|\^/| 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_x1 := proc(t)
> local c1,c2,c3;
> c1 := c(1.0);
> c2 := c(0.0002);
> c3 := c(0.0003);
> return(c(2.0) * c1 + c(6.0) * c3 * exp(neg(c(t))));
> end;
exact_soln_x1 := proc(t)
local c1, c2, c3;
c1 := c(1.0);
c2 := c(0.0002);
c3 := c(0.0003);
return c(2.0)*c1 + c(6.0)*c3*exp(neg(c(t)))
end proc
> exact_soln_x1p := proc(t)
> local c1,c2,c3;
> c1 := c(1.0);
> c2 := c(0.0002);
> c3 := c(0.0003);
> return( c(-6.0) * c3 * exp(neg( c(t))));
> end;
exact_soln_x1p := proc(t)
local c1, c2, c3;
c1 := c(1.0);
c2 := c(0.0002);
c3 := c(0.0003);
return c(-6.0)*c3*exp(neg(c(t)))
end proc
> exact_soln_x2 := proc(t)
> local c1,c2,c3;
> c1 := c(1.0);
> c2 := c(0.0002);
> c3 := c(0.0003);
> return(c1 + c2 * exp(c(2.0) * c(t)) + c3 * exp(neg( c(t))));
> end;
exact_soln_x2 := proc(t)
local c1, c2, c3;
c1 := c(1.0);
c2 := c(0.0002);
c3 := c(0.0003);
return c1 + c2*exp(c(2.0)*c(t)) + c3*exp(neg(c(t)))
end proc
> exact_soln_x2p := proc(t)
> local c1,c2,c3;
> c1 := c(1.0);
> c2 := c(0.0002);
> c3 := c(0.0003);
> return( c(2.0) * c2 * exp(c(2.0) * c(t)) - c3 * exp(neg(c(t))));
> end;
exact_soln_x2p := proc(t)
local c1, c2, c3;
c1 := c(1.0);
c2 := c(0.0002);
c3 := c(0.0003);
return c(2.0)*c2*exp(c(2.0)*c(t)) - c3*exp(neg(c(t)))
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_t ;
> if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1
> rad_given := float_abs(array_t[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_t[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_t;
if glob_type_given_pole = 1 or glob_type_given_pole = 2 then
rad_given := float_abs(array_t[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_t[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_4D0,
> array_const_2D0,
> array_const_2,
> array_const_3D0,
#END CONST
> array_x1_init,
> array_x2_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_x1,
> array_t,
> array_x2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_m1,
> array_x1_higher,
> array_x1_higher_work,
> array_x1_higher_work2,
> array_x1_set_initial,
> array_x2_higher,
> array_x2_higher_work,
> array_x2_higher_work2,
> array_x2_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_x1[1]) < min_size) then # if number 5
> min_size := float_abs(array_x1[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 5;
> if (float_abs(array_x2[1]) < min_size) then # if number 5
> min_size := float_abs(array_x2[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_4D0,
array_const_2D0, array_const_2, array_const_3D0, array_x1_init,
array_x2_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_x1, array_t, array_x2, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_m1,
array_x1_higher, array_x1_higher_work, array_x1_higher_work2,
array_x1_set_initial, array_x2_higher, array_x2_higher_work,
array_x2_higher_work2, array_x2_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_x1[1]) < min_size then
min_size := float_abs(array_x1[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if float_abs(array_x2[1]) < min_size then
min_size := float_abs(array_x2[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_4D0,
> array_const_2D0,
> array_const_2,
> array_const_3D0,
#END CONST
> array_x1_init,
> array_x2_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_x1,
> array_t,
> array_x2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_m1,
> array_x1_higher,
> array_x1_higher_work,
> array_x1_higher_work2,
> array_x1_set_initial,
> array_x2_higher,
> array_x2_higher_work,
> array_x2_higher_work2,
> array_x2_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_x1[no_terms-3] + array_x1[no_terms - 2] * hn_div_ho + array_x1[no_terms - 1] * hn_div_ho_2 + array_x1[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_x2[no_terms-3] + array_x2[no_terms - 2] * hn_div_ho + array_x2[no_terms - 1] * hn_div_ho_2 + array_x2[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_4D0,
array_const_2D0, array_const_2, array_const_3D0, array_x1_init,
array_x2_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_x1, array_t, array_x2, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_m1,
array_x1_higher, array_x1_higher_work, array_x1_higher_work2,
array_x1_set_initial, array_x2_higher, array_x2_higher_work,
array_x2_higher_work2, array_x2_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_x1[no_terms - 3]
+ array_x1[no_terms - 2]*hn_div_ho
+ array_x1[no_terms - 1]*hn_div_ho_2
+ array_x1[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_x2[no_terms - 3]
+ array_x2[no_terms - 2]*hn_div_ho
+ array_x2[no_terms - 1]*hn_div_ho_2
+ array_x2[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_4D0,
> array_const_2D0,
> array_const_2,
> array_const_3D0,
#END CONST
> array_x1_init,
> array_x2_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_x1,
> array_t,
> array_x2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_m1,
> array_x1_higher,
> array_x1_higher_work,
> array_x1_higher_work2,
> array_x1_set_initial,
> array_x2_higher,
> array_x2_higher_work,
> array_x2_higher_work2,
> array_x2_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_x1[no_terms-3])) + c(float_abs(array_x1[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_x1[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_x1[no_terms])) * c(hn_div_ho_3);
> if (glob_prec * c(float_abs(array_x1[1])) > c(est_tmp)) then # if number 5
> est_tmp := c(glob_prec) * c(float_abs(array_x1[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_x2[no_terms-3])) + c(float_abs(array_x2[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_x2[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_x2[no_terms])) * c(hn_div_ho_3);
> if (glob_prec * c(float_abs(array_x2[1])) > c(est_tmp)) then # if number 5
> est_tmp := c(glob_prec) * c(float_abs(array_x2[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_4D0,
array_const_2D0, array_const_2, array_const_3D0, array_x1_init,
array_x2_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_x1, array_t, array_x2, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_m1,
array_x1_higher, array_x1_higher_work, array_x1_higher_work2,
array_x1_set_initial, array_x2_higher, array_x2_higher_work,
array_x2_higher_work2, array_x2_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_x1[no_terms - 3]))
+ c(float_abs(array_x1[no_terms - 2]))*c(hn_div_ho)
+ c(float_abs(array_x1[no_terms - 1]))*c(hn_div_ho_2)
+ c(float_abs(array_x1[no_terms]))*c(hn_div_ho_3);
if c(est_tmp) < glob_prec*c(float_abs(array_x1[1])) then
est_tmp := c(glob_prec)*c(float_abs(array_x1[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_x2[no_terms - 3]))
+ c(float_abs(array_x2[no_terms - 2]))*c(hn_div_ho)
+ c(float_abs(array_x2[no_terms - 1]))*c(hn_div_ho_2)
+ c(float_abs(array_x2[no_terms]))*c(hn_div_ho_3);
if c(est_tmp) < glob_prec*c(float_abs(array_x2[1])) then
est_tmp := c(glob_prec)*c(float_abs(array_x2[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_4D0,
> array_const_2D0,
> array_const_2,
> array_const_3D0,
#END CONST
> array_x1_init,
> array_x2_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_x1,
> array_t,
> array_x2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_m1,
> array_x1_higher,
> array_x1_higher_work,
> array_x1_higher_work2,
> array_x1_set_initial,
> array_x2_higher,
> array_x2_higher_work,
> array_x2_higher_work2,
> array_x2_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_t[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_4D0,
array_const_2D0, array_const_2, array_const_3D0, array_x1_init,
array_x2_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_x1, array_t, array_x2, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_m1,
array_x1_higher, array_x1_higher_work, array_x1_higher_work2,
array_x1_set_initial, array_x2_higher, array_x2_higher_work,
array_x2_higher_work2, array_x2_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_t[1] then ret := true
else ret := false
end if;
return ret
end proc
# End Function number 7
# Begin Function number 8
> display_alot := proc(iter)
> global
> 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_4D0,
> array_const_2D0,
> array_const_2,
> array_const_3D0,
#END CONST
> array_x1_init,
> array_x2_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_x1,
> array_t,
> array_x2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_m1,
> array_x1_higher,
> array_x1_higher_work,
> array_x1_higher_work2,
> array_x1_set_initial,
> array_x2_higher,
> array_x2_higher_work,
> array_x2_higher_work2,
> array_x2_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_t[1];
> omniout_complex(ALWAYS,"t[1] ",33,ind_var,20," ");
> term_no := 1;
> numeric_val := array_x1[term_no];
> omniout_complex(ALWAYS,"h ",33,glob_h,20," ");
> omniout_complex(ALWAYS,"x1[1] (numeric) ",33,numeric_val,20," ");
> closed_form_val_y := evalf(exact_soln_x1(ind_var));
> omniout_complex(ALWAYS,"x1[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_x2[term_no];
> omniout_complex(ALWAYS,"h ",33,glob_h,20," ");
> omniout_complex(ALWAYS,"x2[1] (numeric) ",33,numeric_val,20," ");
> closed_form_val_y := evalf(exact_soln_x2(ind_var));
> omniout_complex(ALWAYS,"x2[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_4D0,
array_const_2D0, array_const_2, array_const_3D0, array_x1_init,
array_x2_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_x1, array_t, array_x2, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_m1,
array_x1_higher, array_x1_higher_work, array_x1_higher_work2,
array_x1_set_initial, array_x2_higher, array_x2_higher_work,
array_x2_higher_work2, array_x2_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_t[1];
omniout_complex(ALWAYS, "t[1] ", 33,
ind_var, 20, " ");
term_no := 1;
numeric_val := array_x1[term_no];
omniout_complex(ALWAYS, "h ", 33, glob_h,
20, " ");
omniout_complex(ALWAYS, "x1[1] (numeric) ", 33,
numeric_val, 20, " ");
closed_form_val_y := evalf(exact_soln_x1(ind_var));
omniout_complex(ALWAYS, "x1[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_x2[term_no];
omniout_complex(ALWAYS, "h ", 33, glob_h,
20, " ");
omniout_complex(ALWAYS, "x2[1] (numeric) ", 33,
numeric_val, 20, " ");
closed_form_val_y := evalf(exact_soln_x2(ind_var));
omniout_complex(ALWAYS, "x2[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(t_start,t_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_4D0,
> array_const_2D0,
> array_const_2,
> array_const_3D0,
#END CONST
> array_x1_init,
> array_x2_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_x1,
> array_t,
> array_x2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_m1,
> array_x1_higher,
> array_x1_higher_work,
> array_x1_higher_work2,
> array_x1_set_initial,
> array_x2_higher,
> array_x2_higher_work,
> array_x2_higher_work2,
> array_x2_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((t_end),(t_start),(array_t[1]) + (glob_h) ,( clock_sec1) - (glob_orig_start_sec));
> opt_clock_sec := ( clock_sec1) - (glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec((t_end),(t_start),(array_t[1]) +( glob_h) ,( opt_clock_sec));
> glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
> percent_done := comp_percent((t_end),(t_start),(array_t[1]) + (glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr((total_clock_sec));
> 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(t_start, t_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_4D0,
array_const_2D0, array_const_2, array_const_3D0, array_x1_init,
array_x2_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_x1, array_t, array_x2, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_m1,
array_x1_higher, array_x1_higher_work, array_x1_higher_work2,
array_x1_set_initial, array_x2_higher, array_x2_higher_work,
array_x2_higher_work2, array_x2_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(t_end, t_start, array_t[1] + glob_h,
clock_sec1 - glob_orig_start_sec);
opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec;
glob_optimal_expect_sec :=
comp_expect_sec(t_end, t_start, array_t[1] + glob_h, opt_clock_sec)
;
glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
percent_done := comp_percent(t_end, t_start, array_t[1] + glob_h);
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(total_clock_sec);
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_4D0,
> array_const_2D0,
> array_const_2,
> array_const_3D0,
#END CONST
> array_x1_init,
> array_x2_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_x1,
> array_t,
> array_x2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_m1,
> array_x1_higher,
> array_x1_higher_work,
> array_x1_higher_work2,
> array_x1_set_initial,
> array_x2_higher,
> array_x2_higher_work,
> array_x2_higher_work2,
> array_x2_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_x1_higher[1,last_no-1],array_x1_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_x1_higher[1,last_no-1],array_x1_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_x2_higher[1,last_no-1],array_x2_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_x2_higher[1,last_no-1],array_x2_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_x1_higher[1,last_no-2],array_x1_higher[1,last_no-1],array_x1_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_x1_higher[1,last_no-2],array_x1_higher[1,last_no-1],array_x1_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_x2_higher[1,last_no-2],array_x2_higher[1,last_no-1],array_x2_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_x2_higher[1,last_no-2],array_x2_higher[1,last_no-1],array_x2_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_x1_higher[1,last_no-5],array_x1_higher[1,last_no-4],array_x1_higher[1,last_no-3],array_x1_higher[1,last_no-2],array_x1_higher[1,last_no-1],array_x1_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_x1_higher[1,last_no-5],array_x1_higher[1,last_no-4],array_x1_higher[1,last_no-3],array_x1_higher[1,last_no-2],array_x1_higher[1,last_no-1],array_x1_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_x2_higher[1,last_no-5],array_x2_higher[1,last_no-4],array_x2_higher[1,last_no-3],array_x2_higher[1,last_no-2],array_x2_higher[1,last_no-1],array_x2_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_x2_higher[1,last_no-5],array_x2_higher[1,last_no-4],array_x2_higher[1,last_no-3],array_x2_higher[1,last_no-2],array_x2_higher[1,last_no-1],array_x2_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_4D0,
array_const_2D0, array_const_2, array_const_3D0, array_x1_init,
array_x2_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_x1, array_t, array_x2, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_m1,
array_x1_higher, array_x1_higher_work, array_x1_higher_work2,
array_x1_set_initial, array_x2_higher, array_x2_higher_work,
array_x2_higher_work2, array_x2_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_x1_higher[1, last_no - 1],
array_x1_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_x1_higher[1, last_no - 1],
array_x1_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_x2_higher[1, last_no - 1],
array_x2_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_x2_higher[1, last_no - 1],
array_x2_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_x1_higher[1, last_no - 2],
array_x1_higher[1, last_no - 1], array_x1_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_x1_higher[1, last_no - 2],
array_x1_higher[1, last_no - 1],
array_x1_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_x2_higher[1, last_no - 2],
array_x2_higher[1, last_no - 1], array_x2_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_x2_higher[1, last_no - 2],
array_x2_higher[1, last_no - 1],
array_x2_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_x1_higher[1, last_no - 5],
array_x1_higher[1, last_no - 4],
array_x1_higher[1, last_no - 3],
array_x1_higher[1, last_no - 2],
array_x1_higher[1, last_no - 1], array_x1_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_x1_higher[1, last_no - 5],
array_x1_higher[1, last_no - 4],
array_x1_higher[1, last_no - 3],
array_x1_higher[1, last_no - 2],
array_x1_higher[1, last_no - 1],
array_x1_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_x2_higher[1, last_no - 5],
array_x2_higher[1, last_no - 4],
array_x2_higher[1, last_no - 3],
array_x2_higher[1, last_no - 2],
array_x2_higher[1, last_no - 1], array_x2_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_x2_higher[1, last_no - 5],
array_x2_higher[1, last_no - 4],
array_x2_higher[1, last_no - 3],
array_x2_higher[1, last_no - 2],
array_x2_higher[1, last_no - 1],
array_x2_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_4D0,
> array_const_2D0,
> array_const_2,
> array_const_3D0,
#END CONST
> array_x1_init,
> array_x2_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_x1,
> array_t,
> array_x2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_m1,
> array_x1_higher,
> array_x1_higher_work,
> array_x1_higher_work2,
> array_x1_set_initial,
> array_x2_higher,
> array_x2_higher_work,
> array_x2_higher_work2,
> array_x2_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> # before write maple main top matter
> # before generate constants assign
> # before generate globals assign
> #END OUTFILE1
> #BEGIN OUTFILE2
> #END OUTFILE2
> #BEGIN ATOMHDR1
> #emit pre mult CONST FULL $eq_no = 1 i = 1
> array_tmp1[1] := array_const_4D0[1] * array_x2[1];
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
> #emit pre diff $eq_no = 1 i = 1 order_d = 1
> array_tmp3[1] := array_x2_higher[2,1];
> #emit pre mult CONST FULL $eq_no = 1 i = 1
> array_tmp4[1] := array_const_2D0[1] * array_tmp3[1];
> #emit pre sub FULL FULL $eq_no = 1 i = 1
> array_tmp5[1] := array_tmp2[1] - array_tmp4[1];
> #emit pre mult CONST FULL $eq_no = 1 i = 1
> array_tmp6[1] := array_const_2D0[1] * array_x1[1];
> #emit pre sub FULL FULL $eq_no = 1 i = 1
> array_tmp7[1] := array_tmp5[1] - array_tmp6[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_x1_set_initial[1,2]) then # if number 1
> if (1 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp7[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
> if (2 <= ATS_MAX_TERMS) then # if number 3
> array_x1[2] := temporary;
> array_x1_higher[1,2] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(1);
> array_x1_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_tmp9[1] := array_x2_higher[2,1];
> #emit pre mult CONST FULL $eq_no = 2 i = 1
> array_tmp10[1] := array_const_3D0[1] * array_tmp9[1];
> #emit pre mult CONST FULL $eq_no = 2 i = 1
> array_tmp11[1] := array_const_2D0[1] * array_x2[1];
> #emit pre sub FULL FULL $eq_no = 2 i = 1
> array_tmp12[1] := array_tmp10[1] - array_tmp11[1];
> #emit pre diff $eq_no = 2 i = 1 order_d = 2
> array_tmp13[1] := array_x1_higher[3,1];
> #emit pre sub FULL FULL $eq_no = 2 i = 1
> array_tmp14[1] := array_tmp12[1] - array_tmp13[1];
> #emit pre diff $eq_no = 2 i = 1 order_d = 1
> array_tmp15[1] := array_x1_higher[2,1];
> #emit pre sub FULL FULL $eq_no = 2 i = 1
> array_tmp16[1] := array_tmp14[1] - array_tmp15[1];
> #emit pre add FULL FULL $eq_no = 2 i = 1
> array_tmp17[1] := array_tmp16[1] + array_x1[1];
> #emit pre assign xxx $eq_no = 2 i = 1 $min_hdrs = 5
> if ( not array_x2_set_initial[2,3]) then # if number 1
> if (1 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp17[1]) * (expt((glob_h) , c(2))) * c(factorial_3(0,2));
> if (3 <= ATS_MAX_TERMS) then # if number 3
> array_x2[3] := temporary;
> array_x2_higher[1,3] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(2);
> array_x2_higher[2,2] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(1);
> array_x2_higher[3,1] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre mult CONST FULL $eq_no = 1 i = 2
> array_tmp1[2] := array_const_4D0[1] * array_x2[2];
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre diff $eq_no = 1 i = 2 order_d = 1
> array_tmp3[2] := array_x2_higher[2,2];
> #emit pre mult CONST FULL $eq_no = 1 i = 2
> array_tmp4[2] := array_const_2D0[1] * array_tmp3[2];
> #emit pre sub FULL FULL $eq_no = 1 i = 2
> array_tmp5[2] := array_tmp2[2] - array_tmp4[2];
> #emit pre mult CONST FULL $eq_no = 1 i = 2
> array_tmp6[2] := array_const_2D0[1] * array_x1[2];
> #emit pre sub FULL FULL $eq_no = 1 i = 2
> array_tmp7[2] := array_tmp5[2] - array_tmp6[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_x1_set_initial[1,3]) then # if number 1
> if (2 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp7[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2));
> if (3 <= ATS_MAX_TERMS) then # if number 3
> array_x1[3] := temporary;
> array_x1_higher[1,3] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(2);
> array_x1_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_tmp9[2] := array_x2_higher[2,2];
> #emit pre mult CONST FULL $eq_no = 2 i = 2
> array_tmp10[2] := array_const_3D0[1] * array_tmp9[2];
> #emit pre mult CONST FULL $eq_no = 2 i = 2
> array_tmp11[2] := array_const_2D0[1] * array_x2[2];
> #emit pre sub FULL FULL $eq_no = 2 i = 2
> array_tmp12[2] := array_tmp10[2] - array_tmp11[2];
> #emit pre diff $eq_no = 2 i = 2 order_d = 2
> array_tmp13[2] := array_x1_higher[3,2];
> #emit pre sub FULL FULL $eq_no = 2 i = 2
> array_tmp14[2] := array_tmp12[2] - array_tmp13[2];
> #emit pre diff $eq_no = 2 i = 2 order_d = 1
> array_tmp15[2] := array_x1_higher[2,2];
> #emit pre sub FULL FULL $eq_no = 2 i = 2
> array_tmp16[2] := array_tmp14[2] - array_tmp15[2];
> #emit pre add FULL FULL $eq_no = 2 i = 2
> array_tmp17[2] := array_tmp16[2] + array_x1[2];
> #emit pre assign xxx $eq_no = 2 i = 2 $min_hdrs = 5
> if ( not array_x2_set_initial[2,4]) then # if number 1
> if (2 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp17[2]) * (expt((glob_h) , c(2))) * c(factorial_3(1,3));
> if (4 <= ATS_MAX_TERMS) then # if number 3
> array_x2[4] := temporary;
> array_x2_higher[1,4] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(3);
> array_x2_higher[2,3] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(2);
> array_x2_higher[3,2] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre mult CONST FULL $eq_no = 1 i = 3
> array_tmp1[3] := array_const_4D0[1] * array_x2[3];
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp2[3] := array_tmp1[3];
> #emit pre diff $eq_no = 1 i = 3 order_d = 1
> array_tmp3[3] := array_x2_higher[2,3];
> #emit pre mult CONST FULL $eq_no = 1 i = 3
> array_tmp4[3] := array_const_2D0[1] * array_tmp3[3];
> #emit pre sub FULL FULL $eq_no = 1 i = 3
> array_tmp5[3] := array_tmp2[3] - array_tmp4[3];
> #emit pre mult CONST FULL $eq_no = 1 i = 3
> array_tmp6[3] := array_const_2D0[1] * array_x1[3];
> #emit pre sub FULL FULL $eq_no = 1 i = 3
> array_tmp7[3] := array_tmp5[3] - array_tmp6[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_x1_set_initial[1,4]) then # if number 1
> if (3 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp7[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3));
> if (4 <= ATS_MAX_TERMS) then # if number 3
> array_x1[4] := temporary;
> array_x1_higher[1,4] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(3);
> array_x1_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_tmp9[3] := array_x2_higher[2,3];
> #emit pre mult CONST FULL $eq_no = 2 i = 3
> array_tmp10[3] := array_const_3D0[1] * array_tmp9[3];
> #emit pre mult CONST FULL $eq_no = 2 i = 3
> array_tmp11[3] := array_const_2D0[1] * array_x2[3];
> #emit pre sub FULL FULL $eq_no = 2 i = 3
> array_tmp12[3] := array_tmp10[3] - array_tmp11[3];
> #emit pre diff $eq_no = 2 i = 3 order_d = 2
> array_tmp13[3] := array_x1_higher[3,3];
> #emit pre sub FULL FULL $eq_no = 2 i = 3
> array_tmp14[3] := array_tmp12[3] - array_tmp13[3];
> #emit pre diff $eq_no = 2 i = 3 order_d = 1
> array_tmp15[3] := array_x1_higher[2,3];
> #emit pre sub FULL FULL $eq_no = 2 i = 3
> array_tmp16[3] := array_tmp14[3] - array_tmp15[3];
> #emit pre add FULL FULL $eq_no = 2 i = 3
> array_tmp17[3] := array_tmp16[3] + array_x1[3];
> #emit pre assign xxx $eq_no = 2 i = 3 $min_hdrs = 5
> if ( not array_x2_set_initial[2,5]) then # if number 1
> if (3 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp17[3]) * (expt((glob_h) , c(2))) * c(factorial_3(2,4));
> if (5 <= ATS_MAX_TERMS) then # if number 3
> array_x2[5] := temporary;
> array_x2_higher[1,5] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(4);
> array_x2_higher[2,4] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(3);
> array_x2_higher[3,3] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre mult CONST FULL $eq_no = 1 i = 4
> array_tmp1[4] := array_const_4D0[1] * array_x2[4];
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp2[4] := array_tmp1[4];
> #emit pre diff $eq_no = 1 i = 4 order_d = 1
> array_tmp3[4] := array_x2_higher[2,4];
> #emit pre mult CONST FULL $eq_no = 1 i = 4
> array_tmp4[4] := array_const_2D0[1] * array_tmp3[4];
> #emit pre sub FULL FULL $eq_no = 1 i = 4
> array_tmp5[4] := array_tmp2[4] - array_tmp4[4];
> #emit pre mult CONST FULL $eq_no = 1 i = 4
> array_tmp6[4] := array_const_2D0[1] * array_x1[4];
> #emit pre sub FULL FULL $eq_no = 1 i = 4
> array_tmp7[4] := array_tmp5[4] - array_tmp6[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_x1_set_initial[1,5]) then # if number 1
> if (4 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp7[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4));
> if (5 <= ATS_MAX_TERMS) then # if number 3
> array_x1[5] := temporary;
> array_x1_higher[1,5] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(4);
> array_x1_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_tmp9[4] := array_x2_higher[2,4];
> #emit pre mult CONST FULL $eq_no = 2 i = 4
> array_tmp10[4] := array_const_3D0[1] * array_tmp9[4];
> #emit pre mult CONST FULL $eq_no = 2 i = 4
> array_tmp11[4] := array_const_2D0[1] * array_x2[4];
> #emit pre sub FULL FULL $eq_no = 2 i = 4
> array_tmp12[4] := array_tmp10[4] - array_tmp11[4];
> #emit pre diff $eq_no = 2 i = 4 order_d = 2
> array_tmp13[4] := array_x1_higher[3,4];
> #emit pre sub FULL FULL $eq_no = 2 i = 4
> array_tmp14[4] := array_tmp12[4] - array_tmp13[4];
> #emit pre diff $eq_no = 2 i = 4 order_d = 1
> array_tmp15[4] := array_x1_higher[2,4];
> #emit pre sub FULL FULL $eq_no = 2 i = 4
> array_tmp16[4] := array_tmp14[4] - array_tmp15[4];
> #emit pre add FULL FULL $eq_no = 2 i = 4
> array_tmp17[4] := array_tmp16[4] + array_x1[4];
> #emit pre assign xxx $eq_no = 2 i = 4 $min_hdrs = 5
> if ( not array_x2_set_initial[2,6]) then # if number 1
> if (4 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp17[4]) * (expt((glob_h) , c(2))) * c(factorial_3(3,5));
> if (6 <= ATS_MAX_TERMS) then # if number 3
> array_x2[6] := temporary;
> array_x2_higher[1,6] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(5);
> array_x2_higher[2,5] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(4);
> array_x2_higher[3,4] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre mult CONST FULL $eq_no = 1 i = 5
> array_tmp1[5] := array_const_4D0[1] * array_x2[5];
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp2[5] := array_tmp1[5];
> #emit pre diff $eq_no = 1 i = 5 order_d = 1
> array_tmp3[5] := array_x2_higher[2,5];
> #emit pre mult CONST FULL $eq_no = 1 i = 5
> array_tmp4[5] := array_const_2D0[1] * array_tmp3[5];
> #emit pre sub FULL FULL $eq_no = 1 i = 5
> array_tmp5[5] := array_tmp2[5] - array_tmp4[5];
> #emit pre mult CONST FULL $eq_no = 1 i = 5
> array_tmp6[5] := array_const_2D0[1] * array_x1[5];
> #emit pre sub FULL FULL $eq_no = 1 i = 5
> array_tmp7[5] := array_tmp5[5] - array_tmp6[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_x1_set_initial[1,6]) then # if number 1
> if (5 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp7[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5));
> if (6 <= ATS_MAX_TERMS) then # if number 3
> array_x1[6] := temporary;
> array_x1_higher[1,6] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(5);
> array_x1_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_tmp9[5] := array_x2_higher[2,5];
> #emit pre mult CONST FULL $eq_no = 2 i = 5
> array_tmp10[5] := array_const_3D0[1] * array_tmp9[5];
> #emit pre mult CONST FULL $eq_no = 2 i = 5
> array_tmp11[5] := array_const_2D0[1] * array_x2[5];
> #emit pre sub FULL FULL $eq_no = 2 i = 5
> array_tmp12[5] := array_tmp10[5] - array_tmp11[5];
> #emit pre diff $eq_no = 2 i = 5 order_d = 2
> array_tmp13[5] := array_x1_higher[3,5];
> #emit pre sub FULL FULL $eq_no = 2 i = 5
> array_tmp14[5] := array_tmp12[5] - array_tmp13[5];
> #emit pre diff $eq_no = 2 i = 5 order_d = 1
> array_tmp15[5] := array_x1_higher[2,5];
> #emit pre sub FULL FULL $eq_no = 2 i = 5
> array_tmp16[5] := array_tmp14[5] - array_tmp15[5];
> #emit pre add FULL FULL $eq_no = 2 i = 5
> array_tmp17[5] := array_tmp16[5] + array_x1[5];
> #emit pre assign xxx $eq_no = 2 i = 5 $min_hdrs = 5
> if ( not array_x2_set_initial[2,7]) then # if number 1
> if (5 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp17[5]) * (expt((glob_h) , c(2))) * c(factorial_3(4,6));
> if (7 <= ATS_MAX_TERMS) then # if number 3
> array_x2[7] := temporary;
> array_x2_higher[1,7] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(6);
> array_x2_higher[2,6] := c(temporary);
> temporary := c(temporary) / c(glob_h) * c(5);
> array_x2_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 mult CONST FULL $eq_no = 1 i = 1
> array_tmp1[kkk] := array_const_4D0[1] * array_x2[kkk];
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp2[kkk] := array_tmp1[kkk];
> #emit diff $eq_no = 1
> if (kkk <= ATS_MAX_TERMS) then # if number 1
> array_tmp3[kkk] := array_x2_higher[2,kkk];
> fi;# end if 1;
> #emit mult CONST FULL $eq_no = 1 i = 1
> array_tmp4[kkk] := array_const_2D0[1] * array_tmp3[kkk];
> #emit FULL - FULL sub $eq_no = 1
> array_tmp5[kkk] := array_tmp2[kkk] - array_tmp4[kkk];
> #emit mult CONST FULL $eq_no = 1 i = 1
> array_tmp6[kkk] := array_const_2D0[1] * array_x1[kkk];
> #emit FULL - FULL sub $eq_no = 1
> array_tmp7[kkk] := array_tmp5[kkk] - array_tmp6[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1
> if ( not array_x1_set_initial[1,kkk + order_d]) then # if number 2
> temporary := c(array_tmp7[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
> array_x1[kkk + order_d] := c(temporary);
> array_x1_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_x1_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_tmp9[kkk] := array_x2_higher[2,kkk];
> fi;# end if 1;
> #emit mult CONST FULL $eq_no = 2 i = 1
> array_tmp10[kkk] := array_const_3D0[1] * array_tmp9[kkk];
> #emit mult CONST FULL $eq_no = 2 i = 1
> array_tmp11[kkk] := array_const_2D0[1] * array_x2[kkk];
> #emit FULL - FULL sub $eq_no = 2
> array_tmp12[kkk] := array_tmp10[kkk] - array_tmp11[kkk];
> #emit diff $eq_no = 2
> if (kkk <= ATS_MAX_TERMS) then # if number 1
> array_tmp13[kkk] := array_x1_higher[3,kkk];
> fi;# end if 1;
> #emit FULL - FULL sub $eq_no = 2
> array_tmp14[kkk] := array_tmp12[kkk] - array_tmp13[kkk];
> #emit diff $eq_no = 2
> if (kkk <= ATS_MAX_TERMS) then # if number 1
> array_tmp15[kkk] := array_x1_higher[2,kkk];
> fi;# end if 1;
> #emit FULL - FULL sub $eq_no = 2
> array_tmp16[kkk] := array_tmp14[kkk] - array_tmp15[kkk];
> #emit FULL - FULL add $eq_no = 2
> array_tmp17[kkk] := array_tmp16[kkk] + array_x1[kkk];
> #emit assign $eq_no = 2
> order_d := 2;
> if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1
> if ( not array_x2_set_initial[2,kkk + order_d]) then # if number 2
> temporary := c(array_tmp17[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
> array_x2[kkk + order_d] := c(temporary);
> array_x2_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_x2_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_4D0,
array_const_2D0, array_const_2, array_const_3D0, array_x1_init,
array_x2_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_x1, array_t, array_x2, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_m1,
array_x1_higher, array_x1_higher_work, array_x1_higher_work2,
array_x1_set_initial, array_x2_higher, array_x2_higher_work,
array_x2_higher_work2, array_x2_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
array_tmp1[1] := array_const_4D0[1]*array_x2[1];
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
array_tmp3[1] := array_x2_higher[2, 1];
array_tmp4[1] := array_const_2D0[1]*array_tmp3[1];
array_tmp5[1] := array_tmp2[1] - array_tmp4[1];
array_tmp6[1] := array_const_2D0[1]*array_x1[1];
array_tmp7[1] := array_tmp5[1] - array_tmp6[1];
if not array_x1_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp7[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
if 2 <= ATS_MAX_TERMS then
array_x1[2] := temporary;
array_x1_higher[1, 2] := temporary
end if;
temporary := c(temporary)*c(1)/c(glob_h);
array_x1_higher[2, 1] := c(temporary)
end if
end if;
kkk := 2;
array_tmp9[1] := array_x2_higher[2, 1];
array_tmp10[1] := array_const_3D0[1]*array_tmp9[1];
array_tmp11[1] := array_const_2D0[1]*array_x2[1];
array_tmp12[1] := array_tmp10[1] - array_tmp11[1];
array_tmp13[1] := array_x1_higher[3, 1];
array_tmp14[1] := array_tmp12[1] - array_tmp13[1];
array_tmp15[1] := array_x1_higher[2, 1];
array_tmp16[1] := array_tmp14[1] - array_tmp15[1];
array_tmp17[1] := array_tmp16[1] + array_x1[1];
if not array_x2_set_initial[2, 3] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp17[1])*expt(glob_h, c(2))*c(factorial_3(0, 2));
if 3 <= ATS_MAX_TERMS then
array_x2[3] := temporary;
array_x2_higher[1, 3] := temporary
end if;
temporary := c(temporary)*c(2)/c(glob_h);
array_x2_higher[2, 2] := c(temporary);
temporary := c(temporary)*c(1)/c(glob_h);
array_x2_higher[3, 1] := c(temporary)
end if
end if;
kkk := 2;
array_tmp1[2] := array_const_4D0[1]*array_x2[2];
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := array_x2_higher[2, 2];
array_tmp4[2] := array_const_2D0[1]*array_tmp3[2];
array_tmp5[2] := array_tmp2[2] - array_tmp4[2];
array_tmp6[2] := array_const_2D0[1]*array_x1[2];
array_tmp7[2] := array_tmp5[2] - array_tmp6[2];
if not array_x1_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp7[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
if 3 <= ATS_MAX_TERMS then
array_x1[3] := temporary;
array_x1_higher[1, 3] := temporary
end if;
temporary := c(temporary)*c(2)/c(glob_h);
array_x1_higher[2, 2] := c(temporary)
end if
end if;
kkk := 3;
array_tmp9[2] := array_x2_higher[2, 2];
array_tmp10[2] := array_const_3D0[1]*array_tmp9[2];
array_tmp11[2] := array_const_2D0[1]*array_x2[2];
array_tmp12[2] := array_tmp10[2] - array_tmp11[2];
array_tmp13[2] := array_x1_higher[3, 2];
array_tmp14[2] := array_tmp12[2] - array_tmp13[2];
array_tmp15[2] := array_x1_higher[2, 2];
array_tmp16[2] := array_tmp14[2] - array_tmp15[2];
array_tmp17[2] := array_tmp16[2] + array_x1[2];
if not array_x2_set_initial[2, 4] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp17[2])*expt(glob_h, c(2))*c(factorial_3(1, 3));
if 4 <= ATS_MAX_TERMS then
array_x2[4] := temporary;
array_x2_higher[1, 4] := temporary
end if;
temporary := c(temporary)*c(3)/c(glob_h);
array_x2_higher[2, 3] := c(temporary);
temporary := c(temporary)*c(2)/c(glob_h);
array_x2_higher[3, 2] := c(temporary)
end if
end if;
kkk := 3;
array_tmp1[3] := array_const_4D0[1]*array_x2[3];
array_tmp2[3] := array_tmp1[3];
array_tmp3[3] := array_x2_higher[2, 3];
array_tmp4[3] := array_const_2D0[1]*array_tmp3[3];
array_tmp5[3] := array_tmp2[3] - array_tmp4[3];
array_tmp6[3] := array_const_2D0[1]*array_x1[3];
array_tmp7[3] := array_tmp5[3] - array_tmp6[3];
if not array_x1_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp7[3])*expt(glob_h, c(1))*c(factorial_3(2, 3));
if 4 <= ATS_MAX_TERMS then
array_x1[4] := temporary;
array_x1_higher[1, 4] := temporary
end if;
temporary := c(temporary)*c(3)/c(glob_h);
array_x1_higher[2, 3] := c(temporary)
end if
end if;
kkk := 4;
array_tmp9[3] := array_x2_higher[2, 3];
array_tmp10[3] := array_const_3D0[1]*array_tmp9[3];
array_tmp11[3] := array_const_2D0[1]*array_x2[3];
array_tmp12[3] := array_tmp10[3] - array_tmp11[3];
array_tmp13[3] := array_x1_higher[3, 3];
array_tmp14[3] := array_tmp12[3] - array_tmp13[3];
array_tmp15[3] := array_x1_higher[2, 3];
array_tmp16[3] := array_tmp14[3] - array_tmp15[3];
array_tmp17[3] := array_tmp16[3] + array_x1[3];
if not array_x2_set_initial[2, 5] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp17[3])*expt(glob_h, c(2))*c(factorial_3(2, 4));
if 5 <= ATS_MAX_TERMS then
array_x2[5] := temporary;
array_x2_higher[1, 5] := temporary
end if;
temporary := c(temporary)*c(4)/c(glob_h);
array_x2_higher[2, 4] := c(temporary);
temporary := c(temporary)*c(3)/c(glob_h);
array_x2_higher[3, 3] := c(temporary)
end if
end if;
kkk := 4;
array_tmp1[4] := array_const_4D0[1]*array_x2[4];
array_tmp2[4] := array_tmp1[4];
array_tmp3[4] := array_x2_higher[2, 4];
array_tmp4[4] := array_const_2D0[1]*array_tmp3[4];
array_tmp5[4] := array_tmp2[4] - array_tmp4[4];
array_tmp6[4] := array_const_2D0[1]*array_x1[4];
array_tmp7[4] := array_tmp5[4] - array_tmp6[4];
if not array_x1_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp7[4])*expt(glob_h, c(1))*c(factorial_3(3, 4));
if 5 <= ATS_MAX_TERMS then
array_x1[5] := temporary;
array_x1_higher[1, 5] := temporary
end if;
temporary := c(temporary)*c(4)/c(glob_h);
array_x1_higher[2, 4] := c(temporary)
end if
end if;
kkk := 5;
array_tmp9[4] := array_x2_higher[2, 4];
array_tmp10[4] := array_const_3D0[1]*array_tmp9[4];
array_tmp11[4] := array_const_2D0[1]*array_x2[4];
array_tmp12[4] := array_tmp10[4] - array_tmp11[4];
array_tmp13[4] := array_x1_higher[3, 4];
array_tmp14[4] := array_tmp12[4] - array_tmp13[4];
array_tmp15[4] := array_x1_higher[2, 4];
array_tmp16[4] := array_tmp14[4] - array_tmp15[4];
array_tmp17[4] := array_tmp16[4] + array_x1[4];
if not array_x2_set_initial[2, 6] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp17[4])*expt(glob_h, c(2))*c(factorial_3(3, 5));
if 6 <= ATS_MAX_TERMS then
array_x2[6] := temporary;
array_x2_higher[1, 6] := temporary
end if;
temporary := c(temporary)*c(5)/c(glob_h);
array_x2_higher[2, 5] := c(temporary);
temporary := c(temporary)*c(4)/c(glob_h);
array_x2_higher[3, 4] := c(temporary)
end if
end if;
kkk := 5;
array_tmp1[5] := array_const_4D0[1]*array_x2[5];
array_tmp2[5] := array_tmp1[5];
array_tmp3[5] := array_x2_higher[2, 5];
array_tmp4[5] := array_const_2D0[1]*array_tmp3[5];
array_tmp5[5] := array_tmp2[5] - array_tmp4[5];
array_tmp6[5] := array_const_2D0[1]*array_x1[5];
array_tmp7[5] := array_tmp5[5] - array_tmp6[5];
if not array_x1_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp7[5])*expt(glob_h, c(1))*c(factorial_3(4, 5));
if 6 <= ATS_MAX_TERMS then
array_x1[6] := temporary;
array_x1_higher[1, 6] := temporary
end if;
temporary := c(temporary)*c(5)/c(glob_h);
array_x1_higher[2, 5] := c(temporary)
end if
end if;
kkk := 6;
array_tmp9[5] := array_x2_higher[2, 5];
array_tmp10[5] := array_const_3D0[1]*array_tmp9[5];
array_tmp11[5] := array_const_2D0[1]*array_x2[5];
array_tmp12[5] := array_tmp10[5] - array_tmp11[5];
array_tmp13[5] := array_x1_higher[3, 5];
array_tmp14[5] := array_tmp12[5] - array_tmp13[5];
array_tmp15[5] := array_x1_higher[2, 5];
array_tmp16[5] := array_tmp14[5] - array_tmp15[5];
array_tmp17[5] := array_tmp16[5] + array_x1[5];
if not array_x2_set_initial[2, 7] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp17[5])*expt(glob_h, c(2))*c(factorial_3(4, 6));
if 7 <= ATS_MAX_TERMS then
array_x2[7] := temporary;
array_x2_higher[1, 7] := temporary
end if;
temporary := c(temporary)*c(6)/c(glob_h);
array_x2_higher[2, 6] := c(temporary);
temporary := c(temporary)*c(5)/c(glob_h);
array_x2_higher[3, 5] := c(temporary)
end if
end if;
kkk := 6;
while kkk <= ATS_MAX_TERMS do
array_tmp1[kkk] := array_const_4D0[1]*array_x2[kkk];
array_tmp2[kkk] := array_tmp1[kkk];
if kkk <= ATS_MAX_TERMS then
array_tmp3[kkk] := array_x2_higher[2, kkk]
end if;
array_tmp4[kkk] := array_const_2D0[1]*array_tmp3[kkk];
array_tmp5[kkk] := array_tmp2[kkk] - array_tmp4[kkk];
array_tmp6[kkk] := array_const_2D0[1]*array_x1[kkk];
array_tmp7[kkk] := array_tmp5[kkk] - array_tmp6[kkk];
order_d := 1;
if kkk + order_d <= ATS_MAX_TERMS then
if not array_x1_set_initial[1, kkk + order_d] then
temporary := c(array_tmp7[kkk])*expt(glob_h, c(order_d))*
c(factorial_3(kkk - 1, kkk + order_d - 1));
array_x1[kkk + order_d] := c(temporary);
array_x1_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_x1_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_tmp9[kkk] := array_x2_higher[2, kkk]
end if;
array_tmp10[kkk] := array_const_3D0[1]*array_tmp9[kkk];
array_tmp11[kkk] := array_const_2D0[1]*array_x2[kkk];
array_tmp12[kkk] := array_tmp10[kkk] - array_tmp11[kkk];
if kkk <= ATS_MAX_TERMS then
array_tmp13[kkk] := array_x1_higher[3, kkk]
end if;
array_tmp14[kkk] := array_tmp12[kkk] - array_tmp13[kkk];
if kkk <= ATS_MAX_TERMS then
array_tmp15[kkk] := array_x1_higher[2, kkk]
end if;
array_tmp16[kkk] := array_tmp14[kkk] - array_tmp15[kkk];
array_tmp17[kkk] := array_tmp16[kkk] + array_x1[kkk];
order_d := 2;
if kkk + order_d <= ATS_MAX_TERMS then
if not array_x2_set_initial[2, kkk + order_d] then
temporary := c(array_tmp17[kkk])*expt(glob_h, c(order_d))*
c(factorial_3(kkk - 1, kkk + order_d - 1));
array_x2[kkk + order_d] := c(temporary);
array_x2_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_x2_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,
> t_start,t_end
> ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it;
> global
> 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_4D0,
> array_const_2D0,
> array_const_2,
> array_const_3D0,
> #END CONST
> array_x1_init,
> array_x2_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_x1,
> array_t,
> array_x2,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_tmp10,
> array_tmp11,
> array_tmp12,
> array_tmp13,
> array_tmp14,
> array_tmp15,
> array_tmp16,
> array_tmp17,
> array_m1,
> array_x1_higher,
> array_x1_higher_work,
> array_x1_higher_work2,
> array_x1_set_initial,
> array_x2_higher,
> array_x2_higher_work,
> array_x2_higher_work2,
> array_x2_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> ATS_MAX_TERMS := 40;
> # before first input block
> #BEGIN FIRST INPUT BLOCK
> #BEGIN BLOCK 1
> #BEGIN FIRST INPUT BLOCK
> Digits:=64;
> max_terms:=40;
> #END BLOCK 1
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> # before generate arrays
> array_x1_init:= Array(0..(40),[]);
> array_x2_init:= Array(0..(40),[]);
> array_norms:= Array(0..(40),[]);
> array_fact_1:= Array(0..(40),[]);
> array_1st_rel_error:= Array(0..(3),[]);
> array_last_rel_error:= Array(0..(3),[]);
> array_est_rel_error:= Array(0..(3),[]);
> array_max_est_error:= Array(0..(3),[]);
> array_type_pole:= Array(0..(3),[]);
> array_type_real_pole:= Array(0..(3),[]);
> array_type_complex_pole:= Array(0..(3),[]);
> array_est_digits:= Array(0..(3),[]);
> array_x1:= Array(0..(40),[]);
> array_t:= Array(0..(40),[]);
> array_x2:= Array(0..(40),[]);
> array_tmp0:= Array(0..(40),[]);
> array_tmp1:= Array(0..(40),[]);
> array_tmp2:= Array(0..(40),[]);
> array_tmp3:= Array(0..(40),[]);
> array_tmp4:= Array(0..(40),[]);
> array_tmp5:= Array(0..(40),[]);
> array_tmp6:= Array(0..(40),[]);
> array_tmp7:= Array(0..(40),[]);
> array_tmp8:= Array(0..(40),[]);
> array_tmp9:= Array(0..(40),[]);
> array_tmp10:= Array(0..(40),[]);
> array_tmp11:= Array(0..(40),[]);
> array_tmp12:= Array(0..(40),[]);
> array_tmp13:= Array(0..(40),[]);
> array_tmp14:= Array(0..(40),[]);
> array_tmp15:= Array(0..(40),[]);
> array_tmp16:= Array(0..(40),[]);
> array_tmp17:= Array(0..(40),[]);
> array_m1:= Array(0..(40),[]);
> array_x1_higher := Array(0..(3) ,(0..40+ 1),[]);
> array_x1_higher_work := Array(0..(3) ,(0..40+ 1),[]);
> array_x1_higher_work2 := Array(0..(3) ,(0..40+ 1),[]);
> array_x1_set_initial := Array(0..(3) ,(0..40+ 1),[]);
> array_x2_higher := Array(0..(3) ,(0..40+ 1),[]);
> array_x2_higher_work := Array(0..(3) ,(0..40+ 1),[]);
> array_x2_higher_work2 := Array(0..(3) ,(0..40+ 1),[]);
> array_x2_set_initial := Array(0..(3) ,(0..40+ 1),[]);
> array_given_rad_poles := Array(0..(3) ,(0..3+ 1),[]);
> array_given_ord_poles := Array(0..(3) ,(0..3+ 1),[]);
> array_rad_test_poles := Array(0..(3) ,(0..4+ 1),[]);
> array_ord_test_poles := Array(0..(3) ,(0..4+ 1),[]);
> array_fact_2 := Array(0..(40) ,(0..40+ 1),[]);
> # before generate constants
> # before generate globals definition
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> # before generate const definition
> # before arrays initialized
> term := 1;
> while (term <= 40) do # do number 1
> array_x1_init[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_x2_init[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_norms[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_fact_1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_1st_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_last_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_est_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_max_est_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_type_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_type_real_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_type_complex_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 3) do # do number 1
> array_est_digits[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_x1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_t[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_x2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp0[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp3[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp4[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp5[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp6[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp7[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp8[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp9[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp10[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp11[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp12[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp13[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp14[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp15[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp16[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp17[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_m1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_x1_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 <= 40) do # do number 2
> array_x1_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 <= 40) do # do number 2
> array_x1_higher_work2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_x1_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 <= 40) do # do number 2
> array_x2_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 <= 40) do # do number 2
> array_x2_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 <= 40) do # do number 2
> array_x2_higher_work2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_x2_set_initial[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_rad_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_ord_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_rad_test_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=3) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_ord_test_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=40) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_fact_2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> # before symbols initialized
> #BEGIN SYMBOLS INITIALIZATED
> zero_ats_ar(array_x1);
> zero_ats_ar(array_t);
> zero_ats_ar(array_x2);
> zero_ats_ar(array_tmp0);
> zero_ats_ar(array_tmp1);
> zero_ats_ar(array_tmp2);
> zero_ats_ar(array_tmp3);
> zero_ats_ar(array_tmp4);
> zero_ats_ar(array_tmp5);
> zero_ats_ar(array_tmp6);
> zero_ats_ar(array_tmp7);
> zero_ats_ar(array_tmp8);
> zero_ats_ar(array_tmp9);
> zero_ats_ar(array_tmp10);
> zero_ats_ar(array_tmp11);
> zero_ats_ar(array_tmp12);
> zero_ats_ar(array_tmp13);
> zero_ats_ar(array_tmp14);
> zero_ats_ar(array_tmp15);
> zero_ats_ar(array_tmp16);
> zero_ats_ar(array_tmp17);
> 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_4D0);
> array_const_4D0[1] := c(4.0);
> zero_ats_ar(array_const_2D0);
> array_const_2D0[1] := c(2.0);
> zero_ats_ar(array_const_2);
> array_const_2[1] := c(2);
> zero_ats_ar(array_const_3D0);
> array_const_3D0[1] := c(3.0);
> zero_ats_ar(array_m1);
> array_m1[1] := glob__m1;
> #END SYMBOLS INITIALIZATED
> # before generate factorials init
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= ATS_MAX_TERMS) do # do number 1
> jjjf := 0;
> while (jjjf <= ATS_MAX_TERMS) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Table
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> glob_yes_pole := 4;
> glob_no_pole := 3;
> glob_not_given := 0;
> glob_no_sing_tests := 4;
> glob_ratio_test := 1;
> glob_three_term_test := 2;
> glob_six_term_test := 3;
> glob_log_10 := log(c(10.0));
> MAX_UNCHANGED := 10;
> glob__small := c(0.1e-50);
> glob_small_float := c(0.1e-50);
> glob_smallish_float := c(0.1e-60);
> glob_large_float := c(1.0e100);
> glob_larger_float := c(1.1e100);
> glob__m2 := c(-2);
> glob__m1 := c(-1);
> glob__0 := c(0);
> glob__1 := c(1);
> glob__2 := c(2);
> glob__3 := c(3);
> glob__4 := c(4);
> glob__5 := c(5);
> glob__8 := c(8);
> glob__10 := c(10);
> glob__100 := c(100);
> glob__pi := c(0.0);
> glob__0_5 := c(0.5);
> glob__0_8 := c(0.8);
> glob__m0_8 := c(-0.8);
> glob__0_25 := c(0.25);
> glob__0_125 := c(0.125);
> glob_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_x1_set_initial[1,1] := true;
> array_x1_set_initial[1,2] := false;
> array_x1_set_initial[1,3] := false;
> array_x1_set_initial[1,4] := false;
> array_x1_set_initial[1,5] := false;
> array_x1_set_initial[1,6] := false;
> array_x1_set_initial[1,7] := false;
> array_x1_set_initial[1,8] := false;
> array_x1_set_initial[1,9] := false;
> array_x1_set_initial[1,10] := false;
> array_x1_set_initial[1,11] := false;
> array_x1_set_initial[1,12] := false;
> array_x1_set_initial[1,13] := false;
> array_x1_set_initial[1,14] := false;
> array_x1_set_initial[1,15] := false;
> array_x1_set_initial[1,16] := false;
> array_x1_set_initial[1,17] := false;
> array_x1_set_initial[1,18] := false;
> array_x1_set_initial[1,19] := false;
> array_x1_set_initial[1,20] := false;
> array_x1_set_initial[1,21] := false;
> array_x1_set_initial[1,22] := false;
> array_x1_set_initial[1,23] := false;
> array_x1_set_initial[1,24] := false;
> array_x1_set_initial[1,25] := false;
> array_x1_set_initial[1,26] := false;
> array_x1_set_initial[1,27] := false;
> array_x1_set_initial[1,28] := false;
> array_x1_set_initial[1,29] := false;
> array_x1_set_initial[1,30] := false;
> array_x1_set_initial[1,31] := false;
> array_x1_set_initial[1,32] := false;
> array_x1_set_initial[1,33] := false;
> array_x1_set_initial[1,34] := false;
> array_x1_set_initial[1,35] := false;
> array_x1_set_initial[1,36] := false;
> array_x1_set_initial[1,37] := false;
> array_x1_set_initial[1,38] := false;
> array_x1_set_initial[1,39] := false;
> array_x1_set_initial[1,40] := false;
> array_x2_set_initial[2,1] := true;
> array_x2_set_initial[2,2] := true;
> array_x2_set_initial[2,3] := false;
> array_x2_set_initial[2,4] := false;
> array_x2_set_initial[2,5] := false;
> array_x2_set_initial[2,6] := false;
> array_x2_set_initial[2,7] := false;
> array_x2_set_initial[2,8] := false;
> array_x2_set_initial[2,9] := false;
> array_x2_set_initial[2,10] := false;
> array_x2_set_initial[2,11] := false;
> array_x2_set_initial[2,12] := false;
> array_x2_set_initial[2,13] := false;
> array_x2_set_initial[2,14] := false;
> array_x2_set_initial[2,15] := false;
> array_x2_set_initial[2,16] := false;
> array_x2_set_initial[2,17] := false;
> array_x2_set_initial[2,18] := false;
> array_x2_set_initial[2,19] := false;
> array_x2_set_initial[2,20] := false;
> array_x2_set_initial[2,21] := false;
> array_x2_set_initial[2,22] := false;
> array_x2_set_initial[2,23] := false;
> array_x2_set_initial[2,24] := false;
> array_x2_set_initial[2,25] := false;
> array_x2_set_initial[2,26] := false;
> array_x2_set_initial[2,27] := false;
> array_x2_set_initial[2,28] := false;
> array_x2_set_initial[2,29] := false;
> array_x2_set_initial[2,30] := false;
> array_x2_set_initial[2,31] := false;
> array_x2_set_initial[2,32] := false;
> array_x2_set_initial[2,33] := false;
> array_x2_set_initial[2,34] := false;
> array_x2_set_initial[2,35] := false;
> array_x2_set_initial[2,36] := false;
> array_x2_set_initial[2,37] := false;
> array_x2_set_initial[2,38] := false;
> array_x2_set_initial[2,39] := false;
> array_x2_set_initial[2,40] := false;
> # before generate init omniout const
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> ATS_MAX_TERMS := 40;
> glob_iolevel := INFO;
> # set default block
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> glob_display_flag := true;
> glob_no_eqs := 2;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 10000;
> glob_max_hours := (0.0);
> glob_max_minutes := (15.0);
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/mtest6postcpx.cpx#################");
> omniout_str(ALWAYS,"diff ( x1 , t , 1 ) = 4.0 * x2 - 2.0 * diff ( x2 , t , 1 ) - 2.0 * x1 ; ");
> omniout_str(ALWAYS,"diff ( x2 , t , 2 ) = 3.0 * diff ( x2 , t , 1 ) - 2.0 * x2 - diff ( x1 , t , 2 ) - diff ( x1 , t , 1 ) + x1 ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=64;");
> omniout_str(ALWAYS,"max_terms:=40;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"t_start := 1.5 + 0.1 * I;");
> omniout_str(ALWAYS,"t_end := 99.0 + 99.0 * I;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_x1_init[0 + 1] := exact_soln_x1(t_start);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_x2_init[0 + 1] := exact_soln_x2(t_start);");
> omniout_str(ALWAYS,"array_x2_init[1 + 1] := exact_soln_x2p(t_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_h := c(0.0001);");
> 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 := 0;");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=8;");
> omniout_str(ALWAYS,"glob_max_minutes:=(3.0);");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"glob_max_iter:=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_x1 := proc(t)");
> omniout_str(ALWAYS,"local c1,c2,c3;");
> omniout_str(ALWAYS,"c1 := c(1.0);");
> omniout_str(ALWAYS,"c2 := c(0.0002);");
> omniout_str(ALWAYS,"c3 := c(0.0003);");
> omniout_str(ALWAYS,"return(c(2.0) * c1 + c(6.0) * c3 * exp(neg(c(t))));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_x1p := proc(t)");
> omniout_str(ALWAYS,"local c1,c2,c3;");
> omniout_str(ALWAYS,"c1 := c(1.0);");
> omniout_str(ALWAYS,"c2 := c(0.0002);");
> omniout_str(ALWAYS,"c3 := c(0.0003);");
> omniout_str(ALWAYS,"return( c(-6.0) * c3 * exp(neg( c(t))));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_x2 := proc(t)");
> omniout_str(ALWAYS,"local c1,c2,c3;");
> omniout_str(ALWAYS,"c1 := c(1.0);");
> omniout_str(ALWAYS,"c2 := c(0.0002);");
> omniout_str(ALWAYS,"c3 := c(0.0003);");
> omniout_str(ALWAYS,"return(c1 + c2 * exp(c(2.0) * c(t)) + c3 * exp(neg( c(t))));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"exact_soln_x2p := proc(t)");
> omniout_str(ALWAYS,"local c1,c2,c3;");
> omniout_str(ALWAYS,"c1 := c(1.0);");
> omniout_str(ALWAYS,"c2 := c(0.0002);");
> omniout_str(ALWAYS,"c3 := c(0.0003);");
> omniout_str(ALWAYS,"return( c(2.0) * c2 * exp(c(2.0) * c(t)) - c3 * exp(neg(c(t))));");
> omniout_str(ALWAYS,"end;");
> 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
> t_start := 1.5 + 0.1 * I;
> t_end := 99.0 + 99.0 * I;
> array_x1_init[0 + 1] := exact_soln_x1(t_start);
> array_x2_init[0 + 1] := exact_soln_x2(t_start);
> array_x2_init[1 + 1] := exact_soln_x2p(t_start);
> glob_look_poles := true;
> glob_max_h := c(0.0001);
> glob_type_given_pole := 0;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=8;
> glob_max_minutes:=(3.0);
> glob_subiter_method:=3;
> glob_max_iter:=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_x1[term] := array_x1[term]* ratio;
> array_x1_higher[1,term] := array_x1_higher[1,term]* ratio;
> array_t[term] := array_t[term]* ratio;
> array_x2[term] := array_x2[term]* ratio;
> array_x2_higher[1,term] := array_x2_higher[1,term]* ratio;
> array_t[term] := array_t[term]* ratio;
> ratio := ratio * h_new / float_abs(glob_h);
> term := term + 1;
> od;# end do number 1;
> glob_h := h_new;
> fi;# end if 17;
> #BOTTOM ADJUST ALL SERIES
> #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_t[1] := c(t_start);
> array_t[2] := c(glob_h);
> glob_next_display := c(t_start);
> glob_min_pole_est := glob_larger_float;
> glob_least_given_sing := glob_larger_float;
> glob_least_ratio_sing := glob_larger_float;
> glob_least_3_sing := glob_larger_float;
> glob_least_6_sing := glob_larger_float;
> order_diff := 2;
> #Start Series array_x1
> term_no := 1;
> while (term_no <= order_diff) do # do number 1
> array_x1[term_no] := array_x1_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_x1_higher[r_order,term_no] := array_x1_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_x2
> term_no := 1;
> while (term_no <= order_diff) do # do number 1
> array_x2[term_no] := array_x2_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_x2_higher[r_order,term_no] := array_x2_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_x1[term] := array_x1[term]* ratio;
> array_x1_higher[1,term] := array_x1_higher[1,term]* ratio;
> array_t[term] := array_t[term]* ratio;
> array_x2[term] := array_x2[term]* ratio;
> array_x2_higher[1,term] := array_x2_higher[1,term]* ratio;
> array_t[term] := array_t[term]* ratio;
> ratio := ratio * h_new / float_abs(glob_h);
> term := term + 1;
> od;# end do number 1;
> glob_h := h_new;
> fi;# end if 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_x1[term] := array_x1[term]* ratio;
> array_x1_higher[1,term] := array_x1_higher[1,term]* ratio;
> array_t[term] := array_t[term]* ratio;
> array_x2[term] := array_x2[term]* ratio;
> array_x2_higher[1,term] := array_x2_higher[1,term]* ratio;
> array_t[term] := array_t[term]* ratio;
> ratio := ratio * h_new / float_abs(glob_h);
> term := term + 1;
> od;# end do number 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_t[1] := array_t[1] + glob_h;
> array_t[2] := glob_h;
> #Jump Series array_x1;
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_x1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_x1
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_x1_higher_work[2,iii] := array_x1_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_x1
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_x1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_x1_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_x1
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_x1_higher_work[1,iii] := array_x1_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_x1
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_x1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_x1_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_x1
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_x1_higher_work[1,iii] := array_x1_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_x1
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_x1_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_x1_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_x1[term_no] := array_x1_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 3
> array_x1_higher[ord,term_no] := array_x1_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_x2;
> order_diff := 3;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =2
> #sum_and_adjust array_x2
> #BEFORE ADJUST SUBSERIES EQ =2
> ord := 3;
> calc_term := 1;
> #adjust_subseriesarray_x2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_x2_higher_work[3,iii] := array_x2_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_x2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_x2_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_x2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_x2_higher_work[2,iii] := array_x2_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_x2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_x2_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_x2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_x2_higher_work[2,iii] := array_x2_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_x2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_x2_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_x2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_x2_higher_work[1,iii] := array_x2_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_x2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_x2_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_x2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_x2_higher_work[1,iii] := array_x2_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_x2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_x2_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_x2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_x2_higher_work[1,iii] := array_x2_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_x2
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_x2_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_x2_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_x2[term_no] := array_x2_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 3
> array_x2_higher[ord,term_no] := array_x2_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 ( x1 , t , 1 ) = 4.0 * x2 - 2.0 * diff ( x2 , t , 1 ) - 2.0 * x1 ; ");
> omniout_str(INFO,"diff ( x2 , t , 2 ) = 3.0 * diff ( x2 , t , 1 ) - 2.0 * x2 - diff ( x1 , t , 2 ) - diff ( x1 , t , 1 ) + x1 ; ");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(t_start,t_end);
> if (glob_html_log) then # if number 19
> logstart(html_log_file);
> logitem_str(html_log_file,"2017-11-26T15:40:44-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"mtest6")
> ;
> logitem_str(html_log_file,"diff ( x1 , t , 1 ) = 4.0 * x2 - 2.0 * diff ( x2 , t , 1 ) - 2.0 * x1 ; ")
> ;
> logitem_complex(html_log_file,t_start)
> ;
> logitem_complex(html_log_file,t_end)
> ;
> logitem_complex(html_log_file,array_t[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,"mtest6 diffeq.mxt")
> ;
> logitem_str(html_log_file,"mtest6 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 ( x2 , t , 2 ) = 3.0 * diff ( x2 , t , 1 ) - 2.0 * x2 - diff ( x1 , t , 2 ) - diff ( x1 , t , 1 ) + x1 ; ")
> ;
> 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, t_start, t_end, it,
last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err,
estimated_step_error, min_value, est_answer, found_h, repeat_it, 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_4D0,
array_const_2D0, array_const_2, array_const_3D0, array_x1_init,
array_x2_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_x1, array_t, array_x2, array_tmp0, array_tmp1,
array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6, array_tmp7,
array_tmp8, array_tmp9, array_tmp10, array_tmp11, array_tmp12, array_tmp13,
array_tmp14, array_tmp15, array_tmp16, array_tmp17, array_m1,
array_x1_higher, array_x1_higher_work, array_x1_higher_work2,
array_x1_set_initial, array_x2_higher, array_x2_higher_work,
array_x2_higher_work2, array_x2_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
ATS_MAX_TERMS := 40;
Digits := 64;
max_terms := 40;
glob_html_log := true;
array_x1_init := Array(0 .. 40, []);
array_x2_init := Array(0 .. 40, []);
array_norms := Array(0 .. 40, []);
array_fact_1 := Array(0 .. 40, []);
array_1st_rel_error := Array(0 .. 3, []);
array_last_rel_error := Array(0 .. 3, []);
array_est_rel_error := Array(0 .. 3, []);
array_max_est_error := Array(0 .. 3, []);
array_type_pole := Array(0 .. 3, []);
array_type_real_pole := Array(0 .. 3, []);
array_type_complex_pole := Array(0 .. 3, []);
array_est_digits := Array(0 .. 3, []);
array_x1 := Array(0 .. 40, []);
array_t := Array(0 .. 40, []);
array_x2 := Array(0 .. 40, []);
array_tmp0 := Array(0 .. 40, []);
array_tmp1 := Array(0 .. 40, []);
array_tmp2 := Array(0 .. 40, []);
array_tmp3 := Array(0 .. 40, []);
array_tmp4 := Array(0 .. 40, []);
array_tmp5 := Array(0 .. 40, []);
array_tmp6 := Array(0 .. 40, []);
array_tmp7 := Array(0 .. 40, []);
array_tmp8 := Array(0 .. 40, []);
array_tmp9 := Array(0 .. 40, []);
array_tmp10 := Array(0 .. 40, []);
array_tmp11 := Array(0 .. 40, []);
array_tmp12 := Array(0 .. 40, []);
array_tmp13 := Array(0 .. 40, []);
array_tmp14 := Array(0 .. 40, []);
array_tmp15 := Array(0 .. 40, []);
array_tmp16 := Array(0 .. 40, []);
array_tmp17 := Array(0 .. 40, []);
array_m1 := Array(0 .. 40, []);
array_x1_higher := Array(0 .. 3, 0 .. 41, []);
array_x1_higher_work := Array(0 .. 3, 0 .. 41, []);
array_x1_higher_work2 := Array(0 .. 3, 0 .. 41, []);
array_x1_set_initial := Array(0 .. 3, 0 .. 41, []);
array_x2_higher := Array(0 .. 3, 0 .. 41, []);
array_x2_higher_work := Array(0 .. 3, 0 .. 41, []);
array_x2_higher_work2 := Array(0 .. 3, 0 .. 41, []);
array_x2_set_initial := Array(0 .. 3, 0 .. 41, []);
array_given_rad_poles := Array(0 .. 3, 0 .. 4, []);
array_given_ord_poles := Array(0 .. 3, 0 .. 4, []);
array_rad_test_poles := Array(0 .. 3, 0 .. 5, []);
array_ord_test_poles := Array(0 .. 3, 0 .. 5, []);
array_fact_2 := Array(0 .. 40, 0 .. 41, []);
term := 1;
while term <= 40 do array_x1_init[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 40 do array_x2_init[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 40 do array_norms[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 40 do array_fact_1[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 3 do array_1st_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 3 do
array_last_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 3 do array_est_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 3 do array_max_est_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 3 do array_type_pole[term] := 0; term := term + 1 end do;
term := 1;
while term <= 3 do array_type_real_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 3 do array_type_complex_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 3 do array_est_digits[term] := 0; term := term + 1 end do
;
term := 1;
while term <= 40 do array_x1[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_t[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_x2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp0[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp1[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp3[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp4[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp5[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp6[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp7[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp8[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp9[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp10[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 40 do array_tmp11[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 40 do array_tmp12[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 40 do array_tmp13[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 40 do array_tmp14[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 40 do array_tmp15[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 40 do array_tmp16[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 40 do array_tmp17[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 40 do array_m1[term] := c(0.); term := term + 1 end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 40 do
array_x1_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 <= 40 do
array_x1_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 <= 40 do
array_x1_higher_work2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 40 do
array_x1_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 <= 40 do
array_x2_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 <= 40 do
array_x2_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 <= 40 do
array_x2_higher_work2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 40 do
array_x2_set_initial[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 3 do
array_given_rad_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 3 do
array_given_ord_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 4 do
array_rad_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 3 do
term := 1;
while term <= 4 do
array_ord_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 40 do
term := 1;
while term <= 40 do
array_fact_2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
zero_ats_ar(array_x1);
zero_ats_ar(array_t);
zero_ats_ar(array_x2);
zero_ats_ar(array_tmp0);
zero_ats_ar(array_tmp1);
zero_ats_ar(array_tmp2);
zero_ats_ar(array_tmp3);
zero_ats_ar(array_tmp4);
zero_ats_ar(array_tmp5);
zero_ats_ar(array_tmp6);
zero_ats_ar(array_tmp7);
zero_ats_ar(array_tmp8);
zero_ats_ar(array_tmp9);
zero_ats_ar(array_tmp10);
zero_ats_ar(array_tmp11);
zero_ats_ar(array_tmp12);
zero_ats_ar(array_tmp13);
zero_ats_ar(array_tmp14);
zero_ats_ar(array_tmp15);
zero_ats_ar(array_tmp16);
zero_ats_ar(array_tmp17);
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_4D0);
array_const_4D0[1] := c(4.0);
zero_ats_ar(array_const_2D0);
array_const_2D0[1] := c(2.0);
zero_ats_ar(array_const_2);
array_const_2[1] := c(2);
zero_ats_ar(array_const_3D0);
array_const_3D0[1] := c(3.0);
zero_ats_ar(array_m1);
array_m1[1] := glob__m1;
iiif := 0;
while iiif <= ATS_MAX_TERMS do
jjjf := 0;
while jjjf <= ATS_MAX_TERMS do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
glob_yes_pole := 4;
glob_no_pole := 3;
glob_not_given := 0;
glob_no_sing_tests := 4;
glob_ratio_test := 1;
glob_three_term_test := 2;
glob_six_term_test := 3;
glob_log_10 := log(c(10.0));
MAX_UNCHANGED := 10;
glob__small := c(0.1*10^(-50));
glob_small_float := c(0.1*10^(-50));
glob_smallish_float := c(0.1*10^(-60));
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob__m2 := c(-2);
glob__m1 := c(-1);
glob__0 := c(0);
glob__1 := c(1);
glob__2 := c(2);
glob__3 := c(3);
glob__4 := c(4);
glob__5 := c(5);
glob__8 := c(8);
glob__10 := c(10);
glob__100 := c(100);
glob__pi := c(0.);
glob__0_5 := c(0.5);
glob__0_8 := c(0.8);
glob__m0_8 := c(-0.8);
glob__0_25 := c(0.25);
glob__0_125 := c(0.125);
glob_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_x1_set_initial[1, 1] := true;
array_x1_set_initial[1, 2] := false;
array_x1_set_initial[1, 3] := false;
array_x1_set_initial[1, 4] := false;
array_x1_set_initial[1, 5] := false;
array_x1_set_initial[1, 6] := false;
array_x1_set_initial[1, 7] := false;
array_x1_set_initial[1, 8] := false;
array_x1_set_initial[1, 9] := false;
array_x1_set_initial[1, 10] := false;
array_x1_set_initial[1, 11] := false;
array_x1_set_initial[1, 12] := false;
array_x1_set_initial[1, 13] := false;
array_x1_set_initial[1, 14] := false;
array_x1_set_initial[1, 15] := false;
array_x1_set_initial[1, 16] := false;
array_x1_set_initial[1, 17] := false;
array_x1_set_initial[1, 18] := false;
array_x1_set_initial[1, 19] := false;
array_x1_set_initial[1, 20] := false;
array_x1_set_initial[1, 21] := false;
array_x1_set_initial[1, 22] := false;
array_x1_set_initial[1, 23] := false;
array_x1_set_initial[1, 24] := false;
array_x1_set_initial[1, 25] := false;
array_x1_set_initial[1, 26] := false;
array_x1_set_initial[1, 27] := false;
array_x1_set_initial[1, 28] := false;
array_x1_set_initial[1, 29] := false;
array_x1_set_initial[1, 30] := false;
array_x1_set_initial[1, 31] := false;
array_x1_set_initial[1, 32] := false;
array_x1_set_initial[1, 33] := false;
array_x1_set_initial[1, 34] := false;
array_x1_set_initial[1, 35] := false;
array_x1_set_initial[1, 36] := false;
array_x1_set_initial[1, 37] := false;
array_x1_set_initial[1, 38] := false;
array_x1_set_initial[1, 39] := false;
array_x1_set_initial[1, 40] := false;
array_x2_set_initial[2, 1] := true;
array_x2_set_initial[2, 2] := true;
array_x2_set_initial[2, 3] := false;
array_x2_set_initial[2, 4] := false;
array_x2_set_initial[2, 5] := false;
array_x2_set_initial[2, 6] := false;
array_x2_set_initial[2, 7] := false;
array_x2_set_initial[2, 8] := false;
array_x2_set_initial[2, 9] := false;
array_x2_set_initial[2, 10] := false;
array_x2_set_initial[2, 11] := false;
array_x2_set_initial[2, 12] := false;
array_x2_set_initial[2, 13] := false;
array_x2_set_initial[2, 14] := false;
array_x2_set_initial[2, 15] := false;
array_x2_set_initial[2, 16] := false;
array_x2_set_initial[2, 17] := false;
array_x2_set_initial[2, 18] := false;
array_x2_set_initial[2, 19] := false;
array_x2_set_initial[2, 20] := false;
array_x2_set_initial[2, 21] := false;
array_x2_set_initial[2, 22] := false;
array_x2_set_initial[2, 23] := false;
array_x2_set_initial[2, 24] := false;
array_x2_set_initial[2, 25] := false;
array_x2_set_initial[2, 26] := false;
array_x2_set_initial[2, 27] := false;
array_x2_set_initial[2, 28] := false;
array_x2_set_initial[2, 29] := false;
array_x2_set_initial[2, 30] := false;
array_x2_set_initial[2, 31] := false;
array_x2_set_initial[2, 32] := false;
array_x2_set_initial[2, 33] := false;
array_x2_set_initial[2, 34] := false;
array_x2_set_initial[2, 35] := false;
array_x2_set_initial[2, 36] := false;
array_x2_set_initial[2, 37] := false;
array_x2_set_initial[2, 38] := false;
array_x2_set_initial[2, 39] := false;
array_x2_set_initial[2, 40] := false;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
ATS_MAX_TERMS := 40;
glob_iolevel := INFO;
glob_orig_start_sec := elapsed_time_seconds();
glob_display_flag := true;
glob_no_eqs := 2;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 10000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/mtest6postcpx.cpx#################");
omniout_str(ALWAYS, "diff ( x1 , t , 1 ) = 4.0 * x2 - 2.0 *\
diff ( x2 , t , 1 ) - 2.0 * x1 ; ");
omniout_str(ALWAYS, "diff ( x2 , t , 2 ) = 3.0 * diff ( x2 , t \
, 1 ) - 2.0 * x2 - diff ( x1 , t , 2 ) - diff ( x1 , \
t , 1 ) + x1 ; ");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=64;");
omniout_str(ALWAYS, "max_terms:=40;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "t_start := 1.5 + 0.1 * I;");
omniout_str(ALWAYS, "t_end := 99.0 + 99.0 * I;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_x1_init[0 + 1] := exact_soln_x1(t_start);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_x2_init[0 + 1] := exact_soln_x2(t_start);");
omniout_str(ALWAYS, "array_x2_init[1 + 1] := exact_soln_x2p(t_start);")
;
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_h := c(0.0001);");
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 := 0;");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=8;");
omniout_str(ALWAYS, "glob_max_minutes:=(3.0);");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "glob_max_iter:=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_x1 := proc(t)");
omniout_str(ALWAYS, "local c1,c2,c3;");
omniout_str(ALWAYS, "c1 := c(1.0);");
omniout_str(ALWAYS, "c2 := c(0.0002);");
omniout_str(ALWAYS, "c3 := c(0.0003);");
omniout_str(ALWAYS,
"return(c(2.0) * c1 + c(6.0) * c3 * exp(neg(c(t))));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_x1p := proc(t)");
omniout_str(ALWAYS, "local c1,c2,c3;");
omniout_str(ALWAYS, "c1 := c(1.0);");
omniout_str(ALWAYS, "c2 := c(0.0002);");
omniout_str(ALWAYS, "c3 := c(0.0003);");
omniout_str(ALWAYS, "return( c(-6.0) * c3 * exp(neg( c(t))));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_x2 := proc(t)");
omniout_str(ALWAYS, "local c1,c2,c3;");
omniout_str(ALWAYS, "c1 := c(1.0);");
omniout_str(ALWAYS, "c2 := c(0.0002);");
omniout_str(ALWAYS, "c3 := c(0.0003);");
omniout_str(ALWAYS,
"return(c1 + c2 * exp(c(2.0) * c(t)) + c3 * exp(neg( c(t))));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "exact_soln_x2p := proc(t)");
omniout_str(ALWAYS, "local c1,c2,c3;");
omniout_str(ALWAYS, "c1 := c(1.0);");
omniout_str(ALWAYS, "c2 := c(0.0002);");
omniout_str(ALWAYS, "c3 := c(0.0003);");
omniout_str(ALWAYS, "return( c(2.0) * c2 * exp(c(2.0) * c(t)) - c3 \
* exp(neg(c(t))));");
omniout_str(ALWAYS, "end;");
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,");
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omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 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);
t_start := 1.5 + 0.1*I;
t_end := 99.0 + 99.0*I;
array_x1_init[1] := exact_soln_x1(t_start);
array_x2_init[1] := exact_soln_x2(t_start);
array_x2_init[2] := exact_soln_x2p(t_start);
glob_look_poles := true;
glob_max_h := c(0.0001);
glob_type_given_pole := 0;
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_x1[term] := array_x1[term]*ratio;
array_x1_higher[1, term] := array_x1_higher[1, term]*ratio;
array_t[term] := array_t[term]*ratio;
array_x2[term] := array_x2[term]*ratio;
array_x2_higher[1, term] := array_x2_higher[1, term]*ratio;
array_t[term] := array_t[term]*ratio;
ratio := ratio*h_new/float_abs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
if 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_t[1] := c(t_start);
array_t[2] := c(glob_h);
glob_next_display := c(t_start);
glob_min_pole_est := glob_larger_float;
glob_least_given_sing := glob_larger_float;
glob_least_ratio_sing := glob_larger_float;
glob_least_3_sing := glob_larger_float;
glob_least_6_sing := glob_larger_float;
order_diff := 2;
term_no := 1;
while term_no <= order_diff do
array_x1[term_no] := array_x1_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_x1_higher[r_order, term_no] := array_x1_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_x2[term_no] := array_x2_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_x2_higher[r_order, term_no] := array_x2_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_x1[term] := array_x1[term]*ratio;
array_x1_higher[1, term] := array_x1_higher[1, term]*ratio;
array_t[term] := array_t[term]*ratio;
array_x2[term] := array_x2[term]*ratio;
array_x2_higher[1, term] := array_x2_higher[1, term]*ratio;
array_t[term] := array_t[term]*ratio;
ratio := ratio*h_new/float_abs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
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_x1[term] := array_x1[term]*ratio;
array_x1_higher[1, term] :=
array_x1_higher[1, term]*ratio;
array_t[term] := array_t[term]*ratio;
array_x2[term] := array_x2[term]*ratio;
array_x2_higher[1, term] :=
array_x2_higher[1, term]*ratio;
array_t[term] := array_t[term]*ratio;
ratio := ratio*h_new/float_abs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
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_t[1] := array_t[1] + glob_h;
array_t[2] := glob_h;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_x1_higher_work[2, iii] := array_x1_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_x1_higher_work[ord, iii];
iii := iii - 1
end do;
array_x1_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_x1_higher_work[1, iii] := array_x1_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_x1_higher_work[ord, iii];
iii := iii - 1
end do;
array_x1_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_x1_higher_work[1, iii] := array_x1_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_x1_higher_work[ord, iii];
iii := iii - 1
end do;
array_x1_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_x1[term_no] := array_x1_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_x1_higher[ord, term_no] :=
array_x1_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_x2_higher_work[3, iii] := array_x2_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_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_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_x2_higher_work[2, iii] := array_x2_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_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_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_x2_higher_work[2, iii] := array_x2_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_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_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_x2_higher_work[1, iii] := array_x2_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_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_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_x2_higher_work[1, iii] := array_x2_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_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_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_x2_higher_work[1, iii] := array_x2_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_x2_higher_work[ord, iii];
iii := iii - 1
end do;
array_x2_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_x2[term_no] := array_x2_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_x2_higher[ord, term_no] :=
array_x2_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 ( x1 , t , 1 ) = 4.0 * x2 - 2.0 \
* diff ( x2 , t , 1 ) - 2.0 * x1 ; ");
omniout_str(INFO, "diff ( x2 , t , 2 ) = 3.0 * diff ( x2 , \
t , 1 ) - 2.0 * x2 - diff ( x1 , t , 2 ) - diff (\
x1 , t , 1 ) + x1 ; ");
omniout_int(INFO, "Iterations ", 32, glob_iter,
4, " ");
prog_report(t_start, t_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2017-11-26T15:40:44-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"mtest6");
logitem_str(html_log_file, "diff ( x1 , t , 1 ) = 4.0 * \
x2 - 2.0 * diff ( x2 , t , 1 ) - 2.0 * x1 ;\
");
logitem_complex(html_log_file, t_start);
logitem_complex(html_log_file, t_end);
logitem_complex(html_log_file, array_t[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,
"mtest6 diffeq.mxt");
logitem_str(html_log_file, "mtest6 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 ( x2 , t , 2 ) = 3.0 * \
diff ( x2 , t , 1 ) - 2.0 * x2 - diff ( x1 , t ,\
2 ) - diff ( x1 , t , 1 ) + x1 ; ");
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
glob_desired_digits_correct := 0.;
logditto(html_log_file);
if array_est_digits[2] <> -16 then
logitem_integer(html_log_file, array_est_digits[2])
else logitem_str(html_log_file, "Unknown")
end if;
if glob_min_good_digits <> -16 then
logitem_integer(html_log_file, glob_min_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
if glob_good_digits <> -16 then
logitem_integer(html_log_file, glob_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
logditto(html_log_file);
if glob_type_given_pole = 0 then
logditto(html_log_file); logditto(html_log_file)
elif glob_type_given_pole = 4 then
logditto(html_log_file); logditto(html_log_file)
elif glob_type_given_pole = 5 then
logditto(html_log_file); logditto(html_log_file)
elif glob_type_given_pole = 3 then
logditto(html_log_file); logditto(html_log_file)
elif glob_type_given_pole = 1 then
logditto(html_log_file); logditto(html_log_file)
elif glob_type_given_pole = 2 then
logditto(html_log_file); logditto(html_log_file)
end if;
if glob_least_ratio_sing < glob_large_float then
glob_least_ratio_sing := 0; logditto(html_log_file)
else logditto(html_log_file)
end if;
if glob_least_3_sing < glob_large_float then
logditto(html_log_file)
else logditto(html_log_file)
end if;
if glob_least_6_sing < glob_large_float then
glob_least_6_sing := 0.; logditto(html_log_file)
else logditto(html_log_file)
end if;
logditto(html_log_file);
logditto(html_log_file);
if c(glob_percent_done) < glob__100 then
logditto(html_log_file); 0
else logditto(html_log_file); 0
end if;
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logditto(html_log_file);
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end if
end proc
# End Function number 12
> main();
memory used=3.7MB, alloc=40.3MB, time=0.08
##############ECHO OF PROBLEM#################
##############temp/mtest6postcpx.cpx#################
diff ( x1 , t , 1 ) = 4.0 * x2 - 2.0 * diff ( x2 , t , 1 ) - 2.0 * x1 ;
diff ( x2 , t , 2 ) = 3.0 * diff ( x2 , t , 1 ) - 2.0 * x2 - diff ( x1 , t , 2 ) - diff ( x1 , t , 1 ) + x1 ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=64;
max_terms:=40;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
t_start := 1.5 + 0.1 * I;
t_end := 99.0 + 99.0 * I;
array_x1_init[0 + 1] := exact_soln_x1(t_start);
array_x2_init[0 + 1] := exact_soln_x2(t_start);
array_x2_init[1 + 1] := exact_soln_x2p(t_start);
glob_look_poles := true;
glob_max_h := c(0.0001);
glob_type_given_pole := 0;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=8;
glob_max_minutes:=(3.0);
glob_subiter_method:=3;
glob_max_iter:=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_x1 := proc(t)
local c1,c2,c3;
c1 := c(1.0);
c2 := c(0.0002);
c3 := c(0.0003);
return(c(2.0) * c1 + c(6.0) * c3 * exp(neg(c(t))));
end;
exact_soln_x1p := proc(t)
local c1,c2,c3;
c1 := c(1.0);
c2 := c(0.0002);
c3 := c(0.0003);
return( c(-6.0) * c3 * exp(neg( c(t))));
end;
exact_soln_x2 := proc(t)
local c1,c2,c3;
c1 := c(1.0);
c2 := c(0.0002);
c3 := c(0.0003);
return(c1 + c2 * exp(c(2.0) * c(t)) + c3 * exp(neg( c(t))));
end;
exact_soln_x2p := proc(t)
local c1,c2,c3;
c1 := c(1.0);
c2 := c(0.0002);
c3 := c(0.0003);
return( c(2.0) * c2 * exp(c(2.0) * c(t)) - c3 * exp(neg(c(t))));
end;
next_delta := proc()
global glob_nxt, x_delta;
x_delta := [ 0.001 + 0.00004 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.000 + 0.000 * I ];
glob_nxt := glob_nxt + 1;
it := x_delta[glob_nxt];
return it;
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
memory used=51.8MB, alloc=40.3MB, time=0.66
t[1] = 1.5 0.1
h = 0.0001 0.005
x1[1] (numeric) = 2.00039962779 -4.00965232402e-05
x1[1] (closed_form) = 2.00039962779 -4.00965232402e-05
absolute error = 0
relative error = 0 %
Correct digits = 62
h = 0.0001 0.005
x2[1] (numeric) = 1.00400363732 0.000791393281964
x2[1] (closed_form) = 1.00400363732 0.000791393281964
absolute error = 0
relative error = 0 %
Correct digits = 62
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=96.2MB, alloc=40.3MB, time=1.21
t[1] = 1.5001 0.105
h = 0.0001 0.003
x1[1] (numeric) = 2.00039947069 -4.20767471160e-05
x1[1] (closed_form) = 2.00039938237 -4.20899434531e-05
absolute error = 8.930e-08
relative error = 4.464e-06 %
Correct digits = 7
h = 0.0001 0.003
x2[1] (numeric) = 1.00399780268 0.000822751320802
x2[1] (closed_form) = 1.00399620479 0.000830558310407
absolute error = 7.969e-06
relative error = 0.0007937 %
Correct digits = 5
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=140.6MB, alloc=40.3MB, time=1.76
memory used=185.4MB, alloc=40.3MB, time=2.32
t[1] = 1.5002 0.108
h = 0.001 0.001
x1[1] (numeric) = 2.00039936545 -4.32654106263e-05
x1[1] (closed_form) = 2.00039921438 -4.32835707949e-05
absolute error = 1.522e-07
relative error = 7.606e-06 %
Correct digits = 7
h = 0.001 0.001
x2[1] (numeric) = 1.0039916904 0.000854066059838
x2[1] (closed_form) = 1.00399186563 0.000854094245543
absolute error = 1.775e-07
relative error = 1.768e-05 %
Correct digits = 7
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=229.7MB, alloc=40.3MB, time=2.88
t[1] = 1.5012 0.109
h = 0.001 0.003
x1[1] (numeric) = 2.00039885998 -4.36104580992e-05
x1[1] (closed_form) = 2.00039877193 -4.36391025393e-05
absolute error = 9.260e-08
relative error = 4.629e-06 %
Correct digits = 7
h = 0.001 0.003
x2[1] (numeric) = 1.00398550103 0.000885386600701
x2[1] (closed_form) = 1.00399791648 0.000863623975896
absolute error = 2.506e-05
relative error = 0.002496 %
Correct digits = 5
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=274.0MB, alloc=40.3MB, time=3.43
memory used=318.3MB, alloc=40.3MB, time=3.98
t[1] = 1.5022 0.112
h = 0.0001 0.004
x1[1] (numeric) = 2.00039798598 -4.48787485299e-05
x1[1] (closed_form) = 2.00039824078 -4.47904073417e-05
absolute error = 2.697e-07
relative error = 1.348e-05 %
Correct digits = 7
h = 0.0001 0.004
x2[1] (numeric) = 1.00397923312 0.00091675888045
x2[1] (closed_form) = 1.00400039201 0.000888795731337
absolute error = 3.507e-05
relative error = 0.003493 %
Correct digits = 4
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=362.5MB, alloc=40.3MB, time=4.53
t[1] = 1.5023 0.116
h = 0.003 0.006
x1[1] (numeric) = 2.00039735267 -4.68078241701e-05
x1[1] (closed_form) = 2.00039801863 -4.63783698061e-05
absolute error = 7.924e-07
relative error = 3.961e-05 %
Correct digits = 6
h = 0.003 0.006
x2[1] (numeric) = 1.00397275795 0.000948145715471
x2[1] (closed_form) = 1.00399384451 0.000920159762743
absolute error = 3.504e-05
relative error = 0.00349 %
Correct digits = 4
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=406.8MB, alloc=40.3MB, time=5.08
t[1] = 1.5053 0.122
h = 0.0001 0.005
x1[1] (numeric) = 2.00039516725 -4.96502185656e-05
x1[1] (closed_form) = 2.00039654178 -4.86195547486e-05
absolute error = 1.718e-06
relative error = 8.588e-05 %
Correct digits = 6
h = 0.0001 0.005
x2[1] (numeric) = 1.00396586444 0.000979756771774
x2[1] (closed_form) = 1.00400574836 0.000972715684599
absolute error = 4.050e-05
relative error = 0.004034 %
Correct digits = 4
memory used=451.2MB, alloc=40.3MB, time=5.63
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=495.7MB, alloc=40.3MB, time=6.19
t[1] = 1.5054 0.127
h = 0.0001 0.003
x1[1] (numeric) = 2.00039490049 -5.24437078629e-05
x1[1] (closed_form) = 2.0003962541 -5.05965877356e-05
absolute error = 2.290e-06
relative error = 0.0001145 %
Correct digits = 6
h = 0.0001 0.003
x2[1] (numeric) = 1.00395847388 0.00101157173567
x2[1] (closed_form) = 1.00399648142 0.00101193711616
absolute error = 3.801e-05
relative error = 0.003786 %
Correct digits = 4
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=540.1MB, alloc=40.3MB, time=6.75
t[1] = 1.5055 0.13
h = 0.001 0.001
x1[1] (numeric) = 2.00039472026 -5.41203280251e-05
x1[1] (closed_form) = 2.00039606092 -5.17799423140e-05
absolute error = 2.697e-06
relative error = 0.0001348 %
Correct digits = 6
h = 0.001 0.001
x2[1] (numeric) = 1.00395080068 0.00104333123763
x2[1] (closed_form) = 1.00399104122 0.00103551282438
absolute error = 4.099e-05
relative error = 0.004083 %
Correct digits = 4
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=584.7MB, alloc=40.3MB, time=7.30
memory used=629.2MB, alloc=40.3MB, time=7.86
t[1] = 1.5065 0.131
h = 0.001 0.003
x1[1] (numeric) = 2.00039402801 -5.46119104565e-05
x1[1] (closed_form) = 2.00039561313 -5.21238273791e-05
absolute error = 2.950e-06
relative error = 0.0001475 %
Correct digits = 6
h = 0.001 0.003
x2[1] (numeric) = 1.0039430483 0.00107509360205
x2[1] (closed_form) = 1.00399672417 0.00104540956576
absolute error = 6.134e-05
relative error = 0.006109 %
Correct digits = 4
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=673.4MB, alloc=40.3MB, time=8.40
t[1] = 1.5075 0.134
h = 0.0001 0.004
x1[1] (numeric) = 2.00039292385 -5.63704802950e-05
x1[1] (closed_form) = 2.00039505972 -5.32571466477e-05
absolute error = 3.776e-06
relative error = 0.0001887 %
Correct digits = 6
h = 0.0001 0.004
x2[1] (numeric) = 1.0039352134 0.00110690582666
x2[1] (closed_form) = 1.00399809328 0.00107094377766
absolute error = 7.244e-05
relative error = 0.007215 %
Correct digits = 4
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=717.7MB, alloc=40.3MB, time=8.96
memory used=762.0MB, alloc=40.3MB, time=9.51
t[1] = 1.5076 0.138
h = 0.003 0.006
x1[1] (numeric) = 2.0003921922 -5.89823403918e-05
x1[1] (closed_form) = 2.00039480405 -5.48314718405e-05
absolute error = 4.904e-06
relative error = 0.0002452 %
Correct digits = 6
h = 0.003 0.006
x2[1] (numeric) = 1.00392716561 0.00113872469569
x2[1] (closed_form) = 1.00399007115 0.00110232677131
absolute error = 7.268e-05
relative error = 0.007239 %
Correct digits = 4
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=806.3MB, alloc=40.3MB, time=10.07
t[1] = 1.5106 0.144
h = 0.0001 0.005
x1[1] (numeric) = 2.00038938325 -6.27895107956e-05
x1[1] (closed_form) = 2.00039328633 -5.70279542208e-05
absolute error = 6.959e-06
relative error = 0.0003479 %
Correct digits = 5
h = 0.0001 0.005
x2[1] (numeric) = 1.00391868041 0.00117075658639
x2[1] (closed_form) = 1.00399973282 0.0011559425288
absolute error = 8.240e-05
relative error = 0.008207 %
Correct digits = 4
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=850.6MB, alloc=40.3MB, time=10.62
t[1] = 1.5107 0.149
h = 0.0001 0.003
x1[1] (numeric) = 2.00038901328 -6.64236129308e-05
x1[1] (closed_form) = 2.00039295697 -5.89877657402e-05
absolute error = 8.417e-06
relative error = 0.0004208 %
Correct digits = 5
h = 0.0001 0.003
x2[1] (numeric) = 1.00390967801 0.00120297759828
x2[1] (closed_form) = 1.00398861149 0.00119513978708
absolute error = 7.932e-05
relative error = 0.007901 %
Correct digits = 4
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=894.9MB, alloc=40.3MB, time=11.16
memory used=939.6MB, alloc=40.3MB, time=11.71
t[1] = 1.5108 0.152
h = 0.001 0.001
x1[1] (numeric) = 2.00038876171 -6.86048339928e-05
x1[1] (closed_form) = 2.00039273897 -6.01603531135e-05
absolute error = 9.334e-06
relative error = 0.0004666 %
Correct digits = 5
h = 0.001 0.001
x2[1] (numeric) = 1.00390038833 0.00123513061089
x2[1] (closed_form) = 1.003982058 0.00121870695932
absolute error = 8.330e-05
relative error = 0.008297 %
Correct digits = 4
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=984.1MB, alloc=40.3MB, time=12.26
t[1] = 1.5118 0.153
h = 0.001 0.003
x1[1] (numeric) = 2.00038787858 -6.92500811773e-05
x1[1] (closed_form) = 2.00039228613 -6.04925391393e-05
absolute error = 9.804e-06
relative error = 0.0004901 %
Correct digits = 5
h = 0.001 0.003
x2[1] (numeric) = 1.00389101743 0.00126728342435
x2[1] (closed_form) = 1.00398735333 0.00122895793893
absolute error = 0.0001037
relative error = 0.01033 %
Correct digits = 4
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1028.4MB, alloc=40.3MB, time=12.80
memory used=1072.7MB, alloc=40.3MB, time=13.35
t[1] = 1.5128 0.156
h = 0.0001 0.004
x1[1] (numeric) = 2.00038654352 -7.15176952779e-05
x1[1] (closed_form) = 2.00039171098 -6.16074852423e-05
absolute error = 1.118e-05
relative error = 0.0005587 %
Correct digits = 5
h = 0.0001 0.004
x2[1] (numeric) = 1.00388156003 0.00129948404828
x2[1] (closed_form) = 1.00398758945 0.0012548091302
absolute error = 0.0001151
relative error = 0.01146 %
Correct digits = 4
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1116.9MB, alloc=40.3MB, time=13.91
t[1] = 1.5129 0.16
h = 0.003 0.006
x1[1] (numeric) = 2.00038571969 -7.48355474163e-05
x1[1] (closed_form) = 2.00039142227 -6.31675150510e-05
absolute error = 1.299e-05
relative error = 0.0006492 %
Correct digits = 5
h = 0.003 0.006
x2[1] (numeric) = 1.00387188433 0.00133168307798
x2[1] (closed_form) = 1.0039780778 0.00128614605144
absolute error = 0.0001155
relative error = 0.01151 %
Correct digits = 4
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1161.1MB, alloc=40.3MB, time=14.46
t[1] = 1.5159 0.166
h = 0.0001 0.005
x1[1] (numeric) = 2.00038228018 -7.96467443641e-05
x1[1] (closed_form) = 2.00038986487 -6.53186474051e-05
absolute error = 1.621e-05
relative error = 0.0008104 %
Correct digits = 5
h = 0.0001 0.005
x2[1] (numeric) = 1.00386175221 0.0013640830743
x2[1] (closed_form) = 1.00398542908 0.00134073256563
absolute error = 0.0001259
relative error = 0.01254 %
Correct digits = 4
memory used=1205.5MB, alloc=40.3MB, time=15.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1249.9MB, alloc=40.3MB, time=15.58
t[1] = 1.516 0.171
h = 0.0001 0.003
x1[1] (numeric) = 2.0003818147 -8.41497445042e-05
x1[1] (closed_form) = 2.00038949446 -6.72604207835e-05
absolute error = 1.855e-05
relative error = 0.0009275 %
Correct digits = 5
h = 0.0001 0.003
x2[1] (numeric) = 1.00385108293 0.00139665645293
x2[1] (closed_form) = 1.00397243679 0.00137982339784
absolute error = 0.0001225
relative error = 0.0122 %
Correct digits = 4
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1294.3MB, alloc=40.3MB, time=16.15
t[1] = 1.5161 0.174
h = 0.001 0.001
x1[1] (numeric) = 2.00038149615 -8.68527868769e-05
x1[1] (closed_form) = 2.00038925199 -6.84217572078e-05
absolute error = 2.000e-05
relative error = 0.0009996 %
Correct digits = 5
h = 0.001 0.001
x2[1] (numeric) = 1.00384012209 0.00142914892531
x2[1] (closed_form) = 1.00396475979 0.0014033327078
absolute error = 0.0001273
relative error = 0.01268 %
Correct digits = 4
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1338.9MB, alloc=40.3MB, time=16.72
memory used=1383.5MB, alloc=40.3MB, time=17.28
t[1] = 1.5171 0.175
h = 0.001 0.003
x1[1] (numeric) = 2.0003804181 -8.76592628964e-05
x1[1] (closed_form) = 2.00038879439 -6.87421983458e-05
absolute error = 2.069e-05
relative error = 0.001034 %
Correct digits = 5
h = 0.001 0.003
x2[1] (numeric) = 1.00382907806 0.0014616380152
x2[1] (closed_form) = 1.00396964814 0.00141392414869
absolute error = 0.0001484
relative error = 0.01479 %
Correct digits = 4
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1427.7MB, alloc=40.3MB, time=17.85
t[1] = 1.5181 0.178
h = 0.0001 0.004
x1[1] (numeric) = 2.00037885197 -9.04554794845e-05
x1[1] (closed_form) = 2.00038819802 -6.98383970970e-05
absolute error = 2.264e-05
relative error = 0.001132 %
Correct digits = 5
h = 0.0001 0.004
x2[1] (numeric) = 1.00381794358 0.00149417269273
x2[1] (closed_form) = 1.00396872648 0.00144004521447
absolute error = 0.0001602
relative error = 0.01596 %
Correct digits = 4
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1472.0MB, alloc=40.3MB, time=18.40
memory used=1516.4MB, alloc=40.3MB, time=18.96
t[1] = 1.5182 0.182
h = 0.003 0.006
x1[1] (numeric) = 2.00037794318 -9.45032689089e-05
x1[1] (closed_form) = 2.00038787677 -7.13834876297e-05
absolute error = 2.516e-05
relative error = 0.001258 %
Correct digits = 5
h = 0.003 0.006
x2[1] (numeric) = 1.00380658555 0.00152669721093
x2[1] (closed_form) = 1.00395771319 0.00147126973075
absolute error = 0.000161
relative error = 0.01603 %
Correct digits = 4
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1560.7MB, alloc=40.3MB, time=19.51
t[1] = 1.5212 0.188
h = 0.0001 0.005
x1[1] (numeric) = 2.00037386713 -0.000100359586342
x1[1] (closed_form) = 2.00038628091 -7.34886524202e-05
absolute error = 2.960e-05
relative error = 0.00148 %
Correct digits = 5
h = 0.0001 0.005
x2[1] (numeric) = 1.00379475222 0.00155940977692
x2[1] (closed_form) = 1.00396268916 0.00152673401309
absolute error = 0.0001711
relative error = 0.01704 %
Correct digits = 4
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1605.0MB, alloc=40.3MB, time=20.06
t[1] = 1.5213 0.193
h = 0.0001 0.003
x1[1] (numeric) = 2.00037331508 -0.000105760681121
x1[1] (closed_form) = 2.00038587005 -7.54115887831e-05
absolute error = 3.284e-05
relative error = 0.001642 %
Correct digits = 5
h = 0.0001 0.003
x2[1] (numeric) = 1.00378236199 0.00159227902743
x2[1] (closed_form) = 1.00394781283 0.00156563462469
absolute error = 0.0001676
relative error = 0.01669 %
Correct digits = 4
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1649.5MB, alloc=40.3MB, time=20.62
memory used=1694.2MB, alloc=40.3MB, time=21.19
t[1] = 1.5214 0.196
h = 0.001 0.001
x1[1] (numeric) = 2.00037293466 -0.000109003325919
x1[1] (closed_form) = 2.00038560352 -7.65612013459e-05
absolute error = 3.483e-05
relative error = 0.001741 %
Correct digits = 5
h = 0.001 0.001
x2[1] (numeric) = 1.00376967629 0.00162505410107
x2[1] (closed_form) = 1.00393900421 0.0015890358093
absolute error = 0.0001731
relative error = 0.01724 %
Correct digits = 4
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1738.7MB, alloc=40.3MB, time=21.75
t[1] = 1.5224 0.197
h = 0.0001 0.004
x1[1] (numeric) = 2.00037165775 -0.000109979037137
x1[1] (closed_form) = 2.00038514143 -7.68698582133e-05
absolute error = 3.575e-05
relative error = 0.001787 %
Correct digits = 5
h = 0.0001 0.004
x2[1] (numeric) = 1.00375690553 0.00165782248777
x2[1] (closed_form) = 1.00394346666 0.00159995293743
absolute error = 0.0001953
relative error = 0.01946 %
Correct digits = 4
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1782.9MB, alloc=40.3MB, time=22.30
memory used=1827.3MB, alloc=40.3MB, time=22.86
t[1] = 1.5225 0.201
h = 0.003 0.006
x1[1] (numeric) = 2.00037076398 -0.000114608471014
x1[1] (closed_form) = 2.00038479239 -7.84019642793e-05
absolute error = 3.883e-05
relative error = 0.001941 %
Correct digits = 5
h = 0.003 0.006
x2[1] (numeric) = 1.00374398851 0.00169056361918
x2[1] (closed_form) = 1.00393115569 0.00163100864078
absolute error = 0.0001964
relative error = 0.01956 %
Correct digits = 4
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1871.6MB, alloc=40.3MB, time=23.42
t[1] = 1.5255 0.207
h = 0.0001 0.005
x1[1] (numeric) = 2.0003663062 -0.000121356522308
x1[1] (closed_form) = 2.00038316384 -8.04675284796e-05
absolute error = 4.423e-05
relative error = 0.002211 %
Correct digits = 5
h = 0.0001 0.005
x2[1] (numeric) = 1.0037305803 0.0017234797064
x2[1] (closed_form) = 1.0039340289 0.00168712182795
absolute error = 0.0002067
relative error = 0.02059 %
Correct digits = 4
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1915.8MB, alloc=40.3MB, time=23.97
t[1] = 1.5256 0.212
h = 0.0001 0.003
x1[1] (numeric) = 2.00036578829 -0.000127472476013
x1[1] (closed_form) = 2.00038271844 -8.23740960164e-05
absolute error = 4.817e-05
relative error = 0.002408 %
Correct digits = 5
h = 0.0001 0.003
x2[1] (numeric) = 1.00371659883 0.00175653593525
x2[1] (closed_form) = 1.00391752678 0.00172576794291
absolute error = 0.0002033
relative error = 0.02025 %
Correct digits = 4
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=1960.2MB, alloc=40.3MB, time=24.52
memory used=2005.0MB, alloc=40.3MB, time=25.09
t[1] = 1.5257 0.215
h = 0.001 0.001
x1[1] (numeric) = 2.00036542006 -0.000131146290478
x1[1] (closed_form) = 2.00038243135 -8.35135271527e-05
absolute error = 5.058e-05
relative error = 0.002528 %
Correct digits = 5
h = 0.001 0.001
x2[1] (numeric) = 1.00370231944 0.00178948578227
x2[1] (closed_form) = 1.00390774137 0.00174902158324
absolute error = 0.0002094
relative error = 0.02086 %
Correct digits = 4
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2049.3MB, alloc=40.3MB, time=25.65
t[1] = 1.5267 0.216
h = 0.001 0.003
x1[1] (numeric) = 2.00036400503 -0.000132277698673
x1[1] (closed_form) = 2.00038196549 -8.38120626977e-05
absolute error = 5.169e-05
relative error = 0.002584 %
Correct digits = 5
h = 0.001 0.003
x2[1] (numeric) = 1.00368795356 0.00182242583218
x2[1] (closed_form) = 1.00391181879 0.0017602010955
absolute error = 0.0002324
relative error = 0.02314 %
Correct digits = 4
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2093.7MB, alloc=40.3MB, time=26.21
memory used=2138.1MB, alloc=40.3MB, time=26.77
t[1] = 1.5277 0.219
h = 0.0001 0.004
x1[1] (numeric) = 2.00036208616 -0.000136083303517
x1[1] (closed_form) = 2.00038133081 -8.48726651698e-05
absolute error = 5.471e-05
relative error = 0.002735 %
Correct digits = 5
h = 0.0001 0.004
x2[1] (numeric) = 1.00367348991 0.00185540661288
x2[1] (closed_form) = 1.00390868135 0.0017866792523
absolute error = 0.000245
relative error = 0.02441 %
Correct digits = 4
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2182.3MB, alloc=40.3MB, time=27.32
t[1] = 1.5278 0.223
h = 0.003 0.006
x1[1] (numeric) = 2.00036112247 -0.000141493320418
x1[1] (closed_form) = 2.00038095017 -8.63886660660e-05
absolute error = 5.856e-05
relative error = 0.002928 %
Correct digits = 5
h = 0.003 0.006
x2[1] (numeric) = 1.0036587939 0.00188835998779
x2[1] (closed_form) = 1.00389485462 0.0018174959832
absolute error = 0.0002465
relative error = 0.02455 %
Correct digits = 4
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2226.5MB, alloc=40.3MB, time=27.86
memory used=2271.0MB, alloc=40.3MB, time=28.42
t[1] = 1.5308 0.229
h = 0.0001 0.005
x1[1] (numeric) = 2.00035601516 -0.000149373380984
x1[1] (closed_form) = 2.00037928542 -8.84071786342e-05
absolute error = 6.526e-05
relative error = 0.003262 %
Correct digits = 4
h = 0.0001 0.005
x2[1] (numeric) = 1.00364358811 0.00192147380938
x2[1] (closed_form) = 1.00389524244 0.00187430321301
absolute error = 0.000256
relative error = 0.0255 %
Correct digits = 4
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2315.3MB, alloc=40.3MB, time=28.97
t[1] = 1.5309 0.234
h = 0.0001 0.003
x1[1] (numeric) = 2.00035542938 -0.000156449395051
x1[1] (closed_form) = 2.00037880077 -9.02934629604e-05
absolute error = 7.016e-05
relative error = 0.003507 %
Correct digits = 4
h = 0.0001 0.003
x2[1] (numeric) = 1.00362778983 0.00195470932127
x2[1] (closed_form) = 1.00387684266 0.00191259951566
absolute error = 0.0002526
relative error = 0.02516 %
Correct digits = 4
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2359.8MB, alloc=40.3MB, time=29.52
t[1] = 1.531 0.237
h = 0.001 0.001
x1[1] (numeric) = 2.00035501003 -0.000160700520029
x1[1] (closed_form) = 2.00037849033 -9.14203147436e-05
absolute error = 7.315e-05
relative error = 0.003657 %
Correct digits = 4
h = 0.001 0.001
x2[1] (numeric) = 1.00361169047 0.00198782455101
x2[1] (closed_form) = 1.00386591695 0.00193564926556
absolute error = 0.0002595
relative error = 0.02585 %
Correct digits = 4
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2404.4MB, alloc=40.3MB, time=30.08
memory used=2448.8MB, alloc=40.3MB, time=30.64
t[1] = 1.532 0.238
h = 0.001 0.003
x1[1] (numeric) = 2.00035338778 -0.000162018058864
x1[1] (closed_form) = 2.00037802051 -9.17070064251e-05
absolute error = 7.450e-05
relative error = 0.003724 %
Correct digits = 4
h = 0.001 0.003
x2[1] (numeric) = 1.00359550291 0.00202092646377
x2[1] (closed_form) = 1.00386953472 0.00194712414231
absolute error = 0.0002838
relative error = 0.02827 %
Correct digits = 4
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2493.2MB, alloc=40.3MB, time=31.19
t[1] = 1.533 0.241
h = 0.0001 0.004
x1[1] (numeric) = 2.00035123926 -0.000166415485688
x1[1] (closed_form) = 2.00037736613 -9.27478593268e-05
absolute error = 7.816e-05
relative error = 0.003907 %
Correct digits = 4
h = 0.0001 0.004
x2[1] (numeric) = 1.00357921368 0.00205406638561
x2[1] (closed_form) = 1.00386517973 0.00197372879219
absolute error = 0.000297
relative error = 0.02959 %
Correct digits = 4
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2537.5MB, alloc=40.3MB, time=31.73
memory used=2581.8MB, alloc=40.3MB, time=32.27
t[1] = 1.5331 0.245
h = 0.003 0.006
x1[1] (numeric) = 2.00035021624 -0.000172632042643
x1[1] (closed_form) = 2.00037695443 -9.42471526705e-05
absolute error = 8.282e-05
relative error = 0.00414 %
Correct digits = 4
h = 0.003 0.006
x2[1] (numeric) = 1.00356268747 0.00208716943314
x2[1] (closed_form) = 1.00384983345 0.00200423716351
absolute error = 0.0002989
relative error = 0.02977 %
Correct digits = 4
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2626.1MB, alloc=40.3MB, time=32.82
t[1] = 1.5361 0.251
h = 0.0001 0.005
x1[1] (numeric) = 2.0003444571 -0.000181690646762
x1[1] (closed_form) = 2.00037525471 -9.62180815629e-05
absolute error = 9.085e-05
relative error = 0.004542 %
Correct digits = 4
h = 0.0001 0.005
x2[1] (numeric) = 1.00354563309 0.002120417534
x2[1] (closed_form) = 1.00384768158 0.00206163494726
absolute error = 0.0003077
relative error = 0.03065 %
Correct digits = 4
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2670.4MB, alloc=40.3MB, time=33.37
t[1] = 1.5362 0.256
h = 0.0001 0.003
x1[1] (numeric) = 2.00034381659 -0.000189758400011
x1[1] (closed_form) = 2.00037473145 -9.80833357400e-05
absolute error = 9.675e-05
relative error = 0.004836 %
Correct digits = 4
h = 0.0001 0.003
x2[1] (numeric) = 1.0035279673 0.00215376790042
x2[1] (closed_form) = 1.00382738166 0.00209949407522
absolute error = 0.0003043
relative error = 0.03031 %
Correct digits = 4
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2714.9MB, alloc=40.3MB, time=33.92
memory used=2759.5MB, alloc=40.3MB, time=34.48
t[1] = 1.5363 0.259
h = 0.001 0.001
x1[1] (numeric) = 2.00034335376 -0.00019460614765
x1[1] (closed_form) = 2.00037439808 -9.91971668295e-05
absolute error = 0.0001003
relative error = 0.005016 %
Correct digits = 4
h = 0.001 0.001
x2[1] (numeric) = 1.0035099977 0.00218698373936
x2[1] (closed_form) = 1.00381531386 0.00212228749592
absolute error = 0.0003121
relative error = 0.03109 %
Correct digits = 4
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2803.9MB, alloc=40.3MB, time=35.04
t[1] = 1.5373 0.26
h = 0.001 0.003
x1[1] (numeric) = 2.00034152076 -0.000196119169977
x1[1] (closed_form) = 2.00037392458 -9.94719934993e-05
absolute error = 0.0001019
relative error = 0.005096 %
Correct digits = 4
h = 0.001 0.003
x2[1] (numeric) = 1.00349193828 0.00222018262261
x2[1] (closed_form) = 1.00381845456 0.00213404017651
absolute error = 0.0003377
relative error = 0.03364 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2848.2MB, alloc=40.3MB, time=35.59
memory used=2892.6MB, alloc=40.3MB, time=36.14
t[1] = 1.5383 0.263
h = 0.0001 0.004
x1[1] (numeric) = 2.00033914527 -0.000201131040976
x1[1] (closed_form) = 2.00037325104 -0.000100492774898
absolute error = 0.0001063
relative error = 0.005312 %
Correct digits = 4
h = 0.0001 0.004
x2[1] (numeric) = 1.00347377328 0.00225341661304
x2[1] (closed_form) = 1.00381286488 0.00216071858555
absolute error = 0.0003515
relative error = 0.03502 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2936.8MB, alloc=40.3MB, time=36.68
t[1] = 1.5384 0.267
h = 0.003 0.006
x1[1] (numeric) = 2.00033807476 -0.00020818072545
x1[1] (closed_form) = 2.00037280881 -0.000101974773168
absolute error = 0.0001117
relative error = 0.005586 %
Correct digits = 4
h = 0.003 0.006
x2[1] (numeric) = 1.00345536697 0.00228660394167
x2[1] (closed_form) = 1.00379599829 0.00219084836282
absolute error = 0.0003538
relative error = 0.03525 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=2981.1MB, alloc=40.3MB, time=37.23
memory used=3025.7MB, alloc=40.3MB, time=37.78
t[1] = 1.5414 0.273
h = 0.0001 0.005
x1[1] (numeric) = 2.00033166293 -0.000218466241692
x1[1] (closed_form) = 2.00037107535 -0.000103897616188
absolute error = 0.0001212
relative error = 0.006057 %
Correct digits = 4
h = 0.0001 0.005
x2[1] (numeric) = 1.00343641428 0.00231992003937
x2[1] (closed_form) = 1.00379125652 0.00224872978162
absolute error = 0.0003619
relative error = 0.03605 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3070.0MB, alloc=40.3MB, time=38.33
t[1] = 1.5415 0.278
h = 0.0001 0.003
x1[1] (numeric) = 2.00033098235 -0.000227558189761
x1[1] (closed_form) = 2.00037051418 -0.000105741111865
absolute error = 0.0001281
relative error = 0.006402 %
Correct digits = 4
h = 0.0001 0.003
x2[1] (numeric) = 1.00341683161 0.00235331800008
x2[1] (closed_form) = 1.00376905783 0.00228606340706
absolute error = 0.0003586
relative error = 0.03572 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3114.5MB, alloc=40.3MB, time=38.88
t[1] = 1.5416 0.281
h = 0.001 0.001
x1[1] (numeric) = 2.00033048461 -0.000233022353269
x1[1] (closed_form) = 2.00037015827 -0.000106841492206
absolute error = 0.0001323
relative error = 0.006612 %
Correct digits = 4
h = 0.001 0.001
x2[1] (numeric) = 1.00339694284 0.00238656685037
x2[1] (closed_form) = 1.0037558485 0.00230854746779
absolute error = 0.0003673
relative error = 0.03659 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3159.1MB, alloc=40.3MB, time=39.44
memory used=3203.5MB, alloc=40.3MB, time=39.99
t[1] = 1.5426 0.282
h = 0.001 0.003
x1[1] (numeric) = 2.00032843748 -0.00023474067836
x1[1] (closed_form) = 2.00036968137 -0.000107104438983
absolute error = 0.0001341
relative error = 0.006705 %
Correct digits = 4
h = 0.001 0.003
x2[1] (numeric) = 1.0033769627 0.00241979498845
x2[1] (closed_form) = 1.0037584953 0.00232055944326
absolute error = 0.0003942
relative error = 0.03927 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3247.9MB, alloc=40.3MB, time=40.54
t[1] = 1.5436 0.285
h = 0.0001 0.004
x1[1] (numeric) = 2.00032583857 -0.000240390367864
x1[1] (closed_form) = 2.00036898922 -0.000108104840563
absolute error = 0.0001391
relative error = 0.006956 %
Correct digits = 4
h = 0.0001 0.004
x2[1] (numeric) = 1.00335687314 0.00245305514988
x2[1] (closed_form) = 1.00375165596 0.00234725759848
absolute error = 0.0004087
relative error = 0.04072 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3292.3MB, alloc=40.3MB, time=41.07
memory used=3336.8MB, alloc=40.3MB, time=41.61
t[1] = 1.5437 0.289
h = 0.003 0.006
x1[1] (numeric) = 2.0003247337 -0.000248300365094
x1[1] (closed_form) = 2.000368517 -0.000109568971243
absolute error = 0.0001455
relative error = 0.007272 %
Correct digits = 4
h = 0.003 0.006
x2[1] (numeric) = 1.00333653817 0.00248625854568
x2[1] (closed_form) = 1.00373327147 0.00237693782742
absolute error = 0.0004115
relative error = 0.041 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3381.1MB, alloc=40.3MB, time=42.15
t[1] = 1.5467 0.295
h = 0.0001 0.005
x1[1] (numeric) = 2.00031766984 -0.000259862986384
x1[1] (closed_form) = 2.00036675105 -0.000111443255982
absolute error = 0.0001563
relative error = 0.007815 %
Correct digits = 4
h = 0.0001 0.005
x2[1] (numeric) = 1.00331563886 0.00251957352911
x2[1] (closed_form) = 1.00372589385 0.00243519268023
absolute error = 0.0004188
relative error = 0.04173 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3425.4MB, alloc=40.3MB, time=42.68
t[1] = 1.5468 0.3
h = 0.0001 0.003
x1[1] (numeric) = 2.0003169655 -0.000270012320789
x1[1] (closed_form) = 2.00036615264 -0.000113264283572
absolute error = 0.0001643
relative error = 0.008213 %
Correct digits = 4
h = 0.0001 0.003
x2[1] (numeric) = 1.00329409136 0.00255294899147
x2[1] (closed_form) = 1.0037018017 0.00247191167228
absolute error = 0.0004157
relative error = 0.04142 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3469.9MB, alloc=40.3MB, time=43.24
memory used=3514.8MB, alloc=40.3MB, time=43.79
t[1] = 1.5469 0.303
h = 0.001 0.001
x1[1] (numeric) = 2.00031644237 -0.000276113150155
x1[1] (closed_form) = 2.00036577462 -0.000114350794496
absolute error = 0.0001691
relative error = 0.008454 %
Correct digits = 4
h = 0.001 0.001
x2[1] (numeric) = 1.00327223592 0.00258616043066
x2[1] (closed_form) = 1.00368745375 0.00249403284757
absolute error = 0.0004253
relative error = 0.04238 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3559.1MB, alloc=40.3MB, time=44.32
t[1] = 1.5479 0.304
h = 0.0001 0.004
x1[1] (numeric) = 2.00031417795 -0.000278047068622
x1[1] (closed_form) = 2.00036529461 -0.000114601852705
absolute error = 0.0001713
relative error = 0.008561 %
Correct digits = 4
h = 0.0001 0.004
x2[1] (numeric) = 1.00325028768 0.00261934728438
x2[1] (closed_form) = 1.00368959048 0.00250628467872
absolute error = 0.0004536
relative error = 0.04519 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3603.4MB, alloc=40.3MB, time=44.85
memory used=3648.0MB, alloc=40.3MB, time=45.38
t[1] = 1.548 0.308
h = 0.003 0.006
x1[1] (numeric) = 2.00031312972 -0.000286628257635
x1[1] (closed_form) = 2.0003647968 -0.000116050504791
absolute error = 0.0001782
relative error = 0.00891 %
Correct digits = 4
h = 0.003 0.006
x2[1] (numeric) = 1.00322818302 0.00265247444616
x2[1] (closed_form) = 1.00366991028 0.0025355026973
absolute error = 0.000457
relative error = 0.04553 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3692.2MB, alloc=40.3MB, time=45.91
t[1] = 1.551 0.314
h = 0.0001 0.005
x1[1] (numeric) = 2.00030568394 -0.000299246713246
x1[1] (closed_form) = 2.00036300329 -0.000117883003522
absolute error = 0.0001902
relative error = 0.009509 %
Correct digits = 4
h = 0.0001 0.005
x2[1] (numeric) = 1.00320549934 0.00268569633403
x2[1] (closed_form) = 1.0036602278 0.00259395629441
absolute error = 0.0004639
relative error = 0.04622 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3736.4MB, alloc=40.3MB, time=46.44
memory used=3780.9MB, alloc=40.3MB, time=46.98
t[1] = 1.5511 0.319
h = 0.0001 0.003
x1[1] (numeric) = 2.00030506526 -0.000310220045156
x1[1] (closed_form) = 2.0003623731 -0.000119684569803
absolute error = 0.000199
relative error = 0.009947 %
Correct digits = 4
h = 0.0001 0.003
x2[1] (numeric) = 1.00318215291 0.00271895805814
x2[1] (closed_form) = 1.00363452194 0.00263005197378
absolute error = 0.000461
relative error = 0.04594 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3825.5MB, alloc=40.3MB, time=47.52
t[1] = 1.5512 0.322
h = 0.001 0.001
x1[1] (numeric) = 2.00030458454 -0.000316818912665
x1[1] (closed_form) = 2.00036197621 -0.000120759072373
absolute error = 0.0002043
relative error = 0.01021 %
Correct digits = 4
h = 0.001 0.001
x2[1] (numeric) = 1.0031584981 0.0027520422518
x2[1] (closed_form) = 1.00361920326 0.00265180415276
absolute error = 0.0004715
relative error = 0.04698 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3870.1MB, alloc=40.3MB, time=48.06
t[1] = 1.5522 0.323
h = 0.001 0.003
x1[1] (numeric) = 2.00030217116 -0.000318942389907
x1[1] (closed_form) = 2.0003614936 -0.0001209999277
absolute error = 0.0002066
relative error = 0.01033 %
Correct digits = 4
h = 0.001 0.003
x2[1] (numeric) = 1.00313474952 0.0027850982753
x2[1] (closed_form) = 1.00362088601 0.00266423985718
absolute error = 0.0005009
relative error = 0.04991 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=3914.4MB, alloc=40.3MB, time=48.58
memory used=3958.7MB, alloc=40.3MB, time=49.12
t[1] = 1.5532 0.326
h = 0.0001 0.004
x1[1] (numeric) = 2.0002992452 -0.000325794657406
x1[1] (closed_form) = 2.00036076803 -0.000121961839532
absolute error = 0.0002129
relative error = 0.01064 %
Correct digits = 4
h = 0.0001 0.004
x2[1] (numeric) = 1.00311088454 0.0028181798229
x2[1] (closed_form) = 1.00361169068 0.00269081177248
absolute error = 0.0005167
relative error = 0.05149 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=4003.0MB, alloc=40.3MB, time=49.64
t[1] = 1.5533 0.33
h = 0.003 0.006
x1[1] (numeric) = 2.00029819008 -0.000335293169333
x1[1] (closed_form) = 2.00036024127 -0.000123391592316
absolute error = 0.0002208
relative error = 0.01104 %
Correct digits = 4
h = 0.003 0.006
x2[1] (numeric) = 1.00308676774 0.00285118455692
x2[1] (closed_form) = 1.00359050638 0.00271944687031
absolute error = 0.0005207
relative error = 0.05188 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=4047.3MB, alloc=40.3MB, time=50.17
memory used=4091.7MB, alloc=40.3MB, time=50.70
t[1] = 1.5563 0.336
h = 0.0001 0.005
x1[1] (numeric) = 2.00029009356 -0.000349294053269
x1[1] (closed_form) = 2.00035841757 -0.000125174717904
absolute error = 0.0002343
relative error = 0.01171 %
Correct digits = 4
h = 0.0001 0.005
x2[1] (numeric) = 1.00306205451 0.00288426520155
x2[1] (closed_form) = 1.00357811595 0.00277806023757
absolute error = 0.0005269
relative error = 0.0525 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=4136.0MB, alloc=40.3MB, time=51.23
t[1] = 1.5564 0.341
h = 0.0001 0.003
x1[1] (numeric) = 2.0002894852 -0.000361394590257
x1[1] (closed_form) = 2.00035775144 -0.000126952537721
absolute error = 0.0002442
relative error = 0.01221 %
Correct digits = 4
h = 0.0001 0.003
x2[1] (numeric) = 1.00303666112 0.0029173625234
x2[1] (closed_form) = 1.00355053837 0.0028133740497
absolute error = 0.0005243
relative error = 0.05224 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=4180.5MB, alloc=40.3MB, time=51.76
t[1] = 1.5565 0.344
h = 0.001 0.001
x1[1] (numeric) = 2.00028899911 -0.000368672684961
x1[1] (closed_form) = 2.00035733324 -0.00012801241727
absolute error = 0.0002502
relative error = 0.01251 %
Correct digits = 4
h = 0.001 0.001
x2[1] (numeric) = 1.00301095838 0.00295026684447
x2[1] (closed_form) = 1.00353409357 0.0028346628773
absolute error = 0.0005358
relative error = 0.05339 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=4225.0MB, alloc=40.3MB, time=52.30
memory used=4269.6MB, alloc=40.3MB, time=52.83
t[1] = 1.5575 0.345
h = 0.001 0.003
x1[1] (numeric) = 2.00028636179 -0.000371033324115
x1[1] (closed_form) = 2.00035684802 -0.000128241380922
absolute error = 0.0002528
relative error = 0.01264 %
Correct digits = 4
h = 0.001 0.003
x2[1] (numeric) = 1.00298516065 0.00298313891766
x2[1] (closed_form) = 1.00353523834 0.00284729968911
absolute error = 0.0005666
relative error = 0.05646 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=4313.8MB, alloc=40.3MB, time=53.36
t[1] = 1.5585 0.348
h = 0.0001 0.004
x1[1] (numeric) = 2.00028322603 -0.000378597947901
x1[1] (closed_form) = 2.00035610541 -0.000129182099586
absolute error = 0.0002598
relative error = 0.01299 %
Correct digits = 4
h = 0.0001 0.004
x2[1] (numeric) = 1.00295924278 0.00301603291177
x2[1] (closed_form) = 1.00352476397 0.00287373045857
absolute error = 0.0005832
relative error = 0.05811 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=4358.2MB, alloc=40.3MB, time=53.89
memory used=4402.6MB, alloc=40.3MB, time=54.42
t[1] = 1.5586 0.352
h = 0.003 0.006
x1[1] (numeric) = 2.00028218134 -0.000389042490338
x1[1] (closed_form) = 2.00035555028 -0.000130592424077
absolute error = 0.0002687
relative error = 0.01343 %
Correct digits = 4
h = 0.003 0.006
x2[1] (numeric) = 1.0029330698 0.003048839125
x2[1] (closed_form) = 1.00350208722 0.0029017104022
absolute error = 0.0005877
relative error = 0.05857 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=4446.8MB, alloc=40.3MB, time=54.95
t[1] = 1.5616 0.358
h = 0.0001 0.005
x1[1] (numeric) = 2.00027343999 -0.000404481259272
x1[1] (closed_form) = 2.00035369764 -0.000132325788855
absolute error = 0.0002837
relative error = 0.01418 %
Correct digits = 4
h = 0.0001 0.005
x2[1] (numeric) = 1.0029062833 0.00308170152166
x2[1] (closed_form) = 1.00348695615 0.0029603649138
absolute error = 0.0005932
relative error = 0.05912 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=4491.3MB, alloc=40.3MB, time=55.48
t[1] = 1.5617 0.363
h = 0.0001 0.003
x1[1] (numeric) = 2.00027286342 -0.000417744060685
x1[1] (closed_form) = 2.00035299629 -0.000134079207033
absolute error = 0.0002948
relative error = 0.01474 %
Correct digits = 4
h = 0.0001 0.003
x2[1] (numeric) = 1.00287879969 0.00311455644782
x2[1] (closed_form) = 1.00345752384 0.00299480642212
absolute error = 0.000591
relative error = 0.05889 %
Correct digits = 3
memory used=4535.8MB, alloc=40.3MB, time=56.01
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=4580.6MB, alloc=40.3MB, time=56.55
t[1] = 1.5618 0.366
h = 0.001 0.001
x1[1] (numeric) = 2.00027238462 -0.000425722798937
x1[1] (closed_form) = 2.00035255721 -0.000135124077883
absolute error = 0.0003015
relative error = 0.01507 %
Correct digits = 4
h = 0.001 0.001
x2[1] (numeric) = 1.00285100626 0.0031472025967
x2[1] (closed_form) = 1.00343996285 0.00301557755167
absolute error = 0.0006035
relative error = 0.06014 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=4625.0MB, alloc=40.3MB, time=57.08
t[1] = 1.5628 0.367
h = 0.001 0.003
x1[1] (numeric) = 2.00026952091 -0.000428332301472
x1[1] (closed_form) = 2.00035206966 -0.00013534115862
absolute error = 0.0003044
relative error = 0.01522 %
Correct digits = 4
h = 0.001 0.003
x2[1] (numeric) = 1.00282311671 0.00317981230686
x2[1] (closed_form) = 1.00344055563 0.00302839350035
absolute error = 0.0006357
relative error = 0.06336 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=4669.5MB, alloc=40.3MB, time=57.61
memory used=4713.9MB, alloc=40.3MB, time=58.14
t[1] = 1.5638 0.37
h = 0.0001 0.004
x1[1] (numeric) = 2.00026618268 -0.000436635461496
x1[1] (closed_form) = 2.00035131057 -0.00013626042841
absolute error = 0.0003122
relative error = 0.01561 %
Correct digits = 4
h = 0.0001 0.004
x2[1] (numeric) = 1.00279510336 0.00321244014724
x2[1] (closed_form) = 1.0034287964 0.00305462503379
absolute error = 0.000653
relative error = 0.06508 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=4758.3MB, alloc=40.3MB, time=58.67
t[1] = 1.5639 0.374
h = 0.003 0.006
x1[1] (numeric) = 2.00026516726 -0.000448055185492
x1[1] (closed_form) = 2.00035072764 -0.000137650811091
absolute error = 0.000322
relative error = 0.0161 %
Correct digits = 4
h = 0.003 0.006
x2[1] (numeric) = 1.00276683191 0.00324496893534
x2[1] (closed_form) = 1.00340464215 0.00308187740041
absolute error = 0.0006583
relative error = 0.06561 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=4802.5MB, alloc=40.3MB, time=59.20
memory used=4847.0MB, alloc=40.3MB, time=59.78
t[1] = 1.5669 0.38
h = 0.0001 0.005
x1[1] (numeric) = 2.00025578897 -0.000464989036794
x1[1] (closed_form) = 2.00034884732 -0.000139334056825
absolute error = 0.0003387
relative error = 0.01693 %
Correct digits = 4
h = 0.0001 0.005
x2[1] (numeric) = 1.00273793019 0.00327753326363
x2[1] (closed_form) = 1.00338674272 0.00314045181453
absolute error = 0.0006631
relative error = 0.06609 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=4891.3MB, alloc=40.3MB, time=60.31
t[1] = 1.567 0.385
h = 0.0001 0.003
x1[1] (numeric) = 2.00025526753 -0.000479449704534
x1[1] (closed_form) = 2.00034811148 -0.000141062437529
absolute error = 0.0003509
relative error = 0.01754 %
Correct digits = 4
h = 0.0001 0.003
x2[1] (numeric) = 1.0027083149 0.00331006498346
x2[1] (closed_form) = 1.00335547686 0.00317393045315
absolute error = 0.0006613
relative error = 0.06591 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=4935.8MB, alloc=40.3MB, time=60.84
t[1] = 1.5671 0.388
h = 0.001 0.001
x1[1] (numeric) = 2.00025480978 -0.000488150844458
x1[1] (closed_form) = 2.00034765196 -0.000142091925711
absolute error = 0.0003583
relative error = 0.01791 %
Correct digits = 4
h = 0.001 0.001
x2[1] (numeric) = 1.00267838984 0.00334237185271
x2[1] (closed_form) = 1.0033368121 0.00319412944695
absolute error = 0.0006749
relative error = 0.06727 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=4980.5MB, alloc=40.3MB, time=61.38
memory used=5024.9MB, alloc=40.3MB, time=61.92
t[1] = 1.5681 0.389
h = 0.001 0.003
x1[1] (numeric) = 2.00025171753 -0.000491021393983
x1[1] (closed_form) = 2.00034716236 -0.000142297138254
absolute error = 0.0003615
relative error = 0.01807 %
Correct digits = 4
h = 0.001 0.003
x2[1] (numeric) = 1.00264836766 0.00337463798077
x2[1] (closed_form) = 1.00333683973 0.00320710172358
absolute error = 0.0007086
relative error = 0.07062 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=5069.2MB, alloc=40.3MB, time=62.45
t[1] = 1.5691 0.392
h = 0.0001 0.004
x1[1] (numeric) = 2.00024818526 -0.000500089934934
x1[1] (closed_form) = 2.00034638734 -0.000143194717085
absolute error = 0.0003702
relative error = 0.0185 %
Correct digits = 4
h = 0.0001 0.004
x2[1] (numeric) = 1.00261821806 0.00340691825957
x2[1] (closed_form) = 1.00332379234 0.00323307510277
absolute error = 0.0007267
relative error = 0.07243 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=5113.6MB, alloc=40.3MB, time=62.97
memory used=5158.1MB, alloc=40.3MB, time=63.50
t[1] = 1.5692 0.396
h = 0.003 0.006
x1[1] (numeric) = 2.00024721949 -0.000512514389956
x1[1] (closed_form) = 2.00034577721 -0.000144564660013
absolute error = 0.0003809
relative error = 0.01904 %
Correct digits = 4
h = 0.003 0.006
x2[1] (numeric) = 1.0025878077 0.00343908791455
x2[1] (closed_form) = 1.00329817894 0.00325952742627
absolute error = 0.0007327
relative error = 0.07303 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=5202.5MB, alloc=40.3MB, time=64.03
t[1] = 1.5722 0.402
h = 0.0001 0.005
x1[1] (numeric) = 2.00023721424 -0.00053100223174
x1[1] (closed_form) = 2.00034387045 -0.000146197457775
absolute error = 0.0003993
relative error = 0.01996 %
Correct digits = 4
h = 0.0001 0.005
x2[1] (numeric) = 1.00255675068 0.00347127154653
x2[1] (closed_form) = 1.00327748852 0.00331789808025
absolute error = 0.0007369
relative error = 0.07345 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=5246.9MB, alloc=40.3MB, time=64.56
t[1] = 1.5723 0.407
h = 0.0001 0.003
x1[1] (numeric) = 2.00023677319 -0.000546696853935
x1[1] (closed_form) = 2.00034310085 -0.000147900184624
absolute error = 0.0004127
relative error = 0.02063 %
Correct digits = 4
h = 0.0001 0.003
x2[1] (numeric) = 1.00252496417 0.00350339644101
x2[1] (closed_form) = 1.00324441455 0.00335032333894
absolute error = 0.0007356
relative error = 0.07332 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=5291.3MB, alloc=40.3MB, time=65.09
memory used=5335.9MB, alloc=40.3MB, time=65.64
t[1] = 1.5724 0.41
h = 0.001 0.001
x1[1] (numeric) = 2.00023635145 -0.000556142461865
x1[1] (closed_form) = 2.00034262135 -0.000148913927951
absolute error = 0.0004209
relative error = 0.02104 %
Correct digits = 4
h = 0.001 0.001
x2[1] (numeric) = 1.00249286847 0.00353528012465
x2[1] (closed_form) = 1.00322466099 0.00336989577914
absolute error = 0.0007502
relative error = 0.07478 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=5380.4MB, alloc=40.3MB, time=66.17
t[1] = 1.5734 0.411
h = 0.0001 0.004
x1[1] (numeric) = 2.00023302882 -0.000559286725391
x1[1] (closed_form) = 2.00034212996 -0.000149107292911
absolute error = 0.0004244
relative error = 0.02122 %
Correct digits = 4
h = 0.0001 0.004
x2[1] (numeric) = 1.00246067477 0.0035671186546
x2[1] (closed_form) = 1.00322411118 0.00338300076566
absolute error = 0.0007853
relative error = 0.07828 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=5424.7MB, alloc=40.3MB, time=66.70
memory used=5469.2MB, alloc=40.3MB, time=67.23
t[1] = 1.5735 0.415
h = 0.003 0.006
x1[1] (numeric) = 2.00023218552 -0.00057248189039
x1[1] (closed_form) = 2.00034149664 -0.000150459569531
absolute error = 0.0004359
relative error = 0.02179 %
Correct digits = 4
h = 0.003 0.006
x2[1] (numeric) = 1.00242831935 0.00359886087498
x2[1] (closed_form) = 1.00319726976 0.00340868946599
absolute error = 0.0007921
relative error = 0.07896 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=5513.5MB, alloc=40.3MB, time=67.76
t[1] = 1.5765 0.421
h = 0.0001 0.005
x1[1] (numeric) = 2.00022182769 -0.000592221881681
x1[1] (closed_form) = 2.00033956751 -0.000152048996934
absolute error = 0.0004556
relative error = 0.02278 %
Correct digits = 4
h = 0.0001 0.005
x2[1] (numeric) = 1.00239530444 0.00363059639779
x2[1] (closed_form) = 1.00317416737 0.00346675049253
absolute error = 0.0007959
relative error = 0.07934 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=5558.0MB, alloc=40.3MB, time=68.29
memory used=5602.4MB, alloc=40.3MB, time=68.82
t[1] = 1.5766 0.426
h = 0.0001 0.003
x1[1] (numeric) = 2.00022155377 -0.000608861913596
x1[1] (closed_form) = 2.00033876915 -0.000153729553086
absolute error = 0.00047
relative error = 0.0235 %
Correct digits = 4
h = 0.0001 0.003
x2[1] (numeric) = 1.00236154797 0.00366224846254
x2[1] (closed_form) = 1.00313957465 0.00349817569392
absolute error = 0.0007951
relative error = 0.07926 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=5647.0MB, alloc=40.3MB, time=69.36
t[1] = 1.5767 0.429
h = 0.001 0.001
x1[1] (numeric) = 2.00022122276 -0.000618880057499
x1[1] (closed_form) = 2.00033827261 -0.000154729693476
absolute error = 0.0004787
relative error = 0.02393 %
Correct digits = 4
h = 0.001 0.001
x2[1] (numeric) = 1.00232748419 0.00369364472298
x2[1] (closed_form) = 1.00311890619 0.00351715266081
absolute error = 0.0008109
relative error = 0.08083 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=5691.6MB, alloc=40.3MB, time=69.90
t[1] = 1.5777 0.43
h = 0.001 0.003
x1[1] (numeric) = 2.00021774432 -0.000622256230328
x1[1] (closed_form) = 2.00033777976 -0.00015491289828
absolute error = 0.0004825
relative error = 0.02412 %
Correct digits = 4
h = 0.001 0.003
x2[1] (numeric) = 1.002293322 0.00372499180868
x2[1] (closed_form) = 1.00311784903 0.00353034531223
absolute error = 0.0008472
relative error = 0.08446 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=5736.1MB, alloc=40.3MB, time=70.43
memory used=5780.7MB, alloc=40.3MB, time=70.96
t[1] = 1.5787 0.433
h = 0.0001 0.004
x1[1] (numeric) = 2.00021395057 -0.00063275126432
x1[1] (closed_form) = 2.00033697635 -0.000155769691324
absolute error = 0.0004926
relative error = 0.02463 %
Correct digits = 4
h = 0.0001 0.004
x2[1] (numeric) = 1.00225902599 0.00375634485368
x2[1] (closed_form) = 1.00310240957 0.00355566379918
absolute error = 0.0008669
relative error = 0.08642 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=5824.9MB, alloc=40.3MB, time=71.49
t[1] = 1.5788 0.437
h = 0.003 0.006
x1[1] (numeric) = 2.00021319944 -0.000647012696849
x1[1] (closed_form) = 2.00033631695 -0.000157100636144
absolute error = 0.0005051
relative error = 0.02525 %
Correct digits = 4
h = 0.003 0.006
x2[1] (numeric) = 1.00222446576 0.00378756460324
x2[1] (closed_form) = 1.00307415305 0.00358041832668
absolute error = 0.0008746
relative error = 0.08719 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=5869.2MB, alloc=40.3MB, time=72.02
memory used=5913.8MB, alloc=40.3MB, time=72.55
t[1] = 1.5818 0.443
h = 0.0001 0.005
x1[1] (numeric) = 2.00020223546 -0.000668429504362
x1[1] (closed_form) = 2.0003343637 -0.000158639066138
absolute error = 0.0005266
relative error = 0.02633 %
Correct digits = 4
h = 0.0001 0.005
x2[1] (numeric) = 1.00218923047 0.00381875443542
x2[1] (closed_form) = 1.00304823331 0.00363803963094
absolute error = 0.0008778
relative error = 0.08751 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=5958.0MB, alloc=40.3MB, time=73.08
t[1] = 1.5819 0.448
h = 0.0001 0.003
x1[1] (numeric) = 2.00020209468 -0.000686378857394
x1[1] (closed_form) = 2.00033353297 -0.000160292864598
absolute error = 0.0005423
relative error = 0.02711 %
Correct digits = 4
h = 0.0001 0.003
x2[1] (numeric) = 1.00215323881 0.00384983291013
x2[1] (closed_form) = 1.00301189225 0.00366824425495
absolute error = 0.0008776
relative error = 0.0875 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=6002.6MB, alloc=40.3MB, time=73.62
t[1] = 1.582 0.451
h = 0.001 0.001
x1[1] (numeric) = 2.00020183091 -0.000697187512657
x1[1] (closed_form) = 2.00033301729 -0.000161276612231
absolute error = 0.0005517
relative error = 0.02758 %
Correct digits = 4
h = 0.001 0.001
x2[1] (numeric) = 1.00211694141 0.00388063875153
x2[1] (closed_form) = 1.00299017033 0.00368649410246
absolute error = 0.0008946
relative error = 0.08919 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=6047.3MB, alloc=40.3MB, time=74.16
memory used=6091.9MB, alloc=40.3MB, time=74.69
t[1] = 1.583 0.452
h = 0.001 0.003
x1[1] (numeric) = 2.00019811828 -0.000700863791244
x1[1] (closed_form) = 2.00033252316 -0.000161448020057
absolute error = 0.0005559
relative error = 0.02779 %
Correct digits = 4
h = 0.001 0.003
x2[1] (numeric) = 1.00208054496 0.00391139081663
x2[1] (closed_form) = 1.0029885157 0.00369977335305
absolute error = 0.0009323
relative error = 0.09295 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=6136.3MB, alloc=40.3MB, time=75.22
t[1] = 1.584 0.455
h = 0.0001 0.004
x1[1] (numeric) = 2.00019415996 -0.000712208807624
x1[1] (closed_form) = 2.00033170545 -0.000162282497854
absolute error = 0.0005669
relative error = 0.02834 %
Correct digits = 4
h = 0.0001 0.004
x2[1] (numeric) = 1.00204401128 0.00394214432768
x2[1] (closed_form) = 1.00297179385 0.00372466157768
absolute error = 0.0009529
relative error = 0.09501 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=6180.6MB, alloc=40.3MB, time=75.76
memory used=6225.0MB, alloc=40.3MB, time=76.28
t[1] = 1.5841 0.459
h = 0.003 0.006
x1[1] (numeric) = 2.00019352636 -0.000727566911214
x1[1] (closed_form) = 2.00033102056 -0.000163591657863
absolute error = 0.0005805
relative error = 0.02902 %
Correct digits = 4
h = 0.003 0.006
x2[1] (numeric) = 1.00200721169 0.00397275216646
x2[1] (closed_form) = 1.00294215036 0.00374841021791
absolute error = 0.0009615
relative error = 0.09587 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=6269.4MB, alloc=40.3MB, time=76.82
t[1] = 1.5871 0.465
h = 0.0001 0.005
x1[1] (numeric) = 2.00018197308 -0.000750724237819
x1[1] (closed_form) = 2.00032904444 -0.000165078844544
absolute error = 0.0006038
relative error = 0.03019 %
Correct digits = 4
h = 0.0001 0.005
x2[1] (numeric) = 1.00196972194 0.00400330594016
x2[1] (closed_form) = 1.00291340617 0.00380546243759
absolute error = 0.0009642
relative error = 0.09614 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=6313.7MB, alloc=40.3MB, time=77.34
t[1] = 1.5872 0.47
h = 0.0001 0.003
x1[1] (numeric) = 2.00018199683 -0.00077002003089
x1[1] (closed_form) = 2.00032818212 -0.00016670532506
absolute error = 0.0006208
relative error = 0.03103 %
Correct digits = 4
h = 0.0001 0.003
x2[1] (numeric) = 1.0019314616 0.00403371946684
x2[1] (closed_form) = 1.00287535448 0.00383435723928
absolute error = 0.0009647
relative error = 0.09619 %
Correct digits = 3
memory used=6358.3MB, alloc=40.3MB, time=77.88
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=6403.0MB, alloc=40.3MB, time=78.42
t[1] = 1.5873 0.473
h = 0.001 0.001
x1[1] (numeric) = 2.00018181896 -0.000781641931238
x1[1] (closed_form) = 2.00032764776 -0.000167672351697
absolute error = 0.0006311
relative error = 0.03155 %
Correct digits = 4
h = 0.001 0.001
x2[1] (numeric) = 1.00189289769 0.00406384327341
x2[1] (closed_form) = 1.00285260149 0.00385182626983
absolute error = 0.0009828
relative error = 0.098 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=6447.6MB, alloc=40.3MB, time=78.96
t[1] = 1.5883 0.474
h = 0.001 0.003
x1[1] (numeric) = 2.0001778714 -0.000785632404003
x1[1] (closed_form) = 2.00032715261 -0.000167831999624
absolute error = 0.0006356
relative error = 0.03177 %
Correct digits = 3
h = 0.001 0.003
x2[1] (numeric) = 1.00185423423 0.00409390859714
x2[1] (closed_form) = 1.00285033987 0.00386516638129
absolute error = 0.001022
relative error = 0.1019 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=6492.1MB, alloc=40.3MB, time=79.48
memory used=6536.4MB, alloc=40.3MB, time=80.02
t[1] = 1.5893 0.477
h = 0.0001 0.004
x1[1] (numeric) = 2.0001737617 -0.000797856603929
x1[1] (closed_form) = 2.00032632116 -0.000168643972414
absolute error = 0.0006474
relative error = 0.03237 %
Correct digits = 3
h = 0.0001 0.004
x2[1] (numeric) = 1.00181543021 0.00412397066077
x2[1] (closed_form) = 1.00283234264 0.00388956327325
absolute error = 0.001044
relative error = 0.1041 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=6580.9MB, alloc=40.3MB, time=80.54
t[1] = 1.5894 0.481
h = 0.003 0.006
x1[1] (numeric) = 2.00017327274 -0.000814341977089
x1[1] (closed_form) = 2.00032561141 -0.000169930910472
absolute error = 0.0006622
relative error = 0.0331 %
Correct digits = 3
h = 0.003 0.006
x2[1] (numeric) = 1.00177635894 0.00415387439271
x2[1] (closed_form) = 1.00280134378 0.00391223486048
absolute error = 0.001053
relative error = 0.105 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=6625.2MB, alloc=40.3MB, time=81.07
memory used=6669.7MB, alloc=40.3MB, time=81.60
t[1] = 1.5924 0.487
h = 0.0001 0.005
x1[1] (numeric) = 2.00016114955 -0.000839305070098
x1[1] (closed_form) = 2.00032361367 -0.000171366636631
absolute error = 0.0006874
relative error = 0.03437 %
Correct digits = 3
h = 0.0001 0.005
x2[1] (numeric) = 1.0017365829 0.00418369898215
x2[1] (closed_form) = 1.00276977373 0.00396858705148
absolute error = 0.001055
relative error = 0.1052 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=6714.1MB, alloc=40.3MB, time=82.13
t[1] = 1.5925 0.492
h = 0.0001 0.003
x1[1] (numeric) = 2.00016137142 -0.000859984653986
x1[1] (closed_form) = 2.00032272052 -0.000172965258775
absolute error = 0.0007057
relative error = 0.03528 %
Correct digits = 3
h = 0.0001 0.003
x2[1] (numeric) = 1.00169602275 0.00421335344661
x2[1] (closed_form) = 1.00273005347 0.00399608358903
absolute error = 0.001057
relative error = 0.1054 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=6758.6MB, alloc=40.3MB, time=82.66
t[1] = 1.5926 0.495
h = 0.001 0.001
x1[1] (numeric) = 2.00016129941 -0.000872442689498
x1[1] (closed_form) = 2.00032216796 -0.000173915248153
absolute error = 0.0007168
relative error = 0.03583 %
Correct digits = 3
h = 0.001 0.001
x2[1] (numeric) = 1.00165516176 0.00424270085791
x2[1] (closed_form) = 1.00270629435 0.00401271857329
absolute error = 0.001076
relative error = 0.1073 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=6803.2MB, alloc=40.3MB, time=83.20
memory used=6847.5MB, alloc=40.3MB, time=83.74
t[1] = 1.5936 0.496
h = 0.001 0.003
x1[1] (numeric) = 2.00015711657 -0.000876761923479
x1[1] (closed_form) = 2.00032167205 -0.000174063178859
absolute error = 0.0007217
relative error = 0.03608 %
Correct digits = 3
h = 0.001 0.003
x2[1] (numeric) = 1.00161420086 0.00427198497693
x2[1] (closed_form) = 1.0027034173 0.00402609313313
absolute error = 0.001117
relative error = 0.1114 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=6892.0MB, alloc=40.3MB, time=84.27
t[1] = 1.5946 0.499
h = 0.0001 0.004
x1[1] (numeric) = 2.00015287005 -0.000889895035309
x1[1] (closed_form) = 2.00032082742 -0.000174852470345
absolute error = 0.0007345
relative error = 0.03672 %
Correct digits = 3
h = 0.0001 0.004
x2[1] (numeric) = 1.00157309616 0.00430126093628
x2[1] (closed_form) = 1.00268415447 0.00404993733538
absolute error = 0.001139
relative error = 0.1136 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=6936.4MB, alloc=40.3MB, time=84.81
memory used=6980.8MB, alloc=40.3MB, time=85.34
t[1] = 1.5947 0.503
h = 0.003 0.006
x1[1] (numeric) = 2.00015255465 -0.000907538413652
x1[1] (closed_form) = 2.00032009344 -0.000176116765242
absolute error = 0.0007504
relative error = 0.03751 %
Correct digits = 3
h = 0.003 0.006
x2[1] (numeric) = 1.00153172326 0.00433036562745
x2[1] (closed_form) = 1.00265183531 0.0040714614119
absolute error = 0.00115
relative error = 0.1147 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=7025.4MB, alloc=40.3MB, time=85.87
t[1] = 1.5977 0.509
h = 0.0001 0.005
x1[1] (numeric) = 2.0001398836 -0.000934374012789
x1[1] (closed_form) = 2.00031807532 -0.000177500842174
absolute error = 0.0007776
relative error = 0.03887 %
Correct digits = 3
h = 0.0001 0.005
x2[1] (numeric) = 1.00148963152 0.00435936516781
x2[1] (closed_form) = 1.0026174438 0.00412698128566
absolute error = 0.001152
relative error = 0.1148 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=7069.8MB, alloc=40.3MB, time=86.40
t[1] = 1.5978 0.514
h = 0.0001 0.003
x1[1] (numeric) = 2.00014033942 -0.000956474897857
x1[1] (closed_form) = 2.00031715213 -0.000179071085403
absolute error = 0.0007973
relative error = 0.03986 %
Correct digits = 3
h = 0.0001 0.003
x2[1] (numeric) = 1.00144674282 0.0043881637193
x2[1] (closed_form) = 1.00257610136 0.00415299212084
absolute error = 0.001154
relative error = 0.1151 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=7114.3MB, alloc=40.3MB, time=86.93
memory used=7159.0MB, alloc=40.3MB, time=87.47
t[1] = 1.5979 0.517
h = 0.001 0.001
x1[1] (numeric) = 2.00014039458 -0.000969792071763
x1[1] (closed_form) = 2.00031658183 -0.000180003733273
absolute error = 0.0008092
relative error = 0.04045 %
Correct digits = 3
h = 0.001 0.001
x2[1] (numeric) = 1.00140355663 0.00441663765037
x2[1] (closed_form) = 1.00255136369 0.00416874041811
absolute error = 0.001174
relative error = 0.1171 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=7203.4MB, alloc=40.3MB, time=88.01
t[1] = 1.5989 0.518
h = 0.0001 0.004
x1[1] (numeric) = 2.00013597658 -0.000974455109639
x1[1] (closed_form) = 2.00031608543 -0.000180139994954
absolute error = 0.0008145
relative error = 0.04072 %
Correct digits = 3
h = 0.0001 0.004
x2[1] (numeric) = 1.00136027031 0.00444504337902
x2[1] (closed_form) = 1.00254786386 0.00418212237987
absolute error = 0.001216
relative error = 0.1213 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=7248.0MB, alloc=40.3MB, time=88.54
memory used=7292.5MB, alloc=40.3MB, time=89.07
t[1] = 1.599 0.522
h = 0.003 0.006
x1[1] (numeric) = 2.00013587852 -0.000992974821185
x1[1] (closed_form) = 2.0003153308 -0.000181384752783
absolute error = 0.0008312
relative error = 0.04155 %
Correct digits = 3
h = 0.003 0.006
x2[1] (numeric) = 1.00131682272 0.00447331241775
x2[1] (closed_form) = 1.00251445377 0.00420258786209
absolute error = 0.001228
relative error = 0.1225 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=7336.8MB, alloc=40.3MB, time=89.60
t[1] = 1.602 0.528
h = 0.0001 0.005
x1[1] (numeric) = 2.00012292384 -0.00102128867751
x1[1] (closed_form) = 2.00031329553 -0.00018272446486
absolute error = 0.0008599
relative error = 0.04299 %
Correct digits = 3
h = 0.0001 0.005
x2[1] (numeric) = 1.00127264593 0.0045014518355
x2[1] (closed_form) = 1.00247765375 0.00425725109853
absolute error = 0.00123
relative error = 0.1226 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=7381.0MB, alloc=40.3MB, time=90.12
memory used=7425.5MB, alloc=40.3MB, time=90.65
t[1] = 1.6021 0.533
h = 0.0001 0.003
x1[1] (numeric) = 2.00012366424 -0.00104446381408
x1[1] (closed_form) = 2.00031234676 -0.000184270223977
absolute error = 0.0008806
relative error = 0.04403 %
Correct digits = 3
h = 0.0001 0.003
x2[1] (numeric) = 1.00122766337 0.00452936156108
x2[1] (closed_form) = 1.00243497455 0.0042818954978
absolute error = 0.001232
relative error = 0.1229 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=7470.0MB, alloc=40.3MB, time=91.20
t[1] = 1.6022 0.536
h = 0.001 0.001
x1[1] (numeric) = 2.0001238802 -0.001058432758
x1[1] (closed_form) = 2.00031176136 -0.00018518791391
absolute error = 0.0008932
relative error = 0.04465 %
Correct digits = 3
h = 0.001 0.001
x2[1] (numeric) = 1.00118238783 0.00455693124685
x2[1] (closed_form) = 1.00240943005 0.00429682778949
absolute error = 0.001254
relative error = 0.1251 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=7514.4MB, alloc=40.3MB, time=91.73
t[1] = 1.6032 0.537
h = 0.001 0.003
x1[1] (numeric) = 2.00011930574 -0.00106337869667
x1[1] (closed_form) = 2.0003112646 -0.000185314175764
absolute error = 0.0008988
relative error = 0.04493 %
Correct digits = 3
h = 0.001 0.003
x2[1] (numeric) = 1.00113701239 0.00458442832298
x2[1] (closed_form) = 1.00240538948 0.00431018649499
absolute error = 0.001298
relative error = 0.1295 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=7558.3MB, alloc=40.3MB, time=92.25
memory used=7602.4MB, alloc=40.3MB, time=92.78
t[1] = 1.6042 0.54
h = 0.0001 0.004
x1[1] (numeric) = 2.00011491389 -0.00107818833254
x1[1] (closed_form) = 2.00031039671 -0.000186060980208
absolute error = 0.0009133
relative error = 0.04566 %
Correct digits = 3
h = 0.0001 0.004
x2[1] (numeric) = 1.00109148763 0.00461190732821
x2[1] (closed_form) = 1.0023838157 0.00433282382222
absolute error = 0.001322
relative error = 0.1319 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=7646.2MB, alloc=40.3MB, time=93.30
t[1] = 1.6043 0.544
h = 0.003 0.006
x1[1] (numeric) = 2.00011504944 -0.00109792968338
x1[1] (closed_form) = 2.00030961902 -0.000187282346062
absolute error = 0.0009312
relative error = 0.04655 %
Correct digits = 3
h = 0.003 0.006
x2[1] (numeric) = 1.00104569473 0.00463919001237
x2[1] (closed_form) = 1.00234916063 0.00435201364144
absolute error = 0.001335
relative error = 0.1332 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=7690.2MB, alloc=40.3MB, time=93.83
memory used=7734.2MB, alloc=40.3MB, time=94.35
t[1] = 1.6073 0.55
h = 0.0001 0.005
x1[1] (numeric) = 2.00010159274 -0.00112825445591
x1[1] (closed_form) = 2.00030756567 -0.000188570118176
absolute error = 0.000962
relative error = 0.04809 %
Correct digits = 3
h = 0.0001 0.005
x2[1] (numeric) = 1.00099915964 0.00466631541173
x2[1] (closed_form) = 1.00230956477 0.00440559589046
absolute error = 0.001336
relative error = 0.1333 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=7778.1MB, alloc=40.3MB, time=94.88
t[1] = 1.6074 0.555
h = 0.0001 0.003
x1[1] (numeric) = 2.00010264155 -0.00115292876828
x1[1] (closed_form) = 2.00030658832 -0.00019008657341
absolute error = 0.0009842
relative error = 0.0492 %
Correct digits = 3
h = 0.0001 0.003
x2[1] (numeric) = 1.00095180737 0.00469317851804
x2[1] (closed_form) = 1.00226536227 0.0044285959266
absolute error = 0.00134
relative error = 0.1337 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=7822.1MB, alloc=40.3MB, time=95.41
t[1] = 1.6075 0.558
h = 0.001 0.001
x1[1] (numeric) = 2.00010302904 -0.00116780456123
x1[1] (closed_form) = 2.00030598608 -0.000190986382015
absolute error = 0.0009977
relative error = 0.04988 %
Correct digits = 3
h = 0.001 0.001
x2[1] (numeric) = 1.00090416658 0.00471968365582
x2[1] (closed_form) = 1.00223889807 0.00444254596525
absolute error = 0.001363
relative error = 0.136 %
Correct digits = 3
memory used=7866.6MB, alloc=40.3MB, time=95.94
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=7910.7MB, alloc=40.3MB, time=96.47
t[1] = 1.6085 0.559
h = 0.001 0.003
x1[1] (numeric) = 2.00009821968 -0.00117312548413
x1[1] (closed_form) = 2.0003054893 -0.000191101075897
absolute error = 0.001004
relative error = 0.05018 %
Correct digits = 3
h = 0.001 0.003
x2[1] (numeric) = 1.00085642597 0.00474611110508
x2[1] (closed_form) = 1.00223422441 0.00445586014994
absolute error = 0.001408
relative error = 0.1405 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=7954.7MB, alloc=40.3MB, time=97.00
t[1] = 1.6095 0.562
h = 0.0001 0.004
x1[1] (numeric) = 2.00009373998 -0.00118893671633
x1[1] (closed_form) = 2.00030460986 -0.000191824761769
absolute error = 0.001019
relative error = 0.05095 %
Correct digits = 3
h = 0.0001 0.004
x2[1] (numeric) = 1.0008085331 0.00477251504223
x2[1] (closed_form) = 1.00221142944 0.00447776900174
absolute error = 0.001434
relative error = 0.143 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=7998.7MB, alloc=40.3MB, time=97.52
memory used=8042.9MB, alloc=40.3MB, time=98.05
t[1] = 1.6096 0.566
h = 0.003 0.006
x1[1] (numeric) = 2.00009414375 -0.00120993044259
x1[1] (closed_form) = 2.00030380975 -0.000193022360174
absolute error = 0.001038
relative error = 0.05191 %
Correct digits = 3
h = 0.003 0.006
x2[1] (numeric) = 1.00076037229 0.00479870899494
x2[1] (closed_form) = 1.00217557436 0.0044956156624
absolute error = 0.001447
relative error = 0.1444 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=8086.7MB, alloc=40.3MB, time=98.57
t[1] = 1.6126 0.572
h = 0.0001 0.005
x1[1] (numeric) = 2.00008021562 -0.00124233687532
x1[1] (closed_form) = 2.00030173957 -0.000194258084037
absolute error = 0.001071
relative error = 0.05355 %
Correct digits = 3
h = 0.0001 0.005
x2[1] (numeric) = 1.00071145691 0.00482471706769
x2[1] (closed_form) = 1.00213320427 0.00454798224227
absolute error = 0.001448
relative error = 0.1445 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=8130.6MB, alloc=40.3MB, time=99.09
memory used=8174.7MB, alloc=40.3MB, time=99.62
t[1] = 1.6127 0.577
h = 0.0001 0.003
x1[1] (numeric) = 2.00008161568 -0.00126854783757
x1[1] (closed_form) = 2.00030073444 -0.000195744771939
absolute error = 0.001095
relative error = 0.05474 %
Correct digits = 3
h = 0.0001 0.003
x2[1] (numeric) = 1.00066171373 0.00485042927082
x2[1] (closed_form) = 1.00208753723 0.00456925452492
absolute error = 0.001453
relative error = 0.145 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=8218.9MB, alloc=40.3MB, time=100.15
t[1] = 1.6128 0.58
h = 0.001 0.001
x1[1] (numeric) = 2.00008220025 -0.00128435351224
x1[1] (closed_form) = 2.00030011584 -0.000196626429429
absolute error = 0.001109
relative error = 0.05546 %
Correct digits = 3
h = 0.001 0.001
x2[1] (numeric) = 1.00061168717 0.00487576537791
x2[1] (closed_form) = 1.00206018834 0.00458217206034
absolute error = 0.001478
relative error = 0.1475 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=8263.0MB, alloc=40.3MB, time=100.68
t[1] = 1.6138 0.581
h = 0.001 0.003
x1[1] (numeric) = 2.00007715759 -0.00129006583187
x1[1] (closed_form) = 2.00029961929 -0.000196729618889
absolute error = 0.001116
relative error = 0.05578 %
Correct digits = 3
h = 0.001 0.003
x2[1] (numeric) = 1.00056156102 0.00490101862357
x2[1] (closed_form) = 1.00205487756 0.00459541312014
absolute error = 0.001524
relative error = 0.1521 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=8307.0MB, alloc=40.3MB, time=101.21
memory used=8350.9MB, alloc=40.3MB, time=101.73
t[1] = 1.6148 0.584
h = 0.0001 0.004
x1[1] (numeric) = 2.00007261036 -0.0013069100904
x1[1] (closed_form) = 2.00029872888 -0.000197430061332
absolute error = 0.001132
relative error = 0.05661 %
Correct digits = 3
h = 0.0001 0.004
x2[1] (numeric) = 1.00051127976 0.00492624272042
x2[1] (closed_form) = 1.00203088225 0.00461653222802
absolute error = 0.001551
relative error = 0.1548 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=8394.8MB, alloc=40.3MB, time=102.26
t[1] = 1.6149 0.588
h = 0.003 0.006
x1[1] (numeric) = 2.00007331893 -0.00132918681137
x1[1] (closed_form) = 2.00029790698 -0.000198603532881
absolute error = 0.001153
relative error = 0.05763 %
Correct digits = 3
h = 0.003 0.006
x2[1] (numeric) = 1.0004607312 0.00495124291593
x2[1] (closed_form) = 1.00199387558 0.00463296957274
absolute error = 0.001566
relative error = 0.1563 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=8438.7MB, alloc=40.3MB, time=102.77
memory used=8482.7MB, alloc=40.3MB, time=103.30
t[1] = 1.6179 0.594
h = 0.0001 0.005
x1[1] (numeric) = 2.00005895309 -0.00136374688416
x1[1] (closed_form) = 2.00029582121 -0.000199787127857
absolute error = 0.001188
relative error = 0.05938 %
Correct digits = 3
h = 0.0001 0.005
x2[1] (numeric) = 1.00040941636 0.00497602770625
x2[1] (closed_form) = 1.00194875908 0.00468398544521
absolute error = 0.001567
relative error = 0.1564 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=8526.7MB, alloc=40.3MB, time=103.82
t[1] = 1.618 0.599
h = 0.0001 0.003
x1[1] (numeric) = 2.00006074971 -0.00139153181297
x1[1] (closed_form) = 2.0002947891 -0.00020124360503
absolute error = 0.001213
relative error = 0.06065 %
Correct digits = 3
h = 0.0001 0.003
x2[1] (numeric) = 1.00035726394 0.0050004820801
x2[1] (closed_form) = 1.00190169052 0.00470344837877
absolute error = 0.001573
relative error = 0.157 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=8570.8MB, alloc=40.3MB, time=104.35
memory used=8615.2MB, alloc=40.3MB, time=104.89
t[1] = 1.6181 0.602
h = 0.001 0.001
x1[1] (numeric) = 2.0000615584 -0.0014082903255
x1[1] (closed_form) = 2.00029415462 -0.000202106853705
absolute error = 0.001228
relative error = 0.06141 %
Correct digits = 3
h = 0.001 0.001
x2[1] (numeric) = 1.00030483394 0.00502454204567
x2[1] (closed_form) = 1.00187349452 0.00471528422453
absolute error = 0.001599
relative error = 0.1596 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=8659.1MB, alloc=40.3MB, time=105.43
t[1] = 1.6191 0.603
h = 0.001 0.003
x1[1] (numeric) = 2.00005628458 -0.00141441090741
x1[1] (closed_form) = 2.00029365856 -0.000202198607487
absolute error = 0.001235
relative error = 0.06175 %
Correct digits = 3
h = 0.001 0.003
x2[1] (numeric) = 1.00025230475 0.0050485138856
x2[1] (closed_form) = 1.00186754383 0.0047284230972
absolute error = 0.001647
relative error = 0.1644 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=8703.1MB, alloc=40.3MB, time=105.95
t[1] = 1.6201 0.606
h = 0.0001 0.004
x1[1] (numeric) = 2.0000516917 -0.00143231995821
x1[1] (closed_form) = 2.00029275774 -0.0002028756948
absolute error = 0.001253
relative error = 0.06263 %
Correct digits = 3
h = 0.0001 0.004
x2[1] (numeric) = 1.00019961774 0.00507245074429
x2[1] (closed_form) = 1.00184237197 0.00474869151995
absolute error = 0.001674
relative error = 0.1671 %
Correct digits = 3
memory used=8747.3MB, alloc=40.3MB, time=106.48
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=8791.2MB, alloc=40.3MB, time=107.00
t[1] = 1.6202 0.61
h = 0.003 0.006
x1[1] (numeric) = 2.00005274371 -0.00145591010527
x1[1] (closed_form) = 2.00029191471 -0.000204024696162
absolute error = 0.001275
relative error = 0.06372 %
Correct digits = 3
h = 0.003 0.006
x2[1] (numeric) = 1.00014666449 0.00509614953851
x2[1] (closed_form) = 1.00180426553 0.00476365489529
absolute error = 0.001691
relative error = 0.1688 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=8835.0MB, alloc=40.3MB, time=107.52
t[1] = 1.6232 0.616
h = 0.0001 0.005
x1[1] (numeric) = 2.00003797708 -0.00149269695789
x1[1] (closed_form) = 2.00028981456 -0.000205156109019
absolute error = 0.001312
relative error = 0.06559 %
Correct digits = 3
h = 0.0001 0.005
x2[1] (numeric) = 1.00009293395 0.00511960247417
x2[1] (closed_form) = 1.0017564367 0.00481318493768
absolute error = 0.001691
relative error = 0.1689 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=8879.0MB, alloc=40.3MB, time=108.04
memory used=8923.1MB, alloc=40.3MB, time=108.57
t[1] = 1.6233 0.621
h = 0.0001 0.003
x1[1] (numeric) = 2.00004021809 -0.00152209292396
x1[1] (closed_form) = 2.00028875629 -0.000206581952129
absolute error = 0.001339
relative error = 0.06693 %
Correct digits = 3
h = 0.0001 0.003
x2[1] (numeric) = 1.00003835693 0.00514268948262
x2[1] (closed_form) = 1.00170803389 0.00483075892886
absolute error = 0.001699
relative error = 0.1696 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=8967.3MB, alloc=40.3MB, time=109.10
t[1] = 1.6234 0.624
h = 0.001 0.001
x1[1] (numeric) = 2.00004127949 -0.00153982710083
x1[1] (closed_form) = 2.00028810643 -0.000207426546385
absolute error = 0.001355
relative error = 0.06774 %
Correct digits = 3
h = 0.001 0.001
x2[1] (numeric) = 0.999983508822 0.0051653636004
x2[1] (closed_form) = 1.00167903091 0.00484146508704
absolute error = 0.001726
relative error = 0.1723 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=9011.4MB, alloc=40.3MB, time=109.63
memory used=9055.5MB, alloc=40.3MB, time=110.16
t[1] = 1.6244 0.625
h = 0.0001 0.004
x1[1] (numeric) = 2.00003577722 -0.00154637325584
x1[1] (closed_form) = 2.00028761111 -0.000207506938329
absolute error = 0.001362
relative error = 0.06811 %
Correct digits = 3
h = 0.0001 0.004
x2[1] (numeric) = 0.999928562074 0.00518794423991
x2[1] (closed_form) = 1.00167243879 0.00485447230247
absolute error = 0.001775
relative error = 0.1772 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=9099.4MB, alloc=40.3MB, time=110.68
t[1] = 1.6245 0.629
h = 0.003 0.006
x1[1] (numeric) = 2.00003717504 -0.0015709464303
x1[1] (closed_form) = 2.0002867501 -0.000208634855105
absolute error = 0.001385
relative error = 0.06924 %
Correct digits = 3
h = 0.003 0.006
x2[1] (numeric) = 0.999873461156 0.00521034457926
x2[1] (closed_form) = 1.00163344837 0.00486810423489
absolute error = 0.001793
relative error = 0.179 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=9143.3MB, alloc=40.3MB, time=111.21
memory used=9187.4MB, alloc=40.3MB, time=111.74
t[1] = 1.6275 0.635
h = 0.0001 0.005
x1[1] (numeric) = 2.00002224379 -0.00160946301701
x1[1] (closed_form) = 2.00028463794 -0.000209721480853
absolute error = 0.001424
relative error = 0.0712 %
Correct digits = 3
h = 0.0001 0.005
x2[1] (numeric) = 0.9998175758 0.00523247087994
x2[1] (closed_form) = 1.00158333686 0.00491621562343
absolute error = 0.001794
relative error = 0.1791 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=9231.4MB, alloc=40.3MB, time=112.27
t[1] = 1.6276 0.64
h = 0.0001 0.003
x1[1] (numeric) = 2.00002492837 -0.00164006321024
x1[1] (closed_form) = 2.00028355743 -0.000211120929984
absolute error = 0.001452
relative error = 0.0726 %
Correct digits = 3
h = 0.0001 0.003
x2[1] (numeric) = 0.999760839193 0.00525419874425
x2[1] (closed_form) = 1.00153386641 0.00493208689697
absolute error = 0.001802
relative error = 0.1799 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=9275.6MB, alloc=40.3MB, time=112.81
t[1] = 1.6277 0.643
h = 0.001 0.001
x1[1] (numeric) = 2.00002624581 -0.00165852935689
x1[1] (closed_form) = 2.0002828945 -0.000211949454938
absolute error = 0.001469
relative error = 0.07345 %
Correct digits = 3
h = 0.001 0.001
x2[1] (numeric) = 0.999703838902 0.0052754977813
x2[1] (closed_form) = 1.00150421708 0.00494177430662
absolute error = 0.001831
relative error = 0.1828 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=9319.8MB, alloc=40.3MB, time=113.34
memory used=9363.9MB, alloc=40.3MB, time=113.88
t[1] = 1.6287 0.644
h = 0.001 0.003
x1[1] (numeric) = 2.00002059504 -0.00166541781351
x1[1] (closed_form) = 2.00028239987 -0.000212020117251
absolute error = 0.001477
relative error = 0.07383 %
Correct digits = 3
h = 0.001 0.003
x2[1] (numeric) = 0.999646740951 0.00529669861015
x2[1] (closed_form) = 1.00149707465 0.00495463668286
absolute error = 0.001882
relative error = 0.1879 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=9407.7MB, alloc=40.3MB, time=114.40
t[1] = 1.6297 0.647
h = 0.0001 0.004
x1[1] (numeric) = 2.00001603423 -0.00168527269598
x1[1] (closed_form) = 2.00028148091 -0.000212653601523
absolute error = 0.001496
relative error = 0.07481 %
Correct digits = 3
h = 0.0001 0.004
x2[1] (numeric) = 0.999589480826 0.00531785282429
x2[1] (closed_form) = 1.00146979866 0.00497314844968
absolute error = 0.001912
relative error = 0.1909 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=9451.5MB, alloc=40.3MB, time=114.92
memory used=9495.6MB, alloc=40.3MB, time=115.45
t[1] = 1.6298 0.651
h = 0.003 0.006
x1[1] (numeric) = 2.00001785534 -0.00171122198983
x1[1] (closed_form) = 2.00028059999 -0.000213756444236
absolute error = 0.00152
relative error = 0.07601 %
Correct digits = 3
h = 0.003 0.006
x2[1] (numeric) = 0.99953195862 0.00533874185456
x2[1] (closed_form) = 1.00142981459 0.00498519139157
absolute error = 0.001931
relative error = 0.1928 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=9539.6MB, alloc=40.3MB, time=115.97
t[1] = 1.6328 0.657
h = 0.0001 0.005
x1[1] (numeric) = 2.00000259977 -0.00175211635397
x1[1] (closed_form) = 2.00027847572 -0.000214790846394
absolute error = 0.001562
relative error = 0.07808 %
Correct digits = 3
h = 0.0001 0.005
x2[1] (numeric) = 0.999473642338 0.00535932476552
x2[1] (closed_form) = 1.00137707266 0.00503156683492
absolute error = 0.001931
relative error = 0.1929 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=9583.6MB, alloc=40.3MB, time=116.50
memory used=9627.7MB, alloc=40.3MB, time=117.02
t[1] = 1.6329 0.662
h = 0.0001 0.003
x1[1] (numeric) = 2.00000582772 -0.0017844041704
x1[1] (closed_form) = 2.00027737056 -0.000216158917365
absolute error = 0.001592
relative error = 0.07957 %
Correct digits = 3
h = 0.0001 0.003
x2[1] (numeric) = 0.999414467664 0.00537947205877
x2[1] (closed_form) = 1.00132640514 0.00504540802085
absolute error = 0.001941
relative error = 0.1938 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=9672.0MB, alloc=40.3MB, time=117.56
t[1] = 1.633 0.665
h = 0.001 0.001
x1[1] (numeric) = 2.00000745704 -0.00180389308717
x1[1] (closed_form) = 2.00027669316 -0.00021696835715
absolute error = 0.00161
relative error = 0.08047 %
Correct digits = 3
h = 0.001 0.001
x2[1] (numeric) = 0.999355037053 0.00539917180885
x2[1] (closed_form) = 1.00129603073 0.00505388056944
absolute error = 0.001971
relative error = 0.1969 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=9716.1MB, alloc=40.3MB, time=118.09
t[1] = 1.634 0.666
h = 0.001 0.003
x1[1] (numeric) = 2.00000158351 -0.00181124283958
x1[1] (closed_form) = 2.00027619972 -0.000217027805425
absolute error = 0.001618
relative error = 0.08087 %
Correct digits = 3
h = 0.001 0.003
x2[1] (numeric) = 0.999295509674 0.00541876785526
x2[1] (closed_form) = 1.00128824786 0.00506655556512
absolute error = 0.002024
relative error = 0.2021 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=9760.1MB, alloc=40.3MB, time=118.62
memory used=9804.2MB, alloc=40.3MB, time=119.14
t[1] = 1.635 0.669
h = 0.0001 0.004
x1[1] (numeric) = 1.99999704917 -0.00183226052236
x1[1] (closed_form) = 2.00027527198 -0.000217637680172
absolute error = 0.001638
relative error = 0.08191 %
Correct digits = 3
h = 0.0001 0.004
x2[1] (numeric) = 0.999235817796 0.00543831091291
x2[1] (closed_form) = 1.00125988027 0.00508404571673
absolute error = 0.002055
relative error = 0.2052 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=9848.1MB, alloc=40.3MB, time=119.66
t[1] = 1.6351 0.673
h = 0.003 0.006
x1[1] (numeric) = 1.9999993385 -0.00185961532481
x1[1] (closed_form) = 2.00027437179 -0.000218715151455
absolute error = 0.001664
relative error = 0.08318 %
Correct digits = 3
h = 0.003 0.006
x2[1] (numeric) = 0.999175866243 0.00545757399814
x2[1] (closed_form) = 1.0012189639 0.00509444027409
absolute error = 0.002075
relative error = 0.2073 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=9892.0MB, alloc=40.3MB, time=120.19
memory used=9936.1MB, alloc=40.3MB, time=120.74
t[1] = 1.6381 0.679
h = 0.0001 0.005
x1[1] (numeric) = 1.99998380579 -0.00190296347134
x1[1] (closed_form) = 2.00027223663 -0.000219697353783
absolute error = 0.001708
relative error = 0.08538 %
Correct digits = 3
h = 0.0001 0.005
x2[1] (numeric) = 0.999115111769 0.00547649796377
x2[1] (closed_form) = 1.00116364387 0.00513894603874
absolute error = 0.002076
relative error = 0.2074 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=9980.2MB, alloc=40.3MB, time=121.27
t[1] = 1.6382 0.684
h = 0.0001 0.003
x1[1] (numeric) = 1.99998763271 -0.00193697464399
x1[1] (closed_form) = 2.00027110764 -0.0002210336806
absolute error = 0.001739
relative error = 0.08695 %
Correct digits = 3
h = 0.0001 0.003
x2[1] (numeric) = 0.999053492763 0.00549494818758
x2[1] (closed_form) = 1.00111185835 0.00515068446723
absolute error = 0.002087
relative error = 0.2085 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=10024.3MB, alloc=40.3MB, time=121.80
t[1] = 1.6383 0.687
h = 0.001 0.001
x1[1] (numeric) = 1.99998960718 -0.00195750840711
x1[1] (closed_form) = 2.00027041627 -0.00022182382415
absolute error = 0.001758
relative error = 0.0879 %
Correct digits = 3
h = 0.001 0.001
x2[1] (numeric) = 0.99899162629 0.00551293202473
x2[1] (closed_form) = 1.00108080609 0.00515789827544
absolute error = 0.002119
relative error = 0.2117 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=10068.7MB, alloc=40.3MB, time=122.34
memory used=10112.7MB, alloc=40.3MB, time=122.86
t[1] = 1.6393 0.688
h = 0.001 0.003
x1[1] (numeric) = 1.9999835155 -0.001965338014
x1[1] (closed_form) = 2.00026992426 -0.000221872146348
absolute error = 0.001767
relative error = 0.08833 %
Correct digits = 3
h = 0.001 0.003
x2[1] (numeric) = 0.998929664124 0.00553080658285
x2[1] (closed_form) = 1.00107238503 0.00517035556484
absolute error = 0.002173
relative error = 0.217 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=10156.7MB, alloc=40.3MB, time=123.39
t[1] = 1.6403 0.691
h = 0.0001 0.004
x1[1] (numeric) = 1.99997903624 -0.00198755109103
x1[1] (closed_form) = 2.0002689883 -0.000222458349862
absolute error = 0.001789
relative error = 0.08943 %
Correct digits = 3
h = 0.0001 0.004
x2[1] (numeric) = 0.998867535286 0.00554862158278
x2[1] (closed_form) = 1.00104296099 0.00518676572498
absolute error = 0.002205
relative error = 0.2203 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=10200.6MB, alloc=40.3MB, time=123.92
memory used=10244.7MB, alloc=40.3MB, time=124.44
t[1] = 1.6404 0.695
h = 0.003 0.006
x1[1] (numeric) = 1.99998184091 -0.0020163402982
x1[1] (closed_form) = 2.00026806951 -0.000223510168406
absolute error = 0.001816
relative error = 0.09076 %
Correct digits = 3
h = 0.003 0.006
x2[1] (numeric) = 0.998805149676 0.00556614160598
x2[1] (closed_form) = 1.00100117691 0.00519545464814
absolute error = 0.002227
relative error = 0.2225 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=10288.7MB, alloc=40.3MB, time=124.96
t[1] = 1.6434 0.701
h = 0.0001 0.005
x1[1] (numeric) = 1.99996608191 -0.00206221903827
x1[1] (closed_form) = 2.00026592466 -0.000224440221002
absolute error = 0.001862
relative error = 0.09309 %
Correct digits = 3
h = 0.0001 0.005
x2[1] (numeric) = 0.998741953132 0.0055832885945
x2[1] (closed_form) = 1.00094333755 0.00523795801886
absolute error = 0.002228
relative error = 0.2226 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=10332.7MB, alloc=40.3MB, time=125.49
memory used=10376.7MB, alloc=40.3MB, time=126.01
t[1] = 1.6435 0.706
h = 0.0001 0.003
x1[1] (numeric) = 1.99997056612 -0.00209798867387
x1[1] (closed_form) = 2.00026477266 -0.0002257444577
absolute error = 0.001895
relative error = 0.09475 %
Correct digits = 3
h = 0.0001 0.003
x2[1] (numeric) = 0.998677886958 0.00559992278421
x2[1] (closed_form) = 1.00089051709 0.00524752382181
absolute error = 0.002241
relative error = 0.2238 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=10421.0MB, alloc=40.3MB, time=126.55
t[1] = 1.6436 0.709
h = 0.001 0.001
x1[1] (numeric) = 1.99997292066 -0.00211958900187
x1[1] (closed_form) = 2.00026406783 -0.000226515106004
absolute error = 0.001915
relative error = 0.09575 %
Correct digits = 3
h = 0.001 0.001
x2[1] (numeric) = 0.998613582526 0.00561607163304
x2[1] (closed_form) = 1.00085883664 0.00525343667948
absolute error = 0.002274
relative error = 0.2272 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=10465.1MB, alloc=40.3MB, time=127.09
t[1] = 1.6446 0.71
h = 0.001 0.003
x1[1] (numeric) = 1.99996661615 -0.00212791742456
x1[1] (closed_form) = 2.00026357747 -0.000226552394825
absolute error = 0.001924
relative error = 0.09621 %
Correct digits = 3
h = 0.001 0.003
x2[1] (numeric) = 0.998549183668 0.00563210555113
x2[1] (closed_form) = 1.000849781 0.00526564574109
absolute error = 0.00233
relative error = 0.2328 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=10509.1MB, alloc=40.3MB, time=127.61
memory used=10553.3MB, alloc=40.3MB, time=128.14
t[1] = 1.6456 0.713
h = 0.0001 0.004
x1[1] (numeric) = 1.99996222239 -0.00215135857769
x1[1] (closed_form) = 2.00026263387 -0.000227114878104
absolute error = 0.001948
relative error = 0.09736 %
Correct digits = 3
h = 0.0001 0.004
x2[1] (numeric) = 0.998484616119 0.00564807314667
x2[1] (closed_form) = 1.00081933857 0.00528091852396
absolute error = 0.002363
relative error = 0.2361 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=10597.1MB, alloc=40.3MB, time=128.66
t[1] = 1.6457 0.717
h = 0.003 0.006
x1[1] (numeric) = 1.99996559174 -0.00218161050827
x1[1] (closed_form) = 2.00026169714 -0.000228140778635
absolute error = 0.001976
relative error = 0.09878 %
Correct digits = 3
h = 0.003 0.006
x2[1] (numeric) = 0.998419795216 0.00566373055473
x2[1] (closed_form) = 1.00077675453 0.00528784687225
absolute error = 0.002387
relative error = 0.2385 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=10641.1MB, alloc=40.3MB, time=129.18
memory used=10685.1MB, alloc=40.3MB, time=129.70
t[1] = 1.6487 0.723
h = 0.0001 0.005
x1[1] (numeric) = 1.99994966109 -0.00223009735743
x1[1] (closed_form) = 2.00025954379 -0.000229018757631
absolute error = 0.002025
relative error = 0.1012 %
Correct digits = 3
h = 0.0001 0.005
x2[1] (numeric) = 0.998354156236 0.00567898010401
x2[1] (closed_form) = 1.00071646108 0.00532821644874
absolute error = 0.002388
relative error = 0.2386 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=10729.2MB, alloc=40.3MB, time=130.23
t[1] = 1.6488 0.728
h = 0.0001 0.003
x1[1] (numeric) = 1.99995486366 -0.00226765983147
x1[1] (closed_form) = 2.00025836962 -0.000230290578237
absolute error = 0.00206
relative error = 0.103 %
Correct digits = 3
h = 0.0001 0.003
x2[1] (numeric) = 0.998287643612 0.00569367687553
x2[1] (closed_form) = 1.00066269267 0.00533554276458
absolute error = 0.002402
relative error = 0.24 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=10773.2MB, alloc=40.3MB, time=130.76
memory used=10817.6MB, alloc=40.3MB, time=131.31
t[1] = 1.6489 0.731
h = 0.001 0.001
x1[1] (numeric) = 1.99995763487 -0.00229034802213
x1[1] (closed_form) = 2.00025765182 -0.000231041544314
absolute error = 0.002081
relative error = 0.104 %
Correct digits = 3
h = 0.001 0.001
x2[1] (numeric) = 0.998220902695 0.00570786925877
x2[1] (closed_form) = 1.00063043601 0.00534011425396
absolute error = 0.002437
relative error = 0.2436 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=10861.6MB, alloc=40.3MB, time=131.85
t[1] = 1.6499 0.732
h = 0.0001 0.004
x1[1] (numeric) = 1.99995112356 -0.00229919461138
x1[1] (closed_form) = 2.00025716336 -0.0002310678971
absolute error = 0.002091
relative error = 0.1045 %
Correct digits = 3
h = 0.0001 0.004
x2[1] (numeric) = 0.998154068815 0.00572194098685
x2[1] (closed_form) = 1.00062075082 0.00535204442946
absolute error = 0.002494
relative error = 0.2493 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=10905.6MB, alloc=40.3MB, time=132.37
t[1] = 1.65 0.736
h = 0.003 0.006
x1[1] (numeric) = 1.99995500482 -0.00233053110643
x1[1] (closed_form) = 2.00025621141 -0.000232071490933
absolute error = 0.00212
relative error = 0.106 %
Correct digits = 3
h = 0.003 0.006
x2[1] (numeric) = 0.998087095469 0.00573578623739
x2[1] (closed_form) = 1.00057755664 0.00535740684889
absolute error = 0.002519
relative error = 0.2518 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=10949.6MB, alloc=40.3MB, time=132.89
memory used=10993.6MB, alloc=40.3MB, time=133.42
t[1] = 1.653 0.742
h = 0.0001 0.005
x1[1] (numeric) = 1.99993908909 -0.00238101793825
x1[1] (closed_form) = 2.00025405108 -0.000232904809334
absolute error = 0.002171
relative error = 0.1085 %
Correct digits = 3
h = 0.0001 0.005
x2[1] (numeric) = 0.998019300869 0.00574919190288
x2[1] (closed_form) = 1.00051523547 0.00539580767482
absolute error = 0.002521
relative error = 0.2519 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=11037.7MB, alloc=40.3MB, time=133.95
t[1] = 1.6531 0.747
h = 0.0001 0.003
x1[1] (numeric) = 1.99994494073 -0.00241990797362
x1[1] (closed_form) = 2.0002528581 -0.000234148732082
absolute error = 0.002207
relative error = 0.1104 %
Correct digits = 3
h = 0.0001 0.003
x2[1] (numeric) = 0.997950632691 0.00576200874568
x2[1] (closed_form) = 1.00046075137 0.00540114540807
absolute error = 0.002536
relative error = 0.2535 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=11081.7MB, alloc=40.3MB, time=134.47
memory used=11126.1MB, alloc=40.3MB, time=135.01
t[1] = 1.6532 0.75
h = 0.001 0.001
x1[1] (numeric) = 1.99994809142 -0.0024434046331
x1[1] (closed_form) = 2.0002521293 -0.000234882762112
absolute error = 0.002229
relative error = 0.1115 %
Correct digits = 3
h = 0.001 0.001
x2[1] (numeric) = 0.997881746845 0.00577430510905
x2[1] (closed_form) = 1.00042805874 0.00540452540764
absolute error = 0.002573
relative error = 0.2572 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=11170.2MB, alloc=40.3MB, time=135.54
t[1] = 1.6542 0.751
h = 0.001 0.003
x1[1] (numeric) = 1.99994145073 -0.00245266066579
x1[1] (closed_form) = 2.00025164252 -0.000234899756682
absolute error = 0.002239
relative error = 0.112 %
Correct digits = 3
h = 0.001 0.003
x2[1] (numeric) = 0.997812769858 0.00578647584307
x2[1] (closed_form) = 1.00041784055 0.00541618352531
absolute error = 0.002631
relative error = 0.263 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=11214.2MB, alloc=40.3MB, time=136.08
memory used=11258.1MB, alloc=40.3MB, time=136.60
t[1] = 1.6552 0.754
h = 0.0001 0.004
x1[1] (numeric) = 1.9999373381 -0.00247832702034
x1[1] (closed_form) = 2.00025068588 -0.000235418090228
absolute error = 0.002265
relative error = 0.1132 %
Correct digits = 3
h = 0.0001 0.004
x2[1] (numeric) = 0.9977436213 0.00579856692568
x2[1] (closed_form) = 1.00038562955 0.00542918023153
absolute error = 0.002668
relative error = 0.2667 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=11302.2MB, alloc=40.3MB, time=137.12
t[1] = 1.6553 0.758
h = 0.0001 0.004
x1[1] (numeric) = 1.99994188566 -0.00251118433174
x1[1] (closed_form) = 2.00024971723 -0.000236395307017
absolute error = 0.002296
relative error = 0.1148 %
Correct digits = 3
h = 0.0001 0.004
x2[1] (numeric) = 0.99767422822 0.00581031903206
x2[1] (closed_form) = 1.00034177026 0.00543268744078
absolute error = 0.002694
relative error = 0.2693 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=11346.1MB, alloc=40.3MB, time=137.65
t[1] = 1.6554 0.762
h = 0.003 0.006
x1[1] (numeric) = 1.9999463693 -0.00254418611027
x1[1] (closed_form) = 2.00024874478 -0.000237368544078
absolute error = 0.002327
relative error = 0.1163 %
Correct digits = 3
h = 0.003 0.006
x2[1] (numeric) = 0.997604629005 0.00582157493235
x2[1] (closed_form) = 1.00029787363 0.00543584628097
absolute error = 0.002721
relative error = 0.272 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=11390.2MB, alloc=40.3MB, time=138.17
memory used=11434.2MB, alloc=40.3MB, time=138.70
t[1] = 1.6584 0.768
h = 0.0001 0.005
x1[1] (numeric) = 1.99993019663 -0.00259760929696
x1[1] (closed_form) = 2.00024657526 -0.000238141234765
absolute error = 0.002381
relative error = 0.119 %
Correct digits = 3
h = 0.0001 0.005
x2[1] (numeric) = 0.997534205997 0.00583234964843
x2[1] (closed_form) = 1.00023293788 0.00547136754031
absolute error = 0.002723
relative error = 0.2722 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=11478.2MB, alloc=40.3MB, time=139.22
t[1] = 1.6585 0.773
h = 0.0001 0.003
x1[1] (numeric) = 1.99993681188 -0.00263853552217
x1[1] (closed_form) = 2.00024535694 -0.000239347193265
absolute error = 0.002419
relative error = 0.1209 %
Correct digits = 3
h = 0.0001 0.003
x2[1] (numeric) = 0.997462911364 0.00584248846306
x2[1] (closed_form) = 1.00017764292 0.00547391203503
absolute error = 0.00274
relative error = 0.2739 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=11522.1MB, alloc=40.3MB, time=139.74
memory used=11566.6MB, alloc=40.3MB, time=140.29
t[1] = 1.6586 0.776
h = 0.001 0.001
x1[1] (numeric) = 1.9999404054 -0.0026632669741
x1[1] (closed_form) = 2.00024461334 -0.000240058178908
absolute error = 0.002442
relative error = 0.1221 %
Correct digits = 3
h = 0.001 0.001
x2[1] (numeric) = 0.997391413792 0.00585208633064
x2[1] (closed_form) = 1.00014445464 0.0054756178001
absolute error = 0.002779
relative error = 0.2778 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=11610.8MB, alloc=40.3MB, time=140.82
t[1] = 1.6596 0.777
h = 0.001 0.003
x1[1] (numeric) = 1.99993352123 -0.00267310194505
x1[1] (closed_form) = 2.0002441289 -0.000240062489613
absolute error = 0.002453
relative error = 0.1226 %
Correct digits = 3
h = 0.001 0.003
x2[1] (numeric) = 0.997319827726 0.00586155216366
x2[1] (closed_form) = 1.00013352794 0.00548685610844
absolute error = 0.002839
relative error = 0.2838 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=11654.8MB, alloc=40.3MB, time=141.34
memory used=11698.9MB, alloc=40.3MB, time=141.87
t[1] = 1.6606 0.78
h = 0.0001 0.004
x1[1] (numeric) = 1.99992951924 -0.00270018845162
x1[1] (closed_form) = 2.00024316433 -0.000240553121507
absolute error = 0.00248
relative error = 0.124 %
Correct digits = 3
h = 0.0001 0.004
x2[1] (numeric) = 0.997248069089 0.00587092995674
x2[1] (closed_form) = 1.00010032398 0.00549829759871
absolute error = 0.002876
relative error = 0.2876 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=11742.8MB, alloc=40.3MB, time=142.39
t[1] = 1.6607 0.784
h = 0.003 0.006
x1[1] (numeric) = 1.99993473629 -0.00273473133368
x1[1] (closed_form) = 2.00024217596 -0.000241499700644
absolute error = 0.002512
relative error = 0.1256 %
Correct digits = 3
h = 0.003 0.006
x2[1] (numeric) = 0.99717607306 0.0058799515298
x2[1] (closed_form) = 1.00005585379 0.00549954882457
absolute error = 0.002905
relative error = 0.2905 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=11786.8MB, alloc=40.3MB, time=142.92
t[1] = 1.6637 0.79
h = 0.0001 0.005
x1[1] (numeric) = 1.99991859176 -0.00279099989162
x1[1] (closed_form) = 2.00024000152 -0.000242220647669
absolute error = 0.002569
relative error = 0.1284 %
Correct digits = 3
h = 0.0001 0.005
x2[1] (numeric) = 0.997103249021 0.00588845458703
x2[1] (closed_form) = 0.999988707442 0.00553255312217
absolute error = 0.002907
relative error = 0.2907 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=11831.0MB, alloc=40.3MB, time=143.44
memory used=11875.0MB, alloc=40.3MB, time=143.97
t[1] = 1.6638 0.795
h = 0.0001 0.003
x1[1] (numeric) = 1.99992613417 -0.00283381389425
x1[1] (closed_form) = 2.00023876355 -0.000243393281994
absolute error = 0.002609
relative error = 0.1304 %
Correct digits = 3
h = 0.0001 0.003
x2[1] (numeric) = 0.997029552922 0.00589627928083
x2[1] (closed_form) = 0.999932753968 0.00553268065748
absolute error = 0.002926
relative error = 0.2926 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=11919.2MB, alloc=40.3MB, time=144.50
t[1] = 1.6639 0.798
h = 0.001 0.001
x1[1] (numeric) = 1.99993026966 -0.00285969232027
x1[1] (closed_form) = 2.00023800849 -0.000244084066669
absolute error = 0.002634
relative error = 0.1317 %
Correct digits = 3
h = 0.001 0.001
x2[1] (numeric) = 0.996955666178 0.00590354392236
x2[1] (closed_form) = 0.999899162677 0.00553293758487
absolute error = 0.002967
relative error = 0.2967 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=11963.6MB, alloc=40.3MB, time=145.04
memory used=12007.7MB, alloc=40.3MB, time=145.57
t[1] = 1.6649 0.799
h = 0.001 0.003
x1[1] (numeric) = 1.99992320379 -0.00287010678498
x1[1] (closed_form) = 2.00023752664 -0.000244077753248
absolute error = 0.002645
relative error = 0.1322 %
Correct digits = 3
h = 0.001 0.003
x2[1] (numeric) = 0.996881693022 0.00591067064202
x2[1] (closed_form) = 0.999887631812 0.00554380428555
absolute error = 0.003028
relative error = 0.3029 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=12051.7MB, alloc=40.3MB, time=146.09
t[1] = 1.6659 0.802
h = 0.0001 0.004
x1[1] (numeric) = 1.99991943381 -0.00289855146819
x1[1] (closed_form) = 2.00023655667 -0.000244544566885
absolute error = 0.002673
relative error = 0.1336 %
Correct digits = 3
h = 0.0001 0.004
x2[1] (numeric) = 0.996807546001 0.00591770182028
x2[1] (closed_form) = 0.999853594892 0.00555389235028
absolute error = 0.003068
relative error = 0.3068 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=12095.5MB, alloc=40.3MB, time=146.61
memory used=12139.6MB, alloc=40.3MB, time=147.14
t[1] = 1.666 0.806
h = 0.003 0.006
x1[1] (numeric) = 1.9999254429 -0.00293466016576
x1[1] (closed_form) = 2.00023555304 -0.000245464287027
absolute error = 0.002707
relative error = 0.1353 %
Correct digits = 3
h = 0.003 0.006
x2[1] (numeric) = 0.996733167196 0.00592436092868
x2[1] (closed_form) = 0.999808630726 0.00555319211054
absolute error = 0.003098
relative error = 0.3098 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=12183.5MB, alloc=40.3MB, time=147.67
t[1] = 1.669 0.812
h = 0.0001 0.005
x1[1] (numeric) = 1.99990939774 -0.00299385270695
x1[1] (closed_form) = 2.00023337485 -0.000246133668753
absolute error = 0.002767
relative error = 0.1383 %
Correct digits = 3
h = 0.0001 0.005
x2[1] (numeric) = 0.996657957194 0.00593046331527
x2[1] (closed_form) = 0.999739364871 0.00558355673925
absolute error = 0.003101
relative error = 0.3102 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=12227.5MB, alloc=40.3MB, time=148.20
t[1] = 1.6691 0.817
h = 0.0001 0.003
x1[1] (numeric) = 1.99991793982 -0.00303858432181
x1[1] (closed_form) = 2.00023211806 -0.000247272732975
absolute error = 0.002809
relative error = 0.1404 %
Correct digits = 3
h = 0.0001 0.003
x2[1] (numeric) = 0.996581875953 0.00593584401168
x2[1] (closed_form) = 0.99968285437 0.00558121478209
absolute error = 0.003121
relative error = 0.3122 %
Correct digits = 3
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=12271.7MB, alloc=40.3MB, time=148.72
memory used=12316.2MB, alloc=40.3MB, time=149.26
t[1] = 1.6692 0.82
h = 0.001 0.001
x1[1] (numeric) = 1.99992266083 -0.00306562836478
x1[1] (closed_form) = 2.00023135206 -0.000247943177822
absolute error = 0.002835
relative error = 0.1417 %
Correct digits = 3
h = 0.001 0.001
x2[1] (numeric) = 0.996505617178 0.00594064553392
x2[1] (closed_form) = 0.999648920829 0.00557999100943
absolute error = 0.003164
relative error = 0.3165 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=12360.4MB, alloc=40.3MB, time=149.79
t[1] = 1.6702 0.821
h = 0.001 0.003
x1[1] (numeric) = 1.99991542259 -0.00307664297596
x1[1] (closed_form) = 2.00023087301 -0.000247926355512
absolute error = 0.002846
relative error = 0.1423 %
Correct digits = 3
h = 0.001 0.003
x2[1] (numeric) = 0.996429274288 0.00594530319083
x2[1] (closed_form) = 0.999636796584 0.0055904555926
absolute error = 0.003227
relative error = 0.3228 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=12404.4MB, alloc=40.3MB, time=150.32
memory used=12448.6MB, alloc=40.3MB, time=150.84
t[1] = 1.6712 0.824
h = 0.0001 0.004
x1[1] (numeric) = 1.99991192486 -0.00310647774389
x1[1] (closed_form) = 2.00022989818 -0.000248369364254
absolute error = 0.002876
relative error = 0.1438 %
Correct digits = 3
h = 0.0001 0.004
x2[1] (numeric) = 0.996352756439 0.00594985761558
x2[1] (closed_form) = 0.999601979083 0.00559914010352
absolute error = 0.003268
relative error = 0.3269 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=12492.6MB, alloc=40.3MB, time=151.37
t[1] = 1.6713 0.828
h = 0.003 0.006
x1[1] (numeric) = 1.999918787 -0.00314417592281
x1[1] (closed_form) = 2.00022887998 -0.000249262040131
absolute error = 0.002911
relative error = 0.1456 %
Correct digits = 3
h = 0.003 0.006
x2[1] (numeric) = 0.996276012996 0.00595402396838
x2[1] (closed_form) = 0.999556603247 0.00559644765255
absolute error = 0.0033
relative error = 0.3301 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=12536.7MB, alloc=40.3MB, time=151.89
memory used=12580.8MB, alloc=40.3MB, time=152.42
t[1] = 1.6743 0.834
h = 0.0001 0.005
x1[1] (numeric) = 1.99990291676 -0.00320637115061
x1[1] (closed_form) = 2.00022669918 -0.000249880059304
absolute error = 0.002974
relative error = 0.1487 %
Correct digits = 3
h = 0.0001 0.005
x2[1] (numeric) = 0.99619843624 0.00595759452971
x2[1] (closed_form) = 0.999485315296 0.00562405275419
absolute error = 0.003304
relative error = 0.3305 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=12624.9MB, alloc=40.3MB, time=152.95
t[1] = 1.6744 0.839
h = 0.0001 0.003
x1[1] (numeric) = 1.99991253397 -0.00325304889844
x1[1] (closed_form) = 2.00022542441 -0.000250985327189
absolute error = 0.003018
relative error = 0.1509 %
Correct digits = 3
h = 0.0001 0.003
x2[1] (numeric) = 0.99611999037 0.00596039922619
x2[1] (closed_form) = 0.999428352575 0.00561919276486
absolute error = 0.003326
relative error = 0.3328 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=12669.3MB, alloc=40.3MB, time=153.48
t[1] = 1.6745 0.842
h = 0.001 0.001
x1[1] (numeric) = 1.99991788581 -0.00328127643016
x1[1] (closed_form) = 2.00022464797 -0.00025163530517
absolute error = 0.003045
relative error = 0.1522 %
Correct digits = 3
h = 0.001 0.001
x2[1] (numeric) = 0.996041380909 0.00596260563086
x2[1] (closed_form) = 0.99939413955 0.0056164588165
absolute error = 0.003371
relative error = 0.3373 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=12713.6MB, alloc=40.3MB, time=154.02
memory used=12757.8MB, alloc=40.3MB, time=154.55
t[1] = 1.6755 0.843
h = 0.001 0.003
x1[1] (numeric) = 1.99991048541 -0.00329291214064
x1[1] (closed_form) = 2.00022417194 -0.000251608093346
absolute error = 0.003057
relative error = 0.1529 %
Correct digits = 3
h = 0.001 0.003
x2[1] (numeric) = 0.995962689854 0.00596466217526
x2[1] (closed_form) = 0.999381434165 0.00562649095429
absolute error = 0.003435
relative error = 0.3438 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=12801.7MB, alloc=40.3MB, time=155.07
t[1] = 1.6765 0.846
h = 0.0001 0.004
x1[1] (numeric) = 1.99990730224 -0.00332416859927
x1[1] (closed_form) = 2.0002231928 -0.00025202732254
absolute error = 0.003088
relative error = 0.1544 %
Correct digits = 3
h = 0.0001 0.004
x2[1] (numeric) = 0.99588382295 0.00596660760906
x2[1] (closed_form) = 0.999345891199 0.00563372362052
absolute error = 0.003478
relative error = 0.348 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=12845.5MB, alloc=40.3MB, time=155.59
memory used=12889.6MB, alloc=40.3MB, time=156.12
t[1] = 1.6766 0.85
h = 0.003 0.006
x1[1] (numeric) = 1.99991508084 -0.0033634787787
x1[1] (closed_form) = 2.00022216069 -0.00025289278461
absolute error = 0.003126
relative error = 0.1563 %
Correct digits = 3
h = 0.003 0.006
x2[1] (numeric) = 0.995804737243 0.00596814882896
x2[1] (closed_form) = 0.999300188608 0.00562900146932
absolute error = 0.003512
relative error = 0.3514 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=12933.6MB, alloc=40.3MB, time=156.64
t[1] = 1.6796 0.856
h = 0.0001 0.005
x1[1] (numeric) = 1.99989946549 -0.00342875535201
x1[1] (closed_form) = 2.00021997842 -0.000253459668001
absolute error = 0.003191
relative error = 0.1596 %
Correct digits = 3
h = 0.0001 0.005
x2[1] (numeric) = 0.995724817218 0.0059690543358
x2[1] (closed_form) = 0.999226982238 0.00565373034391
absolute error = 0.003516
relative error = 0.3519 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=12977.7MB, alloc=40.3MB, time=157.17
memory used=13021.9MB, alloc=40.3MB, time=157.70
t[1] = 1.6797 0.861
h = 0.0001 0.003
x1[1] (numeric) = 1.99991023622 -0.00347740631459
x1[1] (closed_form) = 2.00021868651 -0.000254530932915
absolute error = 0.003238
relative error = 0.1619 %
Correct digits = 3
h = 0.0001 0.003
x2[1] (numeric) = 0.995644031556 0.00596914897332
x2[1] (closed_form) = 0.999169675279 0.00564630796227
absolute error = 0.00354
relative error = 0.3543 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=13066.4MB, alloc=40.3MB, time=158.24
t[1] = 1.6798 0.864
h = 0.001 0.001
x1[1] (numeric) = 1.999916266 -0.00350683436064
x1[1] (closed_form) = 2.00021790014 -0.000255160328758
absolute error = 0.003266
relative error = 0.1633 %
Correct digits = 3
h = 0.001 0.001
x2[1] (numeric) = 0.995563097092 0.00596862622748
x2[1] (closed_form) = 0.99913524745 0.00564203686153
absolute error = 0.003587
relative error = 0.359 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=13110.6MB, alloc=40.3MB, time=158.77
t[1] = 1.6808 0.865
h = 0.0001 0.004
x1[1] (numeric) = 1.99990871455 -0.00351911240278
x1[1] (closed_form) = 2.00021742734 -0.000255122850828
absolute error = 0.003279
relative error = 0.1639 %
Correct digits = 3
h = 0.0001 0.004
x2[1] (numeric) = 0.995482083783 0.00596794757975
x2[1] (closed_form) = 0.999121974632 0.00565160647468
absolute error = 0.003654
relative error = 0.3657 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=13154.6MB, alloc=40.3MB, time=159.29
memory used=13198.7MB, alloc=40.3MB, time=159.81
t[1] = 1.6809 0.869
h = 0.003 0.006
x1[1] (numeric) = 1.99991726727 -0.00355960455558
x1[1] (closed_form) = 2.00021638347 -0.0002559649191
absolute error = 0.003317
relative error = 0.1658 %
Correct digits = 3
h = 0.003 0.006
x2[1] (numeric) = 0.995400961821 0.00596698374991
x2[1] (closed_form) = 0.999076085404 0.00564510733072
absolute error = 0.003689
relative error = 0.3693 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=13242.7MB, alloc=40.3MB, time=160.34
t[1] = 1.6839 0.875
h = 0.0001 0.005
x1[1] (numeric) = 1.99990199475 -0.00362721276991
x1[1] (closed_form) = 2.00021420023 -0.000256487985458
absolute error = 0.003385
relative error = 0.1692 %
Correct digits = 3
h = 0.0001 0.005
x2[1] (numeric) = 0.995319008438 0.00596534853178
x2[1] (closed_form) = 0.999001351559 0.00566724857776
absolute error = 0.003694
relative error = 0.3698 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=13286.7MB, alloc=40.3MB, time=160.86
memory used=13330.9MB, alloc=40.3MB, time=161.39
t[1] = 1.684 0.88
h = 0.0001 0.003
x1[1] (numeric) = 1.99991373866 -0.00367730845148
x1[1] (closed_form) = 2.00021289383 -0.00025753002175
absolute error = 0.003433
relative error = 0.1716 %
Correct digits = 3
h = 0.0001 0.003
x2[1] (numeric) = 0.995236196768 0.00596286265331
x2[1] (closed_form) = 0.998943868227 0.00565758608275
absolute error = 0.00372
relative error = 0.3724 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=13375.2MB, alloc=40.3MB, time=161.92
t[1] = 1.6841 0.883
h = 0.001 0.001
x1[1] (numeric) = 1.9999203432 -0.00370761869379
x1[1] (closed_form) = 2.00021209907 -0.00025814172792
absolute error = 0.003462
relative error = 0.1731 %
Correct digits = 3
h = 0.001 0.001
x2[1] (numeric) = 0.995153251275 0.00595974376526
x2[1] (closed_form) = 0.998909327393 0.00565197076271
absolute error = 0.003769
relative error = 0.3773 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=13419.6MB, alloc=40.3MB, time=162.46
t[1] = 1.6851 0.884
h = 0.001 0.003
x1[1] (numeric) = 1.99991270781 -0.00372039555356
x1[1] (closed_form) = 2.00021162908 -0.000258095473317
absolute error = 0.003475
relative error = 0.1737 %
Correct digits = 3
h = 0.001 0.003
x2[1] (numeric) = 0.995070229953 0.0059564638496
x2[1] (closed_form) = 0.998895584237 0.00566111189338
absolute error = 0.003837
relative error = 0.3841 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=13463.7MB, alloc=40.3MB, time=162.98
memory used=13507.7MB, alloc=40.3MB, time=163.51
t[1] = 1.6861 0.887
h = 0.0001 0.004
x1[1] (numeric) = 1.99991023236 -0.00375420211058
x1[1] (closed_form) = 2.0002106431 -0.000258470598312
absolute error = 0.003509
relative error = 0.1754 %
Correct digits = 3
h = 0.0001 0.004
x2[1] (numeric) = 0.994987032253 0.00595305751516
x2[1] (closed_form) = 0.998858865727 0.00566551439199
absolute error = 0.003882
relative error = 0.3887 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=13551.7MB, alloc=40.3MB, time=164.04
t[1] = 1.6862 0.891
h = 0.003 0.006
x1[1] (numeric) = 1.99991983157 -0.0037963522617
x1[1] (closed_form) = 2.00020958657 -0.000259285170883
absolute error = 0.003549
relative error = 0.1774 %
Correct digits = 3
h = 0.003 0.006
x2[1] (numeric) = 0.99490363125 0.00594921689861
x2[1] (closed_form) = 0.998812814625 0.00565692603868
absolute error = 0.00392
relative error = 0.3925 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=13595.6MB, alloc=40.3MB, time=164.55
memory used=13639.7MB, alloc=40.3MB, time=165.08
t[1] = 1.6892 0.897
h = 0.0001 0.005
x1[1] (numeric) = 1.99990497813 -0.00386720301486
x1[1] (closed_form) = 2.00020740395 -0.000259757572865
absolute error = 0.00362
relative error = 0.181 %
Correct digits = 3
h = 0.0001 0.005
x2[1] (numeric) = 0.994819399965 0.00594466354405
x2[1] (closed_form) = 0.998736372959 0.00567598477899
absolute error = 0.003926
relative error = 0.3931 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=13683.9MB, alloc=40.3MB, time=165.61
t[1] = 1.6893 0.902
h = 0.0001 0.003
x1[1] (numeric) = 1.99991803655 -0.00391932743795
x1[1] (closed_form) = 2.00020608197 -0.000260765263519
absolute error = 0.00367
relative error = 0.1835 %
Correct digits = 3
h = 0.0001 0.003
x2[1] (numeric) = 0.994734316443 0.00593921316537
x2[1] (closed_form) = 0.998678754623 0.00566369045788
absolute error = 0.003954
relative error = 0.3959 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=13727.9MB, alloc=40.3MB, time=166.14
memory used=13772.5MB, alloc=40.3MB, time=166.68
t[1] = 1.6894 0.905
h = 0.001 0.001
x1[1] (numeric) = 1.99992541579 -0.00395087303264
x1[1] (closed_form) = 2.00020527822 -0.000261356198131
absolute error = 0.0037
relative error = 0.185 %
Correct digits = 3
h = 0.001 0.001
x2[1] (numeric) = 0.994649115437 0.00593311083456
x2[1] (closed_form) = 0.998644124372 0.00565649563193
absolute error = 0.004005
relative error = 0.401 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=13816.5MB, alloc=40.3MB, time=167.21
t[1] = 1.6904 0.906
h = 0.001 0.003
x1[1] (numeric) = 1.99991765219 -0.00396433570989
x1[1] (closed_form) = 2.00020481185 -0.000261299915028
absolute error = 0.003714
relative error = 0.1857 %
Correct digits = 3
h = 0.001 0.003
x2[1] (numeric) = 0.994563841775 0.00592684137607
x2[1] (closed_form) = 0.998629843544 0.00566511936584
absolute error = 0.004074
relative error = 0.408 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=13860.6MB, alloc=40.3MB, time=167.74
t[1] = 1.6914 0.909
h = 0.0001 0.004
x1[1] (numeric) = 1.99991562676 -0.00399965893641
x1[1] (closed_form) = 2.0002038231 -0.000261651391533
absolute error = 0.003749
relative error = 0.1874 %
Correct digits = 3
h = 0.0001 0.004
x2[1] (numeric) = 0.994478391476 0.00592043711879
x2[1] (closed_form) = 0.998592572305 0.00566794402034
absolute error = 0.004122
relative error = 0.4128 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=13904.8MB, alloc=40.3MB, time=168.26
memory used=13948.9MB, alloc=40.3MB, time=168.79
t[1] = 1.6915 0.913
h = 0.003 0.006
x1[1] (numeric) = 1.99992634303 -0.00404348554972
x1[1] (closed_form) = 2.00020275459 -0.000262438343405
absolute error = 0.003791
relative error = 0.1895 %
Correct digits = 3
h = 0.003 0.006
x2[1] (numeric) = 0.994392746418 0.00591358214944
x2[1] (closed_form) = 0.998546450972 0.00565723911204
absolute error = 0.004162
relative error = 0.4168 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=13993.0MB, alloc=40.3MB, time=169.31
t[1] = 1.6945 0.919
h = 0.0001 0.005
x1[1] (numeric) = 1.99991200238 -0.00411765642419
x1[1] (closed_form) = 2.0002005737 -0.000262860374593
absolute error = 0.003866
relative error = 0.1933 %
Correct digits = 3
h = 0.0001 0.005
x2[1] (numeric) = 0.99430627345 0.00590597227674
x2[1] (closed_form) = 0.998468422548 0.00567310945686
absolute error = 0.004169
relative error = 0.4175 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=14037.1MB, alloc=40.3MB, time=169.83
memory used=14081.3MB, alloc=40.3MB, time=170.36
t[1] = 1.6946 0.924
h = 0.0001 0.003
x1[1] (numeric) = 1.99992646252 -0.00417183158301
x1[1] (closed_form) = 2.00019923697 -0.000263833568468
absolute error = 0.003918
relative error = 0.1959 %
Correct digits = 3
h = 0.0001 0.003
x2[1] (numeric) = 0.994218955776 0.00589741824091
x2[1] (closed_form) = 0.998410785316 0.00565815192192
absolute error = 0.004199
relative error = 0.4205 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=14125.6MB, alloc=40.3MB, time=170.90
t[1] = 1.6947 0.927
h = 0.001 0.001
x1[1] (numeric) = 1.99993466895 -0.00420462655162
x1[1] (closed_form) = 2.00019842473 -0.000264403649536
absolute error = 0.003949
relative error = 0.1974 %
Correct digits = 3
h = 0.001 0.001
x2[1] (numeric) = 0.994131537848 0.00588819339917
x2[1] (closed_form) = 0.998376135252 0.00564935837508
absolute error = 0.004251
relative error = 0.4258 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=14169.9MB, alloc=40.3MB, time=171.44
memory used=14214.2MB, alloc=40.3MB, time=171.97
t[1] = 1.6957 0.928
h = 0.001 0.003
x1[1] (numeric) = 1.99992679111 -0.00421879695256
x1[1] (closed_form) = 2.00019796216 -0.000264337472344
absolute error = 0.003964
relative error = 0.1982 %
Correct digits = 3
h = 0.001 0.003
x2[1] (numeric) = 0.99404405068 0.00587879529707
x2[1] (closed_form) = 0.998361334651 0.00565743573748
absolute error = 0.004323
relative error = 0.433 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=14258.2MB, alloc=40.3MB, time=172.49
t[1] = 1.6967 0.931
h = 0.0001 0.004
x1[1] (numeric) = 1.99992526654 -0.00425566648052
x1[1] (closed_form) = 2.00019697119 -0.000264665370679
absolute error = 0.004
relative error = 0.2 %
Correct digits = 3
h = 0.0001 0.004
x2[1] (numeric) = 0.993956386854 0.0058692538361
x2[1] (closed_form) = 0.998323575743 0.00565864267637
absolute error = 0.004372
relative error = 0.438 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=14302.3MB, alloc=40.3MB, time=173.02
t[1] = 1.6968 0.935
h = 0.003 0.006
x1[1] (numeric) = 1.99993717289 -0.00430118645586
x1[1] (closed_form) = 2.00019589137 -0.00026542459224
absolute error = 0.004044
relative error = 0.2022 %
Correct digits = 3
h = 0.003 0.006
x2[1] (numeric) = 0.993868537469 0.00585924514398
x2[1] (closed_form) = 0.998277477927 0.00564579766908
absolute error = 0.004414
relative error = 0.4422 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=14346.4MB, alloc=40.3MB, time=173.54
memory used=14390.4MB, alloc=40.3MB, time=174.06
t[1] = 1.6998 0.941
h = 0.0001 0.005
x1[1] (numeric) = 1.99992344353 -0.0043787543977
x1[1] (closed_form) = 2.00019371329 -0.000265796568777
absolute error = 0.004122
relative error = 0.2061 %
Correct digits = 3
h = 0.0001 0.005
x2[1] (numeric) = 0.993779863824 0.00584843858371
x2[1] (closed_form) = 0.998197989679 0.00565837807507
absolute error = 0.004422
relative error = 0.443 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=14434.3MB, alloc=40.3MB, time=174.59
t[1] = 1.6999 0.946
h = 0.0001 0.003
x1[1] (numeric) = 1.99993939566 -0.00443500032927
x1[1] (closed_form) = 2.00019236266 -0.000266735133899
absolute error = 0.004176
relative error = 0.2088 %
Correct digits = 3
h = 0.0001 0.003
x2[1] (numeric) = 0.993690354533 0.00583663996956
x2[1] (closed_form) = 0.998140452179 0.0056407307867
absolute error = 0.004454
relative error = 0.4463 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=14478.5MB, alloc=40.3MB, time=175.11
memory used=14523.1MB, alloc=40.3MB, time=175.66
t[1] = 1.7 0.949
h = 0.001 0.001
x1[1] (numeric) = 1.9999484836 -0.00446905753514
x1[1] (closed_form) = 2.00019154243 -0.000267284290925
absolute error = 0.004209
relative error = 0.2104 %
Correct digits = 3
h = 0.001 0.001
x2[1] (numeric) = 0.993600763121 0.00582415180928
x2[1] (closed_form) = 0.998105853433 0.00563032220642
absolute error = 0.004509
relative error = 0.4518 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=14567.4MB, alloc=40.3MB, time=176.19
t[1] = 1.701 0.95
h = 0.001 0.003
x1[1] (numeric) = 1.9999405065 -0.00448395775027
x1[1] (closed_form) = 2.00019108387 -0.000267208357675
absolute error = 0.004224
relative error = 0.2112 %
Correct digits = 3
h = 0.001 0.003
x2[1] (numeric) = 0.993511106136 0.00581148422907
x2[1] (closed_form) = 0.998090552417 0.00563782473596
absolute error = 0.004583
relative error = 0.4591 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=14611.4MB, alloc=40.3MB, time=176.72
memory used=14655.6MB, alloc=40.3MB, time=177.24
t[1] = 1.702 0.953
h = 0.0001 0.004
x1[1] (numeric) = 1.99993953586 -0.00452240252657
x1[1] (closed_form) = 2.0001900912 -0.00026751275943
absolute error = 0.004262
relative error = 0.2131 %
Correct digits = 3
h = 0.0001 0.004
x2[1] (numeric) = 0.993421272719 0.00579866455253
x2[1] (closed_form) = 0.998052373302 0.00563737658844
absolute error = 0.004634
relative error = 0.4643 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=14699.6MB, alloc=40.3MB, time=177.77
t[1] = 1.7021 0.957
h = 0.003 0.006
x1[1] (numeric) = 1.99995270779 -0.00456963108648
x1[1] (closed_form) = 2.00018900073 -0.000268244156348
absolute error = 0.004308
relative error = 0.2154 %
Correct digits = 3
h = 0.003 0.006
x2[1] (numeric) = 0.993331263615 0.00578536105191
x2[1] (closed_form) = 0.998006394702 0.00562237187003
absolute error = 0.004678
relative error = 0.4687 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=14743.5MB, alloc=40.3MB, time=178.29
t[1] = 1.7051 0.963
h = 0.0001 0.005
x1[1] (numeric) = 1.99993969314 -0.00465067224074
x1[1] (closed_form) = 2.00018682655 -0.000268566416539
absolute error = 0.004389
relative error = 0.2194 %
Correct digits = 3
h = 0.0001 0.005
x2[1] (numeric) = 0.993240435224 0.00577121593645
x2[1] (closed_form) = 0.9979255793 0.00563156544261
absolute error = 0.004687
relative error = 0.4697 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=14787.8MB, alloc=40.3MB, time=178.82
memory used=14832.0MB, alloc=40.3MB, time=179.34
t[1] = 1.7052 0.968
h = 0.0001 0.003
x1[1] (numeric) = 1.99995723054 -0.00470900688439
x1[1] (closed_form) = 2.00018546284 -0.000269470239963
absolute error = 0.004445
relative error = 0.2222 %
Correct digits = 3
h = 0.0001 0.003
x2[1] (numeric) = 0.993148781826 0.0057560301496
x2[1] (closed_form) = 0.997868262487 0.00561120686835
absolute error = 0.004722
relative error = 0.4732 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=14876.2MB, alloc=40.3MB, time=179.87
t[1] = 1.7053 0.971
h = 0.001 0.001
x1[1] (numeric) = 1.99996725615 -0.00474433794798
x1[1] (closed_form) = 2.00018463513 -0.000269998413851
absolute error = 0.00448
relative error = 0.224 %
Correct digits = 3
h = 0.001 0.001
x2[1] (numeric) = 0.993057065361 0.00574013621569
x2[1] (closed_form) = 0.997833787602 0.00559916994053
absolute error = 0.004779
relative error = 0.4789 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=14920.6MB, alloc=40.3MB, time=180.41
memory used=14964.9MB, alloc=40.3MB, time=180.94
t[1] = 1.7063 0.972
h = 0.0001 0.004
x1[1] (numeric) = 1.99995919582 -0.00475999022483
x1[1] (closed_form) = 2.00018418077 -0.000269912866088
absolute error = 0.004496
relative error = 0.2248 %
Correct digits = 3
h = 0.0001 0.004
x2[1] (numeric) = 0.992965287241 0.00572405668129
x2[1] (closed_form) = 0.99781800698 0.00560606975914
absolute error = 0.004854
relative error = 0.4865 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=15009.1MB, alloc=40.3MB, time=181.46
t[1] = 1.7064 0.976
h = 0.003 0.006
x1[1] (numeric) = 1.9999734014 -0.00480846135823
x1[1] (closed_form) = 2.00018308134 -0.000270620364518
absolute error = 0.004543
relative error = 0.2271 %
Correct digits = 3
h = 0.003 0.006
x2[1] (numeric) = 0.992873435622 0.00570764342486
x2[1] (closed_form) = 0.997772234976 0.00558919642751
absolute error = 0.0049
relative error = 0.4911 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=15053.1MB, alloc=40.3MB, time=181.98
memory used=15097.3MB, alloc=40.3MB, time=182.51
t[1] = 1.7094 0.982
h = 0.0001 0.005
x1[1] (numeric) = 1.99996107942 -0.00489210839273
x1[1] (closed_form) = 2.00018091078 -0.000270900054381
absolute error = 0.004626
relative error = 0.2313 %
Correct digits = 3
h = 0.0001 0.005
x2[1] (numeric) = 0.992780773413 0.00569035007975
x2[1] (closed_form) = 0.997690429534 0.00559538735248
absolute error = 0.004911
relative error = 0.4922 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=15141.6MB, alloc=40.3MB, time=183.04
t[1] = 1.7095 0.987
h = 0.0001 0.003
x1[1] (numeric) = 1.99997991074 -0.00495195964615
x1[1] (closed_form) = 2.00017953607 -0.000271774039529
absolute error = 0.004684
relative error = 0.2342 %
Correct digits = 3
h = 0.0001 0.003
x2[1] (numeric) = 0.992687300392 0.00567197378875
x2[1] (closed_form) = 0.997633433717 0.00557268631513
absolute error = 0.004947
relative error = 0.4959 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=15185.9MB, alloc=40.3MB, time=183.57
t[1] = 1.7096 0.99
h = 0.001 0.001
x1[1] (numeric) = 1.99999070465 -0.00498821909971
x1[1] (closed_form) = 2.00017870207 -0.00027228419418
absolute error = 0.00472
relative error = 0.236 %
Correct digits = 3
h = 0.001 0.001
x2[1] (numeric) = 0.99259378307 0.0056528746244
x2[1] (closed_form) = 0.997599144085 0.00555924213096
absolute error = 0.005006
relative error = 0.5018 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=15230.3MB, alloc=40.3MB, time=184.11
memory used=15274.6MB, alloc=40.3MB, time=184.64
t[1] = 1.7106 0.991
h = 0.001 0.003
x1[1] (numeric) = 1.99998261406 -0.0050044491621
x1[1] (closed_form) = 2.00017825136 -0.000272190433509
absolute error = 0.004736
relative error = 0.2368 %
Correct digits = 3
h = 0.001 0.003
x2[1] (numeric) = 0.99250020818 0.00563358473422
x2[1] (closed_form) = 0.997582976014 0.00556559598021
absolute error = 0.005083
relative error = 0.5095 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=15318.7MB, alloc=40.3MB, time=185.16
t[1] = 1.7116 0.994
h = 0.0001 0.004
x1[1] (numeric) = 1.99998279229 -0.0050456976586
x1[1] (closed_form) = 2.00017725664 -0.000272451374286
absolute error = 0.004777
relative error = 0.2388 %
Correct digits = 3
h = 0.0001 0.004
x2[1] (numeric) = 0.992406458626 0.00561412595298
x2[1] (closed_form) = 0.997544223032 0.00556197474521
absolute error = 0.005138
relative error = 0.5151 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=15362.8MB, alloc=40.3MB, time=185.69
memory used=15406.8MB, alloc=40.3MB, time=186.21
t[1] = 1.7117 0.998
h = 0.003 0.006
x1[1] (numeric) = 1.99999841782 -0.00509590835625
x1[1] (closed_form) = 2.00017614781 -0.000273130904902
absolute error = 0.004826
relative error = 0.2413 %
Correct digits = 3
h = 0.003 0.006
x2[1] (numeric) = 0.992312554909 0.00559415288776
x2[1] (closed_form) = 0.997498753097 0.00554291728501
absolute error = 0.005186
relative error = 0.5199 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=15450.6MB, alloc=40.3MB, time=186.74
t[1] = 1.7147 1.004
h = 0.0001 0.005
x1[1] (numeric) = 1.9999870222 -0.00518318425773
x1[1] (closed_form) = 2.00017398313 -0.000273361553041
absolute error = 0.004913
relative error = 0.2456 %
Correct digits = 3
h = 0.0001 0.005
x2[1] (numeric) = 0.992217848093 0.0055732547168
x2[1] (closed_form) = 0.997415883117 0.00554555621093
absolute error = 0.005198
relative error = 0.5211 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=15494.6MB, alloc=40.3MB, time=187.26
t[1] = 1.7148 1.009
h = 0.0001 0.003
x1[1] (numeric) = 2.00000762978 -0.0052451609333
x1[1] (closed_form) = 2.00017259689 -0.000274200626606
absolute error = 0.004974
relative error = 0.2487 %
Correct digits = 3
h = 0.0001 0.003
x2[1] (numeric) = 0.992122344079 0.0055512238437
x2[1] (closed_form) = 0.997359338667 0.00552011915919
absolute error = 0.005237
relative error = 0.5251 %
Correct digits = 2
memory used=15538.6MB, alloc=40.3MB, time=187.78
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=15583.0MB, alloc=40.3MB, time=188.32
t[1] = 1.7149 1.012
h = 0.001 0.001
x1[1] (numeric) = 2.00001947638 -0.00528271794391
x1[1] (closed_form) = 2.00017175634 -0.000274689712252
absolute error = 0.00501
relative error = 0.2505 %
Correct digits = 3
h = 0.001 0.001
x2[1] (numeric) = 0.992026816484 0.00552845186201
x2[1] (closed_form) = 0.9973253113 0.00550503104321
absolute error = 0.005299
relative error = 0.5313 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=15627.1MB, alloc=40.3MB, time=188.86
t[1] = 1.7159 1.013
h = 0.001 0.003
x1[1] (numeric) = 2.00001133541 -0.00529974551138
x1[1] (closed_form) = 2.00017131016 -0.000274586607268
absolute error = 0.005028
relative error = 0.2514 %
Correct digits = 3
h = 0.001 0.003
x2[1] (numeric) = 0.991931235708 0.00550548296605
x2[1] (closed_form) = 0.997308706473 0.0055107323879
absolute error = 0.005377
relative error = 0.5392 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=15671.1MB, alloc=40.3MB, time=189.38
memory used=15715.2MB, alloc=40.3MB, time=189.91
t[1] = 1.7169 1.016
h = 0.0001 0.004
x1[1] (numeric) = 2.00001223604 -0.0053426547742
x1[1] (closed_form) = 2.00017031523 -0.000274824339554
absolute error = 0.00507
relative error = 0.2535 %
Correct digits = 3
h = 0.0001 0.004
x2[1] (numeric) = 0.991835481247 0.00548233597843
x2[1] (closed_form) = 0.997269739047 0.005505365019
absolute error = 0.005434
relative error = 0.5449 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=15759.1MB, alloc=40.3MB, time=190.43
t[1] = 1.717 1.02
h = 0.003 0.006
x1[1] (numeric) = 2.00002936427 -0.00539461456016
x1[1] (closed_form) = 2.00016919766 -0.000275475851122
absolute error = 0.005121
relative error = 0.256 %
Correct digits = 3
h = 0.003 0.006
x2[1] (numeric) = 0.99173958444 0.0054586580306
x2[1] (closed_form) = 0.997224671532 0.00548411575317
absolute error = 0.005485
relative error = 0.55 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=15803.1MB, alloc=40.3MB, time=190.95
memory used=15847.1MB, alloc=40.3MB, time=191.48
t[1] = 1.72 1.026
h = 0.0001 0.005
x1[1] (numeric) = 2.00001901346 -0.00548559197966
x1[1] (closed_form) = 2.00016703989 -0.000275657857149
absolute error = 0.005212
relative error = 0.2606 %
Correct digits = 3
h = 0.0001 0.005
x2[1] (numeric) = 0.991642893476 0.0054340092309
x2[1] (closed_form) = 0.997140885141 0.00548312079024
absolute error = 0.005498
relative error = 0.5514 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=15891.0MB, alloc=40.3MB, time=192.00
t[1] = 1.7201 1.031
h = 0.0001 0.003
x1[1] (numeric) = 2.00004149953 -0.00554970488897
x1[1] (closed_form) = 2.00016564296 -0.000276461959846
absolute error = 0.005275
relative error = 0.2637 %
Correct digits = 3
h = 0.0001 0.003
x2[1] (numeric) = 0.991545420647 0.0054081773202
x2[1] (closed_form) = 0.997084918469 0.00545494134863
absolute error = 0.00554
relative error = 0.5556 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=15935.2MB, alloc=40.3MB, time=192.53
t[1] = 1.7202 1.034
h = 0.001 0.001
x1[1] (numeric) = 2.00005446044 -0.00558856684387
x1[1] (closed_form) = 2.00016479635 -0.000276929949516
absolute error = 0.005313
relative error = 0.2656 %
Correct digits = 3
h = 0.001 0.001
x2[1] (numeric) = 0.991447945914 0.00538158627863
x2[1] (closed_form) = 0.997051229236 0.00543820506845
absolute error = 0.005604
relative error = 0.562 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=15979.6MB, alloc=40.3MB, time=193.07
memory used=16023.7MB, alloc=40.3MB, time=193.61
t[1] = 1.7212 1.035
h = 0.001 0.003
x1[1] (numeric) = 2.00004628839 -0.00560641443339
x1[1] (closed_form) = 2.0001643549 -0.000276817651264
absolute error = 0.005331
relative error = 0.2665 %
Correct digits = 3
h = 0.001 0.003
x2[1] (numeric) = 0.991350422658 0.00535479213055
x2[1] (closed_form) = 0.997034212523 0.00544322810378
absolute error = 0.005684
relative error = 0.5701 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=16067.6MB, alloc=40.3MB, time=194.13
t[1] = 1.7222 1.038
h = 0.0001 0.004
x1[1] (numeric) = 2.00004797363 -0.00565100979276
x1[1] (closed_form) = 2.00016336026 -0.000277032298678
absolute error = 0.005375
relative error = 0.2687 %
Correct digits = 3
h = 0.0001 0.004
x2[1] (numeric) = 0.991252726981 0.00532781052484
x2[1] (closed_form) = 0.996995106459 0.00543608811205
absolute error = 0.005743
relative error = 0.5761 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=16111.5MB, alloc=40.3MB, time=194.66
memory used=16155.5MB, alloc=40.3MB, time=195.18
t[1] = 1.7223 1.042
h = 0.003 0.006
x1[1] (numeric) = 2.00006668979 -0.00570472604943
x1[1] (closed_form) = 2.00016223461 -0.000277655754774
absolute error = 0.005428
relative error = 0.2714 %
Correct digits = 3
h = 0.003 0.006
x2[1] (numeric) = 0.991154901502 0.00530028127092
x2[1] (closed_form) = 0.996950543026 0.00541264374281
absolute error = 0.005797
relative error = 0.5814 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=16199.6MB, alloc=40.3MB, time=195.71
t[1] = 1.7253 1.048
h = 0.0001 0.005
x1[1] (numeric) = 2.00005750748 -0.00579947613176
x1[1] (closed_form) = 2.00016008479 -0.000277789538866
absolute error = 0.005523
relative error = 0.2761 %
Correct digits = 3
h = 0.0001 0.005
x2[1] (numeric) = 0.991056292308 0.00527173471282
x2[1] (closed_form) = 0.996865993418 0.0054079387831
absolute error = 0.005811
relative error = 0.5829 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=16243.5MB, alloc=40.3MB, time=196.23
memory used=16287.6MB, alloc=40.3MB, time=196.76
t[1] = 1.7254 1.053
h = 0.0001 0.003
x1[1] (numeric) = 2.00008197728 -0.00586573341313
x1[1] (closed_form) = 2.00015867798 -0.000278558629847
absolute error = 0.005588
relative error = 0.2794 %
Correct digits = 3
h = 0.0001 0.003
x2[1] (numeric) = 0.990956918351 0.00524195401362
x2[1] (closed_form) = 0.996810732442 0.00537701612472
absolute error = 0.005855
relative error = 0.5874 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=16331.9MB, alloc=40.3MB, time=197.30
t[1] = 1.7255 1.056
h = 0.001 0.001
x1[1] (numeric) = 2.00009611596 -0.00590590610959
x1[1] (closed_form) = 2.0001578258 -0.0002790055076
absolute error = 0.005627
relative error = 0.2813 %
Correct digits = 3
h = 0.001 0.001
x2[1] (numeric) = 0.990857565138 0.0052113964034
x2[1] (closed_form) = 0.996777458132 0.00535863077411
absolute error = 0.005922
relative error = 0.5941 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=16376.0MB, alloc=40.3MB, time=197.83
t[1] = 1.7265 1.057
h = 0.001 0.003
x1[1] (numeric) = 2.00008793331 -0.00592459627327
x1[1] (closed_form) = 2.00015738925 -0.000278884170215
absolute error = 0.005646
relative error = 0.2823 %
Correct digits = 3
h = 0.001 0.003
x2[1] (numeric) = 0.990758168337 0.00518062949752
x2[1] (closed_form) = 0.996760055791 0.00536295054958
absolute error = 0.006005
relative error = 0.6024 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=16420.0MB, alloc=40.3MB, time=198.35
memory used=16464.0MB, alloc=40.3MB, time=198.88
t[1] = 1.7275 1.06
h = 0.0001 0.004
x1[1] (numeric) = 2.00009046773 -0.00597090192943
x1[1] (closed_form) = 2.00015639542 -0.00027907586683
absolute error = 0.005692
relative error = 0.2846 %
Correct digits = 3
h = 0.0001 0.004
x2[1] (numeric) = 0.990658600673 0.0051496656067
x2[1] (closed_form) = 0.996720888802 0.00535401455429
absolute error = 0.006066
relative error = 0.6086 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=16507.8MB, alloc=40.3MB, time=199.40
t[1] = 1.7276 1.064
h = 0.003 0.006
x1[1] (numeric) = 2.00011085951 -0.00602637977235
x1[1] (closed_form) = 2.00015526234 -0.000279671245706
absolute error = 0.005747
relative error = 0.2873 %
Correct digits = 3
h = 0.003 0.006
x2[1] (numeric) = 0.990558916494 0.0051181373865
x2[1] (closed_form) = 0.996676932242 0.0053283762639
absolute error = 0.006122
relative error = 0.6142 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=16551.8MB, alloc=40.3MB, time=199.92
memory used=16596.1MB, alloc=40.3MB, time=200.45
t[1] = 1.7306 1.07
h = 0.0001 0.005
x1[1] (numeric) = 2.00010297467 -0.00612497196171
x1[1] (closed_form) = 2.00015312147 -0.000279757248171
absolute error = 0.005845
relative error = 0.2922 %
Correct digits = 3
h = 0.0001 0.005
x2[1] (numeric) = 0.99045846059 0.00508554472817
x2[1] (closed_form) = 0.99659177747 0.00531989126278
absolute error = 0.006138
relative error = 0.6159 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=16639.9MB, alloc=40.3MB, time=200.97
t[1] = 1.7307 1.075
h = 0.0001 0.003
x1[1] (numeric) = 2.00012953646 -0.00619337892506
x1[1] (closed_form) = 2.00015170561 -0.000280491304853
absolute error = 0.005913
relative error = 0.2956 %
Correct digits = 3
h = 0.0001 0.003
x2[1] (numeric) = 0.990357258844 0.00505166631059
x2[1] (closed_form) = 0.996537351381 0.00528623023
absolute error = 0.006185
relative error = 0.6206 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=16684.1MB, alloc=40.3MB, time=201.50
memory used=16728.5MB, alloc=40.3MB, time=202.04
t[1] = 1.7308 1.078
h = 0.001 0.001
x1[1] (numeric) = 2.00014491821 -0.00623486647677
x1[1] (closed_form) = 2.00015084837 -0.00028091706567
absolute error = 0.005954
relative error = 0.2977 %
Correct digits = 3
h = 0.001 0.001
x2[1] (numeric) = 0.990256101479 0.00501699347407
x2[1] (closed_form) = 0.996504569565 0.00526619830209
absolute error = 0.006253
relative error = 0.6275 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=16772.5MB, alloc=40.3MB, time=202.56
t[1] = 1.7318 1.079
h = 0.0001 0.004
x1[1] (numeric) = 2.00013674662 -0.00625442176756
x1[1] (closed_form) = 2.00015041688 -0.000280786846266
absolute error = 0.005974
relative error = 0.2987 %
Correct digits = 3
h = 0.0001 0.004
x2[1] (numeric) = 0.99015490574 0.00498210516303
x2[1] (closed_form) = 0.996486809215 0.00526979079143
absolute error = 0.006338
relative error = 0.6361 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=16816.4MB, alloc=40.3MB, time=203.09
t[1] = 1.7319 1.083
h = 0.003 0.006
x1[1] (numeric) = 2.00015847595 -0.00631116939687
x1[1] (closed_form) = 2.00014927761 -0.000281358128676
absolute error = 0.00603
relative error = 0.3015 %
Correct digits = 3
h = 0.003 0.006
x2[1] (numeric) = 0.990053682267 0.00494683535045
x2[1] (closed_form) = 0.996443484097 0.00524227739589
absolute error = 0.006397
relative error = 0.6419 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=16860.3MB, alloc=40.3MB, time=203.60
memory used=16904.4MB, alloc=40.3MB, time=204.13
t[1] = 1.7349 1.089
h = 0.0001 0.005
x1[1] (numeric) = 2.00015172434 -0.0064126224586
x1[1] (closed_form) = 2.00014714468 -0.000281403247179
absolute error = 0.006131
relative error = 0.3065 %
Correct digits = 3
h = 0.0001 0.005
x2[1] (numeric) = 0.989951702455 0.00491046035221
x2[1] (closed_form) = 0.996357984574 0.00523048284293
absolute error = 0.006414
relative error = 0.6438 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=16948.3MB, alloc=40.3MB, time=204.66
t[1] = 1.735 1.094
h = 0.0001 0.003
x1[1] (numeric) = 2.00017995538 -0.00648257616978
x1[1] (closed_form) = 2.00014572126 -0.00028210723786
absolute error = 0.006201
relative error = 0.31 %
Correct digits = 3
h = 0.0001 0.003
x2[1] (numeric) = 0.98984899878 0.00487275552932
x2[1] (closed_form) = 0.996304413808 0.00519448505563
absolute error = 0.006463
relative error = 0.6487 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=16992.4MB, alloc=40.3MB, time=205.18
memory used=17036.9MB, alloc=40.3MB, time=205.72
t[1] = 1.7351 1.097
h = 0.001 0.001
x1[1] (numeric) = 2.00019633229 -0.00652501345032
x1[1] (closed_form) = 2.0001448598 -0.000282514878603
absolute error = 0.006243
relative error = 0.3121 %
Correct digits = 3
h = 0.001 0.001
x2[1] (numeric) = 0.98974636226 0.00483424304677
x2[1] (closed_form) = 0.996272138033 0.00517304758652
absolute error = 0.006535
relative error = 0.6559 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=17081.0MB, alloc=40.3MB, time=206.26
t[1] = 1.7361 1.098
h = 0.001 0.003
x1[1] (numeric) = 2.00018820388 -0.00654522744242
x1[1] (closed_form) = 2.00014443271 -0.000282377078804
absolute error = 0.006263
relative error = 0.3131 %
Correct digits = 3
h = 0.001 0.003
x2[1] (numeric) = 0.989643692616 0.00479551010736
x2[1] (closed_form) = 0.99625410169 0.00517599177746
absolute error = 0.006621
relative error = 0.6646 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=17125.0MB, alloc=40.3MB, time=206.78
memory used=17169.1MB, alloc=40.3MB, time=207.31
t[1] = 1.7371 1.101
h = 0.0001 0.004
x1[1] (numeric) = 2.00019242665 -0.00659455310203
x1[1] (closed_form) = 2.00014344141 -0.000282526437826
absolute error = 0.006312
relative error = 0.3156 %
Correct digits = 3
h = 0.0001 0.004
x2[1] (numeric) = 0.989540856574 0.00475656207095
x2[1] (closed_form) = 0.996215056105 0.0051636642722
absolute error = 0.006687
relative error = 0.6712 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=17213.2MB, alloc=40.3MB, time=207.83
t[1] = 1.7372 1.105
h = 0.003 0.006
x1[1] (numeric) = 2.00021601045 -0.00665307265726
x1[1] (closed_form) = 2.00014229593 -0.000283069633357
absolute error = 0.00637
relative error = 0.3185 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.989437932165 0.00471701961385
x2[1] (closed_form) = 0.996172531342 0.00513397264165
absolute error = 0.006747
relative error = 0.6773 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=17257.1MB, alloc=40.3MB, time=208.36
t[1] = 1.7402 1.111
h = 0.0001 0.005
x1[1] (numeric) = 2.00021081961 -0.00675850952111
x1[1] (closed_form) = 2.00014017381 -0.000283067830015
absolute error = 0.006476
relative error = 0.3238 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.989334266318 0.00467632378149
x2[1] (closed_form) = 0.996086733564 0.0051182867931
absolute error = 0.006767
relative error = 0.6793 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=17301.2MB, alloc=40.3MB, time=208.88
memory used=17345.2MB, alloc=40.3MB, time=209.41
t[1] = 1.7403 1.116
h = 0.0001 0.003
x1[1] (numeric) = 2.00024136377 -0.00683062382825
x1[1] (closed_form) = 2.00013874285 -0.000283736782706
absolute error = 0.006548
relative error = 0.3274 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.989229898928 0.00463424565474
x2[1] (closed_form) = 0.996034240417 0.00507957666932
absolute error = 0.006819
relative error = 0.6846 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=17389.4MB, alloc=40.3MB, time=209.94
t[1] = 1.7404 1.119
h = 0.001 0.001
x1[1] (numeric) = 2.00025911714 -0.00687438431711
x1[1] (closed_form) = 2.00013787723 -0.000284123320063
absolute error = 0.006591
relative error = 0.3295 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.989125624097 0.0045913429779
x2[1] (closed_form) = 0.996002602939 0.00505650747656
absolute error = 0.006893
relative error = 0.692 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=17433.6MB, alloc=40.3MB, time=210.47
memory used=17477.7MB, alloc=40.3MB, time=211.00
t[1] = 1.7414 1.12
h = 0.001 0.003
x1[1] (numeric) = 2.00025104401 -0.00689550940186
x1[1] (closed_form) = 2.00013745551 -0.000283976936233
absolute error = 0.006613
relative error = 0.3306 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.989021321868 0.00454821371818
x2[1] (closed_form) = 0.995984263759 0.00505868273755
absolute error = 0.006982
relative error = 0.701 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=17521.8MB, alloc=40.3MB, time=211.54
t[1] = 1.7424 1.123
h = 0.0001 0.004
x1[1] (numeric) = 2.00025631944 -0.00694661495416
x1[1] (closed_form) = 2.00013646643 -0.000284103778375
absolute error = 0.006664
relative error = 0.3332 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.988916855681 0.00450485942668
x2[1] (closed_form) = 0.995945389156 0.00504451150902
absolute error = 0.007049
relative error = 0.7078 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=17565.8MB, alloc=40.3MB, time=212.06
memory used=17609.9MB, alloc=40.3MB, time=212.58
t[1] = 1.7425 1.127
h = 0.003 0.006
x1[1] (numeric) = 2.00028185252 -0.00700690404118
x1[1] (closed_form) = 2.00013531539 -0.000284618906492
absolute error = 0.006724
relative error = 0.3362 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.988812316551 0.00446089419739
x2[1] (closed_form) = 0.995903769655 0.00501265613889
absolute error = 0.007113
relative error = 0.7142 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=17653.8MB, alloc=40.3MB, time=213.11
t[1] = 1.7455 1.133
h = 0.0001 0.005
x1[1] (numeric) = 2.00027836755 -0.00711638781367
x1[1] (closed_form) = 2.00013320504 -0.000284570676968
absolute error = 0.006833
relative error = 0.3416 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.988707052572 0.00441572679428
x2[1] (closed_form) = 0.995817844211 0.00499302783678
absolute error = 0.007134
relative error = 0.7164 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=17697.7MB, alloc=40.3MB, time=213.64
t[1] = 1.7456 1.138
h = 0.0001 0.003
x1[1] (numeric) = 2.00031134182 -0.00719065865399
x1[1] (closed_form) = 2.00013176735 -0.00028520462037
absolute error = 0.006908
relative error = 0.3454 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.988601111331 0.0043691241365
x2[1] (closed_form) = 0.995766560094 0.00495162702552
absolute error = 0.007189
relative error = 0.722 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=17741.7MB, alloc=40.3MB, time=214.15
memory used=17786.2MB, alloc=40.3MB, time=214.70
t[1] = 1.7457 1.141
h = 0.001 0.001
x1[1] (numeric) = 2.00033054231 -0.0072357408769
x1[1] (closed_form) = 2.00013089805 -0.000285570079967
absolute error = 0.006953
relative error = 0.3476 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.988495289077 0.00432168039652
x2[1] (closed_form) = 0.995735639872 0.00492693868463
absolute error = 0.007266
relative error = 0.7297 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=17830.4MB, alloc=40.3MB, time=215.23
t[1] = 1.7467 1.142
h = 0.001 0.003
x1[1] (numeric) = 2.00032254982 -0.00725779936965
x1[1] (closed_form) = 2.00013048187 -0.00028541527718
absolute error = 0.006975
relative error = 0.3487 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.988389445448 0.00427400397866
x2[1] (closed_form) = 0.995717029188 0.00492832403013
absolute error = 0.007357
relative error = 0.7388 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=17874.4MB, alloc=40.3MB, time=215.75
memory used=17918.4MB, alloc=40.3MB, time=216.28
t[1] = 1.7477 1.145
h = 0.0001 0.004
x1[1] (numeric) = 2.00032895202 -0.00731070351086
x1[1] (closed_form) = 2.00012949548 -0.000285519775251
absolute error = 0.007028
relative error = 0.3514 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.988283440634 0.00422609245027
x2[1] (closed_form) = 0.995678409428 0.00491229875381
absolute error = 0.007427
relative error = 0.7459 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=17962.3MB, alloc=40.3MB, time=216.80
t[1] = 1.7478 1.149
h = 0.003 0.006
x1[1] (numeric) = 2.00035653157 -0.0073727569612
x1[1] (closed_form) = 2.00012833953 -0.000286006869509
absolute error = 0.00709
relative error = 0.3545 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.988177379099 0.00417755354898
x2[1] (closed_form) = 0.995637800461 0.00487829893619
absolute error = 0.007493
relative error = 0.7526 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=18006.1MB, alloc=40.3MB, time=217.32
memory used=18050.0MB, alloc=40.3MB, time=217.86
t[1] = 1.7508 1.155
h = 0.0001 0.005
x1[1] (numeric) = 2.0003549031 -0.00748634822758
x1[1] (closed_form) = 2.0001262419 -0.000285912727889
absolute error = 0.007204
relative error = 0.3602 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.988070611038 0.00412776309734
x2[1] (closed_form) = 0.99555192186 0.00485468410156
absolute error = 0.007517
relative error = 0.755 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=18094.1MB, alloc=40.3MB, time=218.38
t[1] = 1.7509 1.16
h = 0.0001 0.003
x1[1] (numeric) = 2.00039042741 -0.00756276808202
x1[1] (closed_form) = 2.00012479828 -0.000286511708233
absolute error = 0.007281
relative error = 0.364 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.987963192017 0.00407648398087
x2[1] (closed_form) = 0.995501978493 0.00481062029431
absolute error = 0.007574
relative error = 0.7609 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=18138.3MB, alloc=40.3MB, time=218.91
t[1] = 1.751 1.163
h = 0.001 0.001
x1[1] (numeric) = 2.00041114745 -0.00760916850183
x1[1] (closed_form) = 2.00012392579 -0.000286856126161
absolute error = 0.007328
relative error = 0.3664 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.987855919445 0.00402434764243
x2[1] (closed_form) = 0.995471854689 0.00478432900728
absolute error = 0.007654
relative error = 0.7688 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=18182.6MB, alloc=40.3MB, time=219.45
memory used=18226.8MB, alloc=40.3MB, time=219.98
t[1] = 1.752 1.164
h = 0.001 0.003
x1[1] (numeric) = 2.00040326222 -0.00763218256843
x1[1] (closed_form) = 2.0001235153 -0.000286693072037
absolute error = 0.007351
relative error = 0.3675 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.987748631823 0.00397197257042
x2[1] (closed_form) = 0.995453005068 0.00478490464024
absolute error = 0.007747
relative error = 0.7782 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=18270.9MB, alloc=40.3MB, time=220.50
t[1] = 1.753 1.167
h = 0.0001 0.004
x1[1] (numeric) = 2.00041086776 -0.00768690235817
x1[1] (closed_form) = 2.00012253207 -0.000286775408407
absolute error = 0.007406
relative error = 0.3703 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.987641186132 0.00391935217078
x2[1] (closed_form) = 0.995414725278 0.00476701861478
absolute error = 0.00782
relative error = 0.7856 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=18314.8MB, alloc=40.3MB, time=221.02
memory used=18358.9MB, alloc=40.3MB, time=221.55
t[1] = 1.7531 1.171
h = 0.003 0.006
x1[1] (numeric) = 2.00044059332 -0.00775071209297
x1[1] (closed_form) = 2.00012137185 -0.000287234516287
absolute error = 0.00747
relative error = 0.3735 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.987533700754 0.00386608806753
x2[1] (closed_form) = 0.995375232278 0.00473089850132
absolute error = 0.007889
relative error = 0.7926 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=18402.9MB, alloc=40.3MB, time=222.08
t[1] = 1.7561 1.177
h = 0.0001 0.005
x1[1] (numeric) = 2.00044097762 -0.00786846869257
x1[1] (closed_form) = 2.00011928787 -0.000287094994621
absolute error = 0.007588
relative error = 0.3794 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.987425528962 0.00381152249225
x2[1] (closed_form) = 0.995289578668 0.004703260377
absolute error = 0.007914
relative error = 0.7952 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=18446.8MB, alloc=40.3MB, time=222.61
memory used=18490.8MB, alloc=40.3MB, time=223.13
t[1] = 1.7562 1.182
h = 0.0001 0.003
x1[1] (numeric) = 2.00047917476 -0.0079470264175
x1[1] (closed_form) = 2.00011783913 -0.000287659075459
absolute error = 0.007668
relative error = 0.3834 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.987316734583 0.00375541443501
x2[1] (closed_form) = 0.99524110781 0.00465656738001
absolute error = 0.007975
relative error = 0.8013 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=18535.1MB, alloc=40.3MB, time=223.68
t[1] = 1.7563 1.185
h = 0.001 0.001
x1[1] (numeric) = 2.00050148855 -0.00799473933244
x1[1] (closed_form) = 2.00011696392 -0.000287982498149
absolute error = 0.007716
relative error = 0.3858 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.987208115162 0.00369843344334
x2[1] (closed_form) = 0.995211859631 0.00462869301954
absolute error = 0.008058
relative error = 0.8096 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=18579.3MB, alloc=40.3MB, time=224.21
t[1] = 1.7573 1.186
h = 0.0001 0.004
x1[1] (numeric) = 2.00049373853 -0.00801873094735
x1[1] (closed_form) = 2.00011655926 -0.000287811362744
absolute error = 0.00774
relative error = 0.387 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.987099487322 0.00364120771041
x2[1] (closed_form) = 0.995192804833 0.00462844039776
absolute error = 0.008153
relative error = 0.8193 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=18623.2MB, alloc=40.3MB, time=224.74
memory used=18667.1MB, alloc=40.3MB, time=225.26
t[1] = 1.7574 1.19
h = 0.003 0.006
x1[1] (numeric) = 2.0005251493 -0.00808379322408
x1[1] (closed_form) = 2.00011539555 -0.000288246469979
absolute error = 0.007806
relative error = 0.3903 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.986990889008 0.0035835549202
x2[1] (closed_form) = 0.995154381586 0.00459053329589
absolute error = 0.008225
relative error = 0.8265 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=18711.1MB, alloc=40.3MB, time=225.78
t[1] = 1.7604 1.196
h = 0.0001 0.005
x1[1] (numeric) = 2.00052720493 -0.00820462921079
x1[1] (closed_form) = 2.00011332352 -0.000288068148645
absolute error = 0.007927
relative error = 0.3963 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.986881627276 0.00352455831546
x2[1] (closed_form) = 0.995069115242 0.00455941401597
absolute error = 0.008253
relative error = 0.8293 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=18755.2MB, alloc=40.3MB, time=226.31
memory used=18799.2MB, alloc=40.3MB, time=226.83
t[1] = 1.7605 1.201
h = 0.0001 0.003
x1[1] (numeric) = 2.00056750031 -0.00828470834476
x1[1] (closed_form) = 2.00011187058 -0.000288602301376
absolute error = 0.008009
relative error = 0.4004 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.986771773685 0.00346397424185
x2[1] (closed_form) = 0.995022047867 0.00451050935679
absolute error = 0.008316
relative error = 0.8358 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=18843.6MB, alloc=40.3MB, time=227.38
t[1] = 1.7606 1.204
h = 0.001 0.001
x1[1] (numeric) = 2.00059106898 -0.00833335917806
x1[1] (closed_form) = 2.00011099317 -0.000288907721696
absolute error = 0.008059
relative error = 0.4029 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.986662122005 0.00340250614927
x2[1] (closed_form) = 0.994993635204 0.0044813027954
absolute error = 0.008401
relative error = 0.8443 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=18887.7MB, alloc=40.3MB, time=227.91
t[1] = 1.7616 1.205
h = 0.001 0.003
x1[1] (numeric) = 2.00058345787 -0.00835808929308
x1[1] (closed_form) = 2.00011059356 -0.000288729696288
absolute error = 0.008083
relative error = 0.4041 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.986552468408 0.00334078864417
x2[1] (closed_form) = 0.99497444185 0.00448032152221
absolute error = 0.008499
relative error = 0.8542 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=18931.9MB, alloc=40.3MB, time=228.43
memory used=18975.8MB, alloc=40.3MB, time=228.96
t[1] = 1.7626 1.208
h = 0.0001 0.004
x1[1] (numeric) = 2.00059339415 -0.00841598778795
x1[1] (closed_form) = 2.0001096172 -0.000288771261499
absolute error = 0.008142
relative error = 0.4071 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.986442664335 0.00327880661411
x2[1] (closed_form) = 0.99493704713 0.00445897451999
absolute error = 0.008576
relative error = 0.862 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=19019.8MB, alloc=40.3MB, time=229.48
t[1] = 1.7627 1.212
h = 0.003 0.006
x1[1] (numeric) = 2.00062715358 -0.00848278988135
x1[1] (closed_form) = 2.0001084504 -0.000289178499685
absolute error = 0.00821
relative error = 0.4105 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.986332855916 0.0032161520651
x2[1] (closed_form) = 0.994899935296 0.00441900642603
absolute error = 0.008651
relative error = 0.8695 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=19063.9MB, alloc=40.3MB, time=230.01
memory used=19108.0MB, alloc=40.3MB, time=230.54
t[1] = 1.7657 1.218
h = 0.0001 0.005
x1[1] (numeric) = 2.00063154021 -0.00860790909984
x1[1] (closed_form) = 2.00010639373 -0.00028895582391
absolute error = 0.008336
relative error = 0.4168 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.986222407517 0.00315210300663
x2[1] (closed_form) = 0.994815234341 0.00438381794791
absolute error = 0.008681
relative error = 0.8726 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=19152.1MB, alloc=40.3MB, time=231.06
t[1] = 1.7658 1.223
h = 0.0001 0.003
x1[1] (numeric) = 2.00067475875 -0.00869010357759
x1[1] (closed_form) = 2.00010493713 -0.000289455231418
absolute error = 0.00842
relative error = 0.421 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.986111399462 0.00308641217612
x2[1] (closed_form) = 0.994769883248 0.00433236503783
absolute error = 0.008748
relative error = 0.8794 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=19196.1MB, alloc=40.3MB, time=231.59
memory used=19240.5MB, alloc=40.3MB, time=232.14
t[1] = 1.7659 1.226
h = 0.001 0.001
x1[1] (numeric) = 2.00070007242 -0.00874005529703
x1[1] (closed_form) = 2.00010405789 -0.000289739764362
absolute error = 0.008471
relative error = 0.4235 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.986000623682 0.00301982252242
x2[1] (closed_form) = 0.994742492811 0.00430162321188
absolute error = 0.008835
relative error = 0.8882 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=19284.7MB, alloc=40.3MB, time=232.67
t[1] = 1.7669 1.227
h = 0.001 0.003
x1[1] (numeric) = 2.00069265346 -0.00876580766849
x1[1] (closed_form) = 2.00010366438 -0.000289553978558
absolute error = 0.008497
relative error = 0.4248 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.98588985317 0.00295297757356
x2[1] (closed_form) = 0.994723160303 0.00429978317711
absolute error = 0.008935
relative error = 0.8983 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=19328.9MB, alloc=40.3MB, time=233.20
t[1] = 1.7679 1.23
h = 0.0001 0.004
x1[1] (numeric) = 2.00070403278 -0.00882556811608
x1[1] (closed_form) = 2.00010269251 -0.000289573949452
absolute error = 0.008557
relative error = 0.4278 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.985778936317 0.00288585755163
x2[1] (closed_form) = 0.994686354655 0.00427657810908
absolute error = 0.009015
relative error = 0.9063 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=19373.1MB, alloc=40.3MB, time=233.72
memory used=19417.1MB, alloc=40.3MB, time=234.26
t[1] = 1.768 1.234
h = 0.003 0.006
x1[1] (numeric) = 2.00074024712 -0.00889409247576
x1[1] (closed_form) = 2.00010152324 -0.000289953405009
absolute error = 0.008628
relative error = 0.4314 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.985668034475 0.0028180491401
x2[1] (closed_form) = 0.994650658861 0.00423458733805
absolute error = 0.009094
relative error = 0.9142 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=19461.2MB, alloc=40.3MB, time=234.78
t[1] = 1.771 1.24
h = 0.0001 0.005
x1[1] (numeric) = 2.00074713783 -0.00902354315321
x1[1] (closed_form) = 2.00009948281 -0.000289686955889
absolute error = 0.008758
relative error = 0.4379 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.985556518019 0.00274879507552
x2[1] (closed_form) = 0.994566710113 0.00419531513108
absolute error = 0.009126
relative error = 0.9175 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=19505.1MB, alloc=40.3MB, time=235.31
memory used=19549.1MB, alloc=40.3MB, time=235.83
t[1] = 1.7711 1.245
h = 0.0001 0.003
x1[1] (numeric) = 2.00079341051 -0.00910783003099
x1[1] (closed_form) = 2.00009802333 -0.000290151730148
absolute error = 0.008845
relative error = 0.4422 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.985444476334 0.00267784465373
x2[1] (closed_form) = 0.994523205586 0.00414136555646
absolute error = 0.009196
relative error = 0.9246 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=19593.4MB, alloc=40.3MB, time=236.37
t[1] = 1.7712 1.248
h = 0.001 0.001
x1[1] (numeric) = 2.00082054843 -0.00915906987951
x1[1] (closed_form) = 2.00009714272 -0.000290415451023
absolute error = 0.008898
relative error = 0.4449 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.985332698364 0.00260598113179
x2[1] (closed_form) = 0.994496915755 0.00410911901728
absolute error = 0.009287
relative error = 0.9338 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=19637.6MB, alloc=40.3MB, time=236.90
memory used=19681.7MB, alloc=40.3MB, time=237.43
t[1] = 1.7722 1.249
h = 0.001 0.003
x1[1] (numeric) = 2.00081335361 -0.00918586562855
x1[1] (closed_form) = 2.00009675545 -0.00029022208128
absolute error = 0.008924
relative error = 0.4462 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.985220933168 0.00253385650478
x2[1] (closed_form) = 0.994477480992 0.00410640563644
absolute error = 0.009389
relative error = 0.9441 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=19725.8MB, alloc=40.3MB, time=237.96
t[1] = 1.7732 1.252
h = 0.0001 0.004
x1[1] (numeric) = 2.00082626221 -0.00924749745666
x1[1] (closed_form) = 2.00009578852 -0.000290220675375
absolute error = 0.008987
relative error = 0.4493 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.985109026151 0.00246144614197
x2[1] (closed_form) = 0.994441352943 0.0040813506024
absolute error = 0.009472
relative error = 0.9525 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=19769.8MB, alloc=40.3MB, time=238.49
t[1] = 1.7733 1.256
h = 0.003 0.006
x1[1] (numeric) = 2.00086503992 -0.00931772307681
x1[1] (closed_form) = 2.00009461741 -0.000290572447963
absolute error = 0.00906
relative error = 0.453 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.984997154368 0.00238833171341
x2[1] (closed_form) = 0.994407177125 0.00403738048462
absolute error = 0.009553
relative error = 0.9607 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=19813.8MB, alloc=40.3MB, time=239.01
memory used=19857.9MB, alloc=40.3MB, time=239.54
t[1] = 1.7763 1.262
h = 0.0001 0.005
x1[1] (numeric) = 2.00087461355 -0.00945154975824
x1[1] (closed_form) = 2.00009259408 -0.000290262822766
absolute error = 0.009195
relative error = 0.4597 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.98488469532 0.00231372008002
x2[1] (closed_form) = 0.994324169847 0.00399401817409
absolute error = 0.009588
relative error = 0.9643 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=19901.9MB, alloc=40.3MB, time=240.07
t[1] = 1.7764 1.267
h = 0.0001 0.003
x1[1] (numeric) = 2.00092407405 -0.00953790179458
x1[1] (closed_form) = 2.0000911325 -0.000290693092209
absolute error = 0.009285
relative error = 0.4642 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.984771747748 0.00223735727393
x2[1] (closed_form) = 0.994282641137 0.00393762980399
absolute error = 0.009662
relative error = 0.9717 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=19945.9MB, alloc=40.3MB, time=240.59
memory used=19990.5MB, alloc=40.3MB, time=241.14
t[1] = 1.7765 1.27
h = 0.001 0.001
x1[1] (numeric) = 2.0009531171 -0.00959041444317
x1[1] (closed_form) = 2.00009025099 -0.000290936086128
absolute error = 0.009339
relative error = 0.467 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.984659096416 0.00216006765715
x2[1] (closed_form) = 0.994257529688 0.00390391287789
absolute error = 0.009756
relative error = 0.9812 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=20034.7MB, alloc=40.3MB, time=241.67
t[1] = 1.7775 1.271
h = 0.001 0.003
x1[1] (numeric) = 2.00094617982 -0.00961827431927
x1[1] (closed_form) = 2.00008987009 -0.000290735310908
absolute error = 0.009367
relative error = 0.4683 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.98454646569 0.00208251120809
x2[1] (closed_form) = 0.994238030571 0.00390031306464
absolute error = 0.009861
relative error = 0.9918 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=20078.7MB, alloc=40.3MB, time=242.20
memory used=20122.9MB, alloc=40.3MB, time=242.73
t[1] = 1.7785 1.274
h = 0.0001 0.004
x1[1] (numeric) = 2.00096070641 -0.00968178475259
x1[1] (closed_form) = 2.00008890853 -0.000290712754317
absolute error = 0.009431
relative error = 0.4716 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.98443369806 0.00200465825341
x2[1] (closed_form) = 0.994202669143 0.00387342017383
absolute error = 0.009946
relative error = 1 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=20166.9MB, alloc=40.3MB, time=243.25
t[1] = 1.7786 1.278
h = 0.003 0.006
x1[1] (numeric) = 2.00100215807 -0.00975368702657
x1[1] (closed_form) = 2.0000877362 -0.000291036956645
absolute error = 0.009507
relative error = 0.4753 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.984320986767 0.00192608577798
x2[1] (closed_form) = 0.994170116314 0.0038275190728
absolute error = 0.01003
relative error = 1.009 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=20210.9MB, alloc=40.3MB, time=243.78
t[1] = 1.7816 1.284
h = 0.0001 0.005
x1[1] (numeric) = 2.00101459927 -0.00989193032002
x1[1] (closed_form) = 2.00008573083 -0.000290684768331
absolute error = 0.009646
relative error = 0.4823 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.984207717596 0.00184596418042
x2[1] (closed_form) = 0.994088241875 0.00378006862782
absolute error = 0.01007
relative error = 1.013 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=20254.9MB, alloc=40.3MB, time=244.30
memory used=20299.0MB, alloc=40.3MB, time=244.83
t[1] = 1.7817 1.289
h = 0.0001 0.003
x1[1] (numeric) = 2.00106738387 -0.00998031579632
x1[1] (closed_form) = 2.00008426791 -0.000291080677615
absolute error = 0.009739
relative error = 0.4869 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.984093998936 0.0017640364185
x2[1] (closed_form) = 0.994048816906 0.00372130562885
absolute error = 0.01015
relative error = 1.021 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=20343.3MB, alloc=40.3MB, time=245.37
t[1] = 1.7818 1.292
h = 0.001 0.001
x1[1] (numeric) = 2.00109841455 -0.0100340832353
x1[1] (closed_form) = 2.00008338595 -0.000291303039351
absolute error = 0.009796
relative error = 0.4898 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.983980610135 0.00168116874219
x2[1] (closed_form) = 0.99402496084 0.00368615642699
absolute error = 0.01024
relative error = 1.03 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=20387.6MB, alloc=40.3MB, time=245.90
memory used=20431.5MB, alloc=40.3MB, time=246.43
t[1] = 1.7828 1.293
h = 0.0001 0.004
x1[1] (numeric) = 2.00109176964 -0.0100630275664
x1[1] (closed_form) = 2.00008301156 -0.000291095039004
absolute error = 0.009824
relative error = 0.4912 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.983867250104 0.00159802859929
x2[1] (closed_form) = 0.99400543622 0.00368165865226
absolute error = 0.01035
relative error = 1.041 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=20475.5MB, alloc=40.3MB, time=246.96
t[1] = 1.7829 1.297
h = 0.003 0.006
x1[1] (numeric) = 2.00113529547 -0.0101361086645
x1[1] (closed_form) = 2.00008183833 -0.000291395614566
absolute error = 0.009901
relative error = 0.495 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.983753989171 0.00151441979063
x2[1] (closed_form) = 0.993974384143 0.00363415898312
absolute error = 0.01044
relative error = 1.05 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=20519.5MB, alloc=40.3MB, time=247.48
memory used=20563.6MB, alloc=40.3MB, time=248.01
t[1] = 1.7859 1.303
h = 0.0001 0.005
x1[1] (numeric) = 2.00115004851 -0.0102775934741
x1[1] (closed_form) = 2.00007984859 -0.000291007064462
absolute error = 0.01004
relative error = 0.5022 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.983640201913 0.00142921878018
x2[1] (closed_form) = 0.993893687914 0.00358321431342
absolute error = 0.01048
relative error = 1.054 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=20607.7MB, alloc=40.3MB, time=248.54
t[1] = 1.786 1.308
h = 0.0001 0.003
x1[1] (numeric) = 2.00120541085 -0.0103674046734
x1[1] (closed_form) = 2.00007838472 -0.000291373529351
absolute error = 0.01014
relative error = 0.5069 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.983526005603 0.00134216677041
x2[1] (closed_form) = 0.993856202116 0.00352249060892
absolute error = 0.01056
relative error = 1.062 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=20652.0MB, alloc=40.3MB, time=249.08
t[1] = 1.7861 1.311
h = 0.001 0.001
x1[1] (numeric) = 2.00123798721 -0.0104220560686
x1[1] (closed_form) = 2.0000775025 -0.000291578212706
absolute error = 0.0102
relative error = 0.5098 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.983412170402 0.00125416668076
x2[1] (closed_form) = 0.993833503954 0.0034861581461
absolute error = 0.01066
relative error = 1.072 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=20696.4MB, alloc=40.3MB, time=249.61
memory used=20740.5MB, alloc=40.3MB, time=250.14
t[1] = 1.7871 1.312
h = 0.001 0.003
x1[1] (numeric) = 2.00123160148 -0.0104518138413
x1[1] (closed_form) = 2.00007713371 -0.000291364059614
absolute error = 0.01023
relative error = 0.5113 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.983298371807 0.00116588996081
x2[1] (closed_form) = 0.993814000022 0.00348087977748
absolute error = 0.01077
relative error = 1.083 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=20784.6MB, alloc=40.3MB, time=250.67
t[1] = 1.7881 1.315
h = 0.0001 0.004
x1[1] (numeric) = 2.00124920614 -0.0105185812353
x1[1] (closed_form) = 2.00007618305 -0.000291302700861
absolute error = 0.01029
relative error = 0.5147 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.983184447473 0.00107729675937
x2[1] (closed_form) = 0.993780324353 0.00345062492084
absolute error = 0.01086
relative error = 1.093 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=20828.8MB, alloc=40.3MB, time=251.19
memory used=20872.9MB, alloc=40.3MB, time=251.72
t[1] = 1.7882 1.319
h = 0.003 0.006
x1[1] (numeric) = 2.00129563069 -0.0105932890583
x1[1] (closed_form) = 2.00007500973 -0.000291575942783
absolute error = 0.01037
relative error = 0.5187 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.983070622545 0.000987957570902
x2[1] (closed_form) = 0.993751082972 0.00340129886673
absolute error = 0.01095
relative error = 1.102 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=20916.9MB, alloc=40.3MB, time=252.24
t[1] = 1.7912 1.325
h = 0.0001 0.005
x1[1] (numeric) = 2.00131362661 -0.0107392733142
x1[1] (closed_form) = 2.00007303949 -0.000291146000659
absolute error = 0.01052
relative error = 0.5261 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.982956304431 0.000896973852175
x2[1] (closed_form) = 0.993671879807 0.00334629484413
absolute error = 0.01099
relative error = 1.106 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=20960.9MB, alloc=40.3MB, time=252.78
memory used=21005.2MB, alloc=40.3MB, time=253.34
t[1] = 1.7913 1.33
h = 0.0001 0.003
x1[1] (numeric) = 2.0013725904 -0.0108310537525
x1[1] (closed_form) = 2.0000715757 -0.000291478407973
absolute error = 0.01062
relative error = 0.531 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.982841620573 0.00080408411316
x2[1] (closed_form) = 0.993636730315 0.0032833341418
absolute error = 0.01108
relative error = 1.115 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=21049.6MB, alloc=40.3MB, time=254.44
t[1] = 1.7914 1.333
h = 0.001 0.001
x1[1] (numeric) = 2.00140732227 -0.0108869233873
x1[1] (closed_form) = 2.00007069387 -0.000291662655361
absolute error = 0.01068
relative error = 0.5339 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.98272733336 0.000710234432181
x2[1] (closed_form) = 0.993615427591 0.00324565128179
absolute error = 0.01118
relative error = 1.125 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=21093.8MB, alloc=40.3MB, time=255.51
t[1] = 1.7924 1.334
h = 0.001 0.003
x1[1] (numeric) = 2.00140129971 -0.0109178069216
x1[1] (closed_form) = 2.0000703318 -0.000291441616002
absolute error = 0.01071
relative error = 0.5355 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.982613091508 0.000616102696806
x2[1] (closed_form) = 0.993595972845 0.00323945832442
absolute error = 0.01129
relative error = 1.136 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=21137.8MB, alloc=40.3MB, time=256.18
memory used=21181.9MB, alloc=40.3MB, time=256.74
t[1] = 1.7934 1.337
h = 0.0001 0.004
x1[1] (numeric) = 2.0014207985 -0.0109864676759
x1[1] (closed_form) = 2.00006938774 -0.000291359794091
absolute error = 0.01078
relative error = 0.539 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.982498729997 0.000521643480253
x2[1] (closed_form) = 0.993563319308 0.00320742397349
absolute error = 0.01139
relative error = 1.146 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=21225.9MB, alloc=40.3MB, time=257.30
t[1] = 1.7935 1.341
h = 0.003 0.006
x1[1] (numeric) = 2.00147023831 -0.0110627660573
x1[1] (closed_form) = 2.00006821493 -0.000291605851401
absolute error = 0.01086
relative error = 0.5431 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.982384491485 0.000426423632515
x2[1] (closed_form) = 0.993535987642 0.00315633428369
absolute error = 0.01148
relative error = 1.156 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=21270.0MB, alloc=40.3MB, time=257.85
memory used=21314.2MB, alloc=40.3MB, time=258.41
t[1] = 1.7965 1.347
h = 0.0001 0.005
x1[1] (numeric) = 2.00149167889 -0.0112132770535
x1[1] (closed_form) = 2.00006626498 -0.000291135172693
absolute error = 0.01101
relative error = 0.5507 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.982269795112 0.000329506685002
x2[1] (closed_form) = 0.993458472855 0.00309729767385
absolute error = 0.01153
relative error = 1.16 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=21358.3MB, alloc=40.3MB, time=258.96
t[1] = 1.7966 1.352
h = 0.0001 0.003
x1[1] (numeric) = 2.00155438765 -0.011306980633
x1[1] (closed_form) = 2.000064802 -0.000291433712218
absolute error = 0.01112
relative error = 0.5558 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.982154778785 0.000230628677124
x2[1] (closed_form) = 0.993425782102 0.00303218209583
absolute error = 0.01161
relative error = 1.169 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=21402.5MB, alloc=40.3MB, time=259.52
t[1] = 1.7967 1.355
h = 0.001 0.001
x1[1] (numeric) = 2.00159136199 -0.0113640418806
x1[1] (closed_form) = 2.00006392102 -0.000291597645267
absolute error = 0.01118
relative error = 0.5588 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.982040195758 0.00013077958695
x2[1] (closed_form) = 0.993405948577 0.00299319774655
absolute error = 0.01172
relative error = 1.18 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=21447.0MB, alloc=40.3MB, time=260.09
memory used=21491.1MB, alloc=40.3MB, time=260.65
t[1] = 1.7977 1.356
h = 0.001 0.003
x1[1] (numeric) = 2.00158574179 -0.0113960699216
x1[1] (closed_form) = 2.00006356579 -0.00029136990484
absolute error = 0.01121
relative error = 0.5604 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.98192566719 3.06431405294e-05
x2[1] (closed_form) = 0.99338658421 0.00298608344359
absolute error = 0.01184
relative error = 1.191 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=21535.3MB, alloc=40.3MB, time=261.20
t[1] = 1.7987 1.359
h = 0.0001 0.004
x1[1] (numeric) = 2.00160723297 -0.0114666212712
x1[1] (closed_form) = 2.00006262874 -0.000291267877211
absolute error = 0.01128
relative error = 0.5641 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.981811025483 -6.98318624592e-05
x2[1] (closed_form) = 0.993355042015 0.00295229768966
absolute error = 0.01193
relative error = 1.201 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=21579.5MB, alloc=40.3MB, time=261.75
memory used=21623.7MB, alloc=40.3MB, time=262.31
t[1] = 1.7988 1.363
h = 0.003 0.006
x1[1] (numeric) = 2.00165980647 -0.0115444698685
x1[1] (closed_form) = 2.00006145702 -0.000291486911211
absolute error = 0.01137
relative error = 0.5683 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.981696531297 -0.000171081812828
x2[1] (closed_form) = 0.993329717246 0.00289951211631
absolute error = 0.01203
relative error = 1.211 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=21667.6MB, alloc=40.3MB, time=262.86
t[1] = 1.8018 1.369
h = 0.0001 0.005
x1[1] (numeric) = 2.0016848993 -0.011699529913
x1[1] (closed_form) = 2.00005952815 -0.000290976165193
absolute error = 0.01152
relative error = 0.5762 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.981581616814 -0.000274081621954
x2[1] (closed_form) = 0.993254086845 0.0028364786194
absolute error = 0.01208
relative error = 1.216 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=21711.9MB, alloc=40.3MB, time=263.41
memory used=21756.2MB, alloc=40.3MB, time=263.96
t[1] = 1.8019 1.374
h = 0.0001 0.003
x1[1] (numeric) = 2.00175149882 -0.0117951053496
x1[1] (closed_form) = 2.00005806673 -0.000291241041967
absolute error = 0.01163
relative error = 0.5814 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.981466430706 -0.000379097486338
x2[1] (closed_form) = 0.993223974792 0.00276929651755
absolute error = 0.01217
relative error = 1.225 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=21800.6MB, alloc=40.3MB, time=264.52
t[1] = 1.802 1.377
h = 0.001 0.001
x1[1] (numeric) = 2.00179080402 -0.0118533284727
x1[1] (closed_form) = 2.00005718703 -0.00029138479137
absolute error = 0.01169
relative error = 0.5845 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.981351715673 -0.000485094806692
x2[1] (closed_form) = 0.993205682765 0.00272906333466
absolute error = 0.01228
relative error = 1.237 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=21844.8MB, alloc=40.3MB, time=265.08
t[1] = 1.803 1.378
h = 0.001 0.003
x1[1] (numeric) = 2.00178562686 -0.0118865191327
x1[1] (closed_form) = 2.00005683875 -0.000291150536533
absolute error = 0.01172
relative error = 0.5862 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.981237064547 -0.000591384651235
x2[1] (closed_form) = 0.993186450667 0.00272102269431
absolute error = 0.0124
relative error = 1.249 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=21889.0MB, alloc=40.3MB, time=265.62
memory used=21933.0MB, alloc=40.3MB, time=266.46
t[1] = 1.804 1.381
h = 0.0001 0.004
x1[1] (numeric) = 2.00180921104 -0.0119589554865
x1[1] (closed_form) = 2.0000559091 -0.000291028568206
absolute error = 0.0118
relative error = 0.5899 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.981122307252 -0.000698024193671
x2[1] (closed_form) = 0.993156108632 0.00268551786238
absolute error = 0.0125
relative error = 1.259 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=21977.0MB, alloc=40.3MB, time=267.19
t[1] = 1.8041 1.385
h = 0.003 0.006
x1[1] (numeric) = 2.0018650385 -0.0120383096287
x1[1] (closed_form) = 2.00005473907 -0.000291220752262
absolute error = 0.01189
relative error = 0.5943 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.981007722943 -0.000805452640302
x2[1] (closed_form) = 0.99313288587 0.00263110912743
absolute error = 0.0126
relative error = 1.269 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=22020.8MB, alloc=40.3MB, time=267.74
memory used=22065.0MB, alloc=40.3MB, time=268.79
t[1] = 1.8071 1.391
h = 0.0001 0.005
x1[1] (numeric) = 2.00189399697 -0.0121979357585
x1[1] (closed_form) = 2.00005283204 -0.00029067062156
absolute error = 0.01205
relative error = 0.6024 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.980892758191 -0.000914683840015
x2[1] (closed_form) = 0.993059336161 0.0025641234956
absolute error = 0.01265
relative error = 1.274 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=22109.0MB, alloc=40.3MB, time=269.58
t[1] = 1.8072 1.396
h = 0.0001 0.003
x1[1] (numeric) = 2.00196463524 -0.0122953263945
x1[1] (closed_form) = 2.00005137289 -0.000290902055605
absolute error = 0.01216
relative error = 0.6078 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.980777572739 -0.00102598597756
x2[1] (closed_form) = 0.993031920001 0.00249496940212
absolute error = 0.01275
relative error = 1.284 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=22153.3MB, alloc=40.3MB, time=270.14
memory used=22197.8MB, alloc=40.3MB, time=270.72
t[1] = 1.8073 1.399
h = 0.001 0.001
x1[1] (numeric) = 2.00200636107 -0.0123546784311
x1[1] (closed_form) = 2.00005049491 -0.000291025760958
absolute error = 0.01222
relative error = 0.611 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.980662897263 -0.00113827913198
x2[1] (closed_form) = 0.993015240127 0.00245354376039
absolute error = 0.01286
relative error = 1.295 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=22241.9MB, alloc=40.3MB, time=271.27
t[1] = 1.8083 1.4
h = 0.003 0.006
x1[1] (numeric) = 2.00200166916 -0.0123890491316
x1[1] (closed_form) = 2.00005015368 -0.000290785179722
absolute error = 0.01225
relative error = 0.6127 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.980548295495 -0.0012508698326
x2[1] (closed_form) = 0.992996182812 0.00244457360396
absolute error = 0.01298
relative error = 1.308 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=22285.9MB, alloc=40.3MB, time=271.83
t[1] = 1.8113 1.406
h = 0.0001 0.005
x1[1] (numeric) = 2.0020337734 -0.012551231035
x1[1] (closed_form) = 2.00004826307 -0.00029020893181
absolute error = 0.01242
relative error = 0.621 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.980433049928 -0.00136486479782
x2[1] (closed_form) = 0.99292408032 0.00237484178355
absolute error = 0.01304
relative error = 1.313 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=22330.0MB, alloc=40.3MB, time=272.38
memory used=22374.3MB, alloc=40.3MB, time=272.94
t[1] = 1.8114 1.411
h = 0.0001 0.003
x1[1] (numeric) = 2.00210733469 -0.0126493227616
x1[1] (closed_form) = 2.00004680674 -0.00029041757532
absolute error = 0.01253
relative error = 0.6265 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.98031762327 -0.00148097361696
x2[1] (closed_form) = 0.992898538389 0.00230431789267
absolute error = 0.01314
relative error = 1.323 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=22418.5MB, alloc=40.3MB, time=273.51
t[1] = 1.8115 1.414
h = 0.001 0.001
x1[1] (numeric) = 2.00215082023 -0.0127091263225
x1[1] (closed_form) = 2.00004593069 -0.000290527634244
absolute error = 0.0126
relative error = 0.6298 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.980202736891 -0.00159808101552
x2[1] (closed_form) = 0.992882979314 0.00226206393103
absolute error = 0.01325
relative error = 1.335 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=22463.0MB, alloc=40.3MB, time=274.09
memory used=22507.2MB, alloc=40.3MB, time=274.65
t[1] = 1.8125 1.415
h = 0.001 0.003
x1[1] (numeric) = 2.00214660007 -0.0127442296806
x1[1] (closed_form) = 2.00004559452 -0.000290282991479
absolute error = 0.01263
relative error = 0.6315 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.980087931843 -0.00171548990491
x2[1] (closed_form) = 0.992864043734 0.00225244779976
absolute error = 0.01338
relative error = 1.347 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=22551.3MB, alloc=40.3MB, time=275.22
t[1] = 1.8135 1.418
h = 0.0001 0.004
x1[1] (numeric) = 2.00217409171 -0.0128195407252
x1[1] (closed_form) = 2.00004467877 -0.000290128195252
absolute error = 0.01271
relative error = 0.6354 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.979973033806 -0.00183326843364
x2[1] (closed_form) = 0.992835886018 0.00221409147988
absolute error = 0.01348
relative error = 1.358 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=22595.4MB, alloc=40.3MB, time=275.78
t[1] = 1.8136 1.422
h = 0.003 0.006
x1[1] (numeric) = 2.00223575715 -0.0129009276631
x1[1] (closed_form) = 2.00004351355 -0.000290275559809
absolute error = 0.0128
relative error = 0.64 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.979858355671 -0.00195186009465
x2[1] (closed_form) = 0.992816383897 0.00215706369414
absolute error = 0.01359
relative error = 1.369 %
Correct digits = 2
memory used=22639.7MB, alloc=40.3MB, time=276.33
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=22683.8MB, alloc=40.3MB, time=276.89
t[1] = 1.8166 1.428
h = 0.0001 0.005
x1[1] (numeric) = 2.00227213011 -0.0130677395418
x1[1] (closed_form) = 2.000041646 -0.000289661126422
absolute error = 0.01297
relative error = 0.6486 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.979743371869 -0.00207234887787
x2[1] (closed_form) = 0.99274669464 0.00208347115356
absolute error = 0.01365
relative error = 1.375 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=22727.9MB, alloc=40.3MB, time=277.45
t[1] = 1.8167 1.433
h = 0.0001 0.003
x1[1] (numeric) = 2.0023500201 -0.0131675607496
x1[1] (closed_form) = 2.00004019316 -0.00028983674965
absolute error = 0.01308
relative error = 0.6541 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.979628262294 -0.00219500613037
x2[1] (closed_form) = 0.992724041999 0.00201114589217
absolute error = 0.01375
relative error = 1.386 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=22771.9MB, alloc=40.3MB, time=278.00
memory used=22816.5MB, alloc=40.3MB, time=278.58
t[1] = 1.8168 1.436
h = 0.001 0.001
x1[1] (numeric) = 2.0023961019 -0.0132284437659
x1[1] (closed_form) = 2.00003931953 -0.000289927030519
absolute error = 0.01315
relative error = 0.6576 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.979513733789 -0.00231867011194
x2[1] (closed_form) = 0.992710211722 0.00196780128052
absolute error = 0.01388
relative error = 1.398 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=22860.7MB, alloc=40.3MB, time=279.15
t[1] = 1.8178 1.437
h = 0.001 0.003
x1[1] (numeric) = 2.00239244465 -0.0132647664195
x1[1] (closed_form) = 2.00003899058 -0.000289676383812
absolute error = 0.01319
relative error = 0.6593 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.979399297009 -0.00244264034889
x2[1] (closed_form) = 0.992691523918 0.00195725340661
absolute error = 0.014
relative error = 1.41 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=22904.9MB, alloc=40.3MB, time=279.71
memory used=22949.1MB, alloc=40.3MB, time=280.28
t[1] = 1.8188 1.44
h = 0.0001 0.004
x1[1] (numeric) = 2.00242232888 -0.0133419525567
x1[1] (closed_form) = 2.00003808327 -0.000289502404621
absolute error = 0.01327
relative error = 0.6634 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.97928477546 -0.0025669915044
x2[1] (closed_form) = 0.992664802829 0.00191728386
absolute error = 0.01411
relative error = 1.422 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=22993.2MB, alloc=40.3MB, time=280.83
t[1] = 1.8189 1.444
h = 0.003 0.006
x1[1] (numeric) = 2.00248760876 -0.0134247201201
x1[1] (closed_form) = 2.00003692127 -0.00028962345749
absolute error = 0.01336
relative error = 0.6681 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.979170501834 -0.00269216866791
x2[1] (closed_form) = 0.99264764843 0.00185885044524
absolute error = 0.01422
relative error = 1.433 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=23037.4MB, alloc=40.3MB, time=281.38
t[1] = 1.8219 1.45
h = 0.0001 0.005
x1[1] (numeric) = 2.0025284809 -0.0135961629856
x1[1] (closed_form) = 2.00003507748 -0.000288971554225
absolute error = 0.01354
relative error = 0.6769 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.979055968729 -0.00281929600183
x2[1] (closed_form) = 0.992580567753 0.00178146674707
absolute error = 0.01429
relative error = 1.439 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=23081.7MB, alloc=40.3MB, time=281.94
memory used=23125.8MB, alloc=40.3MB, time=282.51
t[1] = 1.822 1.455
h = 0.0001 0.003
x1[1] (numeric) = 2.00261085388 -0.0136976408462
x1[1] (closed_form) = 2.00003362883 -0.000289114415883
absolute error = 0.01365
relative error = 0.6827 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.978941367915 -0.00294864613002
x2[1] (closed_form) = 0.9925609128 0.00170745100095
absolute error = 0.01439
relative error = 1.45 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=23170.1MB, alloc=40.3MB, time=283.08
t[1] = 1.8221 1.458
h = 0.001 0.001
x1[1] (numeric) = 2.00265962562 -0.0137595606524
x1[1] (closed_form) = 2.00003275806 -0.000289185081251
absolute error = 0.01372
relative error = 0.6862 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.9788273901 -0.00307901020068
x2[1] (closed_form) = 0.992548876751 0.00166308195967
absolute error = 0.01452
relative error = 1.463 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=23214.5MB, alloc=40.3MB, time=283.66
memory used=23258.7MB, alloc=40.3MB, time=284.22
t[1] = 1.8231 1.459
h = 0.001 0.003
x1[1] (numeric) = 2.002656578 -0.0137971178854
x1[1] (closed_form) = 2.00003243641 -0.000288928621579
absolute error = 0.01376
relative error = 0.688 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.97871351477 -0.00320968511325
x2[1] (closed_form) = 0.992530480588 0.00165160424526
absolute error = 0.01465
relative error = 1.476 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=23302.9MB, alloc=40.3MB, time=284.79
t[1] = 1.8241 1.462
h = 0.0001 0.004
x1[1] (numeric) = 2.00268896466 -0.0138761616224
x1[1] (closed_form) = 2.00003153792 -0.000288735750307
absolute error = 0.01384
relative error = 0.6922 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.978599563386 -0.00334075225202
x2[1] (closed_form) = 0.992505281937 0.00161006958136
absolute error = 0.01476
relative error = 1.487 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=23346.8MB, alloc=40.3MB, time=285.35
memory used=23390.9MB, alloc=40.3MB, time=285.91
t[1] = 1.8242 1.466
h = 0.003 0.006
x1[1] (numeric) = 2.00275798592 -0.013960247212
x1[1] (closed_form) = 2.00003037969 -0.000288830707259
absolute error = 0.01394
relative error = 0.697 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.97848588893 -0.00347265779597
x2[1] (closed_form) = 0.99249056075 0.00155032119822
absolute error = 0.01488
relative error = 1.499 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=23434.9MB, alloc=40.3MB, time=286.46
t[1] = 1.8272 1.472
h = 0.0001 0.005
x1[1] (numeric) = 2.0028035934 -0.0141363156769
x1[1] (closed_form) = 2.00002856036 -0.000288142061256
absolute error = 0.01412
relative error = 0.7062 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.978372003677 -0.00360656648678
x2[1] (closed_form) = 0.992426282787 0.00146922525628
absolute error = 0.01494
relative error = 1.506 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=23478.9MB, alloc=40.3MB, time=287.02
t[1] = 1.8273 1.477
h = 0.0001 0.003
x1[1] (numeric) = 2.00289060545 -0.0142393712632
x1[1] (closed_form) = 2.00002711659 -0.000288252434013
absolute error = 0.01424
relative error = 0.7121 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.978258111576 -0.00374275192826
x2[1] (closed_form) = 0.992409730036 0.00139363579609
absolute error = 0.01505
relative error = 1.517 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=23523.0MB, alloc=40.3MB, time=287.57
memory used=23567.5MB, alloc=40.3MB, time=288.15
t[1] = 1.8274 1.48
h = 0.001 0.001
x1[1] (numeric) = 2.00294216194 -0.0143022815289
x1[1] (closed_form) = 2.00002624908 -0.000288303654712
absolute error = 0.01431
relative error = 0.7157 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.978144885546 -0.00387995753859
x2[1] (closed_form) = 0.99239955133 0.00134831209084
absolute error = 0.01518
relative error = 1.53 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=23611.7MB, alloc=40.3MB, time=288.78
t[1] = 1.8284 1.481
h = 0.0001 0.004
x1[1] (numeric) = 2.00293977223 -0.0143410876996
x1[1] (closed_form) = 2.00002593482 -0.000288041573998
absolute error = 0.01435
relative error = 0.7176 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.978031773129 -0.00401747838575
x2[1] (closed_form) = 0.992381491012 0.00133590840602
absolute error = 0.01532
relative error = 1.543 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=23655.6MB, alloc=40.3MB, time=289.33
memory used=23699.5MB, alloc=40.3MB, time=289.89
t[1] = 1.8285 1.485
h = 0.003 0.006
x1[1] (numeric) = 2.0030116519 -0.0144260573278
x1[1] (closed_form) = 2.00002477997 -0.000288114195813
absolute error = 0.01445
relative error = 0.7225 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.977918914923 -0.00415552724329
x2[1] (closed_form) = 0.992368944377 0.00127513462041
absolute error = 0.01544
relative error = 1.556 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=23743.3MB, alloc=40.3MB, time=290.44
t[1] = 1.8315 1.491
h = 0.0001 0.005
x1[1] (numeric) = 2.00306096572 -0.0146054729726
x1[1] (closed_form) = 2.0000229818 -0.000287394211506
absolute error = 0.01464
relative error = 0.7318 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.977805894895 -0.00429562105163
x2[1] (closed_form) = 0.992307275881 0.00119095016382
absolute error = 0.0155
relative error = 1.562 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=23787.3MB, alloc=40.3MB, time=291.00
memory used=23831.5MB, alloc=40.3MB, time=291.55
t[1] = 1.8316 1.496
h = 0.0001 0.003
x1[1] (numeric) = 2.00315152095 -0.014709580508
x1[1] (closed_form) = 2.00002154239 -0.0002874767785
absolute error = 0.01476
relative error = 0.7379 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.977692927908 -0.00443803301211
x2[1] (closed_form) = 0.992293490653 0.0011141425871
absolute error = 0.01562
relative error = 1.574 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=23875.7MB, alloc=40.3MB, time=292.24
t[1] = 1.8317 1.499
h = 0.001 0.001
x1[1] (numeric) = 2.00320520991 -0.0147731565073
x1[1] (closed_form) = 2.0000206778 -0.00028751135937
absolute error = 0.01483
relative error = 0.7416 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.97758066593 -0.00458146606027
x2[1] (closed_form) = 0.992284969504 0.00106807876292
absolute error = 0.01575
relative error = 1.587 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=23919.8MB, alloc=40.3MB, time=292.86
t[1] = 1.8327 1.5
h = 0.001 0.003
x1[1] (numeric) = 2.00320335726 -0.0148128887024
x1[1] (closed_form) = 2.0000203699 -0.000287244505237
absolute error = 0.01487
relative error = 0.7435 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.977468527916 -0.0047252170602
x2[1] (closed_form) = 0.992267244792 0.0010548873822
absolute error = 0.01589
relative error = 1.601 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=23963.7MB, alloc=40.3MB, time=293.41
memory used=24007.7MB, alloc=40.3MB, time=293.97
t[1] = 1.8337 1.503
h = 0.0001 0.004
x1[1] (numeric) = 2.00324040447 -0.014895080115
x1[1] (closed_form) = 2.00001948858 -0.000287017161526
absolute error = 0.01496
relative error = 0.7479 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.977356332446 -0.00486938068421
x2[1] (closed_form) = 0.992245119876 0.00101060356457
absolute error = 0.01601
relative error = 1.613 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=24051.6MB, alloc=40.3MB, time=294.53
t[1] = 1.8338 1.507
h = 0.003 0.006
x1[1] (numeric) = 2.00331628292 -0.0149812411655
x1[1] (closed_form) = 2.00001833852 -0.000287064111646
absolute error = 0.01506
relative error = 0.753 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.977244471762 -0.00501440198138
x2[1] (closed_form) = 0.992235155606 0.000948696794156
absolute error = 0.01613
relative error = 1.626 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=24095.6MB, alloc=40.3MB, time=295.08
memory used=24139.6MB, alloc=40.3MB, time=295.64
t[1] = 1.8368 1.513
h = 0.0001 0.005
x1[1] (numeric) = 2.00337081089 -0.0151652721477
x1[1] (closed_form) = 2.00001656604 -0.000286308759022
absolute error = 0.01525
relative error = 0.7626 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.977132502465 -0.00516152075823
x2[1] (closed_form) = 0.992176645167 0.000860974193678
absolute error = 0.0162
relative error = 1.633 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=24183.5MB, alloc=40.3MB, time=296.20
t[1] = 1.8369 1.518
h = 0.0001 0.003
x1[1] (numeric) = 2.00346632213 -0.0152707978766
x1[1] (closed_form) = 2.00001513279 -0.000286359372678
absolute error = 0.01538
relative error = 0.7688 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.977020652107 -0.0053110106179
x2[1] (closed_form) = 0.992166143702 0.000782826563785
absolute error = 0.01633
relative error = 1.645 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=24227.4MB, alloc=40.3MB, time=296.76
memory used=24271.8MB, alloc=40.3MB, time=297.34
t[1] = 1.837 1.521
h = 0.001 0.001
x1[1] (numeric) = 2.00352298831 -0.0153352705744
x1[1] (closed_form) = 2.00001427221 -0.000286374843436
absolute error = 0.01545
relative error = 0.7726 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.976909551782 -0.00546152585246
x2[1] (closed_form) = 0.992159589638 0.000735947766658
absolute error = 0.01646
relative error = 1.659 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=24316.0MB, alloc=40.3MB, time=297.88
t[1] = 1.838 1.522
h = 0.001 0.003
x1[1] (numeric) = 2.00352189143 -0.0153762808622
x1[1] (closed_form) = 2.00001397185 -0.000286102726635
absolute error = 0.01549
relative error = 0.7746 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.976798587192 -0.00561236303912
x2[1] (closed_form) = 0.99214228353 0.000721843500981
absolute error = 0.0166
relative error = 1.673 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=24359.8MB, alloc=40.3MB, time=298.41
t[1] = 1.839 1.525
h = 0.0001 0.004
x1[1] (numeric) = 2.0035617799 -0.0154602664533
x1[1] (closed_form) = 2.00001310038 -0.00028585735434
absolute error = 0.01558
relative error = 0.7792 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.976687575291 -0.00576362414008
x2[1] (closed_form) = 0.992121917847 0.000676156709772
absolute error = 0.01672
relative error = 1.686 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=24403.9MB, alloc=40.3MB, time=298.95
memory used=24448.1MB, alloc=40.3MB, time=299.50
t[1] = 1.8391 1.529
h = 0.003 0.006
x1[1] (numeric) = 2.00364178774 -0.0155475408294
x1[1] (closed_form) = 2.00001195565 -0.000285878879533
absolute error = 0.01569
relative error = 0.7844 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.976576929919 -0.0059157537364
x2[1] (closed_form) = 0.992114611573 0.000613220669045
absolute error = 0.01685
relative error = 1.699 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=24491.9MB, alloc=40.3MB, time=300.06
t[1] = 1.8421 1.535
h = 0.0001 0.005
x1[1] (numeric) = 2.00370178249 -0.0157361608704
x1[1] (closed_form) = 2.0000102095 -0.000285088916265
absolute error = 0.01589
relative error = 0.7943 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.976466231786 -0.00607003308462
x2[1] (closed_form) = 0.992059447366 0.00052206569798
absolute error = 0.01693
relative error = 1.706 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=24535.8MB, alloc=40.3MB, time=300.64
memory used=24579.9MB, alloc=40.3MB, time=301.18
t[1] = 1.8422 1.54
h = 0.0001 0.003
x1[1] (numeric) = 2.00380241014 -0.0158430066371
x1[1] (closed_form) = 2.00000878305 -0.000285107887719
absolute error = 0.01601
relative error = 0.8007 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.976355721436 -0.00622673585245
x2[1] (closed_form) = 0.992052321355 0.000442710874789
absolute error = 0.01705
relative error = 1.719 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=24624.1MB, alloc=40.3MB, time=301.74
t[1] = 1.8423 1.543
h = 0.001 0.001
x1[1] (numeric) = 2.00386215111 -0.0159083181415
x1[1] (closed_form) = 2.0000079269 -0.000285104441983
absolute error = 0.01609
relative error = 0.8046 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.976246007284 -0.0063844671512
x2[1] (closed_form) = 0.992047789844 0.000395096570177
absolute error = 0.01719
relative error = 1.733 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=24668.4MB, alloc=40.3MB, time=302.30
t[1] = 1.8433 1.544
h = 0.001 0.003
x1[1] (numeric) = 2.00386186299 -0.0159506177169
x1[1] (closed_form) = 2.00000763415 -0.000284827256609
absolute error = 0.01613
relative error = 0.8066 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.976136441017 -0.00654252417224
x2[1] (closed_form) = 0.992030947012 0.000380089096567
absolute error = 0.01734
relative error = 1.748 %
Correct digits = 2
memory used=24712.6MB, alloc=40.3MB, time=302.85
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=24756.7MB, alloc=40.3MB, time=303.41
t[1] = 1.8443 1.547
h = 0.0001 0.004
x1[1] (numeric) = 2.00390471095 -0.016036365301
x1[1] (closed_form) = 2.00000677286 -0.000284564170808
absolute error = 0.01623
relative error = 0.8113 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.976026838121 -0.00670101637831
x2[1] (closed_form) = 0.992012420132 0.00033306380485
absolute error = 0.01746
relative error = 1.761 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=24800.5MB, alloc=40.3MB, time=303.96
t[1] = 1.8444 1.551
h = 0.003 0.006
x1[1] (numeric) = 2.00398897982 -0.0161246693845
x1[1] (closed_form) = 2.00000563399 -0.000284560528191
absolute error = 0.01633
relative error = 0.8167 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.975917634517 -0.00686038728273
x2[1] (closed_form) = 0.992007843602 0.000269206568911
absolute error = 0.0176
relative error = 1.774 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=24844.5MB, alloc=40.3MB, time=304.51
memory used=24888.6MB, alloc=40.3MB, time=305.05
t[1] = 1.8474 1.557
h = 0.0001 0.005
x1[1] (numeric) = 2.00405469942 -0.01631784457
x1[1] (closed_form) = 2.00000391477 -0.000283736721592
absolute error = 0.01654
relative error = 0.8269 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.975808436701 -0.00702195987931
x2[1] (closed_form) = 0.991956210914 0.000174734384501
absolute error = 0.01768
relative error = 1.782 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=24932.5MB, alloc=40.3MB, time=305.60
t[1] = 1.8475 1.562
h = 0.0001 0.003
x1[1] (numeric) = 2.00416060509 -0.0164259053785
x1[1] (closed_form) = 2.0000024958 -0.000283724374817
absolute error = 0.01667
relative error = 0.8335 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.975699498509 -0.00718600754753
x2[1] (closed_form) = 0.991952547023 9.43105832158e-05
absolute error = 0.01781
relative error = 1.795 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=24976.5MB, alloc=40.3MB, time=306.16
memory used=25021.0MB, alloc=40.3MB, time=306.73
t[1] = 1.8476 1.565
h = 0.001 0.001
x1[1] (numeric) = 2.0042235192 -0.0164919936812
x1[1] (closed_form) = 2.00000164445 -0.000283702213797
absolute error = 0.01675
relative error = 0.8375 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.975591403817 -0.00735108571582
x2[1] (closed_form) = 0.991950090534 4.60434675932e-05
absolute error = 0.01795
relative error = 1.81 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=25065.1MB, alloc=40.3MB, time=307.28
t[1] = 1.8486 1.566
h = 0.001 0.003
x1[1] (numeric) = 2.00422409443 -0.0165355925453
x1[1] (closed_form) = 2.00000135939 -0.000283420154483
absolute error = 0.01679
relative error = 0.8396 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.97548346954 -0.0075164931313
x2[1] (closed_form) = 0.99193375565 3.01445422869e-05
absolute error = 0.0181
relative error = 1.825 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=25109.0MB, alloc=40.3MB, time=307.84
t[1] = 1.8496 1.569
h = 0.0001 0.004
x1[1] (numeric) = 2.00427002211 -0.016623065881
x1[1] (closed_form) = 2.00000050861 -0.000283139675953
absolute error = 0.01689
relative error = 0.8444 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.975375509868 -0.00768234696841
x2[1] (closed_form) = 0.991917145042 -1.81506186270e-05
absolute error = 0.01823
relative error = 1.838 %
Correct digits = 2
memory used=25153.2MB, alloc=40.3MB, time=308.39
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=25197.2MB, alloc=40.3MB, time=308.94
t[1] = 1.8497 1.573
h = 0.003 0.006
x1[1] (numeric) = 2.00435868454 -0.0167123103735
x1[1] (closed_form) = 1.99999937611 -0.000283111132752
absolute error = 0.017
relative error = 0.8499 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.975267983274 -0.00784908904678
x2[1] (closed_form) = 0.991915365888 -8.28167443535e-05
absolute error = 0.01837
relative error = 1.852 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=25241.0MB, alloc=40.3MB, time=309.48
t[1] = 1.8527 1.579
h = 0.0001 0.005
x1[1] (numeric) = 2.00443039242 -0.0169099988215
x1[1] (closed_form) = 1.99999768443 -0.000282254259283
absolute error = 0.01721
relative error = 0.8604 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.975160523771 -0.00801808434719
x2[1] (closed_form) = 0.99186744667 -0.000180481638371
absolute error = 0.01845
relative error = 1.861 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=25285.1MB, alloc=40.3MB, time=310.02
memory used=25329.2MB, alloc=40.3MB, time=310.58
t[1] = 1.8528 1.584
h = 0.0001 0.003
x1[1] (numeric) = 2.00454173876 -0.0170191626412
x1[1] (closed_form) = 1.99999627356 -0.000282210930788
absolute error = 0.01734
relative error = 0.8672 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.975053398777 -0.0081896055922
x2[1] (closed_form) = 0.991867326254 -0.00026183101858
absolute error = 0.01859
relative error = 1.874 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=25373.5MB, alloc=40.3MB, time=311.14
t[1] = 1.8529 1.587
h = 0.001 0.001
x1[1] (numeric) = 2.00460792503 -0.017085961499
x1[1] (closed_form) = 1.99999542741 -0.000282170263107
absolute error = 0.01743
relative error = 0.8713 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.97494716572 -0.00836215806255
x2[1] (closed_form) = 0.991866994085 -0.000310665119683
absolute error = 0.01874
relative error = 1.889 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=25417.7MB, alloc=40.3MB, time=311.72
memory used=25461.7MB, alloc=40.3MB, time=312.28
t[1] = 1.8539 1.588
h = 0.0001 0.004
x1[1] (numeric) = 2.00460941983 -0.0171308683859
x1[1] (closed_form) = 1.99999515009 -0.000281883524914
absolute error = 0.01747
relative error = 0.8735 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.97484110599 -0.00853504304413
x2[1] (closed_form) = 0.991851211729 -0.000327441641058
absolute error = 0.01889
relative error = 1.904 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=25505.6MB, alloc=40.3MB, time=312.83
t[1] = 1.854 1.592
h = 0.003 0.006
x1[1] (numeric) = 2.00470141592 -0.0172206980751
x1[1] (closed_form) = 1.99999402319 -0.000281833685481
absolute error = 0.01758
relative error = 0.879 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.974735407391 -0.00870847551575
x2[1] (closed_form) = 0.991851899053 -0.000392676638069
absolute error = 0.01903
relative error = 1.919 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=25549.5MB, alloc=40.3MB, time=313.38
memory used=25593.6MB, alloc=40.3MB, time=313.92
t[1] = 1.857 1.598
h = 0.0001 0.005
x1[1] (numeric) = 2.00477775989 -0.017421615659
x1[1] (closed_form) = 1.99999235528 -0.000280948640419
absolute error = 0.0178
relative error = 0.8898 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.974629835986 -0.00888420024471
x2[1] (closed_form) = 0.991807354929 -0.000492935803764
absolute error = 0.01912
relative error = 1.928 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=25637.6MB, alloc=40.3MB, time=314.46
t[1] = 1.8571 1.603
h = 0.0001 0.003
x1[1] (numeric) = 2.00489323302 -0.0175314560851
x1[1] (closed_form) = 1.99999095154 -0.000280878815837
absolute error = 0.01793
relative error = 0.8967 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.97452467118 -0.0090624879283
x2[1] (closed_form) = 0.99181035411 -0.000574919816028
absolute error = 0.01926
relative error = 1.942 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=25682.0MB, alloc=40.3MB, time=315.01
t[1] = 1.8572 1.606
h = 0.001 0.001
x1[1] (numeric) = 2.00496190761 -0.0175986984872
x1[1] (closed_form) = 1.99999010994 -0.000280822322914
absolute error = 0.01802
relative error = 0.9009 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.974420441414 -0.00924180221005
x2[1] (closed_form) = 0.991811892722 -0.000624144883444
absolute error = 0.01941
relative error = 1.957 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=25726.1MB, alloc=40.3MB, time=315.56
memory used=25770.1MB, alloc=40.3MB, time=316.10
t[1] = 1.8582 1.607
h = 0.001 0.003
x1[1] (numeric) = 2.00496413694 -0.0176445680081
x1[1] (closed_form) = 1.99998983929 -0.000280531620509
absolute error = 0.01806
relative error = 0.9031 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.974316396792 -0.00942145049997
x2[1] (closed_form) = 0.99179663171 -0.000641656799363
absolute error = 0.01956
relative error = 1.972 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=25814.1MB, alloc=40.3MB, time=316.64
t[1] = 1.8592 1.61
h = 0.0001 0.004
x1[1] (numeric) = 2.00501574867 -0.0177349061056
x1[1] (closed_form) = 1.99998900873 -0.000280219516346
absolute error = 0.01816
relative error = 0.9082 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.974212350233 -0.0096015650563
x2[1] (closed_form) = 0.99178379798 -0.00069209331778
absolute error = 0.0197
relative error = 1.986 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=25858.1MB, alloc=40.3MB, time=317.18
memory used=25901.9MB, alloc=40.3MB, time=317.72
t[1] = 1.8593 1.614
h = 0.003 0.006
x1[1] (numeric) = 2.00511240681 -0.0178254958448
x1[1] (closed_form) = 1.99998788916 -0.000280145293716
absolute error = 0.01828
relative error = 0.9139 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.97410880339 -0.00978258081477
x2[1] (closed_form) = 0.991787395355 -0.000757916786108
absolute error = 0.01985
relative error = 2.001 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=25945.9MB, alloc=40.3MB, time=318.26
t[1] = 1.8623 1.62
h = 0.0001 0.005
x1[1] (numeric) = 2.00519527256 -0.0180308428469
x1[1] (closed_form) = 1.99998624983 -0.000279228642786
absolute error = 0.0185
relative error = 0.925 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.974005449986 -0.00996593926182
x2[1] (closed_form) = 0.991746891109 -0.000861110272702
absolute error = 0.01994
relative error = 2.011 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=25990.1MB, alloc=40.3MB, time=318.79
memory used=26034.1MB, alloc=40.3MB, time=319.32
t[1] = 1.8624 1.625
h = 0.0001 0.003
x1[1] (numeric) = 2.00531651642 -0.0181415600526
x1[1] (closed_form) = 1.99998485538 -0.000279128487612
absolute error = 0.01864
relative error = 0.9321 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.973902583501 -0.0101519097301
x2[1] (closed_form) = 0.991753568207 -0.000943739074316
absolute error = 0.02009
relative error = 2.025 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=26078.5MB, alloc=40.3MB, time=319.87
t[1] = 1.8625 1.628
h = 0.001 0.001
x1[1] (numeric) = 2.00538866407 -0.0182093791172
x1[1] (closed_form) = 1.99998401966 -0.000279053890947
absolute error = 0.01873
relative error = 0.9364 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.97380070239 -0.0103389051174
x2[1] (closed_form) = 0.991757312745 -0.000993362992887
absolute error = 0.02024
relative error = 2.041 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=26122.8MB, alloc=40.3MB, time=320.42
t[1] = 1.8635 1.629
h = 0.001 0.003
x1[1] (numeric) = 2.00539192671 -0.0182565744519
x1[1] (closed_form) = 1.99998375686 -0.000278758872782
absolute error = 0.01877
relative error = 0.9387 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.973699019994 -0.0105262372546
x2[1] (closed_form) = 0.991742686418 -0.00101172055849
absolute error = 0.0204
relative error = 2.057 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=26166.7MB, alloc=40.3MB, time=320.95
memory used=26210.8MB, alloc=40.3MB, time=321.48
t[1] = 1.8645 1.632
h = 0.0001 0.004
x1[1] (numeric) = 2.00544698728 -0.0183485162093
x1[1] (closed_form) = 1.99998293773 -0.00027843031945
absolute error = 0.01888
relative error = 0.9439 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.973597348474 -0.010714046685
x2[1] (closed_form) = 0.991731976167 -0.00106320733847
absolute error = 0.02054
relative error = 2.071 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=26254.8MB, alloc=40.3MB, time=322.01
t[1] = 1.8646 1.636
h = 0.003 0.006
x1[1] (numeric) = 2.00554844174 -0.0184397589532
x1[1] (closed_form) = 1.99998182597 -0.000278332008528
absolute error = 0.019
relative error = 0.9498 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.973496213277 -0.0109027647531
x2[1] (closed_form) = 0.991738538168 -0.00112949575125
absolute error = 0.0207
relative error = 2.087 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=26298.7MB, alloc=40.3MB, time=322.54
memory used=26342.7MB, alloc=40.3MB, time=323.07
t[1] = 1.8676 1.642
h = 0.0001 0.005
x1[1] (numeric) = 2.00563810778 -0.0186494678215
x1[1] (closed_form) = 1.99998021575 -0.000277384551891
absolute error = 0.01922
relative error = 0.9612 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.973395340658 -0.0110938753046
x2[1] (closed_form) = 0.99170224362 -0.00123547276297
absolute error = 0.02079
relative error = 2.097 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=26386.7MB, alloc=40.3MB, time=323.61
t[1] = 1.8677 1.647
h = 0.0001 0.003
x1[1] (numeric) = 2.00576528691 -0.0187609277876
x1[1] (closed_form) = 1.9999788312 -0.000277254436946
absolute error = 0.01937
relative error = 0.9684 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.97329503846 -0.0112876458941
x2[1] (closed_form) = 0.991712663206 -0.00131858927379
absolute error = 0.02094
relative error = 2.112 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=26430.8MB, alloc=40.3MB, time=324.15
t[1] = 1.8678 1.65
h = 0.001 0.001
x1[1] (numeric) = 2.00584100796 -0.0188292440274
x1[1] (closed_form) = 1.99997800174 -0.000277161965421
absolute error = 0.01946
relative error = 0.9728 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.973195773085 -0.0114824383186
x2[1] (closed_form) = 0.991718652935 -0.00136851795126
absolute error = 0.0211
relative error = 2.128 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=26475.2MB, alloc=40.3MB, time=324.69
memory used=26519.1MB, alloc=40.3MB, time=325.23
t[1] = 1.8688 1.651
h = 0.001 0.003
x1[1] (numeric) = 2.00584536484 -0.0188777696893
x1[1] (closed_form) = 1.99997774685 -0.000276862827274
absolute error = 0.0195
relative error = 0.9752 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.973096720385 -0.0116775699294
x2[1] (closed_form) = 0.991704705056 -0.00138770123412
absolute error = 0.02126
relative error = 2.144 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=26563.3MB, alloc=40.3MB, time=325.77
t[1] = 1.8698 1.654
h = 0.0001 0.004
x1[1] (numeric) = 2.0059040016 -0.0189712612924
x1[1] (closed_form) = 1.99997693943 -0.000276518165567
absolute error = 0.01961
relative error = 0.9806 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.972997691967 -0.0118731897668
x2[1] (closed_form) = 0.991696185678 -0.00144015420998
absolute error = 0.02141
relative error = 2.159 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=26607.3MB, alloc=40.3MB, time=326.30
memory used=26651.2MB, alloc=40.3MB, time=326.84
t[1] = 1.8699 1.658
h = 0.003 0.006
x1[1] (numeric) = 2.00601038691 -0.0190630437147
x1[1] (closed_form) = 1.99997583596 -0.000276396070415
absolute error = 0.01973
relative error = 0.9866 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.972899237524 -0.0120697248557
x2[1] (closed_form) = 0.991705761912 -0.00150678042341
absolute error = 0.02157
relative error = 2.175 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=26695.2MB, alloc=40.3MB, time=327.38
t[1] = 1.8729 1.664
h = 0.0001 0.005
x1[1] (numeric) = 2.00610713665 -0.0192770376046
x1[1] (closed_form) = 1.99997425538 -0.000275418615488
absolute error = 0.01997
relative error = 0.9984 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.972801117745 -0.0122687014954
x2[1] (closed_form) = 0.991673841812 -0.00161538115966
absolute error = 0.02167
relative error = 2.185 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=26739.1MB, alloc=40.3MB, time=327.91
memory used=26783.2MB, alloc=40.3MB, time=328.45
t[1] = 1.873 1.669
h = 0.0001 0.003
x1[1] (numeric) = 2.00624041588 -0.0193890985417
x1[1] (closed_form) = 1.99997288133 -0.000275258922945
absolute error = 0.02012
relative error = 1.006 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.972703655116 -0.0124703850316
x2[1] (closed_form) = 0.991688062094 -0.00169882391464
absolute error = 0.02183
relative error = 2.201 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=26827.4MB, alloc=40.3MB, time=329.00
t[1] = 1.8731 1.672
h = 0.001 0.001
x1[1] (numeric) = 2.00631981092 -0.0194578277856
x1[1] (closed_form) = 1.99997205847 -0.000275148812134
absolute error = 0.02021
relative error = 1.01 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.972607281863 -0.0126730858519
x2[1] (closed_form) = 0.991696332473 -0.001748960606
absolute error = 0.02199
relative error = 2.218 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=26871.8MB, alloc=40.3MB, time=329.54
t[1] = 1.8741 1.673
h = 0.001 0.003
x1[1] (numeric) = 2.00632532459 -0.0195076867218
x1[1] (closed_form) = 1.99997181154 -0.000274845749816
absolute error = 0.02026
relative error = 1.013 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.97251113563 -0.0128761279725
x2[1] (closed_form) = 0.99168310634 -0.00176894753539
absolute error = 0.02216
relative error = 2.234 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=26916.0MB, alloc=40.3MB, time=330.08
memory used=26960.1MB, alloc=40.3MB, time=330.62
t[1] = 1.8751 1.676
h = 0.0001 0.004
x1[1] (numeric) = 2.00638766645 -0.0196026695559
x1[1] (closed_form) = 1.99997101613 -0.000274485325138
absolute error = 0.02037
relative error = 1.018 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.972415027694 -0.0130796691419
x2[1] (closed_form) = 0.99167684214 -0.00182227883431
absolute error = 0.02231
relative error = 2.25 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=27004.1MB, alloc=40.3MB, time=331.15
t[1] = 1.8752 1.68
h = 0.003 0.006
x1[1] (numeric) = 2.00649911731 -0.0196948718931
x1[1] (closed_form) = 1.99996992143 -0.000274339758729
absolute error = 0.02049
relative error = 1.024 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.972319532432 -0.0132841313081
x2[1] (closed_form) = 0.991689477038 -0.00188911227337
absolute error = 0.02247
relative error = 2.266 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=27048.0MB, alloc=40.3MB, time=331.68
memory used=27092.0MB, alloc=40.3MB, time=332.23
t[1] = 1.8782 1.686
h = 0.0001 0.005
x1[1] (numeric) = 2.00660323889 -0.0199130643126
x1[1] (closed_form) = 1.99996837097 -0.000273333119694
absolute error = 0.02073
relative error = 1.037 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.972224446914 -0.0134910832703
x2[1] (closed_form) = 0.991662090615 -0.00200016806673
absolute error = 0.02258
relative error = 2.277 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=27136.0MB, alloc=40.3MB, time=332.77
t[1] = 1.8783 1.691
h = 0.0001 0.003
x1[1] (numeric) = 2.00674278314 -0.0200255764704
x1[1] (closed_form) = 1.99996700801 -0.000273144242761
absolute error = 0.02088
relative error = 1.044 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.972130108549 -0.0137007877175
x2[1] (closed_form) = 0.991680163181 -0.00208377145618
absolute error = 0.02274
relative error = 2.293 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=27180.1MB, alloc=40.3MB, time=333.32
memory used=27224.5MB, alloc=40.3MB, time=333.89
t[1] = 1.8784 1.694
h = 0.001 0.001
x1[1] (numeric) = 2.00682595288 -0.0200946297462
x1[1] (closed_form) = 1.9999661921 -0.000273016734741
absolute error = 0.02098
relative error = 1.049 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.9720369132 -0.0139115033678
x2[1] (closed_form) = 0.991690745708 -0.00213401690716
absolute error = 0.02291
relative error = 2.31 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=27268.8MB, alloc=40.3MB, time=334.43
t[1] = 1.8794 1.695
h = 0.0001 0.004
x1[1] (numeric) = 2.00683268746 -0.0201458232564
x1[1] (closed_form) = 1.99996595317 -0.000272709943997
absolute error = 0.02103
relative error = 1.051 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.971943959608 -0.0141225620925
x2[1] (closed_form) = 0.991678284056 -0.00215478327394
absolute error = 0.02308
relative error = 2.327 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=27312.7MB, alloc=40.3MB, time=334.96
t[1] = 1.8795 1.699
h = 0.003 0.006
x1[1] (numeric) = 2.00694795871 -0.0202382046395
x1[1] (closed_form) = 1.99996486612 -0.00027254431956
absolute error = 0.02115
relative error = 1.058 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.971851488055 -0.0143341745776
x2[1] (closed_form) = 0.99169358352 -0.00222165099562
absolute error = 0.02325
relative error = 2.344 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=27356.6MB, alloc=40.3MB, time=335.48
memory used=27400.6MB, alloc=40.3MB, time=336.00
t[1] = 1.8825 1.705
h = 0.0001 0.005
x1[1] (numeric) = 2.00705773905 -0.0204593536967
x1[1] (closed_form) = 1.99996334163 -0.000271512850163
absolute error = 0.0214
relative error = 1.07 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.971759498286 -0.0145483113386
x2[1] (closed_form) = 0.991670248847 -0.00233462182881
absolute error = 0.02336
relative error = 2.355 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=27444.6MB, alloc=40.3MB, time=336.53
t[1] = 1.8826 1.71
h = 0.0001 0.003
x1[1] (numeric) = 2.00720200656 -0.0205720341725
x1[1] (closed_form) = 1.99996198833 -0.00027129903393
absolute error = 0.02155
relative error = 1.078 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.971668340665 -0.0147652310998
x2[1] (closed_form) = 0.991691672559 -0.00241818129773
absolute error = 0.02352
relative error = 2.372 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=27488.6MB, alloc=40.3MB, time=337.05
memory used=27533.1MB, alloc=40.3MB, time=337.60
t[1] = 1.8827 1.713
h = 0.001 0.001
x1[1] (numeric) = 2.00728802926 -0.0206412285687
x1[1] (closed_form) = 1.99996117849 -0.000271156661238
absolute error = 0.02165
relative error = 1.082 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.971578373027 -0.0149831507436
x2[1] (closed_form) = 0.991704267037 -0.00246841110503
absolute error = 0.0237
relative error = 2.39 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=27577.4MB, alloc=40.3MB, time=338.13
t[1] = 1.8837 1.714
h = 0.001 0.003
x1[1] (numeric) = 2.00729572487 -0.0206933958803
x1[1] (closed_form) = 1.99996094643 -0.000270846721967
absolute error = 0.0217
relative error = 1.085 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.971488660419 -0.0152014134146
x2[1] (closed_form) = 0.991692505992 -0.00248981758325
absolute error = 0.02387
relative error = 2.407 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=27621.4MB, alloc=40.3MB, time=338.66
memory used=27665.4MB, alloc=40.3MB, time=339.18
t[1] = 1.8847 1.717
h = 0.0001 0.004
x1[1] (numeric) = 2.00736485255 -0.0207907729109
x1[1] (closed_form) = 1.99996017391 -0.000270457749594
absolute error = 0.02182
relative error = 1.091 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.971399014875 -0.0154201937164
x2[1] (closed_form) = 0.991690605709 -0.00254450823046
absolute error = 0.02403
relative error = 2.423 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=27709.5MB, alloc=40.3MB, time=339.71
t[1] = 1.8848 1.721
h = 0.003 0.006
x1[1] (numeric) = 2.00748546207 -0.0208833325716
x1[1] (closed_form) = 1.99995909649 -0.000270269253725
absolute error = 0.02194
relative error = 1.097 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.971310057515 -0.0156398998192
x2[1] (closed_form) = 0.991709030403 -0.00261133138344
absolute error = 0.0242
relative error = 2.441 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=27753.3MB, alloc=40.3MB, time=340.23
t[1] = 1.8878 1.727
h = 0.0001 0.005
x1[1] (numeric) = 2.00760319736 -0.0211085064956
x1[1] (closed_form) = 1.999957603 -0.000269210126279
absolute error = 0.0222
relative error = 1.11 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.971221662345 -0.0158621765631
x2[1] (closed_form) = 0.991690507225 -0.00272641866447
absolute error = 0.02432
relative error = 2.452 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=27797.4MB, alloc=40.3MB, time=340.75
memory used=27841.6MB, alloc=40.3MB, time=341.28
t[1] = 1.8879 1.732
h = 0.0001 0.003
x1[1] (numeric) = 2.00775406448 -0.0212213360247
x1[1] (closed_form) = 1.99995626186 -0.000268967878931
absolute error = 0.02236
relative error = 1.118 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.971134195101 -0.0160872791657
x2[1] (closed_form) = 0.99171585867 -0.00280982003899
absolute error = 0.02449
relative error = 2.47 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=27885.8MB, alloc=40.3MB, time=341.82
t[1] = 1.888 1.735
h = 0.001 0.001
x1[1] (numeric) = 2.00784406607 -0.0212906747953
x1[1] (closed_form) = 1.99995545961 -0.000268808572161
absolute error = 0.02245
relative error = 1.123 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.971047973261 -0.0163133726524
x2[1] (closed_form) = 0.99173081161 -0.00285996750694
absolute error = 0.02467
relative error = 2.488 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=27930.1MB, alloc=40.3MB, time=342.35
memory used=27974.1MB, alloc=40.3MB, time=342.88
t[1] = 1.889 1.736
h = 0.001 0.003
x1[1] (numeric) = 2.00785311226 -0.0213441794843
x1[1] (closed_form) = 1.99995523561 -0.000268495267816
absolute error = 0.02251
relative error = 1.125 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.970962021849 -0.016539810273
x2[1] (closed_form) = 0.991719892369 -0.00288210221327
absolute error = 0.02485
relative error = 2.506 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=28018.2MB, alloc=40.3MB, time=343.40
t[1] = 1.89 1.739
h = 0.0001 0.004
x1[1] (numeric) = 2.00792633898 -0.0214428560219
x1[1] (closed_form) = 1.99995447588 -0.000268091540995
absolute error = 0.02263
relative error = 1.131 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.970876153234 -0.0167667759022
x2[1] (closed_form) = 0.991720411199 -0.0029373990896
absolute error = 0.02501
relative error = 2.522 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=28062.3MB, alloc=40.3MB, time=343.93
memory used=28106.2MB, alloc=40.3MB, time=344.45
t[1] = 1.8901 1.743
h = 0.003 0.006
x1[1] (numeric) = 2.00805242071 -0.0215354542464
x1[1] (closed_form) = 1.99995340854 -0.000267880510864
absolute error = 0.02276
relative error = 1.138 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.970791014344 -0.0169946703649
x2[1] (closed_form) = 0.991741989619 -0.00300403847632
absolute error = 0.02519
relative error = 2.54 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=28150.2MB, alloc=40.3MB, time=344.98
t[1] = 1.8931 1.749
h = 0.0001 0.005
x1[1] (numeric) = 2.00817841197 -0.021764535797
x1[1] (closed_form) = 1.99995194648 -0.000266794556478
absolute error = 0.02302
relative error = 1.151 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.970706521178 -0.0172251807399
x2[1] (closed_form) = 0.991728418815 -0.00312104920865
absolute error = 0.02531
relative error = 2.553 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=28194.4MB, alloc=40.3MB, time=345.50
t[1] = 1.8932 1.754
h = 0.0001 0.003
x1[1] (numeric) = 2.00833604243 -0.0218773399459
x1[1] (closed_form) = 1.99995061805 -0.000266524301184
absolute error = 0.02318
relative error = 1.159 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.970623055103 -0.0174585582413
x2[1] (closed_form) = 0.991757729264 -0.00320411655959
absolute error = 0.02549
relative error = 2.57 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=28238.5MB, alloc=40.3MB, time=346.03
memory used=28282.9MB, alloc=40.3MB, time=346.57
t[1] = 1.8933 1.757
h = 0.001 0.001
x1[1] (numeric) = 2.0084301231 -0.0219467192264
x1[1] (closed_form) = 1.99994982372 -0.000266348320035
absolute error = 0.02328
relative error = 1.164 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.970540890901 -0.0176929159206
x2[1] (closed_form) = 0.991775059998 -0.00325407617385
absolute error = 0.02568
relative error = 2.589 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=28327.2MB, alloc=40.3MB, time=347.10
t[1] = 1.8943 1.758
h = 0.001 0.003
x1[1] (numeric) = 2.0084405886 -0.0220015571992
x1[1] (closed_form) = 1.99994960781 -0.000266031845682
absolute error = 0.02334
relative error = 1.167 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.970459012913 -0.0179276184501
x2[1] (closed_form) = 0.991765023097 -0.00327690883193
absolute error = 0.02586
relative error = 2.607 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=28371.1MB, alloc=40.3MB, time=347.63
memory used=28415.3MB, alloc=40.3MB, time=348.16
t[1] = 1.8953 1.761
h = 0.0001 0.004
x1[1] (numeric) = 2.00851804855 -0.0221014540641
x1[1] (closed_form) = 1.99994886111 -0.000265613725629
absolute error = 0.02346
relative error = 1.173 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.970377234102 -0.0181628591829
x2[1] (closed_form) = 0.991768011535 -0.00333271044271
absolute error = 0.02603
relative error = 2.624 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=28459.2MB, alloc=40.3MB, time=348.68
t[1] = 1.8954 1.765
h = 0.003 0.006
x1[1] (numeric) = 2.00864973581 -0.0221939441228
x1[1] (closed_form) = 1.99994780429 -0.00026538050633
absolute error = 0.02359
relative error = 1.18 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.970296227609 -0.0183990307293
x2[1] (closed_form) = 0.991792766256 -0.00339902425581
absolute error = 0.02621
relative error = 2.643 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=28503.4MB, alloc=40.3MB, time=349.21
memory used=28547.5MB, alloc=40.3MB, time=349.74
t[1] = 1.8984 1.771
h = 0.0001 0.005
x1[1] (numeric) = 2.00878428813 -0.0224268050165
x1[1] (closed_form) = 1.99994637407 -0.000264268561013
absolute error = 0.02386
relative error = 1.193 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.97021595354 -0.0186378622572
x2[1] (closed_form) = 0.99178428148 -0.00351775731502
absolute error = 0.02634
relative error = 2.656 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=28591.5MB, alloc=40.3MB, time=350.27
t[1] = 1.8985 1.776
h = 0.0001 0.003
x1[1] (numeric) = 2.00894884482 -0.0225394006849
x1[1] (closed_form) = 1.9999450589 -0.000263970730748
absolute error = 0.02403
relative error = 1.201 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.970136809157 -0.0188796004612
x2[1] (closed_form) = 0.991817574676 -0.00360031162551
absolute error = 0.02652
relative error = 2.674 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=28635.9MB, alloc=40.3MB, time=350.80
t[1] = 1.8986 1.779
h = 0.001 0.001
x1[1] (numeric) = 2.0090471043 -0.0226087113775
x1[1] (closed_form) = 1.99994427281 -0.000263778340673
absolute error = 0.02413
relative error = 1.206 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.970059024142 -0.0191223063614
x2[1] (closed_form) = 0.991837298031 -0.00364997599407
absolute error = 0.02671
relative error = 2.693 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=28680.2MB, alloc=40.3MB, time=351.34
memory used=28724.3MB, alloc=40.3MB, time=351.87
t[1] = 1.8996 1.78
h = 0.001 0.003
x1[1] (numeric) = 2.00905905942 -0.0226648765634
x1[1] (closed_form) = 1.99994406502 -0.000263458890938
absolute error = 0.02418
relative error = 1.209 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.969981541513 -0.0193653574183
x2[1] (closed_form) = 0.991828183053 -0.0036734742323
absolute error = 0.0269
relative error = 2.712 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=28768.4MB, alloc=40.3MB, time=352.40
t[1] = 1.9006 1.783
h = 0.0001 0.004
x1[1] (numeric) = 2.00914088781 -0.0227659090092
x1[1] (closed_form) = 1.99994333159 -0.00026302674239
absolute error = 0.02431
relative error = 1.216 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.9699041751 -0.0196089566682
x2[1] (closed_form) = 0.991833687563 -0.00372967585781
absolute error = 0.02707
relative error = 2.73 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=28812.5MB, alloc=40.3MB, time=352.93
memory used=28856.8MB, alloc=40.3MB, time=353.46
t[1] = 1.9007 1.787
h = 0.003 0.006
x1[1] (numeric) = 2.00927831315 -0.0228581370075
x1[1] (closed_form) = 1.99994228572 -0.000262771686678
absolute error = 0.02445
relative error = 1.222 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.969827624642 -0.0198534876075
x2[1] (closed_form) = 0.991861635071 -0.0037955199178
absolute error = 0.02726
relative error = 2.749 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=28900.8MB, alloc=40.3MB, time=353.99
t[1] = 1.9037 1.793
h = 0.0001 0.005
x1[1] (numeric) = 2.0094217354 -0.0230946375469
x1[1] (closed_form) = 1.99994088774 -0.000261634590864
absolute error = 0.02472
relative error = 1.236 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.969751896525 -0.0201007212829
x2[1] (closed_form) = 0.991858362319 -0.00391576629389
absolute error = 0.0274
relative error = 2.762 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=28944.9MB, alloc=40.3MB, time=354.52
memory used=28989.2MB, alloc=40.3MB, time=355.05
t[1] = 1.9038 1.798
h = 0.0001 0.003
x1[1] (numeric) = 2.00959338012 -0.0232068327859
x1[1] (closed_form) = 1.99993958635 -0.000261309628083
absolute error = 0.02489
relative error = 1.245 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.969677404145 -0.0203508993347
x2[1] (closed_form) = 0.991895654273 -0.00399762576385
absolute error = 0.02759
relative error = 2.781 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=29033.4MB, alloc=40.3MB, time=355.59
t[1] = 1.9039 1.801
h = 0.001 0.001
x1[1] (numeric) = 2.00969591758 -0.0232759604474
x1[1] (closed_form) = 1.99993880881 -0.000261101100095
absolute error = 0.025
relative error = 1.25 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.969604329633 -0.020602030757
x2[1] (closed_form) = 0.99191778044 -0.00404688579911
absolute error = 0.02778
relative error = 2.801 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=29077.6MB, alloc=40.3MB, time=356.12
t[1] = 1.9049 1.802
h = 0.0001 0.004
x1[1] (numeric) = 2.00970943412 -0.02333344471
x1[1] (closed_form) = 1.99993860916 -0.000260778869066
absolute error = 0.02506
relative error = 1.253 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.969531574065 -0.0208535072129
x2[1] (closed_form) = 0.991909625907 -0.00407101517282
absolute error = 0.02797
relative error = 2.82 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=29121.6MB, alloc=40.3MB, time=356.64
memory used=29165.9MB, alloc=40.3MB, time=357.17
t[1] = 1.905 1.806
h = 0.003 0.006
x1[1] (numeric) = 2.00985116309 -0.0234253247431
x1[1] (closed_form) = 1.99993757279 -0.00026050516833
absolute error = 0.0252
relative error = 1.26 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.969459435172 -0.0211055271868
x2[1] (closed_form) = 0.991940322119 -0.00413629961841
absolute error = 0.02817
relative error = 2.839 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=29209.9MB, alloc=40.3MB, time=357.70
t[1] = 1.908 1.812
h = 0.0001 0.005
x1[1] (numeric) = 2.01000134659 -0.0236643239096
x1[1] (closed_form) = 1.99993620257 -0.000259346709854
absolute error = 0.02548
relative error = 1.274 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.969388203268 -0.0213602777208
x2[1] (closed_form) = 0.991941644933 -0.00425761143442
absolute error = 0.0283
relative error = 2.853 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=29253.9MB, alloc=40.3MB, time=358.22
memory used=29298.2MB, alloc=40.3MB, time=358.76
t[1] = 1.9081 1.817
h = 0.0001 0.003
x1[1] (numeric) = 2.01017830517 -0.0237760296556
x1[1] (closed_form) = 1.99993491315 -0.00025899858104
absolute error = 0.02565
relative error = 1.283 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.969318305517 -0.0216179942117
x2[1] (closed_form) = 0.991982374384 -0.00433867759202
absolute error = 0.0285
relative error = 2.873 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=29342.5MB, alloc=40.3MB, time=359.30
t[1] = 1.9082 1.82
h = 0.001 0.001
x1[1] (numeric) = 2.01028405786 -0.0238449056238
x1[1] (closed_form) = 1.99993414303 -0.000258776276355
absolute error = 0.02576
relative error = 1.288 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.969249875977 -0.0218766448164
x2[1] (closed_form) = 0.992006566734 -0.00438747238259
absolute error = 0.0287
relative error = 2.893 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=29386.7MB, alloc=40.3MB, time=359.84
t[1] = 1.9092 1.821
h = 0.001 0.003
x1[1] (numeric) = 2.01029879032 -0.0239033422319
x1[1] (closed_form) = 1.99993395037 -0.00025845170903
absolute error = 0.02582
relative error = 1.291 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.969181780063 -0.0221356385007
x2[1] (closed_form) = 0.991999275806 -0.00441210382777
absolute error = 0.02889
relative error = 2.912 %
Correct digits = 2
memory used=29430.9MB, alloc=40.3MB, time=360.37
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=29474.8MB, alloc=40.3MB, time=360.90
t[1] = 1.9102 1.824
h = 0.0001 0.004
x1[1] (numeric) = 2.01038856498 -0.024006078291
x1[1] (closed_form) = 1.9999332421 -0.00025799427409
absolute error = 0.02595
relative error = 1.297 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.969113834844 -0.0223951968458
x2[1] (closed_form) = 0.992009572936 -0.00446872956972
absolute error = 0.02908
relative error = 2.931 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=29518.7MB, alloc=40.3MB, time=361.42
t[1] = 1.9103 1.828
h = 0.003 0.006
x1[1] (numeric) = 2.01053630031 -0.0240973860164
x1[1] (closed_form) = 1.99993221744 -0.000257699408037
absolute error = 0.02609
relative error = 1.305 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.969046789829 -0.0226556814488
x2[1] (closed_form) = 0.992043474075 -0.00453327050216
absolute error = 0.02928
relative error = 2.951 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=29562.9MB, alloc=40.3MB, time=361.94
memory used=29607.2MB, alloc=40.3MB, time=362.47
t[1] = 1.9133 1.834
h = 0.0001 0.005
x1[1] (numeric) = 2.01069597851 -0.0243397441414
x1[1] (closed_form) = 1.99993088015 -0.000256517368965
absolute error = 0.02638
relative error = 1.319 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.968980747372 -0.022918936562
x2[1] (closed_form) = 0.992050218832 -0.00465568538217
absolute error = 0.02942
relative error = 2.966 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=29651.2MB, alloc=40.3MB, time=362.99
t[1] = 1.9134 1.839
h = 0.0001 0.003
x1[1] (numeric) = 2.01088035341 -0.0244506623821
x1[1] (closed_form) = 1.99992960547 -0.000256142949099
absolute error = 0.02656
relative error = 1.328 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.968916151157 -0.0231851915252
x2[1] (closed_form) = 0.992094953347 -0.00473571213352
absolute error = 0.02962
relative error = 2.986 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=29695.4MB, alloc=40.3MB, time=363.52
memory used=29740.0MB, alloc=40.3MB, time=364.06
t[1] = 1.9135 1.842
h = 0.001 0.001
x1[1] (numeric) = 2.01099058513 -0.0245191244047
x1[1] (closed_form) = 1.99992884447 -0.000255905021397
absolute error = 0.02667
relative error = 1.333 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.968853083233 -0.0234523628002
x2[1] (closed_form) = 0.992121553394 -0.00478389576016
absolute error = 0.02983
relative error = 3.007 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=29784.2MB, alloc=40.3MB, time=364.60
t[1] = 1.9145 1.843
h = 0.001 0.003
x1[1] (numeric) = 2.01100702409 -0.0245788638995
x1[1] (closed_form) = 1.99992865998 -0.000255578032066
absolute error = 0.02673
relative error = 1.336 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.968790366136 -0.0237198762021
x2[1] (closed_form) = 0.992115290959 -0.00480908840115
absolute error = 0.03003
relative error = 3.027 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=29828.2MB, alloc=40.3MB, time=365.13
t[1] = 1.9155 1.846
h = 0.0001 0.004
x1[1] (numeric) = 2.0111015783 -0.024682462861
x1[1] (closed_form) = 1.99992796564 -0.000255107627002
absolute error = 0.02686
relative error = 1.343 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.968727818623 -0.0239879635296
x2[1] (closed_form) = 0.992128211871 -0.00486579775401
absolute error = 0.03022
relative error = 3.046 %
Correct digits = 2
memory used=29872.4MB, alloc=40.3MB, time=365.65
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=29916.4MB, alloc=40.3MB, time=366.18
t[1] = 1.9156 1.85
h = 0.003 0.006
x1[1] (numeric) = 2.01125544871 -0.0247730223524
x1[1] (closed_form) = 1.99992695309 -0.000254791968994
absolute error = 0.02701
relative error = 1.35 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.968666217737 -0.0242569745973
x2[1] (closed_form) = 0.992165316107 -0.00492944568707
absolute error = 0.03043
relative error = 3.067 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=29960.4MB, alloc=40.3MB, time=366.70
t[1] = 1.9186 1.856
h = 0.0001 0.005
x1[1] (numeric) = 2.01142494024 -0.025018563691
x1[1] (closed_form) = 1.99992564905 -0.000253587200047
absolute error = 0.0273
relative error = 1.365 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.968605718301 -0.0245287944895
x2[1] (closed_form) = 0.992177584495 -0.00505273370059
absolute error = 0.03058
relative error = 3.082 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=30004.5MB, alloc=40.3MB, time=367.22
memory used=30048.6MB, alloc=40.3MB, time=367.75
t[1] = 1.9187 1.861
h = 0.0001 0.003
x1[1] (numeric) = 2.01161688826 -0.0251284752596
x1[1] (closed_form) = 1.99992438961 -0.000253186957059
absolute error = 0.02749
relative error = 1.374 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.968546780747 -0.0248036459012
x2[1] (closed_form) = 0.992226316882 -0.00513153317248
absolute error = 0.03078
relative error = 3.103 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=30093.0MB, alloc=40.3MB, time=368.29
t[1] = 1.9188 1.864
h = 0.001 0.001
x1[1] (numeric) = 2.01173169536 -0.0251963924434
x1[1] (closed_form) = 1.99992363803 -0.00025293369226
absolute error = 0.0276
relative error = 1.38 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.968489432496 -0.0250793937851
x2[1] (closed_form) = 0.99225532091 -0.00517899282755
absolute error = 0.031
relative error = 3.124 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=30137.4MB, alloc=40.3MB, time=368.83
memory used=30181.5MB, alloc=40.3MB, time=369.36
t[1] = 1.9198 1.865
h = 0.001 0.003
x1[1] (numeric) = 2.01174991697 -0.0252574200154
x1[1] (closed_form) = 1.99992346171 -0.000252604473018
absolute error = 0.02766
relative error = 1.383 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.968432452651 -0.0253554823575
x2[1] (closed_form) = 0.992250121875 -0.00520470647101
absolute error = 0.0312
relative error = 3.144 %
Correct digits = 2
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=30225.7MB, alloc=40.3MB, time=369.88
t[1] = 1.9208 1.868
h = 0.0001 0.004
x1[1] (numeric) = 2.01184938873 -0.0253617735255
x1[1] (closed_form) = 1.9999227815 -0.000252121474196
absolute error = 0.0278
relative error = 1.39 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.968375661973 -0.0256321538292
x2[1] (closed_form) = 0.992265695787 -0.00526138379182
absolute error = 0.0314
relative error = 3.164 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=30269.8MB, alloc=40.3MB, time=370.41
t[1] = 1.9209 1.872
h = 0.003 0.006
x1[1] (numeric) = 2.01200952123 -0.0254514011569
x1[1] (closed_form) = 1.99992178146 -0.000251785404247
absolute error = 0.02795
relative error = 1.397 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.96831986537 -0.0259097452133
x2[1] (closed_form) = 0.99230599462 -0.00532398787733
absolute error = 0.03161
relative error = 3.185 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=30314.0MB, alloc=40.3MB, time=370.93
memory used=30358.1MB, alloc=40.3MB, time=371.46
t[1] = 1.9239 1.878
h = 0.0001 0.005
x1[1] (numeric) = 2.01218914757 -0.0256999371083
x1[1] (closed_form) = 1.99992051099 -0.000250558758756
absolute error = 0.02825
relative error = 1.413 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.968265272469 -0.026190181973
x2[1] (closed_form) = 0.992323879081 -0.00544791234956
absolute error = 0.03177
relative error = 3.201 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=30402.2MB, alloc=40.3MB, time=371.98
t[1] = 1.924 1.883
h = 0.0001 0.003
x1[1] (numeric) = 2.01238882329 -0.0258086133413
x1[1] (closed_form) = 1.99991926726 -0.000250133168795
absolute error = 0.02844
relative error = 1.422 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.96821236066 -0.0264736795511
x2[1] (closed_form) = 0.992376593721 -0.00552529517448
absolute error = 0.03198
relative error = 3.223 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=30446.4MB, alloc=40.3MB, time=372.51
memory used=30491.0MB, alloc=40.3MB, time=373.06
t[1] = 1.9241 1.886
h = 0.001 0.001
x1[1] (numeric) = 2.01250830088 -0.0258758490482
x1[1] (closed_form) = 1.99991852538 -0.000249864857618
absolute error = 0.02855
relative error = 1.428 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.968161100068 -0.0267580516512
x2[1] (closed_form) = 0.992407992958 -0.00557191712632
absolute error = 0.0322
relative error = 3.244 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=30535.0MB, alloc=40.3MB, time=373.59
t[1] = 1.9251 1.887
h = 0.001 0.003
x1[1] (numeric) = 2.0125283827 -0.0259381474651
x1[1] (closed_form) = 1.99991835724 -0.000249533599668
absolute error = 0.02862
relative error = 1.431 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.968110225838 -0.0270427624939
x2[1] (closed_form) = 0.992403890781 -0.00559810963766
absolute error = 0.0324
relative error = 3.265 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=30579.2MB, alloc=40.3MB, time=374.12
memory used=30623.4MB, alloc=40.3MB, time=374.64
t[1] = 1.9261 1.89
h = 0.0001 0.004
x1[1] (numeric) = 2.01263291036 -0.0260431408334
x1[1] (closed_form) = 1.99991769135 -0.000249038385898
absolute error = 0.02876
relative error = 1.438 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.968059561059 -0.0273280648932
x2[1] (closed_form) = 0.992422142048 -0.0056546368667
absolute error = 0.03261
relative error = 3.286 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=30667.5MB, alloc=40.3MB, time=375.17
t[1] = 1.9262 1.894
h = 0.003 0.006
x1[1] (numeric) = 2.01279943002 -0.026131645144
x1[1] (closed_form) = 1.99991670419 -0.000248682290416
absolute error = 0.02891
relative error = 1.446 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.968009938815 -0.0276142820087
x2[1] (closed_form) = 0.992465620188 -0.00571604517766
absolute error = 0.03283
relative error = 3.308 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=30711.5MB, alloc=40.3MB, time=375.70
t[1] = 1.9292 1.9
h = 0.0001 0.005
x1[1] (numeric) = 2.01298951518 -0.0263829738699
x1[1] (closed_form) = 1.99991546758 -0.000247434623856
absolute error = 0.02922
relative error = 1.461 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.967961625917 -0.0279033791564
x2[1] (closed_form) = 0.992489203524 -0.00584036303513
absolute error = 0.03299
relative error = 3.324 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=30755.7MB, alloc=40.3MB, time=376.22
memory used=30799.8MB, alloc=40.3MB, time=376.75
t[1] = 1.9293 1.905
h = 0.0001 0.003
x1[1] (numeric) = 2.01319707067 -0.0264901764427
x1[1] (closed_form) = 1.99991424005 -0.00024698417096
absolute error = 0.02941
relative error = 1.471 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.967915116916 -0.0281955638994
x2[1] (closed_form) = 0.992545876222 -0.00591613871127
absolute error = 0.03321
relative error = 3.346 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=30844.1MB, alloc=40.3MB, time=377.29
t[1] = 1.9294 1.908
h = 0.001 0.001
x1[1] (numeric) = 2.0133213124 -0.0265565881877
x1[1] (closed_form) = 1.99991350813 -0.000246701108722
absolute error = 0.02953
relative error = 1.477 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.96787032191 -0.0284885990297
x2[1] (closed_form) = 0.992579656752 -0.00596180851981
absolute error = 0.03344
relative error = 3.369 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=30888.5MB, alloc=40.3MB, time=377.83
memory used=30932.7MB, alloc=40.3MB, time=378.35
t[1] = 1.9304 1.909
h = 0.0001 0.004
x1[1] (numeric) = 2.01334333339 -0.0266201376987
x1[1] (closed_form) = 1.99991334817 -0.000246368002292
absolute error = 0.0296
relative error = 1.48 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.967825931593 -0.0287819704272
x2[1] (closed_form) = 0.992576683337 -0.00598843586894
absolute error = 0.03365
relative error = 3.39 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=30976.7MB, alloc=40.3MB, time=378.88
t[1] = 1.9305 1.913
h = 0.003 0.006
x1[1] (numeric) = 2.01351461799 -0.0267076333582
x1[1] (closed_form) = 1.99991237216 -0.000245994824246
absolute error = 0.02975
relative error = 1.488 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.967782305589 -0.029075854927
x2[1] (closed_form) = 0.992622863881 -0.00604865513399
absolute error = 0.03387
relative error = 3.412 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=31020.8MB, alloc=40.3MB, time=379.40
memory used=31065.0MB, alloc=40.3MB, time=379.93
t[1] = 1.9335 1.919
h = 0.0001 0.005
x1[1] (numeric) = 2.01371262772 -0.0269607847742
x1[1] (closed_form) = 1.99991116468 -0.000244729342045
absolute error = 0.03007
relative error = 1.504 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.967740086662 -0.0293726381919
x2[1] (closed_form) = 0.992651411924 -0.0061730433019
absolute error = 0.03404
relative error = 3.429 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=31109.1MB, alloc=40.3MB, time=380.46
t[1] = 1.9336 1.924
h = 0.0001 0.003
x1[1] (numeric) = 2.01392605878 -0.0270666749103
x1[1] (closed_form) = 1.99990995116 -0.000244257681202
absolute error = 0.03026
relative error = 1.513 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.967699783725 -0.0296725189036
x2[1] (closed_form) = 0.99271144332 -0.00624723586229
absolute error = 0.03427
relative error = 3.452 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=31153.4MB, alloc=40.3MB, time=380.99
t[1] = 1.9337 1.927
h = 0.001 0.001
x1[1] (numeric) = 2.01405386184 -0.0271323421521
x1[1] (closed_form) = 1.99990922787 -0.000243962038491
absolute error = 0.03038
relative error = 1.519 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.967661247796 -0.0299732214856
x2[1] (closed_form) = 0.992747245249 -0.00629196603688
absolute error = 0.0345
relative error = 3.475 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=31197.8MB, alloc=40.3MB, time=381.53
memory used=31242.1MB, alloc=40.3MB, time=382.06
t[1] = 1.9347 1.928
h = 0.001 0.003
x1[1] (numeric) = 2.01407738022 -0.0271967820891
x1[1] (closed_form) = 1.99990907492 -0.000243627395142
absolute error = 0.03045
relative error = 1.523 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.967623132538 -0.0302742560745
x2[1] (closed_form) = 0.992745272159 -0.00631891707963
absolute error = 0.03471
relative error = 3.497 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=31286.2MB, alloc=40.3MB, time=382.59
t[1] = 1.9357 1.931
h = 0.0001 0.004
x1[1] (numeric) = 2.01419104697 -0.0273025355099
x1[1] (closed_form) = 1.99990843606 -0.000243110292102
absolute error = 0.0306
relative error = 1.53 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.967585267264 -0.030575895569
x2[1] (closed_form) = 0.992768547682 -0.00637481099292
absolute error = 0.03493
relative error = 3.518 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=31330.4MB, alloc=40.3MB, time=383.11
memory used=31374.7MB, alloc=40.3MB, time=383.64
t[1] = 1.9358 1.935
h = 0.003 0.006
x1[1] (numeric) = 2.01436897198 -0.027388522113
x1[1] (closed_form) = 1.99990747361 -0.000242717819436
absolute error = 0.03076
relative error = 1.538 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.967548537088 -0.0308784318047
x2[1] (closed_form) = 0.99281785879 -0.00643355029365
absolute error = 0.03516
relative error = 3.541 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=31418.8MB, alloc=40.3MB, time=384.17
t[1] = 1.9388 1.941
h = 0.0001 0.005
x1[1] (numeric) = 2.01457809571 -0.0276440606935
x1[1] (closed_form) = 1.99990630049 -0.000241432909228
absolute error = 0.03108
relative error = 1.554 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.967513325528 -0.0311838975804
x2[1] (closed_form) = 0.992852229796 -0.00655786308484
absolute error = 0.03533
relative error = 3.559 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=31462.8MB, alloc=40.3MB, time=384.69
memory used=31507.0MB, alloc=40.3MB, time=385.22
t[1] = 1.9389 1.946
h = 0.0001 0.003
x1[1] (numeric) = 2.01479971529 -0.0277479968002
x1[1] (closed_form) = 1.99990510399 -0.000240937300805
absolute error = 0.03128
relative error = 1.564 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.967480158949 -0.0314924825323
x2[1] (closed_form) = 0.992916148675 -0.00663009280798
absolute error = 0.03557
relative error = 3.582 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=31551.4MB, alloc=40.3MB, time=385.76
t[1] = 1.939 1.949
h = 0.001 0.001
x1[1] (numeric) = 2.01493247249 -0.0278125527528
x1[1] (closed_form) = 1.99990439117 -0.00024062746505
absolute error = 0.0314
relative error = 1.57 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.967448823439 -0.0318018611455
x2[1] (closed_form) = 0.992954290664 -0.00667365708552
absolute error = 0.0358
relative error = 3.606 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=31595.5MB, alloc=40.3MB, time=386.30
t[1] = 1.94 1.95
h = 0.001 0.003
x1[1] (numeric) = 2.01495808941 -0.0278782042393
x1[1] (closed_form) = 1.99990424639 -0.000240291324415
absolute error = 0.03147
relative error = 1.574 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.967417927527 -0.0321115682817
x2[1] (closed_form) = 0.992953500661 -0.00670095583629
absolute error = 0.03602
relative error = 3.628 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=31639.5MB, alloc=40.3MB, time=386.82
memory used=31683.6MB, alloc=40.3MB, time=387.34
t[1] = 1.941 1.953
h = 0.0001 0.004
x1[1] (numeric) = 2.01507723024 -0.0279842324514
x1[1] (closed_form) = 1.99990362238 -0.000239763099697
absolute error = 0.03162
relative error = 1.581 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.96738730384 -0.0324218879246
x2[1] (closed_form) = 0.992979493524 -0.00675635024783
absolute error = 0.03624
relative error = 3.65 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=31727.5MB, alloc=40.3MB, time=387.87
t[1] = 1.9411 1.957
h = 0.003 0.006
x1[1] (numeric) = 2.01526191324 -0.0280684946363
x1[1] (closed_form) = 1.99990267383 -0.000239351735765
absolute error = 0.03179
relative error = 1.589 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.967357866346 -0.0327330949653
x2[1] (closed_form) = 0.993031899882 -0.00681345629186
absolute error = 0.03648
relative error = 3.674 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=31771.4MB, alloc=40.3MB, time=388.39
memory used=31815.4MB, alloc=40.3MB, time=388.91
t[1] = 1.9441 1.963
h = 0.0001 0.005
x1[1] (numeric) = 2.01548248049 -0.0283261770817
x1[1] (closed_form) = 1.99990153532 -0.000238048256885
absolute error = 0.03212
relative error = 1.606 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.96733006248 -0.0330472600516
x2[1] (closed_form) = 0.993072146984 -0.00693743454887
absolute error = 0.03667
relative error = 3.692 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=31859.3MB, alloc=40.3MB, time=389.44
t[1] = 1.9442 1.968
h = 0.0001 0.003
x1[1] (numeric) = 2.01571243108 -0.0284278913541
x1[1] (closed_form) = 1.99990035628 -0.000237529205832
absolute error = 0.03232
relative error = 1.616 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.967304436228 -0.0333645630911
x2[1] (closed_form) = 0.993139903934 -0.00700750987068
absolute error = 0.03691
relative error = 3.716 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=31903.4MB, alloc=40.3MB, time=389.97
t[1] = 1.9443 1.971
h = 0.001 0.001
x1[1] (numeric) = 2.01585023054 -0.028491175683
x1[1] (closed_form) = 1.99989965418 -0.000237205484503
absolute error = 0.03245
relative error = 1.622 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.967280705868 -0.0336826291914
x2[1] (closed_form) = 0.993180356931 -0.0070497930928
absolute error = 0.03715
relative error = 3.74 %
Correct digits = 1
memory used=31948.0MB, alloc=40.3MB, time=390.51
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=31992.0MB, alloc=40.3MB, time=391.04
t[1] = 1.9453 1.972
h = 0.001 0.003
x1[1] (numeric) = 2.01587802878 -0.0285580109206
x1[1] (closed_form) = 1.99989951755 -0.000236868033587
absolute error = 0.03252
relative error = 1.626 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.967257434388 -0.0340010197395
x2[1] (closed_form) = 0.993180776919 -0.0070773904173
absolute error = 0.03738
relative error = 3.763 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=32035.9MB, alloc=40.3MB, time=391.56
t[1] = 1.9463 1.975
h = 0.0001 0.004
x1[1] (numeric) = 2.01600278162 -0.0286641726124
x1[1] (closed_form) = 1.99989890854 -0.000236329073517
absolute error = 0.03267
relative error = 1.634 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.967234458105 -0.0343200299778
x2[1] (closed_form) = 0.993209491301 -0.00713215988706
absolute error = 0.0376
relative error = 3.786 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=32079.8MB, alloc=40.3MB, time=392.08
memory used=32123.8MB, alloc=40.3MB, time=392.61
t[1] = 1.9464 1.979
h = 0.003 0.006
x1[1] (numeric) = 2.01619433717 -0.0287464867186
x1[1] (closed_form) = 1.99989797424 -0.000235899227043
absolute error = 0.03284
relative error = 1.642 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.967212720071 -0.034639916675
x2[1] (closed_form) = 0.993264950433 -0.0071874794711
absolute error = 0.03785
relative error = 3.81 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=32167.7MB, alloc=40.3MB, time=393.14
t[1] = 1.9494 1.985
h = 0.0001 0.005
x1[1] (numeric) = 2.01642667871 -0.0290060550366
x1[1] (closed_form) = 1.99989687055 -0.000234578039225
absolute error = 0.03318
relative error = 1.659 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.967192734171 -0.0349627875074
x2[1] (closed_form) = 0.993311115748 -0.0073108591667
absolute error = 0.03804
relative error = 3.829 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=32211.6MB, alloc=40.3MB, time=393.66
memory used=32255.8MB, alloc=40.3MB, time=394.19
t[1] = 1.9495 1.99
h = 0.0001 0.003
x1[1] (numeric) = 2.01666509896 -0.0291052694505
x1[1] (closed_form) = 1.99989570938 -0.000234036057106
absolute error = 0.03339
relative error = 1.669 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.967175062169 -0.0352888119492
x2[1] (closed_form) = 0.993382652358 -0.00737858886917
absolute error = 0.03829
relative error = 3.854 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=32300.0MB, alloc=40.3MB, time=394.73
t[1] = 1.9496 1.993
h = 0.001 0.001
x1[1] (numeric) = 2.01680802656 -0.0291671156271
x1[1] (closed_form) = 1.99989501824 -0.000233698761506
absolute error = 0.03351
relative error = 1.676 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.967159351595 -0.0356155663829
x2[1] (closed_form) = 0.993425381907 -0.00741947605643
absolute error = 0.03853
relative error = 3.879 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=32344.2MB, alloc=40.3MB, time=395.27
t[1] = 1.9506 1.994
h = 0.001 0.003
x1[1] (numeric) = 2.0168380901 -0.0292351039191
x1[1] (closed_form) = 1.99989488976 -0.000233360186009
absolute error = 0.03359
relative error = 1.68 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.967144119532 -0.0359426405739
x2[1] (closed_form) = 0.993427036863 -0.00744732114824
absolute error = 0.03877
relative error = 3.902 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=32388.3MB, alloc=40.3MB, time=395.79
memory used=32432.3MB, alloc=40.3MB, time=396.32
t[1] = 1.9516 1.997
h = 0.0001 0.004
x1[1] (numeric) = 2.01696859237 -0.0293412506904
x1[1] (closed_form) = 1.99989429591 -0.000232810878308
absolute error = 0.03375
relative error = 1.687 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.967129206376 -0.0362703411915
x2[1] (closed_form) = 0.993458471402 -0.00750133883716
absolute error = 0.039
relative error = 3.925 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=32476.1MB, alloc=40.3MB, time=396.84
t[1] = 1.9517 2.001
h = 0.003 0.006
x1[1] (numeric) = 2.0171671317 -0.0294213846439
x1[1] (closed_form) = 1.99989337617 -0.00023236296312
absolute error = 0.03392
relative error = 1.696 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.967115584465 -0.0365989056699
x2[1] (closed_form) = 0.993516933607 -0.0075547191661
absolute error = 0.03925
relative error = 3.951 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=32520.0MB, alloc=40.3MB, time=397.36
memory used=32564.0MB, alloc=40.3MB, time=397.89
t[1] = 1.9547 2.007
h = 0.0001 0.005
x1[1] (numeric) = 2.0174115792 -0.029682565767
x1[1] (closed_form) = 1.99989230749 -0.000231024926053
absolute error = 0.03427
relative error = 1.714 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.967103836706 -0.0369304778057
x2[1] (closed_form) = 0.993569047911 -0.0076772318457
absolute error = 0.03945
relative error = 3.97 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=32607.9MB, alloc=40.3MB, time=398.41
t[1] = 1.9548 2.012
h = 0.0001 0.003
x1[1] (numeric) = 2.01765860352 -0.029778991941
x1[1] (closed_form) = 1.9998911646 -0.00023046053072
absolute error = 0.03448
relative error = 1.724 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.967094542783 -0.0372652159142
x2[1] (closed_form) = 0.993644296694 -0.00774242546015
absolute error = 0.0397
relative error = 3.996 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=32652.0MB, alloc=40.3MB, time=398.94
memory used=32696.4MB, alloc=40.3MB, time=399.48
t[1] = 1.9549 2.015
h = 0.001 0.001
x1[1] (numeric) = 2.01780674267 -0.0298392271567
x1[1] (closed_form) = 1.99989048466 -0.000230109975781
absolute error = 0.03461
relative error = 1.73 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.967087276489 -0.0376006483992
x2[1] (closed_form) = 0.993689262891 -0.00778180205397
absolute error = 0.03996
relative error = 4.021 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=32740.5MB, alloc=40.3MB, time=400.01
t[1] = 1.9559 2.016
h = 0.0001 0.004
x1[1] (numeric) = 2.01783915668 -0.029908334806
x1[1] (closed_form) = 1.99989036429 -0.000229770460019
absolute error = 0.03468
relative error = 1.734 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.967080508677 -0.0379363953121
x2[1] (closed_form) = 0.993692175773 -0.00780984250394
absolute error = 0.0402
relative error = 4.045 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=32784.4MB, alloc=40.3MB, time=400.53
t[1] = 1.956 2.02
h = 0.003 0.006
x1[1] (numeric) = 2.01804287805 -0.0299866542243
x1[1] (closed_form) = 1.99988945715 -0.000229307148341
absolute error = 0.03486
relative error = 1.743 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.967074664526 -0.0382726007406
x2[1] (closed_form) = 0.993753152002 -0.00786139695267
absolute error = 0.04045
relative error = 4.071 %
Correct digits = 1
memory used=32828.5MB, alloc=40.3MB, time=401.05
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=32872.3MB, alloc=40.3MB, time=401.57
t[1] = 1.959 2.026
h = 0.0001 0.005
x1[1] (numeric) = 2.01829644866 -0.0302487310496
x1[1] (closed_form) = 1.99988841855 -0.000227954876231
absolute error = 0.03522
relative error = 1.761 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.96707080555 -0.0386118206832
x2[1] (closed_form) = 0.993810388006 -0.00798287417624
absolute error = 0.04066
relative error = 4.091 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=32916.3MB, alloc=40.3MB, time=402.10
t[1] = 1.9591 2.031
h = 0.0001 0.003
x1[1] (numeric) = 2.01854985361 -0.0303428427577
x1[1] (closed_form) = 1.99988729145 -0.000227371383592
absolute error = 0.03543
relative error = 1.772 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.967069526089 -0.0389542015639
x2[1] (closed_form) = 0.993888737823 -0.0080456902079
absolute error = 0.04092
relative error = 4.117 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=32960.3MB, alloc=40.3MB, time=402.62
memory used=33004.8MB, alloc=40.3MB, time=403.16
t[1] = 1.9592 2.034
h = 0.001 0.001
x1[1] (numeric) = 2.01870186739 -0.0304017320196
x1[1] (closed_form) = 1.99988662118 -0.000227009533176
absolute error = 0.03556
relative error = 1.778 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.967070328975 -0.0392972376573
x2[1] (closed_form) = 0.993935573272 -0.00808364940679
absolute error = 0.04118
relative error = 4.143 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=33049.0MB, alloc=40.3MB, time=403.69
t[1] = 1.9602 2.035
h = 0.001 0.003
x1[1] (numeric) = 2.01873608383 -0.0304716192909
x1[1] (closed_form) = 1.99988650777 -0.000226669258237
absolute error = 0.03564
relative error = 1.782 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.967071647458 -0.0396405811804
x2[1] (closed_form) = 0.993939587161 -0.00811179956055
absolute error = 0.04142
relative error = 4.168 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=33093.0MB, alloc=40.3MB, time=404.22
memory used=33137.0MB, alloc=40.3MB, time=404.75
t[1] = 1.9612 2.038
h = 0.0001 0.004
x1[1] (numeric) = 2.0188769166 -0.0305772968635
x1[1] (closed_form) = 1.99988594239 -0.000226101547422
absolute error = 0.0358
relative error = 1.79 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.967073331682 -0.0399845601899
x2[1] (closed_form) = 0.993976047631 -0.00816404485809
absolute error = 0.04167
relative error = 4.192 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=33180.8MB, alloc=40.3MB, time=405.27
t[1] = 1.9613 2.042
h = 0.003 0.006
x1[1] (numeric) = 2.01908784723 -0.0306529687931
x1[1] (closed_form) = 1.9998850504 -0.000225620946175
absolute error = 0.03598
relative error = 1.799 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.96707640724 -0.0403293700188
x2[1] (closed_form) = 0.994039913252 -0.00821337873697
absolute error = 0.04193
relative error = 4.218 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=33224.8MB, alloc=40.3MB, time=405.79
t[1] = 1.9643 2.048
h = 0.0001 0.005
x1[1] (numeric) = 2.01935419442 -0.0309161096659
memory used=33268.8MB, alloc=40.3MB, time=406.32
x1[1] (closed_form) = 1.99988404713 -0.000224253421114
absolute error = 0.03635
relative error = 1.817 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.967081596017 -0.0406772127643
x2[1] (closed_form) = 0.994103120994 -0.00833347918822
absolute error = 0.04215
relative error = 4.239 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=33312.9MB, alloc=40.3MB, time=406.85
t[1] = 1.9644 2.053
h = 0.0001 0.003
x1[1] (numeric) = 2.01961647682 -0.0310068520666
x1[1] (closed_form) = 1.99988293902 -0.000223648490046
absolute error = 0.03657
relative error = 1.828 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.96708951043 -0.041028222357
x2[1] (closed_form) = 0.994185030863 -0.00839340918011
absolute error = 0.04242
relative error = 4.266 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=33357.2MB, alloc=40.3MB, time=407.38
t[1] = 1.9645 2.056
h = 0.001 0.001
x1[1] (numeric) = 2.01977387158 -0.0310637820407
x1[1] (closed_form) = 1.99988228038 -0.000223273972709
absolute error = 0.0367
relative error = 1.835 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.967099574262 -0.0413798468432
x2[1] (closed_form) = 0.994234012754 -0.00842964721494
absolute error = 0.04268
relative error = 4.293 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=33401.4MB, alloc=40.3MB, time=407.93
memory used=33445.5MB, alloc=40.3MB, time=408.45
t[1] = 1.9655 2.057
h = 0.001 0.003
x1[1] (numeric) = 2.01981061033 -0.0311347210987
x1[1] (closed_form) = 1.99988217505 -0.000222933096869
absolute error = 0.03678
relative error = 1.839 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.967110174191 -0.0417317722265
x2[1] (closed_form) = 0.994239320941 -0.00845789098508
absolute error = 0.04293
relative error = 4.318 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=33489.4MB, alloc=40.3MB, time=408.98
t[1] = 1.9665 2.06
h = 0.0001 0.004
x1[1] (numeric) = 2.019957605 -0.0312399150649
x1[1] (closed_form) = 1.99988162521 -0.000222356151973
absolute error = 0.03695
relative error = 1.847 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.967121165603 -0.0420843383916
x2[1] (closed_form) = 0.994278464534 -0.00850901627875
absolute error = 0.04318
relative error = 4.343 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=33533.3MB, alloc=40.3MB, time=409.50
memory used=33577.3MB, alloc=40.3MB, time=410.03
t[1] = 1.9666 2.064
h = 0.003 0.006
x1[1] (numeric) = 2.02017584431 -0.0313126819815
x1[1] (closed_form) = 1.99988074866 -0.00022185868826
absolute error = 0.03713
relative error = 1.857 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.967133603707 -0.0424377178077
x2[1] (closed_form) = 0.994345148949 -0.0085559798614
absolute error = 0.04346
relative error = 4.37 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=33621.4MB, alloc=40.3MB, time=410.56
t[1] = 1.9696 2.07
h = 0.0001 0.005
x1[1] (numeric) = 2.02045529978 -0.0315765669793
x1[1] (closed_form) = 1.99987978086 -0.000220476767643
absolute error = 0.0375
relative error = 1.875 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.967148286625 -0.0427941455456
x2[1] (closed_form) = 0.994414325101 -0.00867442517403
absolute error = 0.04368
relative error = 4.392 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=33665.3MB, alloc=40.3MB, time=411.08
memory used=33709.3MB, alloc=40.3MB, time=411.61
t[1] = 1.9697 2.075
h = 0.0001 0.003
x1[1] (numeric) = 2.02072657908 -0.0316636203544
x1[1] (closed_form) = 1.99987869212 -0.000219850932322
absolute error = 0.03773
relative error = 1.886 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.967165844951 -0.0431537422585
x2[1] (closed_form) = 0.994499701368 -0.00873128319835
absolute error = 0.04396
relative error = 4.42 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=33753.7MB, alloc=40.3MB, time=412.15
t[1] = 1.9698 2.078
h = 0.001 0.001
x1[1] (numeric) = 2.02088942948 -0.0317183992209
x1[1] (closed_form) = 1.99987804531 -0.000219464072392
absolute error = 0.03786
relative error = 1.893 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.967185620286 -0.0435139107821
x2[1] (closed_form) = 0.994550774071 -0.00876568815284
absolute error = 0.04423
relative error = 4.447 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=33797.7MB, alloc=40.3MB, time=412.68
t[1] = 1.9708 2.079
h = 0.001 0.003
x1[1] (numeric) = 2.02092877876 -0.0317903468703
x1[1] (closed_form) = 1.99987794802 -0.000219122775615
absolute error = 0.03795
relative error = 1.897 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.967205952535 -0.043874372964
x2[1] (closed_form) = 0.994557393231 -0.00879396899873
absolute error = 0.04448
relative error = 4.472 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=33841.7MB, alloc=40.3MB, time=413.20
memory used=33885.8MB, alloc=40.3MB, time=413.73
t[1] = 1.9718 2.082
h = 0.0001 0.004
x1[1] (numeric) = 2.02108206837 -0.0318948793213
x1[1] (closed_form) = 1.99987741385 -0.000218536987877
absolute error = 0.03812
relative error = 1.906 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.967226702763 -0.0442354806584
x2[1] (closed_form) = 0.994599196187 -0.00884384436724
absolute error = 0.04474
relative error = 4.498 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=33929.7MB, alloc=40.3MB, time=414.26
t[1] = 1.9719 2.086
h = 0.003 0.006
x1[1] (numeric) = 2.02130771123 -0.0319644749257
x1[1] (closed_form) = 1.99987655303 -0.000218023092886
absolute error = 0.0383
relative error = 1.915 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.967248955893 -0.0445973821297
x2[1] (closed_form) = 0.994668621455 -0.00888828961872
absolute error = 0.04502
relative error = 4.526 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=33973.6MB, alloc=40.3MB, time=414.78
memory used=34017.7MB, alloc=40.3MB, time=415.30
t[1] = 1.9749 2.092
h = 0.0001 0.005
x1[1] (numeric) = 2.0216006059 -0.0322287676221
x1[1] (closed_form) = 1.99987562082 -0.000216627632402
absolute error = 0.03869
relative error = 1.935 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.967273588989 -0.0449623441627
x2[1] (closed_form) = 0.994743750271 -0.00900479887969
absolute error = 0.04525
relative error = 4.549 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=34061.6MB, alloc=40.3MB, time=415.83
t[1] = 1.975 2.097
h = 0.0001 0.003
x1[1] (numeric) = 2.0218809958 -0.0323118014671
x1[1] (closed_form) = 1.99987455178 -0.00021598143202
absolute error = 0.03892
relative error = 1.946 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.967301250899 -0.0453304733286
x2[1] (closed_form) = 0.994832490103 -0.00905840137517
absolute error = 0.04554
relative error = 4.577 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=34105.8MB, alloc=40.3MB, time=416.36
t[1] = 1.9751 2.1
h = 0.001 0.001
x1[1] (numeric) = 2.02204937309 -0.0323642308547
x1[1] (closed_form) = 1.99987391701 -0.000215582556688
absolute error = 0.03905
relative error = 1.953 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.967331197867 -0.0456991283786
x2[1] (closed_form) = 0.994885592472 -0.00909086272442
absolute error = 0.04582
relative error = 4.605 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=34150.2MB, alloc=40.3MB, time=416.90
memory used=34194.2MB, alloc=40.3MB, time=417.43
t[1] = 1.9761 2.101
h = 0.001 0.003
x1[1] (numeric) = 2.02209142205 -0.0324371405031
x1[1] (closed_form) = 1.99987382773 -0.000215241017259
absolute error = 0.03914
relative error = 1.957 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.967361722866 -0.0460680691163
x2[1] (closed_form) = 0.994893536926 -0.00911912281616
absolute error = 0.04608
relative error = 4.631 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=34238.3MB, alloc=40.3MB, time=417.96
t[1] = 1.9771 2.104
h = 0.0001 0.004
x1[1] (numeric) = 2.02225113803 -0.0325408257348
x1[1] (closed_form) = 1.99987330933 -0.000214646778297
absolute error = 0.03932
relative error = 1.966 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.967392693102 -0.0464376594988
x2[1] (closed_form) = 0.994937969477 -0.00916761813726
absolute error = 0.04634
relative error = 4.658 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=34282.4MB, alloc=40.3MB, time=418.48
memory used=34326.3MB, alloc=40.3MB, time=419.00
t[1] = 1.9772 2.108
h = 0.003 0.006
x1[1] (numeric) = 2.02248427435 -0.032606974867
x1[1] (closed_form) = 1.99987246451 -0.000214116887038
absolute error = 0.0395
relative error = 1.975 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.967425223269 -0.0468080222096
x2[1] (closed_form) = 0.995010050313 -0.00920939905687
absolute error = 0.04663
relative error = 4.686 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=34370.3MB, alloc=40.3MB, time=419.53
t[1] = 1.9802 2.114
h = 0.0001 0.005
x1[1] (numeric) = 2.02279093796 -0.0328713219598
x1[1] (closed_form) = 1.99987156799 -0.000212708740248
absolute error = 0.0399
relative error = 1.995 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.967460272111 -0.0471814543855
x2[1] (closed_form) = 0.995091103399 -0.00932368933349
absolute error = 0.04687
relative error = 4.71 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=34414.3MB, alloc=40.3MB, time=420.05
memory used=34458.4MB, alloc=40.3MB, time=420.58
t[1] = 1.9803 2.119
h = 0.0001 0.003
x1[1] (numeric) = 2.02308054593 -0.0329499948831
x1[1] (closed_form) = 1.999870519 -0.000212042718686
absolute error = 0.04013
relative error = 2.007 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.967498506789 -0.0475580476886
x2[1] (closed_form) = 0.995183094802 -0.00937385553621
absolute error = 0.04716
relative error = 4.739 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=34502.8MB, alloc=40.3MB, time=421.12
t[1] = 1.9804 2.122
h = 0.001 0.001
x1[1] (numeric) = 2.02325451772 -0.0329998698045
x1[1] (closed_form) = 1.99986989647 -0.000211632157817
absolute error = 0.04027
relative error = 2.014 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.967539094964 -0.0479351180253
x2[1] (closed_form) = 0.99523816018 -0.00940426440531
absolute error = 0.04745
relative error = 4.768 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=34547.1MB, alloc=40.3MB, time=421.66
t[1] = 1.9814 2.123
h = 0.0001 0.004
x1[1] (numeric) = 2.02329935637 -0.0330736913562
x1[1] (closed_form) = 1.99986981515 -0.000211290552261
absolute error = 0.04036
relative error = 2.018 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.967580282579 -0.0483124653215
x2[1] (closed_form) = 0.995247441814 -0.00943244471586
absolute error = 0.04772
relative error = 4.794 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=34591.1MB, alloc=40.3MB, time=422.18
memory used=34634.9MB, alloc=40.3MB, time=422.70
t[1] = 1.9815 2.127
h = 0.003 0.006
x1[1] (numeric) = 2.02353802133 -0.0331370652932
x1[1] (closed_form) = 1.99986898414 -0.000210747048184
absolute error = 0.04055
relative error = 2.028 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.96762256292 -0.0486901880782
x2[1] (closed_form) = 0.995321700533 -0.00947178704789
absolute error = 0.04801
relative error = 4.824 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=34678.9MB, alloc=40.3MB, time=423.22
t[1] = 1.9845 2.133
h = 0.0001 0.005
x1[1] (numeric) = 2.02385500869 -0.0334010970402
x1[1] (closed_form) = 1.99986811826 -0.000209328236662
absolute error = 0.04095
relative error = 2.048 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.967667486104 -0.0490709721395
x2[1] (closed_form) = 0.995407789432 -0.00958386972024
absolute error = 0.04826
relative error = 4.848 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=34723.0MB, alloc=40.3MB, time=423.75
memory used=34767.2MB, alloc=40.3MB, time=424.27
t[1] = 1.9846 2.138
h = 0.0001 0.003
x1[1] (numeric) = 2.02415141304 -0.0334762628997
x1[1] (closed_form) = 1.99986708656 -0.000208645348536
absolute error = 0.04119
relative error = 2.06 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.967715733868 -0.0494548938899
x2[1] (closed_form) = 0.995502439226 -0.00963089903457
absolute error = 0.04856
relative error = 4.878 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=34811.5MB, alloc=40.3MB, time=424.81
t[1] = 1.9847 2.141
h = 0.001 0.001
x1[1] (numeric) = 2.02432952031 -0.0335240745814
x1[1] (closed_form) = 1.99986647458 -0.000208224846398
absolute error = 0.04133
relative error = 2.067 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.967766390283 -0.0498392414443
x2[1] (closed_form) = 0.99555911055 -0.00965943326459
absolute error = 0.04886
relative error = 4.907 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=34855.9MB, alloc=40.3MB, time=425.35
memory used=34900.1MB, alloc=40.3MB, time=425.88
t[1] = 1.9857 2.142
h = 0.001 0.003
x1[1] (numeric) = 2.02437648539 -0.0335985071796
x1[1] (closed_form) = 1.99986640009 -0.000207883229682
absolute error = 0.04142
relative error = 2.071 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.967817664137 -0.0502238557619
x2[1] (closed_form) = 0.995569548859 -0.00968748071778
absolute error = 0.04913
relative error = 4.934 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=34943.9MB, alloc=40.3MB, time=426.40
t[1] = 1.9867 2.145
h = 0.0001 0.004
x1[1] (numeric) = 2.02454767977 -0.0337001768497
x1[1] (closed_form) = 1.9998659112 -0.000207274117288
absolute error = 0.0416
relative error = 2.08 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.967869436482 -0.0506091231536
x2[1] (closed_form) = 0.995618754295 -0.00973303198535
absolute error = 0.04941
relative error = 4.962 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=34988.1MB, alloc=40.3MB, time=426.93
t[1] = 1.9868 2.149
h = 0.003 0.006
x1[1] (numeric) = 2.02479402094 -0.0337595504041
x1[1] (closed_form) = 1.99986509667 -0.000206715432741
absolute error = 0.0418
relative error = 2.09 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.967922875157 -0.0509951120502
x2[1] (closed_form) = 0.995695488767 -0.00976944613399
absolute error = 0.04971
relative error = 4.992 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=35032.1MB, alloc=40.3MB, time=427.45
memory used=35076.1MB, alloc=40.3MB, time=427.98
t[1] = 1.9898 2.155
h = 0.0001 0.005
x1[1] (numeric) = 2.02512544412 -0.034022926563
x1[1] (closed_form) = 1.99986426662 -0.000205285515476
absolute error = 0.04221
relative error = 2.111 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.967979101384 -0.0513841646331
x2[1] (closed_form) = 0.995787411317 -0.00987878054769
absolute error = 0.04996
relative error = 5.017 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=35120.1MB, alloc=40.3MB, time=428.50
t[1] = 1.9899 2.16
h = 0.0001 0.003
x1[1] (numeric) = 2.02543128592 -0.034093043769
x1[1] (closed_form) = 1.99986325557 -0.000204583825943
absolute error = 0.04245
relative error = 2.123 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.968038815204 -0.0517763408717
x2[1] (closed_form) = 0.995885077983 -0.00992204773377
absolute error = 0.05027
relative error = 5.048 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=35164.4MB, alloc=40.3MB, time=429.03
memory used=35208.8MB, alloc=40.3MB, time=429.57
t[1] = 1.99 2.163
h = 0.001 0.001
x1[1] (numeric) = 2.02561512539 -0.0341378879175
x1[1] (closed_form) = 1.99986265617 -0.000204152256395
absolute error = 0.0426
relative error = 2.13 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.968101006436 -0.0521688887122
x2[1] (closed_form) = 0.995943572461 -0.00994833312657
absolute error = 0.05057
relative error = 5.078 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=35252.9MB, alloc=40.3MB, time=430.10
t[1] = 1.991 2.164
h = 0.001 0.003
x1[1] (numeric) = 2.02566506177 -0.034213131906
x1[1] (closed_form) = 1.99986258957 -0.000203810897675
absolute error = 0.04269
relative error = 2.135 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.968163836943 -0.0525616931764
x2[1] (closed_form) = 0.995955362596 -0.00997618804119
absolute error = 0.05085
relative error = 5.106 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=35296.9MB, alloc=40.3MB, time=430.63
memory used=35341.0MB, alloc=40.3MB, time=431.16
t[1] = 1.992 2.167
h = 0.0001 0.004
x1[1] (numeric) = 2.02584307353 -0.0343133714135
x1[1] (closed_form) = 1.9998621167 -0.000203194453757
absolute error = 0.04288
relative error = 2.144 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.968227195258 -0.0529551529655
x2[1] (closed_form) = 0.996007077187 -0.0100199888977
absolute error = 0.05114
relative error = 5.134 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=35385.0MB, alloc=40.3MB, time=431.68
t[1] = 1.9921 2.171
h = 0.003 0.006
x1[1] (numeric) = 2.026097164 -0.0343684428707
x1[1] (closed_form) = 1.9998613189 -0.000202621033375
absolute error = 0.04308
relative error = 2.154 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.96829227888 -0.0533493069573
x2[1] (closed_form) = 0.996086181327 -0.0100533366857
absolute error = 0.05145
relative error = 5.165 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=35428.9MB, alloc=40.3MB, time=432.20
t[1] = 1.9951 2.177
h = 0.0001 0.005
x1[1] (numeric) = 2.02644334593 -0.0346307580801
x1[1] (closed_form) = 1.99986052473 -0.000201180855816
absolute error = 0.0435
relative error = 2.175 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.968360298303 -0.053746523194
x2[1] (closed_form) = 0.996183871847 -0.0101596373345
absolute error = 0.05171
relative error = 5.191 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=35473.1MB, alloc=40.3MB, time=432.73
memory used=35517.0MB, alloc=40.3MB, time=433.26
t[1] = 1.9952 2.182
h = 0.0001 0.003
x1[1] (numeric) = 2.02675871148 -0.0346954526092
x1[1] (closed_form) = 1.99985953462 -0.000200460920532
absolute error = 0.04374
relative error = 2.187 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.968431971875 -0.0541468443442
x2[1] (closed_form) = 0.996284417495 -0.0101989721439
absolute error = 0.05203
relative error = 5.222 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=35561.3MB, alloc=40.3MB, time=433.79
t[1] = 1.9953 2.185
h = 0.001 0.001
x1[1] (numeric) = 2.02694833824 -0.0347371043957
x1[1] (closed_form) = 1.99985894798 -0.000200018620096
absolute error = 0.04389
relative error = 2.195 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.968506191821 -0.054547479747
x2[1] (closed_form) = 0.996344652891 -0.0102229060544
absolute error = 0.05234
relative error = 5.253 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=35605.6MB, alloc=40.3MB, time=434.32
memory used=35649.8MB, alloc=40.3MB, time=434.86
t[1] = 1.9963 2.186
h = 0.001 0.003
x1[1] (numeric) = 2.02700133795 -0.0348130986796
x1[1] (closed_form) = 1.99985888921 -0.000199677690526
absolute error = 0.04399
relative error = 2.199 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.968581073129 -0.0549483608051
x2[1] (closed_form) = 0.996357799354 -0.0102505065588
absolute error = 0.05263
relative error = 5.282 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=35693.8MB, alloc=40.3MB, time=435.39
t[1] = 1.9973 2.189
h = 0.0001 0.004
x1[1] (numeric) = 2.02718628937 -0.0349116901697
x1[1] (closed_form) = 1.99985843245 -0.000199054306382
absolute error = 0.04418
relative error = 2.209 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.968656512329 -0.0553498987064
x2[1] (closed_form) = 0.99641196961 -0.0102924287159
absolute error = 0.05292
relative error = 5.311 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=35737.8MB, alloc=40.3MB, time=435.92
memory used=35781.9MB, alloc=40.3MB, time=436.45
t[1] = 1.9974 2.193
h = 0.003 0.006
x1[1] (numeric) = 2.0274481959 -0.0349621487315
x1[1] (closed_form) = 1.99985765161 -0.00019846659762
absolute error = 0.04438
relative error = 2.219 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.968733736496 -0.0557521012701
x2[1] (closed_form) = 0.99649333016 -0.0103225753461
absolute error = 0.05324
relative error = 5.342 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=35825.9MB, alloc=40.3MB, time=436.98
t[1] = 2.0004 2.199
h = 0.0001 0.005
x1[1] (numeric) = 2.02780945625 -0.0352229794025
x1[1] (closed_form) = 1.99985689334 -0.000197017001526
absolute error = 0.04481
relative error = 2.241 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.968814048239 -0.0561573606261
x2[1] (closed_form) = 0.996596709631 -0.0104255568789
absolute error = 0.05351
relative error = 5.369 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=35870.0MB, alloc=40.3MB, time=437.50
t[1] = 2.0005 2.204
h = 0.0001 0.003
x1[1] (numeric) = 2.02813442386 -0.0352818660887
x1[1] (closed_form) = 1.99985592446 -0.000196279379583
absolute error = 0.04506
relative error = 2.253 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.968898184189 -0.0565657012353
x2[1] (closed_form) = 0.996699987462 -0.010460793547
absolute error = 0.05384
relative error = 5.401 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=35914.2MB, alloc=40.3MB, time=438.04
memory used=35958.6MB, alloc=40.3MB, time=438.58
t[1] = 2.0006 2.207
h = 0.001 0.001
x1[1] (numeric) = 2.02832988828 -0.0353200939002
x1[1] (closed_form) = 1.99985535073 -0.000195826686698
absolute error = 0.04522
relative error = 2.261 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.968984935592 -0.0569742955199
x2[1] (closed_form) = 0.996761876177 -0.0104822759937
absolute error = 0.05416
relative error = 5.433 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=36002.8MB, alloc=40.3MB, time=439.12
t[1] = 2.0016 2.208
h = 0.001 0.003
x1[1] (numeric) = 2.02838604387 -0.0353967734747
x1[1] (closed_form) = 1.99985529975 -0.000195486355411
absolute error = 0.04531
relative error = 2.266 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.96907237068 -0.0573831236349
x2[1] (closed_form) = 0.99677638076 -0.0105095594163
absolute error = 0.05445
relative error = 5.462 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=36046.9MB, alloc=40.3MB, time=439.65
memory used=36091.0MB, alloc=40.3MB, time=440.18
t[1] = 2.0026 2.211
h = 0.0001 0.004
x1[1] (numeric) = 2.02857805428 -0.0354934906689
x1[1] (closed_form) = 1.99985485916 -0.000194856421747
absolute error = 0.04551
relative error = 2.276 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.96916039451 -0.0577926093411
x2[1] (closed_form) = 0.996832946967 -0.0105494757216
absolute error = 0.05475
relative error = 5.492 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=36134.9MB, alloc=40.3MB, time=440.70
t[1] = 2.0027 2.215
h = 0.003 0.006
x1[1] (numeric) = 2.02884783685 -0.0355390164068
x1[1] (closed_form) = 1.99985409549 -0.00019425487462
absolute error = 0.04572
relative error = 2.286 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.969250263606 -0.0582027278588
x2[1] (closed_form) = 0.996916443573 -0.0105762901285
absolute error = 0.05508
relative error = 5.525 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=36178.9MB, alloc=40.3MB, time=441.22
memory used=36223.0MB, alloc=40.3MB, time=441.75
t[1] = 2.0057 2.221
h = 0.0001 0.005
x1[1] (numeric) = 2.02922449151 -0.0357979203758
x1[1] (closed_form) = 1.99985337313 -0.000192796697671
absolute error = 0.04616
relative error = 2.308 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.969343375554 -0.0586158935129
x2[1] (closed_form) = 0.997025419519 -0.0106756679432
absolute error = 0.05536
relative error = 5.552 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=36267.1MB, alloc=40.3MB, time=442.28
t[1] = 2.0058 2.226
h = 0.0001 0.003
x1[1] (numeric) = 2.029559131 -0.0358506028586
x1[1] (closed_form) = 1.99985242574 -0.000192041951277
absolute error = 0.04641
relative error = 2.321 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.969440485218 -0.0590321116288
x2[1] (closed_form) = 0.997131273935 -0.0107066456291
absolute error = 0.0557
relative error = 5.585 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=36311.3MB, alloc=40.3MB, time=442.81
t[1] = 2.0059 2.229
h = 0.001 0.001
x1[1] (numeric) = 2.02976047843 -0.0358851682619
x1[1] (closed_form) = 1.9998518651 -0.000191579206105
absolute error = 0.04657
relative error = 2.329 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.969540279449 -0.0594485195337
x2[1] (closed_form) = 0.997194723074 -0.0107255795578
absolute error = 0.05602
relative error = 5.618 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=36355.8MB, alloc=40.3MB, time=443.35
memory used=36399.9MB, alloc=40.3MB, time=443.88
t[1] = 2.0069 2.23
h = 0.0001 0.004
x1[1] (numeric) = 2.02981988292 -0.0359624641052
x1[1] (closed_form) = 1.99985182184 -0.000191239640145
absolute error = 0.04667
relative error = 2.333 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.96964077991 -0.0598651485611
x2[1] (closed_form) = 0.997210584799 -0.0107524825396
absolute error = 0.05632
relative error = 5.648 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=36444.0MB, alloc=40.3MB, time=444.40
t[1] = 2.007 2.234
h = 0.003 0.006
x1[1] (numeric) = 2.0300954397 -0.0360040923421
x1[1] (closed_form) = 1.99985107297 -0.0001906263356
absolute error = 0.04688
relative error = 2.344 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.969742549068 -0.060282036991
x2[1] (closed_form) = 0.997295776589 -0.010776303471
absolute error = 0.05666
relative error = 5.681 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=36488.0MB, alloc=40.3MB, time=444.93
memory used=36532.1MB, alloc=40.3MB, time=445.46
t[1] = 2.01 2.24
h = 0.0001 0.005
x1[1] (numeric) = 2.03048357947 -0.0362611539943
x1[1] (closed_form) = 1.99985038143 -0.000189161012383
absolute error = 0.04732
relative error = 2.366 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.969847697805 -0.0607019458879
x2[1] (closed_form) = 0.997409437877 -0.0108722875287
absolute error = 0.05694
relative error = 5.709 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=36576.1MB, alloc=40.3MB, time=445.98
t[1] = 2.0101 2.245
h = 0.0001 0.003
x1[1] (numeric) = 2.03082530392 -0.0363089381775
x1[1] (closed_form) = 1.99984945255 -0.000188391718006
absolute error = 0.04758
relative error = 2.379 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.969956994999 -0.061124861545
x2[1] (closed_form) = 0.997517325677 -0.0108994465011
absolute error = 0.05729
relative error = 5.743 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=36620.4MB, alloc=40.3MB, time=446.51
t[1] = 2.0102 2.248
h = 0.001 0.001
x1[1] (numeric) = 2.03103097243 -0.0363406020453
x1[1] (closed_form) = 1.99984890316 -0.000187920435589
absolute error = 0.04774
relative error = 2.387 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.970069030744 -0.0615479022816
x2[1] (closed_form) = 0.997582007731 -0.0109160944769
absolute error = 0.05762
relative error = 5.776 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=36664.9MB, alloc=40.3MB, time=447.05
memory used=36709.0MB, alloc=40.3MB, time=447.59
t[1] = 2.0112 2.249
h = 0.001 0.003
x1[1] (numeric) = 2.03109283999 -0.0364182733925
x1[1] (closed_form) = 1.99984886653 -0.000187581569426
absolute error = 0.04784
relative error = 2.392 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.970181791258 -0.0619711502661
x2[1] (closed_form) = 0.997599029129 -0.0109426027155
absolute error = 0.05793
relative error = 5.806 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=36753.1MB, alloc=40.3MB, time=448.12
t[1] = 2.0122 2.252
h = 0.0001 0.004
x1[1] (numeric) = 2.03129738207 -0.0365110826916
x1[1] (closed_form) = 1.99984845608 -0.000186940291781
absolute error = 0.04805
relative error = 2.403 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.970295200136 -0.0623950521244
x2[1] (closed_form) = 0.997659845961 -0.0109784266986
absolute error = 0.05825
relative error = 5.838 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=36797.3MB, alloc=40.3MB, time=448.64
memory used=36841.5MB, alloc=40.3MB, time=449.17
t[1] = 2.0123 2.256
h = 0.003 0.006
x1[1] (numeric) = 2.03158093759 -0.0365471342153
x1[1] (closed_form) = 1.99984772477 -0.000186313989883
absolute error = 0.04826
relative error = 2.413 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.970410565255 -0.062819515319
x2[1] (closed_form) = 0.997746929883 -0.0109986842875
absolute error = 0.05859
relative error = 5.872 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=36885.5MB, alloc=40.3MB, time=449.69
t[1] = 2.0153 2.262
h = 0.0001 0.005
x1[1] (numeric) = 2.03198511099 -0.0368013806081
x1[1] (closed_form) = 1.99984706911 -0.000184841632797
absolute error = 0.04872
relative error = 2.436 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.970529471005 -0.0632469812388
x2[1] (closed_form) = 0.997865976089 -0.0110905406084
absolute error = 0.05889
relative error = 5.901 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=36929.6MB, alloc=40.3MB, time=450.22
memory used=36973.9MB, alloc=40.3MB, time=450.75
t[1] = 2.0154 2.267
h = 0.0001 0.003
x1[1] (numeric) = 2.03233665124 -0.0368421622027
x1[1] (closed_form) = 1.9998461622 -0.000184056264474
absolute error = 0.04898
relative error = 2.449 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.970652704285 -0.0636774153656
x2[1] (closed_form) = 0.99797612625 -0.0111131580092
absolute error = 0.05924
relative error = 5.936 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=37018.2MB, alloc=40.3MB, time=451.29
t[1] = 2.0155 2.27
h = 0.001 0.001
x1[1] (numeric) = 2.0325482958 -0.0368696832832
x1[1] (closed_form) = 1.99984562617 -0.000183575565047
absolute error = 0.04915
relative error = 2.457 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.970778744849 -0.0641079046851
x2[1] (closed_form) = 0.998042180992 -0.0111270868176
absolute error = 0.05958
relative error = 5.97 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=37062.5MB, alloc=40.3MB, time=451.82
t[1] = 2.0165 2.271
h = 0.001 0.003
x1[1] (numeric) = 2.03261359993 -0.0369478323728
x1[1] (closed_form) = 1.99984559715 -0.000183237770031
absolute error = 0.04925
relative error = 2.463 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.970905533005 -0.064538586915
x2[1] (closed_form) = 0.998060549378 -0.0111530953841
absolute error = 0.05989
relative error = 6.001 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=37106.8MB, alloc=40.3MB, time=452.35
memory used=37151.1MB, alloc=40.3MB, time=452.88
t[1] = 2.0175 2.274
h = 0.0001 0.004
x1[1] (numeric) = 2.03282555158 -0.0370380606005
x1[1] (closed_form) = 1.999845203 -0.000182591055216
absolute error = 0.04946
relative error = 2.473 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.971033002407 -0.0649699213881
x2[1] (closed_form) = 0.998123555478 -0.011186559583
absolute error = 0.06022
relative error = 6.033 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=37195.0MB, alloc=40.3MB, time=453.41
t[1] = 2.0176 2.278
h = 0.003 0.006
x1[1] (numeric) = 2.03311714326 -0.0370681884135
x1[1] (closed_form) = 1.99984448943 -0.000181952212023
absolute error = 0.04968
relative error = 2.484 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.971162489712 -0.0654017785623
x2[1] (closed_form) = 0.998212391536 -0.0112031354558
absolute error = 0.06057
relative error = 6.068 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=37239.2MB, alloc=40.3MB, time=453.94
memory used=37283.4MB, alloc=40.3MB, time=454.47
t[1] = 2.0206 2.284
h = 0.0001 0.005
x1[1] (numeric) = 2.03353765105 -0.0373191205158
x1[1] (closed_form) = 1.99984386962 -0.000180473645201
absolute error = 0.05015
relative error = 2.507 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.971295682117 -0.0658366159748
x2[1] (closed_form) = 0.998336691268 -0.0112905851211
absolute error = 0.06088
relative error = 6.098 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=37327.5MB, alloc=40.3MB, time=454.99
t[1] = 2.0207 2.289
h = 0.0001 0.003
x1[1] (numeric) = 2.03389904865 -0.0373524699744
x1[1] (closed_form) = 1.99984298491 -0.000179672772454
absolute error = 0.05041
relative error = 2.521 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.971433384421 -0.0662743773099
x2[1] (closed_form) = 0.998448923914 -0.0113085167076
absolute error = 0.06125
relative error = 6.134 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=37371.6MB, alloc=40.3MB, time=455.52
memory used=37416.2MB, alloc=40.3MB, time=456.06
t[1] = 2.0208 2.292
h = 0.001 0.001
x1[1] (numeric) = 2.03411669783 -0.0373755896021
x1[1] (closed_form) = 1.99984246235 -0.000179183000161
absolute error = 0.05058
relative error = 2.529 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.971573962529 -0.0667121204191
x2[1] (closed_form) = 0.99851624382 -0.011319639181
absolute error = 0.0616
relative error = 6.168 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=37460.3MB, alloc=40.3MB, time=456.59
t[1] = 2.0218 2.293
h = 0.001 0.003
x1[1] (numeric) = 2.03418553219 -0.0374541348947
x1[1] (closed_form) = 1.99984244089 -0.000178846437057
absolute error = 0.05068
relative error = 2.534 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.971715311221 -0.067150041143
x2[1] (closed_form) = 0.998535949986 -0.0113450834414
absolute error = 0.06192
relative error = 6.2 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=37504.3MB, alloc=40.3MB, time=457.12
t[1] = 2.0228 2.296
h = 0.0001 0.004
x1[1] (numeric) = 2.03440499794 -0.0375415213674
x1[1] (closed_form) = 1.99984206307 -0.000178194671814
absolute error = 0.0509
relative error = 2.545 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.971857374792 -0.0675886115585
x2[1] (closed_form) = 0.998601061657 -0.0113760678886
absolute error = 0.06225
relative error = 6.233 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=37548.3MB, alloc=40.3MB, time=457.64
memory used=37592.5MB, alloc=40.3MB, time=458.17
t[1] = 2.0229 2.3
h = 0.003 0.006
x1[1] (numeric) = 2.03470465482 -0.0375653692976
x1[1] (closed_form) = 1.99984136742 -0.000177543744967
absolute error = 0.05112
relative error = 2.556 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.972001518379 -0.0680276634533
x2[1] (closed_form) = 0.998691503235 -0.0113888487505
absolute error = 0.06261
relative error = 6.269 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=37636.6MB, alloc=40.3MB, time=458.70
t[1] = 2.0259 2.306
h = 0.0001 0.005
x1[1] (numeric) = 2.03514179153 -0.03781246829
x1[1] (closed_form) = 1.99984078339 -0.000176059787011
absolute error = 0.0516
relative error = 2.58 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.97214953491 -0.0684696681465
x2[1] (closed_form) = 0.998820911419 -0.0114716159807
absolute error = 0.06293
relative error = 6.3 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=37680.7MB, alloc=40.3MB, time=459.22
memory used=37724.8MB, alloc=40.3MB, time=459.75
t[1] = 2.026 2.311
h = 0.0001 0.003
x1[1] (numeric) = 2.03551307752 -0.0378379448404
x1[1] (closed_form) = 1.99983992109 -0.000175243981254
absolute error = 0.05188
relative error = 2.594 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.972302246927 -0.0689145465183
x2[1] (closed_form) = 0.998935038514 -0.0114847241111
absolute error = 0.0633
relative error = 6.337 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=37769.1MB, alloc=40.3MB, time=460.29
t[1] = 2.0261 2.314
h = 0.001 0.001
x1[1] (numeric) = 2.03573675366 -0.0378563974946
x1[1] (closed_form) = 1.99983941214 -0.000174745481232
absolute error = 0.05204
relative error = 2.602 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.972457902956 -0.0693593296345
x2[1] (closed_form) = 0.999003511141 -0.011492957019
absolute error = 0.06366
relative error = 6.372 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=37813.3MB, alloc=40.3MB, time=460.82
memory used=37857.4MB, alloc=40.3MB, time=461.35
t[1] = 2.0271 2.315
h = 0.001 0.003
x1[1] (numeric) = 2.03580921193 -0.0379352530281
x1[1] (closed_form) = 1.99983939816 -0.000174410308484
absolute error = 0.05215
relative error = 2.608 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.972614352705 -0.0698042740836
x2[1] (closed_form) = 0.999024542916 -0.0115177721218
absolute error = 0.06399
relative error = 6.405 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=37901.6MB, alloc=40.3MB, time=461.88
t[1] = 2.0281 2.318
h = 0.0001 0.004
x1[1] (numeric) = 2.03603629178 -0.0380195281266
x1[1] (closed_form) = 1.99983903669 -0.000173753878052
absolute error = 0.05237
relative error = 2.619 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.97277155171 -0.0702498647092
x2[1] (closed_form) = 0.999091670314 -0.011546159409
absolute error = 0.06433
relative error = 6.439 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=37945.5MB, alloc=40.3MB, time=462.40
t[1] = 2.0282 2.322
h = 0.003 0.006
x1[1] (numeric) = 2.03634403408 -0.0380367308323
x1[1] (closed_form) = 1.99983835913 -0.000173091326519
absolute error = 0.0526
relative error = 2.63 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.972930893242 -0.0706958929307
x2[1] (closed_form) = 0.999183564332 -0.011555037387
absolute error = 0.06471
relative error = 6.475 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=37989.4MB, alloc=40.3MB, time=462.92
memory used=38033.5MB, alloc=40.3MB, time=463.45
t[1] = 2.0312 2.328
h = 0.0001 0.005
x1[1] (numeric) = 2.0367980873 -0.0382794578012
x1[1] (closed_form) = 1.9998378108 -0.000171602790148
absolute error = 0.05309
relative error = 2.655 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.973094278877 -0.0711448413464
x2[1] (closed_form) = 0.999317922223 -0.0116328501798
absolute error = 0.06503
relative error = 6.507 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=38077.6MB, alloc=40.3MB, time=463.98
t[1] = 2.0313 2.333
h = 0.0001 0.003
x1[1] (numeric) = 2.03717928171 -0.0382966094572
x1[1] (closed_form) = 1.99983697112 -0.000170772624377
absolute error = 0.05337
relative error = 2.669 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.97326254872 -0.0715966070055
x2[1] (closed_form) = 0.999433747786 -0.0116410042407
absolute error = 0.06542
relative error = 6.545 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=38121.8MB, alloc=40.3MB, time=464.51
memory used=38166.3MB, alloc=40.3MB, time=465.05
t[1] = 2.0314 2.336
h = 0.001 0.001
x1[1] (numeric) = 2.03740900055 -0.0383101227646
x1[1] (closed_form) = 1.99983647589 -0.000170265742569
absolute error = 0.05354
relative error = 2.677 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.973433830366 -0.0720481966895
x2[1] (closed_form) = 0.999503255897 -0.0116462685461
absolute error = 0.06579
relative error = 6.582 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=38210.4MB, alloc=40.3MB, time=465.58
t[1] = 2.0324 2.337
h = 0.0001 0.004
x1[1] (numeric) = 2.03748517635 -0.0383891980475
x1[1] (closed_form) = 1.99983646932 -0.000169932116243
absolute error = 0.05365
relative error = 2.683 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.973605928989 -0.0724999304109
x2[1] (closed_form) = 0.999525598107 -0.0116703895519
absolute error = 0.06612
relative error = 6.615 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=38254.6MB, alloc=40.3MB, time=466.11
memory used=38298.7MB, alloc=40.3MB, time=466.63
t[1] = 2.0325 2.341
h = 0.003 0.006
x1[1] (numeric) = 2.03779880265 -0.0384012160131
x1[1] (closed_form) = 1.99983580732 -0.000169259708988
absolute error = 0.05388
relative error = 2.694 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.973779475425 -0.0729517697896
x2[1] (closed_form) = 0.999618566823 -0.0116758113633
absolute error = 0.0665
relative error = 6.652 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=38342.9MB, alloc=40.3MB, time=467.16
t[1] = 2.0355 2.347
h = 0.0001 0.005
x1[1] (numeric) = 2.03826541264 -0.0386402283135
x1[1] (closed_form) = 1.9998352896 -0.000167767454082
absolute error = 0.05438
relative error = 2.719 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.973957214107 -0.0734064803626
x2[1] (closed_form) = 0.99975698438 -0.011749088955
absolute error = 0.06684
relative error = 6.685 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=38387.0MB, alloc=40.3MB, time=467.69
t[1] = 2.0356 2.352
h = 0.0001 0.003
x1[1] (numeric) = 2.03865381029 -0.0386508882255
x1[1] (closed_form) = 1.99983446938 -0.000166925115061
absolute error = 0.05466
relative error = 2.733 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.97413999802 -0.0738639360454
x2[1] (closed_form) = 0.999874048107 -0.0117528628905
absolute error = 0.06723
relative error = 6.723 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=38431.1MB, alloc=40.3MB, time=468.23
memory used=38475.8MB, alloc=40.3MB, time=468.78
t[1] = 2.0357 2.355
h = 0.001 0.001
x1[1] (numeric) = 2.03888793457 -0.0386605381889
x1[1] (closed_form) = 1.99983398595 -0.000166411130825
absolute error = 0.05484
relative error = 2.742 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.974325844554 -0.074321136205
x2[1] (closed_form) = 0.999944313534 -0.0117555016723
absolute error = 0.06761
relative error = 6.761 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=38519.9MB, alloc=40.3MB, time=469.31
t[1] = 2.0367 2.356
h = 0.001 0.003
x1[1] (numeric) = 2.03896691433 -0.0387396771685
x1[1] (closed_form) = 1.99983398572 -0.000166078871656
absolute error = 0.05495
relative error = 2.748 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.974512526701 -0.0747784623588
x2[1] (closed_form) = 0.999967759936 -0.0117789579445
absolute error = 0.06795
relative error = 6.795 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=38564.1MB, alloc=40.3MB, time=469.84
memory used=38608.4MB, alloc=40.3MB, time=470.37
t[1] = 2.0377 2.359
h = 0.0001 0.004
x1[1] (numeric) = 2.03920742368 -0.0388177812917
x1[1] (closed_form) = 1.99983365466 -0.00016541458488
absolute error = 0.05518
relative error = 2.759 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.974700023829 -0.0752364221368
x2[1] (closed_form) = 1.00003834409 -0.0118021888395
absolute error = 0.06831
relative error = 6.83 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=38652.4MB, alloc=40.3MB, time=470.89
t[1] = 2.0378 2.363
h = 0.003 0.006
x1[1] (numeric) = 2.03952917834 -0.0388224188281
x1[1] (closed_form) = 1.99983301103 -0.000164731408003
absolute error = 0.05541
relative error = 2.771 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.974889776701 -0.075694724414
x2[1] (closed_form) = 1.00013246272 -0.0118035246284
absolute error = 0.0687
relative error = 6.868 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=38696.4MB, alloc=40.3MB, time=471.42
t[1] = 2.0408 2.369
h = 0.0001 0.005
x1[1] (numeric) = 2.04001328774 -0.0390559760811
x1[1] (closed_form) = 1.99983252882 -0.000163236071532
absolute error = 0.05592
relative error = 2.796 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.975083898293 -0.0761558554772
x2[1] (closed_form) = 1.00027549524 -0.0118713561866
absolute error = 0.06904
relative error = 6.902 %
Correct digits = 1
memory used=38740.7MB, alloc=40.3MB, time=471.95
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=38784.9MB, alloc=40.3MB, time=472.48
t[1] = 2.0409 2.374
h = 0.0001 0.003
x1[1] (numeric) = 2.04041163784 -0.0390574006619
x1[1] (closed_form) = 1.99983173157 -0.000162380439828
absolute error = 0.05621
relative error = 2.811 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.975283258682 -0.0766196635744
x2[1] (closed_form) = 1.0003938711 -0.0118699556999
absolute error = 0.06945
relative error = 6.942 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=38829.1MB, alloc=40.3MB, time=473.01
t[1] = 2.041 2.377
h = 0.001 0.001
x1[1] (numeric) = 2.04065183852 -0.0390615625544
x1[1] (closed_form) = 1.99983126206 -0.000161858717891
absolute error = 0.05639
relative error = 2.82 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.975485748226 -0.0770831287995
x2[1] (closed_form) = 1.00046494078 -0.0118694923613
absolute error = 0.06983
relative error = 6.98 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=38873.6MB, alloc=40.3MB, time=473.56
memory used=38917.8MB, alloc=40.3MB, time=474.09
t[1] = 2.042 2.378
h = 0.001 0.003
x1[1] (numeric) = 2.04073472472 -0.0391407396356
x1[1] (closed_form) = 1.9998312691 -0.000161528289966
absolute error = 0.0565
relative error = 2.825 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.975689096727 -0.0775467008699
x2[1] (closed_form) = 1.00048966051 -0.0118921341891
absolute error = 0.07018
relative error = 7.014 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=38961.9MB, alloc=40.3MB, time=474.62
t[1] = 2.043 2.381
h = 0.0001 0.004
x1[1] (numeric) = 2.04098313591 -0.0392148938285
x1[1] (closed_form) = 1.9998309544 -0.000160860430257
absolute error = 0.05673
relative error = 2.837 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.975893296523 -0.0780109001189
x2[1] (closed_form) = 1.0005619687 -0.0119124501553
absolute error = 0.07055
relative error = 7.051 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=39006.0MB, alloc=40.3MB, time=475.15
memory used=39050.1MB, alloc=40.3MB, time=475.67
t[1] = 2.0431 2.385
h = 0.003 0.006
x1[1] (numeric) = 2.04131301016 -0.0392117587625
x1[1] (closed_form) = 1.99983032928 -0.000160166945298
absolute error = 0.05697
relative error = 2.849 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.976099815148 -0.07847539024
x2[1] (closed_form) = 1.00065706679 -0.011909609488
absolute error = 0.07095
relative error = 7.09 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=39094.1MB, alloc=40.3MB, time=476.20
t[1] = 2.0461 2.391
h = 0.0001 0.005
x1[1] (numeric) = 2.04181488153 -0.0394392610237
x1[1] (closed_form) = 1.99982988246 -0.000158669321422
absolute error = 0.0575
relative error = 2.875 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.976310882116 -0.07894266098
x2[1] (closed_form) = 1.00080451679 -0.011971737549
absolute error = 0.07131
relative error = 7.125 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=39138.2MB, alloc=40.3MB, time=476.73
t[1] = 2.0462 2.396
h = 0.0001 0.003
x1[1] (numeric) = 2.04222316785 -0.0394309654874
x1[1] (closed_form) = 1.99982910833 -0.000157800973023
absolute error = 0.05779
relative error = 2.89 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.976527384324 -0.0794125338381
x2[1] (closed_form) = 1.00092398754 -0.0119650545184
absolute error = 0.07172
relative error = 7.165 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=39182.4MB, alloc=40.3MB, time=477.26
memory used=39227.0MB, alloc=40.3MB, time=477.80
t[1] = 2.0463 2.399
h = 0.001 0.001
x1[1] (numeric) = 2.04246943912 -0.0394293468724
x1[1] (closed_form) = 1.99982865284 -0.000157271860718
absolute error = 0.05797
relative error = 2.899 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.976747081498 -0.0798819725705
x2[1] (closed_form) = 1.00099573141 -0.0119614234571
absolute error = 0.07212
relative error = 7.204 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=39271.2MB, alloc=40.3MB, time=478.34
t[1] = 2.0473 2.4
h = 0.001 0.003
x1[1] (numeric) = 2.04255632427 -0.0395084575544
x1[1] (closed_form) = 1.99982866707 -0.000156943413037
absolute error = 0.05809
relative error = 2.905 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.976967661025 -0.0803514979089
x2[1] (closed_form) = 1.00102170055 -0.0119831864284
absolute error = 0.07248
relative error = 7.24 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=39315.4MB, alloc=40.3MB, time=478.86
memory used=39359.5MB, alloc=40.3MB, time=479.39
t[1] = 2.0483 2.403
h = 0.0001 0.004
x1[1] (numeric) = 2.04281271586 -0.0395783560922
x1[1] (closed_form) = 1.99982836873 -0.000156272358249
absolute error = 0.05832
relative error = 2.916 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.977189128871 -0.0808216428502
x2[1] (closed_form) = 1.00109561987 -0.0120004828036
absolute error = 0.07286
relative error = 7.277 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=39403.7MB, alloc=40.3MB, time=479.92
t[1] = 2.0484 2.407
h = 0.003 0.006
x1[1] (numeric) = 2.04315069029 -0.0395670472626
x1[1] (closed_form) = 1.99982776224 -0.000155569027133
absolute error = 0.05857
relative error = 2.929 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.977412978777 -0.0812920240923
x2[1] (closed_form) = 1.00119152132 -0.0119933819484
absolute error = 0.07326
relative error = 7.317 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=39447.6MB, alloc=40.3MB, time=480.44
memory used=39491.7MB, alloc=40.3MB, time=480.97
t[1] = 2.0514 2.413
h = 0.0001 0.005
x1[1] (numeric) = 2.04367057641 -0.0397878734907
x1[1] (closed_form) = 1.99982735065 -0.000154069902808
absolute error = 0.0591
relative error = 2.955 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.977641559719 -0.0817651318017
x2[1] (closed_form) = 1.00134317793 -0.0120495553327
absolute error = 0.07363
relative error = 7.353 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=39535.9MB, alloc=40.3MB, time=481.50
t[1] = 2.0515 2.418
h = 0.0001 0.003
x1[1] (numeric) = 2.04408876944 -0.0397693620886
x1[1] (closed_form) = 1.99982659981 -0.000153189414103
absolute error = 0.0594
relative error = 2.97 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.977875775105 -0.0822407596285
x2[1] (closed_form) = 1.00146351941 -0.0120374902477
absolute error = 0.07406
relative error = 7.395 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=39579.9MB, alloc=40.3MB, time=482.03
t[1] = 2.0516 2.421
h = 0.001 0.001
x1[1] (numeric) = 2.04434109755 -0.0397616638097
x1[1] (closed_form) = 1.99982615841 -0.000152653258865
absolute error = 0.05959
relative error = 2.98 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.978113250418 -0.082715858097
x2[1] (closed_form) = 1.00153580323 -0.0120306310086
absolute error = 0.07446
relative error = 7.435 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=39624.2MB, alloc=40.3MB, time=482.57
memory used=39668.3MB, alloc=40.3MB, time=483.10
t[1] = 2.0526 2.422
h = 0.001 0.003
x1[1] (numeric) = 2.04443207356 -0.0398405986705
x1[1] (closed_form) = 1.99982617975 -0.000152326937846
absolute error = 0.05971
relative error = 2.986 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.978351631507 -0.0831910218134
x2[1] (closed_form) = 1.00156299476 -0.0120514511503
absolute error = 0.07483
relative error = 7.471 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=39712.3MB, alloc=40.3MB, time=483.62
t[1] = 2.0536 2.425
h = 0.0001 0.004
x1[1] (numeric) = 2.04469651784 -0.0399059265439
x1[1] (closed_form) = 1.99982589774 -0.000151653063481
absolute error = 0.05995
relative error = 2.998 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.978590938632 -0.0836667963805
x2[1] (closed_form) = 1.00163840657 -0.0120656272768
absolute error = 0.07522
relative error = 7.509 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=39756.1MB, alloc=40.3MB, time=484.15
memory used=39800.0MB, alloc=40.3MB, time=484.67
t[1] = 2.0537 2.429
h = 0.003 0.006
x1[1] (numeric) = 2.04504256187 -0.0398860338688
x1[1] (closed_form) = 1.99982530999 -0.000150940348277
absolute error = 0.0602
relative error = 3.01 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.978832691121 -0.0841427496573
x2[1] (closed_form) = 1.00173492981 -0.0120541895211
absolute error = 0.07564
relative error = 7.55 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=39843.9MB, alloc=40.3MB, time=485.19
t[1] = 2.0567 2.435
h = 0.0001 0.005
x1[1] (numeric) = 2.04558070492 -0.0400995416804
x1[1] (closed_form) = 1.99982493349 -0.000149440502923
absolute error = 0.06074
relative error = 3.037 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.979079360319 -0.0846213690363
x2[1] (closed_form) = 1.00189056898 -0.0121041639882
absolute error = 0.07602
relative error = 7.587 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=39887.8MB, alloc=40.3MB, time=485.72
memory used=39931.9MB, alloc=40.3MB, time=486.25
t[1] = 2.0568 2.44
h = 0.0001 0.003
x1[1] (numeric) = 2.04600876125 -0.0400703077914
x1[1] (closed_form) = 1.99982420605 -0.000148548450408
absolute error = 0.06105
relative error = 3.053 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.979331865798 -0.0851024192006
x2[1] (closed_form) = 1.00201155044 -0.01208662634
absolute error = 0.07646
relative error = 7.63 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=39976.2MB, alloc=40.3MB, time=486.79
t[1] = 2.0569 2.443
h = 0.001 0.001
x1[1] (numeric) = 2.04626712416 -0.0400562240216
x1[1] (closed_form) = 1.99982377882 -0.000148005599596
absolute error = 0.06123
relative error = 3.062 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.979587695187 -0.0855828407211
x2[1] (closed_form) = 1.00208423595 -0.012076483851
absolute error = 0.07687
relative error = 7.671 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=40020.4MB, alloc=40.3MB, time=487.32
t[1] = 2.0579 2.444
h = 0.0001 0.004
x1[1] (numeric) = 2.0463622822 -0.0401348686162
x1[1] (closed_form) = 1.99982380719 -0.000147681549033
absolute error = 0.06136
relative error = 3.068 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.97984445377 -0.0860633049852
x2[1] (closed_form) = 1.00211261976 -0.0120962977705
absolute error = 0.07725
relative error = 7.708 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=40064.3MB, alloc=40.3MB, time=487.84
memory used=40108.2MB, alloc=40.3MB, time=488.36
t[1] = 2.058 2.448
h = 0.003 0.006
x1[1] (numeric) = 2.0467141451 -0.0401083403149
x1[1] (closed_form) = 1.99982323555 -0.000146960901387
absolute error = 0.06161
relative error = 3.081 %
Correct digits = 2
h = 0.003 0.006
x2[1] (numeric) = 0.980102837563 -0.086543678758
x2[1] (closed_form) = 1.00220947613 -0.0120810667453
absolute error = 0.07767
relative error = 7.75 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=40152.2MB, alloc=40.3MB, time=488.89
t[1] = 2.061 2.454
h = 0.0001 0.005
x1[1] (numeric) = 2.04726576675 -0.0403158901821
x1[1] (closed_form) = 1.9998228891 -0.000145460638619
absolute error = 0.06217
relative error = 3.109 %
Correct digits = 2
h = 0.0001 0.005
x2[1] (numeric) = 0.980366295825 -0.0870266431892
x2[1] (closed_form) = 1.00236827629 -0.0121254720253
absolute error = 0.07807
relative error = 7.788 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=40196.0MB, alloc=40.3MB, time=489.41
memory used=40240.0MB, alloc=40.3MB, time=489.94
t[1] = 2.0611 2.459
h = 0.0001 0.003
x1[1] (numeric) = 2.04770092596 -0.0402783710472
x1[1] (closed_form) = 1.9998221818 -0.000144558812961
absolute error = 0.06247
relative error = 3.124 %
Correct digits = 2
h = 0.0001 0.003
x2[1] (numeric) = 0.980635759173 -0.0875119354196
x2[1] (closed_form) = 1.00248955257 -0.0121031546873
absolute error = 0.07851
relative error = 7.831 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=40284.1MB, alloc=40.3MB, time=490.48
t[1] = 2.0612 2.462
h = 0.001 0.001
x1[1] (numeric) = 2.04796364819 -0.0402593395221
x1[1] (closed_form) = 1.99982176675 -0.000144010306892
absolute error = 0.06266
relative error = 3.134 %
Correct digits = 2
h = 0.001 0.001
x2[1] (numeric) = 0.980908591667 -0.0879965033762
x2[1] (closed_form) = 1.00256243036 -0.0120901437914
absolute error = 0.07893
relative error = 7.873 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=40328.3MB, alloc=40.3MB, time=491.01
memory used=40372.4MB, alloc=40.3MB, time=491.54
t[1] = 2.0622 2.463
h = 0.001 0.003
x1[1] (numeric) = 2.04806194478 -0.0403376506057
x1[1] (closed_form) = 1.99982180111 -0.000143688241554
absolute error = 0.06279
relative error = 3.14 %
Correct digits = 2
h = 0.001 0.003
x2[1] (numeric) = 0.98118237152 -0.0884810913788
x2[1] (closed_form) = 1.00259180094 -0.0121090277185
absolute error = 0.07932
relative error = 7.911 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=40416.3MB, alloc=40.3MB, time=492.07
t[1] = 2.0632 2.466
h = 0.0001 0.004
x1[1] (numeric) = 2.04834048995 -0.0403941547736
x1[1] (closed_form) = 1.99982154939 -0.000143009917655
absolute error = 0.06304
relative error = 3.152 %
Correct digits = 2
h = 0.0001 0.004
x2[1] (numeric) = 0.981457148707 -0.0889662669952
x2[1] (closed_form) = 1.00266961516 -0.0121171306444
absolute error = 0.07972
relative error = 7.95 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=40460.2MB, alloc=40.3MB, time=492.60
t[1] = 2.0633 2.47
h = 0.003 0.006
x1[1] (numeric) = 2.0487003636 -0.0403582173991
x1[1] (closed_form) = 1.99982099668 -0.000142280744261
absolute error = 0.0633
relative error = 3.165 %
Correct digits = 1
h = 0.003 0.006
x2[1] (numeric) = 0.981734483695 -0.0894514996076
x2[1] (closed_form) = 1.00276674125 -0.0120974420113
absolute error = 0.08016
relative error = 7.994 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=40504.1MB, alloc=40.3MB, time=493.11
memory used=40548.1MB, alloc=40.3MB, time=493.64
t[1] = 2.0663 2.476
h = 0.0001 0.005
x1[1] (numeric) = 2.04927073429 -0.0405571577796
x1[1] (closed_form) = 1.99982068498 -0.000140781192029
absolute error = 0.06387
relative error = 3.194 %
Correct digits = 1
h = 0.0001 0.005
x2[1] (numeric) = 0.982017083382 -0.0899392508533
x2[1] (closed_form) = 1.00292906979 -0.0121352176401
absolute error = 0.08057
relative error = 8.032 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=40592.0MB, alloc=40.3MB, time=494.16
t[1] = 2.0664 2.481
h = 0.0001 0.003
x1[1] (numeric) = 2.04971567366 -0.0405078955585
x1[1] (closed_form) = 1.99982000132 -0.000139868873306
absolute error = 0.06418
relative error = 3.209 %
Correct digits = 1
h = 0.0001 0.003
x2[1] (numeric) = 0.982305893769 -0.0904292269249
x2[1] (closed_form) = 1.00305053947 -0.0121072874947
absolute error = 0.08102
relative error = 8.077 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=40636.1MB, alloc=40.3MB, time=494.69
memory used=40680.4MB, alloc=40.3MB, time=495.24
t[1] = 2.0665 2.484
h = 0.001 0.001
x1[1] (numeric) = 2.04998438857 -0.0404818623989
x1[1] (closed_form) = 1.99981960056 -0.000139314316529
absolute error = 0.06437
relative error = 3.219 %
Correct digits = 1
h = 0.001 0.001
x2[1] (numeric) = 0.982598134966 -0.0909183722267
x2[1] (closed_form) = 1.00312355131 -0.0120909077295
absolute error = 0.08146
relative error = 8.12 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=40724.4MB, alloc=40.3MB, time=495.77
t[1] = 2.0675 2.485
h = 0.001 0.003
x1[1] (numeric) = 2.05008705125 -0.0405596534529
x1[1] (closed_form) = 1.99981964179 -0.00013899478316
absolute error = 0.0645
relative error = 3.225 %
Correct digits = 1
h = 0.001 0.003
x2[1] (numeric) = 0.982891346776 -0.0914075129937
x2[1] (closed_form) = 1.00315404909 -0.0121086699604
absolute error = 0.08185
relative error = 8.158 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=40768.3MB, alloc=40.3MB, time=496.30
memory used=40812.3MB, alloc=40.3MB, time=496.83
t[1] = 2.0685 2.488
h = 0.0001 0.004
x1[1] (numeric) = 2.05037384798 -0.0406106109543
x1[1] (closed_form) = 1.9998194063 -0.000138314699974
absolute error = 0.06476
relative error = 3.238 %
Correct digits = 1
h = 0.0001 0.004
x2[1] (numeric) = 0.983185595389 -0.0918972290884
x2[1] (closed_form) = 1.00323298476 -0.0121133910493
absolute error = 0.08226
relative error = 8.199 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=40856.2MB, alloc=40.3MB, time=497.35
t[1] = 2.0686 2.492
h = 0.003 0.006
x1[1] (numeric) = 2.05074166571 -0.0405648287662
x1[1] (closed_form) = 1.9998188726 -0.000137577462143
absolute error = 0.06502
relative error = 3.251 %
Correct digits = 1
h = 0.003 0.006
x2[1] (numeric) = 0.98348246467 -0.0923869358814
x2[1] (closed_form) = 1.00333018508 -0.012089189907
absolute error = 0.08271
relative error = 8.243 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=40900.2MB, alloc=40.3MB, time=497.89
t[1] = 2.0716 2.498
h = 0.0001 0.005
x1[1] (numeric) = 2.051330991 -0.0407544530208
x1[1] (closed_form) = 1.99981859543 -0.000136079376771
absolute error = 0.0656
relative error = 3.28 %
Correct digits = 1
h = 0.0001 0.005
x2[1] (numeric) = 0.983784791589 -0.092879082428
x2[1] (closed_form) = 1.00349578134 -0.012120115251
absolute error = 0.08313
relative error = 8.283 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=40944.3MB, alloc=40.3MB, time=498.41
memory used=40988.3MB, alloc=40.3MB, time=498.94
t[1] = 2.0717 2.503
h = 0.0001 0.003
x1[1] (numeric) = 2.05178562211 -0.0406929098463
x1[1] (closed_form) = 1.99981793551 -0.000135157140325
absolute error = 0.06592
relative error = 3.296 %
Correct digits = 1
h = 0.0001 0.003
x2[1] (numeric) = 0.984093537078 -0.0933733428061
x2[1] (closed_form) = 1.00361719683 -0.0120865096669
absolute error = 0.0836
relative error = 8.329 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=41032.5MB, alloc=40.3MB, time=499.47
t[1] = 2.0718 2.506
h = 0.001 0.001
x1[1] (numeric) = 2.05206028077 -0.0406595500278
x1[1] (closed_form) = 1.99981754911 -0.000134596879111
absolute error = 0.06612
relative error = 3.306 %
Correct digits = 1
h = 0.001 0.001
x2[1] (numeric) = 0.984405773689 -0.0938666616692
x2[1] (closed_form) = 1.00369019429 -0.0120667226419
absolute error = 0.08404
relative error = 8.373 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=41076.7MB, alloc=40.3MB, time=500.01
memory used=41120.8MB, alloc=40.3MB, time=500.54
t[1] = 2.0728 2.507
h = 0.001 0.003
x1[1] (numeric) = 2.05216739749 -0.0407366911858
x1[1] (closed_form) = 1.99981759709 -0.000134280013772
absolute error = 0.06625
relative error = 3.313 %
Correct digits = 1
h = 0.001 0.003
x2[1] (numeric) = 0.984719004077 -0.0943599501938
x2[1] (closed_form) = 1.00372178027 -0.0120833022807
absolute error = 0.08444
relative error = 8.412 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=41164.6MB, alloc=40.3MB, time=501.06
t[1] = 2.0738 2.51
h = 0.0001 0.004
x1[1] (numeric) = 2.05246248899 -0.0407817499531
x1[1] (closed_form) = 1.99981737779 -0.000133598536259
absolute error = 0.06651
relative error = 3.326 %
Correct digits = 1
h = 0.0001 0.004
x2[1] (numeric) = 0.985033311369 -0.0948538004024
x2[1] (closed_form) = 1.00380169789 -0.0120845591326
absolute error = 0.08487
relative error = 8.454 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=41208.6MB, alloc=40.3MB, time=501.58
memory used=41252.7MB, alloc=40.3MB, time=502.11
t[1] = 2.0739 2.514
h = 0.003 0.006
x1[1] (numeric) = 2.05283817101 -0.0407256787493
x1[1] (closed_form) = 1.99981686317 -0.000132853694543
absolute error = 0.06678
relative error = 3.339 %
Correct digits = 1
h = 0.003 0.006
x2[1] (numeric) = 0.985350301951 -0.0953475717105
x2[1] (closed_form) = 1.00389877258 -0.0120557987393
absolute error = 0.08533
relative error = 8.499 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=41296.8MB, alloc=40.3MB, time=502.64
t[1] = 2.0769 2.52
h = 0.0001 0.005
x1[1] (numeric) = 2.05344664253 -0.04090525819
x1[1] (closed_form) = 1.99981662032 -0.000131357823637
absolute error = 0.06737
relative error = 3.369 %
Correct digits = 1
h = 0.0001 0.005
x2[1] (numeric) = 0.985672945696 -0.0958436967974
x2[1] (closed_form) = 1.00406736356 -0.012079662613
absolute error = 0.08576
relative error = 8.541 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=41340.7MB, alloc=40.3MB, time=503.16
t[1] = 2.077 2.525
h = 0.0001 0.003
x1[1] (numeric) = 2.05391086057 -0.0408308859187
x1[1] (closed_form) = 1.99981598422 -0.000130426243793
absolute error = 0.0677
relative error = 3.385 %
Correct digits = 1
h = 0.0001 0.003
x2[1] (numeric) = 0.986002217971 -0.0963418164434
x2[1] (closed_form) = 1.00418847208 -0.0120403293588
absolute error = 0.08624
relative error = 8.587 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=41384.8MB, alloc=40.3MB, time=503.69
memory used=41429.2MB, alloc=40.3MB, time=504.23
t[1] = 2.0771 2.528
h = 0.001 0.001
x1[1] (numeric) = 2.05419140429 -0.0407898680855
x1[1] (closed_form) = 1.99981561221 -0.000129860623666
absolute error = 0.0679
relative error = 3.395 %
Correct digits = 1
h = 0.001 0.001
x2[1] (numeric) = 0.986335040182 -0.0968388795131
x2[1] (closed_form) = 1.00426130357 -0.0120171029104
absolute error = 0.0867
relative error = 8.632 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=41473.2MB, alloc=40.3MB, time=504.76
t[1] = 2.0781 2.529
h = 0.001 0.003
x1[1] (numeric) = 2.05430306161 -0.0408662240956
x1[1] (closed_form) = 1.99981566687 -0.000129546559626
absolute error = 0.06803
relative error = 3.402 %
Correct digits = 1
h = 0.001 0.003
x2[1] (numeric) = 0.986668879206 -0.097335885191
x2[1] (closed_form) = 1.00429393567 -0.012032440204
absolute error = 0.08711
relative error = 8.673 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=41517.2MB, alloc=40.3MB, time=505.29
memory used=41561.2MB, alloc=40.3MB, time=505.81
t[1] = 2.0791 2.532
h = 0.0001 0.004
x1[1] (numeric) = 2.05460648277 -0.0409050226423
x1[1] (closed_form) = 1.99981546369 -0.000128864049607
absolute error = 0.0683
relative error = 3.415 %
Correct digits = 1
h = 0.0001 0.004
x2[1] (numeric) = 0.987003835846 -0.0978334375015
x2[1] (closed_form) = 1.00437469072 -0.0120301558218
absolute error = 0.08754
relative error = 8.716 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=41605.2MB, alloc=40.3MB, time=506.34
t[1] = 2.0792 2.536
h = 0.003 0.006
x1[1] (numeric) = 2.05498993561 -0.0408382099033
x1[1] (closed_form) = 1.99981496822 -0.000128112063578
absolute error = 0.06857
relative error = 3.429 %
Correct digits = 1
h = 0.003 0.006
x2[1] (numeric) = 0.987341538056 -0.0983308379376
x2[1] (closed_form) = 1.00447143593 -0.0119967978666
absolute error = 0.08802
relative error = 8.762 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=41649.2MB, alloc=40.3MB, time=506.86
memory used=41693.2MB, alloc=40.3MB, time=507.39
t[1] = 2.0822 2.542
h = 0.0001 0.005
x1[1] (numeric) = 2.05561773013 -0.0410069936329
x1[1] (closed_form) = 1.99981475943 -0.000126619145731
absolute error = 0.06917
relative error = 3.459 %
Correct digits = 1
h = 0.0001 0.005
x2[1] (numeric) = 0.987685091411 -0.0988304988396
x2[1] (closed_form) = 1.00464273658 -0.0120133991727
absolute error = 0.08846
relative error = 8.804 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=41737.2MB, alloc=40.3MB, time=507.92
t[1] = 2.0823 2.547
h = 0.0001 0.003
x1[1] (numeric) = 2.05609141329 -0.0409192340312
x1[1] (closed_form) = 1.99981414724 -0.000125678795519
absolute error = 0.06951
relative error = 3.476 %
Correct digits = 1
h = 0.0001 0.003
x2[1] (numeric) = 0.988035485171 -0.0993320264921
x2[1] (closed_form) = 1.00476328059 -0.0119682967478
absolute error = 0.08895
relative error = 8.852 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=41781.4MB, alloc=40.3MB, time=508.44
t[1] = 2.0824 2.55
h = 0.001 0.001
x1[1] (numeric) = 2.0563777732 -0.0408702206024
x1[1] (closed_form) = 1.99981378967 -0.00012510816109
absolute error = 0.06971
relative error = 3.486 %
Correct digits = 1
h = 0.001 0.001
x2[1] (numeric) = 0.988389486026 -0.0998323781273
x2[1] (closed_form) = 1.00483579163 -0.0119416051391
absolute error = 0.08942
relative error = 8.898 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=41825.6MB, alloc=40.3MB, time=508.98
memory used=41869.6MB, alloc=40.3MB, time=509.51
t[1] = 2.0834 2.551
h = 0.0001 0.004
x1[1] (numeric) = 2.0564940561 -0.0409456507352
x1[1] (closed_form) = 1.99981385089 -0.000124797028784
absolute error = 0.06985
relative error = 3.493 %
Correct digits = 1
h = 0.0001 0.004
x2[1] (numeric) = 0.988744526564 -0.10033264404
x2[1] (closed_form) = 1.0048694247 -0.0119556416258
absolute error = 0.08984
relative error = 8.939 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=41913.6MB, alloc=40.3MB, time=510.04
t[1] = 2.0835 2.555
h = 0.003 0.006
x1[1] (numeric) = 2.05688304456 -0.0408705948019
x1[1] (closed_form) = 1.99981337186 -0.000124039031443
absolute error = 0.07012
relative error = 3.506 %
Correct digits = 1
h = 0.003 0.006
x2[1] (numeric) = 0.989101361907 -0.100832576316
x2[1] (closed_form) = 1.00496566502 -0.0119183094911
absolute error = 0.09032
relative error = 8.987 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=41957.6MB, alloc=40.3MB, time=510.56
memory used=42001.6MB, alloc=40.3MB, time=511.09
t[1] = 2.0865 2.561
h = 0.0001 0.005
x1[1] (numeric) = 2.05752501927 -0.0410307865371
x1[1] (closed_form) = 1.99981319225 -0.000122548838085
absolute error = 0.07074
relative error = 3.537 %
Correct digits = 1
h = 0.0001 0.005
x2[1] (numeric) = 0.989464213188 -0.101334662824
x2[1] (closed_form) = 1.00513897129 -0.0119284791175
absolute error = 0.09077
relative error = 9.03 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=42045.7MB, alloc=40.3MB, time=511.62
t[1] = 2.0866 2.566
h = 0.0001 0.003
x1[1] (numeric) = 2.05800543291 -0.040932757368
x1[1] (closed_form) = 1.99981260059 -0.000121601110667
absolute error = 0.07108
relative error = 3.554 %
Correct digits = 1
h = 0.0001 0.003
x2[1] (numeric) = 0.989834078052 -0.101838477653
x2[1] (closed_form) = 1.00525875063 -0.0118783969565
absolute error = 0.09127
relative error = 9.079 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=42089.9MB, alloc=40.3MB, time=512.15
memory used=42134.3MB, alloc=40.3MB, time=512.69
t[1] = 2.0867 2.569
h = 0.001 0.001
x1[1] (numeric) = 2.0582959432 -0.0408775943173
x1[1] (closed_form) = 1.9998122554 -0.000121026262838
absolute error = 0.07128
relative error = 3.565 %
Correct digits = 1
h = 0.001 0.001
x2[1] (numeric) = 0.990207586794 -0.102341003699
x2[1] (closed_form) = 1.00533081855 -0.0118487134621
absolute error = 0.09175
relative error = 9.125 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=42178.2MB, alloc=40.3MB, time=513.22
t[1] = 2.0877 2.57
h = 0.001 0.003
x1[1] (numeric) = 2.05841567988 -0.0409521996829
x1[1] (closed_form) = 1.99981232224 -0.000120717679701
absolute error = 0.07143
relative error = 3.572 %
Correct digits = 1
h = 0.001 0.003
x2[1] (numeric) = 0.990582152214 -0.102843416208
x2[1] (closed_form) = 1.00536525832 -0.0118615734034
absolute error = 0.09218
relative error = 9.168 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=42222.2MB, alloc=40.3MB, time=513.74
t[1] = 2.0887 2.573
h = 0.0001 0.004
x1[1] (numeric) = 2.05873356534 -0.0409791211832
x1[1] (closed_form) = 1.99981214888 -0.000120034009998
absolute error = 0.0717
relative error = 3.585 %
Correct digits = 1
h = 0.0001 0.004
x2[1] (numeric) = 0.990957911265 -0.103346339434
x2[1] (closed_form) = 1.00544712651 -0.0118525086363
absolute error = 0.09263
relative error = 9.213 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=42266.2MB, alloc=40.3MB, time=514.26
memory used=42310.1MB, alloc=40.3MB, time=514.79
t[1] = 2.0888 2.577
h = 0.003 0.006
x1[1] (numeric) = 2.0591301396 -0.0408924130125
x1[1] (closed_form) = 1.99981168908 -0.000119269719683
absolute error = 0.07198
relative error = 3.599 %
Correct digits = 1
h = 0.003 0.006
x2[1] (numeric) = 0.991336523755 -0.103848959529
x2[1] (closed_form) = 1.00554264827 -0.011810533499
absolute error = 0.09313
relative error = 9.261 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=42354.1MB, alloc=40.3MB, time=515.32
t[1] = 2.0918 2.583
h = 0.0001 0.005
x1[1] (numeric) = 2.05979179858 -0.0410402996693
x1[1] (closed_form) = 1.99981154308 -0.000117783832041
absolute error = 0.07261
relative error = 3.631 %
Correct digits = 1
h = 0.0001 0.005
x2[1] (numeric) = 0.991721353615 -0.104353626915
x2[1] (closed_form) = 1.00571810086 -0.0118130990905
absolute error = 0.09359
relative error = 9.305 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=42398.1MB, alloc=40.3MB, time=515.85
memory used=42442.2MB, alloc=40.3MB, time=516.37
t[1] = 2.0919 2.588
h = 0.0001 0.003
x1[1] (numeric) = 2.06028143697 -0.0409277583573
x1[1] (closed_form) = 1.99981097542 -0.000116828395625
absolute error = 0.07295
relative error = 3.648 %
Correct digits = 1
h = 0.0001 0.003
x2[1] (numeric) = 0.992113411239 -0.104859879085
x2[1] (closed_form) = 1.00583682504 -0.011757203349
absolute error = 0.09411
relative error = 9.356 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=42486.4MB, alloc=40.3MB, time=516.91
t[1] = 2.092 2.591
h = 0.001 0.001
x1[1] (numeric) = 2.06057762729 -0.0408639194996
x1[1] (closed_form) = 1.99981064472 -0.000116249171503
absolute error = 0.07316
relative error = 3.659 %
Correct digits = 1
h = 0.001 0.001
x2[1] (numeric) = 0.992509166308 -0.105364715321
x2[1] (closed_form) = 1.00590827811 -0.0117240264658
absolute error = 0.09459
relative error = 9.403 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=42530.7MB, alloc=40.3MB, time=517.44
t[1] = 2.093 2.592
h = 0.001 0.003
x1[1] (numeric) = 2.06070216135 -0.0409373164147
x1[1] (closed_form) = 1.99981071794 -0.000115943756383
memory used=42574.9MB, alloc=40.3MB, time=517.98
absolute error = 0.07331
relative error = 3.666 %
Correct digits = 1
h = 0.001 0.003
x2[1] (numeric) = 0.992906000455 -0.105869407398
x2[1] (closed_form) = 1.00594362613 -0.0117354813854
absolute error = 0.09503
relative error = 9.446 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=42618.7MB, alloc=40.3MB, time=518.50
t[1] = 2.094 2.595
h = 0.0001 0.004
x1[1] (numeric) = 2.06102845675 -0.0409568616217
x1[1] (closed_form) = 1.9998105605 -0.000115260071594
absolute error = 0.07359
relative error = 3.68 %
Correct digits = 1
h = 0.0001 0.004
x2[1] (numeric) = 0.993304070405 -0.106374590959
x2[1] (closed_form) = 1.00602589168 -0.0117226892912
absolute error = 0.0955
relative error = 9.492 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=42662.7MB, alloc=40.3MB, time=519.02
t[1] = 2.0941 2.599
h = 0.003 0.006
x1[1] (numeric) = 2.06143247952 -0.040858025344
x1[1] (closed_form) = 1.99981011996 -0.00011448994396
absolute error = 0.07387
relative error = 3.694 %
Correct digits = 1
h = 0.003 0.006
x2[1] (numeric) = 0.993705054372 -0.106879388773
x2[1] (closed_form) = 1.00612048156 -0.0116760583869
absolute error = 0.09601
relative error = 9.542 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=42706.7MB, alloc=40.3MB, time=519.55
memory used=42751.0MB, alloc=40.3MB, time=520.08
t[1] = 2.0971 2.605
h = 0.0001 0.005
x1[1] (numeric) = 2.06211394956 -0.0409927898226
x1[1] (closed_form) = 1.99981000728 -0.000113009073491
absolute error = 0.07452
relative error = 3.726 %
Correct digits = 1
h = 0.0001 0.005
x2[1] (numeric) = 0.994112459205 -0.10738611892
x2[1] (closed_form) = 1.00629776306 -0.0116708512972
absolute error = 0.09649
relative error = 9.588 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=42795.0MB, alloc=40.3MB, time=520.60
t[1] = 2.0972 2.61
h = 0.0001 0.003
x1[1] (numeric) = 2.06261263632 -0.0408651498556
x1[1] (closed_form) = 1.99980946367 -0.000112046496026
absolute error = 0.07487
relative error = 3.744 %
Correct digits = 1
h = 0.0001 0.003
x2[1] (numeric) = 0.994527307376 -0.107894281062
x2[1] (closed_form) = 1.00641516347 -0.0116091329013
absolute error = 0.09702
relative error = 9.639 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=42839.2MB, alloc=40.3MB, time=521.13
memory used=42883.7MB, alloc=40.3MB, time=521.68
t[1] = 2.0973 2.613
h = 0.001 0.001
x1[1] (numeric) = 2.06291440515 -0.0407922801246
x1[1] (closed_form) = 1.99980914747 -0.000111463236791
absolute error = 0.07508
relative error = 3.754 %
Correct digits = 1
h = 0.001 0.001
x2[1] (numeric) = 0.994945904462 -0.10840089557
x2[1] (closed_form) = 1.00648584046 -0.0115724563235
absolute error = 0.09751
relative error = 9.688 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=42927.7MB, alloc=40.3MB, time=522.21
t[1] = 2.0983 2.614
h = 0.001 0.003
x1[1] (numeric) = 2.06304381577 -0.0408643111704
x1[1] (closed_form) = 1.99980922697 -0.000111161111851
absolute error = 0.07523
relative error = 3.762 %
Correct digits = 1
h = 0.001 0.003
x2[1] (numeric) = 0.995365602755 -0.108907333948
x2[1] (closed_form) = 1.006522043 -0.0115824523103
absolute error = 0.09796
relative error = 9.732 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=42971.6MB, alloc=40.3MB, time=522.73
t[1] = 2.0993 2.617
h = 0.0001 0.004
x1[1] (numeric) = 2.06337851837 -0.0408760815547
x1[1] (closed_form) = 1.99980908536 -0.000110477760381
absolute error = 0.07552
relative error = 3.776 %
Correct digits = 1
h = 0.0001 0.004
x2[1] (numeric) = 0.995786579536 -0.109414242975
x2[1] (closed_form) = 1.00660454402 -0.0115658793265
absolute error = 0.09844
relative error = 9.779 %
Correct digits = 1
memory used=43015.9MB, alloc=40.3MB, time=523.26
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=43059.7MB, alloc=40.3MB, time=523.78
t[1] = 2.0994 2.621
h = 0.003 0.006
x1[1] (numeric) = 2.0637898365 -0.0407646337752
x1[1] (closed_form) = 1.99980866411 -0.000109702249251
absolute error = 0.07581
relative error = 3.791 %
Correct digits = 1
h = 0.003 0.006
x2[1] (numeric) = 0.99621053018 -0.109920679996
x2[1] (closed_form) = 1.00669798604 -0.0115145892501
absolute error = 0.09896
relative error = 9.83 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=43103.6MB, alloc=40.3MB, time=524.31
t[1] = 2.1024 2.627
h = 0.0001 0.005
x1[1] (numeric) = 2.06449122575 -0.0408854364531
x1[1] (closed_form) = 1.99980858445 -0.000108227097356
absolute error = 0.07646
relative error = 3.824 %
Correct digits = 1
h = 0.0001 0.005
x2[1] (numeric) = 0.996641107077 -0.110428926123
x2[1] (closed_form) = 1.00687676849 -0.0115014533054
absolute error = 0.09946
relative error = 9.877 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=43147.7MB, alloc=40.3MB, time=524.83
memory used=43191.8MB, alloc=40.3MB, time=525.36
t[1] = 2.1025 2.632
h = 0.0001 0.003
x1[1] (numeric) = 2.06499876484 -0.0407421022395
x1[1] (closed_form) = 1.99980806491 -0.000107257944439
absolute error = 0.07682
relative error = 3.841 %
Correct digits = 1
h = 0.0001 0.003
x2[1] (numeric) = 0.997079344061 -0.110938441938
x2[1] (closed_form) = 1.00699257348 -0.0114339150339
absolute error = 0.1
relative error = 9.93 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=43235.9MB, alloc=40.3MB, time=525.90
t[1] = 2.1026 2.635
h = 0.001 0.001
x1[1] (numeric) = 2.06530599884 -0.0406598409311
x1[1] (closed_form) = 1.99980776322 -0.000106670989729
absolute error = 0.07704
relative error = 3.852 %
Correct digits = 1
h = 0.001 0.001
x2[1] (numeric) = 0.997521379157 -0.111446273819
x2[1] (closed_form) = 1.00706231131 -0.0113937395617
absolute error = 0.1005
relative error = 9.98 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=43280.3MB, alloc=40.3MB, time=526.43
memory used=43324.5MB, alloc=40.3MB, time=526.96
t[1] = 2.1036 2.636
h = 0.001 0.003
x1[1] (numeric) = 2.06544036292 -0.0407303428976
x1[1] (closed_form) = 1.99980784889 -0.000106372274169
absolute error = 0.07719
relative error = 3.86 %
Correct digits = 1
h = 0.001 0.003
x2[1] (numeric) = 0.99796453727 -0.111953896223
x2[1] (closed_form) = 1.00709931173 -0.0114022245697
absolute error = 0.101
relative error = 10.02 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=43368.6MB, alloc=40.3MB, time=527.50
t[1] = 2.1046 2.639
h = 0.0001 0.004
x1[1] (numeric) = 2.06578345933 -0.0407339306491
x1[1] (closed_form) = 1.99980772302 -0.000105689600576
absolute error = 0.07748
relative error = 3.874 %
Correct digits = 1
h = 0.0001 0.004
x2[1] (numeric) = 0.998409017042 -0.112461966788
x2[1] (closed_form) = 1.00718188239 -0.0113818238101
absolute error = 0.1015
relative error = 10.07 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=43412.6MB, alloc=40.3MB, time=528.04
t[1] = 2.1047 2.643
h = 0.003 0.006
x1[1] (numeric) = 2.06620190329 -0.0406093806845
x1[1] (closed_form) = 1.99980732106 -0.000104909157731
absolute error = 0.07777
relative error = 3.889 %
Correct digits = 1
h = 0.003 0.006
x2[1] (numeric) = 0.99885652967 -0.112969475374
x2[1] (closed_form) = 1.00727395832 -0.0113258807238
absolute error = 0.102
relative error = 10.12 %
Correct digits = 1
memory used=43456.6MB, alloc=40.3MB, time=528.56
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=43500.5MB, alloc=40.3MB, time=529.09
t[1] = 2.1077 2.649
h = 0.0001 0.005
x1[1] (numeric) = 2.06692330017 -0.0407153593676
x1[1] (closed_form) = 1.99980727413 -0.000103440415504
absolute error = 0.07845
relative error = 3.923 %
Correct digits = 1
h = 0.0001 0.005
x2[1] (numeric) = 0.999310875652 -0.113478661316
x2[1] (closed_form) = 1.00745390363 -0.0113046728135
absolute error = 0.1025
relative error = 10.17 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=43544.5MB, alloc=40.3MB, time=529.61
t[1] = 2.1078 2.654
h = 0.0001 0.003
x1[1] (numeric) = 2.06743947516 -0.0405557265361
x1[1] (closed_form) = 1.99980677866 -0.000102465250117
absolute error = 0.07881
relative error = 3.941 %
Correct digits = 1
h = 0.0001 0.003
x2[1] (numeric) = 0.99977309941 -0.11398894486
x2[1] (closed_form) = 1.00756783906 -0.0112313295467
absolute error = 0.1031
relative error = 10.23 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=43588.6MB, alloc=40.3MB, time=530.14
memory used=43633.1MB, alloc=40.3MB, time=530.68
t[1] = 2.1079 2.657
h = 0.001 0.001
x1[1] (numeric) = 2.0677520488 -0.0404637074835
x1[1] (closed_form) = 1.99980649149 -0.00010187493787
absolute error = 0.07903
relative error = 3.952 %
Correct digits = 1
h = 0.001 0.001
x2[1] (numeric) = 1.00023916802 -0.114497403519
x2[1] (closed_form) = 1.00763647309 -0.0111876632367
absolute error = 0.1036
relative error = 10.28 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=43677.4MB, alloc=40.3MB, time=531.22
t[1] = 2.1089 2.658
h = 0.0001 0.004
x1[1] (numeric) = 2.06789144069 -0.0405325112909
x1[1] (closed_form) = 1.99980658322 -0.000101579747896
absolute error = 0.07918
relative error = 3.96 %
Correct digits = 1
h = 0.0001 0.004
x2[1] (numeric) = 1.0007063811 -0.115005617956
x2[1] (closed_form) = 1.00767421189 -0.0111945872324
absolute error = 0.104
relative error = 10.32 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=43721.4MB, alloc=40.3MB, time=531.74
memory used=43765.5MB, alloc=40.3MB, time=532.27
t[1] = 2.109 2.662
h = 0.003 0.006
x1[1] (numeric) = 2.06831487181 -0.04039796774
x1[1] (closed_form) = 1.99980619783 -0.000100795190185
absolute error = 0.07948
relative error = 3.974 %
Correct digits = 1
h = 0.003 0.006
x2[1] (numeric) = 1.00117554333 -0.115513204328
x2[1] (closed_form) = 1.00776488064 -0.0111346712151
absolute error = 0.1046
relative error = 10.38 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=43809.5MB, alloc=40.3MB, time=532.79
t[1] = 2.112 2.668
h = 0.0001 0.005
x1[1] (numeric) = 2.06905084922 -0.0404923175117
x1[1] (closed_form) = 1.99980617889 -9.93321260248e-05
absolute error = 0.08016
relative error = 4.009 %
Correct digits = 1
h = 0.0001 0.005
x2[1] (numeric) = 1.00165170724 -0.116022326542
x2[1] (closed_form) = 1.00794545057 -0.0111064028338
absolute error = 0.1051
relative error = 10.43 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=43853.6MB, alloc=40.3MB, time=533.32
t[1] = 2.1121 2.673
h = 0.0001 0.003
x1[1] (numeric) = 2.06957305222 -0.0403202577927
x1[1] (closed_form) = 1.99980570408 -9.83519471734e-05
absolute error = 0.08053
relative error = 4.027 %
Correct digits = 1
h = 0.0001 0.003
x2[1] (numeric) = 1.00213592203 -0.11653236783
x2[1] (closed_form) = 1.00805748699 -0.0110281108952
absolute error = 0.1057
relative error = 10.48 %
Correct digits = 1
memory used=43897.8MB, alloc=40.3MB, time=533.85
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=43942.2MB, alloc=40.3MB, time=534.39
t[1] = 2.1122 2.676
h = 0.001 0.001
x1[1] (numeric) = 2.06988936932 -0.0402207800892
x1[1] (closed_form) = 1.99980542936 -9.77588413433e-05
absolute error = 0.08076
relative error = 4.038 %
Correct digits = 1
h = 0.001 0.001
x2[1] (numeric) = 1.00262400665 -0.117040453559
x2[1] (closed_form) = 1.00812499682 -0.0109814677229
absolute error = 0.1062
relative error = 10.53 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=43986.3MB, alloc=40.3MB, time=534.93
t[1] = 2.1132 2.677
h = 0.001 0.003
x1[1] (numeric) = 2.07003249512 -0.0402881660613
x1[1] (closed_form) = 1.99980552627 -9.74667064013e-05
absolute error = 0.08091
relative error = 4.046 %
Correct digits = 1
h = 0.001 0.003
x2[1] (numeric) = 1.00311325071 -0.11754826171
x2[1] (closed_form) = 1.00816330204 -0.0109870018517
absolute error = 0.1067
relative error = 10.58 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=44030.4MB, alloc=40.3MB, time=535.46
memory used=44074.6MB, alloc=40.3MB, time=535.98
t[1] = 2.1142 2.68
h = 0.0001 0.004
x1[1] (numeric) = 2.07039001908 -0.0402764221593
x1[1] (closed_form) = 1.99980542941 -9.67860130656e-05
absolute error = 0.08122
relative error = 4.061 %
Correct digits = 1
h = 0.0001 0.004
x2[1] (numeric) = 1.00360389594 -0.118056467321
x2[1] (closed_form) = 1.00824550184 -0.010959381568
absolute error = 0.1072
relative error = 10.63 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=44118.6MB, alloc=40.3MB, time=536.51
t[1] = 2.1143 2.684
h = 0.003 0.006
x1[1] (numeric) = 2.07082023843 -0.0401277887378
x1[1] (closed_form) = 1.99980506332 -9.59973582931e-05
absolute error = 0.08152
relative error = 4.076 %
Correct digits = 1
h = 0.003 0.006
x2[1] (numeric) = 1.00409767267 -0.118563927415
x2[1] (closed_form) = 1.00833439421 -0.0108948527607
absolute error = 0.1078
relative error = 10.69 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=44162.7MB, alloc=40.3MB, time=537.04
memory used=44206.8MB, alloc=40.3MB, time=537.57
t[1] = 2.1173 2.69
h = 0.0001 0.005
x1[1] (numeric) = 2.07157640788 -0.0402055811046
x1[1] (closed_form) = 1.9998050765 -9.45419655341e-05
absolute error = 0.08222
relative error = 4.111 %
Correct digits = 1
h = 0.0001 0.005
x2[1] (numeric) = 1.00459866012 -0.119072775928
x2[1] (closed_form) = 1.0085154713 -0.010858287138
absolute error = 0.1083
relative error = 10.74 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=44250.8MB, alloc=40.3MB, time=538.10
t[1] = 2.1174 2.695
h = 0.0001 0.003
x1[1] (numeric) = 2.07210681656 -0.0400160045992
x1[1] (closed_form) = 1.99980462577 -9.35568141669e-05
absolute error = 0.08259
relative error = 4.13 %
Correct digits = 1
h = 0.0001 0.003
x2[1] (numeric) = 1.00510791652 -0.119582353576
x2[1] (closed_form) = 1.00862512364 -0.0107742541804
absolute error = 0.1089
relative error = 10.79 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=44294.9MB, alloc=40.3MB, time=538.63
t[1] = 2.1175 2.698
h = 0.001 0.001
x1[1] (numeric) = 2.07242822341 -0.0399060311626
x1[1] (closed_form) = 1.99980436554 -9.29609747756e-05
absolute error = 0.08282
relative error = 4.141 %
Correct digits = 1
h = 0.001 0.001
x2[1] (numeric) = 1.0056210844 -0.120089826623
x2[1] (closed_form) = 1.00869122061 -0.0107241569326
absolute error = 0.1094
relative error = 10.85 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=44339.4MB, alloc=40.3MB, time=539.17
memory used=44383.6MB, alloc=40.3MB, time=539.70
t[1] = 2.1185 2.699
h = 0.001 0.003
x1[1] (numeric) = 2.07257652758 -0.0399713794246
x1[1] (closed_form) = 1.99980446831 -9.26725749403e-05
absolute error = 0.08298
relative error = 4.15 %
Correct digits = 1
h = 0.001 0.003
x2[1] (numeric) = 1.00613543233 -0.120596984859
x2[1] (closed_form) = 1.00873014555 -0.010728043593
absolute error = 0.1099
relative error = 10.89 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=44427.6MB, alloc=40.3MB, time=540.23
t[1] = 2.1195 2.702
h = 0.0001 0.004
x1[1] (numeric) = 2.07294237362 -0.0399501980237
x1[1] (closed_form) = 1.99980438688 -9.19935241746e-05
absolute error = 0.08329
relative error = 4.165 %
Correct digits = 1
h = 0.0001 0.004
x2[1] (numeric) = 1.00665122563 -0.1211045132
x2[1] (closed_form) = 1.00881192083 -0.0106965024945
absolute error = 0.1104
relative error = 10.95 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=44471.7MB, alloc=40.3MB, time=540.75
memory used=44515.8MB, alloc=40.3MB, time=541.28
t[1] = 2.1196 2.706
h = 0.003 0.006
x1[1] (numeric) = 2.07337915957 -0.0397869643582
x1[1] (closed_form) = 1.99980404007 -9.12012172530e-05
absolute error = 0.0836
relative error = 4.18 %
Correct digits = 1
h = 0.003 0.006
x2[1] (numeric) = 1.00717020618 -0.121611195542
x2[1] (closed_form) = 1.00889881457 -0.0106273954451
absolute error = 0.111
relative error = 11 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=44559.7MB, alloc=40.3MB, time=541.80
t[1] = 2.1226 2.712
h = 0.0001 0.005
x1[1] (numeric) = 2.07415554441 -0.039847270644
x1[1] (closed_form) = 1.99980408502 -8.97541563315e-05
absolute error = 0.08431
relative error = 4.216 %
Correct digits = 1
h = 0.0001 0.005
x2[1] (numeric) = 1.00769660767 -0.122119109659
x2[1] (closed_form) = 1.00908003471 -0.0105824300686
absolute error = 0.1115
relative error = 11.05 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=44603.8MB, alloc=40.3MB, time=542.33
memory used=44648.0MB, alloc=40.3MB, time=542.86
t[1] = 2.1227 2.717
h = 0.0001 0.003
x1[1] (numeric) = 2.07469387758 -0.0396395493509
x1[1] (closed_form) = 1.99980365833 -8.87645866792e-05
absolute error = 0.08469
relative error = 4.235 %
Correct digits = 1
h = 0.0001 0.003
x2[1] (numeric) = 1.00823149643 -0.122627552462
x2[1] (closed_form) = 1.00918702468 -0.0104927067909
absolute error = 0.1121
relative error = 11.11 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=44692.4MB, alloc=40.3MB, time=543.40
t[1] = 2.1228 2.72
h = 0.001 0.001
x1[1] (numeric) = 2.07502020979 -0.0395186992483
x1[1] (closed_form) = 1.99980341258 -8.81663460484e-05
absolute error = 0.08493
relative error = 4.247 %
Correct digits = 1
h = 0.001 0.001
x2[1] (numeric) = 1.00877033535 -0.123133736848
x2[1] (closed_form) = 1.00925154154 -0.0104391850141
absolute error = 0.1127
relative error = 11.17 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=44736.6MB, alloc=40.3MB, time=543.94
t[1] = 2.1238 2.721
h = 0.001 0.003
x1[1] (numeric) = 2.07517375783 -0.0395818229859
x1[1] (closed_form) = 1.99980352109 -8.78817888374e-05
absolute error = 0.08509
relative error = 4.255 %
Correct digits = 1
h = 0.001 0.003
x2[1] (numeric) = 1.00931037443 -0.123639567721
x2[1] (closed_form) = 1.00929101892 -0.0104413807671
absolute error = 0.1132
relative error = 11.22 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=44780.8MB, alloc=40.3MB, time=544.46
memory used=44825.0MB, alloc=40.3MB, time=544.99
t[1] = 2.1248 2.724
h = 0.0001 0.004
x1[1] (numeric) = 2.07554786541 -0.0395507604636
x1[1] (closed_form) = 1.99980345498 -8.72047092063e-05
absolute error = 0.08541
relative error = 4.271 %
Correct digits = 1
h = 0.0001 0.004
x2[1] (numeric) = 1.00985190344 -0.124145739489
x2[1] (closed_form) = 1.0093721912 -0.0104058999459
absolute error = 0.1137
relative error = 11.27 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=44869.0MB, alloc=40.3MB, time=545.52
t[1] = 2.1249 2.728
h = 0.003 0.006
x1[1] (numeric) = 2.0759909776 -0.039372410078
x1[1] (closed_form) = 1.99980312742 -8.64091922163e-05
absolute error = 0.08572
relative error = 4.286 %
Correct digits = 1
h = 0.003 0.006
x2[1] (numeric) = 1.01039667413 -0.124650960817
x2[1] (closed_form) = 1.00945686344 -0.0103322594159
absolute error = 0.1143
relative error = 11.32 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=44913.0MB, alloc=40.3MB, time=546.04
memory used=44957.2MB, alloc=40.3MB, time=546.57
t[1] = 2.1279 2.734
h = 0.0001 0.005
x1[1] (numeric) = 2.07678757717 -0.0394142792252
x1[1] (closed_form) = 1.99980320378 -8.49711123616e-05
absolute error = 0.08645
relative error = 4.323 %
Correct digits = 1
h = 0.0001 0.005
x2[1] (numeric) = 1.01094907693 -0.125157247794
x2[1] (closed_form) = 1.00963785444 -0.0102788069617
absolute error = 0.1149
relative error = 11.38 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=45001.1MB, alloc=40.3MB, time=547.09
t[1] = 2.128 2.739
h = 0.0001 0.003
x1[1] (numeric) = 2.07733353047 -0.0391877778622
x1[1] (closed_form) = 1.99980280111 -8.39776750616e-05
absolute error = 0.08683
relative error = 4.342 %
Correct digits = 1
h = 0.0001 0.003
x2[1] (numeric) = 1.01151018528 -0.125663852235
x2[1] (closed_form) = 1.0097419033 -0.0101834569233
absolute error = 0.1155
relative error = 11.44 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=45045.1MB, alloc=40.3MB, time=547.62
t[1] = 2.1281 2.742
h = 0.001 0.001
x1[1] (numeric) = 2.07766460973 -0.0390556655782
memory used=45089.8MB, alloc=40.3MB, time=548.17
x1[1] (closed_form) = 1.99980256981 -8.33773632322e-05
absolute error = 0.08707
relative error = 4.354 %
Correct digits = 1
h = 0.001 0.001
x2[1] (numeric) = 1.01207527931 -0.126168039633
x2[1] (closed_form) = 1.00980467252 -0.0101265478829
absolute error = 0.1161
relative error = 11.49 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=45133.9MB, alloc=40.3MB, time=548.70
t[1] = 2.1291 2.743
h = 0.001 0.003
x1[1] (numeric) = 2.07782346376 -0.0391163718649
x1[1] (closed_form) = 1.99980268395 -8.30967530717e-05
absolute error = 0.08724
relative error = 4.362 %
Correct digits = 1
h = 0.001 0.003
x2[1] (numeric) = 1.01264159305 -0.12667183333
x2[1] (closed_form) = 1.00984463245 -0.0101270118592
absolute error = 0.1166
relative error = 11.54 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=45177.9MB, alloc=40.3MB, time=549.22
t[1] = 2.1301 2.746
h = 0.0001 0.004
x1[1] (numeric) = 2.07820575916 -0.0390749757961
x1[1] (closed_form) = 1.99980263301 -8.24219686713e-05
absolute error = 0.08756
relative error = 4.379 %
Correct digits = 1
h = 0.0001 0.004
x2[1] (numeric) = 1.0132094416 -0.127175936798
x2[1] (closed_form) = 1.0099250207 -0.0100875801557
absolute error = 0.1171
relative error = 11.6 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=45222.0MB, alloc=40.3MB, time=549.75
memory used=45266.2MB, alloc=40.3MB, time=550.28
t[1] = 2.1302 2.75
h = 0.003 0.006
x1[1] (numeric) = 2.07865493795 -0.0388809864554
x1[1] (closed_form) = 1.99980232467 -8.16236806674e-05
absolute error = 0.08788
relative error = 4.394 %
Correct digits = 1
h = 0.003 0.006
x2[1] (numeric) = 1.01378058478 -0.127678981367
x2[1] (closed_form) = 1.01000724838 -0.0100094612461
absolute error = 0.1177
relative error = 11.66 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=45310.1MB, alloc=40.3MB, time=550.80
t[1] = 2.1332 2.756
h = 0.0001 0.005
x1[1] (numeric) = 2.07947172643 -0.0389034451186
x1[1] (closed_form) = 1.99980243208 -8.01952196888e-05
absolute error = 0.08863
relative error = 4.432 %
Correct digits = 1
h = 0.0001 0.005
x2[1] (numeric) = 1.01435957195 -0.128182915718
x2[1] (closed_form) = 1.01018763056 -0.00994745008536
absolute error = 0.1183
relative error = 11.71 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=45354.2MB, alloc=40.3MB, time=551.33
memory used=45398.4MB, alloc=40.3MB, time=551.86
t[1] = 2.1333 2.761
h = 0.0001 0.003
x1[1] (numeric) = 2.08002497156 -0.0386575215564
x1[1] (closed_form) = 1.99980205337 -7.91984615427e-05
absolute error = 0.08902
relative error = 4.451 %
Correct digits = 1
h = 0.0001 0.003
x2[1] (numeric) = 1.01494748264 -0.12868694528
x2[1] (closed_form) = 1.01028845969 -0.00984654985026
absolute error = 0.1189
relative error = 11.77 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=45442.9MB, alloc=40.3MB, time=552.40
t[1] = 2.1334 2.764
h = 0.001 0.001
x1[1] (numeric) = 2.08036060518 -0.0385137572485
x1[1] (closed_form) = 1.99980183649 -7.85964061304e-05
absolute error = 0.08926
relative error = 4.463 %
Correct digits = 1
h = 0.001 0.001
x2[1] (numeric) = 1.01553941113 -0.129188394333
x2[1] (closed_form) = 1.01034931376 -0.00978629861914
absolute error = 0.1195
relative error = 11.83 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=45487.2MB, alloc=40.3MB, time=552.94
t[1] = 2.1344 2.765
h = 0.0001 0.004
x1[1] (numeric) = 2.08052482367 -0.0385718469885
x1[1] (closed_form) = 1.99980195613 -7.83198443354e-05
absolute error = 0.08943
relative error = 4.472 %
Correct digits = 1
h = 0.0001 0.004
x2[1] (numeric) = 1.0161325783 -0.129689407986
x2[1] (closed_form) = 1.01038968387 -0.00978499265877
absolute error = 0.12
relative error = 11.88 %
Correct digits = 1
memory used=45531.4MB, alloc=40.3MB, time=553.46
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=45575.5MB, alloc=40.3MB, time=553.99
t[1] = 2.1345 2.769
h = 0.003 0.006
x1[1] (numeric) = 2.08097812561 -0.0383659929089
x1[1] (closed_form) = 1.99980166427 -7.75192921057e-05
absolute error = 0.08975
relative error = 4.488 %
Correct digits = 1
h = 0.003 0.006
x2[1] (numeric) = 1.01672782481 -0.13018944413
x2[1] (closed_form) = 1.0104695767 -0.00970310373591
absolute error = 0.1206
relative error = 11.94 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=45619.3MB, alloc=40.3MB, time=554.52
t[1] = 2.1375 2.775
h = 0.0001 0.005
x1[1] (numeric) = 2.0818095019 -0.0383733808976
x1[1] (closed_form) = 1.99980179823 -7.60992490074e-05
absolute error = 0.09051
relative error = 4.526 %
Correct digits = 1
h = 0.0001 0.005
x2[1] (numeric) = 1.01733108264 -0.130690188732
x2[1] (closed_form) = 1.01064902271 -0.00963369404269
absolute error = 0.1212
relative error = 12 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=45663.5MB, alloc=40.3MB, time=555.04
memory used=45707.7MB, alloc=40.3MB, time=555.57
t[1] = 2.1376 2.78
h = 0.0001 0.003
x1[1] (numeric) = 2.08236768052 -0.0381127281477
x1[1] (closed_form) = 1.99980144007 -7.50997826876e-05
absolute error = 0.09091
relative error = 4.546 %
Correct digits = 1
h = 0.0001 0.003
x2[1] (numeric) = 1.0179434314 -0.131190805347
x2[1] (closed_form) = 1.01074679318 -0.00952813056788
absolute error = 0.1219
relative error = 12.06 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=45751.9MB, alloc=40.3MB, time=556.11
t[1] = 2.1377 2.783
h = 0.001 0.001
x1[1] (numeric) = 2.08270641507 -0.0379601054168
x1[1] (closed_form) = 1.99980123554 -7.44963158339e-05
absolute error = 0.09115
relative error = 4.558 %
Correct digits = 1
h = 0.001 0.001
x2[1] (numeric) = 1.01855980727 -0.131688692473
x2[1] (closed_form) = 1.01080582597 -0.00946507012034
absolute error = 0.1225
relative error = 12.12 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=45796.3MB, alloc=40.3MB, time=556.65
memory used=45840.4MB, alloc=40.3MB, time=557.18
t[1] = 2.1387 2.784
h = 0.001 0.003
x1[1] (numeric) = 2.08287459394 -0.0380160760344
x1[1] (closed_form) = 1.99980135988 -7.42232537815e-05
absolute error = 0.09133
relative error = 4.567 %
Correct digits = 1
h = 0.001 0.003
x2[1] (numeric) = 1.01917743378 -0.132186104957
x2[1] (closed_form) = 1.01084646772 -0.00946220860142
absolute error = 0.123
relative error = 12.17 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=45884.4MB, alloc=40.3MB, time=557.70
t[1] = 2.1397 2.787
h = 0.0001 0.004
x1[1] (numeric) = 2.08327077733 -0.0379555047395
x1[1] (closed_form) = 1.99980133687 -7.35534101210e-05
absolute error = 0.09166
relative error = 4.584 %
Correct digits = 1
h = 0.0001 0.004
x2[1] (numeric) = 1.01979667641 -0.132683759544
x2[1] (closed_form) = 1.01092486078 -0.00941543737258
absolute error = 0.1236
relative error = 12.22 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=45928.4MB, alloc=40.3MB, time=558.24
t[1] = 2.1398 2.791
h = 0.003 0.006
x1[1] (numeric) = 2.08372962752 -0.037732960211
x1[1] (closed_form) = 1.99980106414 -7.27508958402e-05
absolute error = 0.09199
relative error = 4.6 %
Correct digits = 1
h = 0.003 0.006
x2[1] (numeric) = 1.02041929752 -0.133180137007
x2[1] (closed_form) = 1.01100189609 -0.00932920311401
absolute error = 0.1242
relative error = 12.29 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=45972.5MB, alloc=40.3MB, time=558.77
memory used=46016.5MB, alloc=40.3MB, time=559.29
t[1] = 2.1428 2.797
h = 0.0001 0.005
x1[1] (numeric) = 2.0845811483 -0.0377189803636
x1[1] (closed_form) = 1.99980122843 -7.13416320808e-05
absolute error = 0.09276
relative error = 4.639 %
Correct digits = 1
h = 0.0001 0.005
x2[1] (numeric) = 1.0210501418 -0.133677029319
x2[1] (closed_form) = 1.0111800086 -0.00925114954955
absolute error = 0.1248
relative error = 12.34 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=46060.5MB, alloc=40.3MB, time=559.82
t[1] = 2.1429 2.802
h = 0.0001 0.003
x1[1] (numeric) = 2.08514596395 -0.0374376105674
x1[1] (closed_form) = 1.99980089412 -7.03398522623e-05
absolute error = 0.09317
relative error = 4.659 %
Correct digits = 1
h = 0.0001 0.003
x2[1] (numeric) = 1.0216902929 -0.134173551437
x2[1] (closed_form) = 1.0112740445 -0.00914021664016
absolute error = 0.1255
relative error = 12.41 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=46104.6MB, alloc=40.3MB, time=560.35
memory used=46149.1MB, alloc=40.3MB, time=560.89
t[1] = 2.143 2.805
h = 0.001 0.001
x1[1] (numeric) = 2.08548886815 -0.0372725498287
x1[1] (closed_form) = 1.99980070393 -6.97352451121e-05
absolute error = 0.09342
relative error = 4.671 %
Correct digits = 1
h = 0.001 0.001
x2[1] (numeric) = 1.02233449643 -0.134667172295
x2[1] (closed_form) = 1.01133085249 -0.00907392087253
absolute error = 0.1261
relative error = 12.47 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=46193.3MB, alloc=40.3MB, time=561.42
t[1] = 2.144 2.806
h = 0.001 0.003
x1[1] (numeric) = 2.08566253024 -0.0373255039973
x1[1] (closed_form) = 1.99980083356 -6.94664130459e-05
absolute error = 0.0936
relative error = 4.68 %
Correct digits = 1
h = 0.001 0.003
x2[1] (numeric) = 1.02297996825 -0.135160274155
x2[1] (closed_form) = 1.01137176307 -0.00906922701607
absolute error = 0.1266
relative error = 12.52 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=46237.3MB, alloc=40.3MB, time=561.95
memory used=46281.3MB, alloc=40.3MB, time=562.48
t[1] = 2.145 2.809
h = 0.0001 0.004
x1[1] (numeric) = 2.08606664074 -0.0372532116344
x1[1] (closed_form) = 1.99980082533 -6.87997678339e-05
absolute error = 0.09394
relative error = 4.697 %
Correct digits = 1
h = 0.0001 0.004
x2[1] (numeric) = 1.02362710155 -0.135653581428
x2[1] (closed_form) = 1.01144884311 -0.00901851964097
absolute error = 0.1272
relative error = 12.58 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=46325.3MB, alloc=40.3MB, time=563.00
t[1] = 2.1451 2.813
h = 0.003 0.006
x1[1] (numeric) = 2.08653071872 -0.0370134399743
x1[1] (closed_form) = 1.99980057167 -6.79957209615e-05
absolute error = 0.09427
relative error = 4.714 %
Correct digits = 1
h = 0.003 0.006
x2[1] (numeric) = 1.02427766119 -0.136145491857
x2[1] (closed_form) = 1.01152280004 -0.00892802523789
absolute error = 0.1279
relative error = 12.64 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=46369.4MB, alloc=40.3MB, time=563.53
t[1] = 2.1481 2.819
h = 0.0001 0.005
x1[1] (numeric) = 2.08740227624 -0.0369770542883
x1[1] (closed_form) = 1.99980076588 -6.65978407115e-05
absolute error = 0.09506
relative error = 4.753 %
Correct digits = 1
h = 0.0001 0.005
x2[1] (numeric) = 1.02493665587 -0.13663771308
x2[1] (closed_form) = 1.01169918169 -0.00884130373293
absolute error = 0.1285
relative error = 12.7 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=46413.5MB, alloc=40.3MB, time=564.05
memory used=46457.5MB, alloc=40.3MB, time=564.58
t[1] = 2.1482 2.824
h = 0.0001 0.003
x1[1] (numeric) = 2.08797332516 -0.0366743082977
x1[1] (closed_form) = 1.99980045534 -6.55942820580e-05
absolute error = 0.09547
relative error = 4.774 %
Correct digits = 1
h = 0.0001 0.003
x2[1] (numeric) = 1.02560517206 -0.137129310152
x2[1] (closed_form) = 1.01178920815 -0.00872511571062
absolute error = 0.1291
relative error = 12.76 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=46501.8MB, alloc=40.3MB, time=565.12
t[1] = 2.1483 2.827
h = 0.001 0.001
x1[1] (numeric) = 2.08832016101 -0.0364964088409
x1[1] (closed_form) = 1.99980027943 -6.49888545996e-05
absolute error = 0.09572
relative error = 4.787 %
Correct digits = 1
h = 0.001 0.001
x2[1] (numeric) = 1.026277762 -0.137617829285
x2[1] (closed_form) = 1.01184362596 -0.00865565237458
absolute error = 0.1298
relative error = 12.82 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=46546.2MB, alloc=40.3MB, time=565.66
memory used=46590.4MB, alloc=40.3MB, time=566.19
t[1] = 2.1493 2.828
h = 0.001 0.003
x1[1] (numeric) = 2.08849935239 -0.0365461289974
x1[1] (closed_form) = 1.99980041423 -6.47243448518e-05
absolute error = 0.09591
relative error = 4.796 %
Correct digits = 1
h = 0.001 0.003
x2[1] (numeric) = 1.02695163717 -0.138105783502
x2[1] (closed_form) = 1.01188472646 -0.00864909654359
absolute error = 0.1303
relative error = 12.88 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=46634.5MB, alloc=40.3MB, time=566.72
t[1] = 2.1503 2.831
h = 0.0001 0.004
x1[1] (numeric) = 2.08891125866 -0.0364616300471
x1[1] (closed_form) = 1.99980042063 -6.40612039288e-05
absolute error = 0.09626
relative error = 4.813 %
Correct digits = 1
h = 0.0001 0.004
x2[1] (numeric) = 1.02762721928 -0.13859390432
x2[1] (closed_form) = 1.01196030572 -0.00859447345253
absolute error = 0.1309
relative error = 12.94 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=46678.6MB, alloc=40.3MB, time=567.25
memory used=46722.8MB, alloc=40.3MB, time=567.78
t[1] = 2.1504 2.835
h = 0.003 0.006
x1[1] (numeric) = 2.08938022231 -0.0362040904562
x1[1] (closed_form) = 1.99980018597 -6.32560501769e-05
absolute error = 0.0966
relative error = 4.83 %
Correct digits = 1
h = 0.003 0.006
x2[1] (numeric) = 1.02830627356 -0.139080504349
x2[1] (closed_form) = 1.01203096506 -0.00849981473675
absolute error = 0.1316
relative error = 13 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=46766.9MB, alloc=40.3MB, time=568.31
t[1] = 2.1534 2.841
h = 0.0001 0.005
x1[1] (numeric) = 2.09027167889 -0.0361442394588
x1[1] (closed_form) = 1.9998004097 -6.18701454377e-05
absolute error = 0.0974
relative error = 4.871 %
Correct digits = 1
h = 0.0001 0.005
x2[1] (numeric) = 1.02899397446 -0.139567200413
x2[1] (closed_form) = 1.01220521358 -0.00840441864757
absolute error = 0.1322
relative error = 13.06 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=46810.9MB, alloc=40.3MB, time=568.83
t[1] = 2.1535 2.846
h = 0.0001 0.003
x1[1] (numeric) = 2.09084853051 -0.0358194533429
x1[1] (closed_form) = 1.99980012283 -6.08653378817e-05
absolute error = 0.09782
relative error = 4.891 %
Correct digits = 1
h = 0.0001 0.003
x2[1] (numeric) = 1.02969141003 -0.140053006363
x2[1] (closed_form) = 1.01229095812 -0.00828310315761
absolute error = 0.1329
relative error = 13.13 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=46854.9MB, alloc=40.3MB, time=569.36
memory used=46899.4MB, alloc=40.3MB, time=569.90
t[1] = 2.1536 2.849
h = 0.001 0.001
x1[1] (numeric) = 2.09119904384 -0.035628311351
x1[1] (closed_form) = 1.99979996114 -6.02594071473e-05
absolute error = 0.09808
relative error = 4.904 %
Correct digits = 1
h = 0.001 0.001
x2[1] (numeric) = 1.03039293647 -0.140535552782
x2[1] (closed_form) = 1.01234282178 -0.00821054801106
absolute error = 0.1336
relative error = 13.19 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=46943.7MB, alloc=40.3MB, time=570.44
t[1] = 2.1546 2.85
h = 0.001 0.003
x1[1] (numeric) = 2.09138380594 -0.0356745736174
x1[1] (closed_form) = 1.99980010098 -5.99993088750e-05
absolute error = 0.09826
relative error = 4.914 %
Correct digits = 1
h = 0.001 0.003
x2[1] (numeric) = 1.03109576424 -0.141017486784
x2[1] (closed_form) = 1.01238403121 -0.00820210378819
absolute error = 0.1341
relative error = 13.25 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=46987.9MB, alloc=40.3MB, time=570.96
memory used=47032.0MB, alloc=40.3MB, time=571.49
t[1] = 2.1556 2.853
h = 0.0001 0.004
x1[1] (numeric) = 2.09180336074 -0.0355773746463
x1[1] (closed_form) = 1.99980012186 -5.93399730716e-05
absolute error = 0.09862
relative error = 4.932 %
Correct digits = 1
h = 0.0001 0.004
x2[1] (numeric) = 1.0318003445 -0.141499546401
x2[1] (closed_form) = 1.01245792101 -0.00814359395355
absolute error = 0.1348
relative error = 13.31 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=47076.1MB, alloc=40.3MB, time=572.02
t[1] = 2.1557 2.857
h = 0.003 0.006
x1[1] (numeric) = 2.09227684563 -0.0353015226785
x1[1] (closed_form) = 1.99979990611 -5.85341342272e-05
absolute error = 0.09896
relative error = 4.949 %
Correct digits = 1
h = 0.003 0.006
x2[1] (numeric) = 1.03250844055 -0.141979957007
x2[1] (closed_form) = 1.0125250657 -0.00804487742726
absolute error = 0.1354
relative error = 13.37 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=47120.1MB, alloc=40.3MB, time=572.54
memory used=47164.1MB, alloc=40.3MB, time=573.07
t[1] = 2.1587 2.863
h = 0.0001 0.005
x1[1] (numeric) = 2.0931880324 -0.0352171256949
x1[1] (closed_form) = 1.99980015893 -5.71607846586e-05
absolute error = 0.09979
relative error = 4.99 %
Correct digits = 1
h = 0.0001 0.005
x2[1] (numeric) = 1.03322539424 -0.142460237935
x2[1] (closed_form) = 1.0126967746 -0.00794081792304
absolute error = 0.1361
relative error = 13.44 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=47208.4MB, alloc=40.3MB, time=573.60
t[1] = 2.1588 2.868
h = 0.0001 0.003
x1[1] (numeric) = 2.09377022853 -0.0348696313286
x1[1] (closed_form) = 1.99979989564 -5.61552531811e-05
absolute error = 0.1002
relative error = 5.011 %
Correct digits = 1
h = 0.0001 0.003
x2[1] (numeric) = 1.03395229385 -0.142939350532
x2[1] (closed_form) = 1.01277796781 -0.00781451595573
absolute error = 0.1368
relative error = 13.5 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=47252.7MB, alloc=40.3MB, time=574.14
t[1] = 2.1589 2.871
h = 0.001 0.001
x1[1] (numeric) = 2.09412414855 -0.0346648402258
x1[1] (closed_form) = 1.9997997481 -5.55491331164e-05
absolute error = 0.1005
relative error = 5.024 %
Correct digits = 1
h = 0.001 0.001
x2[1] (numeric) = 1.03468329698 -0.143415017086
x2[1] (closed_form) = 1.01282711512 -0.00773895277763
absolute error = 0.1374
relative error = 13.57 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=47297.3MB, alloc=40.3MB, time=574.67
memory used=47341.5MB, alloc=40.3MB, time=575.20
t[1] = 2.1599 2.872
h = 0.001 0.003
x1[1] (numeric) = 2.09431451786 -0.0347074143801
x1[1] (closed_form) = 1.99979989286 -5.52935322895e-05
absolute error = 0.1007
relative error = 5.034 %
Correct digits = 1
h = 0.001 0.003
x2[1] (numeric) = 1.03541561666 -0.143890022122
x2[1] (closed_form) = 1.01286835052 -0.0077285970889
absolute error = 0.138
relative error = 13.63 %
Correct digits = 1
NO INFO (given) for Equation 1
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
NO INFO (given) for Equation 2
NO POLE (ratio test) for Equation 2
NO REAL POLE (three term test) for Equation 2
NO COMPLEX POLE (six term test) for Equation 2
memory used=47387.7MB, alloc=40.3MB, time=575.80
Finished!
Maximum Time Reached before Solution Completed!
diff ( x1 , t , 1 ) = 4.0 * x2 - 2.0 * diff ( x2 , t , 1 ) - 2.0 * x1 ;
diff ( x2 , t , 2 ) = 3.0 * diff ( x2 , t , 1 ) - 2.0 * x2 - diff ( x1 , t , 2 ) - diff ( x1 , t , 1 ) + x1 ;
Iterations = 754
Total Elapsed Time = 9 Minutes 35 Seconds
Expected Time Remaining = 0 Seconds
Optimized Time Remaining = 0 Seconds
Expected Total Time = 9 Minutes 35 Seconds
> quit
memory used=47402.7MB, alloc=40.3MB, time=576.00