = 0.0001 0.004
y2[1] (numeric) = -0.48498606743 -0.123085144644
y2[1] (closed_form) = -0.490363648019 -0.11746172656
absolute error = 0.007781
relative error = 1.543 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5076 0.138
h = 0.003 0.006
y1[1] (numeric) = -0.882361180766 0.0672161185378
y1[1] (closed_form) = -0.882248238342 0.0672923255928
absolute error = 0.0001362
relative error = 0.0154 %
Correct digits = 4
h = 0.003 0.006
y2[1] (numeric) = -0.485337654194 -0.126595164822
y2[1] (closed_form) = -0.490717071886 -0.120983228645
absolute error = 0.007774
relative error = 1.538 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=346.4MB, alloc=40.3MB, time=4.53
x[1] = 0.5106 0.144
h = 0.0001 0.005
y1[1] (numeric) = -0.881674715123 0.0705142734282
y1[1] (closed_form) = -0.881512662359 0.0706163770997
absolute error = 0.0001915
relative error = 0.02166 %
Correct digits = 4
h = 0.0001 0.005
y2[1] (numeric) = -0.485702023896 -0.130098980266
y2[1] (closed_form) = -0.493776417208 -0.126067646031
absolute error = 0.009025
relative error = 1.771 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5107 0.149
h = 0.0001 0.003
y1[1] (numeric) = -0.882285365317 0.0729569116733
y1[1] (closed_form) = -0.882104604169 0.0730991994942
absolute error = 0.00023
relative error = 0.02599 %
Correct digits = 4
h = 0.0001 0.003
y2[1] (numeric) = -0.486081405741 -0.133597193111
y2[1] (closed_form) = -0.494223885714 -0.130469494289
absolute error = 0.008723
relative error = 1.706 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=394.9MB, alloc=40.3MB, time=5.16
x[1] = 0.5108 0.152
h = 0.001 0.001
y1[1] (numeric) = -0.882642779301 0.0744292711122
y1[1] (closed_form) = -0.88245053376 0.074595513589
absolute error = 0.0002542
relative error = 0.0287 %
Correct digits = 4
h = 0.001 0.001
y2[1] (numeric) = -0.486469151741 -0.137097277604
y2[1] (closed_form) = -0.494533655177 -0.133108940299
absolute error = 0.008997
relative error = 1.757 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5118 0.153
h = 0.001 0.003
y1[1] (numeric) = -0.882294962507 0.0750547826865
y1[1] (closed_form) = -0.88208903424 0.0752240385145
absolute error = 0.0002666
relative error = 0.03011 %
Correct digits = 4
h = 0.001 0.003
y2[1] (numeric) = -0.48685926288 -0.140597340602
y2[1] (closed_form) = -0.495490834602 -0.133916300466
absolute error = 0.01092
relative error = 2.127 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=443.5MB, alloc=40.3MB, time=5.80
x[1] = 0.5128 0.156
h = 0.0001 0.004
y1[1] (numeric) = -0.88223494782 0.0766582950537
y1[1] (closed_form) = -0.881998593246 0.0768473765524
absolute error = 0.0003027
relative error = 0.03419 %
Correct digits = 3
h = 0.0001 0.004
y2[1] (numeric) = -0.4872518867 -0.144096022958
y2[1] (closed_form) = -0.496600983514 -0.136486395042
absolute error = 0.01205
relative error = 2.341 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5129 0.16
h = 0.003 0.006
y1[1] (numeric) = -0.882769583712 0.0786226823992
y1[1] (closed_form) = -0.882501900633 0.0788484017183
absolute error = 0.0003501
relative error = 0.03952 %
Correct digits = 3
h = 0.003 0.006
y2[1] (numeric) = -0.487650842534 -0.147594782088
y2[1] (closed_form) = -0.497000599328 -0.140007606575
absolute error = 0.01204
relative error = 2.332 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=492.0MB, alloc=40.3MB, time=6.43
x[1] = 0.5159 0.166
h = 0.0001 0.005
y1[1] (numeric) = -0.882202071905 0.0819978418782
y1[1] (closed_form) = -0.88186141561 0.0822673890946
absolute error = 0.0004344
relative error = 0.04905 %
Correct digits = 3
h = 0.0001 0.005
y2[1] (numeric) = -0.488063017444 -0.151087745009
y2[1] (closed_form) = -0.500130469478 -0.145059020862
absolute error = 0.01349
relative error = 2.59 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=540.5MB, alloc=40.3MB, time=7.06
x[1] = 0.516 0.171
h = 0.0001 0.003
y1[1] (numeric) = -0.882917401318 0.0844545040494
y1[1] (closed_form) = -0.882547677808 0.084784026798
absolute error = 0.0004953
relative error = 0.05586 %
Correct digits = 3
h = 0.0001 0.003
y2[1] (numeric) = -0.488490654211 -0.15457560754
y2[1] (closed_form) = -0.500636317052 -0.149461681898
absolute error = 0.01318
relative error = 2.522 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5161 0.174
h = 0.001 0.001
y1[1] (numeric) = -0.883337492165 0.0859362610339
y1[1] (closed_form) = -0.882949941287 0.0863015300991
absolute error = 0.0005326
relative error = 0.06003 %
Correct digits = 3
h = 0.001 0.001
y2[1] (numeric) = -0.488926712721 -0.158065696246
y2[1] (closed_form) = -0.500981219878 -0.152101372088
absolute error = 0.01345
relative error = 2.569 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=588.9MB, alloc=40.3MB, time=7.70
x[1] = 0.5171 0.175
h = 0.001 0.003
y1[1] (numeric) = -0.883008157105 0.0865852178078
y1[1] (closed_form) = -0.88260097492 0.0869554955247
absolute error = 0.0005504
relative error = 0.06206 %
Correct digits = 3
h = 0.001 0.003
y2[1] (numeric) = -0.489365174601 -0.161555854519
y2[1] (closed_form) = -0.501950623716 -0.152897519195
absolute error = 0.01528
relative error = 2.911 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5181 0.178
h = 0.0001 0.004
y1[1] (numeric) = -0.883008473052 0.0882172741264
y1[1] (closed_form) = -0.882560984675 0.088617242712
absolute error = 0.0006002
relative error = 0.06766 %
Correct digits = 3
h = 0.0001 0.004
y2[1] (numeric) = -0.489806243077 -0.165044705915
y2[1] (closed_form) = -0.503096561759 -0.155457474632
absolute error = 0.01639
relative error = 3.112 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=637.4MB, alloc=40.3MB, time=8.33
x[1] = 0.5182 0.182
h = 0.003 0.006
y1[1] (numeric) = -0.883626626526 0.0901940703574
y1[1] (closed_form) = -0.883139526808 0.0906462417082
absolute error = 0.0006646
relative error = 0.07486 %
Correct digits = 3
h = 0.003 0.006
y2[1] (numeric) = -0.490253745505 -0.168533876708
y2[1] (closed_form) = -0.503543372924 -0.158979907817
absolute error = 0.01637
relative error = 3.1 %
Correct digits = 2
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5212 0.188
h = 0.0001 0.005
y1[1] (numeric) = -0.883176839509 0.093647797192
y1[1] (closed_form) = -0.882593043364 0.0941615743757
absolute error = 0.0007777
relative error = 0.08762 %
Correct digits = 3
h = 0.0001 0.005
y2[1] (numeric) = -0.490714908274 -0.172017653183
y2[1] (closed_form) = -0.50674637296 -0.163999892117
absolute error = 0.01792
relative error = 3.365 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=685.8MB, alloc=40.3MB, time=8.96
x[1] = 0.5213 0.193
h = 0.0001 0.003
y1[1] (numeric) = -0.883996528857 0.0961199349427
y1[1] (closed_form) = -0.883373351909 0.096713334829
absolute error = 0.0008605
relative error = 0.09683 %
Correct digits = 3
h = 0.0001 0.003
y2[1] (numeric) = -0.491191989077 -0.175496824571
y2[1] (closed_form) = -0.507311857008 -0.168405255233
absolute error = 0.01761
relative error = 3.295 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5214 0.196
h = 0.001 0.001
y1[1] (numeric) = -0.884479098193 0.0976119618856
y1[1] (closed_form) = -0.883831778768 0.0982528130157
absolute error = 0.0009109
relative error = 0.1024 %
Correct digits = 3
h = 0.001 0.001
y2[1] (numeric) = -0.491677554123 -0.178978575451
y2[1] (closed_form) = -0.507692666069 -0.171046312662
absolute error = 0.01787
relative error = 3.336 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=734.3MB, alloc=40.3MB, time=9.60
x[1] = 0.5224 0.197
h = 0.0001 0.004
y1[1] (numeric) = -0.884167896278 0.0982846030265
y1[1] (closed_form) = -0.883495033935 0.098932435714
absolute error = 0.000934
relative error = 0.1051 %
Correct digits = 3
h = 0.0001 0.004
y2[1] (numeric) = -0.492165562015 -0.182460486327
y2[1] (closed_form) = -0.508674921969 -0.171831383608
absolute error = 0.01964
relative error = 3.657 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=782.7MB, alloc=40.3MB, time=10.23
x[1] = 0.5225 0.201
h = 0.003 0.006
y1[1] (numeric) = -0.884855461653 0.10027266716
y1[1] (closed_form) = -0.884138517379 0.100985468458
absolute error = 0.001011
relative error = 0.1136 %
Correct digits = 3
h = 0.003 0.006
y2[1] (numeric) = -0.492657760826 -0.18594317632
y2[1] (closed_form) = -0.50916313857 -0.17535665015
absolute error = 0.01961
relative error = 3.641 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5255 0.207
h = 0.0001 0.005
y1[1] (numeric) = -0.884502832313 0.103793171523
y1[1] (closed_form) = -0.883673262341 0.104583808369
absolute error = 0.001146
relative error = 0.1288 %
Correct digits = 3
h = 0.0001 0.005
y2[1] (numeric) = -0.493163992028 -0.189420801697
y2[1] (closed_form) = -0.512431541731 -0.18035173014
absolute error = 0.0213
relative error = 3.92 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=831.2MB, alloc=40.3MB, time=10.86
x[1] = 0.5256 0.212
h = 0.0001 0.003
y1[1] (numeric) = -0.885409275684 0.106279408318
y1[1] (closed_form) = -0.884534770179 0.107165760755
absolute error = 0.001245
relative error = 0.1397 %
Correct digits = 3
h = 0.0001 0.003
y2[1] (numeric) = -0.493686526908 -0.192894229343
y2[1] (closed_form) = -0.513049324401 -0.184761653611
absolute error = 0.021
relative error = 3.851 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5257 0.215
h = 0.001 0.001
y1[1] (numeric) = -0.885943777292 0.107780726599
y1[1] (closed_form) = -0.885041694642 0.108724134349
absolute error = 0.001305
relative error = 0.1464 %
Correct digits = 3
h = 0.001 0.001
y2[1] (numeric) = -0.49421760221 -0.196370530084
y2[1] (closed_form) = -0.513461637626 -0.187405221854
absolute error = 0.02123
relative error = 3.884 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=879.8MB, alloc=40.3MB, time=11.50
x[1] = 0.5267 0.216
h = 0.001 0.003
y1[1] (numeric) = -0.885647401827 0.108473319824
y1[1] (closed_form) = -0.884715529268 0.109425886141
absolute error = 0.001333
relative error = 0.1495 %
Correct digits = 3
h = 0.001 0.003
y2[1] (numeric) = -0.494751154316 -0.199847065694
y2[1] (closed_form) = -0.514455591119 -0.188181025621
absolute error = 0.0229
relative error = 4.18 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5277 0.219
h = 0.0001 0.004
y1[1] (numeric) = -0.885757137513 0.110159961354
y1[1] (closed_form) = -0.884768825674 0.111160528153
absolute error = 0.001406
relative error = 0.1577 %
Correct digits = 3
h = 0.0001 0.004
y2[1] (numeric) = -0.495287487846 -0.203322425965
y2[1] (closed_form) = -0.515671210835 -0.190724957858
absolute error = 0.02396
relative error = 4.358 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=928.3MB, alloc=40.3MB, time=12.13
x[1] = 0.5278 0.223
h = 0.003 0.006
y1[1] (numeric) = -0.886527822667 0.112162700561
y1[1] (closed_form) = -0.885487189275 0.113243533773
absolute error = 0.0015
relative error = 0.1681 %
Correct digits = 3
h = 0.003 0.006
y2[1] (numeric) = -0.495830451358 -0.206798546204
y2[1] (closed_form) = -0.516208530809 -0.194254245018
absolute error = 0.02393
relative error = 4.339 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5308 0.229
h = 0.0001 0.005
y1[1] (numeric) = -0.886290712094 0.115764951025
y1[1] (closed_form) = -0.885113981011 0.11694102958
absolute error = 0.001664
relative error = 0.1863 %
Correct digits = 3
h = 0.0001 0.005
y2[1] (numeric) = -0.496387899255 -0.210269991427
y2[1] (closed_form) = -0.519554963825 -0.199220770548
absolute error = 0.02567
relative error = 4.613 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=976.9MB, alloc=40.3MB, time=12.76
x[1] = 0.5309 0.234
h = 0.0001 0.003
y1[1] (numeric) = -0.887301061981 0.11826952116
y1[1] (closed_form) = -0.886069133915 0.119560641277
absolute error = 0.001785
relative error = 0.1996 %
Correct digits = 3
h = 0.0001 0.003
y2[1] (numeric) = -0.496962120364 -0.213737721554
y2[1] (closed_form) = -0.520234775374 -0.203636894112
absolute error = 0.02537
relative error = 4.541 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1025.4MB, alloc=40.3MB, time=13.40
x[1] = 0.531 0.237
h = 0.001 0.001
y1[1] (numeric) = -0.887897755852 0.119782827928
y1[1] (closed_form) = -0.886631968815 0.121142514964
absolute error = 0.001858
relative error = 0.2076 %
Correct digits = 3
h = 0.001 0.001
y2[1] (numeric) = -0.497544954085 -0.217208676304
y2[1] (closed_form) = -0.520684464694 -0.206283908648
absolute error = 0.02559
relative error = 4.569 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.532 0.238
h = 0.001 0.003
y1[1] (numeric) = -0.887618862657 0.120499609921
y1[1] (closed_form) = -0.886317446874 0.121870369864
absolute error = 0.00189
relative error = 0.2113 %
Correct digits = 3
h = 0.001 0.003
y2[1] (numeric) = -0.498130306578 -0.220679955262
y2[1] (closed_form) = -0.521692445717 -0.207048877081
absolute error = 0.02722
relative error = 4.85 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1074.0MB, alloc=40.3MB, time=14.03
x[1] = 0.533 0.241
h = 0.0001 0.004
y1[1] (numeric) = -0.887787684107 0.122217296999
y1[1] (closed_form) = -0.886420079079 0.123645644978
absolute error = 0.001978
relative error = 0.2209 %
Correct digits = 3
h = 0.0001 0.004
y2[1] (numeric) = -0.498718537407 -0.224150128653
y2[1] (closed_form) = -0.522947086398 -0.209585224299
absolute error = 0.02827
relative error = 5.018 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5331 0.245
h = 0.003 0.006
y1[1] (numeric) = -0.88864132436 0.124235946919
y1[1] (closed_form) = -0.88721316456 0.125759740699
absolute error = 0.002088
relative error = 0.2331 %
Correct digits = 3
h = 0.003 0.006
y2[1] (numeric) = -0.499313510263 -0.227621300215
y2[1] (closed_form) = -0.523534577813 -0.213120015846
absolute error = 0.02823
relative error = 4.994 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1122.3MB, alloc=40.3MB, time=14.66
x[1] = 0.5361 0.251
h = 0.0001 0.005
y1[1] (numeric) = -0.88851860873 0.127921714022
y1[1] (closed_form) = -0.886930970596 0.129557991137
absolute error = 0.00228
relative error = 0.2544 %
Correct digits = 3
h = 0.0001 0.005
y2[1] (numeric) = -0.499923425579 -0.231088179942
y2[1] (closed_form) = -0.526961724682 -0.218059470822
absolute error = 0.03001
relative error = 5.263 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5362 0.256
h = 0.0001 0.003
y1[1] (numeric) = -0.889632682921 0.130446175714
y1[1] (closed_form) = -0.887979593103 0.132216679243
absolute error = 0.002422
relative error = 0.2698 %
Correct digits = 3
h = 0.0001 0.003
y2[1] (numeric) = -0.50055059116 -0.234551820644
y2[1] (closed_form) = -0.527704904969 -0.222483649346
absolute error = 0.02972
relative error = 5.189 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1170.9MB, alloc=40.3MB, time=15.30
x[1] = 0.5363 0.259
h = 0.001 0.001
y1[1] (numeric) = -0.890291451938 0.131972408638
y1[1] (closed_form) = -0.888598226127 0.133822905498
absolute error = 0.002508
relative error = 0.2791 %
Correct digits = 3
h = 0.001 0.001
y2[1] (numeric) = -0.501186446831 -0.238019036745
y2[1] (closed_form) = -0.528192792739 -0.225135212134
absolute error = 0.02992
relative error = 5.211 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5373 0.26
h = 0.001 0.003
y1[1] (numeric) = -0.890029699257 0.132713667188
y1[1] (closed_form) = -0.888295034472 0.134577122
absolute error = 0.002546
relative error = 0.2834 %
Correct digits = 3
h = 0.001 0.003
y2[1] (numeric) = -0.501824864615 -0.241486665855
y2[1] (closed_form) = -0.529215439258 -0.225889458921
absolute error = 0.03152
relative error = 5.478 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1219.4MB, alloc=40.3MB, time=15.93
x[1] = 0.5383 0.263
h = 0.0001 0.004
y1[1] (numeric) = -0.890257214304 0.134463322555
y1[1] (closed_form) = -0.888446635244 0.136393863541
absolute error = 0.002647
relative error = 0.2945 %
Correct digits = 3
h = 0.0001 0.004
y2[1] (numeric) = -0.502466258809 -0.244953257807
y2[1] (closed_form) = -0.530510264443 -0.228419084893
absolute error = 0.03256
relative error = 5.636 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1267.9MB, alloc=40.3MB, time=16.56
x[1] = 0.5384 0.267
h = 0.003 0.006
y1[1] (numeric) = -0.891193682838 0.136499150036
y1[1] (closed_form) = -0.889314311147 0.138540198188
absolute error = 0.002775
relative error = 0.3083 %
Correct digits = 3
h = 0.003 0.006
y2[1] (numeric) = -0.503114510789 -0.248421084763
y2[1] (closed_form) = -0.531149019526 -0.231960855406
absolute error = 0.03251
relative error = 5.609 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5414 0.273
h = 0.0001 0.005
y1[1] (numeric) = -0.891184273397 0.140270278743
y1[1] (closed_form) = -0.889122117004 0.142440869153
absolute error = 0.002994
relative error = 0.3325 %
Correct digits = 2
h = 0.0001 0.005
y2[1] (numeric) = -0.503778169728 -0.251884996717
y2[1] (closed_form) = -0.53465959473 -0.236874692565
absolute error = 0.03434
relative error = 5.872 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1316.4MB, alloc=40.3MB, time=17.20
x[1] = 0.5415 0.278
h = 0.0001 0.003
y1[1] (numeric) = -0.892401937026 0.14281622923
y1[1] (closed_form) = -0.890264067151 0.145140090382
absolute error = 0.003158
relative error = 0.3501 %
Correct digits = 2
h = 0.0001 0.003
y2[1] (numeric) = -0.504459563877 -0.255346139264
y2[1] (closed_form) = -0.535467514386 -0.241308769811
absolute error = 0.03404
relative error = 5.795 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5416 0.281
h = 0.001 0.001
y1[1] (numeric) = -0.893122692119 0.14435634985
y1[1] (closed_form) = -0.890938405748 0.146771545797
absolute error = 0.003256
relative error = 0.3606 %
Correct digits = 2
h = 0.001 0.001
y2[1] (numeric) = -0.505149731021 -0.258811207388
y2[1] (closed_form) = -0.535994441437 -0.243965975974
absolute error = 0.03423
relative error = 5.813 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1365.0MB, alloc=40.3MB, time=17.84
x[1] = 0.5426 0.282
h = 0.001 0.003
y1[1] (numeric) = -0.89287774012 0.145122390001
y1[1] (closed_form) = -0.890646230251 0.147552397056
absolute error = 0.003299
relative error = 0.3654 %
Correct digits = 2
h = 0.001 0.003
y2[1] (numeric) = -0.50584250504 -0.26227677682
y2[1] (closed_form) = -0.537032395602 -0.244709606494
absolute error = 0.0358
relative error = 6.066 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5436 0.285
h = 0.0001 0.004
y1[1] (numeric) = -0.893163577621 0.146904969036
y1[1] (closed_form) = -0.89084644501 0.149411468673
absolute error = 0.003413
relative error = 0.3779 %
Correct digits = 2
h = 0.0001 0.004
y2[1] (numeric) = -0.506538354772 -0.265741376145
y2[1] (closed_form) = -0.538368585586 -0.247233362559
absolute error = 0.03682
relative error = 6.215 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1413.3MB, alloc=40.3MB, time=18.47
x[1] = 0.5437 0.289
h = 0.003 0.006
y1[1] (numeric) = -0.894182785067 0.148959272745
y1[1] (closed_form) = -0.891788606366 0.151591223167
absolute error = 0.003558
relative error = 0.3933 %
Correct digits = 2
h = 0.003 0.006
y2[1] (numeric) = -0.507241181888 -0.269207446027
y2[1] (closed_form) = -0.539059721564 -0.250783577843
absolute error = 0.03677
relative error = 6.184 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5467 0.295
h = 0.0001 0.005
y1[1] (numeric) = -0.89428562706 0.152817683089
y1[1] (closed_form) = -0.891685414712 0.15559604824
absolute error = 0.003805
relative error = 0.4204 %
Correct digits = 2
h = 0.0001 0.005
y2[1] (numeric) = -0.507959887228 -0.272669971456
y2[1] (closed_form) = -0.542656471649 -0.255673218788
absolute error = 0.03864
relative error = 6.441 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1461.8MB, alloc=40.3MB, time=19.10
x[1] = 0.5468 0.3
h = 0.0001 0.003
y1[1] (numeric) = -0.895606792092 0.155386759407
y1[1] (closed_form) = -0.892920583635 0.158337299553
absolute error = 0.00399
relative error = 0.44 %
Correct digits = 2
h = 0.0001 0.003
y2[1] (numeric) = -0.508696820994 -0.276130190744
y2[1] (closed_form) = -0.543530533127 -0.260119027931
absolute error = 0.03834
relative error = 6.362 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1510.4MB, alloc=40.3MB, time=19.74
x[1] = 0.5469 0.303
h = 0.001 0.001
y1[1] (numeric) = -0.896389471926 0.156941753603
y1[1] (closed_form) = -0.893650554768 0.159994885213
absolute error = 0.004102
relative error = 0.4518 %
Correct digits = 2
h = 0.001 0.001
y2[1] (numeric) = -0.509442616224 -0.279594685347
y2[1] (closed_form) = -0.544097359404 -0.262782966062
absolute error = 0.03852
relative error = 6.375 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5479 0.304
h = 0.0001 0.004
y1[1] (numeric) = -0.896160982445 0.157732897709
y1[1] (closed_form) = -0.89336908011 0.160802659095
absolute error = 0.004149
relative error = 0.4571 %
Correct digits = 2
h = 0.0001 0.004
y2[1] (numeric) = -0.510191064562 -0.283059769087
y2[1] (closed_form) = -0.545151267871 -0.263516077282
absolute error = 0.04005
relative error = 6.615 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1558.9MB, alloc=40.3MB, time=20.37
x[1] = 0.548 0.308
h = 0.003 0.006
y1[1] (numeric) = -0.89724909674 0.159803644294
y1[1] (closed_form) = -0.894375709836 0.163011264757
absolute error = 0.004306
relative error = 0.4737 %
Correct digits = 2
h = 0.003 0.006
y2[1] (numeric) = -0.510943989469 -0.286526411007
y2[1] (closed_form) = -0.545888281739 -0.267075371473
absolute error = 0.03999
relative error = 6.581 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.551 0.314
h = 0.0001 0.005
y1[1] (numeric) = -0.897444670998 0.163736380735
y1[1] (closed_form) = -0.894349612437 0.167106138178
absolute error = 0.004575
relative error = 0.5029 %
Correct digits = 2
h = 0.0001 0.005
y2[1] (numeric) = -0.511713190959 -0.289989812321
y2[1] (closed_form) = -0.549561699053 -0.271946371395
absolute error = 0.04193
relative error = 6.838 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1607.4MB, alloc=40.3MB, time=21.01
x[1] = 0.5511 0.319
h = 0.0001 0.003
y1[1] (numeric) = -0.898852060324 0.166326082854
y1[1] (closed_form) = -0.895665484464 0.169883688258
absolute error = 0.004776
relative error = 0.5239 %
Correct digits = 2
h = 0.0001 0.003
y2[1] (numeric) = -0.512501038836 -0.293451288583
y2[1] (closed_form) = -0.550493672061 -0.27640455044
absolute error = 0.04164
relative error = 6.76 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5512 0.322
h = 0.001 0.001
y1[1] (numeric) = -0.899686322764 0.167894298366
y1[1] (closed_form) = -0.896443624794 0.17156384465
absolute error = 0.004897
relative error = 0.5365 %
Correct digits = 2
h = 0.001 0.001
y2[1] (numeric) = -0.513297826533 -0.296917331402
y2[1] (closed_form) = -0.551095448232 -0.279075639756
absolute error = 0.0418
relative error = 6.766 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1656.1MB, alloc=40.3MB, time=21.64
x[1] = 0.5522 0.323
h = 0.001 0.003
y1[1] (numeric) = -0.899471276016 0.168706646653
y1[1] (closed_form) = -0.896171433145 0.172394912091
absolute error = 0.004949
relative error = 0.5423 %
Correct digits = 2
h = 0.001 0.003
y2[1] (numeric) = -0.51409730711 -0.300384036197
y2[1] (closed_form) = -0.552163735019 -0.279799968085
absolute error = 0.04328
relative error = 6.991 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5532 0.326
h = 0.0001 0.004
y1[1] (numeric) = -0.899863128889 0.170552258224
y1[1] (closed_form) = -0.896461735263 0.174334584231
absolute error = 0.005087
relative error = 0.557 %
Correct digits = 2
h = 0.0001 0.004
y2[1] (numeric) = -0.514900048992 -0.303849890225
y2[1] (closed_form) = -0.553580143645 -0.28231555212
absolute error = 0.04427
relative error = 7.124 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1704.7MB, alloc=40.3MB, time=22.28
x[1] = 0.5533 0.33
h = 0.003 0.006
y1[1] (numeric) = -0.901033932034 0.17264403383
y1[1] (closed_form) = -0.897542739507 0.176578894873
absolute error = 0.00526
relative error = 0.5751 %
Correct digits = 2
h = 0.003 0.006
y2[1] (numeric) = -0.515709998266 -0.307317643587
y2[1] (closed_form) = -0.554371669534 -0.285886010691
absolute error = 0.0442
relative error = 7.087 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5563 0.336
h = 0.0001 0.005
y1[1] (numeric) = -0.901339873832 0.176667914219
y1[1] (closed_form) = -0.897603854065 0.180781341716
absolute error = 0.005557
relative error = 0.6069 %
Correct digits = 2
h = 0.0001 0.005
y2[1] (numeric) = -0.516536709241 -0.310782515222
y2[1] (closed_form) = -0.558136447116 -0.2907354105
absolute error = 0.04618
relative error = 7.338 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1753.2MB, alloc=40.3MB, time=22.91
x[1] = 0.5564 0.341
h = 0.0001 0.003
y1[1] (numeric) = -0.902850746011 0.179283958281
y1[1] (closed_form) = -0.899012848017 0.183603817141
absolute error = 0.005778
relative error = 0.6298 %
Correct digits = 2
h = 0.0001 0.003
y2[1] (numeric) = -0.517382576628 -0.314245913414
y2[1] (closed_form) = -0.559137238391 -0.295208723765
absolute error = 0.04589
relative error = 7.258 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1801.8MB, alloc=40.3MB, time=23.55
x[1] = 0.5565 0.344
h = 0.001 0.001
y1[1] (numeric) = -0.903746904628 0.180868985146
y1[1] (closed_form) = -0.899846547522 0.185311847373
absolute error = 0.005912
relative error = 0.6435 %
Correct digits = 2
h = 0.001 0.001
y2[1] (numeric) = -0.518237483253 -0.317714227557
y2[1] (closed_form) = -0.559780554241 -0.2978885651
absolute error = 0.04603
relative error = 7.259 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5575 0.345
h = 0.001 0.003
y1[1] (numeric) = -0.903547687219 0.181707100246
y1[1] (closed_form) = -0.899584469935 0.186170416252
absolute error = 0.005969
relative error = 0.6498 %
Correct digits = 2
h = 0.001 0.003
y2[1] (numeric) = -0.519095131911 -0.321183290719
y2[1] (closed_form) = -0.560866010763 -0.298602539658
absolute error = 0.04748
relative error = 7.473 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1850.3MB, alloc=40.3MB, time=24.19
x[1] = 0.5585 0.348
h = 0.0001 0.004
y1[1] (numeric) = -0.903996914507 0.183588593111
y1[1] (closed_form) = -0.899922449835 0.188155063239
absolute error = 0.00612
relative error = 0.6657 %
Correct digits = 2
h = 0.0001 0.004
y2[1] (numeric) = -0.519956145142 -0.324651566284
y2[1] (closed_form) = -0.562327250212 -0.301114636353
absolute error = 0.04847
relative error = 7.599 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5586 0.352
h = 0.003 0.006
y1[1] (numeric) = -0.905250421025 0.185702790172
y1[1] (closed_form) = -0.901077798039 0.190436354203
absolute error = 0.00631
relative error = 0.6851 %
Correct digits = 2
h = 0.003 0.006
y2[1] (numeric) = -0.520824497214 -0.328121973563
y2[1] (closed_form) = -0.563174481691 -0.30469770256
absolute error = 0.0484
relative error = 7.558 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1898.8MB, alloc=40.3MB, time=24.82
x[1] = 0.5616 0.358
h = 0.0001 0.005
y1[1] (numeric) = -0.905665766017 0.189819951204
y1[1] (closed_form) = -0.901225172334 0.194748304712
absolute error = 0.006634
relative error = 0.7195 %
Correct digits = 2
h = 0.0001 0.005
y2[1] (numeric) = -0.521710103848 -0.331589851859
y2[1] (closed_form) = -0.567033466954 -0.309526835194
absolute error = 0.05041
relative error = 7.803 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5617 0.363
h = 0.0001 0.003
y1[1] (numeric) = -0.907280162986 0.192464091616
y1[1] (closed_form) = -0.902727272353 0.197617320915
absolute error = 0.006876
relative error = 0.7441 %
Correct digits = 2
h = 0.0001 0.003
y2[1] (numeric) = -0.522615386276 -0.335056702235
y2[1] (closed_form) = -0.568104576035 -0.314017088763
absolute error = 0.05012
relative error = 7.721 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1947.3MB, alloc=40.3MB, time=25.46
x[1] = 0.5618 0.366
h = 0.001 0.001
y1[1] (numeric) = -0.908238233369 0.194066987442
y1[1] (closed_form) = -0.903616512791 0.199354198151
absolute error = 0.007022
relative error = 0.7589 %
Correct digits = 2
h = 0.001 0.001
y2[1] (numeric) = -0.523529813337 -0.338528817946
y2[1] (closed_form) = -0.568790349855 -0.316706753884
absolute error = 0.05025
relative error = 7.718 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5628 0.367
h = 0.001 0.003
y1[1] (numeric) = -0.908054510383 0.19493124119
y1[1] (closed_form) = -0.903364229545 0.200240598787
absolute error = 0.007084
relative error = 0.7656 %
Correct digits = 2
h = 0.001 0.003
y2[1] (numeric) = -0.524447033191 -0.342001769338
y2[1] (closed_form) = -0.569893637507 -0.317410447041
absolute error = 0.05167
relative error = 7.921 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1995.8MB, alloc=40.3MB, time=26.09
x[1] = 0.5638 0.37
h = 0.0001 0.004
y1[1] (numeric) = -0.908560817273 0.196849699673
y1[1] (closed_form) = -0.903749578467 0.20227120429
absolute error = 0.007248
relative error = 0.7827 %
Correct digits = 2
h = 0.0001 0.004
y2[1] (numeric) = -0.525367722381 -0.345473994965
y2[1] (closed_form) = -0.571400959856 -0.319919860932
absolute error = 0.05265
relative error = 8.04 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2044.2MB, alloc=40.3MB, time=26.72
x[1] = 0.5639 0.374
h = 0.003 0.006
y1[1] (numeric) = -0.909897077612 0.198987745081
y1[1] (closed_form) = -0.904979265343 0.204590785117
absolute error = 0.007455
relative error = 0.8035 %
Correct digits = 2
h = 0.003 0.006
y2[1] (numeric) = -0.526295886197 -0.348948583728
y2[1] (closed_form) = -0.572305118833 -0.323516970787
absolute error = 0.05257
relative error = 7.996 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5669 0.38
h = 0.0001 0.005
y1[1] (numeric) = -0.910420891256 0.203200401467
y1[1] (closed_form) = -0.905211960941 0.209014239578
absolute error = 0.007806
relative error = 0.8402 %
Correct digits = 2
h = 0.0001 0.005
y2[1] (numeric) = -0.527241805529 -0.352420990159
y2[1] (closed_form) = -0.576261197414 -0.328327137974
absolute error = 0.05462
relative error = 8.236 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2092.8MB, alloc=40.3MB, time=27.36
x[1] = 0.567 0.385
h = 0.0001 0.003
y1[1] (numeric) = -0.91213889991 0.205874435784
y1[1] (closed_form) = -0.906807182763 0.211931454926
absolute error = 0.008069
relative error = 0.8665 %
Correct digits = 2
h = 0.0001 0.003
y2[1] (numeric) = -0.528207929782 -0.355892808192
y2[1] (closed_form) = -0.577404159852 -0.332836129254
absolute error = 0.05433
relative error = 8.152 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5671 0.388
h = 0.001 0.001
y1[1] (numeric) = -0.913158924239 0.20749628453
y1[1] (closed_form) = -0.907751964489 0.213698178433
absolute error = 0.008228
relative error = 0.8823 %
Correct digits = 2
h = 0.001 0.001
y2[1] (numeric) = -0.529183310191 -0.359370241082
y2[1] (closed_form) = -0.578133331578 -0.335536684507
absolute error = 0.05444
relative error = 8.145 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2141.5MB, alloc=40.3MB, time=28.00
x[1] = 0.5681 0.389
h = 0.001 0.003
y1[1] (numeric) = -0.912990361383 0.2083870664
y1[1] (closed_form) = -0.907509153839 0.21461275612
absolute error = 0.008295
relative error = 0.8895 %
Correct digits = 2
h = 0.001 0.003
y2[1] (numeric) = -0.53016153581 -0.362848595963
y2[1] (closed_form) = -0.579255117489 -0.336230159786
absolute error = 0.05585
relative error = 8.338 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5691 0.392
h = 0.0001 0.004
y1[1] (numeric) = -0.913553471872 0.210343609564
y1[1] (closed_form) = -0.907941573898 0.21669033581
absolute error = 0.008472
relative error = 0.9076 %
Correct digits = 2
h = 0.0001 0.004
y2[1] (numeric) = -0.531143337094 -0.366326285575
y2[1] (closed_form) = -0.5808097952 -0.338737683437
absolute error = 0.05681
relative error = 8.45 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2190.0MB, alloc=40.3MB, time=28.63
x[1] = 0.5692 0.396
h = 0.003 0.006
y1[1] (numeric) = -0.914972572029 0.21250696541
y1[1] (closed_form) = -0.909245619121 0.219049550833
absolute error = 0.008695
relative error = 0.9297 %
Correct digits = 2
h = 0.003 0.006
y2[1] (numeric) = -0.532132753258 -0.36980656887
y2[1] (closed_form) = -0.58177213281 -0.342350266079
absolute error = 0.05673
relative error = 8.404 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5722 0.402
h = 0.0001 0.005
y1[1] (numeric) = -0.915603948496 0.216817410749
y1[1] (closed_form) = -0.909562710487 0.223586580269
absolute error = 0.009073
relative error = 0.9687 %
Correct digits = 2
h = 0.0001 0.005
y2[1] (numeric) = -0.533140434337 -0.373285010426
y2[1] (closed_form) = -0.585828230194 -0.347142738256
absolute error = 0.05882
relative error = 8.637 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2238.4MB, alloc=40.3MB, time=29.27
x[1] = 0.5723 0.407
h = 0.0001 0.003
y1[1] (numeric) = -0.917425700232 0.219523180613
y1[1] (closed_form) = -0.911251101062 0.226553696821
absolute error = 0.009357
relative error = 0.9965 %
Correct digits = 2
h = 0.0001 0.003
y2[1] (numeric) = -0.5341688596 -0.376763297181
y2[1] (closed_form) = -0.587044618667 -0.35167225644
absolute error = 0.05853
relative error = 8.553 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2286.9MB, alloc=40.3MB, time=29.90
x[1] = 0.5724 0.41
h = 0.001 0.001
y1[1] (numeric) = -0.918507746997 0.221165093149
y1[1] (closed_form) = -0.912251442793 0.228351292429
absolute error = 0.009528
relative error = 1.013 %
Correct digits = 2
h = 0.001 0.001
y2[1] (numeric) = -0.535206658826 -0.380247548601
y2[1] (closed_form) = -0.587818150563 -0.354384763013
absolute error = 0.05862
relative error = 8.541 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5734 0.411
h = 0.0001 0.004
y1[1] (numeric) = -0.91835401032 0.222082810361
y1[1] (closed_form) = -0.91201778074 0.229294407516
absolute error = 0.0096
relative error = 1.021 %
Correct digits = 2
h = 0.0001 0.004
y2[1] (numeric) = -0.536247357385 -0.383732808
y2[1] (closed_form) = -0.588959107911 -0.355068074965
absolute error = 0.06
relative error = 8.725 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2335.4MB, alloc=40.3MB, time=30.54
x[1] = 0.5735 0.415
h = 0.003 0.006
y1[1] (numeric) = -0.919842237875 0.224268435489
y1[1] (closed_form) = -0.913386360312 0.231687955329
absolute error = 0.009835
relative error = 1.044 %
Correct digits = 2
h = 0.003 0.006
y2[1] (numeric) = -0.537292882551 -0.387220394094
y2[1] (closed_form) = -0.589972341252 -0.358695829362
absolute error = 0.05991
relative error = 8.676 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5765 0.421
h = 0.0001 0.005
y1[1] (numeric) = -0.92056255489 0.228662263619
y1[1] (closed_form) = -0.913776752582 0.23632346874
absolute error = 0.01023
relative error = 1.084 %
Correct digits = 2
h = 0.0001 0.005
y2[1] (numeric) = -0.538357104111 -0.390706417499
y2[1] (closed_form) = -0.594117096529 -0.363475303245
absolute error = 0.06205
relative error = 8.91 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2384.0MB, alloc=40.3MB, time=31.17
x[1] = 0.5766 0.426
h = 0.0001 0.003
y1[1] (numeric) = -0.922470908813 0.2313960018
y1[1] (closed_form) = -0.915546023711 0.239333824328
absolute error = 0.01053
relative error = 1.113 %
Correct digits = 2
h = 0.0001 0.003
y2[1] (numeric) = -0.539442527696 -0.394192642791
y2[1] (closed_form) = -0.595397702854 -0.368024817954
absolute error = 0.06177
relative error = 8.825 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5767 0.429
h = 0.001 0.001
y1[1] (numeric) = -0.9236047257 0.233055564323
y1[1] (closed_form) = -0.91659460336 0.241158173225
absolute error = 0.01071
relative error = 1.13 %
Correct digits = 2
h = 0.001 0.001
y2[1] (numeric) = -0.540537428635 -0.397685124636
y2[1] (closed_form) = -0.596210047137 -0.370749002294
absolute error = 0.06185
relative error = 8.809 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2432.5MB, alloc=40.3MB, time=31.81
x[1] = 0.5777 0.43
h = 0.001 0.003
y1[1] (numeric) = -0.92346307141 0.233996082604
y1[1] (closed_form) = -0.916368900834 0.242126048794
absolute error = 0.01079
relative error = 1.138 %
Correct digits = 2
h = 0.001 0.003
y2[1] (numeric) = -0.541635275453 -0.401178685887
y2[1] (closed_form) = -0.597368170888 -0.371423842128
absolute error = 0.06318
relative error = 8.982 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5787 0.433
h = 0.0001 0.004
y1[1] (numeric) = -0.924129661456 0.236025564364
y1[1] (closed_form) = -0.916888741813 0.244293298165
absolute error = 0.01099
relative error = 1.158 %
Correct digits = 2
h = 0.0001 0.004
y2[1] (numeric) = -0.542736897322 -0.404671689235
y2[1] (closed_form) = -0.599014426379 -0.373930518071
absolute error = 0.06413
relative error = 9.081 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2480.9MB, alloc=40.3MB, time=32.44
x[1] = 0.5788 0.437
h = 0.003 0.006
y1[1] (numeric) = -0.925701009137 0.238239369881
y1[1] (closed_form) = -0.918331798762 0.246729075483
absolute error = 0.01124
relative error = 1.182 %
Correct digits = 2
h = 0.003 0.006
y2[1] (numeric) = -0.543846403657 -0.408167706925
y2[1] (closed_form) = -0.600088230479 -0.377576403247
absolute error = 0.06402
relative error = 9.03 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2529.6MB, alloc=40.3MB, time=33.08
x[1] = 0.5818 0.443
h = 0.0001 0.005
y1[1] (numeric) = -0.926527279057 0.242735567193
y1[1] (closed_form) = -0.918804922498 0.25148221905
absolute error = 0.01167
relative error = 1.225 %
Correct digits = 2
h = 0.0001 0.005
y2[1] (numeric) = -0.544975132854 -0.411662491242
y2[1] (closed_form) = -0.604338545589 -0.382340498501
absolute error = 0.06621
relative error = 9.259 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5819 0.448
h = 0.0001 0.003
y1[1] (numeric) = -0.928539771037 0.245504654169
y1[1] (closed_form) = -0.920667553086 0.254545760562
absolute error = 0.01199
relative error = 1.255 %
Correct digits = 2
h = 0.0001 0.003
y2[1] (numeric) = -0.546125623727 -0.415157900142
y2[1] (closed_form) = -0.605695585955 -0.38691386888
absolute error = 0.06593
relative error = 9.173 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2578.1MB, alloc=40.3MB, time=33.71
x[1] = 0.582 0.451
h = 0.001 0.001
y1[1] (numeric) = -0.929735826383 0.247186460759
y1[1] (closed_form) = -0.921771788637 0.256402961982
absolute error = 0.01218
relative error = 1.273 %
Correct digits = 2
h = 0.001 0.001
y2[1] (numeric) = -0.547285722098 -0.418659916428
y2[1] (closed_form) = -0.606554130226 -0.389651978448
absolute error = 0.06599
relative error = 9.153 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.583 0.452
h = 0.001 0.003
y1[1] (numeric) = -0.929608370778 0.24815473956
y1[1] (closed_form) = -0.92155462975 0.25740008979
absolute error = 0.01226
relative error = 1.281 %
Correct digits = 2
h = 0.001 0.003
y2[1] (numeric) = -0.548448823853 -0.422163097599
y2[1] (closed_form) = -0.60773269485 -0.390316740327
absolute error = 0.0673
relative error = 9.317 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2626.8MB, alloc=40.3MB, time=34.35
x[1] = 0.584 0.455
h = 0.0001 0.004
y1[1] (numeric) = -0.930331082327 0.25022574921
y1[1] (closed_form) = -0.922120759832 0.259617402398
absolute error = 0.01247
relative error = 1.302 %
Correct digits = 2
h = 0.0001 0.004
y2[1] (numeric) = -0.549615811945 -0.42566577752
y2[1] (closed_form) = -0.609430056398 -0.392823743843
absolute error = 0.06824
relative error = 9.411 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5841 0.459
h = 0.003 0.006
y1[1] (numeric) = -0.931985734894 0.252469301285
y1[1] (closed_form) = -0.923638384015 0.262096856294
absolute error = 0.01274
relative error = 1.327 %
Correct digits = 2
h = 0.003 0.006
y2[1] (numeric) = -0.550790838473 -0.429171700289
y2[1] (closed_form) = -0.610565771115 -0.396489171609
absolute error = 0.06813
relative error = 9.358 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2675.3MB, alloc=40.3MB, time=34.98
x[1] = 0.5871 0.465
h = 0.0001 0.005
y1[1] (numeric) = -0.932917127149 0.257070390145
y1[1] (closed_form) = -0.924193346408 0.266969907423
absolute error = 0.01319
relative error = 1.372 %
Correct digits = 2
h = 0.0001 0.005
y2[1] (numeric) = -0.55198562379 -0.432676713021
y2[1] (closed_form) = -0.614924694944 -0.401239069044
absolute error = 0.07035
relative error = 9.582 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5872 0.47
h = 0.0001 0.003
y1[1] (numeric) = -0.935034012257 0.259876798012
y1[1] (closed_form) = -0.926149471199 0.270088465997
absolute error = 0.01354
relative error = 1.403 %
Correct digits = 2
h = 0.0001 0.003
y2[1] (numeric) = -0.553202741702 -0.43618276729
y2[1] (closed_form) = -0.616359854647 -0.405838063712
absolute error = 0.07007
relative error = 9.495 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2723.7MB, alloc=40.3MB, time=35.61
x[1] = 0.5873 0.473
h = 0.001 0.001
y1[1] (numeric) = -0.936292447603 0.261582039117
y1[1] (closed_form) = -0.927309432966 0.271979624208
absolute error = 0.01374
relative error = 1.422 %
Correct digits = 2
h = 0.001 0.001
y2[1] (numeric) = -0.554429603993 -0.439695780472
y2[1] (closed_form) = -0.617265628911 -0.408591146646
absolute error = 0.07011
relative error = 9.472 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5883 0.474
h = 0.001 0.003
y1[1] (numeric) = -0.936178856115 0.262578536615
y1[1] (closed_form) = -0.927100486162 0.273006408223
absolute error = 0.01383
relative error = 1.431 %
Correct digits = 2
h = 0.001 0.003
y2[1] (numeric) = -0.555659529029 -0.443210043776
y2[1] (closed_form) = -0.618465326778 -0.40924585879
absolute error = 0.0714
relative error = 9.628 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2772.3MB, alloc=40.3MB, time=36.25
x[1] = 0.5893 0.477
h = 0.0001 0.004
y1[1] (numeric) = -0.936957481019 0.264692331243
y1[1] (closed_form) = -0.927712646342 0.275274927022
absolute error = 0.01405
relative error = 1.452 %
Correct digits = 2
h = 0.0001 0.004
y2[1] (numeric) = -0.55689345353 -0.446723861145
y2[1] (closed_form) = -0.620215152926 -0.411753937024
absolute error = 0.07234
relative error = 9.717 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2820.7MB, alloc=40.3MB, time=36.90
x[1] = 0.5894 0.481
h = 0.003 0.006
y1[1] (numeric) = -0.938695657424 0.266967234404
y1[1] (closed_form) = -0.929304951424 0.277799541872
absolute error = 0.01434
relative error = 1.478 %
Correct digits = 2
h = 0.003 0.006
y2[1] (numeric) = -0.558135575439 -0.450241149284
y2[1] (closed_form) = -0.621414150901 -0.415440313664
absolute error = 0.07222
relative error = 9.661 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5924 0.487
h = 0.0001 0.005
y1[1] (numeric) = -0.939731365835 0.271675819925
y1[1] (closed_form) = -0.929940869013 0.282794851727
absolute error = 0.01482
relative error = 1.524 %
Correct digits = 2
h = 0.0001 0.005
y2[1] (numeric) = -0.559398001883 -0.453757844755
y2[1] (closed_form) = -0.625884778543 -0.420177162289
absolute error = 0.07449
relative error = 9.881 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2869.2MB, alloc=40.3MB, time=37.53
x[1] = 0.5925 0.492
h = 0.0001 0.003
y1[1] (numeric) = -0.941952941973 0.274521568869
y1[1] (closed_form) = -0.931990652545 0.285970305386
absolute error = 0.01518
relative error = 1.557 %
Correct digits = 2
h = 0.0001 0.003
y2[1] (numeric) = -0.560683343517 -0.457275993033
y2[1] (closed_form) = -0.627399784471 -0.424803543326
absolute error = 0.0742
relative error = 9.793 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5926 0.495
h = 0.001 0.001
y1[1] (numeric) = -0.943273924143 0.276251464255
y1[1] (closed_form) = -0.933206428329 0.287896553134
absolute error = 0.01539
relative error = 1.576 %
Correct digits = 2
h = 0.001 0.001
y2[1] (numeric) = -0.561978573318 -0.460801452584
y2[1] (closed_form) = -0.62835384376 -0.427572643578
absolute error = 0.07423
relative error = 9.766 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2917.7MB, alloc=40.3MB, time=38.17
x[1] = 0.5936 0.496
h = 0.001 0.003
y1[1] (numeric) = -0.943173861413 0.277276656872
y1[1] (closed_form) = -0.933005358881 0.288953412761
absolute error = 0.01548
relative error = 1.585 %
Correct digits = 2
h = 0.001 0.003
y2[1] (numeric) = -0.563276927134 -0.46432824728
y2[1] (closed_form) = -0.629575374529 -0.428217324692
absolute error = 0.07549
relative error = 9.915 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5946 0.499
h = 0.0001 0.004
y1[1] (numeric) = -0.944008208121 0.279434530949
y1[1] (closed_form) = -0.933663299198 0.291274314787
absolute error = 0.01572
relative error = 1.608 %
Correct digits = 2
h = 0.0001 0.004
y2[1] (numeric) = -0.564579395457 -0.467854650014
y2[1] (closed_form) = -0.631379047992 -0.430727213044
absolute error = 0.07642
relative error = 9.999 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2965.3MB, alloc=40.3MB, time=38.79
x[1] = 0.5947 0.503
h = 0.003 0.006
y1[1] (numeric) = -0.945830161168 0.281742428963
y1[1] (closed_form) = -0.935330422364 0.293845612975
absolute error = 0.01602
relative error = 1.634 %
Correct digits = 2
h = 0.003 0.006
y2[1] (numeric) = -0.565890225307 -0.471384750926
y2[1] (closed_form) = -0.632642735602 -0.434435939633
absolute error = 0.0763
relative error = 9.942 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5977 0.509
h = 0.0001 0.005
y1[1] (numeric) = -0.946969402814 0.286561200108
y1[1] (closed_form) = -0.936046420083 0.298965607338
absolute error = 0.01653
relative error = 1.682 %
Correct digits = 2
h = 0.0001 0.005
y2[1] (numeric) = -0.567221915623 -0.474914570587
y2[1] (closed_form) = -0.637228210035 -0.439160856455
absolute error = 0.07861
relative error = 10.16 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3013.8MB, alloc=40.3MB, time=39.42
x[1] = 0.5978 0.514
h = 0.0001 0.003
y1[1] (numeric) = -0.949296010306 0.289448359522
y1[1] (closed_form) = -0.938190056327 0.30219988189
absolute error = 0.01691
relative error = 1.716 %
Correct digits = 2
h = 0.0001 0.003
y2[1] (numeric) = -0.568577115813 -0.478446248682
y2[1] (closed_form) = -0.638824831869 -0.44381637981
absolute error = 0.07832
relative error = 10.07 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3062.3MB, alloc=40.3MB, time=40.05
x[1] = 0.5979 0.517
h = 0.001 0.001
y1[1] (numeric) = -0.950679731144 0.291204158935
y1[1] (closed_form) = -0.939461751193 0.304162380936
absolute error = 0.01714
relative error = 1.736 %
Correct digits = 2
h = 0.001 0.001
y2[1] (numeric) = -0.569942355033 -0.481985591388
y2[1] (closed_form) = -0.639828256962 -0.446602537371
absolute error = 0.07833
relative error = 10.04 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.5989 0.518
h = 0.0001 0.004
y1[1] (numeric) = -0.950592860724 0.292258541491
y1[1] (closed_form) = -0.939268220949 0.305249751127
absolute error = 0.01723
relative error = 1.745 %
Correct digits = 2
h = 0.0001 0.004
y2[1] (numeric) = -0.571310781505 -0.48552635407
y2[1] (closed_form) = -0.641072327909 -0.447237196498
absolute error = 0.07958
relative error = 10.18 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3110.8MB, alloc=40.3MB, time=40.68
x[1] = 0.599 0.522
h = 0.003 0.006
y1[1] (numeric) = -0.952484851721 0.294595258559
y1[1] (closed_form) = -0.94100045411 0.307861587525
absolute error = 0.01755
relative error = 1.772 %
Correct digits = 2
h = 0.003 0.006
y2[1] (numeric) = -0.57268445829 -0.489070208413
y2[1] (closed_form) = -0.642392562012 -0.4509670734
absolute error = 0.07944
relative error = 10.12 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.602 0.528
h = 0.0001 0.005
y1[1] (numeric) = -0.95370977055 0.299508061974
y1[1] (closed_form) = -0.941786213075 0.31308996643
absolute error = 0.01807
relative error = 1.821 %
Correct digits = 2
h = 0.0001 0.005
y2[1] (numeric) = -0.574079467193 -0.492614036295
y2[1] (closed_form) = -0.647079571978 -0.455684009518
absolute error = 0.08181
relative error = 10.34 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3159.2MB, alloc=40.3MB, time=41.32
x[1] = 0.6021 0.533
h = 0.0001 0.003
y1[1] (numeric) = -0.956124222099 0.302431439286
y1[1] (closed_form) = -0.944011544937 0.316375329687
absolute error = 0.01847
relative error = 1.855 %
Correct digits = 2
h = 0.0001 0.003
y2[1] (numeric) = -0.575498491571 -0.496160056211
y2[1] (closed_form) = -0.648747521242 -0.460367021035
absolute error = 0.08153
relative error = 10.25 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6022 0.536
h = 0.001 0.001
y1[1] (numeric) = -0.957560410941 0.304209870854
y1[1] (closed_form) = -0.945331921443 0.318369317382
absolute error = 0.01871
relative error = 1.876 %
Correct digits = 2
h = 0.001 0.001
y2[1] (numeric) = -0.576927686573 -0.499714036124
y2[1] (closed_form) = -0.649794104462 -0.463169296955
absolute error = 0.08152
relative error = 10.22 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3207.9MB, alloc=40.3MB, time=41.96
x[1] = 0.6032 0.537
h = 0.001 0.003
y1[1] (numeric) = -0.957484258987 0.305289006543
y1[1] (closed_form) = -0.945144977895 0.319483226053
absolute error = 0.01881
relative error = 1.885 %
Correct digits = 2
h = 0.001 0.003
y2[1] (numeric) = -0.57836012318 -0.503269506585
y2[1] (closed_form) = -0.651058269079 -0.463795609344
absolute error = 0.08272
relative error = 10.35 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6042 0.54
h = 0.0001 0.004
y1[1] (numeric) = -0.958420322258 0.307531287194
y1[1] (closed_form) = -0.945888127154 0.321904313805
absolute error = 0.01907
relative error = 1.909 %
Correct digits = 2
h = 0.0001 0.004
y2[1] (numeric) = -0.579796890588 -0.506824680466
y2[1] (closed_form) = -0.652965864412 -0.466311464508
absolute error = 0.08364
relative error = 10.42 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3256.4MB, alloc=40.3MB, time=42.59
x[1] = 0.6043 0.544
h = 0.003 0.006
y1[1] (numeric) = -0.960396685119 0.309904222783
y1[1] (closed_form) = -0.947695514491 0.324565767718
absolute error = 0.0194
relative error = 1.936 %
Correct digits = 2
h = 0.003 0.006
y2[1] (numeric) = -0.581242334711 -0.510383968385
y2[1] (closed_form) = -0.654353481657 -0.470066303376
absolute error = 0.08349
relative error = 10.36 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3304.9MB, alloc=40.3MB, time=43.23
x[1] = 0.6073 0.55
h = 0.0001 0.005
y1[1] (numeric) = -0.961723751681 0.314932554802
y1[1] (closed_form) = -0.948559775364 0.329923556902
absolute error = 0.01995
relative error = 1.987 %
Correct digits = 2
h = 0.0001 0.005
y2[1] (numeric) = -0.582709687301 -0.513943530125
y2[1] (closed_form) = -0.659161307627 -0.474773339092
absolute error = 0.0859
relative error = 10.57 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6074 0.555
h = 0.0001 0.003
y1[1] (numeric) = -0.964244024135 0.317901399274
y1[1] (closed_form) = -0.9508794223 0.333271451769
absolute error = 0.02037
relative error = 2.021 %
Correct digits = 2
h = 0.0001 0.003
y2[1] (numeric) = -0.584201674189 -0.517505679119
y2[1] (closed_form) = -0.660914263066 -0.479488767662
absolute error = 0.08562
relative error = 10.49 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3353.5MB, alloc=40.3MB, time=43.86
x[1] = 0.6075 0.558
h = 0.001 0.001
y1[1] (numeric) = -0.965743400553 0.319708185442
y1[1] (closed_form) = -0.952255973255 0.335303929935
absolute error = 0.02062
relative error = 2.042 %
Correct digits = 2
h = 0.001 0.001
y2[1] (numeric) = -0.58570399645 -0.52107614377
y2[1] (closed_form) = -0.662012281944 -0.482310039927
absolute error = 0.08559
relative error = 10.45 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6085 0.559
h = 0.001 0.003
y1[1] (numeric) = -0.965679806089 0.320817504428
y1[1] (closed_form) = -0.952075935327 0.336449204453
absolute error = 0.02072
relative error = 2.052 %
Correct digits = 2
h = 0.001 0.003
y2[1] (numeric) = -0.587209627429 -0.524648183541
y2[1] (closed_form) = -0.663300324363 -0.482926329529
absolute error = 0.08678
relative error = 10.58 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3402.0MB, alloc=40.3MB, time=44.50
x[1] = 0.6095 0.562
h = 0.0001 0.004
y1[1] (numeric) = -0.966671144145 0.323107830493
y1[1] (closed_form) = -0.952864211522 0.338926237867
absolute error = 0.021
relative error = 2.076 %
Correct digits = 2
h = 0.0001 0.004
y2[1] (numeric) = -0.588719710232 -0.528219976823
y2[1] (closed_form) = -0.66526585503 -0.485446051331
absolute error = 0.08769
relative error = 10.65 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6096 0.566
h = 0.003 0.006
y1[1] (numeric) = -0.968732225816 0.325518744667
y1[1] (closed_form) = -0.954746956367 0.341638944229
absolute error = 0.02134
relative error = 2.105 %
Correct digits = 2
h = 0.003 0.006
y2[1] (numeric) = -0.590238649605 -0.531796110528
y2[1] (closed_form) = -0.666722363759 -0.489227240466
absolute error = 0.08753
relative error = 10.58 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3450.4MB, alloc=40.3MB, time=45.13
x[1] = 0.6126 0.572
h = 0.0001 0.005
y1[1] (numeric) = -0.970160716709 0.330665538389
y1[1] (closed_form) = -0.955688863651 0.347128787991
absolute error = 0.02192
relative error = 2.156 %
Correct digits = 2
h = 0.0001 0.005
y2[1] (numeric) = -0.591780085043 -0.535372812374
y2[1] (closed_form) = -0.671654295495 -0.493925400553
absolute error = 0.08999
relative error = 10.79 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6127 0.577
h = 0.0001 0.003
y1[1] (numeric) = -0.972787268406 0.333682065333
y1[1] (closed_form) = -0.958103102455 0.350541281831
absolute error = 0.02236
relative error = 2.191 %
Correct digits = 2
h = 0.0001 0.003
y2[1] (numeric) = -0.59334678688 -0.538952491153
y2[1] (closed_form) = -0.67349415604 -0.498674987227
absolute error = 0.0897
relative error = 10.7 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3499.0MB, alloc=40.3MB, time=45.76
x[1] = 0.6128 0.58
h = 0.001 0.001
y1[1] (numeric) = -0.974350093789 0.335518544721
y1[1] (closed_form) = -0.959535981448 0.352613498159
absolute error = 0.02262
relative error = 2.213 %
Correct digits = 2
h = 0.001 0.001
y2[1] (numeric) = -0.594923996423 -0.542540842615
y2[1] (closed_form) = -0.67464476916 -0.501516286043
absolute error = 0.08966
relative error = 10.67 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3547.5MB, alloc=40.3MB, time=46.39
x[1] = 0.6138 0.581
h = 0.001 0.003
y1[1] (numeric) = -0.974298715537 0.336658594868
y1[1] (closed_form) = -0.95936249996 0.353790618692
absolute error = 0.02273
relative error = 2.223 %
Correct digits = 2
h = 0.001 0.003
y2[1] (numeric) = -0.596504583924 -0.546130853649
y2[1] (closed_form) = -0.675957420358 -0.502122533444
absolute error = 0.09083
relative error = 10.79 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6148 0.584
h = 0.0001 0.004
y1[1] (numeric) = -0.975345196125 0.338998410041
y1[1] (closed_form) = -0.960195684795 0.356324910944
absolute error = 0.02302
relative error = 2.247 %
Correct digits = 2
h = 0.0001 0.004
y2[1] (numeric) = -0.598089746471 -0.549720666918
y2[1] (closed_form) = -0.677982370133 -0.504646812286
absolute error = 0.09173
relative error = 10.85 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3596.1MB, alloc=40.3MB, time=47.03
x[1] = 0.6149 0.588
h = 0.003 0.006
y1[1] (numeric) = -0.977491376171 0.341449105813
y1[1] (closed_form) = -0.962154012882 0.359090545629
absolute error = 0.02338
relative error = 2.276 %
Correct digits = 2
h = 0.003 0.006
y2[1] (numeric) = -0.59968395117 -0.553315046743
y2[1] (closed_form) = -0.679509316243 -0.508455735935
absolute error = 0.09157
relative error = 10.79 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6179 0.594
h = 0.0001 0.005
y1[1] (numeric) = -0.979020586721 0.346717382973
y1[1] (closed_form) = -0.963172715686 0.364715166582
absolute error = 0.02398
relative error = 2.328 %
Correct digits = 2
h = 0.0001 0.005
y2[1] (numeric) = -0.601301251156 -0.556910283056
y2[1] (closed_form) = -0.684568698018 -0.513146012177
absolute error = 0.09407
relative error = 11 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3644.6MB, alloc=40.3MB, time=47.67
x[1] = 0.618 0.599
h = 0.0001 0.003
y1[1] (numeric) = -0.981753916907 0.349783861604
y1[1] (closed_form) = -0.965681851209 0.368194378273
absolute error = 0.02444
relative error = 2.365 %
Correct digits = 2
h = 0.0001 0.003
y2[1] (numeric) = -0.602944463354 -0.560508880466
y2[1] (closed_form) = -0.686497410193 -0.517931493312
absolute error = 0.09378
relative error = 10.9 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6181 0.602
h = 0.001 0.001
y1[1] (numeric) = -0.983380476725 0.351651405633
y1[1] (closed_form) = -0.967171228247 0.370307611705
absolute error = 0.02471
relative error = 2.386 %
Correct digits = 2
h = 0.001 0.001
y2[1] (numeric) = -0.604598363363 -0.564116509077
y2[1] (closed_form) = -0.687701804786 -0.520793845748
absolute error = 0.09372
relative error = 10.86 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3693.1MB, alloc=40.3MB, time=48.30
x[1] = 0.6191 0.603
h = 0.001 0.003
y1[1] (numeric) = -0.983340971077 0.352822753873
y1[1] (closed_form) = -0.967003949577 0.371517074471
absolute error = 0.02483
relative error = 2.397 %
Correct digits = 2
h = 0.001 0.003
y2[1] (numeric) = -0.606255712754 -0.56772588162
y2[1] (closed_form) = -0.689039804619 -0.521390021216
absolute error = 0.09487
relative error = 10.98 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6201 0.606
h = 0.0001 0.004
y1[1] (numeric) = -0.984442476279 0.355213542435
y1[1] (closed_form) = -0.967881831879 0.374109975317
absolute error = 0.02513
relative error = 2.421 %
Correct digits = 2
h = 0.0001 0.004
y2[1] (numeric) = -0.607917762692 -0.571335103748
y2[1] (closed_form) = -0.691125685429 -0.52391953572
absolute error = 0.09577
relative error = 11.04 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3741.6MB, alloc=40.3MB, time=48.93
x[1] = 0.6202 0.61
h = 0.003 0.006
y1[1] (numeric) = -0.986674166575 0.357705866794
y1[1] (closed_form) = -0.96991599106 0.376930255957
absolute error = 0.0255
relative error = 2.451 %
Correct digits = 2
h = 0.003 0.006
y2[1] (numeric) = -0.609589046242 -0.574949118375
y2[1] (closed_form) = -0.692724653396 -0.527757574347
absolute error = 0.0956
relative error = 10.98 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3790.1MB, alloc=40.3MB, time=49.56
x[1] = 0.6232 0.616
h = 0.0001 0.005
y1[1] (numeric) = -0.988303409635 0.363098739105
y1[1] (closed_form) = -0.971010642073 0.382692456075
absolute error = 0.02613
relative error = 2.504 %
Correct digits = 2
h = 0.0001 0.005
y2[1] (numeric) = -0.611284036316 -0.578564271842
y2[1] (closed_form) = -0.697914885754 -0.532440925211
absolute error = 0.09814
relative error = 11.18 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6233 0.621
h = 0.0001 0.003
y1[1] (numeric) = -0.991144058089 0.366217493833
y1[1] (closed_form) = -0.973615006874 0.386240557043
absolute error = 0.02661
relative error = 2.541 %
Correct digits = 2
h = 0.0001 0.003
y2[1] (numeric) = -0.613005598564 -0.58218316507
y2[1] (closed_form) = -0.699934444962 -0.537264032807
absolute error = 0.09785
relative error = 11.09 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3838.7MB, alloc=40.3MB, time=50.20
x[1] = 0.6234 0.624
h = 0.001 0.001
y1[1] (numeric) = -0.992834661658 0.368117507508
y1[1] (closed_form) = -0.975161068153 0.3883961184
absolute error = 0.0269
relative error = 2.563 %
Correct digits = 2
h = 0.001 0.001
y2[1] (numeric) = -0.614738036688 -0.585811449647
y2[1] (closed_form) = -0.701193837691 -0.540148462988
absolute error = 0.09777
relative error = 11.05 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6244 0.625
h = 0.0001 0.004
y1[1] (numeric) = -0.992806682348 0.369320740036
y1[1] (closed_form) = -0.974999633968 0.389638435808
absolute error = 0.02702
relative error = 2.573 %
Correct digits = 2
h = 0.0001 0.004
y2[1] (numeric) = -0.616473997865 -0.589441562443
y2[1] (closed_form) = -0.702557935221 -0.54073452629
absolute error = 0.09891
relative error = 11.16 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3887.2MB, alloc=40.3MB, time=50.83
x[1] = 0.6245 0.629
h = 0.003 0.006
y1[1] (numeric) = -0.995109979156 0.371849241798
y1[1] (closed_form) = -0.977099960752 0.392506254078
absolute error = 0.02741
relative error = 2.603 %
Correct digits = 2
h = 0.003 0.006
y2[1] (numeric) = -0.618215716878 -0.593075534787
y2[1] (closed_form) = -0.704219827109 -0.544599613205
absolute error = 0.09872
relative error = 11.09 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6275 0.635
h = 0.0001 0.005
y1[1] (numeric) = -0.996822054967 0.377348496041
y1[1] (closed_form) = -0.978260994674 0.39838829188
absolute error = 0.02806
relative error = 2.656 %
Correct digits = 2
h = 0.0001 0.005
y2[1] (numeric) = -0.619981661619 -0.59671087649
y2[1] (closed_form) = -0.709525526203 -0.54927935964
absolute error = 0.1013
relative error = 11.29 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3935.6MB, alloc=40.3MB, time=51.46
x[1] = 0.6276 0.64
h = 0.0001 0.003
y1[1] (numeric) = -0.999752614172 0.380512733269
y1[1] (closed_form) = -0.980948473664 0.401996329902
absolute error = 0.02855
relative error = 2.693 %
Correct digits = 2
h = 0.0001 0.003
y2[1] (numeric) = -0.621774740201 -0.600350269177
y2[1] (closed_form) = -0.711624443455 -0.554137354138
absolute error = 0.101
relative error = 11.2 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6277 0.643
h = 0.001 0.001
y1[1] (numeric) = -1.00149686972 0.382440979615
y1[1] (closed_form) = -0.982544014215 0.404188721669
absolute error = 0.02885
relative error = 2.715 %
Correct digits = 2
h = 0.001 0.001
y2[1] (numeric) = -0.623578857988 -0.603999354807
y2[1] (closed_form) = -0.712931894532 -0.557042281506
absolute error = 0.1009
relative error = 11.16 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3984.1MB, alloc=40.3MB, time=52.10
x[1] = 0.6287 0.644
h = 0.001 0.003
y1[1] (numeric) = -1.00147821206 0.383671287175
y1[1] (closed_form) = -0.982387719989 0.405459678337
absolute error = 0.02897
relative error = 2.726 %
Correct digits = 2
h = 0.001 0.003
y2[1] (numeric) = -0.625386562109 -0.607650338871
y2[1] (closed_form) = -0.714319184503 -0.557619923405
absolute error = 0.102
relative error = 11.26 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=4032.7MB, alloc=40.3MB, time=52.73
x[1] = 0.6297 0.647
h = 0.0001 0.004
y1[1] (numeric) = -1.00268034701 0.386159639361
y1[1] (closed_form) = -0.983348972324 0.408164829379
absolute error = 0.02929
relative error = 2.751 %
Correct digits = 2
h = 0.0001 0.004
y2[1] (numeric) = -0.627199203225 -0.611301255649
y2[1] (closed_form) = -0.71652248687 -0.560161715596
absolute error = 0.1029
relative error = 11.32 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6298 0.651
h = 0.003 0.006
y1[1] (numeric) = -1.00507005024 0.388733390001
y1[1] (closed_form) = -0.985525670948 0.411090600197
absolute error = 0.0297
relative error = 2.781 %
Correct digits = 2
h = 0.003 0.006
y2[1] (numeric) = -0.629021445285 -0.61495737895
y2[1] (closed_form) = -0.718259438888 -0.564058497035
absolute error = 0.1027
relative error = 11.25 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=4081.2MB, alloc=40.3MB, time=53.36
x[1] = 0.6328 0.657
h = 0.0001 0.005
y1[1] (numeric) = -1.00688094563 0.394363400663
y1[1] (closed_form) = -0.986761118045 0.417115655962
absolute error = 0.03037
relative error = 2.835 %
Correct digits = 2
h = 0.0001 0.005
y2[1] (numeric) = -0.63086854825 -0.618615142702
y2[1] (closed_form) = -0.723702461569 -0.568733053829
absolute error = 0.1054
relative error = 11.45 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6329 0.662
h = 0.0001 0.003
y1[1] (numeric) = -1.00991999014 0.397584468379
y1[1] (closed_form) = -0.989544545045 0.420796762599
absolute error = 0.03089
relative error = 2.872 %
Correct digits = 2
h = 0.0001 0.003
y2[1] (numeric) = -0.63274347313 -0.6222773259
y2[1] (closed_form) = -0.725896052922 -0.573631912346
absolute error = 0.1051
relative error = 11.36 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=4129.8MB, alloc=40.3MB, time=54.00
x[1] = 0.633 0.665
h = 0.001 0.001
y1[1] (numeric) = -1.01172896056 0.399547937833
y1[1] (closed_form) = -0.99119717519 0.423034005809
absolute error = 0.0312
relative error = 2.895 %
Correct digits = 2
h = 0.001 0.001
y2[1] (numeric) = -0.634629640898 -0.625949565751
y2[1] (closed_form) = -0.727260834992 -0.576560831262
absolute error = 0.105
relative error = 11.31 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.634 0.666
h = 0.001 0.003
y1[1] (numeric) = -1.01172117289 0.400811299069
y1[1] (closed_form) = -0.991046051717 0.424338818623
absolute error = 0.03132
relative error = 2.905 %
Correct digits = 2
h = 0.001 0.003
y2[1] (numeric) = -0.636519473089 -0.629623788282
y2[1] (closed_form) = -0.728675642923 -0.577128266699
absolute error = 0.1061
relative error = 11.41 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=4178.3MB, alloc=40.3MB, time=54.64
x[1] = 0.635 0.669
h = 0.0001 0.004
y1[1] (numeric) = -1.01297808906 0.403355158404
y1[1] (closed_form) = -0.992051450615 0.427106649003
absolute error = 0.03166
relative error = 2.931 %
Correct digits = 2
h = 0.0001 0.004
y2[1] (numeric) = -0.638414374826 -0.633297986867
y2[1] (closed_form) = -0.730944357089 -0.579677189654
absolute error = 0.1069
relative error = 11.46 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6351 0.673
h = 0.003 0.006
y1[1] (numeric) = -1.01545470047 0.40597613545
y1[1] (closed_form) = -0.994304831144 0.43009221394
absolute error = 0.03208
relative error = 2.961 %
Correct digits = 2
h = 0.003 0.006
y2[1] (numeric) = -0.640319086913 -0.636977617795
y2[1] (closed_form) = -0.73275806995 -0.583607037159
absolute error = 0.1067
relative error = 11.39 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=4226.7MB, alloc=40.3MB, time=55.26
x[1] = 0.6381 0.679
h = 0.0001 0.005
y1[1] (numeric) = -1.0173637712 0.411740277097
y1[1] (closed_form) = -0.995613849535 0.436263322757
absolute error = 0.03278
relative error = 3.016 %
Correct digits = 2
h = 0.0001 0.005
y2[1] (numeric) = -0.64224930821 -0.640659154181
y2[1] (closed_form) = -0.738341988007 -0.58827726614
absolute error = 0.1094
relative error = 11.59 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6382 0.684
h = 0.0001 0.003
y1[1] (numeric) = -1.02051195361 0.415020663642
y1[1] (closed_form) = -0.998493635074 0.440019825453
absolute error = 0.03331
relative error = 3.053 %
Correct digits = 2
h = 0.0001 0.003
y2[1] (numeric) = -0.644208054916 -0.644345472982
y2[1] (closed_form) = -0.74063239607 -0.593218710594
absolute error = 0.1091
relative error = 11.5 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=4275.4MB, alloc=40.3MB, time=55.90
x[1] = 0.6383 0.687
h = 0.001 0.001
y1[1] (numeric) = -1.02238601452 0.417020860902
y1[1] (closed_form) = -1.00020358652 0.44230332554
absolute error = 0.03363
relative error = 3.075 %
Correct digits = 2
h = 0.001 0.001
y2[1] (numeric) = -0.646178256721 -0.648042214145
y2[1] (closed_form) = -0.742055814443 -0.596172638127
absolute error = 0.109
relative error = 11.45 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=4323.9MB, alloc=40.3MB, time=56.54
x[1] = 0.6393 0.688
h = 0.001 0.003
y1[1] (numeric) = -1.02238874113 0.41831791775
y1[1] (closed_form) = -1.00005726059 0.443642554147
absolute error = 0.03376
relative error = 3.086 %
Correct digits = 2
h = 0.001 0.003
y2[1] (numeric) = -0.648152203461 -0.651741022223
y2[1] (closed_form) = -0.743498917714 -0.596729795851
absolute error = 0.1101
relative error = 11.55 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6403 0.691
h = 0.0001 0.004
y1[1] (numeric) = -1.02370037108 0.420918931133
y1[1] (closed_form) = -1.00110661893 0.446474560259
absolute error = 0.03411
relative error = 3.112 %
Correct digits = 2
h = 0.0001 0.004
y2[1] (numeric) = -0.650131354876 -0.655439848269
y2[1] (closed_form) = -0.74583467249 -0.599286482577
absolute error = 0.111
relative error = 11.6 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=4372.6MB, alloc=40.3MB, time=57.17
x[1] = 0.6404 0.695
h = 0.003 0.006
y1[1] (numeric) = -1.02626442361 0.423589160387
y1[1] (closed_form) = -1.00343701245 0.44952180603
absolute error = 0.03455
relative error = 3.142 %
Correct digits = 2
h = 0.003 0.006
y2[1] (numeric) = -0.652120532558 -0.65914433252
y2[1] (closed_form) = -0.747726889618 -0.603250764865
absolute error = 0.1107
relative error = 11.53 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6434 0.701
h = 0.0001 0.005
y1[1] (numeric) = -1.02827103812 0.429490903301
y1[1] (closed_form) = -1.00481875973 0.455842086734
absolute error = 0.03528
relative error = 3.197 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -0.654135881295 -0.662850981103
y2[1] (closed_form) = -0.753455338065 -0.607917493028
absolute error = 0.1135
relative error = 11.72 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=4421.0MB, alloc=40.3MB, time=57.80
x[1] = 0.6435 0.706
h = 0.0001 0.003
y1[1] (numeric) = -1.03152905017 0.432833157647
y1[1] (closed_form) = -1.00779534068 0.459676369782
absolute error = 0.03583
relative error = 3.235 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -0.656180474806 -0.666562769568
y2[1] (closed_form) = -0.75584475952 -0.612903242172
absolute error = 0.1132
relative error = 11.63 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6436 0.709
h = 0.001 0.001
y1[1] (numeric) = -1.03346860014 0.434871624257
y1[1] (closed_form) = -1.00956286048 0.462007566636
absolute error = 0.03616
relative error = 3.257 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -0.658236744371 -0.670285348225
y2[1] (closed_form) = -0.757328152075 -0.615883193119
absolute error = 0.113
relative error = 11.58 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=4469.8MB, alloc=40.3MB, time=58.44
x[1] = 0.6446 0.71
h = 0.001 0.003
y1[1] (numeric) = -1.03348148128 0.436203038761
y1[1] (closed_form) = -1.00942095306 0.463381787497
absolute error = 0.0363
relative error = 3.268 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -0.660296841868 -0.674010078046
y2[1] (closed_form) = -0.758800338567 -0.616429990594
absolute error = 0.1141
relative error = 11.67 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6456 0.713
h = 0.0001 0.004
y1[1] (numeric) = -1.03484776955 0.438862897463
y1[1] (closed_form) = -1.01051408879 0.466279505245
absolute error = 0.03666
relative error = 3.294 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -0.662362281826 -0.677734866309
y2[1] (closed_form) = -0.761204795142 -0.618995062002
absolute error = 0.115
relative error = 11.72 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=4518.2MB, alloc=40.3MB, time=59.07
x[1] = 0.6457 0.717
h = 0.003 0.006
y1[1] (numeric) = -1.037499827 0.441584454185
y1[1] (closed_form) = -1.0129218471 0.469390364648
absolute error = 0.03711
relative error = 3.324 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -0.664437970657 -0.681465538731
y2[1] (closed_form) = -0.763177303783 -0.622995145182
absolute error = 0.1148
relative error = 11.65 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=4566.7MB, alloc=40.3MB, time=59.70
x[1] = 0.6487 0.723
h = 0.0001 0.005
y1[1] (numeric) = -1.03960336518 0.447627365959
y1[1] (closed_form) = -1.01437547925 0.475863021047
absolute error = 0.03786
relative error = 3.379 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -0.666540506332 -0.685198628177
y2[1] (closed_form) = -0.769053982715 -0.627659164219
absolute error = 0.1176
relative error = 11.84 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6488 0.728
h = 0.0001 0.003
y1[1] (numeric) = -1.04297193736 0.451034099198
y1[1] (closed_form) = -1.01744931848 0.479777526775
absolute error = 0.03844
relative error = 3.417 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -0.668673022489 -0.688937209448
y2[1] (closed_form) = -0.771544669719 -0.632690933914
absolute error = 0.1172
relative error = 11.75 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=4615.2MB, alloc=40.3MB, time=60.33
x[1] = 0.6489 0.731
h = 0.001 0.001
y1[1] (numeric) = -1.04497739768 0.453112414449
y1[1] (closed_form) = -1.01927466881 0.482157895459
absolute error = 0.03878
relative error = 3.44 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -0.670817444612 -0.692686950994
y2[1] (closed_form) = -0.773089407744 -0.635697920949
absolute error = 0.1171
relative error = 11.7 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6499 0.732
h = 0.0001 0.004
y1[1] (numeric) = -1.04500006924 0.454478868997
y1[1] (closed_form) = -1.0191367947 0.483567702017
absolute error = 0.03892
relative error = 3.451 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -0.672965780212 -0.696438927982
y2[1] (closed_form) = -0.774591476185 -0.636234264132
absolute error = 0.1181
relative error = 11.78 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=4663.8MB, alloc=40.3MB, time=60.96
x[1] = 0.65 0.736
h = 0.003 0.006
y1[1] (numeric) = -1.04772593042 0.457244869366
y1[1] (closed_form) = -1.02161223334 0.486733973888
absolute error = 0.03939
relative error = 3.481 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -0.675120476173 -0.700195541282
y2[1] (closed_form) = -0.776634113998 -0.640267241867
absolute error = 0.1179
relative error = 11.71 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.653 0.742
h = 0.0001 0.005
y1[1] (numeric) = -1.04990976034 0.463408343633
y1[1] (closed_form) = -1.02312893226 0.493339578981
absolute error = 0.04016
relative error = 3.536 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -0.67730259353 -0.703954777232
y2[1] (closed_form) = -0.782641418896 -0.644931362562
absolute error = 0.1207
relative error = 11.91 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=4712.2MB, alloc=40.3MB, time=61.60
x[1] = 0.6531 0.747
h = 0.0001 0.003
y1[1] (numeric) = -1.05337109896 0.466870964641
y1[1] (closed_form) = -1.02628787473 0.497323972161
absolute error = 0.04075
relative error = 3.574 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -0.679515317939 -0.707719793932
y2[1] (closed_form) = -0.78522054282 -0.65000536105
absolute error = 0.1204
relative error = 11.81 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6532 0.75
h = 0.001 0.001
y1[1] (numeric) = -1.05543185886 0.468983806957
y1[1] (closed_form) = -1.02816383529 0.499747181499
absolute error = 0.04111
relative error = 3.596 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -0.681740147336 -0.711496281283
y2[1] (closed_form) = -0.786818870787 -0.653037182866
absolute error = 0.1202
relative error = 11.76 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=4760.7MB, alloc=40.3MB, time=62.23
x[1] = 0.6542 0.751
h = 0.001 0.003
y1[1] (numeric) = -1.05546239021 0.470380047185
y1[1] (closed_form) = -1.02802955337 0.501188065672
absolute error = 0.04125
relative error = 3.607 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -0.683968963645 -0.715275074367
y2[1] (closed_form) = -0.788347435017 -0.653564812191
absolute error = 0.1213
relative error = 11.84 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=4809.1MB, alloc=40.3MB, time=62.86
x[1] = 0.6552 0.754
h = 0.0001 0.004
y1[1] (numeric) = -1.05692879805 0.473152467658
y1[1] (closed_form) = -1.02920450747 0.504211766832
absolute error = 0.04163
relative error = 3.633 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -0.686203382426 -0.719053996224
y2[1] (closed_form) = -0.790884148814 -0.656147962913
absolute error = 0.1221
relative error = 11.88 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6553 0.758
h = 0.0001 0.004
y1[1] (numeric) = -1.05974384832 0.47597386209
y1[1] (closed_form) = -1.03175804408 0.50744537003
absolute error = 0.04211
relative error = 3.663 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -0.688448476718 -0.722839217022
y2[1] (closed_form) = -0.79301050811 -0.660219299876
absolute error = 0.1219
relative error = 11.81 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=4857.7MB, alloc=40.3MB, time=63.50
x[1] = 0.6554 0.762
h = 0.003 0.006
y1[1] (numeric) = -1.06257383639 0.478804639131
y1[1] (closed_form) = -1.03432767256 0.510687912699
absolute error = 0.0426
relative error = 3.693 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -0.690705157588 -0.726635445274
y2[1] (closed_form) = -0.795150075838 -0.664300559349
absolute error = 0.1216
relative error = 11.74 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6584 0.768
h = 0.0001 0.005
y1[1] (numeric) = -1.06486951744 0.485141308738
y1[1] (closed_form) = -1.03593276328 0.517477267128
absolute error = 0.04339
relative error = 3.747 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -0.692990081764 -0.730434577217
y2[1] (closed_form) = -0.801339934099 -0.668969100952
absolute error = 0.1246
relative error = 11.93 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=4906.1MB, alloc=40.3MB, time=64.14
x[1] = 0.6585 0.773
h = 0.0001 0.003
y1[1] (numeric) = -1.06846178159 0.488685276262
y1[1] (closed_form) = -1.03921017298 0.521557865079
absolute error = 0.044
relative error = 3.784 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -0.6953065104 -0.734239888622
y2[1] (closed_form) = -0.804041273022 -0.674104996066
absolute error = 0.1243
relative error = 11.84 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6586 0.776
h = 0.001 0.001
y1[1] (numeric) = -1.0706005785 0.49084830215
y1[1] (closed_form) = -1.04115660129 0.524040059475
absolute error = 0.04437
relative error = 3.807 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -0.697635333252 -0.738057108522
y2[1] (closed_form) = -0.805713686842 -0.677173264116
absolute error = 0.124
relative error = 11.79 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=4954.8MB, alloc=40.3MB, time=64.78
x[1] = 0.6596 0.777
h = 0.001 0.003
y1[1] (numeric) = -1.07064174387 0.492287070855
y1[1] (closed_form) = -1.04102753633 0.52552398754
absolute error = 0.04452
relative error = 3.817 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -0.699968248849 -0.741876732796
y2[1] (closed_form) = -0.807279560848 -0.677689574422
absolute error = 0.125
relative error = 11.86 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6606 0.78
h = 0.0001 0.004
y1[1] (numeric) = -1.07217196657 0.495134267602
y1[1] (closed_form) = -1.04225591156 0.528628746339
absolute error = 0.04491
relative error = 3.843 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -0.702306937487 -0.745696528238
y2[1] (closed_form) = -0.809902428625 -0.680287422807
absolute error = 0.1259
relative error = 11.9 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=5003.3MB, alloc=40.3MB, time=65.41
x[1] = 0.6607 0.784
h = 0.003 0.006
y1[1] (numeric) = -1.07509205353 0.498022951575
y1[1] (closed_form) = -1.044904199 0.531941037258
absolute error = 0.04541
relative error = 3.873 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -0.704656585487 -0.749522887591
y2[1] (closed_form) = -0.812127922958 -0.684408709196
absolute error = 0.1257
relative error = 11.83 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=5051.8MB, alloc=40.3MB, time=66.05
x[1] = 0.6637 0.79
h = 0.0001 0.005
y1[1] (numeric) = -1.07748315576 0.504512318061
y1[1] (closed_form) = -1.04657876465 0.538893061663
absolute error = 0.04623
relative error = 3.927 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -0.707035198157 -0.753352385402
y2[1] (closed_form) = -0.818477621409 -0.689076915484
absolute error = 0.1286
relative error = 12.02 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6638 0.795
h = 0.0001 0.003
y1[1] (numeric) = -1.08118867624 0.508129040515
y1[1] (closed_form) = -1.04995512236 0.543061632128
absolute error = 0.04686
relative error = 3.964 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -0.709446104162 -0.757188399128
y2[1] (closed_form) = -0.821287328554 -0.694264141898
absolute error = 0.1283
relative error = 11.93 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=5100.5MB, alloc=40.3MB, time=66.68
x[1] = 0.6639 0.798
h = 0.001 0.001
y1[1] (numeric) = -1.08339494656 0.510336923656
y1[1] (closed_form) = -1.05196034543 0.545597680574
absolute error = 0.04724
relative error = 3.986 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -0.71186966272 -0.761036699856
y2[1] (closed_form) = -0.823025411839 -0.6973625799
absolute error = 0.1281
relative error = 11.88 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6649 0.799
h = 0.001 0.003
y1[1] (numeric) = -1.08344482536 0.511812969278
y1[1] (closed_form) = -1.05183413649 0.547119120485
absolute error = 0.04739
relative error = 3.997 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -0.714297407745 -0.764887489678
y2[1] (closed_form) = -0.824623667397 -0.697868119007
absolute error = 0.1291
relative error = 11.95 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=5149.1MB, alloc=40.3MB, time=67.32
x[1] = 0.6659 0.802
h = 0.0001 0.004
y1[1] (numeric) = -1.08502975048 0.514726322255
y1[1] (closed_form) = -1.05310568168 0.550296209087
absolute error = 0.0478
relative error = 4.022 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -0.716731075318 -0.768738485373
y2[1] (closed_form) = -0.827322257197 -0.700476820679
absolute error = 0.13
relative error = 11.99 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.666 0.806
h = 0.003 0.006
y1[1] (numeric) = -1.08804062083 0.517675198921
y1[1] (closed_form) = -1.05583306301 0.553680376034
absolute error = 0.04831
relative error = 4.052 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -0.719175953713 -0.772596272449
y2[1] (closed_form) = -0.829635653944 -0.704639493947
absolute error = 0.1297
relative error = 11.91 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=5197.7MB, alloc=40.3MB, time=67.95
x[1] = 0.669 0.812
h = 0.0001 0.005
y1[1] (numeric) = -1.09052655654 0.52432123652
y1[1] (closed_form) = -1.05757624571 0.560798630539
absolute error = 0.04916
relative error = 4.106 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -0.721650533784 -0.776457426286
y2[1] (closed_form) = -0.836149176266 -0.7093080124
absolute error = 0.1327
relative error = 12.11 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6691 0.817
h = 0.0001 0.003
y1[1] (numeric) = -1.09434621559 0.528013589526
y1[1] (closed_form) = -1.06105211862 0.56505786149
absolute error = 0.04981
relative error = 4.143 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -0.724158214344 -0.780325426822
y2[1] (closed_form) = -0.839069742395 -0.714548279816
absolute error = 0.1324
relative error = 12.01 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=5246.2MB, alloc=40.3MB, time=68.58
x[1] = 0.6692 0.82
h = 0.001 0.001
y1[1] (numeric) = -1.09662046943 0.530268069844
y1[1] (closed_form) = -1.06311645922 0.567649387883
absolute error = 0.0502
relative error = 4.165 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -0.726678815665 -0.784206095609
y2[1] (closed_form) = -0.840875010189 -0.717677895066
absolute error = 0.1322
relative error = 11.95 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6702 0.821
h = 0.001 0.003
y1[1] (numeric) = -1.09667867614 0.531782158809
y1[1] (closed_form) = -1.06299269394 0.569209003864
absolute error = 0.05035
relative error = 4.176 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -0.729203700002 -0.788089338314
y2[1] (closed_form) = -0.842506493879 -0.718172520719
absolute error = 0.1331
relative error = 12.03 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=5294.9MB, alloc=40.3MB, time=69.22
x[1] = 0.6712 0.824
h = 0.0001 0.004
y1[1] (numeric) = -1.0983183006 0.53476359462
y1[1] (closed_form) = -1.06430724785 0.572460167325
absolute error = 0.05077
relative error = 4.201 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -0.731734659472 -0.791972820053
y2[1] (closed_form) = -0.845282644446 -0.720792635687
absolute error = 0.134
relative error = 12.06 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=5343.3MB, alloc=40.3MB, time=69.85
x[1] = 0.6713 0.828
h = 0.003 0.006
y1[1] (numeric) = -1.10142066836 0.537775005704
y1[1] (closed_form) = -1.06711417729 0.575918389291
absolute error = 0.0513
relative error = 4.231 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -0.734277088829 -0.795863320984
y2[1] (closed_form) = -0.847685969148 -0.724998054166
absolute error = 0.1337
relative error = 11.99 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6743 0.834
h = 0.0001 0.005
y1[1] (numeric) = -1.10400085458 0.544581794931
y1[1] (closed_form) = -1.06892511171 0.583206525812
absolute error = 0.05217
relative error = 4.285 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -0.73684997295 -0.799757410426
y2[1] (closed_form) = -0.854367373785 -0.729667494199
absolute error = 0.1368
relative error = 12.18 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=5391.8MB, alloc=40.3MB, time=70.48
x[1] = 0.6744 0.839
h = 0.0001 0.003
y1[1] (numeric) = -1.10793557156 0.548352724445
y1[1] (closed_form) = -1.0725010912 0.587559169765
absolute error = 0.05285
relative error = 4.321 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -0.739456783495 -0.803658671625
y2[1] (closed_form) = -0.857401352575 -0.734962510647
absolute error = 0.1365
relative error = 12.09 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6745 0.842
h = 0.001 0.001
y1[1] (numeric) = -1.11027834073 0.550655584551
y1[1] (closed_form) = -1.07462488614 0.590207837082
absolute error = 0.05325
relative error = 4.343 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -0.742076793123 -0.807572985187
y2[1] (closed_form) = -0.859275357822 -0.738124308988
absolute error = 0.1362
relative error = 12.03 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=5440.3MB, alloc=40.3MB, time=71.12
x[1] = 0.6755 0.843
h = 0.001 0.003
y1[1] (numeric) = -1.11034448347 0.552208505
y1[1] (closed_form) = -1.07450314435 0.591806311333
absolute error = 0.05341
relative error = 4.354 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -0.744701185218 -0.811489957609
y2[1] (closed_form) = -0.860940928831 -0.738607866207
absolute error = 0.1372
relative error = 12.09 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6765 0.846
h = 0.0001 0.004
y1[1] (numeric) = -1.11203881311 0.555260000188
y1[1] (closed_form) = -1.0758605481 0.595133338509
absolute error = 0.05384
relative error = 4.379 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -0.747331808192 -0.815407200656
y2[1] (closed_form) = -0.863796516932 -0.741239941593
absolute error = 0.1381
relative error = 12.13 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=5488.9MB, alloc=40.3MB, time=71.77
x[1] = 0.6766 0.85
h = 0.003 0.006
y1[1] (numeric) = -1.11523342154 0.558336344773
y1[1] (closed_form) = -1.07874749888 0.598667846803
absolute error = 0.05439
relative error = 4.408 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -0.749974167923 -0.819331691092
y2[1] (closed_form) = -0.866291846097 -0.745489462132
absolute error = 0.1378
relative error = 12.06 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6796 0.856
h = 0.0001 0.005
y1[1] (numeric) = -1.11790727859 0.565308074339
y1[1] (closed_form) = -1.08062531093 0.606129610508
absolute error = 0.05528
relative error = 4.462 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -0.75264775203 -0.823259985139
y2[1] (closed_form) = -0.87314526825 -0.750160394426
absolute error = 0.1409
relative error = 12.24 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=5537.5MB, alloc=40.3MB, time=72.40
x[1] = 0.6797 0.861
h = 0.0001 0.003
y1[1] (numeric) = -1.12195800967 0.569160598416
y1[1] (closed_form) = -1.08430201227 0.610578485915
absolute error = 0.05598
relative error = 4.498 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -0.755356107791 -0.827195770213
y2[1] (closed_form) = -0.876295277852 -0.755511866447
absolute error = 0.1406
relative error = 12.15 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=5586.2MB, alloc=40.3MB, time=73.04
x[1] = 0.6798 0.864
h = 0.001 0.001
y1[1] (numeric) = -1.12436984742 0.571513664659
y1[1] (closed_form) = -1.08648561211 0.613285997049
absolute error = 0.05639
relative error = 4.52 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -0.758077951321 -0.831144994739
y2[1] (closed_form) = -0.878239612341 -0.758706852363
absolute error = 0.1403
relative error = 12.09 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6808 0.865
h = 0.0001 0.004
y1[1] (numeric) = -1.12444352755 0.573106226741
y1[1] (closed_form) = -1.08636546551 0.614924029959
absolute error = 0.05656
relative error = 4.531 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -0.760804279741 -0.835096963205
y2[1] (closed_form) = -0.879940142815 -0.759179173172
absolute error = 0.1413
relative error = 12.16 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=5634.6MB, alloc=40.3MB, time=73.67
x[1] = 0.6809 0.869
h = 0.003 0.006
y1[1] (numeric) = -1.12771560933 0.576238614218
y1[1] (closed_form) = -1.08932263511 0.618525069295
absolute error = 0.05712
relative error = 4.559 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -0.763537866414 -0.839054554228
y2[1] (closed_form) = -0.8825158217 -0.763468871374
absolute error = 0.141
relative error = 12.08 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6839 0.875
h = 0.0001 0.005
y1[1] (numeric) = -1.13046707471 0.583351219571
y1[1] (closed_form) = -1.09125943638 0.626138574543
absolute error = 0.05803
relative error = 4.613 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -0.766303332279 -0.843016122758
y2[1] (closed_form) = -0.889520655954 -0.768143632619
absolute error = 0.1442
relative error = 12.27 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=5683.1MB, alloc=40.3MB, time=74.31
x[1] = 0.684 0.88
h = 0.0001 0.003
y1[1] (numeric) = -1.13461529993 0.58727423019
y1[1] (closed_form) = -1.0950245396 0.630671380905
absolute error = 0.05874
relative error = 4.649 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -0.769104290039 -0.846985443772
y2[1] (closed_form) = -0.89277198782 -0.773546491081
absolute error = 0.1438
relative error = 12.18 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6841 0.883
h = 0.001 0.001
y1[1] (numeric) = -1.137085178 0.589670660882
y1[1] (closed_form) = -1.09726063788 0.633430219248
absolute error = 0.05917
relative error = 4.67 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -0.771918984733 -0.850968529384
y2[1] (closed_form) = -0.894777752815 -0.776771711451
absolute error = 0.1435
relative error = 12.11 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=5731.7MB, alloc=40.3MB, time=74.96
x[1] = 0.6851 0.884
h = 0.001 0.003
y1[1] (numeric) = -1.13716481113 0.591296950967
y1[1] (closed_form) = -1.09714199785 0.635102865933
absolute error = 0.05934
relative error = 4.681 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -0.774738252172 -0.854954429977
y2[1] (closed_form) = -0.896509220598 -0.777234646515
absolute error = 0.1445
relative error = 12.18 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6861 0.887
h = 0.0001 0.004
y1[1] (numeric) = -1.13895950301 0.594482348934
y1[1] (closed_form) = -1.09857967427 0.638575466142
absolute error = 0.05979
relative error = 4.705 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -0.777564044803 -0.858940654865
y2[1] (closed_form) = -0.899517595599 -0.77989138959
absolute error = 0.1453
relative error = 12.21 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=5780.3MB, alloc=40.3MB, time=75.60
x[1] = 0.6862 0.891
h = 0.003 0.006
y1[1] (numeric) = -1.14232535083 0.597684370463
y1[1] (closed_form) = -1.10161782338 0.642257080714
absolute error = 0.06036
relative error = 4.734 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -0.780402085042 -0.862934546799
y2[1] (closed_form) = -0.902189266718 -0.784227737358
absolute error = 0.145
relative error = 12.13 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=5828.8MB, alloc=40.3MB, time=76.23
x[1] = 0.6892 0.897
h = 0.0001 0.005
y1[1] (numeric) = -1.14516945545 0.604970170961
y1[1] (closed_form) = -1.10361989554 0.650051446131
absolute error = 0.06131
relative error = 4.787 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -0.783272806769 -0.866932618689
y2[1] (closed_form) = -0.90937401868 -0.788904998755
absolute error = 0.1483
relative error = 12.32 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6893 0.902
h = 0.0001 0.003
y1[1] (numeric) = -1.14943565269 0.608980687598
y1[1] (closed_form) = -1.10748696314 0.654685900855
absolute error = 0.06204
relative error = 4.822 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -0.786179903721 -0.870938751443
y2[1] (closed_form) = -0.912746409912 -0.794367517939
absolute error = 0.1479
relative error = 12.23 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=5877.4MB, alloc=40.3MB, time=76.87
x[1] = 0.6894 0.905
h = 0.001 0.001
y1[1] (numeric) = -1.15197573355 0.611430901951
y1[1] (closed_form) = -1.10978357596 0.65750685635
absolute error = 0.06248
relative error = 4.843 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -0.789101046598 -0.874959042009
y2[1] (closed_form) = -0.914825560854 -0.797627811772
absolute error = 0.1476
relative error = 12.16 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6904 0.906
h = 0.001 0.003
y1[1] (numeric) = -1.15206214051 0.613098436532
y1[1] (closed_form) = -1.10966572013 0.659220419467
absolute error = 0.06265
relative error = 4.854 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -0.792026870491 -0.878982232976
y2[1] (closed_form) = -0.916593649065 -0.798079173077
absolute error = 0.1485
relative error = 12.22 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=5926.0MB, alloc=40.3MB, time=77.50
x[1] = 0.6914 0.909
h = 0.0001 0.004
y1[1] (numeric) = -1.15391162979 0.616359906821
y1[1] (closed_form) = -1.11114582342 0.662774251679
absolute error = 0.06311
relative error = 4.878 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -0.794959385009 -0.883005775174
y2[1] (closed_form) = -0.919687043446 -0.800749392823
absolute error = 0.1494
relative error = 12.25 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6915 0.913
h = 0.003 0.006
y1[1] (numeric) = -1.15737206818 0.619634132022
y1[1] (closed_form) = -1.11426547859 0.666538828571
absolute error = 0.0637
relative error = 4.906 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -0.797904437722 -0.887037214076
y2[1] (closed_form) = -0.922456936188 -0.805133744115
absolute error = 0.1491
relative error = 12.17 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=5974.5MB, alloc=40.3MB, time=78.15
x[1] = 0.6945 0.919
h = 0.0001 0.005
y1[1] (numeric) = -1.16030823355 0.627097634074
y1[1] (closed_form) = -1.11633191664 0.674518074704
absolute error = 0.06467
relative error = 4.958 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -0.800882992046 -0.891073028418
y2[1] (closed_form) = -0.92982597237 -0.809813962523
absolute error = 0.1524
relative error = 12.36 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6946 0.924
h = 0.0001 0.003
y1[1] (numeric) = -1.16469346126 0.631198889223
y1[1] (closed_form) = -1.12030163088 0.679257192611
absolute error = 0.06542
relative error = 4.994 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -0.803898825715 -0.895117205984
y2[1] (closed_form) = -0.933322234474 -0.815337846416
absolute error = 0.152
relative error = 12.27 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=6023.0MB, alloc=40.3MB, time=78.78
x[1] = 0.6947 0.927
h = 0.001 0.001
y1[1] (numeric) = -1.16730435775 0.633704843649
y1[1] (closed_form) = -1.12265914741 0.682142087007
absolute error = 0.06587
relative error = 5.015 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -0.806929025405 -0.899175937884
y2[1] (closed_form) = -0.935476479654 -0.818634215258
absolute error = 0.1517
relative error = 12.2 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=6071.7MB, alloc=40.3MB, time=79.42
x[1] = 0.6957 0.928
h = 0.001 0.003
y1[1] (numeric) = -1.16739711831 0.635414496952
y1[1] (closed_form) = -1.12254162242 0.683897320322
absolute error = 0.06605
relative error = 5.025 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -0.809964017574 -0.903237655781
y2[1] (closed_form) = -0.937282099669 -0.81907379624
absolute error = 0.1526
relative error = 12.26 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6967 0.931
h = 0.0001 0.004
y1[1] (numeric) = -1.16930143987 0.638754217307
y1[1] (closed_form) = -1.12406399858 0.687534349997
absolute error = 0.06653
relative error = 5.049 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -0.813005869309 -0.90729975016
y2[1] (closed_form) = -0.940462546523 -0.821757988637
absolute error = 0.1535
relative error = 12.29 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=6120.0MB, alloc=40.3MB, time=80.05
x[1] = 0.6968 0.935
h = 0.003 0.006
y1[1] (numeric) = -1.17285732148 0.642103278949
y1[1] (closed_form) = -1.12726570417 0.691384333124
absolute error = 0.06714
relative error = 5.077 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -0.81606055842 -0.911369971438
y2[1] (closed_form) = -0.943332946254 -0.826191696392
absolute error = 0.1531
relative error = 12.21 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.6998 0.941
h = 0.0001 0.005
y1[1] (numeric) = -1.17588496657 0.649749105193
y1[1] (closed_form) = -1.12939558933 0.699552579823
absolute error = 0.06813
relative error = 5.128 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -0.819149587561 -0.915444756542
y2[1] (closed_form) = -0.950890717877 -0.830875287038
absolute error = 0.1565
relative error = 12.4 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=6168.5MB, alloc=40.3MB, time=80.69
x[1] = 0.6999 0.946
h = 0.0001 0.003
y1[1] (numeric) = -1.18039031861 0.653944410751
y1[1] (closed_form) = -1.13346865485 0.704399447394
absolute error = 0.0689
relative error = 5.163 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -0.822276821503 -0.919528201114
y2[1] (closed_form) = -0.954513733147 -0.836462238714
absolute error = 0.1562
relative error = 12.3 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7 0.949
h = 0.001 0.001
y1[1] (numeric) = -1.18307266415 0.656508109798
y1[1] (closed_form) = -1.13588747714 0.707350145793
absolute error = 0.06936
relative error = 5.184 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -0.825418752936 -0.923626599964
y2[1] (closed_form) = -0.956744823505 -0.839795683047
absolute error = 0.1558
relative error = 12.24 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=6217.2MB, alloc=40.3MB, time=81.33
x[1] = 0.701 0.95
h = 0.001 0.003
y1[1] (numeric) = -1.18317134961 0.658260779289
y1[1] (closed_form) = -1.13576982005 0.709147822148
absolute error = 0.06954
relative error = 5.194 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -0.828565591587 -0.927728070593
y2[1] (closed_form) = -0.958588901066 -0.840223263019
absolute error = 0.1567
relative error = 12.3 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.702 0.953
h = 0.0001 0.004
y1[1] (numeric) = -1.1851305445 0.661680982616
y1[1] (closed_form) = -1.13733431494 0.712870062537
absolute error = 0.07003
relative error = 5.218 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -0.831719462348 -0.931829941239
y2[1] (closed_form) = -0.961858476432 -0.842921910115
absolute error = 0.1576
relative error = 12.32 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=6265.7MB, alloc=40.3MB, time=81.96
x[1] = 0.7021 0.957
h = 0.003 0.006
y1[1] (numeric) = -1.18878274979 0.665107578194
y1[1] (closed_form) = -1.14061863278 0.716807953888
absolute error = 0.07066
relative error = 5.245 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -0.834886478473 -0.935940169548
y2[1] (closed_form) = -0.964831725851 -0.847406326332
absolute error = 0.1572
relative error = 12.24 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=6314.2MB, alloc=40.3MB, time=82.59
x[1] = 0.7051 0.963
h = 0.0001 0.005
y1[1] (numeric) = -1.19190128945 0.672940469694
y1[1] (closed_form) = -1.14281103116 0.72516942197
absolute error = 0.07168
relative error = 5.296 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -0.838088691827 -0.940055142834
y2[1] (closed_form) = -0.972582770973 -0.852093661967
absolute error = 0.1607
relative error = 12.43 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7052 0.968
h = 0.0001 0.003
y1[1] (numeric) = -1.19652789476 0.677233218952
y1[1] (closed_form) = -1.14698817457 0.730127198913
absolute error = 0.07247
relative error = 5.33 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -0.841330057325 -0.944179065611
y2[1] (closed_form) = -0.976335494199 -0.857745383693
absolute error = 0.1603
relative error = 12.33 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=6362.8MB, alloc=40.3MB, time=83.24
x[1] = 0.7053 0.971
h = 0.001 0.001
y1[1] (numeric) = -1.19928234312 0.6798567165
y1[1] (closed_form) = -1.14946871726 0.733145610719
absolute error = 0.07295
relative error = 5.35 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -0.844586463442 -0.948318346141
y2[1] (closed_form) = -0.978645224359 -0.86111690298
absolute error = 0.1599
relative error = 12.27 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7063 0.972
h = 0.0001 0.004
y1[1] (numeric) = -1.1993865158 0.681653323228
y1[1] (closed_form) = -1.14935045518 0.734986522276
absolute error = 0.07313
relative error = 5.36 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -0.847847894874 -0.952460784434
y2[1] (closed_form) = -0.980528699943 -0.861532246813
absolute error = 0.1608
relative error = 12.32 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=6411.3MB, alloc=40.3MB, time=83.87
x[1] = 0.7064 0.976
h = 0.003 0.006
y1[1] (numeric) = -1.20311970369 0.685146702528
y1[1] (closed_form) = -1.15270743476 0.739001137395
absolute error = 0.07377
relative error = 5.387 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -0.851117446171 -0.956609662363
y2[1] (closed_form) = -0.983591773773 -0.866062657378
absolute error = 0.1605
relative error = 12.24 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7094 0.982
h = 0.0001 0.005
y1[1] (numeric) = -1.2063135292 0.693139355714
y1[1] (closed_form) = -1.15495525393 0.747531653058
absolute error = 0.07481
relative error = 5.438 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -0.854422924318 -0.960763430376
y2[1] (closed_form) = -0.991512834276 -0.870755859462
absolute error = 0.164
relative error = 12.43 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=6459.8MB, alloc=40.3MB, time=84.50
x[1] = 0.7095 0.987
h = 0.0001 0.003
y1[1] (numeric) = -1.21104213469 0.697516108912
y1[1] (closed_form) = -1.15922395625 0.752586232443
absolute error = 0.07562
relative error = 5.471 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -0.857768362061 -0.9649263846
y2[1] (closed_form) = -0.995378829423 -0.876466290023
absolute error = 0.1636
relative error = 12.33 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7096 0.99
h = 0.001 0.001
y1[1] (numeric) = -1.21385723497 0.700191154585
y1[1] (closed_form) = -1.16175880566 0.755663751064
absolute error = 0.0761
relative error = 5.491 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -0.861129136027 -0.969105035827
y2[1] (closed_form) = -0.997757251584 -0.879872349234
absolute error = 0.1632
relative error = 12.27 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=6508.4MB, alloc=40.3MB, time=85.14
x[1] = 0.7106 0.991
h = 0.001 0.003
y1[1] (numeric) = -1.21396561917 0.70202516263
y1[1] (closed_form) = -1.16164016447 0.757542542384
absolute error = 0.07629
relative error = 5.501 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -0.864495036544 -0.973286916664
y2[1] (closed_form) = -0.999675554149 -0.880277445892
absolute error = 0.1641
relative error = 12.32 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7116 0.994
h = 0.0001 0.004
y1[1] (numeric) = -1.21602557215 0.705599082291
y1[1] (closed_form) = -1.16328369349 0.761428368402
absolute error = 0.0768
relative error = 5.524 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -0.867868295469 -0.977469235996
y2[1] (closed_form) = -1.00311646879 -0.883005346125
absolute error = 0.165
relative error = 12.34 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=6557.0MB, alloc=40.3MB, time=85.77
x[1] = 0.7117 0.998
h = 0.003 0.006
y1[1] (numeric) = -1.21985687025 0.709175280918
y1[1] (closed_form) = -1.16672440772 0.765535699141
absolute error = 0.07746
relative error = 5.551 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -0.87125528876 -0.981660337827
y2[1] (closed_form) = -1.0062868928 -0.887589008228
absolute error = 0.1646
relative error = 12.26 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=6605.4MB, alloc=40.3MB, time=86.40
x[1] = 0.7147 1.004
h = 0.0001 0.005
y1[1] (numeric) = -1.22314053634 0.71736433107
y1[1] (closed_form) = -1.16903301032 0.774267576362
absolute error = 0.07852
relative error = 5.6 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -0.874679103163 -0.985856497055
y2[1] (closed_form) = -1.01440990638 -0.892286589368
absolute error = 0.1682
relative error = 12.45 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7148 1.009
h = 0.0001 0.003
y1[1] (numeric) = -1.22799268201 0.721845174692
y1[1] (closed_form) = -1.17340723953 0.779439135789
absolute error = 0.07935
relative error = 5.633 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -0.878143867658 -0.99006212073
y2[1] (closed_form) = -1.01841128636 -0.898064992957
absolute error = 0.1677
relative error = 12.35 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=6654.0MB, alloc=40.3MB, time=87.04
x[1] = 0.7149 1.012
h = 0.001 0.001
y1[1] (numeric) = -1.23088121053 0.724584042097
y1[1] (closed_form) = -1.17600463759 0.782588036723
absolute error = 0.07985
relative error = 5.653 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -0.881624334345 -0.994283852056
y2[1] (closed_form) = -1.0208717957 -0.901511006956
absolute error = 0.1673
relative error = 12.29 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7159 1.013
h = 0.001 0.003
y1[1] (numeric) = -1.23099424003 0.726463805647
y1[1] (closed_form) = -1.17588449357 0.78451159549
absolute error = 0.08004
relative error = 5.662 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -0.88511005227 -0.998508899434
y2[1] (closed_form) = -1.02283129001 -0.901903402032
absolute error = 0.1682
relative error = 12.34 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=6702.6MB, alloc=40.3MB, time=87.69
x[1] = 0.7169 1.016
h = 0.0001 0.004
y1[1] (numeric) = -1.23310924872 0.730124993847
y1[1] (closed_form) = -1.17756972077 0.788488665444
absolute error = 0.08057
relative error = 5.685 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -0.88860331214 -1.00273440371
y2[1] (closed_form) = -1.02636751378 -0.904647083162
absolute error = 0.1691
relative error = 12.36 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.717 1.02
h = 0.003 0.006
y1[1] (numeric) = -1.23703961468 0.733786901779
y1[1] (closed_form) = -1.18109478044 0.792691386863
absolute error = 0.08124
relative error = 5.711 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -0.892110641117 -1.00696892321
y2[1] (closed_form) = -1.02964780243 -0.9092853472
absolute error = 0.1687
relative error = 12.28 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=6751.0MB, alloc=40.3MB, time=88.32
x[1] = 0.72 1.026
h = 0.0001 0.005
y1[1] (numeric) = -1.24041251549 0.742177438196
y1[1] (closed_form) = -1.18346318258 0.801629145113
absolute error = 0.08233
relative error = 5.76 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -0.895655705649 -1.01120865974
y2[1] (closed_form) = -1.03797756812 -0.9139875547
absolute error = 0.1724
relative error = 12.46 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7201 1.031
h = 0.0001 0.003
y1[1] (numeric) = -1.24538942757 0.746766007665
y1[1] (closed_form) = -1.1879437269 0.806921062561
absolute error = 0.08318
relative error = 5.792 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -0.899242734283 -1.01545813238
y2[1] (closed_form) = -1.04211750488 -0.91983563263
absolute error = 0.1719
relative error = 12.37 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=6799.6MB, alloc=40.3MB, time=88.95
x[1] = 0.7202 1.034
h = 0.001 0.001
y1[1] (numeric) = -1.24835209445 0.749570897395
y1[1] (closed_form) = -1.19060412344 0.810143387223
absolute error = 0.08369
relative error = 5.811 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -0.902845843565 -1.01972412716
y2[1] (closed_form) = -1.04466202686 -0.923322598698
absolute error = 0.1715
relative error = 12.3 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=6848.2MB, alloc=40.3MB, time=89.58
x[1] = 0.7212 1.035
h = 0.001 0.003
y1[1] (numeric) = -1.24846930351 0.75149740629
y1[1] (closed_form) = -1.19048197321 0.812112562412
absolute error = 0.08389
relative error = 5.821 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -0.906454332375 -1.02399352467
y2[1] (closed_form) = -1.04666369782 -0.923702014105
absolute error = 0.1724
relative error = 12.35 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7222 1.038
h = 0.0001 0.004
y1[1] (numeric) = -1.25063942688 0.755248318489
y1[1] (closed_form) = -1.19220873938 0.816183082564
absolute error = 0.08442
relative error = 5.843 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -0.910070550639 -1.02826339561
y2[1] (closed_form) = -1.05029748285 -0.926461902328
absolute error = 0.1733
relative error = 12.37 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=6896.9MB, alloc=40.3MB, time=90.22
x[1] = 0.7223 1.042
h = 0.003 0.006
y1[1] (numeric) = -1.25466984499 0.758998896984
y1[1] (closed_form) = -1.19581877151 0.820483932886
absolute error = 0.08511
relative error = 5.869 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -0.913701182435 -1.03254251517
y2[1] (closed_form) = -1.05369021342 -0.93115611797
absolute error = 0.1728
relative error = 12.29 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7253 1.048
h = 0.0001 0.005
y1[1] (numeric) = -1.25813136405 0.767596136536
y1[1] (closed_form) = -1.19824596855 0.829632199444
absolute error = 0.08622
relative error = 5.916 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -0.917370484919 -1.03682700356
y2[1] (closed_form) = -1.06223162559 -0.935863153026
absolute error = 0.1766
relative error = 12.47 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=6945.3MB, alloc=40.3MB, time=90.85
x[1] = 0.7254 1.053
h = 0.0001 0.003
y1[1] (numeric) = -1.26323430239 0.772296156934
y1[1] (closed_form) = -1.2028336366 0.835047932562
absolute error = 0.0871
relative error = 5.948 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -0.921082789619 -1.04112149299
y2[1] (closed_form) = -1.06651337049 -0.941782606061
absolute error = 0.1761
relative error = 12.38 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7255 1.056
h = 0.001 0.001
y1[1] (numeric) = -1.26627183717 0.775169323884
y1[1] (closed_form) = -1.20555749305 0.838345770535
absolute error = 0.08762
relative error = 5.967 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -0.924811566224 -1.045432923
y2[1] (closed_form) = -1.06914387845 -0.945311520558
absolute error = 0.1757
relative error = 12.31 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=6993.9MB, alloc=40.3MB, time=91.48
x[1] = 0.7265 1.057
h = 0.001 0.003
y1[1] (numeric) = -1.26639274917 0.777143592957
y1[1] (closed_form) = -1.20543282167 0.84036143145
absolute error = 0.08782
relative error = 5.976 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -0.928545854336 -1.04974784264
y2[1] (closed_form) = -1.07118872715 -0.945677662456
absolute error = 0.1766
relative error = 12.36 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7275 1.06
h = 0.0001 0.004
y1[1] (numeric) = -1.26861804929 0.780986745706
y1[1] (closed_form) = -1.20720096477 0.844527660355
absolute error = 0.08837
relative error = 5.998 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -0.932288063485 -1.05406325035
y2[1] (closed_form) = -1.0749223738 -0.948454168605
absolute error = 0.1775
relative error = 12.38 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=7042.5MB, alloc=40.3MB, time=92.12
x[1] = 0.7276 1.064
h = 0.003 0.006
y1[1] (numeric) = -1.27274953017 0.784829029088
y1[1] (closed_form) = -1.21089661222 0.84892944236
absolute error = 0.08908
relative error = 6.023 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -0.936045040511 -1.05838814077
y2[1] (closed_form) = -1.07843018789 -0.953205684807
absolute error = 0.177
relative error = 12.3 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=7091.0MB, alloc=40.3MB, time=92.74
x[1] = 0.7306 1.07
h = 0.0001 0.005
y1[1] (numeric) = -1.27629903863 0.7936383187
y1[1] (closed_form) = -1.21338157724 0.858292954195
absolute error = 0.09022
relative error = 6.07 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -0.939841644571 -1.06271854379
y2[1] (closed_form) = -1.08718823853 -0.957917701452
absolute error = 0.1808
relative error = 12.48 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7307 1.075
h = 0.0001 0.003
y1[1] (numeric) = -1.28152929632 0.79845360702
y1[1] (closed_form) = -1.21807719758 0.863836042064
absolute error = 0.09111
relative error = 6.101 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -0.94368231367 -1.06705920592
y2[1] (closed_form) = -1.09161512424 -0.963910229829
absolute error = 0.1803
relative error = 12.38 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=7139.6MB, alloc=40.3MB, time=93.39
x[1] = 0.7308 1.078
h = 0.001 0.001
y1[1] (numeric) = -1.28464244768 0.80139736174
y1[1] (closed_form) = -1.2208649867 0.867211532159
absolute error = 0.09165
relative error = 6.12 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -0.947539859044 -1.07141723111
y2[1] (closed_form) = -1.09433364049 -0.967482088187
absolute error = 0.1799
relative error = 12.31 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7318 1.079
h = 0.0001 0.004
y1[1] (numeric) = -1.2847665746 0.803420431207
y1[1] (closed_form) = -1.22073726725 0.86927456871
absolute error = 0.09185
relative error = 6.129 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -0.951403051687 -1.07577883309
y2[1] (closed_form) = -1.09642268461 -0.967834646611
absolute error = 0.1808
relative error = 12.36 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=7188.2MB, alloc=40.3MB, time=94.02
x[1] = 0.7319 1.083
h = 0.003 0.006
y1[1] (numeric) = -1.28898308842 0.807341578864
y1[1] (closed_form) = -1.22450838509 0.873764493516
absolute error = 0.09257
relative error = 6.154 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -0.955275366325 -1.08014771636
y2[1] (closed_form) = -1.10003101989 -0.972637979803
absolute error = 0.1803
relative error = 12.28 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7349 1.089
h = 0.0001 0.005
y1[1] (numeric) = -1.29260542183 0.816331943147
y1[1] (closed_form) = -1.22704487722 0.883316488671
absolute error = 0.09373
relative error = 6.199 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -0.959188122201 -1.08452222551
y2[1] (closed_form) = -1.10897955844 -0.977357034344
absolute error = 0.1842
relative error = 12.46 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=7236.8MB, alloc=40.3MB, time=94.66
x[1] = 0.735 1.094
h = 0.0001 0.003
y1[1] (numeric) = -1.297942868 0.821246438868
y1[1] (closed_form) = -1.23183567368 0.888970797052
absolute error = 0.09464
relative error = 6.23 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -0.963145849101 -1.08890720331
y2[1] (closed_form) = -1.11353321069 -0.98341560912
absolute error = 0.1837
relative error = 12.37 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7351 1.097
h = 0.001 0.001
y1[1] (numeric) = -1.30111967809 0.824250947287
y1[1] (closed_form) = -1.23467984151 0.892414109159
absolute error = 0.09519
relative error = 6.248 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -0.967120800126 -1.09330989969
y2[1] (closed_form) = -1.11632861155 -0.987026310582
absolute error = 0.1832
relative error = 12.29 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=7285.4MB, alloc=40.3MB, time=95.29
x[1] = 0.7361 1.098
h = 0.001 0.003
y1[1] (numeric) = -1.30124608035 0.826315571496
y1[1] (closed_form) = -1.23454964609 0.894518698718
absolute error = 0.09539
relative error = 6.257 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -0.97110151473 -1.09771624571
y2[1] (closed_form) = -1.11845669264 -0.987367459277
absolute error = 0.1841
relative error = 12.34 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7371 1.101
h = 0.0001 0.004
y1[1] (numeric) = -1.30357274381 0.830334775368
y1[1] (closed_form) = -1.23639554454 0.898868725619
memory used=7334.0MB, alloc=40.3MB, time=95.96
absolute error = 0.09597
relative error = 6.278 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -0.975090512857 -1.10212310141
y2[1] (closed_form) = -1.12238224235 -0.99017718344
absolute error = 0.185
relative error = 12.36 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7372 1.105
h = 0.003 0.006
y1[1] (numeric) = -1.307892355 0.834353573811
y1[1] (closed_form) = -1.24025355014 0.903464966073
absolute error = 0.0967
relative error = 6.302 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -0.979094955931 -1.10653987111
y2[1] (closed_form) = -1.1261107369 -0.995040358713
absolute error = 0.1845
relative error = 12.28 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=7382.4MB, alloc=40.3MB, time=96.59
x[1] = 0.7402 1.111
h = 0.0001 0.005
y1[1] (numeric) = -1.3116015274 0.843566502737
y1[1] (closed_form) = -1.24284589424 0.91324133238
absolute error = 0.09789
relative error = 6.347 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -0.983140838387 -1.11096239502
y2[1] (closed_form) = -1.13528547015 -0.999764614493
absolute error = 0.1884
relative error = 12.46 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7403 1.116
h = 0.0001 0.003
y1[1] (numeric) = -1.31706889282 0.848603743797
y1[1] (closed_form) = -1.24774628092 0.919029793465
absolute error = 0.09882
relative error = 6.377 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -0.98723280334 -1.11539563252
y2[1] (closed_form) = -1.13999066726 -1.00589946899
absolute error = 0.1879
relative error = 12.36 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=7431.0MB, alloc=40.3MB, time=97.22
x[1] = 0.7404 1.119
h = 0.001 0.001
y1[1] (numeric) = -1.32032282575 0.851683366298
y1[1] (closed_form) = -1.25065531717 0.922554866345
absolute error = 0.09938
relative error = 6.395 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -0.991342422484 -1.11984701926
y2[1] (closed_form) = -1.14287796198 -1.00955498956
absolute error = 0.1874
relative error = 12.29 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7414 1.12
h = 0.001 0.003
y1[1] (numeric) = -1.3204515005 0.853798841044
y1[1] (closed_form) = -1.25052107093 0.924708549908
absolute error = 0.09959
relative error = 6.403 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -0.995457948391 -1.12430214334
y2[1] (closed_form) = -1.14505218183 -1.00988194641
absolute error = 0.1883
relative error = 12.34 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=7479.6MB, alloc=40.3MB, time=97.86
x[1] = 0.7424 1.123
h = 0.0001 0.004
y1[1] (numeric) = -1.32283357091 0.857917926936
y1[1] (closed_form) = -1.25240789061 0.929161046614
absolute error = 0.1002
relative error = 6.424 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -0.999581961803 -1.12875778598
y2[1] (closed_form) = -1.14908444661 -1.01270940518
absolute error = 0.1893
relative error = 12.36 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7425 1.127
h = 0.003 0.006
y1[1] (numeric) = -1.32725736283 0.862037627753
y1[1] (closed_form) = -1.256353471 0.933866598002
absolute error = 0.1009
relative error = 6.447 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -1.00372180463 -1.13322357901
y2[1] (closed_form) = -1.1529359345 -1.01763377022
absolute error = 0.1887
relative error = 12.27 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=7528.1MB, alloc=40.3MB, time=98.49
x[1] = 0.7455 1.133
h = 0.0001 0.005
y1[1] (numeric) = -1.33105270022 0.871478851099
y1[1] (closed_form) = -1.25900056897 0.94387239731
absolute error = 0.1021
relative error = 6.491 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -1.00790410772 -1.13769524599
y2[1] (closed_form) = -1.1623421472 -1.02236324142
absolute error = 0.1928
relative error = 12.45 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7456 1.138
h = 0.0001 0.003
y1[1] (numeric) = -1.33665136988 0.876642927881
y1[1] (closed_form) = -1.26401143009 0.949798793048
absolute error = 0.1031
relative error = 6.52 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -1.01213363125 -1.14217786414
y2[1] (closed_form) = -1.16720246513 -1.02857607533
absolute error = 0.1922
relative error = 12.36 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=7576.8MB, alloc=40.3MB, time=99.12
x[1] = 0.7457 1.141
h = 0.001 0.001
y1[1] (numeric) = -1.3399832272 0.879800140522
y1[1] (closed_form) = -1.26698583896 0.953407912301
absolute error = 0.1037
relative error = 6.538 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -1.01638125309 -1.14667906651
y2[1] (closed_form) = -1.17018382263 -1.03227740827
absolute error = 0.1917
relative error = 12.28 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=7625.5MB, alloc=40.3MB, time=99.76
x[1] = 0.7467 1.142
h = 0.001 0.003
y1[1] (numeric) = -1.34011365105 0.881967580172
y1[1] (closed_form) = -1.2668469784 0.955611640472
absolute error = 0.1039
relative error = 6.546 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -1.02063492894 -1.15118409416
y2[1] (closed_form) = -1.17240524877 -1.03258981528
absolute error = 0.1926
relative error = 12.33 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7477 1.145
h = 0.0001 0.004
y1[1] (numeric) = -1.34255119603 0.886189311354
y1[1] (closed_form) = -1.26877454116 0.960169077019
absolute error = 0.1045
relative error = 6.566 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -1.02489730074 -1.15568964718
y2[1] (closed_form) = -1.17654672642 -1.03543535737
absolute error = 0.1935
relative error = 12.35 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=7674.1MB, alloc=40.3MB, time=100.39
x[1] = 0.7478 1.149
h = 0.003 0.006
y1[1] (numeric) = -1.34708027709 0.890413246581
y1[1] (closed_form) = -1.2728083978 0.964987004888
absolute error = 0.1052
relative error = 6.589 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -1.02917589732 -1.16020558776
y2[1] (closed_form) = -1.1805241121 -1.04042225906
absolute error = 0.193
relative error = 12.27 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7508 1.155
h = 0.0001 0.005
y1[1] (numeric) = -1.35096108584 0.900088634508
y1[1] (closed_form) = -1.27550912299 0.975227416419
absolute error = 0.1065
relative error = 6.632 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -1.03349799832 -1.16472751317
y2[1] (closed_form) = -1.19016719574 -1.04515690827
absolute error = 0.1971
relative error = 12.44 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=7722.6MB, alloc=40.3MB, time=101.03
x[1] = 0.7509 1.16
h = 0.0001 0.003
y1[1] (numeric) = -1.35669247635 0.905383738618
y1[1] (closed_form) = -1.28063136097 0.981295617409
absolute error = 0.1075
relative error = 6.661 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -1.03786848484 -1.16926061978
y2[1] (closed_form) = -1.19518629937 -1.05144942064
absolute error = 0.1965
relative error = 12.35 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.751 1.163
h = 0.001 0.001
y1[1] (numeric) = -1.36010307771 0.90862107871
y1[1] (closed_form) = -1.28367165684 0.9849911222
absolute error = 0.108
relative error = 6.678 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -1.04225752819 -1.17381275002
y2[1] (closed_form) = -1.19826394214 -1.05519755818
absolute error = 0.196
relative error = 12.27 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=7771.2MB, alloc=40.3MB, time=101.66
x[1] = 0.752 1.164
h = 0.001 0.003
y1[1] (numeric) = -1.3602347137 0.910841624612
y1[1] (closed_form) = -1.28352760471 0.987245867324
absolute error = 0.1083
relative error = 6.686 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -1.04665277693 -1.17836879378
y2[1] (closed_form) = -1.20053366022 -1.05549503969
absolute error = 0.1969
relative error = 12.32 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.753 1.167
h = 0.0001 0.004
y1[1] (numeric) = -1.36272780059 0.915168832129
y1[1] (closed_form) = -1.2854957265 0.991910771093
absolute error = 0.1089
relative error = 6.705 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -1.05105693466 -1.18292536753
y2[1] (closed_form) = -1.20478690257 -1.05835899659
absolute error = 0.1979
relative error = 12.34 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=7819.7MB, alloc=40.3MB, time=102.30
x[1] = 0.7531 1.171
h = 0.003 0.006
y1[1] (numeric) = -1.36736330384 0.919500416262
y1[1] (closed_form) = -1.28961857489 0.996844212813
absolute error = 0.1097
relative error = 6.728 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -1.05547772371 -1.18749256679
y2[1] (closed_form) = -1.20889316245 -1.06340978099
absolute error = 0.1973
relative error = 12.26 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=7868.1MB, alloc=40.3MB, time=102.93
x[1] = 0.7561 1.177
h = 0.0001 0.005
y1[1] (numeric) = -1.37132886871 0.929415982111
y1[1] (closed_form) = -1.29237177036 1.00732453526
absolute error = 0.1109
relative error = 6.769 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -1.05994308517 -1.19206585271
y2[1] (closed_form) = -1.21877861775 -1.06814951789
absolute error = 0.2015
relative error = 12.43 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7562 1.182
h = 0.0001 0.003
y1[1] (numeric) = -1.37719442788 0.934846408908
y1[1] (closed_form) = -1.29760630535 1.01353850273
absolute error = 0.1119
relative error = 6.798 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -1.06445802501 -1.19665054208
y2[1] (closed_form) = -1.22396026293 -1.07452340709
absolute error = 0.2009
relative error = 12.33 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=7916.8MB, alloc=40.3MB, time=103.57
x[1] = 0.7563 1.185
h = 0.001 0.001
y1[1] (numeric) = -1.38068461079 0.938166476538
y1[1] (closed_form) = -1.30071301249 1.01732278698
absolute error = 0.1125
relative error = 6.814 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -1.06899199495 -1.20125469905
y2[1] (closed_form) = -1.22713646826 -1.07831934031
absolute error = 0.2003
relative error = 12.26 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7573 1.186
h = 0.0001 0.004
y1[1] (numeric) = -1.38081690779 0.940441297455
y1[1] (closed_form) = -1.30056317727 1.01962954345
absolute error = 0.1127
relative error = 6.822 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -1.07353232593 -1.205862858
y2[1] (closed_form) = -1.22945558247 -1.07860150263
absolute error = 0.2013
relative error = 12.31 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=7965.3MB, alloc=40.3MB, time=104.21
x[1] = 0.7574 1.19
h = 0.003 0.006
y1[1] (numeric) = -1.38554200507 0.944865338877
y1[1] (closed_form) = -1.30476463839 1.02466391206
absolute error = 0.1135
relative error = 6.844 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -1.0780829392 -1.21047916808
y2[1] (closed_form) = -1.23367442981 -1.08370993706
absolute error = 0.2007
relative error = 12.22 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7604 1.196
h = 0.0001 0.005
y1[1] (numeric) = -1.38957762583 0.954985961135
y1[1] (closed_form) = -1.30756499367 1.035354472
absolute error = 0.1148
relative error = 6.885 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -1.08267903427 -1.21510164232
y2[1] (closed_form) = -1.24377294245 -1.088456918
absolute error = 0.2049
relative error = 12.4 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=8013.9MB, alloc=40.3MB, time=104.84
x[1] = 0.7605 1.201
h = 0.0001 0.003
y1[1] (numeric) = -1.39555620695 0.96053270285
y1[1] (closed_form) = -1.31289874244 1.04169580021
absolute error = 0.1158
relative error = 6.912 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -1.08732572457 -1.21973569895
y2[1] (closed_form) = -1.24909657969 -1.09490421184
absolute error = 0.2043
relative error = 12.3 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7606 1.204
h = 0.001 0.001
y1[1] (numeric) = -1.39911342652 0.96392388276
y1[1] (closed_form) = -1.31606413874 1.04555766276
absolute error = 0.1165
relative error = 6.928 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -1.09199185161 -1.22438959698
y2[1] (closed_form) = -1.25235890539 -1.09874329078
absolute error = 0.2037
relative error = 12.23 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=8062.5MB, alloc=40.3MB, time=105.48
x[1] = 0.7616 1.205
h = 0.001 0.003
y1[1] (numeric) = -1.39924581733 0.966244929484
y1[1] (closed_form) = -1.31590947678 1.04791008097
absolute error = 0.1167
relative error = 6.936 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -1.09666447296 -1.22904757098
y2[1] (closed_form) = -1.25472162603 -1.09901254411
absolute error = 0.2047
relative error = 12.27 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=8111.1MB, alloc=40.3MB, time=106.11
x[1] = 0.7626 1.208
h = 0.0001 0.004
y1[1] (numeric) = -1.4018409429 0.970773318311
y1[1] (closed_form) = -1.31795391055 1.0527814063
absolute error = 0.1173
relative error = 6.955 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -1.10134640649 -1.2337060776
y2[1] (closed_form) = -1.25918959052 -1.10191299375
absolute error = 0.2056
relative error = 12.29 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7627 1.212
h = 0.003 0.006
y1[1] (numeric) = -1.4066747306 0.975311700336
y1[1] (closed_form) = -1.32224577024 1.05793731443
absolute error = 0.1181
relative error = 6.976 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -1.10604574751 -1.23837564823
y2[1] (closed_form) = -1.2635430318 -1.10708785057
absolute error = 0.205
relative error = 12.21 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=8159.7MB, alloc=40.3MB, time=106.75
x[1] = 0.7657 1.218
h = 0.0001 0.005
y1[1] (numeric) = -1.41079377765 0.985684317612
y1[1] (closed_form) = -1.32509642299 1.068877985
absolute error = 0.1194
relative error = 7.016 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -1.11079168526 -1.24305146736
y2[1] (closed_form) = -1.27389445345 -1.11183967456
absolute error = 0.2093
relative error = 12.38 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7658 1.223
h = 0.0001 0.003
y1[1] (numeric) = -1.41690942269 0.991374797657
y1[1] (closed_form) = -1.33054427614 1.07537268734
absolute error = 0.1205
relative error = 7.042 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -1.11558946575 -1.24773907621
y2[1] (closed_form) = -1.27938785018 -1.11837155063
absolute error = 0.2087
relative error = 12.28 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=8208.3MB, alloc=40.3MB, time=107.38
x[1] = 0.7659 1.226
h = 0.001 0.001
y1[1] (numeric) = -1.42054789939 0.994853799148
y1[1] (closed_form) = -1.33377711463 1.07932792726
absolute error = 0.1211
relative error = 7.058 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -1.12040718518 -1.25244697949
y2[1] (closed_form) = -1.28275311445 -1.12226029494
absolute error = 0.2081
relative error = 12.21 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7669 1.227
h = 0.001 0.003
y1[1] (numeric) = -1.42067988343 0.997231421513
y1[1] (closed_form) = -1.33361554168 1.08173427439
absolute error = 0.1213
relative error = 7.066 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -1.1252315629 -1.25715904781
y2[1] (closed_form) = -1.28516734184 -1.12251346057
absolute error = 0.2091
relative error = 12.25 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=8256.8MB, alloc=40.3MB, time=108.02
x[1] = 0.7679 1.23
h = 0.0001 0.004
y1[1] (numeric) = -1.4233307815 1.001873878
y1[1] (closed_form) = -1.33570000178 1.08672062639
absolute error = 0.122
relative error = 7.084 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -1.13006547976 -1.2618716469
y2[1] (closed_form) = -1.28975467744 -1.12543320678
absolute error = 0.21
relative error = 12.27 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.768 1.234
h = 0.003 0.006
y1[1] (numeric) = -1.42827446048 1.00653026028
y1[1] (closed_form) = -1.34008301433 1.09200142567
absolute error = 0.1228
relative error = 7.104 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -1.13491724451 -1.2665955504
y2[1] (closed_form) = -1.29424590437 -1.13067583002
absolute error = 0.2094
relative error = 12.19 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=8305.4MB, alloc=40.3MB, time=108.65
x[1] = 0.771 1.24
h = 0.0001 0.005
y1[1] (numeric) = -1.43247614592 1.01716130772
y1[1] (closed_form) = -1.34298271269 1.1031978598
absolute error = 0.1241
relative error = 7.143 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -1.13981674643 -1.27132577695
y2[1] (closed_form) = -1.30485606267 -1.1354322494
absolute error = 0.2138
relative error = 12.36 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7711 1.245
h = 0.0001 0.003
y1[1] (numeric) = -1.4387303885 1.02300013001
y1[1] (closed_form) = -1.34854563933 1.10985016789
absolute error = 0.1252
relative error = 7.169 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -1.14476936831 -1.27606799213
y2[1] (closed_form) = -1.3105232468 -1.14205040457
absolute error = 0.2132
relative error = 12.26 %
Correct digits = 1
memory used=8354.0MB, alloc=40.3MB, time=109.29
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7712 1.248
h = 0.001 0.001
y1[1] (numeric) = -1.44245100872 1.02656973982
y1[1] (closed_form) = -1.35184647151 1.11390134241
absolute error = 0.1258
relative error = 7.184 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -1.14974244714 -1.28083095957
y2[1] (closed_form) = -1.31399389088 -1.14598980239
absolute error = 0.2125
relative error = 12.19 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=8402.7MB, alloc=40.3MB, time=109.93
x[1] = 0.7722 1.249
h = 0.001 0.003
y1[1] (numeric) = -1.4425819913 1.02900518677
y1[1] (closed_form) = -1.3516773527 1.11636267789
absolute error = 0.1261
relative error = 7.192 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -1.1547223528 -1.28559818138
y2[1] (closed_form) = -1.31646078476 -1.1462264327
absolute error = 0.2135
relative error = 12.23 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7732 1.252
h = 0.0001 0.004
y1[1] (numeric) = -1.44528872085 1.03376481587
y1[1] (closed_form) = -1.35380162656 1.12146681608
absolute error = 0.1267
relative error = 7.209 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -1.15971202957 -1.29036592972
y2[1] (closed_form) = -1.32117026388 -1.14916573682
absolute error = 0.2145
relative error = 12.25 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=8451.4MB, alloc=40.3MB, time=110.57
x[1] = 0.7733 1.256
h = 0.003 0.006
y1[1] (numeric) = -1.45034351514 1.0385429488
y1[1] (closed_form) = -1.35827655873 1.12687593636
absolute error = 0.1276
relative error = 7.229 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -1.16472000687 -1.29514522368
y2[1] (closed_form) = -1.32580254677 -1.15447746928
absolute error = 0.2139
relative error = 12.16 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7763 1.262
h = 0.0001 0.005
y1[1] (numeric) = -1.45462702123 1.04943901631
y1[1] (closed_form) = -1.36122401352 1.13833391501
absolute error = 0.1289
relative error = 7.267 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -1.16977688789 -1.29993090516
y2[1] (closed_form) = -1.33667738843 -1.15923817813
absolute error = 0.2183
relative error = 12.34 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=8499.9MB, alloc=40.3MB, time=111.20
x[1] = 0.7764 1.267
h = 0.0001 0.003
y1[1] (numeric) = -1.46102142434 1.055430899
y1[1] (closed_form) = -1.36690299848 1.14514815916
absolute error = 0.13
relative error = 7.292 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -1.1748881965 -1.30472876552
y2[1] (closed_form) = -1.34252248724 -1.16594430808
absolute error = 0.2176
relative error = 12.24 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7765 1.27
h = 0.001 0.001
y1[1] (numeric) = -1.46482509115 1.05909397293
y1[1] (closed_form) = -1.37027238447 1.14929788512
absolute error = 0.1307
relative error = 7.307 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -1.18002049628 -1.30954784084
y2[1] (closed_form) = -1.34610101219 -1.16993534604
absolute error = 0.217
relative error = 12.17 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=8548.6MB, alloc=40.3MB, time=111.84
x[1] = 0.7775 1.271
h = 0.001 0.003
y1[1] (numeric) = -1.46495446097 1.06158852261
y1[1] (closed_form) = -1.37009506866 1.15181529169
absolute error = 0.1309
relative error = 7.314 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -1.1851597961 -1.31437126013
y2[1] (closed_form) = -1.34862175247 -1.1701549736
absolute error = 0.218
relative error = 12.21 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7785 1.274
h = 0.0001 0.004
y1[1] (numeric) = -1.46771707681 1.06646850455
y1[1] (closed_form) = -1.37225893443 1.15704003859
absolute error = 0.1316
relative error = 7.331 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -1.19030910412 -1.31919519927
y2[1] (closed_form) = -1.35345620776 -1.17311407738
absolute error = 0.219
relative error = 12.23 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=8597.1MB, alloc=40.3MB, time=112.48
x[1] = 0.7786 1.278
h = 0.003 0.006
y1[1] (numeric) = -1.47288423318 1.07137223154
y1[1] (closed_form) = -1.37682656493 1.16258098963
absolute error = 0.1325
relative error = 7.351 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -1.19547717787 -1.324030926
y2[1] (closed_form) = -1.35823289737 -1.17849626048
absolute error = 0.2183
relative error = 12.14 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=8645.6MB, alloc=40.3MB, time=113.11
x[1] = 0.7816 1.284
h = 0.0001 0.005
y1[1] (numeric) = -1.47724871014 1.08254006693
y1[1] (closed_form) = -1.37982044775 1.17430642416
absolute error = 0.1338
relative error = 7.387 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -1.20069534859 -1.3288730944
y2[1] (closed_form) = -1.36937849076 -1.18326089311
absolute error = 0.2228
relative error = 12.31 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7817 1.289
h = 0.0001 0.003
y1[1] (numeric) = -1.4837848656 1.0886898452
y1[1] (closed_form) = -1.38561649102 1.18128703558
absolute error = 0.1349
relative error = 7.411 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -1.20596928567 -1.33372762295
y2[1] (closed_form) = -1.37540573314 -1.19005669214
absolute error = 0.2221
relative error = 12.21 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=8694.2MB, alloc=40.3MB, time=113.74
x[1] = 0.7818 1.292
h = 0.001 0.001
y1[1] (numeric) = -1.48767249836 1.09244930984
y1[1] (closed_form) = -1.3890549992 1.18553799073
absolute error = 0.1356
relative error = 7.426 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -1.21126476475 -1.33860383415
y2[1] (closed_form) = -1.37909470129 -1.19410035527
absolute error = 0.2215
relative error = 12.14 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7828 1.293
h = 0.0001 0.004
y1[1] (numeric) = -1.48779962685 1.09500427007
y1[1] (closed_form) = -1.38886881846 1.18811257478
absolute error = 0.1359
relative error = 7.433 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -1.21656742186 -1.34348447919
y2[1] (closed_form) = -1.38167048844 -1.19430249233
absolute error = 0.2225
relative error = 12.18 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=8742.9MB, alloc=40.3MB, time=114.38
x[1] = 0.7829 1.297
h = 0.003 0.006
y1[1] (numeric) = -1.49306141503 1.10001575421
y1[1] (closed_form) = -1.39351850177 1.19376875717
absolute error = 0.1367
relative error = 7.452 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -1.22188169948 -1.34837417627
y2[1] (closed_form) = -1.38657336358 -1.19974816597
absolute error = 0.2218
relative error = 12.1 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7859 1.303
h = 0.0001 0.005
y1[1] (numeric) = -1.49749267966 1.11141556843
y1[1] (closed_form) = -1.39655453737 1.20572871301
absolute error = 0.1381
relative error = 7.487 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -1.22724709014 -1.35327035166
y2[1] (closed_form) = -1.39795692562 -1.2045191623
absolute error = 0.2264
relative error = 12.27 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=8791.5MB, alloc=40.3MB, time=115.01
x[1] = 0.786 1.308
h = 0.0001 0.003
y1[1] (numeric) = -1.50414829395 1.11770091845
y1[1] (closed_form) = -1.40245420792 1.21285474404
absolute error = 0.1393
relative error = 7.511 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -1.23266938835 -1.35817903105
y2[1] (closed_form) = -1.40414332125 -1.21139574119
absolute error = 0.2257
relative error = 12.17 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7861 1.311
h = 0.001 0.001
y1[1] (numeric) = -1.50810668525 1.12154315445
y1[1] (closed_form) = -1.40595392579 1.21719419294
absolute error = 0.1399
relative error = 7.525 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -1.23811370137 -1.36310978703
y2[1] (closed_form) = -1.40792881202 -1.21548684807
absolute error = 0.225
relative error = 12.1 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=8840.2MB, alloc=40.3MB, time=115.64
x[1] = 0.7871 1.312
h = 0.001 0.003
y1[1] (numeric) = -1.50823142358 1.12414957137
y1[1] (closed_form) = -1.40576026576 1.21981901449
absolute error = 0.1402
relative error = 7.532 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -1.24356534474 -1.36804505197
y2[1] (closed_form) = -1.41055317569 -1.215674199
absolute error = 0.2261
relative error = 12.14 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=8888.8MB, alloc=40.3MB, time=116.28
x[1] = 0.7881 1.315
h = 0.0001 0.004
y1[1] (numeric) = -1.51109666664 1.12925896865
y1[1] (closed_form) = -1.4079986963 1.22527545428
absolute error = 0.1409
relative error = 7.548 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -1.24902744512 -1.37298081777
y2[1] (closed_form) = -1.41562769199 -1.21867229074
absolute error = 0.2271
relative error = 12.16 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7882 1.319
h = 0.003 0.006
y1[1] (numeric) = -1.51647330225 1.13440358021
y1[1] (closed_form) = -1.41274260139 1.23107020762
absolute error = 0.1418
relative error = 7.567 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -1.25450919875 -1.37792881711
y2[1] (closed_form) = -1.42068141327 -1.22419094904
absolute error = 0.2264
relative error = 12.07 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=8937.4MB, alloc=40.3MB, time=116.91
x[1] = 0.7912 1.325
h = 0.0001 0.005
y1[1] (numeric) = -1.52098393483 1.14608841614
y1[1] (closed_form) = -1.41582255616 1.24330899123
absolute error = 0.1432
relative error = 7.601 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -1.26004331121 -1.38288332882
y2[1] (closed_form) = -1.43234735804 -1.22896509997
absolute error = 0.231
relative error = 12.24 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7913 1.33
h = 0.0001 0.003
y1[1] (numeric) = -1.52778447185 1.15254113643
y1[1] (closed_form) = -1.42184123979 1.25060989896
absolute error = 0.1444
relative error = 7.624 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -1.26563573121 -1.38785050854
y2[1] (closed_form) = -1.43872402459 -1.23593454953
absolute error = 0.2303
relative error = 12.14 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=8986.1MB, alloc=40.3MB, time=117.56
x[1] = 0.7914 1.333
h = 0.001 0.001
y1[1] (numeric) = -1.53182866082 1.15648549753
y1[1] (closed_form) = -1.42541119193 1.25505571955
absolute error = 0.1451
relative error = 7.638 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -1.27125074939 -1.39284024246
y2[1] (closed_form) = -1.44262488251 -1.24008014199
absolute error = 0.2296
relative error = 12.07 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7924 1.334
h = 0.001 0.003
y1[1] (numeric) = -1.53194993665 1.15915489694
y1[1] (closed_form) = -1.42520739124 1.25773984992
absolute error = 0.1453
relative error = 7.644 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -1.27687328528 -1.39783457577
y2[1] (closed_form) = -1.44530658956 -1.24024905394
absolute error = 0.2307
relative error = 12.11 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=9034.6MB, alloc=40.3MB, time=118.20
x[1] = 0.7934 1.337
h = 0.0001 0.004
y1[1] (numeric) = -1.53487124338 1.16439429369
y1[1] (closed_form) = -1.42748475688 1.26332533504
absolute error = 0.146
relative error = 7.66 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -1.28250653084 -1.40282939584
y2[1] (closed_form) = -1.45051452843 -1.24326756016
absolute error = 0.2317
relative error = 12.13 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7935 1.341
h = 0.003 0.006
y1[1] (numeric) = -1.54036403526 1.16967615252
y1[1] (closed_form) = -1.43232369517 1.26926240764
absolute error = 0.1469
relative error = 7.678 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -1.28815993289 -1.40783669387
y2[1] (closed_form) = -1.45572268702 -1.24886054057
absolute error = 0.231
relative error = 12.04 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=9083.3MB, alloc=40.3MB, time=118.84
x[1] = 0.7965 1.347
h = 0.0001 0.005
y1[1] (numeric) = -1.54495308218 1.18165322334
y1[1] (closed_form) = -1.43544611904 1.28178631726
absolute error = 0.1484
relative error = 7.711 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -1.29386696807 -1.41285052707
y2[1] (closed_form) = -1.46767744669 -1.25363730205
absolute error = 0.2357
relative error = 12.21 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=9131.9MB, alloc=40.3MB, time=119.47
x[1] = 0.7966 1.352
h = 0.0001 0.003
y1[1] (numeric) = -1.55190021251 1.18827849713
y1[1] (closed_form) = -1.4415848571 1.28926683401
absolute error = 0.1496
relative error = 7.733 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -1.29963374402 -1.41787718253
y2[1] (closed_form) = -1.47424891685 -1.26070131267
absolute error = 0.2349
relative error = 12.11 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7967 1.355
h = 0.001 0.001
y1[1] (numeric) = -1.55603116283 1.19232812029
y1[1] (closed_form) = -1.44522563428 1.2938218858
absolute error = 0.1503
relative error = 7.746 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -1.30542371934 -1.422926875
y2[1] (closed_form) = -1.47826788723 -1.26490237102
absolute error = 0.2342
relative error = 12.04 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=9180.6MB, alloc=40.3MB, time=120.11
x[1] = 0.7977 1.356
h = 0.001 0.003
y1[1] (numeric) = -1.55614829479 1.1950618969
y1[1] (closed_form) = -1.44501097403 1.29656650122
absolute error = 0.1505
relative error = 7.753 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -1.31122140484 -1.42798125755
y2[1] (closed_form) = -1.4810081997 -1.26505229559
absolute error = 0.2353
relative error = 12.08 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.7987 1.359
h = 0.0001 0.004
y1[1] (numeric) = -1.55912569581 1.2004347777
y1[1] (closed_form) = -1.44732701043 1.30228410934
absolute error = 0.1512
relative error = 7.768 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -1.31703005826 -1.43303611
y2[1] (closed_form) = -1.48635263953 -1.26809137791
absolute error = 0.2364
relative error = 12.1 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=9229.3MB, alloc=40.3MB, time=120.74
x[1] = 0.7988 1.363
h = 0.003 0.006
y1[1] (numeric) = -1.56473597381 1.20585810598
y1[1] (closed_form) = -1.45226180347 1.30836733658
absolute error = 0.1522
relative error = 7.785 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -1.32285938516 -1.43810368561
y2[1] (closed_form) = -1.49171891433 -1.27376001577
absolute error = 0.2356
relative error = 12.01 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8018 1.369
h = 0.0001 0.005
y1[1] (numeric) = -1.56940244007 1.2181347957
y1[1] (closed_form) = -1.45542519923 1.32118281035
absolute error = 0.1537
relative error = 7.817 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -1.32874364865 -1.44317780757
y2[1] (closed_form) = -1.50396905338 -1.27853877755
absolute error = 0.2404
relative error = 12.18 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=9277.8MB, alloc=40.3MB, time=121.38
x[1] = 0.8019 1.374
h = 0.0001 0.003
y1[1] (numeric) = -1.57649786098 1.224937935
y1[1] (closed_form) = -1.46168504592 1.32884777832
absolute error = 0.1549
relative error = 7.839 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -1.33468912018 -1.44826489595
y2[1] (closed_form) = -1.51073997066 -1.28569903729
absolute error = 0.2396
relative error = 12.08 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.802 1.377
h = 0.001 0.001
y1[1] (numeric) = -1.58071655126 1.22909603499
y1[1] (closed_form) = -1.46539724575 1.33351498717
absolute error = 0.1556
relative error = 7.852 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -1.34065841049 -1.45337550943
y2[1] (closed_form) = -1.51487986561 -1.2899565396
absolute error = 0.2389
relative error = 12.01 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=9326.6MB, alloc=40.3MB, time=122.02
x[1] = 0.803 1.378
h = 0.001 0.003
y1[1] (numeric) = -1.58082883793 1.23189561519
y1[1] (closed_form) = -1.46517098797 1.3363212889
absolute error = 0.1558
relative error = 7.858 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -1.3466356087 -1.45849090392
y2[1] (closed_form) = -1.51768006785 -1.29008690605
absolute error = 0.24
relative error = 12.05 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.804 1.381
h = 0.0001 0.004
y1[1] (numeric) = -1.58386235531 1.23740554829
y1[1] (closed_form) = -1.46752541763 1.34217416696
absolute error = 0.1566
relative error = 7.872 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -1.3526240388 -1.46360674866
y2[1] (closed_form) = -1.52316415405 -1.29314670363
absolute error = 0.2411
relative error = 12.07 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=9375.0MB, alloc=40.3MB, time=122.65
x[1] = 0.8041 1.385
h = 0.003 0.006
y1[1] (numeric) = -1.58959146979 1.24297467303
y1[1] (closed_form) = -1.47255689659 1.3484074732
absolute error = 0.1575
relative error = 7.889 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -1.35863367346 -1.46873556246
y2[1] (closed_form) = -1.52869231369 -1.29889233189
absolute error = 0.2403
relative error = 11.98 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=9423.6MB, alloc=40.3MB, time=123.28
x[1] = 0.8071 1.391
h = 0.0001 0.005
y1[1] (numeric) = -1.59433431644 1.25555853997
y1[1] (closed_form) = -1.4757597177 1.36152109175
absolute error = 0.159
relative error = 7.92 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -1.364699578 -1.47387092186
y2[1] (closed_form) = -1.54124453173 -1.30367241579
absolute error = 0.2452
relative error = 12.15 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8072 1.396
h = 0.0001 0.003
y1[1] (numeric) = -1.60157975131 1.26254498876
y1[1] (closed_form) = -1.48214173942 1.36937546547
absolute error = 0.1602
relative error = 7.941 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -1.37082819266 -1.4790193814
y2[1] (closed_form) = -1.54821965306 -1.31093061007
absolute error = 0.2444
relative error = 12.05 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=9472.2MB, alloc=40.3MB, time=123.92
x[1] = 0.8073 1.399
h = 0.001 0.001
y1[1] (numeric) = -1.60588717468 1.26681486009
y1[1] (closed_form) = -1.48592596588 1.37415782501
absolute error = 0.161
relative error = 7.954 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -1.37698126422 -1.4841918595
y2[1] (closed_form) = -1.55248335297 -1.31524553194
absolute error = 0.2436
relative error = 11.97 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8083 1.4
h = 0.003 0.006
y1[1] (numeric) = -1.60599389384 1.26968170246
y1[1] (closed_form) = -1.48568735295 1.37702703975
absolute error = 0.1612
relative error = 7.959 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -1.38314244674 -1.48936920976
y2[1] (closed_form) = -1.55534475205 -1.31535574665
absolute error = 0.2448
relative error = 12.02 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=9520.8MB, alloc=40.3MB, time=124.56
x[1] = 0.8113 1.406
h = 0.0001 0.005
y1[1] (numeric) = -1.61078691053 1.28247500299
y1[1] (closed_form) = -1.48890865817 1.39035058693
absolute error = 0.1628
relative error = 7.99 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -1.38935065685 -1.49454037503
y2[1] (closed_form) = -1.56810873591 -1.32012849579
absolute error = 0.2497
relative error = 12.18 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8114 1.411
h = 0.0001 0.003
y1[1] (numeric) = -1.61813330991 1.28958713396
y1[1] (closed_form) = -1.49537042406 1.39834129467
absolute error = 0.164
relative error = 8.011 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -1.39562260002 -1.49972472253
y2[1] (closed_form) = -1.57522966412 -1.32744974425
absolute error = 0.2489
relative error = 12.08 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=9569.4MB, alloc=40.3MB, time=125.19
x[1] = 0.8115 1.414
h = 0.001 0.001
y1[1] (numeric) = -1.62250041697 1.29393367645
y1[1] (closed_form) = -1.49920155776 1.40320647045
absolute error = 0.1648
relative error = 8.023 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -1.40191943753 -1.50493342043
y2[1] (closed_form) = -1.57958171089 -1.33180152179
absolute error = 0.2481
relative error = 12.01 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8125 1.415
h = 0.001 0.003
y1[1] (numeric) = -1.62260288571 1.29684628865
y1[1] (closed_form) = -1.49895237339 1.40611935281
absolute error = 0.165
relative error = 8.029 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -1.40822452485 -1.51014705124
y2[1] (closed_form) = -1.58248545075 -1.33189593633
absolute error = 0.2493
relative error = 12.05 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=9618.0MB, alloc=40.3MB, time=125.83
x[1] = 0.8135 1.418
h = 0.0001 0.004
y1[1] (numeric) = -1.6257297658 1.30259318606
y1[1] (closed_form) = -1.50136735034 1.41220883696
absolute error = 0.1658
relative error = 8.043 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -1.41454129755 -1.51536109248
y2[1] (closed_form) = -1.58821309754 -1.33498725263
absolute error = 0.2504
relative error = 12.07 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=9666.6MB, alloc=40.3MB, time=126.46
x[1] = 0.8136 1.422
h = 0.003 0.006
y1[1] (numeric) = -1.63165988642 1.30841581837
y1[1] (closed_form) = -1.50655992954 1.41870709722
absolute error = 0.1668
relative error = 8.059 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -1.42088019383 -1.52058851348
y2[1] (closed_form) = -1.59402531763 -1.34086155395
absolute error = 0.2496
relative error = 11.98 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8166 1.428
h = 0.0001 0.005
y1[1] (numeric) = -1.63652691093 1.32152986424
y1[1] (closed_form) = -1.50981775776 1.43234018522
absolute error = 0.1683
relative error = 8.088 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -1.42727765326 -1.52582244754
y2[1] (closed_form) = -1.60710298227 -1.34563414458
absolute error = 0.2546
relative error = 12.15 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=9715.2MB, alloc=40.3MB, time=127.10
x[1] = 0.8167 1.433
h = 0.0001 0.003
y1[1] (numeric) = -1.64402607532 1.32883523817
y1[1] (closed_form) = -1.51640339322 1.44052895071
absolute error = 0.1696
relative error = 8.109 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -1.43374040995 -1.53106967645
y2[1] (closed_form) = -1.61443645028 -1.35305603916
absolute error = 0.2537
relative error = 12.04 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8168 1.436
h = 0.001 0.001
y1[1] (numeric) = -1.6484834909 1.33329955889
y1[1] (closed_form) = -1.52030750711 1.44551450362
absolute error = 0.1704
relative error = 8.121 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -1.44022873316 -1.53634175768
y2[1] (closed_form) = -1.61891734742 -1.35746680025
absolute error = 0.2528
relative error = 11.97 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=9763.9MB, alloc=40.3MB, time=127.74
x[1] = 0.8178 1.437
h = 0.001 0.003
y1[1] (numeric) = -1.64857899458 1.33628201631
y1[1] (closed_form) = -1.52004461005 1.44849240799
absolute error = 0.1706
relative error = 8.126 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -1.44672551894 -1.54161886304
y2[1] (closed_form) = -1.62188452693 -1.35753997335
absolute error = 0.2541
relative error = 12.01 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8188 1.44
h = 0.0001 0.004
y1[1] (numeric) = -1.65176178834 1.34217620808
y1[1] (closed_form) = -1.52249707719 1.4547259664
absolute error = 0.1714
relative error = 8.139 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -1.4532342703 -1.54689635067
y2[1] (closed_form) = -1.62776061986 -1.36065217756
absolute error = 0.2552
relative error = 12.03 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=9812.5MB, alloc=40.3MB, time=128.39
x[1] = 0.8189 1.444
h = 0.003 0.006
y1[1] (numeric) = -1.6578142983 1.34815715387
y1[1] (closed_form) = -1.52778851351 1.46138533207
absolute error = 0.1724
relative error = 8.155 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -1.45976571677 -1.55218746502
y2[1] (closed_form) = -1.63374534836 -1.36660693564
absolute error = 0.2544
relative error = 11.94 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8219 1.45
h = 0.0001 0.005
y1[1] (numeric) = -1.66275416078 1.36159998617
y1[1] (closed_form) = -1.53108117056 1.4753349363
absolute error = 0.174
relative error = 8.183 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -1.46635714439 -1.55748505515
y2[1] (closed_form) = -1.64714376923 -1.37137849375
absolute error = 0.2595
relative error = 12.11 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=9861.0MB, alloc=40.3MB, time=129.02
x[1] = 0.822 1.455
h = 0.0001 0.003
y1[1] (numeric) = -1.67040787958 1.3691044155
y1[1] (closed_form) = -1.53779176836 1.48372702887
absolute error = 0.1753
relative error = 8.203 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -1.47301547047 -1.56279604134
y2[1] (closed_form) = -1.65469485144 -1.37890270796
absolute error = 0.2585
relative error = 12 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=9909.8MB, alloc=40.3MB, time=129.66
x[1] = 0.8221 1.458
h = 0.001 0.001
y1[1] (numeric) = -1.67495663327 1.37369003154
y1[1] (closed_form) = -1.5417694797 1.48883614244
absolute error = 0.1761
relative error = 8.215 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -1.47970005521 -1.56813238729
y2[1] (closed_form) = -1.65930767058 -1.38337341855
absolute error = 0.2577
relative error = 11.93 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8231 1.459
h = 0.001 0.003
y1[1] (numeric) = -1.67504439021 1.37674388133
y1[1] (closed_form) = -1.5414920556 1.4918803652
absolute error = 0.1763
relative error = 8.22 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -1.48639332099 -1.57347384882
y2[1] (closed_form) = -1.66233965959 -1.38342469157
absolute error = 0.259
relative error = 11.98 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=9958.4MB, alloc=40.3MB, time=130.29
x[1] = 0.8241 1.462
h = 0.0001 0.004
y1[1] (numeric) = -1.67828307926 1.38278925868
y1[1] (closed_form) = -1.54398167728 1.49826141186
absolute error = 0.1771
relative error = 8.233 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -1.49309883874 -1.57881566133
y2[1] (closed_form) = -1.66836760354 -1.38655783221
absolute error = 0.2602
relative error = 11.99 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8242 1.466
h = 0.003 0.006
y1[1] (numeric) = -1.68445939913 1.38893325239
y1[1] (closed_form) = -1.54937283012 1.50508615314
absolute error = 0.1782
relative error = 8.248 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -1.49982763852 -1.58417134815
y2[1] (closed_form) = -1.67452895778 -1.39259436621
absolute error = 0.2593
relative error = 11.9 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=10006.9MB, alloc=40.3MB, time=130.94
x[1] = 0.8272 1.472
h = 0.0001 0.005
y1[1] (numeric) = -1.68947087536 1.40271310008
y1[1] (closed_form) = -1.55269856391 1.51935940145
absolute error = 0.1798
relative error = 8.275 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -1.50661786982 -1.58953346005
y2[1] (closed_form) = -1.68825535635 -1.39736394251
absolute error = 0.2644
relative error = 12.07 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8273 1.477
h = 0.0001 0.003
y1[1] (numeric) = -1.6972809613 1.41042254178
y1[1] (closed_form) = -1.55953522638 1.52796021229
absolute error = 0.1811
relative error = 8.294 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -1.51347663862 -1.59490905743
y2[1] (closed_form) = -1.69602925024 -1.40499214577
absolute error = 0.2634
relative error = 11.96 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=10055.7MB, alloc=40.3MB, time=131.58
x[1] = 0.8274 1.48
h = 0.001 0.001
y1[1] (numeric) = -1.70192209549 1.41513305752
y1[1] (closed_form) = -1.56358715716 1.53319614354
absolute error = 0.1819
relative error = 8.305 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -1.52036237866 -1.60031052764
y2[1] (closed_form) = -1.70077713711 -1.40952376837
absolute error = 0.2626
relative error = 11.89 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8284 1.481
h = 0.0001 0.004
y1[1] (numeric) = -1.70200130017 1.41825988107
y1[1] (closed_form) = -1.56329436956 1.53630800794
absolute error = 0.1821
relative error = 8.31 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -1.52725702408 -1.60571720508
y2[1] (closed_form) = -1.70387532995 -1.40955245757
absolute error = 0.264
relative error = 11.94 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=10104.3MB, alloc=40.3MB, time=132.21
x[1] = 0.8285 1.485
h = 0.003 0.006
y1[1] (numeric) = -1.70828192467 1.42454356121
y1[1] (closed_form) = -1.56877408953 1.54327739189
absolute error = 0.1832
relative error = 8.325 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -1.53416614523 -1.61113459786
y2[1] (closed_form) = -1.71019109535 -1.4156626075
absolute error = 0.263
relative error = 11.85 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8315 1.491
h = 0.0001 0.005
y1[1] (numeric) = -1.71335207823 1.43861096602
y1[1] (closed_form) = -1.57213081927 1.55783468402
absolute error = 0.1848
relative error = 8.351 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -1.54113793283 -1.61655836253
y2[1] (closed_form) = -1.72420574309 -1.42043368542
absolute error = 0.2683
relative error = 12.01 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=10152.9MB, alloc=40.3MB, time=132.85
x[1] = 0.8316 1.496
h = 0.0001 0.003
y1[1] (numeric) = -1.72129398157 1.44649617061
y1[1] (closed_form) = -1.57907945942 1.56661804501
absolute error = 0.1862
relative error = 8.369 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -1.54817965482 -1.6219956776
y2[1] (closed_form) = -1.73217441819 -1.42815547306
absolute error = 0.2673
relative error = 11.9 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=10201.6MB, alloc=40.3MB, time=133.49
x[1] = 0.8317 1.499
h = 0.001 0.001
y1[1] (numeric) = -1.72601298931 1.45131378244
y1[1] (closed_form) = -1.58319734201 1.5719649079
absolute error = 0.187
relative error = 8.38 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -1.55524895883 -1.6274592978
y2[1] (closed_form) = -1.73704040259 -1.43274195592
absolute error = 0.2664
relative error = 11.83 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8327 1.5
h = 0.001 0.003
y1[1] (numeric) = -1.72608439543 1.45450276433
y1[1] (closed_form) = -1.58289147054 1.57513627336
absolute error = 0.1872
relative error = 8.385 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -1.56232736006 -1.63292820176
y2[1] (closed_form) = -1.74019699758 -1.43275145027
absolute error = 0.2678
relative error = 11.88 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=10250.3MB, alloc=40.3MB, time=134.13
x[1] = 0.8337 1.503
h = 0.0001 0.004
y1[1] (numeric) = -1.7294255118 1.46083604011
y1[1] (closed_form) = -1.5854511308 1.58180067646
absolute error = 0.188
relative error = 8.396 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -1.56941855541 -1.63839739069
y2[1] (closed_form) = -1.74651656851 -1.43592549674
absolute error = 0.269
relative error = 11.9 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8338 1.507
h = 0.003 0.006
y1[1] (numeric) = -1.73583276266 1.46729205041
y1[1] (closed_form) = -1.591032238 1.58894363572
absolute error = 0.1891
relative error = 8.411 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -1.57653415123 -1.64388090962
y2[1] (closed_form) = -1.75301687222 -1.44211991844
absolute error = 0.2681
relative error = 11.81 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=10298.7MB, alloc=40.3MB, time=134.77
x[1] = 0.8368 1.513
h = 0.0001 0.005
y1[1] (numeric) = -1.74097217714 1.48171262423
y1[1] (closed_form) = -1.59441871088 1.60383827328
absolute error = 0.1908
relative error = 8.435 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -1.58371392749 -1.64937072366
y2[1] (closed_form) = -1.76737334777 -1.44688713076
absolute error = 0.2734
relative error = 11.97 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8369 1.518
h = 0.0001 0.003
y1[1] (numeric) = -1.74907403917 1.48981451712
y1[1] (closed_form) = -1.60149555748 1.61284070453
absolute error = 0.1921
relative error = 8.453 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -1.59096535149 -1.6548741546
y2[1] (closed_form) = -1.7755748232 -1.45471606687
absolute error = 0.2723
relative error = 11.86 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=10347.4MB, alloc=40.3MB, time=135.41
x[1] = 0.837 1.521
h = 0.001 0.001
y1[1] (numeric) = -1.75388749314 1.4947640928
y1[1] (closed_form) = -1.6056888688 1.6183206394
absolute error = 0.1929
relative error = 8.464 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -1.59824511019 -1.66040441488
y2[1] (closed_form) = -1.78058192045 -1.45936528221
absolute error = 0.2714
relative error = 11.79 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.838 1.522
h = 0.001 0.003
y1[1] (numeric) = -1.75394877627 1.49802915468
y1[1] (closed_form) = -1.60536603276 1.62156219218
absolute error = 0.1932
relative error = 8.468 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -1.60553420189 -1.66594005097
y2[1] (closed_form) = -1.78380738932 -1.45935086878
absolute error = 0.2729
relative error = 11.84 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=10396.1MB, alloc=40.3MB, time=136.04
x[1] = 0.839 1.525
h = 0.0001 0.004
y1[1] (numeric) = -1.75734571592 1.50452541253
y1[1] (closed_form) = -1.6079618314 1.62838427925
absolute error = 0.1941
relative error = 8.48 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -1.61283639292 -1.67147593119
y2[1] (closed_form) = -1.79028896704 -1.46254588845
absolute error = 0.2741
relative error = 11.86 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=10444.7MB, alloc=40.3MB, time=136.68
x[1] = 0.8391 1.529
h = 0.003 0.006
y1[1] (numeric) = -1.7638810623 1.51115882839
y1[1] (closed_form) = -1.61364520451 1.63570537207
absolute error = 0.1951
relative error = 8.493 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -1.6201636179 -1.67702639085
y2[1] (closed_form) = -1.79697821736 -1.46882589012
absolute error = 0.2731
relative error = 11.77 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8421 1.535
h = 0.0001 0.005
y1[1] (numeric) = -1.76908834298 1.52594135425
y1[1] (closed_form) = -1.61705949081 1.65094493566
absolute error = 0.1968
relative error = 8.517 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -1.62755657181 -1.68258305416
y2[1] (closed_form) = -1.81168417795 -1.47358806214
absolute error = 0.2785
relative error = 11.93 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=10493.2MB, alloc=40.3MB, time=137.31
x[1] = 0.8422 1.54
h = 0.0001 0.003
y1[1] (numeric) = -1.7773520386 1.53426632179
y1[1] (closed_form) = -1.62426567083 1.66017219203
absolute error = 0.1982
relative error = 8.534 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -1.63502292711 -1.68815338787
y2[1] (closed_form) = -1.82012401879 -1.48152580336
absolute error = 0.2774
relative error = 11.82 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8423 1.543
h = 0.001 0.001
y1[1] (numeric) = -1.78226101481 1.53935172494
y1[1] (closed_form) = -1.62853504469 1.66578867525
absolute error = 0.199
relative error = 8.544 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -1.64251839169 -1.69375108092
y2[1] (closed_form) = -1.82527559604 -1.48623870312
absolute error = 0.2765
relative error = 11.75 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=10542.1MB, alloc=40.3MB, time=137.96
x[1] = 0.8433 1.544
h = 0.001 0.003
y1[1] (numeric) = -1.78231129712 1.5426945485
y1[1] (closed_form) = -1.6281943409 1.66910181797
absolute error = 0.1993
relative error = 8.548 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -1.65002343133 -1.69935424196
y2[1] (closed_form) = -1.82857140598 -1.48619962312
absolute error = 0.2781
relative error = 11.8 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8443 1.547
h = 0.0001 0.004
y1[1] (numeric) = -1.78576398326 1.54935804623
y1[1] (closed_form) = -1.63082587037 1.67608530474
absolute error = 0.2002
relative error = 8.559 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -1.65754188224 -1.70495760279
y2[1] (closed_form) = -1.83521869073 -1.48941556105
absolute error = 0.2793
relative error = 11.82 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=10590.7MB, alloc=40.3MB, time=138.61
x[1] = 0.8444 1.551
h = 0.003 0.006
y1[1] (numeric) = -1.79242891023 1.55617406917
y1[1] (closed_form) = -1.63661239317 1.68358919444
absolute error = 0.2013
relative error = 8.572 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -1.66508601741 -1.71057579294
y2[1] (closed_form) = -1.84210140205 -1.49578244583
absolute error = 0.2783
relative error = 11.73 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8474 1.557
h = 0.0001 0.005
y1[1] (numeric) = -1.79770259622 1.57132753351
y1[1] (closed_form) = -1.6400524954 1.69918142838
absolute error = 0.203
relative error = 8.595 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -1.67269746523 -1.71620008017
y2[1] (closed_form) = -1.85716466309 -1.50053831905
absolute error = 0.2838
relative error = 11.89 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=10639.3MB, alloc=40.3MB, time=139.24
x[1] = 0.8475 1.562
h = 0.0001 0.003
y1[1] (numeric) = -1.8061300207 1.57988212084
y1[1] (closed_form) = -1.64738914233 1.70863939739
absolute error = 0.2044
relative error = 8.612 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -1.68038410933 -1.72183807781
y2[1] (closed_form) = -1.86584856848 -1.50858651607
absolute error = 0.2826
relative error = 11.78 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8476 1.565
h = 0.001 0.001
y1[1] (numeric) = -1.81113560604 1.58510731093
y1[1] (closed_form) = -1.65173521538 1.71439598535
absolute error = 0.2052
relative error = 8.621 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -1.68810065975 -1.72750397064
y2[1] (closed_form) = -1.87114807356 -1.51336404752
absolute error = 0.2817
relative error = 11.71 %
Correct digits = 1
memory used=10688.1MB, alloc=40.3MB, time=139.88
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8486 1.566
h = 0.001 0.003
y1[1] (numeric) = -1.81117398246 1.58852961446
y1[1] (closed_form) = -1.65137571583 1.71778214909
absolute error = 0.2055
relative error = 8.625 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -1.69582703369 -1.73317542378
y2[1] (closed_form) = -1.87451571811 -1.51329951448
absolute error = 0.2833
relative error = 11.76 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=10736.8MB, alloc=40.3MB, time=140.54
x[1] = 0.8496 1.569
h = 0.0001 0.004
y1[1] (numeric) = -1.81468232014 1.59536471064
y1[1] (closed_form) = -1.65404254722 1.72493083321
absolute error = 0.2064
relative error = 8.636 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -1.70356713774 -1.73884702871
y2[1] (closed_form) = -1.88133249055 -1.51653628663
absolute error = 0.2846
relative error = 11.78 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8497 1.573
h = 0.003 0.006
y1[1] (numeric) = -1.821478328 1.60236867135
y1[1] (closed_form) = -1.65993310788 1.7326222905
absolute error = 0.2075
relative error = 8.648 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -1.71133359358 -1.74453371327
y2[1] (closed_form) = -1.88841328571 -1.52299135216
absolute error = 0.2836
relative error = 11.69 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=10785.3MB, alloc=40.3MB, time=141.17
x[1] = 0.8527 1.579
h = 0.0001 0.005
y1[1] (numeric) = -1.82681688898 1.61790226824
y1[1] (closed_form) = -1.66339695808 1.74857510594
absolute error = 0.2092
relative error = 8.67 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -1.71916898181 -1.75022637269
y2[1] (closed_form) = -1.90384182404 -1.52773958186
absolute error = 0.2891
relative error = 11.85 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8528 1.584
h = 0.0001 0.003
y1[1] (numeric) = -1.83540995715 1.62669318314
y1[1] (closed_form) = -1.67086521111 1.75826981074
absolute error = 0.2107
relative error = 8.686 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -1.72708140335 -1.7559327686
y2[1] (closed_form) = -1.91277563016 -1.53589987879
absolute error = 0.2879
relative error = 11.74 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=10833.9MB, alloc=40.3MB, time=141.81
x[1] = 0.8529 1.587
h = 0.001 0.001
y1[1] (numeric) = -1.84051324885 1.63206221781
y1[1] (closed_form) = -1.67528862228 1.76417014158
absolute error = 0.2115
relative error = 8.695 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -1.73502455128 -1.76166760145
y2[1] (closed_form) = -1.91822659345 -1.54074298419
absolute error = 0.287
relative error = 11.66 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8539 1.588
h = 0.0001 0.004
y1[1] (numeric) = -1.84053878612 1.63556575681
y1[1] (closed_form) = -1.67490937334 1.76763078632
absolute error = 0.2118
relative error = 8.699 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -1.74297777773 -1.76740808701
y2[1] (closed_form) = -1.92166759293 -1.54065218329
absolute error = 0.2887
relative error = 11.72 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=10882.6MB, alloc=40.3MB, time=142.44
x[1] = 0.854 1.592
h = 0.003 0.006
y1[1] (numeric) = -1.84744521786 1.64273062565
y1[1] (closed_form) = -1.68089251405 1.77548634579
absolute error = 0.213
relative error = 8.711 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -1.75094743374 -1.77316027972
y2[1] (closed_form) = -1.92892160719 -1.54718662299
absolute error = 0.2876
relative error = 11.63 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.857 1.598
h = 0.0001 0.005
y1[1] (numeric) = -1.85283658689 1.65858849622
y1[1] (closed_form) = -1.68437952052 1.79175575447
absolute error = 0.2147
relative error = 8.732 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -1.75898740111 -1.77891833266
y2[1] (closed_form) = -1.94467119187 -1.55193161252
absolute error = 0.2933
relative error = 11.79 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=10931.1MB, alloc=40.3MB, time=143.08
x[1] = 0.8571 1.603
h = 0.0001 0.003
y1[1] (numeric) = -1.86156928595 1.6675818906
y1[1] (closed_form) = -1.69196489181 1.80165757623
absolute error = 0.2162
relative error = 8.747 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -1.76710596725 -1.78469013247
y2[1] (closed_form) = -1.95382352267 -1.56019278644
absolute error = 0.292
relative error = 11.68 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=10979.9MB, alloc=40.3MB, time=143.72
x[1] = 0.8572 1.606
h = 0.001 0.001
y1[1] (numeric) = -1.86675493568 1.67307418817
y1[1] (closed_form) = -1.69645715882 1.80768368159
absolute error = 0.2171
relative error = 8.756 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -1.77525596222 -1.79049082562
y2[1] (closed_form) = -1.95940695123 -1.56509494906
absolute error = 0.2911
relative error = 11.61 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8582 1.607
h = 0.001 0.003
y1[1] (numeric) = -1.86676899421 1.67664691832
y1[1] (closed_form) = -1.69606103796 1.81120987981
absolute error = 0.2174
relative error = 8.76 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -1.78341625375 -1.79629724859
y2[1] (closed_form) = -1.96291265713 -1.56498176196
absolute error = 0.2928
relative error = 11.66 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=11028.4MB, alloc=40.3MB, time=144.36
x[1] = 0.8592 1.61
h = 0.0001 0.004
y1[1] (numeric) = -1.87037909327 1.68380862292
y1[1] (closed_form) = -1.69879441739 1.81867594525
absolute error = 0.2182
relative error = 8.77 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -1.79159087889 -1.80210372538
y2[1] (closed_form) = -1.97005490719 -1.56825910362
absolute error = 0.2942
relative error = 11.68 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8593 1.614
h = 0.003 0.006
y1[1] (numeric) = -1.87741957412 1.69117188213
y1[1] (closed_form) = -1.70488331784 1.82672823287
absolute error = 0.2194
relative error = 8.781 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -1.79979312722 -1.80792574184
y2[1] (closed_form) = -1.97751588905 -1.57488418055
absolute error = 0.2931
relative error = 11.59 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=11077.0MB, alloc=40.3MB, time=144.99
x[1] = 0.8623 1.62
h = 0.0001 0.005
y1[1] (numeric) = -1.88287285748 1.70742792952
y1[1] (closed_form) = -1.70839012617 1.84337342532
absolute error = 0.2212
relative error = 8.801 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -1.80806737737 -1.81375346579
y2[1] (closed_form) = -1.99364605369 -1.57961888613
absolute error = 0.2988
relative error = 11.75 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8624 1.625
h = 0.0001 0.003
y1[1] (numeric) = -1.89177498624 1.71667080075
y1[1] (closed_form) = -1.71610931106 1.85352354814
absolute error = 0.2227
relative error = 8.816 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -1.81642214609 -1.81959493553
y2[1] (closed_form) = -2.0030595008 -1.58799527322
absolute error = 0.2974
relative error = 11.64 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=11125.7MB, alloc=40.3MB, time=145.63
x[1] = 0.8625 1.628
h = 0.001 0.001
y1[1] (numeric) = -1.89706051218 1.72231489633
y1[1] (closed_form) = -1.72068015501 1.85970038229
absolute error = 0.2236
relative error = 8.824 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -1.82480920883 -1.82546585202
y2[1] (closed_form) = -2.00880117162 -1.59296479278
absolute error = 0.2965
relative error = 11.56 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8635 1.629
h = 0.001 0.003
y1[1] (numeric) = -1.89705990899 1.72597230858
y1[1] (closed_form) = -1.72026245773 1.8633038688
absolute error = 0.2239
relative error = 8.828 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -1.83320683598 -1.83134259096
y2[1] (closed_form) = -2.01238314507 -1.59282376256
absolute error = 0.2983
relative error = 11.62 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=11174.4MB, alloc=40.3MB, time=146.27
x[1] = 0.8645 1.632
h = 0.0001 0.004
y1[1] (numeric) = -1.9007253401 1.73331882176
y1[1] (closed_form) = -1.72302983307 1.87094646895
absolute error = 0.2248
relative error = 8.837 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -1.84161913646 -1.83721932467
y2[1] (closed_form) = -2.01970616019 -1.59612157729
absolute error = 0.2997
relative error = 11.64 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=11222.9MB, alloc=40.3MB, time=146.90
x[1] = 0.8646 1.636
h = 0.003 0.006
y1[1] (numeric) = -1.90790140945 1.74088618559
y1[1] (closed_form) = -1.7292253914 1.87920057598
absolute error = 0.226
relative error = 8.848 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -1.85005977986 -1.84311184947
y2[1] (closed_form) = -2.02737905637 -1.60283857195
absolute error = 0.2986
relative error = 11.55 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8676 1.642
h = 0.0001 0.005
y1[1] (numeric) = -1.91341486142 1.757550216
y1[1] (closed_form) = -1.73274971847 1.89622995898
absolute error = 0.2278
relative error = 8.867 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -1.85857415385 -1.84900991191
y2[1] (closed_form) = -2.04389825931 -1.60756139041
absolute error = 0.3044
relative error = 11.71 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=11271.4MB, alloc=40.3MB, time=147.53
x[1] = 0.8677 1.647
h = 0.0001 0.003
y1[1] (numeric) = -1.92248838509 1.76704975496
y1[1] (closed_form) = -1.74060386913 1.90663481078
absolute error = 0.2293
relative error = 8.881 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -1.86717101109 -1.85492170362
y2[1] (closed_form) = -2.05357906804 -1.61605461426
absolute error = 0.303
relative error = 11.59 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8678 1.65
h = 0.001 0.001
y1[1] (numeric) = -1.92787491055 1.7728499977
y1[1] (closed_form) = -1.74525393342 1.91296625589
absolute error = 0.2302
relative error = 8.889 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -1.87580105217 -1.86086350152
y2[1] (closed_form) = -2.05948275786 -1.62109241743
absolute error = 0.302
relative error = 11.52 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=11320.0MB, alloc=40.3MB, time=148.18
x[1] = 0.8688 1.651
h = 0.001 0.003
y1[1] (numeric) = -1.92785862704 1.77659395655
y1[1] (closed_form) = -1.74481362888 1.91664857617
absolute error = 0.2305
relative error = 8.892 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -1.88444193255 -1.86681121453
y2[1] (closed_form) = -2.06314259908 -1.6209226444
absolute error = 0.304
relative error = 11.59 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8698 1.654
h = 0.0001 0.004
y1[1] (numeric) = -1.93157921356 1.78413004435
y1[1] (closed_form) = -1.74761447944 1.92447184087
absolute error = 0.2314
relative error = 8.901 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -1.89309783345 -1.87275885918
y2[1] (closed_form) = -2.0706504871 -1.6242407279
absolute error = 0.3054
relative error = 11.61 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=11368.6MB, alloc=40.3MB, time=148.82
x[1] = 0.8699 1.658
h = 0.003 0.006
y1[1] (numeric) = -1.93889242311 1.79190736887
y1[1] (closed_form) = -1.75391759535 1.93293297546
absolute error = 0.2326
relative error = 8.912 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -1.90178281585 -1.87872254648
y2[1] (closed_form) = -2.07854036237 -1.63105091326
absolute error = 0.3043
relative error = 11.52 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8729 1.664
h = 0.0001 0.005
y1[1] (numeric) = -1.94446421504 1.80898941325
y1[1] (closed_form) = -1.75745707643 1.95035513502
absolute error = 0.2344
relative error = 8.929 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -1.91054329674 -1.88469158387
y2[1] (closed_form) = -2.09545723652 -1.63576014526
absolute error = 0.3101
relative error = 11.67 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=11417.3MB, alloc=40.3MB, time=149.45
x[1] = 0.873 1.669
h = 0.0001 0.003
y1[1] (numeric) = -1.95371111478 1.81875298936
y1[1] (closed_form) = -1.76544734714 1.96102129134
absolute error = 0.236
relative error = 8.943 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -1.91938827143 -1.89067431807
y2[1] (closed_form) = -2.10541180135 -1.6443718204
absolute error = 0.3087
relative error = 11.55 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8731 1.672
h = 0.001 0.001
y1[1] (numeric) = -1.95919977109 1.82471383615
y1[1] (closed_form) = -1.77017727523 1.96751131854
absolute error = 0.2369
relative error = 8.951 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -1.92826734507 -1.89668762394
y2[1] (closed_form) = -2.1114813767 -1.64947882718
absolute error = 0.3077
relative error = 11.48 %
Correct digits = 1
memory used=11466.2MB, alloc=40.3MB, time=150.09
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8741 1.673
h = 0.001 0.003
y1[1] (numeric) = -1.95916675657 1.82854624588
y1[1] (closed_form) = -1.76971330392 1.97127404877
absolute error = 0.2372
relative error = 8.954 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -1.93715754007 -1.90270693758
y2[1] (closed_form) = -2.1152207147 -1.64927938041
absolute error = 0.3097
relative error = 11.55 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=11514.8MB, alloc=40.3MB, time=150.72
x[1] = 0.8751 1.676
h = 0.0001 0.004
y1[1] (numeric) = -1.96294229717 1.83627678634
y1[1] (closed_form) = -1.77254708215 1.97928219803
absolute error = 0.2381
relative error = 8.962 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -1.9460631104 -1.90872611551
y2[1] (closed_form) = -2.12291767247 -1.65261749448
absolute error = 0.3112
relative error = 11.57 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8752 1.68
h = 0.003 0.006
y1[1] (numeric) = -1.9703942101 1.84427007283
y1[1] (closed_form) = -1.77895865608 1.9879556878
absolute error = 0.2394
relative error = 8.972 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -1.95499852012 -1.91476158775
y2[1] (closed_form) = -2.13102971226 -1.65952213541
absolute error = 0.3101
relative error = 11.48 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=11563.4MB, alloc=40.3MB, time=151.36
x[1] = 0.8782 1.686
h = 0.0001 0.005
y1[1] (numeric) = -1.97602242671 1.86178039151
y1[1] (closed_form) = -1.78251084174 2.00577939256
absolute error = 0.2412
relative error = 8.989 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -1.96401123619 -1.92080220422
y2[1] (closed_form) = -2.14835306868 -1.66421598269
absolute error = 0.3159
relative error = 11.63 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8783 1.691
h = 0.0001 0.003
y1[1] (numeric) = -1.98544469852 1.87181555711
y1[1] (closed_form) = -1.79063838791 2.01671357981
absolute error = 0.2428
relative error = 9.002 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -1.97311050352 -1.92685646849
y2[1] (closed_form) = -2.15858793654 -1.67294771378
absolute error = 0.3144
relative error = 11.51 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=11612.1MB, alloc=40.3MB, time=152.00
x[1] = 0.8784 1.694
h = 0.001 0.001
y1[1] (numeric) = -1.99103662439 1.87794157513
y1[1] (closed_form) = -1.7954488227 2.02336625115
absolute error = 0.2437
relative error = 9.01 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -1.98224481081 -1.93294187601
y2[1] (closed_form) = -2.16482735571 -1.67812483704
absolute error = 0.3135
relative error = 11.44 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8794 1.695
h = 0.0001 0.004
y1[1] (numeric) = -1.990985795 1.88186438044
y1[1] (closed_form) = -1.79496009554 2.02721099863
absolute error = 0.244
relative error = 9.013 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -1.99139052884 -1.93903338393
y2[1] (closed_form) = -2.16864784883 -1.67789475351
absolute error = 0.3156
relative error = 11.51 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=11660.8MB, alloc=44.3MB, time=152.65
x[1] = 0.8795 1.699
h = 0.003 0.006
y1[1] (numeric) = -1.99855453021 1.89004246845
y1[1] (closed_form) = -1.80146836574 2.03607032949
absolute error = 0.2453
relative error = 9.023 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -2.00055490587 -1.94513762456
y2[1] (closed_form) = -2.17695422138 -1.68488443761
absolute error = 0.3144
relative error = 11.42 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8825 1.705
h = 0.0001 0.005
y1[1] (numeric) = -2.00422819486 1.90791804699
y1[1] (closed_form) = -1.80503438745 2.0542467246
absolute error = 0.2472
relative error = 9.038 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -2.00979812824 -1.95124682288
y2[1] (closed_form) = -2.19463487283 -1.68956851279
absolute error = 0.3204
relative error = 11.57 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=11709.4MB, alloc=44.3MB, time=153.28
x[1] = 0.8826 1.71
h = 0.0001 0.003
y1[1] (numeric) = -2.01379827049 1.91818577509
y1[1] (closed_form) = -1.81328432577 2.06541547398
absolute error = 0.2488
relative error = 9.051 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -2.01912965485 -1.95736961467
y2[1] (closed_form) = -2.20511492171 -1.69840830893
absolute error = 0.3188
relative error = 11.45 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=11758.1MB, alloc=44.3MB, time=153.92
x[1] = 0.8827 1.713
h = 0.001 0.001
y1[1] (numeric) = -2.01947722568 1.92445325481
y1[1] (closed_form) = -1.81816657692 2.07221049827
absolute error = 0.2497
relative error = 9.058 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -2.02849702706 -1.96352403115
y2[1] (closed_form) = -2.21150292816 -1.70364860038
absolute error = 0.3178
relative error = 11.39 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8837 1.714
h = 0.001 0.003
y1[1] (numeric) = -2.01941064414 1.92845304569
y1[1] (closed_form) = -1.81765664908 2.07612746779
absolute error = 0.25
relative error = 9.061 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -2.03787605735 -1.96968462522
y2[1] (closed_form) = -2.2153950088 -1.70339234366
absolute error = 0.32
relative error = 11.45 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=11806.7MB, alloc=44.3MB, time=154.55
x[1] = 0.8847 1.717
h = 0.0001 0.004
y1[1] (numeric) = -2.02328636637 1.93655352393
y1[1] (closed_form) = -1.82055246885 2.08449081668
absolute error = 0.251
relative error = 9.068 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -2.0472711345 -1.97584494847
y2[1] (closed_form) = -2.22345503372 -1.70676934997
absolute error = 0.3216
relative error = 11.47 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8848 1.721
h = 0.003 0.006
y1[1] (numeric) = -2.03099689217 1.94495934282
y1[1] (closed_form) = -1.82717093867 2.09357273254
absolute error = 0.2523
relative error = 9.078 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -2.05669749377 -1.98202202763
y2[1] (closed_form) = -2.23199353514 -1.71385588473
absolute error = 0.3204
relative error = 11.38 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=11855.2MB, alloc=44.3MB, time=155.18
x[1] = 0.8878 1.727
h = 0.0001 0.005
y1[1] (numeric) = -2.03672325869 1.96328332942
y1[1] (closed_form) = -1.8307449806 2.11216751873
absolute error = 0.2542
relative error = 9.093 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -2.06620458474 -1.98820382288
y2[1] (closed_form) = -2.25009757505 -1.71852106593
absolute error = 0.3264
relative error = 11.53 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8879 1.732
h = 0.0001 0.003
y1[1] (numeric) = -2.04647264632 1.97383745357
y1[1] (closed_form) = -1.83913442824 2.12361721465
absolute error = 0.2558
relative error = 9.105 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -2.07580212944 -1.99439913031
y2[1] (closed_form) = -2.26087050767 -1.72748395745
absolute error = 0.3248
relative error = 11.42 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=11903.9MB, alloc=44.3MB, time=155.81
x[1] = 0.888 1.735
h = 0.001 0.001
y1[1] (numeric) = -2.05225711904 1.9802790577
y1[1] (closed_form) = -1.84409842962 2.13058268289
absolute error = 0.2568
relative error = 9.112 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -2.08543651152 -2.00062664604
y2[1] (closed_form) = -2.26743596397 -1.73279609309
absolute error = 0.3238
relative error = 11.35 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.889 1.736
h = 0.001 0.003
y1[1] (numeric) = -2.05217060358 1.98437306094
y1[1] (closed_form) = -1.84356165783 2.13458475887
absolute error = 0.2571
relative error = 9.114 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -2.09508285547 -2.00686043194
y2[1] (closed_form) = -2.27141237779 -1.73250734007
absolute error = 0.3261
relative error = 11.42 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=11952.5MB, alloc=44.3MB, time=156.44
x[1] = 0.89 1.739
h = 0.0001 0.004
y1[1] (numeric) = -2.05610062232 1.9926827733
y1[1] (closed_form) = -1.84648873332 2.1431455867
absolute error = 0.258
relative error = 9.121 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -2.10474562422 -2.01309386681
y2[1] (closed_form) = -2.27967399129 -1.73590355235
absolute error = 0.3278
relative error = 11.44 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=12001.1MB, alloc=44.3MB, time=157.07
x[1] = 0.8901 1.743
h = 0.003 0.006
y1[1] (numeric) = -2.06395452948 2.00132275541
y1[1] (closed_form) = -1.85321830222 2.15245577175
absolute error = 0.2593
relative error = 9.13 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -2.11444049143 -2.01934430932
y2[1] (closed_form) = -2.28845016719 -1.74308817737
absolute error = 0.3265
relative error = 11.35 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8931 1.749
h = 0.0001 0.005
y1[1] (numeric) = -2.06973141561 2.02010608662
y1[1] (closed_form) = -1.85679765722 2.17147826034
absolute error = 0.2613
relative error = 9.144 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -2.12421801919 -2.02559920624
y2[1] (closed_form) = -2.30698693758 -1.74773236936
absolute error = 0.3326
relative error = 11.49 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=12049.8MB, alloc=44.3MB, time=157.70
x[1] = 0.8932 1.754
h = 0.0001 0.003
y1[1] (numeric) = -2.07966214733 2.03095470208
y1[1] (closed_form) = -1.86532776885 2.18321607954
absolute error = 0.2629
relative error = 9.156 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -2.13408820004 -2.03186751573
y2[1] (closed_form) = -2.31805975589 -1.75681993021
absolute error = 0.3309
relative error = 11.38 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8933 1.757
h = 0.001 0.001
y1[1] (numeric) = -2.08555329323 2.03757532529
y1[1] (closed_form) = -1.87037415919 2.19035632515
absolute error = 0.2639
relative error = 9.162 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -2.14399623779 -2.03816862332
y2[1] (closed_form) = -2.32480689427 -1.76220480078
absolute error = 0.3299
relative error = 11.31 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=12098.5MB, alloc=44.3MB, time=158.34
x[1] = 0.8943 1.758
h = 0.001 0.003
y1[1] (numeric) = -2.0854456599 2.04176560406
y1[1] (closed_form) = -1.86980936538 2.19444520703
absolute error = 0.2642
relative error = 9.165 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -2.15391654905 -2.04447609351
y2[1] (closed_form) = -2.32886938685 -1.76188249245
absolute error = 0.3324
relative error = 11.38 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8953 1.761
h = 0.0001 0.004
y1[1] (numeric) = -2.08942966522 2.05028988133
y1[1] (closed_form) = -1.87276703456 2.20320809952
absolute error = 0.2652
relative error = 9.171 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -2.16385367132 -2.05078312773
y2[1] (closed_form) = -2.33733714766 -1.76529753236
absolute error = 0.3341
relative error = 11.41 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=12147.0MB, alloc=44.3MB, time=158.97
x[1] = 0.8954 1.765
h = 0.003 0.006
y1[1] (numeric) = -2.09742855238 2.05917061829
y1[1] (closed_form) = -1.8796085994 2.21275236794
absolute error = 0.2665
relative error = 9.18 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -2.1738237295 -2.05710742103
y2[1] (closed_form) = -2.34635667487 -1.7725814765
absolute error = 0.3328
relative error = 11.32 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8984 1.771
h = 0.0001 0.005
y1[1] (numeric) = -2.10325367374 2.0784244789
y1[1] (closed_form) = -1.88319046299 2.23221206649
absolute error = 0.2685
relative error = 9.193 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -2.18387842046 -2.06343588633
y2[1] (closed_form) = -2.3653357102 -1.77720247357
absolute error = 0.3389
relative error = 11.45 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=12195.5MB, alloc=44.3MB, time=159.60
x[1] = 0.8985 1.776
h = 0.0001 0.003
y1[1] (numeric) = -2.11336779211 2.0895758816
y1[1] (closed_form) = -1.89186239022 2.24424534988
absolute error = 0.2702
relative error = 9.204 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -2.19402801483 -2.06977764564
y2[1] (closed_form) = -2.37671558192 -1.7864162646
absolute error = 0.3371
relative error = 11.34 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.8986 1.779
h = 0.001 0.001
y1[1] (numeric) = -2.1193667714 2.09638053952
y1[1] (closed_form) = -1.89699180505 2.25156480516
absolute error = 0.2712
relative error = 9.21 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -2.20421651408 -2.07615279901
y2[1] (closed_form) = -2.38364873439 -1.79187475164
absolute error = 0.3362
relative error = 11.27 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=12244.4MB, alloc=44.3MB, time=160.23
x[1] = 0.8996 1.78
h = 0.001 0.003
y1[1] (numeric) = -2.11923679866 2.10066920021
y1[1] (closed_form) = -1.89639777811 2.25574222544
absolute error = 0.2715
relative error = 9.212 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -2.21441760648 -2.08253440726
y2[1] (closed_form) = -2.38779908276 -1.79151779361
absolute error = 0.3388
relative error = 11.35 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=12292.9MB, alloc=44.3MB, time=160.86
x[1] = 0.9006 1.783
h = 0.0001 0.004
y1[1] (numeric) = -2.12327444843 2.10941349757
y1[1] (closed_form) = -1.89938534579 2.26471186758
absolute error = 0.2725
relative error = 9.218 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -2.22463590457 -2.08891548968
y2[1] (closed_form) = -2.39647764796 -1.7949512433
absolute error = 0.3405
relative error = 11.37 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.9007 1.787
h = 0.003 0.006
y1[1] (numeric) = -2.13141992113 2.11854174415
y1[1] (closed_form) = -1.90633979991 2.2744961664
absolute error = 0.2738
relative error = 9.227 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -2.23488799761 -2.09531408225
y2[1] (closed_form) = -2.40574633744 -1.80233572396
absolute error = 0.3392
relative error = 11.28 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=12341.5MB, alloc=44.3MB, time=161.49
x[1] = 0.9037 1.793
h = 0.0001 0.005
y1[1] (numeric) = -2.1372908869 2.13827757228
y1[1] (closed_form) = -1.90992126681 2.29440278238
absolute error = 0.2758
relative error = 9.239 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -2.24522673996 -2.10171654297
y2[1] (closed_form) = -2.42517736838 -1.80693120669
absolute error = 0.3454
relative error = 11.42 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.9038 1.798
h = 0.0001 0.003
y1[1] (numeric) = -2.14759044369 2.14974026356
y1[1] (closed_form) = -1.91873615698 2.30673903865
absolute error = 0.2775
relative error = 9.25 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -2.25566268816 -2.1081321595
y2[1] (closed_form) = -2.43687163067 -1.81627277468
absolute error = 0.3435
relative error = 11.3 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=12390.0MB, alloc=44.3MB, time=162.12
x[1] = 0.9039 1.801
h = 0.001 0.001
y1[1] (numeric) = -2.15369842029 2.15673409567
y1[1] (closed_form) = -1.9239492279 2.31424223699
absolute error = 0.2786
relative error = 9.256 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -2.2661386183 -2.11458177225
y2[1] (closed_form) = -2.44399523124 -1.82180574991
absolute error = 0.3426
relative error = 11.24 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.9049 1.802
h = 0.0001 0.004
y1[1] (numeric) = -2.15354484783 2.16112328859
y1[1] (closed_form) = -1.92332472275 2.31850996171
absolute error = 0.2789
relative error = 9.258 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -2.2766274695 -2.12103793194
y2[1] (closed_form) = -2.44823524438 -1.82141301149
absolute error = 0.3453
relative error = 11.32 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=12438.7MB, alloc=44.3MB, time=162.76
x[1] = 0.905 1.806
h = 0.003 0.006
y1[1] (numeric) = -2.16181374081 2.17046323286
y1[1] (closed_form) = -1.9303800183 2.32850437736
absolute error = 0.2802
relative error = 9.266 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -2.28713751848 -2.12750788137
y2[1] (closed_form) = -2.45772194516 -1.82888806093
absolute error = 0.3439
relative error = 11.23 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.908 1.812
h = 0.0001 0.005
y1[1] (numeric) = -2.16772094571 2.19061002413
y1[1] (closed_form) = -1.93396422245 2.34880366761
absolute error = 0.2823
relative error = 9.277 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -2.29773593315 -2.13398142816
y2[1] (closed_form) = -2.47755032731 -1.83346518077
absolute error = 0.3502
relative error = 11.36 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=12487.4MB, alloc=44.3MB, time=163.40
x[1] = 0.9081 1.817
h = 0.0001 0.003
y1[1] (numeric) = -2.17817674002 2.20233914492
y1[1] (closed_form) = -1.9429068189 2.36140513496
absolute error = 0.284
relative error = 9.287 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -2.30843351503 -2.14046799957
y2[1] (closed_form) = -2.48951966715 -1.84292182924
absolute error = 0.3483
relative error = 11.25 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=12536.1MB, alloc=44.3MB, time=164.04
x[1] = 0.9082 1.82
h = 0.001 0.001
y1[1] (numeric) = -2.18437654106 2.20949492038
y1[1] (closed_form) = -1.94819466452 2.36906919554
absolute error = 0.285
relative error = 9.293 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -2.31917200061 -2.14698907419
y2[1] (closed_form) = -2.49680992798 -1.84852195391
absolute error = 0.3473
relative error = 11.18 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.9092 1.821
h = 0.001 0.003
y1[1] (numeric) = -2.18420224689 2.21396972117
y1[1] (closed_form) = -1.94754400603 2.3734164754
absolute error = 0.2854
relative error = 9.295 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -2.32992368738 -2.15351677231
y2[1] (closed_form) = -2.50112904022 -1.84809858113
absolute error = 0.3501
relative error = 11.26 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=12584.7MB, alloc=44.3MB, time=164.67
x[1] = 0.9102 1.824
h = 0.0001 0.004
y1[1] (numeric) = -2.18833728101 2.22313241879
y1[1] (closed_form) = -1.95058783736 2.38278331292
absolute error = 0.2864
relative error = 9.3 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -2.34069332661 -2.16004376633
y2[1] (closed_form) = -2.51021239804 -1.85156768123
absolute error = 0.352
relative error = 11.28 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.9103 1.828
h = 0.003 0.006
y1[1] (numeric) = -2.19675592584 2.2327331205
y1[1] (closed_form) = -1.9577577464 2.3930291781
absolute error = 0.2878
relative error = 9.308 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -2.35149839535 -2.16658872977
y2[1] (closed_form) = -2.51995942681 -1.85914557233
absolute error = 0.3506
relative error = 11.19 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=12633.3MB, alloc=44.3MB, time=165.30
x[1] = 0.9133 1.834
h = 0.0001 0.005
y1[1] (numeric) = -2.20270431294 2.25338432169
y1[1] (closed_form) = -1.96133598851 2.41379403172
absolute error = 0.2898
relative error = 9.318 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -2.36239393328 -2.17313694478
y2[1] (closed_form) = -2.54025847772 -1.86369266938
absolute error = 0.3569
relative error = 11.33 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.9134 1.839
h = 0.0001 0.003
y1[1] (numeric) = -2.21334958991 2.26544139988
y1[1] (closed_form) = -1.97042376166 2.42671288966
absolute error = 0.2916
relative error = 9.328 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -2.37339104307 -2.17969800779
y2[1] (closed_form) = -2.55255630661 -1.87328002447
absolute error = 0.355
relative error = 11.21 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=12681.9MB, alloc=44.3MB, time=165.94
x[1] = 0.9135 1.842
h = 0.001 0.001
y1[1] (numeric) = -2.21966068278 2.27279642552
y1[1] (closed_form) = -1.9757964824 2.43456939808
absolute error = 0.2926
relative error = 9.333 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -2.38443019075 -2.18629418838
y2[1] (closed_form) = -2.56004553515 -1.87895628685
absolute error = 0.354
relative error = 11.15 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.9145 1.843
h = 0.001 0.003
y1[1] (numeric) = -2.21946032265 2.27737597772
y1[1] (closed_form) = -1.97511295711 2.43901037547
absolute error = 0.293
relative error = 9.335 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -2.39548288363 -2.19289708414
y2[1] (closed_form) = -2.56445777984 -1.87849495242
absolute error = 0.3569
relative error = 11.23 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=12730.6MB, alloc=44.3MB, time=166.57
x[1] = 0.9155 1.846
h = 0.0001 0.004
y1[1] (numeric) = -2.22364790052 2.28677522274
y1[1] (closed_form) = -1.97818456212 2.44859794099
absolute error = 0.294
relative error = 9.34 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -2.40655394918 -2.19949917097
y2[1] (closed_form) = -2.57376583312 -1.88198109687
absolute error = 0.3589
relative error = 11.25 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=12779.2MB, alloc=44.3MB, time=167.20
x[1] = 0.9156 1.85
h = 0.003 0.006
y1[1] (numeric) = -2.23221791629 2.29664392059
y1[1] (closed_form) = -1.98546996407 2.45910159918
absolute error = 0.2954
relative error = 9.347 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -2.41766136872 -2.20611947693
y2[1] (closed_form) = -2.58377940108 -1.88966301137
absolute error = 0.3574
relative error = 11.17 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.9186 1.856
h = 0.0001 0.005
y1[1] (numeric) = -2.23820476858 2.31781171654
y1[1] (closed_form) = -1.98903903281 2.48034231785
absolute error = 0.2975
relative error = 9.357 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -2.42886140799 -2.21274266513
y2[1] (closed_form) = -2.60455943602 -1.89417742467
absolute error = 0.3638
relative error = 11.3 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=12827.7MB, alloc=44.3MB, time=167.84
x[1] = 0.9187 1.861
h = 0.0001 0.003
y1[1] (numeric) = -2.24904159862 2.33020586311
y1[1] (closed_form) = -1.99827311307 2.4935865758
absolute error = 0.2993
relative error = 9.366 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -2.44016547912 -2.21937850299
y2[1] (closed_form) = -2.61719359674 -1.9038969894
absolute error = 0.3618
relative error = 11.18 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.9188 1.864
h = 0.001 0.001
y1[1] (numeric) = -2.25546515315 2.3377656459
y1[1] (closed_form) = -2.00373132621 2.50164036704
absolute error = 0.3004
relative error = 9.372 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -2.45151275357 -2.226050079
y2[1] (closed_form) = -2.62488653133 -1.90965023079
absolute error = 0.3608
relative error = 11.11 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=12876.3MB, alloc=44.3MB, time=168.48
x[1] = 0.9198 1.865
h = 0.001 0.003
y1[1] (numeric) = -2.25523734986 2.34245222855
y1[1] (closed_form) = -2.00301358675 2.5061769073
absolute error = 0.3007
relative error = 9.373 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -2.46287392597 -2.23272846149
y2[1] (closed_form) = -2.62939381251 -1.90914969536
absolute error = 0.3639
relative error = 11.2 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.9208 1.868
h = 0.0001 0.004
y1[1] (numeric) = -2.25947698952 2.35209397893
y1[1] (closed_form) = -2.00611212988 2.51599028835
absolute error = 0.3018
relative error = 9.377 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -2.4742539004 -2.23940592471
y2[1] (closed_form) = -2.63893161805 -1.91265230277
absolute error = 0.3659
relative error = 11.23 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=12924.8MB, alloc=44.3MB, time=169.11
x[1] = 0.9209 1.872
h = 0.003 0.006
y1[1] (numeric) = -2.26819999788 2.36223809038
y1[1] (closed_form) = -2.01351389667 2.5267582275
absolute error = 0.3032
relative error = 9.384 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -2.48567117692 -2.24610185593
y2[1] (closed_form) = -2.64921808216 -1.92043940771
absolute error = 0.3644
relative error = 11.14 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.9239 1.878
h = 0.0001 0.005
y1[1] (numeric) = -2.27422247414 2.38393494004
y1[1] (closed_form) = -2.01707046555 2.54848532771
absolute error = 0.3053
relative error = 9.393 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -2.49718327173 -2.25280027574
y2[1] (closed_form) = -2.67048962807 -1.9249183492
absolute error = 0.3709
relative error = 11.27 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=12973.3MB, alloc=44.3MB, time=169.74
x[1] = 0.924 1.883
h = 0.0001 0.003
y1[1] (numeric) = -2.28525293148 2.39667549112
y1[1] (closed_form) = -2.02645197415 2.56206317759
absolute error = 0.3071
relative error = 9.402 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -2.50880191495 -2.25951112434
y2[1] (closed_form) = -2.6834681476 -1.93477160843
absolute error = 0.3687
relative error = 11.15 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=13022.0MB, alloc=44.3MB, time=170.38
x[1] = 0.9241 1.886
h = 0.001 0.001
y1[1] (numeric) = -2.29179011782 2.40444567376
y1[1] (closed_form) = -2.03199628992 2.57031919651
absolute error = 0.3082
relative error = 9.407 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -2.52046495889 -2.26625833787
y2[1] (closed_form) = -2.69136963737 -1.94060265774
absolute error = 0.3678
relative error = 11.08 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.9251 1.887
h = 0.001 0.003
y1[1] (numeric) = -2.2915334504 2.4092416128
y1[1] (closed_form) = -2.03124295108 2.57495320056
absolute error = 0.3086
relative error = 9.408 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -2.53214226254 -2.27301244879
y2[1] (closed_form) = -2.69597389328 -1.94006164193
absolute error = 0.3711
relative error = 11.17 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=13070.7MB, alloc=44.3MB, time=171.01
x[1] = 0.9261 1.89
h = 0.0001 0.004
y1[1] (numeric) = -2.29582462891 2.41913196465
y1[1] (closed_form) = -2.03436755635 2.58499759392
absolute error = 0.3096
relative error = 9.413 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -2.5438388069 -2.27976552439
y2[1] (closed_form) = -2.70574661645 -1.94358008483
absolute error = 0.3731
relative error = 11.2 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.9262 1.894
h = 0.003 0.006
y1[1] (numeric) = -2.30470225283 2.42955909018
y1[1] (closed_form) = -2.04188655135 2.59603644959
absolute error = 0.3111
relative error = 9.419 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -2.55557362559 -2.28653731589
y2[1] (closed_form) = -2.71631248263 -1.95147353153
absolute error = 0.3716
relative error = 11.11 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=13119.3MB, alloc=44.3MB, time=171.64
x[1] = 0.9292 1.9
h = 0.0001 0.005
y1[1] (numeric) = -2.3107573827 2.45179773212
y1[1] (closed_form) = -2.04542717475 2.61826066668
absolute error = 0.3132
relative error = 9.427 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -2.56740551018 -2.2933111772
y2[1] (closed_form) = -2.73808628226 -1.95591408237
absolute error = 0.3781
relative error = 11.24 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.9293 1.905
h = 0.0001 0.003
y1[1] (numeric) = -2.32198354381 2.4648942544
y1[1] (closed_form) = -2.05495722234 2.63218048687
absolute error = 0.3151
relative error = 9.436 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -2.57934651751 -2.30009722313
y2[1] (closed_form) = -2.75141737577 -1.96590250161
absolute error = 0.3759
relative error = 11.12 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=13168.0MB, alloc=44.3MB, time=172.28
x[1] = 0.9294 1.908
h = 0.001 0.001
y1[1] (numeric) = -2.32863553148 2.47288061847
y1[1] (closed_form) = -2.06058824307 2.64064379062
absolute error = 0.3162
relative error = 9.441 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -2.59133315572 -2.30692026692
y2[1] (closed_form) = -2.75953238308 -1.97181217457
absolute error = 0.375
relative error = 11.06 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.9304 1.909
h = 0.0001 0.004
y1[1] (numeric) = -2.32834853379 2.47778828759
y1[1] (closed_form) = -2.05979788064 2.64537719551
absolute error = 0.3166
relative error = 9.442 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -2.60333442459 -2.31375029855
y2[1] (closed_form) = -2.76423558674 -1.97122935793
absolute error = 0.3784
relative error = 11.15 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=13216.7MB, alloc=44.3MB, time=172.91
x[1] = 0.9305 1.913
h = 0.003 0.006
y1[1] (numeric) = -2.3373562788 2.48845737845
y1[1] (closed_form) = -2.06742180324 2.65665326554
absolute error = 0.318
relative error = 9.448 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -2.61535977702 -2.32059520457
y2[1] (closed_form) = -2.7750459937 -1.97921868585
absolute error = 0.3769
relative error = 11.06 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.9335 1.919
h = 0.0001 0.005
y1[1] (numeric) = -2.34343617844 2.51115789631
y1[1] (closed_form) = -2.07095194799 2.67931439902
absolute error = 0.3202
relative error = 9.455 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -2.62748410809 -2.32744181083
y2[1] (closed_form) = -2.79726139411 -1.98362991232
absolute error = 0.3834
relative error = 11.18 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=13265.4MB, alloc=44.3MB, time=173.54
x[1] = 0.9336 1.924
h = 0.0001 0.003
y1[1] (numeric) = -2.35482715111 2.52455896422
y1[1] (closed_form) = -2.08061494613 2.69353364325
absolute error = 0.3221
relative error = 9.464 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -2.63971975454 -2.33430037915
y2[1] (closed_form) = -2.81090106331 -1.99374016724
absolute error = 0.3812
relative error = 11.06 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=13314.1MB, alloc=44.3MB, time=174.18
x[1] = 0.9337 1.927
h = 0.001 0.001
y1[1] (numeric) = -2.36157580566 2.53273031536
y1[1] (closed_form) = -2.08632362851 2.70217846559
absolute error = 0.3232
relative error = 9.468 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -2.65200208418 -2.34119647799
y2[1] (closed_form) = -2.81920297188 -1.99972078543
absolute error = 0.3802
relative error = 11 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.9347 1.928
h = 0.001 0.003
y1[1] (numeric) = -2.36126230383 2.5377331142
y1[1] (closed_form) = -2.08550144254 2.7069994754
absolute error = 0.3236
relative error = 9.469 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -2.66429936132 -2.34809963968
y2[1] (closed_form) = -2.82399347349 -1.99910210979
absolute error = 0.3838
relative error = 11.09 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=13362.8MB, alloc=44.3MB, time=174.82
x[1] = 0.9357 1.931
h = 0.0001 0.004
y1[1] (numeric) = -2.36564649982 2.54809602979
y1[1] (closed_form) = -2.08867497016 2.71748765957
absolute error = 0.3247
relative error = 9.473 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -2.67661670907 -2.35500153758
y2[1] (closed_form) = -2.83421728381 -2.00265113359
absolute error = 0.386
relative error = 11.12 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.9358 1.935
h = 0.003 0.006
y1[1] (numeric) = -2.37481205707 2.55906304255
y1[1] (closed_form) = -2.096417784 2.72904738742
absolute error = 0.3262
relative error = 9.479 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -2.68897418033 -2.36192260311
y2[1] (closed_form) = -2.84531959321 -2.0107489823
absolute error = 0.3844
relative error = 11.03 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=13411.4MB, alloc=44.3MB, time=175.45
x[1] = 0.9388 1.941
h = 0.0001 0.005
y1[1] (numeric) = -2.38091880492 2.5823303446
y1[1] (closed_form) = -2.09992537488 2.75222625483
absolute error = 0.3284
relative error = 9.485 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -2.70143297405 -2.3688449009
y2[1] (closed_form) = -2.86805786461 -2.0151161597
absolute error = 0.391
relative error = 11.16 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.9389 1.946
h = 0.0001 0.003
y1[1] (numeric) = -2.39250956942 2.596106143
y1[1] (closed_form) = -2.10973905074 2.76680355707
absolute error = 0.3303
relative error = 9.493 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -2.71400577087 -2.37577887091
y2[1] (closed_form) = -2.88206589234 -2.0253643491
absolute error = 0.3886
relative error = 11.03 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=13460.1MB, alloc=44.3MB, time=176.08
x[1] = 0.939 1.949
h = 0.001 0.001
y1[1] (numeric) = -2.39937532791 2.60450501133
y1[1] (closed_form) = -2.11553559823 2.77566537473
absolute error = 0.3315
relative error = 9.497 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -2.72662654527 -2.38275101653
y2[1] (closed_form) = -2.89059085278 -2.03142513351
absolute error = 0.3877
relative error = 10.97 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.94 1.95
h = 0.001 0.003
y1[1] (numeric) = -2.39902862483 2.60962419665
y1[1] (closed_form) = -2.11467365521 2.78058950597
absolute error = 0.3318
relative error = 9.498 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -2.73926265614 -2.38973031461
y2[1] (closed_form) = -2.89548408495 -2.03076211151
absolute error = 0.3915
relative error = 11.07 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=13508.8MB, alloc=44.3MB, time=176.72
x[1] = 0.941 1.953
h = 0.0001 0.004
y1[1] (numeric) = -2.403462694 2.62025417956
y1[1] (closed_form) = -2.11787056792 2.79132420421
absolute error = 0.3329
relative error = 9.501 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -2.7519193045 -2.39670821542
y2[1] (closed_form) = -2.90595821887 -2.03432497385
absolute error = 0.3938
relative error = 11.1 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=13557.3MB, alloc=44.3MB, time=177.34
x[1] = 0.9411 1.957
h = 0.003 0.006
y1[1] (numeric) = -2.41278768299 2.63152725745
y1[1] (closed_form) = -2.12573310719 2.80317466597
absolute error = 0.3345
relative error = 9.507 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -2.76461712181 -2.40370552851
y2[1] (closed_form) = -2.91735938105 -2.04253244608
absolute error = 0.3921
relative error = 11.01 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.9441 1.963
h = 0.0001 0.005
y1[1] (numeric) = -2.41891791439 2.6553749064
y1[1] (closed_form) = -2.12921433767 2.82688265311
absolute error = 0.3367
relative error = 9.513 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -2.77741865742 -2.41070357828
y2[1] (closed_form) = -2.94063190885 -2.04685226254
absolute error = 0.3988
relative error = 11.13 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=13605.9MB, alloc=44.3MB, time=177.97
x[1] = 0.9442 1.968
h = 0.0001 0.003
y1[1] (numeric) = -2.43071054464 2.66953568577
y1[1] (closed_form) = -2.13917976585 2.84182694821
absolute error = 0.3386
relative error = 9.52 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -2.7903369452 -2.41771298464
y2[1] (closed_form) = -2.95501707174 -2.05723979188
absolute error = 0.3963
relative error = 11.01 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.9443 1.971
h = 0.001 0.001
y1[1] (numeric) = -2.43769456907 2.67816826489
y1[1] (closed_form) = -2.14506475449 2.85091115336
absolute error = 0.3398
relative error = 9.524 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -2.80330454006 -2.42476121782
y2[1] (closed_form) = -2.96377038425 -2.06338151759
absolute error = 0.3954
relative error = 10.95 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=13654.6MB, alloc=44.3MB, time=178.62
x[1] = 0.9453 1.972
h = 0.001 0.003
y1[1] (numeric) = -2.4373130627 2.68340635011
y1[1] (closed_form) = -2.14416151303 2.85594045003
absolute error = 0.3402
relative error = 9.525 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -2.81628787017 -2.43181669242
y2[1] (closed_form) = -2.96876842331 -2.06267270576
absolute error = 0.3994
relative error = 11.05 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.9463 1.975
h = 0.0001 0.004
y1[1] (numeric) = -2.4417963061 2.69431005439
y1[1] (closed_form) = -2.14738076487 2.86692730211
absolute error = 0.3413
relative error = 9.528 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -2.82929221472 -2.43887062986
y2[1] (closed_form) = -2.97949848713 -2.06624858828
absolute error = 0.4018
relative error = 11.08 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=13703.2MB, alloc=44.3MB, time=179.25
x[1] = 0.9464 1.979
h = 0.003 0.006
y1[1] (numeric) = -2.45128234239 2.70589754109
y1[1] (closed_form) = -2.15536385055 2.87907573436
absolute error = 0.3429
relative error = 9.533 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -2.84233880007 -2.44594422266
y2[1] (closed_form) = -2.99120561428 -2.07456676706
absolute error = 0.4001
relative error = 10.99 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.9494 1.985
h = 0.0001 0.005
y1[1] (numeric) = -2.4574325431 2.73033940208
y1[1] (closed_form) = -2.15881477868 2.90332446214
absolute error = 0.3451
relative error = 9.539 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -2.85549155261 -2.45301802807
y2[1] (closed_form) = -3.01502401642 -2.0788357645
absolute error = 0.4068
relative error = 11.11 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=13751.9MB, alloc=44.3MB, time=179.88
x[1] = 0.9495 1.99
h = 0.0001 0.003
y1[1] (numeric) = -2.46942910875 2.74489566536
y1[1] (closed_form) = -2.16893301736 2.91864488766
absolute error = 0.3471
relative error = 9.546 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -2.86876386912 -2.4601028477
y2[1] (closed_form) = -3.02979529554 -2.08936401483
absolute error = 0.4042
relative error = 10.98 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.9496 1.993
h = 0.001 0.001
y1[1] (numeric) = -2.47653255633 2.75376830095
y1[1] (closed_form) = -2.17490701165 2.92795699447
absolute error = 0.3483
relative error = 9.55 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -2.88208685813 -2.46722715145
y2[1] (closed_form) = -3.03878238332 -2.09558744056
absolute error = 0.4033
relative error = 10.93 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=13800.6MB, alloc=44.3MB, time=180.51
x[1] = 0.9506 1.994
h = 0.001 0.003
y1[1] (numeric) = -2.47611459377 2.75912785041
y1[1] (closed_form) = -2.17396088704 2.93309353889
absolute error = 0.3487
relative error = 9.55 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -2.8954259912 -2.47435878487
y2[1] (closed_form) = -3.04388734267 -2.0948313501
absolute error = 0.4075
relative error = 11.03 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=13849.2MB, alloc=44.3MB, time=181.14
x[1] = 0.9516 1.997
h = 0.0001 0.004
y1[1] (numeric) = -2.48064626131 2.77031208338
y1[1] (closed_form) = -2.1772013834 2.94433830475
absolute error = 0.3498
relative error = 9.553 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -2.90878662597 -2.48148873463
y2[1] (closed_form) = -3.05487906244 -2.09841938069
absolute error = 0.41
relative error = 11.06 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.9517 2.001
h = 0.003 0.006
y1[1] (numeric) = -2.49029495502 2.78222252768
y1[1] (closed_form) = -2.18530582192 2.95679210804
absolute error = 0.3514
relative error = 9.558 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -2.92219060038 -2.48863858108
y2[1] (closed_form) = -3.06689943205 -2.10684932814
absolute error = 0.4083
relative error = 10.97 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=13897.8MB, alloc=44.3MB, time=181.78
x[1] = 0.9547 2.007
h = 0.0001 0.005
y1[1] (numeric) = -2.49646145553 2.80727277436
y1[1] (closed_form) = -2.18872236582 2.98159343681
absolute error = 0.3537
relative error = 9.562 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -2.93570324509 -2.49578808661
y2[1] (closed_form) = -3.09127556348 -2.11106389804
absolute error = 0.415
relative error = 11.09 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.9548 2.012
h = 0.0001 0.003
y1[1] (numeric) = -2.50866402009 2.82223528293
y1[1] (closed_form) = -2.19899445516 2.99729933743
absolute error = 0.3557
relative error = 9.569 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -2.94933832955 -2.50294823633
y2[1] (closed_form) = -3.10644214878 -2.12173422449
absolute error = 0.4123
relative error = 10.96 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=13946.5MB, alloc=44.3MB, time=182.41
x[1] = 0.9549 2.015
h = 0.001 0.001
y1[1] (numeric) = -2.5158880421 2.83135447631
y1[1] (closed_form) = -2.20505800704 3.00684498476
absolute error = 0.3569
relative error = 9.573 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -2.96302548878 -2.51014853348
y2[1] (closed_form) = -3.11566856066 -2.12804009171
absolute error = 0.4115
relative error = 10.91 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.9559 2.016
h = 0.0001 0.004
y1[1] (numeric) = -2.51543191805 2.83683810612
y1[1] (closed_form) = -2.20406736997 3.01209089814
absolute error = 0.3573
relative error = 9.573 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -2.97672921117 -2.51735624781
y2[1] (closed_form) = -3.12088259142 -2.12723518732
absolute error = 0.4159
relative error = 11.01 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=13995.1MB, alloc=44.3MB, time=183.04
x[1] = 0.956 2.02
h = 0.003 0.006
y1[1] (numeric) = -2.52521741873 2.84902456505
y1[1] (closed_form) = -2.21228065932 3.02481215028
absolute error = 0.3589
relative error = 9.578 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -2.99046029192 -2.52457994295
y2[1] (closed_form) = -3.13317719797 -2.13576602768
absolute error = 0.4142
relative error = 10.92 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.959 2.026
h = 0.0001 0.005
y1[1] (numeric) = -2.53139448611 2.87459335051
y1[1] (closed_form) = -2.21567100689 3.05009930159
absolute error = 0.3612
relative error = 9.582 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -3.00430217279 -2.53180281178
y2[1] (closed_form) = -3.15804379136 -2.13993758072
absolute error = 0.4209
relative error = 11.03 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=14043.7MB, alloc=44.3MB, time=183.67
x[1] = 0.9591 2.031
h = 0.0001 0.003
y1[1] (numeric) = -2.54377043007 2.88990328733
y1[1] (closed_form) = -2.22608109081 3.06614280161
absolute error = 0.3633
relative error = 9.588 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -3.01826894239 -2.53903599382
y2[1] (closed_form) = -3.17355645102 -2.15073612766
absolute error = 0.4182
relative error = 10.91 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=14092.3MB, alloc=44.3MB, time=184.30
x[1] = 0.9592 2.034
h = 0.001 0.001
y1[1] (numeric) = -2.55109591596 2.89923338416
y1[1] (closed_form) = -2.23222503816 3.07589300992
absolute error = 0.3645
relative error = 9.592 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -3.03228898586 -2.5463098811
y2[1] (closed_form) = -3.18299241265 -2.15711648075
absolute error = 0.4174
relative error = 10.85 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.9602 2.035
h = 0.001 0.003
y1[1] (numeric) = -2.55060656 2.90482264228
y1[1] (closed_form) = -2.23119608456 3.0812353507
absolute error = 0.3649
relative error = 9.592 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -3.04632595035 -2.55359125789
y2[1] (closed_form) = -3.18830268754 -2.15626962802
absolute error = 0.4219
relative error = 10.96 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=14141.0MB, alloc=44.3MB, time=184.93
x[1] = 0.9612 2.038
h = 0.0001 0.004
y1[1] (numeric) = -2.55522490001 2.91653993005
y1[1] (closed_form) = -2.23447626448 3.09297556584
absolute error = 0.3661
relative error = 9.594 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -3.0603853381 -2.56087066407
y2[1] (closed_form) = -3.19979683062 -2.15988103443
absolute error = 0.4245
relative error = 11 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.9613 2.042
h = 0.003 0.006
y1[1] (numeric) = -2.56517622595 2.92906611573
y1[1] (closed_form) = -2.24281245683 3.10601639922
absolute error = 0.3677
relative error = 9.599 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -3.07449015462 -2.5681704045
y2[1] (closed_form) = -3.21241866159 -2.16852565159
absolute error = 0.4228
relative error = 10.91 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=14189.7MB, alloc=44.3MB, time=185.56
x[1] = 0.9643 2.048
h = 0.0001 0.005
y1[1] (numeric) = -2.57136241018 2.95527109249
y1[1] (closed_form) = -2.24616058463 3.13187892636
absolute error = 0.3701
relative error = 9.602 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -3.08870838068 -2.57546870738
y2[1] (closed_form) = -3.23786573754 -2.17263579482
absolute error = 0.4296
relative error = 11.02 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.9644 2.053
h = 0.0001 0.003
y1[1] (numeric) = -2.58394841115 2.97100837814
y1[1] (closed_form) = -2.25672651808 3.14832584471
absolute error = 0.3722
relative error = 9.608 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -3.10305449687 -2.58277689922
y2[1] (closed_form) = -3.25379135975 -2.18357898088
absolute error = 0.4267
relative error = 10.89 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=14238.2MB, alloc=44.3MB, time=186.20
x[1] = 0.9645 2.056
h = 0.001 0.001
y1[1] (numeric) = -2.59139673562 2.98059778054
y1[1] (closed_form) = -2.26296108371 3.15832042101
absolute error = 0.3734
relative error = 9.611 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -3.11745536141 -2.59012647146
y2[1] (closed_form) = -3.26347730595 -2.19004317561
absolute error = 0.4259
relative error = 10.84 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.9655 2.057
h = 0.001 0.003
y1[1] (numeric) = -2.59086587714 2.98631625015
y1[1] (closed_form) = -2.26188448944 3.1637762041
absolute error = 0.3738
relative error = 9.611 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -3.13187358621 -2.59748361924
y2[1] (closed_form) = -3.2689007772 -2.18914455099
absolute error = 0.4307
relative error = 10.95 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=14287.0MB, alloc=44.3MB, time=186.83
x[1] = 0.9665 2.06
h = 0.0001 0.004
y1[1] (numeric) = -2.59553026924 2.99833468344
y1[1] (closed_form) = -2.26518257092 3.17579151104
absolute error = 0.375
relative error = 9.613 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -3.14631475258 -2.60483862964
y2[1] (closed_form) = -3.28067365264 -2.19276537119
absolute error = 0.4334
relative error = 10.98 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=14335.5MB, alloc=44.3MB, time=187.46
x[1] = 0.9666 2.064
h = 0.003 0.006
y1[1] (numeric) = -2.60564900644 3.01120975281
y1[1] (closed_form) = -2.2736424256 3.18915981544
absolute error = 0.3767
relative error = 9.618 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -3.16080252839 -2.61221420996
y2[1] (closed_form) = -3.29363047869 -2.20152476281
absolute error = 0.4316
relative error = 10.9 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.9696 2.07
h = 0.0001 0.005
y1[1] (numeric) = -2.61184016547 3.03806600341
y1[1] (closed_form) = -2.2769438285 3.21561029054
absolute error = 0.379
relative error = 9.62 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -3.17540638057 -2.61958770918
y2[1] (closed_form) = -3.31967059767 -2.20556943543
absolute error = 0.4384
relative error = 11 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=14384.1MB, alloc=44.3MB, time=188.09
x[1] = 0.9697 2.075
h = 0.0001 0.003
y1[1] (numeric) = -2.62463825866 3.05424216551
y1[1] (closed_form) = -2.28766659303 3.23247058992
absolute error = 0.3812
relative error = 9.626 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -3.19014119224 -2.62697064255
y2[1] (closed_form) = -3.33601899542 -2.21665853571
absolute error = 0.4355
relative error = 10.87 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.9698 2.078
h = 0.001 0.001
y1[1] (numeric) = -2.63221054923 3.06409783625
y1[1] (closed_form) = -2.2939922885 3.24271554499
absolute error = 0.3825
relative error = 9.629 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -3.20493226618 -2.63439563733
y2[1] (closed_form) = -3.34596084979 -2.22320726032
absolute error = 0.4347
relative error = 10.82 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=14432.8MB, alloc=44.3MB, time=188.72
x[1] = 0.9708 2.079
h = 0.001 0.003
y1[1] (numeric) = -2.63163632546 3.06994828502
y1[1] (closed_form) = -2.29286629034 3.24828700671
absolute error = 0.3828
relative error = 9.629 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -3.21974115057 -2.64182829272
y2[1] (closed_form) = -3.35149978052 -2.22225518926
absolute error = 0.4398
relative error = 10.94 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.9718 2.082
h = 0.0001 0.004
y1[1] (numeric) = -2.63634580155 3.0822752899
y1[1] (closed_form) = -2.29618097486 3.26058365269
absolute error = 0.3841
relative error = 9.631 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -3.23457350595 -2.64925863648
y2[1] (closed_form) = -3.36355760028 -2.22588432843
absolute error = 0.4426
relative error = 10.97 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=14481.3MB, alloc=44.3MB, time=189.35
x[1] = 0.9719 2.086
h = 0.003 0.006
y1[1] (numeric) = -2.64663352421 3.09550862437
y1[1] (closed_form) = -2.30476523118 3.27428749599
absolute error = 0.3858
relative error = 9.635 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -3.24945368092 -2.65670978332
y2[1] (closed_form) = -3.37685737158 -2.23475946635
absolute error = 0.4408
relative error = 10.88 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.9749 2.092
h = 0.0001 0.005
y1[1] (numeric) = -2.6528253372 3.12303156482
y1[1] (closed_form) = -2.30801524566 3.3013387484
absolute error = 0.3882
relative error = 9.637 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -3.26445265771 -2.66415817215
y2[1] (closed_form) = -3.40350334915 -2.23873443941
absolute error = 0.4476
relative error = 10.99 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=14530.0MB, alloc=44.3MB, time=189.98
x[1] = 0.975 2.097
h = 0.0001 0.003
y1[1] (numeric) = -2.66583754377 3.13965841377
y1[1] (closed_form) = -2.31889579788 3.31862261653
absolute error = 0.3904
relative error = 9.643 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -3.27958573273 -2.67161550868
y2[1] (closed_form) = -3.42028456223 -2.24997069695
absolute error = 0.4445
relative error = 10.86 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.9751 2.1
h = 0.001 0.001
y1[1] (numeric) = -2.67353491705 3.14978748589
y1[1] (closed_form) = -2.32531311793 3.32912409653
absolute error = 0.3917
relative error = 9.646 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -3.29477662434 -2.67911559339
y2[1] (closed_form) = -3.43048838477 -2.25660461852
absolute error = 0.4438
relative error = 10.81 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=14578.8MB, alloc=44.3MB, time=190.62
x[1] = 0.9761 2.101
h = 0.001 0.003
y1[1] (numeric) = -2.67291540635 3.1557727367
y1[1] (closed_form) = -2.32413590314 3.33481351445
absolute error = 0.392
relative error = 9.645 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -3.3099857878 -2.68662342272
y2[1] (closed_form) = -3.43614507825 -2.25559737517
absolute error = 0.4491
relative error = 10.93 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=14627.2MB, alloc=44.3MB, time=191.25
x[1] = 0.9771 2.104
h = 0.0001 0.004
y1[1] (numeric) = -2.6776689354 3.16841590912
y1[1] (closed_form) = -2.32746583416 3.34739787882
absolute error = 0.3933
relative error = 9.646 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -3.325218963 -2.69412875846
y2[1] (closed_form) = -3.44849418616 -2.25923367583
absolute error = 0.452
relative error = 10.96 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.9772 2.108
h = 0.003 0.006
y1[1] (numeric) = -2.68812720413 3.18201711981
y1[1] (closed_form) = -2.33617520989 3.36144551093
absolute error = 0.3951
relative error = 9.651 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -3.3405011981 -2.70165512776
y2[1] (closed_form) = -3.4621450362 -2.26822550468
absolute error = 0.4502
relative error = 10.88 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=14675.9MB, alloc=44.3MB, time=191.88
x[1] = 0.9802 2.114
h = 0.0001 0.005
y1[1] (numeric) = -2.69431516496 3.21022250617
y1[1] (closed_form) = -2.33936900886 3.38911063187
absolute error = 0.3975
relative error = 9.652 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -3.35590502027 -2.70917802764
y2[1] (closed_form) = -3.48940994791 -2.27212637614
absolute error = 0.457
relative error = 10.97 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.9803 2.119
h = 0.0001 0.003
y1[1] (numeric) = -2.70754348974 3.22731214178
y1[1] (closed_form) = -2.35040827858 3.40682848641
absolute error = 0.3997
relative error = 9.657 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -3.37144615028 -2.71670935597
y2[1] (closed_form) = -3.50663424775 -2.28351100013
absolute error = 0.4538
relative error = 10.84 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=14724.4MB, alloc=44.3MB, time=192.51
x[1] = 0.9804 2.122
h = 0.001 0.001
y1[1] (numeric) = -2.71536704998 3.23772192253
y1[1] (closed_form) = -2.35691769986 3.41759277584
absolute error = 0.401
relative error = 9.66 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -3.38704669258 -2.72428412498
y2[1] (closed_form) = -3.51710623776 -2.29023076352
absolute error = 0.4531
relative error = 10.8 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.9814 2.123
h = 0.0001 0.004
y1[1] (numeric) = -2.71470027009 3.2438448544
y1[1] (closed_form) = -2.35568740486 3.42340246935
absolute error = 0.4014
relative error = 9.66 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -3.4026659796 -2.73186672148
y2[1] (closed_form) = -3.52288303812 -2.28916656942
absolute error = 0.4587
relative error = 10.92 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=14773.1MB, alloc=44.3MB, time=193.14
x[1] = 0.9815 2.127
h = 0.003 0.006
y1[1] (numeric) = -2.72530187405 3.25776036643
y1[1] (closed_form) = -2.36450926877 3.43775126991
absolute error = 0.4032
relative error = 9.663 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -3.4183163357 -2.73946641888
y2[1] (closed_form) = -3.53684133622 -2.29826389388
absolute error = 0.4568
relative error = 10.83 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.9845 2.133
h = 0.0001 0.005
y1[1] (numeric) = -2.73148292136 3.28654729674
y1[1] (closed_form) = -2.36765821475 3.46595622613
absolute error = 0.4057
relative error = 9.664 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -3.43409064836 -2.74706202576
y2[1] (closed_form) = -3.56465063584 -2.30210490988
absolute error = 0.4637
relative error = 10.93 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=14821.7MB, alloc=44.3MB, time=193.77
x[1] = 0.9846 2.138
h = 0.0001 0.003
y1[1] (numeric) = -2.74489300918 3.30403258472
y1[1] (closed_form) = -2.37884016865 3.4840542579
absolute error = 0.4079
relative error = 9.669 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -3.4500050016 -2.75466560161
y2[1] (closed_form) = -3.58226294933 -2.31362363279
absolute error = 0.4604
relative error = 10.8 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=14870.5MB, alloc=44.3MB, time=194.40
x[1] = 0.9847 2.141
h = 0.001 0.001
y1[1] (numeric) = -2.75282267272 3.31468240298
y1[1] (closed_form) = -2.3854324697 3.4950488007
absolute error = 0.4093
relative error = 9.672 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -3.4659801312 -2.7623132
y2[1] (closed_form) = -3.59296980919 -2.32042108204
absolute error = 0.4598
relative error = 10.75 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.9857 2.142
h = 0.001 0.003
y1[1] (numeric) = -2.75211483743 3.32092252132
y1[1] (closed_form) = -2.38415642395 3.5009645766
absolute error = 0.4096
relative error = 9.671 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -3.48197440923 -2.76996869401
y2[1] (closed_form) = -3.59885261051 -2.31930787078
absolute error = 0.4656
relative error = 10.87 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=14919.0MB, alloc=44.3MB, time=195.03
x[1] = 0.9867 2.145
h = 0.0001 0.004
y1[1] (numeric) = -2.75694624182 3.33416625728
y1[1] (closed_form) = -2.38751452004 3.51410161949
absolute error = 0.4109
relative error = 9.672 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -3.49799372147 -2.77762133952
y2[1] (closed_form) = -3.61176103485 -2.32295784812
absolute error = 0.4687
relative error = 10.91 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.9868 2.149
h = 0.003 0.006
y1[1] (numeric) = -2.76772145905 3.34846849969
y1[1] (closed_form) = -2.39646287973 3.52881005002
absolute error = 0.4127
relative error = 9.676 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -3.51406445085 -2.78529543353
y2[1] (closed_form) = -3.62608603736 -2.33217364601
absolute error = 0.4668
relative error = 10.83 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=14967.6MB, alloc=44.3MB, time=195.66
x[1] = 0.9898 2.155
h = 0.0001 0.005
y1[1] (numeric) = -2.77388982421 3.37796878442
y1[1] (closed_form) = -2.39954633831 3.55765401063
absolute error = 0.4152
relative error = 9.676 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -3.53026203935 -2.79296465803
y2[1] (closed_form) = -3.65453936807 -2.33593205447
absolute error = 0.4736
relative error = 10.92 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.9899 2.16
h = 0.0001 0.003
y1[1] (numeric) = -2.78751996889 3.39594058879
y1[1] (closed_form) = -2.41088879225 3.5762060324
absolute error = 0.4175
relative error = 9.681 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -3.54660301705 -2.800641268
y2[1] (closed_form) = -3.67261450132 -2.3476014265
absolute error = 0.4702
relative error = 10.79 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=15016.4MB, alloc=44.3MB, time=196.29
x[1] = 0.99 2.163
h = 0.001 0.001
y1[1] (numeric) = -2.79557798873 3.40688544458
y1[1] (closed_form) = -2.41757410805 3.5874754519
absolute error = 0.4189
relative error = 9.684 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -3.56300644795 -2.80836260419
y2[1] (closed_form) = -3.68360143812 -2.35448593217
absolute error = 0.4696
relative error = 10.74 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.991 2.164
h = 0.001 0.003
y1[1] (numeric) = -2.79481899907 3.41326888995
y1[1] (closed_form) = -2.41624140305 3.5935159564
absolute error = 0.4193
relative error = 9.683 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -3.57942952265 -2.81609191665
y2[1] (closed_form) = -3.68960884177 -2.35331234522
absolute error = 0.4757
relative error = 10.87 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=15065.1MB, alloc=44.3MB, time=196.92
x[1] = 0.992 2.167
h = 0.0001 0.004
y1[1] (numeric) = -2.79969121389 3.4268517951
y1[1] (closed_form) = -2.41961060672 3.60695973934
absolute error = 0.4206
relative error = 9.684 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -3.5958782065 -2.8238181751
y2[1] (closed_form) = -3.70282747068 -2.35696588956
absolute error = 0.4789
relative error = 10.91 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=15113.6MB, alloc=44.3MB, time=197.55
x[1] = 0.9921 2.171
h = 0.003 0.006
y1[1] (numeric) = -2.81064155594 3.44155105969
y1[1] (closed_form) = -2.42868611169 3.62203659265
absolute error = 0.4225
relative error = 9.687 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -3.61237963919 -2.83156610385
y2[1] (closed_form) = -3.71752785797 -2.36630102172
absolute error = 0.477
relative error = 10.82 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.9951 2.177
h = 0.0001 0.005
y1[1] (numeric) = -2.81679217034 3.4717814565
y1[1] (closed_form) = -2.43169876178 3.65153342741
absolute error = 0.425
relative error = 9.687 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -3.62901089689 -2.83930834626
y2[1] (closed_form) = -3.74663906883 -2.36997190039
absolute error = 0.4839
relative error = 10.91 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=15162.3MB, alloc=44.3MB, time=198.18
x[1] = 0.9952 2.182
h = 0.0001 0.003
y1[1] (numeric) = -2.83064431729 3.49025273483
y1[1] (closed_form) = -2.44320256037 3.67055054272
absolute error = 0.4273
relative error = 9.692 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -3.64578896757 -2.8470573545
y2[1] (closed_form) = -3.7651879842 -2.38179302642
absolute error = 0.4803
relative error = 10.78 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.9953 2.185
h = 0.001 0.001
y1[1] (numeric) = -2.83883175444 3.50150045172
y1[1] (closed_form) = -2.44998131068 3.68210153604
absolute error = 0.4287
relative error = 9.694 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -3.66263121258 -2.85485179807
y2[1] (closed_form) = -3.77646161272 -2.38876516497
absolute error = 0.4798
relative error = 10.74 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=15211.0MB, alloc=44.3MB, time=198.81
x[1] = 0.9963 2.186
h = 0.001 0.003
y1[1] (numeric) = -2.83801944617 3.50803026732
y1[1] (closed_form) = -2.44858993007 3.68826921233
absolute error = 0.4291
relative error = 9.693 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -3.679493609 -2.86265429715
y2[1] (closed_form) = -3.78259608392 -2.38752926624
absolute error = 0.4862
relative error = 10.87 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 0.9973 2.189
h = 0.0001 0.004
y1[1] (numeric) = -2.84293117369 3.5219606232
y1[1] (closed_form) = -2.4519686421 3.7020266504
absolute error = 0.4304
relative error = 9.694 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -3.6963822017 -2.87045352801
y2[1] (closed_form) = -3.79613179615 -2.39118496049
absolute error = 0.4895
relative error = 10.91 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=15259.5MB, alloc=44.3MB, time=199.44
x[1] = 0.9974 2.193
h = 0.003 0.006
y1[1] (numeric) = -2.85405813087 3.53706745296
y1[1] (closed_form) = -2.46117191388 3.71748091695
absolute error = 0.4323
relative error = 9.697 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -3.71332490788 -2.87827464733
y2[1] (closed_form) = -3.81121644758 -2.40064025463
absolute error = 0.4876
relative error = 10.82 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.0004 2.199
h = 0.0001 0.005
y1[1] (numeric) = -2.86018571356 3.56804508681
y1[1] (closed_form) = -2.46410824982 3.74764477673
absolute error = 0.4349
relative error = 9.696 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -3.73040046957 -2.88608922445
y2[1] (closed_form) = -3.84099966716 -2.40421848788
absolute error = 0.4944
relative error = 10.91 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=15308.1MB, alloc=44.3MB, time=200.07
x[1] = 1.0005 2.204
h = 0.0001 0.003
y1[1] (numeric) = -2.87426178233 3.5870291131
y1[1] (closed_form) = -2.47577420279 3.76713833882
absolute error = 0.4373
relative error = 9.701 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -3.74762634475 -2.89390991034
y2[1] (closed_form) = -3.86003357844 -2.41619243151
absolute error = 0.4908
relative error = 10.78 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.0006 2.207
h = 0.001 0.001
y1[1] (numeric) = -2.88257967943 3.59858770512
y1[1] (closed_form) = -2.4826467843 3.77897775323
absolute error = 0.4387
relative error = 9.703 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -3.76491816075 -2.90177674595
y2[1] (closed_form) = -3.87160066461 -2.42325275247
absolute error = 0.4903
relative error = 10.73 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=15356.9MB, alloc=44.3MB, time=200.71
x[1] = 1.0016 2.208
h = 0.001 0.003
y1[1] (numeric) = -2.88171182037 3.6052669939
y1[1] (closed_form) = -2.48119465531 3.78527508881
absolute error = 0.4391
relative error = 9.702 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -3.78223064829 -2.9096517148
y2[1] (closed_form) = -3.87786471196 -2.42195254782
absolute error = 0.497
relative error = 10.87 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=15405.5MB, alloc=44.3MB, time=201.34
x[1] = 1.0026 2.211
h = 0.0001 0.004
y1[1] (numeric) = -2.88666168628 3.61955327022
y1[1] (closed_form) = -2.48458120764 3.79935324232
absolute error = 0.4405
relative error = 9.702 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -3.7995699317 -2.91752319229
y2[1] (closed_form) = -3.89172453132 -2.42560890194
absolute error = 0.5005
relative error = 10.91 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.0027 2.215
h = 0.003 0.006
y1[1] (numeric) = -2.89796672545 3.63507846509
y1[1] (closed_form) = -2.49391283802 3.81519411441
absolute error = 0.4424
relative error = 9.706 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -3.8169647269 -2.92541677247
y2[1] (closed_form) = -3.90720252948 -2.43518515093
absolute error = 0.4985
relative error = 10.83 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=15454.0MB, alloc=44.3MB, time=201.97
x[1] = 1.0057 2.221
h = 0.0001 0.005
y1[1] (numeric) = -2.90406577572 3.66682083551
y1[1] (closed_form) = -2.49676716381 3.84603943641
absolute error = 0.445
relative error = 9.704 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -3.83449547403 -2.93330291427
y2[1] (closed_form) = -3.93767217114 -2.43866542419
absolute error = 0.5053
relative error = 10.91 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.0058 2.226
h = 0.0001 0.003
y1[1] (numeric) = -2.91836765724 3.68633120753
y1[1] (closed_form) = -2.50859604368 3.86602105355
absolute error = 0.4474
relative error = 9.709 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -3.85218011348 -2.94119446904
y2[1] (closed_form) = -3.95720254884 -2.45079320556
absolute error = 0.5015
relative error = 10.77 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=15502.6MB, alloc=44.3MB, time=202.60
x[1] = 1.0059 2.229
h = 0.001 0.001
y1[1] (numeric) = -2.92681703691 3.6982088835
y1[1] (closed_form) = -2.51556282859 3.87815588972
absolute error = 0.4489
relative error = 9.711 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -3.86993250673 -2.94913289309
y2[1] (closed_form) = -3.96907001295 -2.45794223025
absolute error = 0.5011
relative error = 10.73 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.0069 2.23
h = 0.0001 0.004
y1[1] (numeric) = -2.92589132496 3.70504080917
y1[1] (closed_form) = -2.51404782051 3.88458541703
absolute error = 0.4493
relative error = 9.71 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -3.88770610445 -2.95707952652
y2[1] (closed_form) = -3.97546618915 -2.45657566599
absolute error = 0.5081
relative error = 10.87 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=15551.3MB, alloc=44.3MB, time=203.24
x[1] = 1.007 2.234
h = 0.003 0.006
y1[1] (numeric) = -2.93734589752 3.72092333559
y1[1] (closed_form) = -2.52349514553 3.90076504656
absolute error = 0.4512
relative error = 9.713 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -3.90551497011 -2.96504438377
y2[1] (closed_form) = -3.9912887455 -2.46626147255
absolute error = 0.5061
relative error = 10.79 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.01 2.24
h = 0.0001 0.005
y1[1] (numeric) = -2.94341665117 3.75331724478
y1[1] (closed_form) = -2.52628252579 3.93220980481
absolute error = 0.4539
relative error = 9.711 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -3.92346242142 -2.9730010228
y2[1] (closed_form) = -4.02236225645 -2.46966142886
absolute error = 0.513
relative error = 10.87 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=15599.9MB, alloc=44.3MB, time=203.87
x[1] = 1.0101 2.245
h = 0.0001 0.003
y1[1] (numeric) = -2.95790827991 3.77327747326
y1[1] (closed_form) = -2.53825824293 3.95261906523
absolute error = 0.4564
relative error = 9.715 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -3.94156681163 -2.98096246327
y2[1] (closed_form) = -4.04232751306 -2.48192851545
absolute error = 0.5091
relative error = 10.73 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=15648.7MB, alloc=44.3MB, time=204.50
x[1] = 1.0102 2.248
h = 0.001 0.001
y1[1] (numeric) = -2.9664681095 3.78542792139
y1[1] (closed_form) = -2.54531002873 3.96501278838
absolute error = 0.4578
relative error = 9.717 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -3.95974050501 -2.98897137701
y2[1] (closed_form) = -4.0544581298 -2.48915798146
absolute error = 0.5087
relative error = 10.69 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.0112 2.249
h = 0.001 0.003
y1[1] (numeric) = -2.96549225245 3.79238973971
y1[1] (closed_form) = -2.54374076138 3.97155894928
absolute error = 0.4582
relative error = 9.716 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -3.97793585771 -2.99698856225
y2[1] (closed_form) = -4.06097094131 -2.48773422207
absolute error = 0.516
relative error = 10.83 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=15697.2MB, alloc=44.3MB, time=205.13
x[1] = 1.0122 2.252
h = 0.0001 0.004
y1[1] (numeric) = -2.97050819466 3.80735186491
y1[1] (closed_form) = -2.54714124325 3.98625313676
absolute error = 0.4596
relative error = 9.716 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -3.99615913973 -3.00500182225
y2[1] (closed_form) = -4.07545308895 -2.49139164384
absolute error = 0.5197
relative error = 10.88 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.0123 2.256
h = 0.003 0.006
y1[1] (numeric) = -2.98214372904 3.82367394382
y1[1] (closed_form) = -2.55671805769 4.00283702266
absolute error = 0.4616
relative error = 9.719 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -4.01444059011 -3.0130375668
y2[1] (closed_form) = -4.09168643995 -2.50119989594
absolute error = 0.5176
relative error = 10.79 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=15745.8MB, alloc=44.3MB, time=205.76
x[1] = 1.0153 2.262
h = 0.0001 0.005
y1[1] (numeric) = -2.98817516344 3.85686691689
y1[1] (closed_form) = -2.55941248196 4.03499096096
absolute error = 0.4643
relative error = 9.717 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -4.03286385185 -3.02106411786
y2[1] (closed_form) = -4.12347403832 -2.50449163354
absolute error = 0.5245
relative error = 10.87 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.0154 2.267
h = 0.0001 0.003
y1[1] (numeric) = -3.00289631595 3.87738015998
y1[1] (closed_form) = -2.57155260211 4.05591056627
absolute error = 0.4668
relative error = 9.721 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -4.05144778499 -3.02909469859
y2[1] (closed_form) = -4.1439577967 -2.51691447701
absolute error = 0.5205
relative error = 10.73 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=15794.1MB, alloc=44.3MB, time=206.39
x[1] = 1.0155 2.27
h = 0.001 0.001
y1[1] (numeric) = -3.0115896348 3.88986578967
y1[1] (closed_form) = -2.57869930155 4.06861315363
absolute error = 0.4683
relative error = 9.723 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -4.0701029254 -3.0371734823
y2[1] (closed_form) = -4.15640208518 -2.52423362382
absolute error = 0.5201
relative error = 10.7 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.0165 2.271
h = 0.001 0.003
y1[1] (numeric) = -3.01055141143 3.89698644849
y1[1] (closed_form) = -2.57706306225 4.07529636749
absolute error = 0.4687
relative error = 9.721 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -4.08878028316 -3.0452606105
y2[1] (closed_form) = -4.16305192137 -2.52273955135
absolute error = 0.5278
relative error = 10.84 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=15842.6MB, alloc=44.3MB, time=207.02
x[1] = 1.0175 2.274
h = 0.0001 0.004
y1[1] (numeric) = -3.01560118875 3.91233013756
y1[1] (closed_form) = -2.58046630086 4.09033231862
absolute error = 0.4701
relative error = 9.721 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -4.10748620741 -3.05334356292
y2[1] (closed_form) = -4.17787911737 -2.52639303603
absolute error = 0.5316
relative error = 10.89 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=15890.8MB, alloc=44.3MB, time=207.64
x[1] = 1.0176 2.278
h = 0.003 0.006
y1[1] (numeric) = -3.02741907275 3.92910333007
y1[1] (closed_form) = -2.59017310336 4.10733025533
absolute error = 0.4722
relative error = 9.724 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -4.12625180032 -3.06144920177
y2[1] (closed_form) = -4.19453295164 -2.53632441959
absolute error = 0.5295
relative error = 10.8 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.0206 2.284
h = 0.0001 0.005
y1[1] (numeric) = -3.03340502135 3.96311396924
y1[1] (closed_form) = -2.59276830122 4.14020866179
absolute error = 0.4749
relative error = 9.721 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -4.14516250006 -3.06954462767
y2[1] (closed_form) = -4.2270498978 -2.53950202583
absolute error = 0.5363
relative error = 10.88 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=15939.0MB, alloc=44.3MB, time=208.27
x[1] = 1.0207 2.289
h = 0.0001 0.003
y1[1] (numeric) = -3.0483574917 3.98419478395
y1[1] (closed_form) = -2.60507348052 4.16165098101
absolute error = 0.4775
relative error = 9.725 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -4.16423768674 -3.07764326881
y2[1] (closed_form) = -4.24806439418 -2.55208151285
absolute error = 0.5322
relative error = 10.74 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.0208 2.292
h = 0.001 0.001
y1[1] (numeric) = -3.05718525571 3.99702438119
y1[1] (closed_form) = -2.61231538947 4.17466989071
absolute error = 0.479
relative error = 9.727 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -4.1833860345 -3.08579084737
y2[1] (closed_form) = -4.260829735 -2.5594907752
absolute error = 0.532
relative error = 10.7 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=15987.3MB, alloc=44.3MB, time=208.90
x[1] = 1.0218 2.293
h = 0.001 0.003
y1[1] (numeric) = -3.05608215417 4.00430722182
y1[1] (closed_form) = -2.61060987356 4.18149282297
absolute error = 0.4794
relative error = 9.725 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -4.20255717132 -3.09394684148
y2[1] (closed_form) = -4.26761927925 -2.55792415761
absolute error = 0.54
relative error = 10.85 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.0228 2.296
h = 0.0001 0.004
y1[1] (numeric) = -3.06116406916 4.02004170345
y1[1] (closed_form) = -2.61401391388 4.19687818666
absolute error = 0.4808
relative error = 9.725 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -4.22175752517 -3.10209839921
y2[1] (closed_form) = -4.28279913572 -2.56157191294
absolute error = 0.544
relative error = 10.9 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=16035.6MB, alloc=44.3MB, time=209.52
x[1] = 1.0229 2.3
h = 0.003 0.006
y1[1] (numeric) = -3.07316565797 4.03727785147
y1[1] (closed_form) = -2.62385116578 4.21430018774
absolute error = 0.4829
relative error = 9.728 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -4.24101908474 -3.11027284017
y2[1] (closed_form) = -4.29988336228 -2.57162707192
absolute error = 0.5419
relative error = 10.81 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.0259 2.306
h = 0.0001 0.005
y1[1] (numeric) = -3.07909970338 4.07212516313
y1[1] (closed_form) = -2.62634065261 4.24791865761
absolute error = 0.4857
relative error = 9.725 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -4.26042911773 -3.11843600314
y2[1] (closed_form) = -4.33314522254 -2.57468441202
absolute error = 0.5486
relative error = 10.88 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=16084.0MB, alloc=44.3MB, time=210.15
x[1] = 1.026 2.311
h = 0.0001 0.003
y1[1] (numeric) = -3.09428524555 4.09378846027
y1[1] (closed_form) = -2.63881150054 4.26989633658
absolute error = 0.4883
relative error = 9.729 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -4.28000753796 -3.12660152274
y2[1] (closed_form) = -4.35470297167 -2.58742137692
absolute error = 0.5443
relative error = 10.75 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=16132.4MB, alloc=44.3MB, time=210.78
x[1] = 1.0261 2.314
h = 0.001 0.001
y1[1] (numeric) = -3.10324838342 4.10697102385
y1[1] (closed_form) = -2.64614888451 4.28323919317
absolute error = 0.4899
relative error = 9.731 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -4.29966112403 -3.1348167188
y2[1] (closed_form) = -4.3677969128 -2.59492115576
absolute error = 0.5442
relative error = 10.71 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.0271 2.315
h = 0.001 0.003
y1[1] (numeric) = -3.10207781362 4.11441945221
y1[1] (closed_form) = -2.64437172319 4.29020455679
absolute error = 0.4903
relative error = 9.729 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -4.31933808479 -3.1430403994
y2[1] (closed_form) = -4.37472889525 -2.59327969534
absolute error = 0.5525
relative error = 10.86 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=16180.7MB, alloc=44.3MB, time=211.41
x[1] = 1.0281 2.318
h = 0.0001 0.004
y1[1] (numeric) = -3.10719007643 4.1305541633
y1[1] (closed_form) = -2.64777452907 4.30594714148
absolute error = 0.4918
relative error = 9.728 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -4.33904492681 -3.15125937263
y2[1] (closed_form) = -4.39026918375 -2.59691984422
absolute error = 0.5567
relative error = 10.91 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.0282 2.322
h = 0.003 0.006
y1[1] (numeric) = -3.11937668998 4.14826539588
y1[1] (closed_form) = -2.65774265226 4.32380344423
absolute error = 0.4939
relative error = 9.731 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -4.35881454917 -3.15950142053
y2[1] (closed_form) = -4.40779393675 -2.60709937865
absolute error = 0.5546
relative error = 10.83 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=16228.9MB, alloc=44.3MB, time=212.04
x[1] = 1.0312 2.328
h = 0.0001 0.005
y1[1] (numeric) = -3.12525215542 4.18396879857
y1[1] (closed_form) = -2.66011972265 4.35817788553
absolute error = 0.4967
relative error = 9.728 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -4.37873608412 -3.16773107829
y2[1] (closed_form) = -4.44181658896 -2.61003008926
absolute error = 0.5613
relative error = 10.89 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.0313 2.333
h = 0.0001 0.003
y1[1] (numeric) = -3.14067248002 4.20622985078
y1[1] (closed_form) = -2.67275679937 4.38070385279
absolute error = 0.4994
relative error = 9.731 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -4.3988299931 -3.1759621884
y2[1] (closed_form) = -4.46393039 -2.62292531146
absolute error = 0.5569
relative error = 10.76 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=16277.2MB, alloc=44.3MB, time=212.67
x[1] = 1.0314 2.336
h = 0.001 0.001
y1[1] (numeric) = -3.14977189119 4.21977459715
y1[1] (closed_form) = -2.68018989186 4.3943784508
absolute error = 0.501
relative error = 9.733 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -4.41900112482 -3.18424371841
y2[1] (closed_form) = -4.47736065035 -2.63051597237
absolute error = 0.5568
relative error = 10.72 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.0324 2.337
h = 0.0001 0.004
y1[1] (numeric) = -3.14853118254 4.22739208479
y1[1] (closed_form) = -2.67833865043 4.40148900699
absolute error = 0.5014
relative error = 9.731 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -4.43919623117 -3.19253379976
y2[1] (closed_form) = -4.48443784864 -2.62879730409
absolute error = 0.5655
relative error = 10.88 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=16325.5MB, alloc=44.3MB, time=213.29
x[1] = 1.0325 2.341
h = 0.003 0.006
y1[1] (numeric) = -3.16087298996 4.24550898384
y1[1] (closed_form) = -2.68842507301 4.41972594925
absolute error = 0.5035
relative error = 9.734 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -4.45943135066 -3.2008432167
y2[1] (closed_form) = -4.50234859218 -2.63908975827
absolute error = 0.5634
relative error = 10.8 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=16373.8MB, alloc=44.3MB, time=213.92
x[1] = 1.0355 2.347
h = 0.0001 0.005
y1[1] (numeric) = -3.16669415465 4.28194161612
y1[1] (closed_form) = -2.69070910492 4.4547655393
absolute error = 0.5064
relative error = 9.73 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -4.47982130743 -3.20913927818
y2[1] (closed_form) = -4.53704068138 -2.64191552129
absolute error = 0.5701
relative error = 10.86 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.0356 2.352
h = 0.0001 0.003
y1[1] (numeric) = -3.18231155181 4.30471341701
y1[1] (closed_form) = -2.70349642084 4.47777203974
absolute error = 0.5091
relative error = 9.734 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -4.50038703146 -3.21743600104
y2[1] (closed_form) = -4.55964168745 -2.65495438295
absolute error = 0.5656
relative error = 10.72 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=16422.0MB, alloc=44.3MB, time=214.55
x[1] = 1.0357 2.355
h = 0.001 0.001
y1[1] (numeric) = -3.19152530431 4.31856769531
y1[1] (closed_form) = -2.71101613857 4.49173742054
absolute error = 0.5108
relative error = 9.735 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -4.52103173561 -3.22578376706
y2[1] (closed_form) = -4.57336666661 -2.66262767126
absolute error = 0.5656
relative error = 10.69 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.0367 2.356
h = 0.001 0.003
y1[1] (numeric) = -3.19022390123 4.32632902381
y1[1] (closed_form) = -2.70910090543 4.49897612526
absolute error = 0.5112
relative error = 9.733 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -4.54170092632 -3.2341401383
y2[1] (closed_form) = -4.5805720822 -2.66084237421
absolute error = 0.5746
relative error = 10.85 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=16470.4MB, alloc=44.3MB, time=215.18
x[1] = 1.0377 2.359
h = 0.0001 0.004
y1[1] (numeric) = -3.19538680227 4.34322347894
y1[1] (closed_form) = -2.71250018806 4.51540483237
absolute error = 0.5127
relative error = 9.733 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -4.56240125354 -3.24249127663
y2[1] (closed_form) = -4.59680444155 -2.66446759107
absolute error = 0.579
relative error = 10.9 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.0378 2.363
h = 0.003 0.006
y1[1] (numeric) = -3.20791622259 4.36183925837
y1[1] (closed_form) = -2.72271828297 4.53409573368
absolute error = 0.5149
relative error = 9.735 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -4.58316735166 -3.25086582558
y2[1] (closed_form) = -4.61517517843 -2.67488554033
absolute error = 0.5769
relative error = 10.81 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=16518.6MB, alloc=44.3MB, time=215.80
x[1] = 1.0408 2.369
h = 0.0001 0.005
y1[1] (numeric) = -3.21366570772 4.39916607225
y1[1] (closed_form) = -2.72487700885 4.56992183465
absolute error = 0.5178
relative error = 9.731 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -4.60409186856 -3.25922581456
y2[1] (closed_form) = -4.65065853617 -2.67757240025
absolute error = 0.5835
relative error = 10.87 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.0409 2.374
h = 0.0001 0.003
y1[1] (numeric) = -3.22952124046 4.42256558321
y1[1] (closed_form) = -2.73783161733 4.59350144843
absolute error = 0.5206
relative error = 9.735 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -4.6251963092 -3.26758547101
y2[1] (closed_form) = -4.67384018044 -2.6907709751
absolute error = 0.5789
relative error = 10.73 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=16566.9MB, alloc=44.3MB, time=216.43
x[1] = 1.041 2.377
h = 0.001 0.001
y1[1] (numeric) = -3.23887302884 4.4368001185
y1[1] (closed_form) = -2.74544748472 4.60781353739
absolute error = 0.5222
relative error = 9.736 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -4.64638188913 -3.27599692268
y2[1] (closed_form) = -4.68791630594 -2.69853582289
absolute error = 0.579
relative error = 10.7 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=16615.3MB, alloc=44.3MB, time=217.06
x[1] = 1.042 2.378
h = 0.001 0.003
y1[1] (numeric) = -3.23749624991 4.44473731295
y1[1] (closed_form) = -2.74345349396 4.61520273431
absolute error = 0.5226
relative error = 9.734 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -4.66759258355 -3.2844170421
y2[1] (closed_form) = -4.69527226487 -2.69666876647
absolute error = 0.5884
relative error = 10.87 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.043 2.381
h = 0.0001 0.004
y1[1] (numeric) = -3.24268391426 4.46206056469
y1[1] (closed_form) = -2.74684534393 4.63201193683
absolute error = 0.5242
relative error = 9.733 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -4.68883511993 -3.29283162588
y2[1] (closed_form) = -4.71188822342 -2.70028061329
absolute error = 0.593
relative error = 10.92 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=16663.5MB, alloc=44.3MB, time=217.68
x[1] = 1.0431 2.385
h = 0.003 0.006
y1[1] (numeric) = -3.25540215242 4.4811882039
y1[1] (closed_form) = -2.75719541079 4.65116770183
absolute error = 0.5264
relative error = 9.736 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -4.71014511562 -3.30126979479
y2[1] (closed_form) = -4.73072975892 -2.71082452303
absolute error = 0.5908
relative error = 10.84 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.0461 2.391
h = 0.0001 0.005
y1[1] (numeric) = -3.26107249676 4.51942983067
y1[1] (closed_form) = -2.75922145955 4.68779715111
absolute error = 0.5293
relative error = 9.731 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -4.73161718827 -3.30969214768
y2[1] (closed_form) = -4.76702118951 -2.71336542951
absolute error = 0.5974
relative error = 10.89 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=16711.8MB, alloc=44.3MB, time=218.31
x[1] = 1.0462 2.396
h = 0.0001 0.003
y1[1] (numeric) = -3.27716773389 4.54347339607
y1[1] (closed_form) = -2.77234376772 4.71196364995
absolute error = 0.5322
relative error = 9.735 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -4.75327343277 -3.31811312387
y2[1] (closed_form) = -4.79079711914 -2.7267243287
absolute error = 0.5926
relative error = 10.75 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.0463 2.399
h = 0.001 0.001
y1[1] (numeric) = -3.28665836285 4.55809804933
y1[1] (closed_form) = -2.78005591917 4.72663074845
absolute error = 0.5339
relative error = 9.736 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -4.77501303155 -3.32658665116
y2[1] (closed_form) = -4.80523261952 -2.73458099335
absolute error = 0.5928
relative error = 10.72 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=16760.2MB, alloc=44.3MB, time=218.94
x[1] = 1.0473 2.4
h = 0.001 0.003
y1[1] (numeric) = -3.28520329627 4.56621477306
y1[1] (closed_form) = -2.7779805384 4.73417334143
absolute error = 0.5343
relative error = 9.734 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -4.79677838797 -3.33506890616
y2[1] (closed_form) = -4.81274204012 -2.73262961079
absolute error = 0.6027
relative error = 10.89 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.0483 2.403
h = 0.0001 0.004
y1[1] (numeric) = -3.29041354566 4.58397709776
y1[1] (closed_form) = -2.78136258192 4.75137149409
absolute error = 0.5359
relative error = 9.733 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -4.81857630647 -3.34354531109
y2[1] (closed_form) = -4.82975001579 -2.73622585915
absolute error = 0.6074
relative error = 10.94 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=16808.6MB, alloc=44.3MB, time=219.57
x[1] = 1.0484 2.407
h = 0.003 0.006
y1[1] (numeric) = -3.30332176035 4.60362988969
y1[1] (closed_form) = -2.79184487209 4.77100327016
absolute error = 0.5382
relative error = 9.736 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -4.84044341364 -3.35204546891
y2[1] (closed_form) = -4.84907339924 -2.74689614239
absolute error = 0.6052
relative error = 10.86 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=16856.7MB, alloc=44.3MB, time=220.20
x[1] = 1.0514 2.413
h = 0.0001 0.005
y1[1] (numeric) = -3.3089052076 4.64280740499
y1[1] (closed_form) = -2.79373062484 4.80845324046
absolute error = 0.5412
relative error = 9.731 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -4.86247633421 -3.36052850147
y2[1] (closed_form) = -4.88619004134 -2.7492837901
absolute error = 0.6117
relative error = 10.91 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.0515 2.418
h = 0.0001 0.003
y1[1] (numeric) = -3.32524166084 4.66751176432
y1[1] (closed_form) = -2.80702097938 4.83322070278
absolute error = 0.5441
relative error = 9.734 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -4.88469776825 -3.36900906119
y2[1] (closed_form) = -4.91057421187 -2.76280355929
absolute error = 0.6068
relative error = 10.77 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=16905.0MB, alloc=44.3MB, time=220.83
x[1] = 1.0516 2.421
h = 0.001 0.001
y1[1] (numeric) = -3.33487189724 4.68253663408
y1[1] (closed_form) = -2.81482951042 4.84825129649
absolute error = 0.5458
relative error = 9.736 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -4.90700482868 -3.37754293147
y2[1] (closed_form) = -4.92537750091 -2.77075225621
absolute error = 0.6071
relative error = 10.74 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.0526 2.422
h = 0.001 0.003
y1[1] (numeric) = -3.33333554131 4.69083662016
y1[1] (closed_form) = -2.81267003436 4.85595024036
absolute error = 0.5462
relative error = 9.734 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -4.92933830545 -3.38608558668
y2[1] (closed_form) = -4.93304335179 -2.76871390649
absolute error = 0.6174
relative error = 10.91 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=16953.3MB, alloc=44.3MB, time=221.46
x[1] = 1.0536 2.425
h = 0.0001 0.004
y1[1] (numeric) = -3.33856608672 4.70904852431
y1[1] (closed_form) = -2.81603980247 4.87354597294
absolute error = 0.5478
relative error = 9.733 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -4.95170507941 -3.39462206537
y2[1] (closed_form) = -4.95045193763 -2.77229222946
absolute error = 0.6223
relative error = 10.97 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.0537 2.429
h = 0.003 0.006
y1[1] (numeric) = -3.35166538726 4.72924008254
y1[1] (closed_form) = -2.8266545166 4.89366515531
absolute error = 0.5502
relative error = 9.735 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -4.97414281329 -3.40318245754
y2[1] (closed_form) = -4.97026846748 -2.78308924447
absolute error = 0.6201
relative error = 10.89 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=17001.5MB, alloc=44.3MB, time=222.09
x[1] = 1.0567 2.435
h = 0.0001 0.005
y1[1] (numeric) = -3.35715387629 4.76937501497
y1[1] (closed_form) = -2.82839209908 4.93195316072
absolute error = 0.5532
relative error = 9.73 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -4.99675017676 -3.41172436031
y2[1] (closed_form) = -5.00822780026 -2.78531606571
absolute error = 0.6265
relative error = 10.93 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.0568 2.44
h = 0.0001 0.003
y1[1] (numeric) = -3.37373299634 4.79475731175
y1[1] (closed_form) = -2.84185078317 4.95733597811
absolute error = 0.5562
relative error = 9.733 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -5.01955049076 -3.42026264035
y2[1] (closed_form) = -5.03323448203 -2.79899718205
absolute error = 0.6214
relative error = 10.79 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=17049.8MB, alloc=44.3MB, time=222.72
x[1] = 1.0569 2.443
h = 0.001 0.001
y1[1] (numeric) = -3.38350356678 4.81019273945
y1[1] (closed_form) = -2.84975574849 4.9727387409
absolute error = 0.5579
relative error = 9.735 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -5.04243876174 -3.42885499376
y2[1] (closed_form) = -5.04841416267 -2.80703808285
absolute error = 0.6218
relative error = 10.77 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=17098.1MB, alloc=44.3MB, time=223.35
x[1] = 1.0579 2.444
h = 0.0001 0.004
y1[1] (numeric) = -3.38188282735 4.81867979176
y1[1] (closed_form) = -2.84750939705 4.98059704215
absolute error = 0.5584
relative error = 9.732 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -5.06535412369 -3.43745618646
y2[1] (closed_form) = -5.05623946348 -2.80491004884
absolute error = 0.6326
relative error = 10.94 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.058 2.448
h = 0.003 0.006
y1[1] (numeric) = -3.39514219557 4.83933127801
y1[1] (closed_form) = -2.85824421274 5.00114350602
absolute error = 0.5608
relative error = 9.735 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -5.08831485501 -3.44607779765
y2[1] (closed_form) = -5.07648820455 -2.81582245584
absolute error = 0.6304
relative error = 10.86 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=17146.4MB, alloc=44.3MB, time=223.98
x[1] = 1.061 2.454
h = 0.0001 0.005
y1[1] (numeric) = -3.4005449339 4.88028159592
y1[1] (closed_form) = -2.85985802216 5.04016905163
absolute error = 0.5638
relative error = 9.73 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -5.11144846063 -3.45467973775
y2[1] (closed_form) = -5.11518920222 -2.8179149051
absolute error = 0.6368
relative error = 10.9 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.0611 2.459
h = 0.0001 0.003
y1[1] (numeric) = -3.41732748173 4.90624300642
y1[1] (closed_form) = -2.87346934391 5.06609130607
absolute error = 0.5669
relative error = 9.733 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -5.13477879253 -3.46327705287
y2[1] (closed_form) = -5.14074146512 -2.83174288383
absolute error = 0.6316
relative error = 10.76 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=17194.8MB, alloc=44.3MB, time=224.61
x[1] = 1.0612 2.462
h = 0.001 0.001
y1[1] (numeric) = -3.42721563542 4.92202922121
y1[1] (closed_form) = -2.88146190523 5.08182036323
absolute error = 0.5687
relative error = 9.734 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -5.15819907214 -3.47192907987
y2[1] (closed_form) = -5.15625106716 -2.83986787981
absolute error = 0.6321
relative error = 10.74 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.0622 2.463
h = 0.001 0.003
y1[1] (numeric) = -3.42552197335 4.93067540407
y1[1] (closed_form) = -2.87914043756 5.08981936286
absolute error = 0.5691
relative error = 9.732 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -5.18164701827 -3.48058998908
y2[1] (closed_form) = -5.16421718856 -2.83766236245
absolute error = 0.6432
relative error = 10.91 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=17243.3MB, alloc=44.3MB, time=225.24
x[1] = 1.0632 2.466
h = 0.0001 0.004
y1[1] (numeric) = -3.43078334216 4.94974047077
y1[1] (closed_form) = -2.88248544068 5.1081787013
absolute error = 0.5707
relative error = 9.731 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -5.2051296504 -3.48924408995
y2[1] (closed_form) = -5.18239498471 -2.84120580896
absolute error = 0.6484
relative error = 10.97 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.0633 2.47
h = 0.003 0.006
y1[1] (numeric) = -3.44423596777 4.97095743244
y1[1] (closed_form) = -2.89335305274 5.12923445221
absolute error = 0.5732
relative error = 9.733 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -5.22868660539 -3.49792237878
y2[1] (closed_form) = -5.20315857454 -2.85224560196
absolute error = 0.6462
relative error = 10.89 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=17291.6MB, alloc=44.3MB, time=225.88
x[1] = 1.0663 2.476
h = 0.0001 0.005
y1[1] (numeric) = -3.4495279269 5.01290739607
y1[1] (closed_form) = -2.89480355231 5.16913165361
absolute error = 0.5763
relative error = 9.727 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -5.25242040736 -3.50657952466
y2[1] (closed_form) = -5.24273581296 -2.85416263704
absolute error = 0.6525
relative error = 10.93 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=17339.9MB, alloc=44.3MB, time=226.51
x[1] = 1.0664 2.481
h = 0.0001 0.003
y1[1] (numeric) = -3.46655598065 5.03958036954
y1[1] (closed_form) = -2.90858373082 5.19569689744
absolute error = 0.5794
relative error = 9.731 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -5.2763555598 -3.51523079022
y2[1] (closed_form) = -5.26893799797 -2.86815283686
absolute error = 0.6471
relative error = 10.79 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.0665 2.484
h = 0.001 0.001
y1[1] (numeric) = -3.47658588951 5.0557974233
y1[1] (closed_form) = -2.9166728214 5.21181477889
absolute error = 0.5812
relative error = 9.732 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -5.30038310529 -3.52393753697
y2[1] (closed_form) = -5.28484051599 -2.87637034075
absolute error = 0.6478
relative error = 10.77 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=17388.2MB, alloc=44.3MB, time=227.14
x[1] = 1.0675 2.485
h = 0.001 0.003
y1[1] (numeric) = -3.47480177529 5.06463813004
y1[1] (closed_form) = -2.91425913669 5.21997890561
absolute error = 0.5817
relative error = 9.73 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -5.32443902313 -3.53265321465
y2[1] (closed_form) = -5.29297187919 -2.87406991124
absolute error = 0.6593
relative error = 10.95 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.0685 2.488
h = 0.0001 0.004
y1[1] (numeric) = -3.48007631924 5.08418457598
y1[1] (closed_form) = -2.91758435732 5.23876154221
absolute error = 0.5833
relative error = 9.728 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -5.34853040724 -3.54136172074
y2[1] (closed_form) = -5.31157589745 -2.87758831321
absolute error = 0.6648
relative error = 11 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=17436.4MB, alloc=44.3MB, time=227.77
x[1] = 1.0686 2.492
h = 0.003 0.006
y1[1] (numeric) = -3.49372315363 5.10598157568
y1[1] (closed_form) = -2.92858480998 5.26033871447
absolute error = 0.5858
relative error = 9.731 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -5.37269801227 -3.55009455298
y2[1] (closed_form) = -5.33286637731 -2.88875568307
absolute error = 0.6625
relative error = 10.92 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.0716 2.498
h = 0.0001 0.005
y1[1] (numeric) = -3.4988953519 5.14895404597
y1[1] (closed_form) = -2.92986335627 5.30112609998
absolute error = 0.589
relative error = 9.725 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -5.39704652122 -3.55880471041
y2[1] (closed_form) = -5.37333834774 -2.89048894787
absolute error = 0.6687
relative error = 10.96 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=17484.6MB, alloc=44.3MB, time=228.40
x[1] = 1.0717 2.503
h = 0.0001 0.003
y1[1] (numeric) = -3.51617016679 5.17635692215
y1[1] (closed_form) = -2.94381247875 5.32834965869
absolute error = 0.5922
relative error = 9.728 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -5.42160110586 -3.56750767309
y2[1] (closed_form) = -5.4002056638 -2.90464163643
absolute error = 0.6632
relative error = 10.82 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.0718 2.506
h = 0.001 0.001
y1[1] (numeric) = -3.52634242926 5.19301587544
y1[1] (closed_form) = -2.95199802763 5.34486559946
absolute error = 0.5941
relative error = 9.73 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -5.44625059143 -3.57626688885
y2[1] (closed_form) = -5.41651026458 -2.91295168602
absolute error = 0.664
relative error = 10.8 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=17532.9MB, alloc=44.3MB, time=229.03
x[1] = 1.0728 2.507
h = 0.001 0.003
y1[1] (numeric) = -3.52446449187 5.20205511662
y1[1] (closed_form) = -2.94948912141 5.35319801258
absolute error = 0.5945
relative error = 9.727 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -5.47092917214 -3.58503508092
y2[1] (closed_form) = -5.42481004036 -2.91055339917
absolute error = 0.6761
relative error = 10.98 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=17581.3MB, alloc=44.3MB, time=229.66
x[1] = 1.0738 2.51
h = 0.0001 0.004
y1[1] (numeric) = -3.52974945798 5.2220943758
y1[1] (closed_form) = -2.95279169513 5.37241328626
absolute error = 0.5962
relative error = 9.726 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -5.49564401547 -3.59379572462
y2[1] (closed_form) = -5.44384958328 -2.91404402194
absolute error = 0.6817
relative error = 11.04 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.0739 2.514
h = 0.003 0.006
y1[1] (numeric) = -3.54359139007 5.24448632594
y1[1] (closed_form) = -2.96392497156 5.39452428291
absolute error = 0.5988
relative error = 9.728 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -5.52043702341 -3.60258082384
y2[1] (closed_form) = -5.46567926441 -2.9253390948
absolute error = 0.6795
relative error = 10.96 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=17629.5MB, alloc=44.3MB, time=230.29
x[1] = 1.0769 2.52
h = 0.0001 0.005
y1[1] (numeric) = -3.54863450006 5.2885046518
y1[1] (closed_form) = -2.96502263516 5.43622074661
absolute error = 0.602
relative error = 9.722 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -5.54541507813 -3.61134165444
y2[1] (closed_form) = -5.50706482317 -2.92687994076
absolute error = 0.6855
relative error = 10.99 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.077 2.525
h = 0.0001 0.003
y1[1] (numeric) = -3.56615725389 5.31665621128
y1[1] (closed_form) = -2.97914071231 5.46411828521
absolute error = 0.6053
relative error = 9.725 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -5.57060403683 -3.62009391484
y2[1] (closed_form) = -5.53461282035 -2.94119530466
absolute error = 0.6799
relative error = 10.85 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=17677.7MB, alloc=44.3MB, time=230.92
x[1] = 1.0771 2.528
h = 0.001 0.001
y1[1] (numeric) = -3.57647241796 5.33376838955
y1[1] (closed_form) = -2.98742259965 5.48104172432
absolute error = 0.6072
relative error = 9.727 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -5.59589046838 -3.62890320247
y2[1] (closed_form) = -5.55132887559 -2.94959788617
absolute error = 0.6808
relative error = 10.83 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.0781 2.529
h = 0.001 0.003
y1[1] (numeric) = -3.57449718326 5.34301025084
y1[1] (closed_form) = -2.98481538479 5.48954563764
absolute error = 0.6076
relative error = 9.724 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -5.6212067352 -3.63772150825
y2[1] (closed_form) = -5.55980028868 -2.9470987129
absolute error = 0.6933
relative error = 11.02 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=17726.1MB, alloc=44.3MB, time=231.55
x[1] = 1.0791 2.532
h = 0.0001 0.004
y1[1] (numeric) = -3.57978968667 5.36355401141
y1[1] (closed_form) = -2.98809233599 5.50920307931
absolute error = 0.6094
relative error = 9.723 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -5.64656007738 -3.64653187494
y2[1] (closed_form) = -5.57928485089 -2.95055870755
absolute error = 0.6992
relative error = 11.08 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.0792 2.536
h = 0.003 0.006
y1[1] (numeric) = -3.5938275392 5.38655618206
y1[1] (closed_form) = -2.99935835543 5.53186057773
absolute error = 0.612
relative error = 9.725 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -5.67199357451 -3.65536681722
y2[1] (closed_form) = -5.60166632016 -2.96198154203
absolute error = 0.6969
relative error = 11 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=17774.3MB, alloc=44.3MB, time=232.18
x[1] = 1.0822 2.542
h = 0.0001 0.005
y1[1] (numeric) = -3.5987318765 5.43164420964
y1[1] (closed_form) = -3.00026591243 5.57448538599
absolute error = 0.6153
relative error = 9.719 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -5.69761634887 -3.66417583319
y2[1] (closed_form) = -5.64398469522 -2.96332101982
absolute error = 0.7029
relative error = 11.03 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=17822.7MB, alloc=44.3MB, time=232.81
x[1] = 1.0823 2.547
h = 0.0001 0.003
y1[1] (numeric) = -3.61650366501 5.46056368375
y1[1] (closed_form) = -3.01455287481 5.60307291619
absolute error = 0.6186
relative error = 9.722 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -5.72345496063 -3.67297484041
y2[1] (closed_form) = -5.67222927189 -2.97779916108
absolute error = 0.6971
relative error = 10.88 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.0824 2.55
h = 0.001 0.001
y1[1] (numeric) = -3.62696222536 5.47814068335
y1[1] (closed_form) = -3.02293092967 5.6204135009
absolute error = 0.6206
relative error = 9.724 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -5.74939368275 -3.68183165096
y2[1] (closed_form) = -5.68936636244 -2.98629420696
absolute error = 0.6981
relative error = 10.86 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=17871.0MB, alloc=44.3MB, time=233.44
x[1] = 1.0834 2.551
h = 0.0001 0.004
y1[1] (numeric) = -3.62488611318 5.48758932662
y1[1] (closed_form) = -3.02022223421 5.6290921835
absolute error = 0.621
relative error = 9.721 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -5.77536299797 -3.69069751778
y2[1] (closed_form) = -5.6980126923 -2.98369103214
absolute error = 0.7112
relative error = 11.06 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.0835 2.555
h = 0.003 0.006
y1[1] (numeric) = -3.6390878232 5.51111230188
y1[1] (closed_form) = -3.03160911935 5.65222887917
absolute error = 0.6237
relative error = 9.723 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -5.8013837217 -3.69958483506
y2[1] (closed_form) = -5.72087789475 -2.99523061494
absolute error = 0.7089
relative error = 10.98 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=17919.3MB, alloc=44.3MB, time=234.08
x[1] = 1.0865 2.561
h = 0.0001 0.005
y1[1] (numeric) = -3.64386856776 5.5571111716
y1[1] (closed_form) = -3.0323567992 5.6956709123
absolute error = 0.627
relative error = 9.717 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -5.8275973189 -3.70844479235
y2[1] (closed_form) = -5.76401744243 -2.9964007898
absolute error = 0.7149
relative error = 11 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.0866 2.566
h = 0.0001 0.003
y1[1] (numeric) = -3.66184879707 5.5866864661
y1[1] (closed_form) = -3.04679749808 5.72486344701
absolute error = 0.6304
relative error = 9.72 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -5.85403095085 -3.71729349045
y2[1] (closed_form) = -5.79287267473 -3.01102762077
absolute error = 0.7089
relative error = 10.86 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=17967.6MB, alloc=44.3MB, time=234.72
x[1] = 1.0867 2.569
h = 0.001 0.001
y1[1] (numeric) = -3.67242730135 5.60466052366
y1[1] (closed_form) = -3.05526328247 5.74256984246
absolute error = 0.6324
relative error = 9.722 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -5.88056694551 -3.72620064029
y2[1] (closed_form) = -5.81037891416 -3.01960733472
absolute error = 0.7101
relative error = 10.84 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.0877 2.57
h = 0.001 0.003
y1[1] (numeric) = -3.67026411115 5.61428503334
y1[1] (closed_form) = -3.05246676538 5.75140288304
absolute error = 0.6328
relative error = 9.719 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -5.90713417969 -3.73511687511
y2[1] (closed_form) = -5.819179766 -3.01691421485
absolute error = 0.7236
relative error = 11.04 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=18015.9MB, alloc=44.3MB, time=235.34
x[1] = 1.0887 2.573
h = 0.0001 0.004
y1[1] (numeric) = -3.6755623932 5.63578589831
y1[1] (closed_form) = -3.05569326773 5.77190953011
absolute error = 0.6346
relative error = 9.718 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -5.93374002426 -3.74402441601
y2[1] (closed_form) = -5.83951879937 -3.02031480659
absolute error = 0.7298
relative error = 11.1 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=18064.2MB, alloc=44.3MB, time=235.98
x[1] = 1.0888 2.577
h = 0.003 0.006
y1[1] (numeric) = -3.68996162942 5.65994905386
y1[1] (closed_form) = -3.0672127241 5.79561707014
absolute error = 0.6374
relative error = 9.72 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -5.96042980157 -3.75295672672
y2[1] (closed_form) = -5.86295996586 -3.03198222826
absolute error = 0.7275
relative error = 11.02 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.0918 2.583
h = 0.0001 0.005
y1[1] (numeric) = -3.69458459024 5.70706439888
y1[1] (closed_form) = -3.06775256036 5.84002443024
absolute error = 0.6408
relative error = 9.714 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -5.98731685459 -3.76185989436
y2[1] (closed_form) = -5.90706923619 -3.03293379205
absolute error = 0.7333
relative error = 11.04 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=18112.4MB, alloc=44.3MB, time=236.61
x[1] = 1.0919 2.588
h = 0.0001 0.003
y1[1] (numeric) = -3.71281599284 5.73744532944
y1[1] (closed_form) = -3.08236198975 5.86993770164
absolute error = 0.6442
relative error = 9.717 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -6.01442908198 -3.77075024045
y2[1] (closed_form) = -5.93665158441 -3.04772355199
absolute error = 0.7272
relative error = 10.9 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.092 2.591
h = 0.001 0.001
y1[1] (numeric) = -3.72353885705 5.75590695086
y1[1] (closed_form) = -3.09092360049 5.88807976685
absolute error = 0.6463
relative error = 9.718 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -6.04164643821 -3.77969981812
y2[1] (closed_form) = -5.95459726101 -3.0563955739
absolute error = 0.7285
relative error = 10.88 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=18160.8MB, alloc=44.3MB, time=237.24
x[1] = 1.093 2.592
h = 0.001 0.003
y1[1] (numeric) = -3.72126776672 5.76574640154
y1[1] (closed_form) = -3.08801950772 5.89709384964
absolute error = 0.6467
relative error = 9.715 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -6.06889582654 -3.78865851162
y2[1] (closed_form) = -5.96357931984 -3.05359246014
absolute error = 0.7426
relative error = 11.08 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.094 2.595
h = 0.0001 0.004
y1[1] (numeric) = -3.72656463384 5.78778713826
y1[1] (closed_form) = -3.09121134987 5.91807106364
absolute error = 0.6486
relative error = 9.714 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -6.09618468741 -3.79760807793
y2[1] (closed_form) = -5.98439166709 -3.05695373214
absolute error = 0.749
relative error = 11.15 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=18209.0MB, alloc=44.3MB, time=237.87
x[1] = 1.0941 2.599
h = 0.003 0.006
y1[1] (numeric) = -3.74116200999 5.81260680234
y1[1] (closed_form) = -3.10286310043 5.94236294336
absolute error = 0.6514
relative error = 9.716 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -6.12355961261 -3.80658250512
y2[1] (closed_form) = -6.00842220601 -3.06874884522
absolute error = 0.7468
relative error = 11.07 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.0971 2.605
h = 0.0001 0.005
y1[1] (numeric) = -3.74561642618 5.86086393083
y1[1] (closed_form) = -3.10318498265 5.98775600266
absolute error = 0.6548
relative error = 9.71 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -6.15113630822 -3.81552593637
y2[1] (closed_form) = -6.05352153133 -3.06947194472
absolute error = 0.7524
relative error = 11.09 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=18257.3MB, alloc=44.3MB, time=238.49
x[1] = 1.0972 2.61
h = 0.0001 0.003
y1[1] (numeric) = -3.76409983843 5.89207106268
y1[1] (closed_form) = -3.11796282701 6.01840705608
absolute error = 0.6584
relative error = 9.713 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -6.17894342906 -3.82445491447
y2[1] (closed_form) = -6.08384793197 -3.08442447748
absolute error = 0.7461
relative error = 10.94 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=18305.6MB, alloc=44.3MB, time=239.12
x[1] = 1.0973 2.613
h = 0.001 0.001
y1[1] (numeric) = -3.77496738937 5.91103264579
y1[1] (closed_form) = -3.12661993647 6.03699505915
absolute error = 0.6605
relative error = 9.715 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -6.20685851494 -3.83344390494
y2[1] (closed_form) = -6.10224325006 -3.09318857588
absolute error = 0.7476
relative error = 10.93 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.0983 2.614
h = 0.001 0.003
y1[1] (numeric) = -3.77258450154 5.92109142164
y1[1] (closed_form) = -3.12360484174 6.04619361659
absolute error = 0.6609
relative error = 9.712 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -6.23480644438 -3.84244203781
y2[1] (closed_form) = -6.11140995728 -3.09027209546
absolute error = 0.7622
relative error = 11.13 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=18353.9MB, alloc=44.3MB, time=239.75
x[1] = 1.0993 2.617
h = 0.0001 0.004
y1[1] (numeric) = -3.77787651767 5.943684742
y1[1] (closed_form) = -3.12675858667 6.06765170589
absolute error = 0.6628
relative error = 9.71 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -6.2627947261 -3.85143059456
y2[1] (closed_form) = -6.13270589112 -3.09359072637
absolute error = 0.7689
relative error = 11.19 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.0994 2.621
h = 0.003 0.006
y1[1] (numeric) = -3.79267256573 5.96917763274
y1[1] (closed_form) = -3.13854227842 6.09254171794
absolute error = 0.6657
relative error = 9.713 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -6.29087125454 -3.86044409198
y2[1] (closed_form) = -6.15733950939 -3.10551330419
absolute error = 0.7666
relative error = 11.12 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=18402.2MB, alloc=44.3MB, time=240.38
x[1] = 1.1024 2.627
h = 0.0001 0.005
y1[1] (numeric) = -3.79694727257 6.01860238804
y1[1] (closed_form) = -3.13863576688 6.13894124723
absolute error = 0.6692
relative error = 9.706 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -6.31915414232 -3.86942466863
y2[1] (closed_form) = -6.20344962015 -3.10599775111
absolute error = 0.7721
relative error = 11.13 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.1025 2.632
h = 0.0001 0.003
y1[1] (numeric) = -3.81568342927 6.05065677782
y1[1] (closed_form) = -3.1535816154 6.17034750363
absolute error = 0.6728
relative error = 9.71 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -6.34767281964 -3.878389089
y2[1] (closed_form) = -6.2345373869 -3.12111280125
absolute error = 0.7657
relative error = 10.98 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=18450.4MB, alloc=44.3MB, time=241.00
x[1] = 1.1026 2.635
h = 0.001 0.001
y1[1] (numeric) = -3.82669592832 6.07013101564
y1[1] (closed_form) = -3.16233383552 6.18939193824
absolute error = 0.675
relative error = 9.711 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -6.37630236997 -3.88741430304
y2[1] (closed_form) = -6.25339277726 -3.12996868176
absolute error = 0.7674
relative error = 10.97 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.1036 2.636
h = 0.001 0.003
y1[1] (numeric) = -3.82419722755 6.08041358153
y1[1] (closed_form) = -3.1592042189 6.19877846099
absolute error = 0.6754
relative error = 9.708 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -6.40496559461 -3.89644868159
y2[1] (closed_form) = -6.262747632 -3.12693536715
absolute error = 0.7825
relative error = 11.18 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=18498.7MB, alloc=44.3MB, time=241.63
x[1] = 1.1046 2.639
h = 0.0001 0.004
y1[1] (numeric) = -3.82948080032 6.10357247779
y1[1] (closed_form) = -3.16231630007 6.22072794434
absolute error = 0.6774
relative error = 9.707 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -6.43367006917 -3.90547301898
y2[1] (closed_form) = -6.2845376357 -3.13020790343
absolute error = 0.7895
relative error = 11.24 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=18547.0MB, alloc=44.3MB, time=242.27
x[1] = 1.1047 2.643
h = 0.003 0.006
y1[1] (numeric) = -3.8444759661 6.12975571186
y1[1] (closed_form) = -3.17423150068 6.2462301848
absolute error = 0.6803
relative error = 9.709 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -6.46246502476 -3.91452236498
y2[1] (closed_form) = -6.3097883449 -3.14225763676
absolute error = 0.7872
relative error = 11.17 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.1077 2.649
h = 0.0001 0.005
y1[1] (numeric) = -3.84855938216 6.1803744826
y1[1] (closed_form) = -3.17408581681 6.2936573605
absolute error = 0.6839
relative error = 9.703 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -6.49147102468 -3.92353679111
y2[1] (closed_form) = -6.35693037674 -3.14249289829
absolute error = 0.7925
relative error = 11.18 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=18595.4MB, alloc=44.3MB, time=242.90
x[1] = 1.1078 2.654
h = 0.0001 0.003
y1[1] (numeric) = -3.86754891108 6.21329768926
y1[1] (closed_form) = -3.18919915915 6.32583662434
absolute error = 0.6876
relative error = 9.706 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -6.52071829418 -3.93253328396
y2[1] (closed_form) = -6.38879720831 -3.15777010687
absolute error = 0.7859
relative error = 11.03 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.1079 2.657
h = 0.001 0.001
y1[1] (numeric) = -3.87870655079 6.23329757652
y1[1] (closed_form) = -3.19804603875 6.34534821447
absolute error = 0.6898
relative error = 9.708 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -6.55007941809 -3.94159135192
y2[1] (closed_form) = -6.4081233329 -3.16671740969
absolute error = 0.7878
relative error = 11.02 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=18643.8MB, alloc=44.3MB, time=243.54
x[1] = 1.1089 2.658
h = 0.0001 0.004
y1[1] (numeric) = -3.87608790028 6.24380847917
y1[1] (closed_form) = -3.19479828428 6.35492625217
absolute error = 0.6903
relative error = 9.705 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -6.57947506678 -3.95065860178
y2[1] (closed_form) = -6.41766989282 -3.16356369621
absolute error = 0.8036
relative error = 11.23 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.109 2.662
h = 0.003 0.006
y1[1] (numeric) = -3.89124927537 6.27058077082
y1[1] (closed_form) = -3.20683380109 6.3809654446
absolute error = 0.6933
relative error = 9.708 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -6.60892892591 -3.95974825596
y2[1] (closed_form) = -6.44346172264 -3.1757301513
absolute error = 0.8013
relative error = 11.15 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=18692.0MB, alloc=44.3MB, time=244.17
x[1] = 1.112 2.668
h = 0.0001 0.005
y1[1] (numeric) = -3.89516377993 6.32221604738
y1[1] (closed_form) = -3.20648594075 6.42929748673
absolute error = 0.697
relative error = 9.701 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -6.63859781121 -3.96880126365
y2[1] (closed_form) = -6.49151238286 -3.17575486023
absolute error = 0.8066
relative error = 11.16 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.1121 2.673
h = 0.0001 0.003
y1[1] (numeric) = -3.91436497737 6.35588108358
y1[1] (closed_form) = -3.22175247224 6.46215470066
absolute error = 0.7007
relative error = 9.704 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -6.66851262762 -3.97783479673
y2[1] (closed_form) = -6.52406235618 -3.19118085424
absolute error = 0.7998
relative error = 11.01 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=18740.4MB, alloc=44.3MB, time=244.80
x[1] = 1.1122 2.676
h = 0.001 0.001
y1[1] (numeric) = -3.92564376515 6.37632989067
y1[1] (closed_form) = -3.23068616309 6.48207605045
absolute error = 0.703
relative error = 9.706 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -6.69854384392 -3.9869305563
y2[1] (closed_form) = -6.543801309 -3.20021229487
absolute error = 0.8018
relative error = 11.01 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=18788.7MB, alloc=44.3MB, time=245.45
x[1] = 1.1132 2.677
h = 0.001 0.003
y1[1] (numeric) = -3.92292167289 6.38703495123
y1[1] (closed_form) = -3.22733608875 6.49182329362
absolute error = 0.7034
relative error = 9.703 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -6.72861031029 -3.99603550836
y2[1] (closed_form) = -6.55351727034 -3.19695435795
absolute error = 0.818
relative error = 11.22 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.1142 2.68
h = 0.0001 0.004
y1[1] (numeric) = -3.92817976403 6.41126651001
y1[1] (closed_form) = -3.2303668496 6.51471648263
absolute error = 0.7054
relative error = 9.701 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -6.75871972143 -4.00512952218
y2[1] (closed_form) = -6.57625591472 -3.20013765171
absolute error = 0.8254
relative error = 11.29 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=18836.9MB, alloc=44.3MB, time=246.10
x[1] = 1.1143 2.684
h = 0.003 0.006
y1[1] (numeric) = -3.94354111953 6.4387627284
y1[1] (closed_form) = -3.24253302435 6.54139497
absolute error = 0.7085
relative error = 9.704 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -6.78892385322 -4.01424863613
y2[1] (closed_form) = -6.60269174658 -3.21243063127
absolute error = 0.8232
relative error = 11.21 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.1173 2.69
h = 0.0001 0.005
y1[1] (numeric) = -3.94724159503 6.49164377993
y1[1] (closed_form) = -3.24192526345 6.59079530535
absolute error = 0.7123
relative error = 9.697 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -6.81934788454 -4.0233289588
y2[1] (closed_form) = -6.65181489504 -3.21218586864
absolute error = 0.8283
relative error = 11.21 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=18885.4MB, alloc=44.3MB, time=246.76
x[1] = 1.1174 2.695
h = 0.0001 0.003
y1[1] (numeric) = -3.96669738093 6.52621992074
y1[1] (closed_form) = -3.25735828236 6.62445971397
absolute error = 0.7161
relative error = 9.701 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -6.85002355393 -4.03238788484
y2[1] (closed_form) = -6.68517792599 -3.22777328507
absolute error = 0.8213
relative error = 11.06 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.1175 2.698
h = 0.001 0.001
y1[1] (numeric) = -3.97812167786 6.54721986277
y1[1] (closed_form) = -3.26638575039 6.64486881069
absolute error = 0.7184
relative error = 9.703 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -6.8808187487 -4.04150981899
y2[1] (closed_form) = -6.70540809037 -3.23689542887
absolute error = 0.8235
relative error = 11.06 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=18933.7MB, alloc=44.3MB, time=247.42
x[1] = 1.1185 2.699
h = 0.001 0.003
y1[1] (numeric) = -3.97527152066 6.55816217305
y1[1] (closed_form) = -3.26291058955 6.65481437944
absolute error = 0.7189
relative error = 9.699 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -6.91165008268 -4.05064095379
y2[1] (closed_form) = -6.7153225807 -3.2335102371
absolute error = 0.8404
relative error = 11.28 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.1195 2.702
h = 0.0001 0.004
y1[1] (numeric) = -3.98051004427 6.58299861776
y1[1] (closed_form) = -3.26588886545 6.67823029958
absolute error = 0.7209
relative error = 9.698 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -6.94252531304 -4.05976063614
y2[1] (closed_form) = -6.73858653037 -3.23663692349
absolute error = 0.848
relative error = 11.34 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=18982.0MB, alloc=44.3MB, time=248.09
x[1] = 1.1196 2.706
h = 0.003 0.006
y1[1] (numeric) = -3.99607155644 6.61123705834
y1[1] (closed_form) = -3.27818502308 6.70556308261
absolute error = 0.7241
relative error = 9.701 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -6.97349765555 -4.06890544968
y2[1] (closed_form) = -6.7656812839 -3.24905586686
absolute error = 0.8458
relative error = 11.27 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=19030.3MB, alloc=44.3MB, time=248.76
x[1] = 1.1226 2.712
h = 0.0001 0.005
y1[1] (numeric) = -3.99954516639 6.6653918757
y1[1] (closed_form) = -3.27730556351 6.75605409217
absolute error = 0.7279
relative error = 9.694 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -7.00469487226 -4.07800924615
y2[1] (closed_form) = -6.81589925989 -3.24853006469
absolute error = 0.8507
relative error = 11.27 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.1227 2.717
h = 0.0001 0.003
y1[1] (numeric) = -4.0192558333 6.70090216612
y1[1] (closed_form) = -3.29290425496 6.7905446431
absolute error = 0.7319
relative error = 9.698 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -7.03614955634 -4.08708964298
y2[1] (closed_form) = -6.85009419469 -3.26427822936
absolute error = 0.8436
relative error = 11.12 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=19078.8MB, alloc=44.3MB, time=249.42
x[1] = 1.1228 2.72
h = 0.001 0.001
y1[1] (numeric) = -4.03082561709 6.72246713035
y1[1] (closed_form) = -3.30202485624 6.81145289709
absolute error = 0.7342
relative error = 9.699 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -7.06772696977 -4.09623382841
y2[1] (closed_form) = -6.87082692147 -3.27349051728
absolute error = 0.846
relative error = 11.12 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.1238 2.721
h = 0.001 0.003
y1[1] (numeric) = -4.02784289528 6.73365147557
y1[1] (closed_form) = -3.298420705 6.82160051535
absolute error = 0.7347
relative error = 9.696 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -7.09934143252 -4.10538721727
y2[1] (closed_form) = -6.88094367154 -3.26997421504
absolute error = 0.8635
relative error = 11.33 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=19127.2MB, alloc=44.3MB, time=250.08
x[1] = 1.1248 2.724
h = 0.0001 0.004
y1[1] (numeric) = -4.03305760719 6.7591069272
y1[1] (closed_form) = -3.30134239283 6.84555053708
absolute error = 0.7368
relative error = 9.695 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -7.13100076248 -4.11452862141
y2[1] (closed_form) = -6.90474426227 -3.27304029402
absolute error = 0.8714
relative error = 11.4 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.1249 2.728
h = 0.003 0.006
y1[1] (numeric) = -4.04881934769 6.78810631953
y1[1] (closed_form) = -3.31376776494 6.87355294508
absolute error = 0.74
relative error = 9.698 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -7.16275965258 -4.12369517357
y2[1] (closed_form) = -6.9325131869 -3.2855845443
absolute error = 0.8692
relative error = 11.33 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=19175.3MB, alloc=44.3MB, time=250.74
x[1] = 1.1279 2.734
h = 0.0001 0.005
y1[1] (numeric) = -4.05205278528 6.84356347985
y1[1] (closed_form) = -3.31260443033 6.92515744375
absolute error = 0.7439
relative error = 9.691 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -7.19474849478 -4.13281839935
y2[1] (closed_form) = -6.98384876331 -3.28476575115
absolute error = 0.8739
relative error = 11.32 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.128 2.739
h = 0.0001 0.003
y1[1] (numeric) = -4.07201849562 6.8800315121
y1[1] (closed_form) = -3.32836786232 6.9604934999
absolute error = 0.748
relative error = 9.695 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -7.2270007584 -4.14191613887
y2[1] (closed_form) = -7.01889486498 -3.30067386912
absolute error = 0.8666
relative error = 11.17 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=19223.7MB, alloc=44.3MB, time=251.41
x[1] = 1.1281 2.742
h = 0.001 0.001
y1[1] (numeric) = -4.08373366084 6.90217571435
y1[1] (closed_form) = -3.33758087896 6.9819125708
absolute error = 0.7504
relative error = 9.697 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -7.25937903566 -4.15107844583
y2[1] (closed_form) = -7.04014175514 -3.30997566603
absolute error = 0.8692
relative error = 11.17 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=19272.2MB, alloc=44.3MB, time=252.08
x[1] = 1.1291 2.743
h = 0.001 0.003
y1[1] (numeric) = -4.08061373978 6.91360696623
y1[1] (closed_form) = -3.33384372751 6.99226602456
absolute error = 0.7509
relative error = 9.694 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -7.29179529383 -4.16024995338
y2[1] (closed_form) = -7.05046455735 -3.30632429075
absolute error = 0.8874
relative error = 11.4 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.1301 2.746
h = 0.0001 0.004
y1[1] (numeric) = -4.08580021134 6.93969585474
y1[1] (closed_form) = -3.33670457374 7.01676174862
absolute error = 0.753
relative error = 9.692 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -7.32425740955 -4.16940892533
y2[1] (closed_form) = -7.07481335542 -3.30932560949
absolute error = 0.8955
relative error = 11.47 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=19320.4MB, alloc=44.3MB, time=252.75
x[1] = 1.1302 2.75
h = 0.003 0.006
y1[1] (numeric) = -4.10176214205 6.9694753721
y1[1] (closed_form) = -3.34925829469 7.04544944634
absolute error = 0.7563
relative error = 9.695 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -7.35682159118 -4.17859304724
y2[1] (closed_form) = -7.10327203719 -3.32199440968
absolute error = 0.8933
relative error = 11.39 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.1332 2.756
h = 0.0001 0.005
y1[1] (numeric) = -4.10474161544 7.02626404962
y1[1] (closed_form) = -3.34779851957 7.09819069048
absolute error = 0.7604
relative error = 9.688 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -7.38962090797 -4.18773144734
y2[1] (closed_form) = -7.15574842812 -3.32087027988
absolute error = 0.8979
relative error = 11.38 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=19368.7MB, alloc=44.3MB, time=253.43
x[1] = 1.1333 2.761
h = 0.0001 0.003
y1[1] (numeric) = -4.12496239501 7.06371397522
y1[1] (closed_form) = -3.36372563801 7.13439203868
absolute error = 0.7645
relative error = 9.693 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -7.42268972745 -4.19684218824
y2[1] (closed_form) = -7.19166538502 -3.33693743067
absolute error = 0.8904
relative error = 11.23 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.1334 2.764
h = 0.001 0.001
y1[1] (numeric) = -4.13682274907 7.0864519671
y1[1] (closed_form) = -3.37303027513 7.15633384057
absolute error = 0.767
relative error = 9.695 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -7.45588792709 -4.20601827323
y2[1] (closed_form) = -7.21343829485 -3.3463280223
absolute error = 0.8932
relative error = 11.23 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=19417.1MB, alloc=44.3MB, time=254.11
x[1] = 1.1344 2.765
h = 0.0001 0.004
y1[1] (numeric) = -4.13356085544 7.09813508505
y1[1] (closed_form) = -3.369156005 7.16689697863
absolute error = 0.7675
relative error = 9.691 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -7.48912506114 -4.2152035501
y2[1] (closed_form) = -7.22397100403 -3.34253750178
absolute error = 0.9121
relative error = 11.46 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.1345 2.769
h = 0.003 0.006
y1[1] (numeric) = -4.14968948957 7.12858013042
y1[1] (closed_form) = -3.38182785739 7.19618584307
absolute error = 0.7708
relative error = 9.695 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -7.52242805886 -4.22441207389
y2[1] (closed_form) = -7.25303467929 -3.35532130027
absolute error = 0.9099
relative error = 11.39 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=19465.3MB, alloc=44.3MB, time=254.78
x[1] = 1.1375 2.775
h = 0.0001 0.005
y1[1] (numeric) = -4.1524460138 7.18650216512
y1[1] (closed_form) = -3.38011647499 7.24992826792
absolute error = 0.7749
relative error = 9.688 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -7.55597059604 -4.23357280928
y2[1] (closed_form) = -7.30651582194 -3.35393812566
absolute error = 0.9143
relative error = 11.37 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=19513.6MB, alloc=44.3MB, time=255.46
x[1] = 1.1376 2.78
h = 0.0001 0.003
y1[1] (numeric) = -4.17287937855 7.22479029353
y1[1] (closed_form) = -3.39619418436 7.28688867518
absolute error = 0.7792
relative error = 9.692 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -7.58978780786 -4.24270400399
y2[1] (closed_form) = -7.34319660209 -3.37015203075
absolute error = 0.9067
relative error = 11.22 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.1377 2.783
h = 0.001 0.001
y1[1] (numeric) = -4.18486060227 7.2480352934
y1[1] (closed_form) = -3.40558341244 7.30928908809
absolute error = 0.7817
relative error = 9.694 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -7.62373727353 -4.25190118829
y2[1] (closed_form) = -7.36543094048 -3.37962488227
absolute error = 0.9097
relative error = 11.23 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=19562.1MB, alloc=44.3MB, time=256.13
x[1] = 1.1387 2.784
h = 0.001 0.003
y1[1] (numeric) = -4.18147637674 7.25993253021
y1[1] (closed_form) = -3.40159029351 7.32003754816
absolute error = 0.7822
relative error = 9.691 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -7.65772648662 -4.2611075523
y2[1] (closed_form) = -7.37614919131 -3.37571380759
absolute error = 0.9291
relative error = 11.45 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.1397 2.787
h = 0.0001 0.004
y1[1] (numeric) = -4.18659875382 7.28722244827
y1[1] (closed_form) = -3.40433291013 7.34558123125
absolute error = 0.7844
relative error = 9.689 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -7.69176342653 -4.27030031942
y2[1] (closed_form) = -7.40155056271 -3.37858989379
absolute error = 0.9377
relative error = 11.53 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=19610.3MB, alloc=44.3MB, time=256.80
x[1] = 1.1398 2.791
h = 0.003 0.006
y1[1] (numeric) = -4.20292748766 7.31848523767
y1[1] (closed_form) = -3.41713142414 7.37558546373
absolute error = 0.7879
relative error = 9.692 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -7.72590718569 -4.27951819857
y2[1] (closed_form) = -7.43133392877 -3.39149674891
absolute error = 0.9356
relative error = 11.45 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.1428 2.797
h = 0.0001 0.005
y1[1] (numeric) = -4.2054029672 7.37779601186
y1[1] (closed_form) = -3.41509943557 7.43050927118
absolute error = 0.7921
relative error = 9.686 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -7.76029587365 -4.28868572487
y2[1] (closed_form) = -7.4860004414 -3.38978446724
absolute error = 0.9398
relative error = 11.44 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=19658.5MB, alloc=44.3MB, time=257.46
x[1] = 1.1429 2.802
h = 0.0001 0.003
y1[1] (numeric) = -4.22609143205 7.41711340721
y1[1] (closed_form) = -3.43133877553 7.4683729638
absolute error = 0.7964
relative error = 9.69 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -7.79496556698 -4.29782136807
y2[1] (closed_form) = -7.52358988925 -3.4061555877
absolute error = 0.932
relative error = 11.29 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.143 2.805
h = 0.001 0.001
y1[1] (numeric) = -4.23821745504 7.44098073589
y1[1] (closed_form) = -3.44081807856 7.49131898407
absolute error = 0.799
relative error = 9.692 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -7.82977104194 -4.30702377321
y2[1] (closed_form) = -7.54637301747 -3.41571583236
absolute error = 0.9353
relative error = 11.29 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=19706.8MB, alloc=44.3MB, time=258.12
x[1] = 1.144 2.806
h = 0.001 0.003
y1[1] (numeric) = -4.23468189247 7.45313956019
y1[1] (closed_form) = -3.4366799264 7.50228451236
absolute error = 0.7995
relative error = 9.689 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -7.86461726082 -4.31623533779
y2[1] (closed_form) = -7.5573085689 -3.41165778144
absolute error = 0.9554
relative error = 11.52 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=19754.9MB, alloc=44.3MB, time=258.78
x[1] = 1.145 2.809
h = 0.0001 0.004
y1[1] (numeric) = -4.23976234037 7.4811065673
y1[1] (closed_form) = -3.4393488085 7.52840845251
absolute error = 0.8018
relative error = 9.687 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -7.89951225574 -4.32543269785
y2[1] (closed_form) = -7.58329260399 -3.41445648918
absolute error = 0.9643
relative error = 11.59 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.1451 2.813
h = 0.003 0.006
y1[1] (numeric) = -4.25629079468 7.51320758583
y1[1] (closed_form) = -3.45227282175 7.55914471749
absolute error = 0.8053
relative error = 9.691 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -7.93451675046 -4.33465512566
y2[1] (closed_form) = -7.61381224987 -3.42748533946
absolute error = 0.9622
relative error = 11.52 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=19803.2MB, alloc=44.3MB, time=259.44
x[1] = 1.1481 2.819
h = 0.0001 0.005
y1[1] (numeric) = -4.25846997833 7.57393802742
y1[1] (closed_form) = -3.44990649138 7.61527447465
absolute error = 0.8096
relative error = 9.684 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -7.96977167417 -4.34382454231
y2[1] (closed_form) = -7.66968865686 -3.42543042086
absolute error = 0.9662
relative error = 11.5 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.1482 2.824
h = 0.0001 0.003
y1[1] (numeric) = -4.27941314425 7.61431049517
y1[1] (closed_form) = -3.46630603533 7.65406250287
absolute error = 0.8141
relative error = 9.689 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -8.00531406836 -4.35295963895
y2[1] (closed_form) = -7.70820772834 -3.44195745412
absolute error = 0.9582
relative error = 11.35 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=19851.7MB, alloc=44.3MB, time=260.11
x[1] = 1.1483 2.827
h = 0.001 0.001
y1[1] (numeric) = -4.29168350364 7.63881569718
y1[1] (closed_form) = -3.47587438372 7.67756680285
absolute error = 0.8167
relative error = 9.691 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -8.04099585978 -4.3621622661
y2[1] (closed_form) = -7.73155226335 -3.45160413722
absolute error = 0.9617
relative error = 11.36 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.1493 2.828
h = 0.001 0.003
y1[1] (numeric) = -4.28799141622 7.65124132358
y1[1] (closed_form) = -3.4715867543 7.6887534337
absolute error = 0.8173
relative error = 9.688 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -8.07671941495 -4.37137402575
y2[1] (closed_form) = -7.74270915474 -3.44739470954
absolute error = 0.9825
relative error = 11.59 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=19900.0MB, alloc=44.3MB, time=260.77
x[1] = 1.1503 2.831
h = 0.0001 0.004
y1[1] (numeric) = -4.29302473855 7.67990109279
y1[1] (closed_form) = -3.47417702613 7.71547016383
absolute error = 0.8196
relative error = 9.686 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -8.1124928163 -4.38057095243
y2[1] (closed_form) = -7.76928835295 -3.45011125489
absolute error = 0.9917
relative error = 11.67 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.1504 2.835
h = 0.003 0.006
y1[1] (numeric) = -4.30975240257 7.7128613085
y1[1] (closed_form) = -3.48722526271 7.74695548879
absolute error = 0.8232
relative error = 9.69 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -8.14837846078 -4.38979288488
y2[1] (closed_form) = -7.80056123182 -3.46326092274
absolute error = 0.9897
relative error = 11.6 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=19948.3MB, alloc=44.3MB, time=261.86
x[1] = 1.1534 2.841
h = 0.0001 0.005
y1[1] (numeric) = -4.31161949281 7.77504298672
y1[1] (closed_form) = -3.48451042123 7.80431623464
absolute error = 0.8276
relative error = 9.683 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -8.18452014737 -4.3989590511
y2[1] (closed_form) = -7.85767252925 -3.46084939897
absolute error = 0.9934
relative error = 11.57 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=19996.6MB, alloc=44.3MB, time=262.50
x[1] = 1.1535 2.846
h = 0.0001 0.003
y1[1] (numeric) = -4.33281679685 7.81649694113
y1[1] (closed_form) = -3.50106860004 7.84405010745
absolute error = 0.8322
relative error = 9.688 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -8.22095590656 -4.40808836286
y2[1] (closed_form) = -7.89714264047 -3.47753089676
absolute error = 0.9853
relative error = 11.42 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.1536 2.849
h = 0.001 0.001
y1[1] (numeric) = -4.34523092577 7.84165592639
y1[1] (closed_form) = -3.51072487461 7.8681256348
absolute error = 0.8349
relative error = 9.691 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -8.25753476846 -4.41728596934
y2[1] (closed_form) = -7.92106147535 -3.48726297209
absolute error = 0.989
relative error = 11.43 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=20044.9MB, alloc=44.3MB, time=263.14
x[1] = 1.1546 2.85
h = 0.001 0.003
y1[1] (numeric) = -4.34137697161 7.85435366196
y1[1] (closed_form) = -3.50628320417 7.87953746849
absolute error = 0.8355
relative error = 9.687 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -8.29415643776 -4.42649267438
y2[1] (closed_form) = -7.93244381167 -3.48289764647
absolute error = 1.011
relative error = 11.66 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.1556 2.853
h = 0.0001 0.004
y1[1] (numeric) = -4.34635775509 7.8837222064
y1[1] (closed_form) = -3.50878981587 7.90685977348
absolute error = 0.8379
relative error = 9.686 %
Correct digits = 1
h = 0.0001 0.004
y2[1] (numeric) = -8.33082904465 -4.43568389659
y2[1] (closed_form) = -7.9596309246 -3.48552706922
absolute error = 1.02
relative error = 11.74 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=20093.1MB, alloc=44.3MB, time=263.78
x[1] = 1.1557 2.857
h = 0.003 0.006
y1[1] (numeric) = -4.36328398038 7.91756308087
y1[1] (closed_form) = -3.52196088186 7.93911155637
absolute error = 0.8416
relative error = 9.69 %
Correct digits = 1
h = 0.003 0.006
y2[1] (numeric) = -8.36761670222 -4.44490004407
y2[1] (closed_form) = -7.99167436121 -3.4987962565
absolute error = 1.018
relative error = 11.67 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.1587 2.863
h = 0.0001 0.005
y1[1] (numeric) = -4.36482261651 7.98122821793
y1[1] (closed_form) = -3.51888291395 7.99772880982
absolute error = 0.8461
relative error = 9.683 %
Correct digits = 1
h = 0.0001 0.005
y2[1] (numeric) = -8.40466613002 -4.45405757053
y2[1] (closed_form) = -8.05004602502 -3.49601370872
absolute error = 1.022
relative error = 11.64 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=20141.3MB, alloc=44.3MB, time=264.42
x[1] = 1.1588 2.868
h = 0.0001 0.003
y1[1] (numeric) = -4.38627332421 8.02379069542
y1[1] (closed_form) = -3.53559801023 8.03843050447
absolute error = 0.8508
relative error = 9.688 %
Correct digits = 1
h = 0.0001 0.003
y2[1] (numeric) = -8.4420163722 -4.46317560742
y2[1] (closed_form) = -8.09048906172 -3.51284807138
absolute error = 1.013
relative error = 11.49 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
x[1] = 1.1589 2.871
h = 0.001 0.001
y1[1] (numeric) = -4.39883054705 8.04961974718
y1[1] (closed_form) = -3.54534099864 8.06309048778
absolute error = 0.8536
relative error = 9.691 %
Correct digits = 1
h = 0.001 0.001
y2[1] (numeric) = -8.47951351454 -4.4723626982
y2[1] (closed_form) = -8.11499537131 -3.52266439771
absolute error = 1.017
relative error = 11.5 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=20189.7MB, alloc=44.3MB, time=265.06
x[1] = 1.1599 2.872
h = 0.001 0.003
y1[1] (numeric) = -4.39480922597 8.06259499265
y1[1] (closed_form) = -3.5407406007 8.07473169136
absolute error = 0.8542
relative error = 9.688 %
Correct digits = 1
h = 0.001 0.003
y2[1] (numeric) = -8.5170545323 -4.48155884635
y2[1] (closed_form) = -8.12660732396 -3.51813852936
absolute error = 1.04
relative error = 11.74 %
Correct digits = 1
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO POLE (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=20238.4MB, alloc=44.3MB, time=265.71
Finished!
Maximum Time Reached before Solution Completed!
diff ( y1 , x , 1 ) = neg ( y2 ) ;
diff ( y2 , x , 2 ) = diff ( y1 , x , 1 ) ;
Iterations = 754
Total Elapsed Time = 4 Minutes 25 Seconds
Expected Time Remaining = 0 Seconds
Optimized Time Remaining = 0 Seconds
Expected Total Time = 4 Minutes 25 Seconds
> quit
memory used=20240.9MB, alloc=44.3MB, time=265.74