|\^/| 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_y := proc(x)
> return(c(1.0) / (c(x) * c( x) + c(1.0)));
> end;
exact_soln_y := proc(x) return c(1.0)/(c(x)*c(x) + c(1.0)) end proc
> next_delta := proc()
> global glob_nxt, x_delta;
> x_delta := [ 0.001 + 0.00004 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.000 + 0.000 * I ];
> glob_nxt := glob_nxt + 1;
> it := x_delta[glob_nxt];
> return it;
> end;
Warning, `it` is implicitly declared local to procedure `next_delta`
next_delta := proc()
local it;
global glob_nxt, x_delta;
x_delta := [0.001 + 0.00004*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0. + 0.*I];
glob_nxt := glob_nxt + 1;
it := x_delta[glob_nxt];
return it
end proc
#END USER DEF BLOCK
#END BLOCK 3
#END USER FUNCTION BLOCK
# before write_aux functions
# Begin Function number 2
> display_poles := proc()
> local rad_given;
> global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ;
> if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1
> rad_given := float_abs(array_x[1] - (array_given_rad_poles[1,1] + array_given_rad_poles[1,2] * I ));
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," ");
> omniout_complex(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," ");
> if ((float_abs(rad_given) < float_abs(glob_least_given_sing)) and
> (float_abs(rad_given) > 0.0)) then # if number 2
> glob_least_given_sing := rad_given;
> fi;# end if 2;
> elif
> (glob_type_given_pole = 3) then # if number 2
> omniout_str(ALWAYS,"NO POLE (given) for Equation 1");
> elif
> (glob_type_given_pole = 5) then # if number 3
> omniout_str(ALWAYS,"SOME POLE (given) for Equation 1");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 1");
> fi;# end if 3;
> if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," ");
> if ((float_abs(array_rad_test_poles[1,1]) < glob_least_ratio_sing)) then # if number 4
> glob_least_ratio_sing := array_rad_test_poles[1,1];
> fi;# end if 4;
> omniout_complex(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," ");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," ");
> if ((float_abs(array_rad_test_poles[1,2]) < glob_least_3_sing)) then # if number 4
> glob_least_3_sing := array_rad_test_poles[1,2];
> fi;# end if 4;
> omniout_complex(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," ");
> if ((float_abs(array_rad_test_poles[1,3]) < glob_least_6_sing)) then # if number 4
> glob_least_6_sing := array_rad_test_poles[1,3];
> fi;# end if 4;
> omniout_complex(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1");
> fi;# end if 3
> ;
> end;
display_poles := proc()
local rad_given;
global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float,
glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord,
glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
glob_least_3_sing, glob_least_6_sing, glob_least_given_sing,
glob_least_ratio_sing, array_x;
if glob_type_given_pole = 1 or glob_type_given_pole = 2 then
rad_given := float_abs(array_x[1] - array_given_rad_poles[1, 1]
- array_given_rad_poles[1, 2]*I);
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 1 ", 4,
rad_given, 4, " ");
omniout_complex(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles[1, 1], 4, " ");
if float_abs(rad_given) < float_abs(glob_least_given_sing) and
0. < float_abs(rad_given) then glob_least_given_sing := rad_given
end if
elif glob_type_given_pole = 3 then
omniout_str(ALWAYS, "NO POLE (given) for Equation 1")
elif glob_type_given_pole = 5 then
omniout_str(ALWAYS, "SOME POLE (given) for Equation 1")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 1")
end if;
if array_rad_test_poles[1, 1] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (ratio test) for eq 1 ", 4,
array_rad_test_poles[1, 1], 4, " ");
if float_abs(array_rad_test_poles[1, 1]) < glob_least_ratio_sing
then glob_least_ratio_sing := array_rad_test_poles[1, 1]
end if;
omniout_complex(ALWAYS,
"Order of pole (ratio test) ", 4,
array_ord_test_poles[1, 1], 4, " ")
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 2] and
array_rad_test_poles[1, 2] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 1 ", 4,
array_rad_test_poles[1, 2], 4, " ");
if float_abs(array_rad_test_poles[1, 2]) < glob_least_3_sing then
glob_least_3_sing := array_rad_test_poles[1, 2]
end if;
omniout_complex(ALWAYS,
"Order of pole (three term test) ", 4,
array_ord_test_poles[1, 2], 4, " ")
else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 3] and
array_rad_test_poles[1, 3] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 1 ", 4,
array_rad_test_poles[1, 3], 4, " ");
if float_abs(array_rad_test_poles[1, 3]) < glob_least_6_sing then
glob_least_6_sing := array_rad_test_poles[1, 3]
end if;
omniout_complex(ALWAYS,
"Order of pole (six term test) ", 4,
array_ord_test_poles[1, 3], 4, " ")
else omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 1")
end if
end proc
# End Function number 2
# Begin Function number 3
> my_check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 3
> ret := glob__1;
> else
> ret := glob__m1;
> fi;# end if 3;
> 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_2D0,
> array_const_1D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local min_size;
> min_size := glob_estimated_size_answer;
> if (float_abs(array_y[1]) < min_size) then # if number 3
> min_size := float_abs(array_y[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> if (min_size < glob__1) then # if number 3
> min_size := glob__1;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> 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_2D0,
array_const_1D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
min_size := glob_estimated_size_answer;
if float_abs(array_y[1]) < min_size then
min_size := float_abs(array_y[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if min_size < 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_2D0,
> array_const_1D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> 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_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3);
> if (est_tmp >= max_estimated_step_error) then # if number 3
> max_estimated_step_error := est_tmp;
> fi;# end if 3;
> 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_2D0,
array_const_1D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, 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_y[no_terms - 3]
+ array_y[no_terms - 2]*hn_div_ho
+ array_y[no_terms - 1]*hn_div_ho_2
+ array_y[no_terms]*hn_div_ho_3);
if max_estimated_step_error <= est_tmp then
max_estimated_step_error := est_tmp
end if;
omniout_float(ALWAYS, "max_estimated_step_error", 32,
max_estimated_step_error, 32, "");
max_estimated_step_error
end proc
# End Function number 5
# Begin Function number 6
> track_estimated_error := proc()
> global
> 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_2D0,
> array_const_1D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> 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_y[no_terms-3])) + c(float_abs(array_y[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y[no_terms])) * c(hn_div_ho_3);
> if (glob_prec * c(float_abs(array_y[1])) > c(est_tmp)) then # if number 3
> est_tmp := c(glob_prec) * c(float_abs(array_y[1]));
> fi;# end if 3;
> if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 3
> array_max_est_error[1] := c(est_tmp);
> fi;# end if 3
> ;
> 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_2D0,
array_const_1D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, 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_y[no_terms - 3]))
+ c(float_abs(array_y[no_terms - 2]))*c(hn_div_ho)
+ c(float_abs(array_y[no_terms - 1]))*c(hn_div_ho_2)
+ c(float_abs(array_y[no_terms]))*c(hn_div_ho_3);
if c(est_tmp) < glob_prec*c(float_abs(array_y[1])) then
est_tmp := c(glob_prec)*c(float_abs(array_y[1]))
end if;
if c(array_max_est_error[1]) <= c(est_tmp) then
array_max_est_error[1] := 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_2D0,
> array_const_1D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local ret;
> if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 3
> ret := true;
> else
> ret := false;
> fi;# end if 3;
> 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_2D0,
array_const_1D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
if glob_check_sign*glob_next_display - glob_h/glob__10 <=
glob_check_sign*array_x[1] then ret := true
else ret := false
end if;
return ret
end proc
# End Function number 7
# Begin Function number 8
> display_alot := proc(iter)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_1D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err;
> #TOP DISPLAY ALOT
> ind_var := array_x[1];
> omniout_complex(ALWAYS,"x[1] ",33,ind_var,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> omniout_complex(ALWAYS,"h ",33,glob_h,20," ");
> omniout_complex(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> closed_form_val_y := evalf(exact_soln_y(ind_var));
> omniout_complex(ALWAYS,"y[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 3
> relerr := abserr/float_abs(closed_form_val_y);
> if (float_abs(c(relerr)) > 0.0) then # if number 4
> glob_good_digits := round(-log10(relerr));
> else
> relerr := 0.0 ;
> glob_good_digits := Digits - 2;
> fi;# end if 4;
> else
> ;
> relerr := glob__m1 ;
> glob_good_digits := -16;
> fi;# end if 3;
> if (glob_good_digits < glob_min_good_digits) then # if number 3
> glob_min_good_digits := glob_good_digits;
> fi;# end if 3;
> 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_2D0,
array_const_1D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
ind_var := array_x[1];
omniout_complex(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
omniout_complex(ALWAYS, "h ", 33, glob_h,
20, " ");
omniout_complex(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
closed_form_val_y := evalf(exact_soln_y(ind_var));
omniout_complex(ALWAYS, "y[1] (closed_form) ", 33,
closed_form_val_y, 20, " ");
abserr := float_abs(numeric_val - closed_form_val_y);
if 0. < float_abs(closed_form_val_y) then
relerr := abserr/float_abs(closed_form_val_y);
if 0. < float_abs(c(relerr)) then
glob_good_digits := round(-log10(relerr))
else relerr := 0.; glob_good_digits := Digits - 2
end if
else relerr := glob__m1; glob_good_digits := -16
end if;
if glob_good_digits < glob_min_good_digits then
glob_min_good_digits := glob_good_digits
end if;
omniout_float(ALWAYS, "absolute error ", 4, abserr, 4,
" ");
omniout_float(ALWAYS, "relative error ", 4,
relerr*glob__100, 4, "%");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ")
end proc
# End Function number 8
# Begin Function number 9
> prog_report := proc(x_start,x_end)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_1D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := (clock_sec1) - (glob_orig_start_sec);
> glob_clock_sec := (clock_sec1) - (glob_clock_start_sec);
> left_sec := (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1);
> expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h) ,( clock_sec1) - (glob_orig_start_sec));
> opt_clock_sec := ( clock_sec1) - (glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec));
> glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
> percent_done := comp_percent((x_end),(x_start),(array_x[1]) + (glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr((total_clock_sec));
> if (c(percent_done) < glob__100) then # if number 3
> 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 3;
> #BOTTOM PROGRESS REPORT
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_1D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec := clock_sec1 - glob_orig_start_sec;
glob_clock_sec := clock_sec1 - glob_clock_start_sec;
left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1;
expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h,
clock_sec1 - glob_orig_start_sec);
opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec;
glob_optimal_expect_sec :=
comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec)
;
glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h);
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(total_clock_sec);
if c(percent_done) < glob__100 then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(expect_sec);
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(glob_optimal_expect_sec);
omniout_str_noeol(INFO, "Expected Total Time ");
omniout_timestr(glob_total_exp_sec)
end if
end proc
# End Function number 9
# Begin Function number 10
> check_for_pole := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_1D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> 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_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 3
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 3;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 3
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 4
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 5
> found_sing := 0;
> fi;# end if 5;
> 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 5
> if (rad_c < array_rad_test_poles[1,1]) then # if number 6
> array_rad_test_poles[1,1] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,1] := rad_c;
> array_ord_test_poles[1,1] := tmp_ord;
> fi;# end if 6;
> fi;# end if 5;
> #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[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_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_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[1,2]) then # if number 8
> array_rad_test_poles[1,2] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,2] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 9
> glob_min_pole_est := rad_c;
> fi;# end if 9;
> array_ord_test_poles[1,2] := 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[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_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> 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[1,3]) then # if number 10
> array_rad_test_poles[1,3] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,3] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 11
> glob_min_pole_est := rad_c;
> fi;# end if 11;
> array_ord_test_poles[1,3] := tmp_ord;
> fi;# end if 10;
> fi;# end if 9;
> #BOTTOM general radius test1
> ;
> if (true) then # if number 9
> display_poles();
> fi;# end if 9
> 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_2D0,
array_const_1D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, 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_y_higher[1, last_no - 1],
array_y_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_y_higher[1, last_no - 1],
array_y_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[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_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
array_y_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_y_higher[1, last_no - 2],
array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
last_no);
array_rad_test_poles[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[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_y_higher[1, last_no - 5],
array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3],
array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
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_y_higher[1, last_no - 5],
array_y_higher[1, last_no - 4],
array_y_higher[1, last_no - 3],
array_y_higher[1, last_no - 2],
array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
last_no);
array_rad_test_poles[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;
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_2D0,
> array_const_1D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> # before write maple main top matter
> # before generate constants assign
> # before generate globals assign
> #END OUTFILE1
> #BEGIN OUTFILE2
> #END OUTFILE2
> #BEGIN ATOMHDR1
> #emit pre neg ID_CONST $eq_no = 1
> array_tmp1[1] := neg(array_const_2D0[1]);
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 1
> array_tmp2[1] := array_tmp1[1] * array_x[1];
> #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 1
> array_tmp3[1] := array_x[1] * array_x[1];
> #emit pre add FULL - CONST $eq_no = 1 i = 1
> array_tmp4[1] := array_tmp3[1] + array_const_1D0[1];
> #emit pre div LINEAR - FULL $eq_no = 1 i = 1
> array_tmp5[1] := array_tmp2[1] / array_tmp4[1];
> #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 1
> array_tmp6[1] := array_x[1] * array_x[1];
> #emit pre add FULL - CONST $eq_no = 1 i = 1
> array_tmp7[1] := array_tmp6[1] + array_const_1D0[1];
> #emit pre div FULL - FULL $eq_no = 1 i = 1
> array_tmp8[1] := (array_tmp5[1] / (array_tmp7[1]));
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp9[1] := array_const_0D0[1] + array_tmp8[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y_set_initial[1,2]) then # if number 1
> if (1 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp9[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
> if (2 <= ATS_MAX_TERMS) then # if number 3
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(1);
> array_y_higher[2,1] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[1] * array_x[2];
> #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 2
> array_tmp3[2] := array_x[1] * array_x[2] + array_x[2] * array_x[1];
> #emit pre add FULL CONST $eq_no = 1 i = 2
> array_tmp4[2] := array_tmp3[2];
> #emit pre div LINEAR - FULL $eq_no = 1 i = 2
> array_tmp5[2] := (array_tmp2[2] - array_tmp5[1] * array_tmp4[2]) / array_tmp4[1];
> #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 2
> array_tmp6[2] := array_x[1] * array_x[2] + array_x[2] * array_x[1];
> #emit pre add FULL CONST $eq_no = 1 i = 2
> array_tmp7[2] := array_tmp6[2];
> #emit pre div FULL - FULL $eq_no = 1 i = 2
> array_tmp8[2] := ((array_tmp5[2] - ats(2,array_tmp7,array_tmp8,2))/array_tmp7[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp9[2] := array_tmp8[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y_set_initial[1,3]) then # if number 1
> if (2 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp9[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2));
> if (3 <= ATS_MAX_TERMS) then # if number 3
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y_higher[2,2] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 3
> array_tmp3[3] := array_x[2] * array_x[2];
> #emit pre add FULL CONST $eq_no = 1 i = 3
> array_tmp4[3] := array_tmp3[3];
> #emit pre div LINEAR FULL $eq_no = 1 i = 3
> array_tmp5[3] := neg( ats(3,array_tmp4,array_tmp5,2)) / array_tmp4[1];
> #emit pre mult LINEAR - LINEAR $eq_no = 1 i = 3
> array_tmp6[3] := array_x[2] * array_x[2];
> #emit pre add FULL CONST $eq_no = 1 i = 3
> array_tmp7[3] := array_tmp6[3];
> #emit pre div FULL - FULL $eq_no = 1 i = 3
> array_tmp8[3] := ((array_tmp5[3] - ats(3,array_tmp7,array_tmp8,2))/array_tmp7[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp9[3] := array_tmp8[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y_set_initial[1,4]) then # if number 1
> if (3 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp9[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3));
> if (4 <= ATS_MAX_TERMS) then # if number 3
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y_higher[2,3] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre add FULL CONST $eq_no = 1 i = 4
> array_tmp4[4] := array_tmp3[4];
> #emit pre div LINEAR FULL $eq_no = 1 i = 4
> array_tmp5[4] := neg( ats(4,array_tmp4,array_tmp5,2)) / array_tmp4[1];
> #emit pre add FULL CONST $eq_no = 1 i = 4
> array_tmp7[4] := array_tmp6[4];
> #emit pre div FULL - FULL $eq_no = 1 i = 4
> array_tmp8[4] := ((array_tmp5[4] - ats(4,array_tmp7,array_tmp8,2))/array_tmp7[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp9[4] := array_tmp8[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y_set_initial[1,5]) then # if number 1
> if (4 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp9[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4));
> if (5 <= ATS_MAX_TERMS) then # if number 3
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y_higher[2,4] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre add FULL CONST $eq_no = 1 i = 5
> array_tmp4[5] := array_tmp3[5];
> #emit pre div LINEAR FULL $eq_no = 1 i = 5
> array_tmp5[5] := neg( ats(5,array_tmp4,array_tmp5,2)) / array_tmp4[1];
> #emit pre add FULL CONST $eq_no = 1 i = 5
> array_tmp7[5] := array_tmp6[5];
> #emit pre div FULL - FULL $eq_no = 1 i = 5
> array_tmp8[5] := ((array_tmp5[5] - ats(5,array_tmp7,array_tmp8,2))/array_tmp7[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp9[5] := array_tmp8[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y_set_initial[1,6]) then # if number 1
> if (5 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp9[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5));
> if (6 <= ATS_MAX_TERMS) then # if number 3
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y_higher[2,5] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= ATS_MAX_TERMS) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit mult LINEAR - LINEAR $eq_no = 1 i = 1
> #emit FULL - NOT FULL add $eq_no = 1
> array_tmp4[kkk] := array_tmp3[kkk];
> #emit div LINEAR FULL $eq_no = 1 i = 1
> array_tmp5[kkk] := neg(ats(kkk,array_tmp4,array_tmp5,2)) / array_tmp4[1];
> #emit mult LINEAR - LINEAR $eq_no = 1 i = 1
> #emit FULL - NOT FULL add $eq_no = 1
> array_tmp7[kkk] := array_tmp6[kkk];
> #emit div FULL FULL $eq_no = 1
> array_tmp8[kkk] := ((array_tmp5[kkk] - ats(kkk,array_tmp7,array_tmp8,2)) /array_tmp7[1]);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp9[kkk] := array_tmp8[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1
> if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2
> temporary := c(array_tmp9[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
> array_y[kkk + order_d] := c(temporary);
> array_y_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_y_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_2D0,
array_const_1D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
array_tmp1[1] := neg(array_const_2D0[1]);
array_tmp2[1] := array_tmp1[1]*array_x[1];
array_tmp3[1] := array_x[1]*array_x[1];
array_tmp4[1] := array_tmp3[1] + array_const_1D0[1];
array_tmp5[1] := array_tmp2[1]/array_tmp4[1];
array_tmp6[1] := array_x[1]*array_x[1];
array_tmp7[1] := array_tmp6[1] + array_const_1D0[1];
array_tmp8[1] := array_tmp5[1]/array_tmp7[1];
array_tmp9[1] := array_const_0D0[1] + array_tmp8[1];
if not array_y_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp9[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
if 2 <= ATS_MAX_TERMS then
array_y[2] := temporary; array_y_higher[1, 2] := temporary
end if;
temporary := c(temporary)*c(1)/c(glob_h);
array_y_higher[2, 1] := c(temporary)
end if
end if;
kkk := 2;
array_tmp2[2] := array_tmp1[1]*array_x[2];
array_tmp3[2] := array_x[1]*array_x[2] + array_x[1]*array_x[2];
array_tmp4[2] := array_tmp3[2];
array_tmp5[2] :=
(-array_tmp4[2]*array_tmp5[1] + array_tmp2[2])/array_tmp4[1];
array_tmp6[2] := array_x[1]*array_x[2] + array_x[1]*array_x[2];
array_tmp7[2] := array_tmp6[2];
array_tmp8[2] :=
(array_tmp5[2] - ats(2, array_tmp7, array_tmp8, 2))/array_tmp7[1];
array_tmp9[2] := array_tmp8[2];
if not array_y_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp9[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
if 3 <= ATS_MAX_TERMS then
array_y[3] := temporary; array_y_higher[1, 3] := temporary
end if;
temporary := c(temporary)*c(2)/c(glob_h);
array_y_higher[2, 2] := c(temporary)
end if
end if;
kkk := 3;
array_tmp3[3] := array_x[2]*array_x[2];
array_tmp4[3] := array_tmp3[3];
array_tmp5[3] := neg(ats(3, array_tmp4, array_tmp5, 2))/array_tmp4[1];
array_tmp6[3] := array_x[2]*array_x[2];
array_tmp7[3] := array_tmp6[3];
array_tmp8[3] :=
(array_tmp5[3] - ats(3, array_tmp7, array_tmp8, 2))/array_tmp7[1];
array_tmp9[3] := array_tmp8[3];
if not array_y_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp9[3])*expt(glob_h, c(1))*c(factorial_3(2, 3));
if 4 <= ATS_MAX_TERMS then
array_y[4] := temporary; array_y_higher[1, 4] := temporary
end if;
temporary := c(temporary)*c(3)/c(glob_h);
array_y_higher[2, 3] := c(temporary)
end if
end if;
kkk := 4;
array_tmp4[4] := array_tmp3[4];
array_tmp5[4] := neg(ats(4, array_tmp4, array_tmp5, 2))/array_tmp4[1];
array_tmp7[4] := array_tmp6[4];
array_tmp8[4] :=
(array_tmp5[4] - ats(4, array_tmp7, array_tmp8, 2))/array_tmp7[1];
array_tmp9[4] := array_tmp8[4];
if not array_y_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp9[4])*expt(glob_h, c(1))*c(factorial_3(3, 4));
if 5 <= ATS_MAX_TERMS then
array_y[5] := temporary; array_y_higher[1, 5] := temporary
end if;
temporary := c(temporary)*c(4)/c(glob_h);
array_y_higher[2, 4] := c(temporary)
end if
end if;
kkk := 5;
array_tmp4[5] := array_tmp3[5];
array_tmp5[5] := neg(ats(5, array_tmp4, array_tmp5, 2))/array_tmp4[1];
array_tmp7[5] := array_tmp6[5];
array_tmp8[5] :=
(array_tmp5[5] - ats(5, array_tmp7, array_tmp8, 2))/array_tmp7[1];
array_tmp9[5] := array_tmp8[5];
if not array_y_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp9[5])*expt(glob_h, c(1))*c(factorial_3(4, 5));
if 6 <= ATS_MAX_TERMS then
array_y[6] := temporary; array_y_higher[1, 6] := temporary
end if;
temporary := c(temporary)*c(5)/c(glob_h);
array_y_higher[2, 5] := c(temporary)
end if
end if;
kkk := 6;
while kkk <= ATS_MAX_TERMS do
array_tmp4[kkk] := array_tmp3[kkk];
array_tmp5[kkk] :=
neg(ats(kkk, array_tmp4, array_tmp5, 2))/array_tmp4[1];
array_tmp7[kkk] := array_tmp6[kkk];
array_tmp8[kkk] := (
array_tmp5[kkk] - ats(kkk, array_tmp7, array_tmp8, 2))/
array_tmp7[1];
array_tmp9[kkk] := array_tmp8[kkk];
order_d := 1;
if kkk + order_d <= ATS_MAX_TERMS then
if not array_y_set_initial[1, kkk + order_d] then
temporary := c(array_tmp9[kkk])*expt(glob_h, c(order_d))*
c(factorial_3(kkk - 1, kkk + order_d - 1));
array_y[kkk + order_d] := c(temporary);
array_y_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_y_higher[adj3, term] := c(temporary)
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
# End Function number 12
#END OUTFILE5
# Begin Function number 12
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it;
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_1D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_tmp7,
> array_tmp8,
> array_tmp9,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> ATS_MAX_TERMS := 30;
> # before first input block
> #BEGIN FIRST INPUT BLOCK
> #BEGIN BLOCK 1
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=30;
> #END BLOCK 1
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> # before generate arrays
> array_y_init:= Array(0..(30),[]);
> array_norms:= Array(0..(30),[]);
> array_fact_1:= Array(0..(30),[]);
> array_1st_rel_error:= Array(0..(2),[]);
> array_last_rel_error:= Array(0..(2),[]);
> array_est_rel_error:= Array(0..(2),[]);
> array_max_est_error:= Array(0..(2),[]);
> array_type_pole:= Array(0..(2),[]);
> array_type_real_pole:= Array(0..(2),[]);
> array_type_complex_pole:= Array(0..(2),[]);
> array_est_digits:= Array(0..(2),[]);
> array_y:= Array(0..(30),[]);
> array_x:= Array(0..(30),[]);
> array_tmp0:= Array(0..(30),[]);
> array_tmp1:= Array(0..(30),[]);
> array_tmp2:= Array(0..(30),[]);
> array_tmp3:= Array(0..(30),[]);
> array_tmp4:= Array(0..(30),[]);
> array_tmp5:= Array(0..(30),[]);
> array_tmp6:= Array(0..(30),[]);
> array_tmp7:= Array(0..(30),[]);
> array_tmp8:= Array(0..(30),[]);
> array_tmp9:= Array(0..(30),[]);
> array_m1:= Array(0..(30),[]);
> array_y_higher := Array(0..(2) ,(0..30+ 1),[]);
> array_y_higher_work := Array(0..(2) ,(0..30+ 1),[]);
> array_y_higher_work2 := Array(0..(2) ,(0..30+ 1),[]);
> array_y_set_initial := Array(0..(2) ,(0..30+ 1),[]);
> array_given_rad_poles := Array(0..(2) ,(0..3+ 1),[]);
> array_given_ord_poles := Array(0..(2) ,(0..3+ 1),[]);
> array_rad_test_poles := Array(0..(2) ,(0..4+ 1),[]);
> array_ord_test_poles := Array(0..(2) ,(0..4+ 1),[]);
> array_fact_2 := Array(0..(30) ,(0..30+ 1),[]);
> # before generate constants
> # before generate globals definition
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> # before generate const definition
> # before arrays initialized
> term := 1;
> while (term <= 30) do # do number 1
> array_y_init[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_norms[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_fact_1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_1st_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_last_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_est_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_max_est_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_real_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_complex_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_est_digits[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_y[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_x[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp0[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp3[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp4[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp5[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp6[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp7[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp8[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp9[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_m1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y_higher[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y_higher_work[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y_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 <=2) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y_set_initial[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 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 <=2) 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 <=2) 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 <=2) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_ord_test_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=30) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_fact_2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> # before symbols initialized
> #BEGIN SYMBOLS INITIALIZATED
> zero_ats_ar(array_y);
> zero_ats_ar(array_x);
> 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_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_2D0);
> array_const_2D0[1] := c(2.0);
> zero_ats_ar(array_const_1D0);
> array_const_1D0[1] := c(1.0);
> 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_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> # before generate init omniout const
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> ATS_MAX_TERMS := 30;
> glob_iolevel := INFO;
> # set default block
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> glob_display_flag := true;
> glob_no_eqs := 1;
> 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/sing4postcpx.cpx#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = neg ( 2.0 ) * x / ( x * x + 1.0 ) / ( x * x + 1.0 ) ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := -2.0 + 0.1 * I;");
> omniout_str(ALWAYS,"x_end := 99.0 + 99.0 * I;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_h := c(0.1);");
> omniout_str(ALWAYS,"glob_max_h := c(0.001);");
> omniout_str(ALWAYS,"glob_min_h := c(0.001);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_type_given_pole := 2;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_rad_poles[1,1] := c(0.0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_rad_poles[1,2] := c(1.0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_ord_poles[1,1] := c(1.0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_ord_poles[1,2] := c(0.0);");
> omniout_str(ALWAYS,"");
> 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_y := proc(x)");
> omniout_str(ALWAYS,"return(c(1.0) / (c(x) * c( x) + c(1.0)));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"next_delta := proc()");
> omniout_str(ALWAYS,"global glob_nxt, x_delta;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"x_delta := [ 0.001 + 0.00004 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.000 + 0.000 * I ];");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_nxt := glob_nxt + 1;");
> omniout_str(ALWAYS,"it := x_delta[glob_nxt];");
> omniout_str(ALWAYS,"return it;");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := glob__0;
> glob_smallish_float := glob__0;
> glob_large_float := c(1.0e100);
> glob_larger_float := c( 1.1e100);
> glob_almost_1 := c( 0.99);
> # before second block
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #BEGIN BLOCK 2
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := -2.0 + 0.1 * I;
> x_end := 99.0 + 99.0 * I;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_max_h := c(0.1);
> glob_max_h := c(0.001);
> glob_min_h := c(0.001);
> glob_type_given_pole := 2;
> array_given_rad_poles[1,1] := c(0.0);
> array_given_rad_poles[1,2] := c(1.0);
> array_given_ord_poles[1,1] := c(1.0);
> array_given_ord_poles[1,2] := c(0.0);
> #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 9
> 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 10
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> h_new := glob_min_h;
> glob_h_reason := 5;
> fi;# end if 10;
> term := 1;
> ratio := c(1.0);
> while (term <= ATS_MAX_TERMS) do # do number 1
> array_y[term] := array_y[term]* ratio;
> array_y_higher[1,term] := array_y_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / float_abs(glob_h);
> term := term + 1;
> od;# end do number 1;
> glob_h := h_new;
> fi;# end if 9;
> #BOTTOM ADJUST ALL SERIES
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 9
> html_log_file := fopen("entry.html",WRITE,TEXT);
> fi;# end if 9;
> #BEGIN SOLUTION CODE
> found_h := true;
> if (found_h) then # if number 9
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := c(x_start);
> array_x[2] := c(glob_h);
> glob_next_display := c(x_start);
> glob_min_pole_est := glob_larger_float;
> glob_least_given_sing := glob_larger_float;
> glob_least_ratio_sing := glob_larger_float;
> glob_least_3_sing := glob_larger_float;
> glob_least_6_sing := glob_larger_float;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 1
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , 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 10
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 10;
> 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 10
> 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 11
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> h_new := glob_min_h;
> glob_h_reason := 5;
> fi;# end if 11;
> term := 1;
> ratio := c(1.0);
> while (term <= ATS_MAX_TERMS) do # do number 1
> array_y[term] := array_y[term]* ratio;
> array_y_higher[1,term] := array_y_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / float_abs(glob_h);
> term := term + 1;
> od;# end do number 1;
> glob_h := h_new;
> fi;# end if 10;
> #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 10
> omniout_str(INFO," ");
> fi;# end if 10;
> 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 10
> 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 11
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> h_new := glob_min_h;
> glob_h_reason := 5;
> fi;# end if 11;
> term := 1;
> ratio := c(1.0);
> while (term <= ATS_MAX_TERMS) do # do number 2
> array_y[term] := array_y[term]* ratio;
> array_y_higher[1,term] := array_y_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / float_abs(glob_h);
> term := term + 1;
> od;# end do number 2;
> glob_h := h_new;
> fi;# end if 10;
> #BOTTOM ADJUST ALL SERIES
> #END OPTIMIZE CODE
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> atomall();
> if ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0))) then # if number 10
> display_alot(current_iter);
> fi;# end if 10;
> if ((glob_look_poles) and ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0)))) then # if number 10
> check_for_pole();
> fi;# end if 10;
> if (true) then # if number 10
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 10;
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y;
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[2,iii] := array_y_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_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , 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_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_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_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , 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_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_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_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , 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_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 3
> array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 3;
> term_no := term_no - 1;
> od;# end do number 2;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> ;
> od;# end do number 1;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 10
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 10;
> if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec )) then # if number 10
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 10;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 1 ) = neg ( 2.0 ) * x / ( x * x + 1.0 ) / ( x * x + 1.0 ) ; ");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 10
> logstart(html_log_file);
> logitem_str(html_log_file,"2017-11-26T16:23:32-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"sing4")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = neg ( 2.0 ) * x / ( x * x + 1.0 ) / ( x * x + 1.0 ) ; ")
> ;
> logitem_complex(html_log_file,x_start)
> ;
> logitem_complex(html_log_file,x_end)
> ;
> logitem_complex(html_log_file,array_x[1])
> ;
> logitem_complex(html_log_file,glob_h)
> ;
> logitem_h_reason(html_log_file)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> glob_desired_digits_correct := 0.0;
> logitem_float(html_log_file,glob_desired_digits_correct)
> ;
> if (array_est_digits[1] <> -16) then # if number 11
> logitem_integer(html_log_file,array_est_digits[1])
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_min_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_min_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> 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 11
> logitem_str(html_log_file,"Not Given")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 4) then # if number 12
> logitem_str(html_log_file,"No Solution")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 5) then # if number 13
> logitem_str(html_log_file,"Some Pole")
> ;
> logitem_str(html_log_file,"????")
> ;
> elif
> (glob_type_given_pole = 3) then # if number 14
> logitem_str(html_log_file,"No Pole")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 1) then # if number 15
> 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 16
> logitem_str(html_log_file,"Complex Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> fi;# end if 16;
> if (glob_least_ratio_sing < glob_large_float) then # if number 16
> glob_least_ratio_sing := 0;
> logitem_float(html_log_file,glob_least_ratio_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_3_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_3_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_6_sing < glob_large_float) then # if number 16
> 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 16;
> 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 16
> logitem_time(html_log_file,(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 16;
> log_revs(html_log_file," 309 | ")
> ;
> logitem_str(html_log_file,"sing4 diffeq.mxt")
> ;
> logitem_str(html_log_file,"sing4 maple results")
> ;
> logitem_str(html_log_file,"OK")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 15;
> if (glob_html_log) then # if number 15
> fclose(html_log_file);
> fi;# end if 15
> ;
> ;;
> end;
> # End Function number 12
> #END OUTFILEMAIN
> end;
Warning, `h_new` is implicitly declared local to procedure `main`
Warning, `ratio` is implicitly declared local to procedure `main`
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max,
term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order,
sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it,
last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err,
estimated_step_error, min_value, est_answer, found_h, repeat_it, h_new,
ratio;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_1D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_tmp7, array_tmp8, array_tmp9, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
ATS_MAX_TERMS := 30;
Digits := 32;
max_terms := 30;
glob_html_log := true;
array_y_init := Array(0 .. 30, []);
array_norms := Array(0 .. 30, []);
array_fact_1 := Array(0 .. 30, []);
array_1st_rel_error := Array(0 .. 2, []);
array_last_rel_error := Array(0 .. 2, []);
array_est_rel_error := Array(0 .. 2, []);
array_max_est_error := Array(0 .. 2, []);
array_type_pole := Array(0 .. 2, []);
array_type_real_pole := Array(0 .. 2, []);
array_type_complex_pole := Array(0 .. 2, []);
array_est_digits := Array(0 .. 2, []);
array_y := Array(0 .. 30, []);
array_x := Array(0 .. 30, []);
array_tmp0 := Array(0 .. 30, []);
array_tmp1 := Array(0 .. 30, []);
array_tmp2 := Array(0 .. 30, []);
array_tmp3 := Array(0 .. 30, []);
array_tmp4 := Array(0 .. 30, []);
array_tmp5 := Array(0 .. 30, []);
array_tmp6 := Array(0 .. 30, []);
array_tmp7 := Array(0 .. 30, []);
array_tmp8 := Array(0 .. 30, []);
array_tmp9 := Array(0 .. 30, []);
array_m1 := Array(0 .. 30, []);
array_y_higher := Array(0 .. 2, 0 .. 31, []);
array_y_higher_work := Array(0 .. 2, 0 .. 31, []);
array_y_higher_work2 := Array(0 .. 2, 0 .. 31, []);
array_y_set_initial := Array(0 .. 2, 0 .. 31, []);
array_given_rad_poles := Array(0 .. 2, 0 .. 4, []);
array_given_ord_poles := Array(0 .. 2, 0 .. 4, []);
array_rad_test_poles := Array(0 .. 2, 0 .. 5, []);
array_ord_test_poles := Array(0 .. 2, 0 .. 5, []);
array_fact_2 := Array(0 .. 30, 0 .. 31, []);
term := 1;
while term <= 30 do array_y_init[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 30 do array_norms[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 30 do array_fact_1[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_1st_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do
array_last_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_est_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_max_est_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_type_pole[term] := 0; term := term + 1 end do;
term := 1;
while term <= 2 do array_type_real_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 2 do array_type_complex_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 2 do array_est_digits[term] := 0; term := term + 1 end do
;
term := 1;
while term <= 30 do array_y[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_x[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp0[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp1[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp3[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp4[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp5[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp6[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp7[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp8[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp9[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_m1[term] := c(0.); term := term + 1 end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 do
array_y_higher[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 do
array_y_higher_work[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 do
array_y_higher_work2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 do
array_y_set_initial[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_rad_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 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 <= 2 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 <= 2 do
term := 1;
while term <= 4 do
array_ord_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 30 do
term := 1;
while term <= 30 do
array_fact_2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
zero_ats_ar(array_y);
zero_ats_ar(array_x);
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_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_2D0);
array_const_2D0[1] := c(2.0);
zero_ats_ar(array_const_1D0);
array_const_1D0[1] := c(1.0);
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_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
ATS_MAX_TERMS := 30;
glob_iolevel := INFO;
glob_orig_start_sec := elapsed_time_seconds();
glob_display_flag := true;
glob_no_eqs := 1;
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/sing4postcpx.cpx#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = neg ( 2.0 ) * \
x / ( x * x + 1.0 ) / ( x * x + 1.0 ) ; ");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := -2.0 + 0.1 * I;");
omniout_str(ALWAYS, "x_end := 99.0 + 99.0 * I;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_h := c(0.1);");
omniout_str(ALWAYS, "glob_max_h := c(0.001);");
omniout_str(ALWAYS, "glob_min_h := c(0.001);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_type_given_pole := 2;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_rad_poles[1,1] := c(0.0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_rad_poles[1,2] := c(1.0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_ord_poles[1,1] := c(1.0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_ord_poles[1,2] := c(0.0);");
omniout_str(ALWAYS, "");
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_y := proc(x)");
omniout_str(ALWAYS, "return(c(1.0) / (c(x) * c( x) + c(1.0)));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "next_delta := proc()");
omniout_str(ALWAYS, "global glob_nxt, x_delta;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "x_delta := [ 0.001 + 0.00004 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
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omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 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(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob_almost_1 := c(0.99);
x_start := -2.0 + 0.1*I;
x_end := 99.0 + 99.0*I;
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_h := c(0.1);
glob_max_h := c(0.001);
glob_min_h := c(0.001);
glob_type_given_pole := 2;
array_given_rad_poles[1, 1] := c(0.);
array_given_rad_poles[1, 2] := c(1.0);
array_given_ord_poles[1, 1] := c(1.0);
array_given_ord_poles[1, 2] := c(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_y[term] := array_y[term]*ratio;
array_y_higher[1, term] := array_y_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/float_abs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT)
end if;
found_h := true;
if found_h then
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := c(x_start);
array_x[2] := c(glob_h);
glob_next_display := c(x_start);
glob_min_pole_est := glob_larger_float;
glob_least_given_sing := glob_larger_float;
glob_least_ratio_sing := glob_larger_float;
glob_least_3_sing := glob_larger_float;
glob_least_6_sing := glob_larger_float;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_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_y_higher[r_order, term_no] := array_y_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_y[term] := array_y[term]*ratio;
array_y_higher[1, term] := array_y_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/float_abs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_iter < glob_max_iter and
(glob_iter < 10 or not (Re(glob_h) = 0. and Im(glob_h) = 0.)) do
omniout_str(INFO, " ");
found_h := true;
glob_h := next_delta();
if float_abs(glob_min_pole_est)*glob_ratio_of_radius <
float_abs(glob_h) then
h_new :=
glob_check_sign*glob_min_pole_est*glob_ratio_of_radius;
omniout_str(ALWAYS, "SETTING H FOR POLE");
glob_h_reason := 6;
if glob_check_sign*h_new < glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
h_new := glob_min_h;
glob_h_reason := 5
end if;
term := 1;
ratio := c(1.0);
while term <= ATS_MAX_TERMS do
array_y[term] := array_y[term]*ratio;
array_y_higher[1, term] :=
array_y_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/float_abs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
atomall();
if not (Re(glob_h) = 0. and Im(glob_h) = 0.) then
display_alot(current_iter)
end if;
if
glob_look_poles and not (Re(glob_h) = 0. and Im(glob_h) = 0.)
then check_for_pole()
end if;
glob_next_display := glob_next_display + glob_display_interval;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_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_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_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_y_higher_work[1, iii] := array_y_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_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_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_y_higher_work[1, iii] := array_y_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_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_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_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if glob_max_sec <= elapsed_time_seconds() - glob_orig_start_sec
then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff ( y , x , 1 ) = neg ( 2.0 ) *\
x / ( x * x + 1.0 ) / ( x * x + 1.0 ) ; ");
omniout_int(INFO, "Iterations ", 32, glob_iter,
4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2017-11-26T16:23:32-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"sing4");
logitem_str(html_log_file, "diff ( y , x , 1 ) = ne\
g ( 2.0 ) * x / ( x * x + 1.0 ) / ( x * \
x + 1.0 ) ; ");
logitem_complex(html_log_file, x_start);
logitem_complex(html_log_file, x_end);
logitem_complex(html_log_file, array_x[1]);
logitem_complex(html_log_file, glob_h);
logitem_h_reason(html_log_file);
logitem_integer(html_log_file, Digits);
glob_desired_digits_correct := 0.;
logitem_float(html_log_file, glob_desired_digits_correct);
if array_est_digits[1] <> -16 then
logitem_integer(html_log_file, array_est_digits[1])
else logitem_str(html_log_file, "Unknown")
end if;
if glob_min_good_digits <> -16 then
logitem_integer(html_log_file, glob_min_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
if glob_good_digits <> -16 then
logitem_integer(html_log_file, glob_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
logitem_integer(html_log_file, ATS_MAX_TERMS);
if glob_type_given_pole = 0 then
logitem_str(html_log_file, "Not Given");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 4 then
logitem_str(html_log_file, "No Solution");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 5 then
logitem_str(html_log_file, "Some Pole");
logitem_str(html_log_file, "????")
elif glob_type_given_pole = 3 then
logitem_str(html_log_file, "No Pole");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 1 then
logitem_str(html_log_file, "Real Sing");
logitem_float(html_log_file, glob_least_given_sing)
elif glob_type_given_pole = 2 then
logitem_str(html_log_file, "Complex Sing");
logitem_float(html_log_file, glob_least_given_sing)
end if;
if glob_least_ratio_sing < glob_large_float then
glob_least_ratio_sing := 0;
logitem_float(html_log_file, glob_least_ratio_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_3_sing < glob_large_float then
logitem_float(html_log_file, glob_least_3_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_6_sing < glob_large_float then
glob_least_6_sing := 0.;
logitem_float(html_log_file, glob_least_6_sing)
else logitem_str(html_log_file, "NONE")
end if;
logitem_integer(html_log_file, glob_iter);
logitem_time(html_log_file, glob_clock_sec);
if c(glob_percent_done) < glob__100 then
logitem_time(html_log_file, glob_total_exp_sec); 0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 309 | ");
logitem_str(html_log_file,
"sing4 diffeq.mxt");
logitem_str(html_log_file,
"sing4 maple results")
;
logitem_str(html_log_file, "OK");
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=3.8MB, alloc=40.3MB, time=0.08
##############ECHO OF PROBLEM#################
##############temp/sing4postcpx.cpx#################
diff ( y , x , 1 ) = neg ( 2.0 ) * x / ( x * x + 1.0 ) / ( x * x + 1.0 ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := -2.0 + 0.1 * I;
x_end := 99.0 + 99.0 * I;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_h := c(0.1);
glob_max_h := c(0.001);
glob_min_h := c(0.001);
glob_type_given_pole := 2;
array_given_rad_poles[1,1] := c(0.0);
array_given_rad_poles[1,2] := c(1.0);
array_given_ord_poles[1,1] := c(1.0);
array_given_ord_poles[1,2] := c(0.0);
#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_y := proc(x)
return(c(1.0) / (c(x) * c( x) + c(1.0)));
end;
next_delta := proc()
global glob_nxt, x_delta;
x_delta := [ 0.001 + 0.00004 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.000 + 0.000 * I ];
glob_nxt := glob_nxt + 1;
it := x_delta[glob_nxt];
return it;
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = -2 0.1
h = 0.0001 0.005
y[1] (numeric) = 0.199121312365 0.0159616282457
y[1] (closed_form) = 0.199121312365 0.0159616282457
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 2.193
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9999 0.105
h = 0.0001 0.003
y[1] (numeric) = 0.19904770631 0.0167574757646
y[1] (closed_form) = 0.199047269268 0.0167574253033
absolute error = 4.399e-07
relative error = 0.0002202 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.191
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9998 0.108
h = 0.001 0.001
y[1] (numeric) = 0.199007000603 0.017235451109
y[1] (closed_form) = 0.199007088669 0.0172354574502
absolute error = 8.829e-08
relative error = 4.420e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.19
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9988 0.109
h = 0.001 0.003
y[1] (numeric) = 0.199146455464 0.0174133246607
y[1] (closed_form) = 0.199146810011 0.0174132716136
absolute error = 3.585e-07
relative error = 0.0001793 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.188
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9978 0.112
h = 0.0001 0.004
y[1] (numeric) = 0.199247634854 0.0179093217751
y[1] (closed_form) = 0.199247440466 0.0179093670076
absolute error = 1.996e-07
relative error = 9.977e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.186
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9977 0.116
h = 0.003 0.006
y[1] (numeric) = 0.199183654595 0.0185472738767
y[1] (closed_form) = 0.199183149413 0.0185469598014
absolute error = 5.949e-07
relative error = 0.0002974 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.185
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=39.5MB, alloc=40.3MB, time=0.52
x[1] = -1.9947 0.122
h = 0.0001 0.005
y[1] (numeric) = 0.199535604576 0.0195623560456
y[1] (closed_form) = 0.199534489413 0.019564038408
absolute error = 2.018e-06
relative error = 0.001007 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.179
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9946 0.127
h = 0.0001 0.003
y[1] (numeric) = 0.199441074758 0.0203615078085
y[1] (closed_form) = 0.199440584001 0.0203619814823
absolute error = 6.821e-07
relative error = 0.0003402 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.177
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9945 0.13
h = 0.001 0.001
y[1] (numeric) = 0.199388455377 0.0208408518438
y[1] (closed_form) = 0.199388491412 0.0208413979842
absolute error = 5.473e-07
relative error = 0.000273 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.176
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9935 0.131
h = 0.001 0.003
y[1] (numeric) = 0.199524240004 0.0210230217587
y[1] (closed_form) = 0.199524545946 0.0210235159001
absolute error = 5.812e-07
relative error = 0.0002897 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.175
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9925 0.134
h = 0.0001 0.004
y[1] (numeric) = 0.1996137603 0.0215239505969
y[1] (closed_form) = 0.199613510951 0.0215245276411
absolute error = 6.286e-07
relative error = 0.0003131 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.173
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9924 0.138
h = 0.003 0.006
y[1] (numeric) = 0.199533818965 0.0221634742962
y[1] (closed_form) = 0.199533267325 0.0221636806871
absolute error = 5.890e-07
relative error = 0.0002934 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.171
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9894 0.144
h = 0.0001 0.005
y[1] (numeric) = 0.199862593092 0.0231921632987
y[1] (closed_form) = 0.19986136936 0.0231943610042
absolute error = 2.515e-06
relative error = 0.00125 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.166
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9893 0.149
h = 0.0001 0.003
y[1] (numeric) = 0.19974797292 0.023992885
y[1] (closed_form) = 0.199747412839 0.0239938845766
absolute error = 1.146e-06
relative error = 0.0005695 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.164
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9892 0.152
h = 0.001 0.001
y[1] (numeric) = 0.199683324325 0.0244732588977
y[1] (closed_form) = 0.199683292257 0.0244743467816
absolute error = 1.088e-06
relative error = 0.000541 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.162
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9882 0.153
h = 0.001 0.003
y[1] (numeric) = 0.199815290093 0.0246596453563
y[1] (closed_form) = 0.19981553116 0.0246606887941
absolute error = 1.071e-06
relative error = 0.0005319 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.161
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=86.2MB, alloc=44.3MB, time=1.12
x[1] = -1.9872 0.156
h = 0.0001 0.004
y[1] (numeric) = 0.199892933401 0.0251651970512
y[1] (closed_form) = 0.199892613238 0.0251663076982
absolute error = 1.156e-06
relative error = 0.0005737 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.159
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9871 0.16
h = 0.003 0.006
y[1] (numeric) = 0.199796883878 0.0258058364617
y[1] (closed_form) = 0.199796270339 0.0258065652764
absolute error = 9.527e-07
relative error = 0.0004729 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.157
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9841 0.166
h = 0.0001 0.005
y[1] (numeric) = 0.200101938054 0.0268475418371
y[1] (closed_form) = 0.200100589962 0.0268502549129
absolute error = 3.030e-06
relative error = 0.001501 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.152
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.984 0.171
h = 0.0001 0.003
y[1] (numeric) = 0.19996705439 0.027649256367
y[1] (closed_form) = 0.199966409193 0.0276507831537
absolute error = 1.658e-06
relative error = 0.0008211 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.15
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9839 0.174
h = 0.001 0.001
y[1] (numeric) = 0.199890270404 0.028130315029
y[1] (closed_form) = 0.19989015397 0.0281319461317
absolute error = 1.635e-06
relative error = 0.0008101 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.149
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9829 0.175
h = 0.001 0.003
y[1] (numeric) = 0.200018269904 0.0283208330403
y[1] (closed_form) = 0.200018429629 0.0283224274105
absolute error = 1.602e-06
relative error = 0.0007932 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.148
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9819 0.178
h = 0.0001 0.004
y[1] (numeric) = 0.200083825945 0.0288306895793
y[1] (closed_form) = 0.20008341893 0.0288323351542
absolute error = 1.695e-06
relative error = 0.0008386 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.146
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9818 0.182
h = 0.003 0.006
y[1] (numeric) = 0.199971533779 0.029471980601
y[1] (closed_form) = 0.199970842721 0.0294732333434
absolute error = 1.431e-06
relative error = 0.0007078 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.144
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9788 0.188
h = 0.0001 0.005
y[1] (numeric) = 0.200252337401 0.0305260904593
y[1] (closed_form) = 0.200250849019 0.0305293184466
absolute error = 3.555e-06
relative error = 0.001755 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.139
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9787 0.193
h = 0.0001 0.003
y[1] (numeric) = 0.200097033229 0.0313282106311
y[1] (closed_form) = 0.200096286959 0.0313302654656
absolute error = 2.186e-06
relative error = 0.001079 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.137
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9786 0.196
h = 0.001 0.001
y[1] (numeric) = 0.200008017307 0.0318096028375
y[1] (closed_form) = 0.200007800066 0.0318117781553
absolute error = 2.186e-06
relative error = 0.001079 %
Correct digits = 5
memory used=132.8MB, alloc=44.3MB, time=1.72
Radius of convergence (given) for eq 1 = 2.136
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9776 0.197
h = 0.0001 0.004
y[1] (numeric) = 0.200131904485 0.0320041622037
y[1] (closed_form) = 0.200131966218 0.0320063086604
absolute error = 2.147e-06
relative error = 0.00106 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.134
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9775 0.201
h = 0.003 0.006
y[1] (numeric) = 0.200006238168 0.0326456102763
y[1] (closed_form) = 0.200005319549 0.0326471853565
absolute error = 1.823e-06
relative error = 0.0008998 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.133
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9745 0.207
h = 0.0001 0.005
y[1] (numeric) = 0.20026561619 0.0337095939839
y[1] (closed_form) = 0.200263846145 0.0337131341989
absolute error = 3.958e-06
relative error = 0.001949 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.128
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9744 0.212
h = 0.0001 0.003
y[1] (numeric) = 0.200092626512 0.0345113401263
y[1] (closed_form) = 0.200091632108 0.0345137200132
absolute error = 2.579e-06
relative error = 0.00127 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.126
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9743 0.215
h = 0.001 0.001
y[1] (numeric) = 0.199993013824 0.0349925865412
y[1] (closed_form) = 0.19999254809 0.0349951009425
absolute error = 2.557e-06
relative error = 0.001259 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.125
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9733 0.216
h = 0.001 0.003
y[1] (numeric) = 0.200113198857 0.0351904970151
y[1] (closed_form) = 0.20011301425 0.0351929894849
absolute error = 2.499e-06
relative error = 0.00123 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.123
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9723 0.219
h = 0.0001 0.004
y[1] (numeric) = 0.20015568913 0.035707336907
y[1] (closed_form) = 0.200154928914 0.0357098499428
absolute error = 2.626e-06
relative error = 0.001291 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.121
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9722 0.223
h = 0.003 0.006
y[1] (numeric) = 0.200012865865 0.0363483812671
y[1] (closed_form) = 0.200011840202 0.0363504816419
absolute error = 2.337e-06
relative error = 0.00115 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.12
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9692 0.229
h = 0.0001 0.005
y[1] (numeric) = 0.200247052184 0.0374235681049
y[1] (closed_form) = 0.200245111893 0.0374276208527
absolute error = 4.493e-06
relative error = 0.002206 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.115
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9691 0.234
h = 0.0001 0.003
y[1] (numeric) = 0.200053401595 0.03822459994
y[1] (closed_form) = 0.200052276004 0.0382275079535
absolute error = 3.118e-06
relative error = 0.001531 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.113
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=179.5MB, alloc=44.3MB, time=2.32
x[1] = -1.969 0.237
h = 0.001 0.001
y[1] (numeric) = 0.19994140826 0.0387055097274
y[1] (closed_form) = 0.199940810679 0.0387085686857
absolute error = 3.117e-06
relative error = 0.00153 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.112
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.968 0.238
h = 0.001 0.003
y[1] (numeric) = 0.20005721453 0.0389072780384
y[1] (closed_form) = 0.200056900481 0.0389103232199
absolute error = 3.061e-06
relative error = 0.001502 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.11
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.967 0.241
h = 0.0001 0.004
y[1] (numeric) = 0.200087065035 0.0394274609624
y[1] (closed_form) = 0.20008617117 0.0394305098576
absolute error = 3.177e-06
relative error = 0.001558 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.108
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9669 0.245
h = 0.003 0.006
y[1] (numeric) = 0.199927693505 0.040067784657
y[1] (closed_form) = 0.199926544713 0.0400704104767
absolute error = 2.866e-06
relative error = 0.001406 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.107
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9639 0.251
h = 0.0001 0.005
y[1] (numeric) = 0.20013620028 0.0411535019042
y[1] (closed_form) = 0.200134073481 0.0411580652724
absolute error = 5.035e-06
relative error = 0.002464 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.102
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9638 0.256
h = 0.0001 0.003
y[1] (numeric) = 0.199921780595 0.0419532050782
y[1] (closed_form) = 0.199920507431 0.0419566406528
absolute error = 3.664e-06
relative error = 0.001794 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.1
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9637 0.259
h = 0.001 0.001
y[1] (numeric) = 0.199797339259 0.0424334104943
y[1] (closed_form) = 0.19979659293 0.042437013574
absolute error = 3.680e-06
relative error = 0.001801 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.099
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9627 0.26
h = 0.001 0.003
y[1] (numeric) = 0.199908625477 0.0426389313615
y[1] (closed_form) = 0.199908164855 0.042642528968
absolute error = 3.627e-06
relative error = 0.001774 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.098
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9617 0.263
h = 0.0001 0.004
y[1] (numeric) = 0.199925658505 0.0431621047688
y[1] (closed_form) = 0.199924614342 0.0431656889522
absolute error = 3.733e-06
relative error = 0.001825 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.096
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9616 0.267
h = 0.003 0.006
y[1] (numeric) = 0.199749656717 0.0438012141105
y[1] (closed_form) = 0.199748368567 0.0438043650334
absolute error = 3.404e-06
relative error = 0.001665 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.094
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=226.4MB, alloc=44.3MB, time=2.92
x[1] = -1.9586 0.273
h = 0.0001 0.005
y[1] (numeric) = 0.199932012433 0.0448967678333
y[1] (closed_form) = 0.19992968277 0.0449018393791
absolute error = 5.581e-06
relative error = 0.002724 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.089
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9585 0.278
h = 0.0001 0.003
y[1] (numeric) = 0.199696733469 0.0456945189757
y[1] (closed_form) = 0.199695296212 0.0456984810348
absolute error = 4.215e-06
relative error = 0.002057 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.087
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9584 0.281
h = 0.001 0.001
y[1] (numeric) = 0.199559787544 0.0461736467868
y[1] (closed_form) = 0.199558875424 0.04617779303
absolute error = 4.245e-06
relative error = 0.002073 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.086
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9574 0.282
h = 0.001 0.003
y[1] (numeric) = 0.199666414376 0.0463828095736
y[1] (closed_form) = 0.199665789899 0.0463869587927
absolute error = 4.196e-06
relative error = 0.002047 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.085
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9564 0.285
h = 0.0001 0.004
y[1] (numeric) = 0.199670461491 0.0469086121352
y[1] (closed_form) = 0.199669250245 0.0469127305173
absolute error = 4.293e-06
relative error = 0.002093 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.083
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9563 0.289
h = 0.003 0.006
y[1] (numeric) = 0.199477762002 0.0475460062881
y[1] (closed_form) = 0.19947631813 0.047549681469
absolute error = 3.949e-06
relative error = 0.001926 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.081
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9533 0.295
h = 0.0001 0.005
y[1] (numeric) = 0.199633512292 0.0486506814085
y[1] (closed_form) = 0.199630963326 0.0486562581464
absolute error = 6.132e-06
relative error = 0.002984 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.077
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9532 0.3
h = 0.0001 0.003
y[1] (numeric) = 0.199377302403 0.0494458484452
y[1] (closed_form) = 0.199375684414 0.0494503353892
absolute error = 4.770e-06
relative error = 0.002322 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.075
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9531 0.303
h = 0.001 0.001
y[1] (numeric) = 0.1992278064 0.0499235201156
y[1] (closed_form) = 0.199226711311 0.0499282080295
absolute error = 4.814e-06
relative error = 0.002344 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.074
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9521 0.304
h = 0.0001 0.004
y[1] (numeric) = 0.199329636638 0.0501362087887
y[1] (closed_form) = 0.199328830883 0.0501409082695
absolute error = 4.768e-06
relative error = 0.00232 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.072
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=273.0MB, alloc=44.3MB, time=3.52
x[1] = -1.952 0.308
h = 0.003 0.006
y[1] (numeric) = 0.19912324575 0.0507717973423
y[1] (closed_form) = 0.199121522279 0.0507757685977
absolute error = 4.329e-06
relative error = 0.002107 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.071
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.949 0.314
h = 0.0001 0.005
y[1] (numeric) = 0.199255648188 0.0518834112086
y[1] (closed_form) = 0.199252765137 0.0518892651072
absolute error = 6.525e-06
relative error = 0.003169 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.066
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9489 0.319
h = 0.0001 0.003
y[1] (numeric) = 0.198981420037 0.052675591256
y[1] (closed_form) = 0.198979500717 0.0526803738921
absolute error = 5.153e-06
relative error = 0.002504 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.064
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9488 0.322
h = 0.001 0.001
y[1] (numeric) = 0.198821117221 0.0531515524888
y[1] (closed_form) = 0.198819718231 0.0531565505838
absolute error = 5.190e-06
relative error = 0.002522 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.063
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9478 0.323
h = 0.001 0.003
y[1] (numeric) = 0.198918670579 0.0533671197435
y[1] (closed_form) = 0.198917562072 0.0533721369265
absolute error = 5.138e-06
relative error = 0.002495 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.062
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9468 0.326
h = 0.0001 0.004
y[1] (numeric) = 0.198898118289 0.0538966642071
y[1] (closed_form) = 0.198896418602 0.0539016174178
absolute error = 5.237e-06
relative error = 0.002541 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.06
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9467 0.33
h = 0.003 0.006
y[1] (numeric) = 0.198674255285 0.0545293103165
y[1] (closed_form) = 0.198672345346 0.0545338026801
absolute error = 4.882e-06
relative error = 0.002369 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.059
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9437 0.336
h = 0.0001 0.005
y[1] (numeric) = 0.19877926455 0.0556486541211
y[1] (closed_form) = 0.198776131489 0.0556550059711
absolute error = 7.083e-06
relative error = 0.003431 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.054
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9436 0.341
h = 0.0001 0.003
y[1] (numeric) = 0.198484031209 0.0564370516281
y[1] (closed_form) = 0.198481899948 0.0564423545368
absolute error = 5.715e-06
relative error = 0.00277 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.052
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9435 0.344
h = 0.001 0.001
y[1] (numeric) = 0.198311129035 0.0569108387341
y[1] (closed_form) = 0.198309514831 0.0569163740451
absolute error = 5.766e-06
relative error = 0.002795 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.051
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=319.5MB, alloc=44.3MB, time=4.12
x[1] = -1.9425 0.345
h = 0.001 0.003
y[1] (numeric) = 0.198403638323 0.0571296998989
y[1] (closed_form) = 0.198402315811 0.0571352631384
absolute error = 5.718e-06
relative error = 0.00277 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.05
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9415 0.348
h = 0.0001 0.004
y[1] (numeric) = 0.198369677691 0.0576607906158
y[1] (closed_form) = 0.198367762291 0.0576662717317
absolute error = 5.806e-06
relative error = 0.002811 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.048
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9414 0.352
h = 0.003 0.006
y[1] (numeric) = 0.198129014646 0.0582902515041
y[1] (closed_form) = 0.198126901557 0.058295262625
absolute error = 5.438e-06
relative error = 0.002633 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.047
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9384 0.358
h = 0.0001 0.005
y[1] (numeric) = 0.198206230574 0.0594165504516
y[1] (closed_form) = 0.198202830916 0.0594233956438
absolute error = 7.643e-06
relative error = 0.003694 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.042
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9383 0.363
h = 0.0001 0.003
y[1] (numeric) = 0.197889976717 0.0602005106557
y[1] (closed_form) = 0.197887616605 0.0602063306705
absolute error = 6.280e-06
relative error = 0.003036 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.04
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9382 0.366
h = 0.001 0.001
y[1] (numeric) = 0.197704463431 0.0606717312566
y[1] (closed_form) = 0.197702616527 0.060677800685
absolute error = 6.344e-06
relative error = 0.003068 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.039
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9372 0.367
h = 0.001 0.003
y[1] (numeric) = 0.197791798644 0.0608937546774
y[1] (closed_form) = 0.19779024437 0.0608998610037
absolute error = 6.301e-06
relative error = 0.003045 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.038
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9362 0.37
h = 0.0001 0.004
y[1] (numeric) = 0.197744300967 0.0614259975188
y[1] (closed_form) = 0.197742152661 0.0614320033297
absolute error = 6.378e-06
relative error = 0.00308 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.036
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9361 0.374
h = 0.003 0.006
y[1] (numeric) = 0.197486830984 0.062051747573
y[1] (closed_form) = 0.197484497976 0.0620572745503
absolute error = 5.999e-06
relative error = 0.002898 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.035
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9331 0.38
h = 0.0001 0.005
y[1] (numeric) = 0.197535874125 0.0631842061845
y[1] (closed_form) = 0.197532191264 0.0631915395167
absolute error = 8.206e-06
relative error = 0.003957 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.03
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=366.2MB, alloc=44.3MB, time=4.72
x[1] = -1.933 0.385
h = 0.0001 0.003
y[1] (numeric) = 0.197198605264 0.0639630671035
y[1] (closed_form) = 0.19719599932 0.0639694004852
absolute error = 6.849e-06
relative error = 0.003303 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.028
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9329 0.388
h = 0.001 0.001
y[1] (numeric) = 0.197000481604 0.0644313244106
y[1] (closed_form) = 0.196998384429 0.0644379242693
absolute error = 6.925e-06
relative error = 0.003341 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.027
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9319 0.389
h = 0.001 0.003
y[1] (numeric) = 0.197082515634 0.0646563728966
y[1] (closed_form) = 0.197080711748 0.064663018746
absolute error = 6.886e-06
relative error = 0.00332 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.026
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9309 0.392
h = 0.0001 0.004
y[1] (numeric) = 0.197021363557 0.0651893655303
y[1] (closed_form) = 0.197018965076 0.0651958922441
absolute error = 6.953e-06
relative error = 0.003351 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.024
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9308 0.396
h = 0.003 0.006
y[1] (numeric) = 0.196747096601 0.0658108734779
y[1] (closed_form) = 0.196744526827 0.0658169128478
absolute error = 6.563e-06
relative error = 0.003164 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.023
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9278 0.402
h = 0.0001 0.005
y[1] (numeric) = 0.196767609253 0.0669486757817
y[1] (closed_form) = 0.19676362658 0.066956491446
absolute error = 8.772e-06
relative error = 0.00422 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.018
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9277 0.407
h = 0.0001 0.003
y[1] (numeric) = 0.196409352389 0.0677217686877
y[1] (closed_form) = 0.196406483576 0.0677286111105
absolute error = 7.419e-06
relative error = 0.003571 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.017
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9276 0.41
h = 0.001 0.001
y[1] (numeric) = 0.196198631972 0.0681866617861
y[1] (closed_form) = 0.196196266887 0.0681937877845
absolute error = 7.508e-06
relative error = 0.003615 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.016
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9266 0.411
h = 0.0001 0.004
y[1] (numeric) = 0.196275240838 0.0684145925822
y[1] (closed_form) = 0.19627316941 0.0684217737817
absolute error = 7.474e-06
relative error = 0.003596 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.015
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9265 0.415
h = 0.003 0.006
y[1] (numeric) = 0.195987264455 0.0690322069378
y[1] (closed_form) = 0.195984365345 0.0690385069815
absolute error = 6.935e-06
relative error = 0.003338 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.013
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9235 0.421
h = 0.0001 0.005
y[1] (numeric) = 0.195982899931 0.0701735948067
y[1] (closed_form) = 0.1959785343 0.0701816426144
absolute error = 9.156e-06
relative error = 0.004398 %
Correct digits = 4
memory used=413.0MB, alloc=44.3MB, time=5.31
Radius of convergence (given) for eq 1 = 2.009
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9234 0.426
h = 0.0001 0.003
y[1] (numeric) = 0.195606695474 0.070940933375
y[1] (closed_form) = 0.195603474777 0.0709480325645
absolute error = 7.796e-06
relative error = 0.003747 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.007
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9233 0.429
h = 0.001 0.001
y[1] (numeric) = 0.195385199872 0.0714024571299
y[1] (closed_form) = 0.195382477865 0.0714098545571
absolute error = 7.882e-06
relative error = 0.003789 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.006
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9223 0.43
h = 0.001 0.003
y[1] (numeric) = 0.195457010302 0.0716326837729
y[1] (closed_form) = 0.195454581919 0.0716401444177
absolute error = 7.846e-06
relative error = 0.003769 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.005
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9213 0.433
h = 0.0001 0.004
y[1] (numeric) = 0.195370181881 0.0721658080211
y[1] (closed_form) = 0.195367159701 0.0721731143307
absolute error = 7.907e-06
relative error = 0.003796 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.003
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9212 0.437
h = 0.003 0.006
y[1] (numeric) = 0.195064811863 0.0727777916952
y[1] (closed_form) = 0.195061644549 0.0727845959395
absolute error = 7.505e-06
relative error = 0.003605 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.002
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9182 0.443
h = 0.0001 0.005
y[1] (numeric) = 0.195031323176 0.0739229476257
y[1] (closed_form) = 0.195026626976 0.0739314651034
absolute error = 9.726e-06
relative error = 0.004663 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.997
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9181 0.448
h = 0.0001 0.003
y[1] (numeric) = 0.194634248571 0.0746832586544
y[1] (closed_form) = 0.194630733285 0.0746908570228
absolute error = 8.372e-06
relative error = 0.004016 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.996
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.918 0.451
h = 0.001 0.001
y[1] (numeric) = 0.194400222106 0.0751406628486
y[1] (closed_form) = 0.194397199308 0.0751485765614
absolute error = 8.471e-06
relative error = 0.004065 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.995
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.917 0.452
h = 0.001 0.003
y[1] (numeric) = 0.194466387677 0.0753734899136
y[1] (closed_form) = 0.194463658305 0.075381476251
absolute error = 8.440e-06
relative error = 0.004047 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.994
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.916 0.455
h = 0.0001 0.004
y[1] (numeric) = 0.194365641321 0.0759061684192
y[1] (closed_form) = 0.194362319366 0.0759139812322
absolute error = 8.490e-06
relative error = 0.004069 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.992
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=459.8MB, alloc=44.3MB, time=5.92
x[1] = -1.9159 0.459
h = 0.003 0.006
y[1] (numeric) = 0.194043607232 0.0765123634106
y[1] (closed_form) = 0.194040154745 0.0765196667059
absolute error = 8.078e-06
relative error = 0.003873 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.991
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9129 0.465
h = 0.0001 0.005
y[1] (numeric) = 0.193980705289 0.0776604145861
y[1] (closed_form) = 0.193975662027 0.0776693941214
absolute error = 1.030e-05
relative error = 0.004929 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.986
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9128 0.47
h = 0.0001 0.003
y[1] (numeric) = 0.193562852797 0.0784130133808
y[1] (closed_form) = 0.193559025833 0.0784211048467
absolute error = 8.951e-06
relative error = 0.004286 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.985
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9127 0.473
h = 0.001 0.001
y[1] (numeric) = 0.193316348231 0.0788658873024
y[1] (closed_form) = 0.193313006911 0.078874311198
absolute error = 9.062e-06
relative error = 0.004341 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.984
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9117 0.474
h = 0.001 0.003
y[1] (numeric) = 0.193376755341 0.0791011560742
y[1] (closed_form) = 0.193373706929 0.0791096620979
absolute error = 9.036e-06
relative error = 0.004325 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.983
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9107 0.477
h = 0.0001 0.004
y[1] (numeric) = 0.193262022313 0.0796329568491
y[1] (closed_form) = 0.193258383193 0.0796412699895
absolute error = 9.075e-06
relative error = 0.004341 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.981
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9106 0.481
h = 0.003 0.006
y[1] (numeric) = 0.192923404307 0.0802328143189
y[1] (closed_form) = 0.192919649667 0.0802406109001
absolute error = 8.654e-06
relative error = 0.004142 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.98
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9076 0.487
h = 0.0001 0.005
y[1] (numeric) = 0.192830826206 0.0813828686556
y[1] (closed_form) = 0.192825419475 0.0813923019811
absolute error = 1.087e-05
relative error = 0.005195 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.975
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9075 0.492
h = 0.0001 0.003
y[1] (numeric) = 0.192392312215 0.0821270660897
y[1] (closed_form) = 0.192388156502 0.0821356439311
absolute error = 9.531e-06
relative error = 0.004556 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.974
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9074 0.495
h = 0.001 0.001
y[1] (numeric) = 0.19213339679 0.0825749962944
y[1] (closed_form) = 0.192129719218 0.0825839236066
absolute error = 9.655e-06
relative error = 0.004617 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.973
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=506.4MB, alloc=44.3MB, time=6.52
x[1] = -1.9064 0.496
h = 0.001 0.003
y[1] (numeric) = 0.192187935961 0.0828125424638
y[1] (closed_form) = 0.192184550452 0.0828215614949
absolute error = 9.634e-06
relative error = 0.004603 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.972
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9054 0.499
h = 0.0001 0.004
y[1] (numeric) = 0.192059161398 0.0833430264276
y[1] (closed_form) = 0.192055187736 0.0833518330658
absolute error = 9.662e-06
relative error = 0.004615 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.97
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9053 0.503
h = 0.003 0.006
y[1] (numeric) = 0.191704059145 0.083935994194
y[1] (closed_form) = 0.191699985382 0.0839442776665
absolute error = 9.231e-06
relative error = 0.004411 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.969
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9023 0.509
h = 0.0001 0.005
y[1] (numeric) = 0.191581569437 0.0850871408124
y[1] (closed_form) = 0.191575782937 0.0850970189944
absolute error = 1.145e-05
relative error = 0.005461 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.965
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9022 0.514
h = 0.0001 0.003
y[1] (numeric) = 0.191122535168 0.0858222440699
y[1] (closed_form) = 0.191118033676 0.0858313009102
absolute error = 1.011e-05
relative error = 0.004827 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.963
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9021 0.517
h = 0.001 0.001
y[1] (numeric) = 0.190851291026 0.0862648148286
y[1] (closed_form) = 0.190847259501 0.0862742381122
absolute error = 1.025e-05
relative error = 0.004894 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.962
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9011 0.518
h = 0.0001 0.004
y[1] (numeric) = 0.1908998572 0.0865044685105
y[1] (closed_form) = 0.190896116551 0.0865139931815
absolute error = 1.023e-05
relative error = 0.004882 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.961
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.901 0.522
h = 0.003 0.006
y[1] (numeric) = 0.190531373927 0.0870913643805
y[1] (closed_form) = 0.190526924971 0.0870998635856
absolute error = 9.593e-06
relative error = 0.004579 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.96
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.898 0.528
h = 0.0001 0.005
y[1] (numeric) = 0.190382972773 0.0882423482603
y[1] (closed_form) = 0.190376760041 0.0882524032242
absolute error = 1.182e-05
relative error = 0.005633 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.956
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8979 0.533
h = 0.0001 0.003
y[1] (numeric) = 0.189906527512 0.0889688248747
y[1] (closed_form) = 0.189901627967 0.088978089531
absolute error = 1.048e-05
relative error = 0.004997 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.955
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=553.1MB, alloc=44.3MB, time=7.12
x[1] = -1.8978 0.536
h = 0.001 0.001
y[1] (numeric) = 0.189624819303 0.0894063028695
y[1] (closed_form) = 0.189620381944 0.089415948395
absolute error = 1.062e-05
relative error = 0.005064 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.954
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8968 0.537
h = 0.001 0.003
y[1] (numeric) = 0.189668141341 0.0896475575908
y[1] (closed_form) = 0.189663993439 0.0896573128602
absolute error = 1.060e-05
relative error = 0.005053 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.952
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8958 0.54
h = 0.0001 0.004
y[1] (numeric) = 0.189513170967 0.0901742316315
y[1] (closed_form) = 0.189508441786 0.0901837379282
absolute error = 1.062e-05
relative error = 0.005059 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.951
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8957 0.544
h = 0.003 0.006
y[1] (numeric) = 0.189127827548 0.0907527081642
y[1] (closed_form) = 0.189123028086 0.0907616804386
absolute error = 1.018e-05
relative error = 0.004851 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.95
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8927 0.55
h = 0.0001 0.005
y[1] (numeric) = 0.188949165557 0.091903039348
y[1] (closed_form) = 0.188942543246 0.0919135205455
absolute error = 1.240e-05
relative error = 0.005901 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.945
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8926 0.555
h = 0.0001 0.003
y[1] (numeric) = 0.188452539617 0.0926191280416
y[1] (closed_form) = 0.188447262901 0.0926288559822
absolute error = 1.107e-05
relative error = 0.00527 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.944
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8925 0.558
h = 0.001 0.001
y[1] (numeric) = 0.188158701648 0.0930504700561
y[1] (closed_form) = 0.188153877664 0.0930605956309
absolute error = 1.122e-05
relative error = 0.005343 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.943
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8915 0.559
h = 0.001 0.003
y[1] (numeric) = 0.188195870185 0.0932935003454
y[1] (closed_form) = 0.188191333809 0.0933037454435
absolute error = 1.120e-05
relative error = 0.005334 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.942
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8905 0.562
h = 0.0001 0.004
y[1] (numeric) = 0.188026788542 0.0938175653655
y[1] (closed_form) = 0.188021675506 0.0938275416819
absolute error = 1.121e-05
relative error = 0.005335 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.941
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8904 0.566
h = 0.003 0.006
y[1] (numeric) = 0.187625365465 0.0943875618383
y[1] (closed_form) = 0.187620198687 0.094396998913
absolute error = 1.076e-05
relative error = 0.005123 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.94
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=599.9MB, alloc=44.3MB, time=7.72
x[1] = -1.8874 0.572
h = 0.0001 0.005
y[1] (numeric) = 0.187416293199 0.095536279408
y[1] (closed_form) = 0.187409245496 0.0955471759461
absolute error = 1.298e-05
relative error = 0.006169 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.935
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8873 0.577
h = 0.0001 0.003
y[1] (numeric) = 0.186899702717 0.0962412818614
y[1] (closed_form) = 0.18689403206 0.0962514637664
absolute error = 1.165e-05
relative error = 0.005544 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.934
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8872 0.58
h = 0.001 0.001
y[1] (numeric) = 0.186593862095 0.0966660686707
y[1] (closed_form) = 0.186588634013 0.0966766648259
absolute error = 1.182e-05
relative error = 0.005623 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.933
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8862 0.581
h = 0.001 0.003
y[1] (numeric) = 0.186624786494 0.096910688997
y[1] (closed_form) = 0.186619843801 0.0969214144986
absolute error = 1.181e-05
relative error = 0.005616 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.932
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8852 0.584
h = 0.0001 0.004
y[1] (numeric) = 0.186441597755 0.0974316821965
y[1] (closed_form) = 0.186436083782 0.0974421190495
absolute error = 1.180e-05
relative error = 0.005611 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.931
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8851 0.588
h = 0.003 0.006
y[1] (numeric) = 0.186024275291 0.0979926400768
y[1] (closed_form) = 0.186018724487 0.0980025330028
absolute error = 1.134e-05
relative error = 0.005395 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.93
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8821 0.594
h = 0.0001 0.005
y[1] (numeric) = 0.185784675933 0.0991387669743
y[1] (closed_form) = 0.185777187255 0.0991500672586
absolute error = 1.356e-05
relative error = 0.006438 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.925
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.882 0.599
h = 0.0001 0.003
y[1] (numeric) = 0.185248364526 0.0998319847256
y[1] (closed_form) = 0.185242283306 0.0998426105721
absolute error = 1.224e-05
relative error = 0.005818 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.924
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8819 0.602
h = 0.001 0.001
y[1] (numeric) = 0.184930664858 0.100249796955
y[1] (closed_form) = 0.184925015339 0.100260853488
absolute error = 1.242e-05
relative error = 0.005903 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.924
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8809 0.603
h = 0.001 0.003
y[1] (numeric) = 0.184955260139 0.10049581644
y[1] (closed_form) = 0.184949893409 0.100507012172
absolute error = 1.242e-05
relative error = 0.005898 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.922
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=646.6MB, alloc=44.3MB, time=8.32
x[1] = -1.8799 0.606
h = 0.0001 0.004
y[1] (numeric) = 0.18475798518 0.101013269951
y[1] (closed_form) = 0.18475205333 0.101024157139
absolute error = 1.240e-05
relative error = 0.005888 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.921
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8798 0.61
h = 0.003 0.006
y[1] (numeric) = 0.184324965778 0.101564630912
y[1] (closed_form) = 0.18431901437 0.101574970049
absolute error = 1.193e-05
relative error = 0.005669 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.92
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8768 0.616
h = 0.0001 0.005
y[1] (numeric) = 0.184054756531 0.10270717487
y[1] (closed_form) = 0.184046811556 0.1027188666
absolute error = 1.414e-05
relative error = 0.006707 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.916
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8767 0.621
h = 0.0001 0.003
y[1] (numeric) = 0.18349899594 0.10338791042
y[1] (closed_form) = 0.183492487708 0.103398969472
absolute error = 1.283e-05
relative error = 0.006092 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.915
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8766 0.624
h = 0.001 0.001
y[1] (numeric) = 0.183169597714 0.103798329211
y[1] (closed_form) = 0.183163509586 0.103809835171
absolute error = 1.302e-05
relative error = 0.006183 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.914
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8756 0.625
h = 0.0001 0.004
y[1] (numeric) = 0.1831877849 0.104045551735
y[1] (closed_form) = 0.183181976571 0.104057206762
absolute error = 1.302e-05
relative error = 0.006181 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.913
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8755 0.629
h = 0.003 0.006
y[1] (numeric) = 0.182742110719 0.104588626374
y[1] (closed_form) = 0.182735744164 0.104599126554
absolute error = 1.228e-05
relative error = 0.005832 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.912
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8725 0.635
h = 0.0001 0.005
y[1] (numeric) = 0.182445573231 0.105726915529
y[1] (closed_form) = 0.18243716698 0.105738718384
absolute error = 1.449e-05
relative error = 0.006872 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.908
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8724 0.64
h = 0.0001 0.003
y[1] (numeric) = 0.181873470907 0.106396123148
y[1] (closed_form) = 0.181866525111 0.106407330845
absolute error = 1.319e-05
relative error = 0.006258 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.907
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8723 0.643
h = 0.001 0.001
y[1] (numeric) = 0.181534239463 0.106799706992
y[1] (closed_form) = 0.181527703013 0.106811375211
absolute error = 1.337e-05
relative error = 0.00635 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.906
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8713 0.644
h = 0.001 0.003
y[1] (numeric) = 0.181546841321 0.107047726604
y[1] (closed_form) = 0.181540581658 0.107059552344
absolute error = 1.338e-05
relative error = 0.006349 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.905
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=693.5MB, alloc=44.3MB, time=8.92
x[1] = -1.8703 0.647
h = 0.0001 0.004
y[1] (numeric) = 0.181323525931 0.107557166968
y[1] (closed_form) = 0.181316714989 0.107568647269
absolute error = 1.335e-05
relative error = 0.006332 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.903
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8702 0.651
h = 0.003 0.006
y[1] (numeric) = 0.180862045006 0.108089008614
y[1] (closed_form) = 0.180855247585 0.108099934997
absolute error = 1.287e-05
relative error = 0.006107 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.902
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8672 0.657
h = 0.0001 0.005
y[1] (numeric) = 0.180534851102 0.109221831681
y[1] (closed_form) = 0.180525961039 0.109234001024
absolute error = 1.507e-05
relative error = 0.007142 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.898
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8671 0.662
h = 0.0001 0.003
y[1] (numeric) = 0.179943890365 0.109877269955
y[1] (closed_form) = 0.179936487682 0.109888888762
absolute error = 1.378e-05
relative error = 0.006534 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.897
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.867 0.665
h = 0.001 0.001
y[1] (numeric) = 0.1795933101 0.110272687216
y[1] (closed_form) = 0.179586303801 0.110284782264
absolute error = 1.398e-05
relative error = 0.006633 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.897
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.866 0.666
h = 0.001 0.003
y[1] (numeric) = 0.179599376582 0.110521530695
y[1] (closed_form) = 0.179592643328 0.110533793112
absolute error = 1.399e-05
relative error = 0.006634 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.896
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.865 0.669
h = 0.0001 0.004
y[1] (numeric) = 0.1793621379 0.111026071153
y[1] (closed_form) = 0.179354861861 0.111037968345
absolute error = 1.395e-05
relative error = 0.006611 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.894
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8649 0.673
h = 0.003 0.006
y[1] (numeric) = 0.178885672607 0.11154673153
y[1] (closed_form) = 0.178878428296 0.111558072444
absolute error = 1.346e-05
relative error = 0.006383 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.893
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8619 0.679
h = 0.0001 0.005
y[1] (numeric) = 0.178527844678 0.112673059389
y[1] (closed_form) = 0.178518456452 0.112685580887
absolute error = 1.565e-05
relative error = 0.007413 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.889
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8618 0.684
h = 0.0001 0.003
y[1] (numeric) = 0.177918380861 0.113314040762
y[1] (closed_form) = 0.177910505542 0.113326057861
absolute error = 1.437e-05
relative error = 0.006811 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.888
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=740.2MB, alloc=44.3MB, time=9.52
x[1] = -1.8617 0.687
h = 0.001 0.001
y[1] (numeric) = 0.177556662444 0.113700878379
y[1] (closed_form) = 0.177549169808 0.113713387118
absolute error = 1.458e-05
relative error = 0.006916 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.888
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8607 0.688
h = 0.001 0.003
y[1] (numeric) = 0.177556133788 0.113950335509
y[1] (closed_form) = 0.177548910037 0.11396302143
absolute error = 1.460e-05
relative error = 0.006919 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.887
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8597 0.691
h = 0.0001 0.004
y[1] (numeric) = 0.177305062656 0.114449494636
y[1] (closed_form) = 0.177297305464 0.114461795652
absolute error = 1.454e-05
relative error = 0.006891 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.885
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8596 0.695
h = 0.003 0.006
y[1] (numeric) = 0.176813905434 0.114958425624
y[1] (closed_form) = 0.176806198466 0.114970168671
absolute error = 1.405e-05
relative error = 0.00666 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.884
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8566 0.701
h = 0.0001 0.005
y[1] (numeric) = 0.176425505245 0.116077218691
y[1] (closed_form) = 0.176415604917 0.116090077298
absolute error = 1.623e-05
relative error = 0.007684 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.881
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8565 0.706
h = 0.0001 0.003
y[1] (numeric) = 0.175797923865 0.116703061608
y[1] (closed_form) = 0.175789560475 0.116715463442
absolute error = 1.496e-05
relative error = 0.007089 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.88
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8564 0.709
h = 0.001 0.001
y[1] (numeric) = 0.175425296084 0.117080910065
y[1] (closed_form) = 0.175417300933 0.117093818577
absolute error = 1.518e-05
relative error = 0.007199 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.879
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8554 0.71
h = 0.001 0.003
y[1] (numeric) = 0.175418119929 0.117330766041
y[1] (closed_form) = 0.175410389082 0.117343861495
absolute error = 1.521e-05
relative error = 0.007206 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.878
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8544 0.713
h = 0.0001 0.004
y[1] (numeric) = 0.175153326644 0.117824060623
y[1] (closed_form) = 0.175145072559 0.117836751638
absolute error = 1.514e-05
relative error = 0.007172 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.876
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8543 0.717
h = 0.003 0.006
y[1] (numeric) = 0.174647794193 0.118320719349
y[1] (closed_form) = 0.174639609094 0.118332851403
absolute error = 1.463e-05
relative error = 0.006938 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.876
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=786.9MB, alloc=44.3MB, time=10.12
x[1] = -1.8513 0.723
h = 0.0001 0.005
y[1] (numeric) = 0.174228924219 0.119430929114
y[1] (closed_form) = 0.174218498304 0.119444109083
absolute error = 1.681e-05
relative error = 0.007956 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.872
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8512 0.728
h = 0.0001 0.003
y[1] (numeric) = 0.173583641368 0.120040959525
y[1] (closed_form) = 0.173574774826 0.120053731795
absolute error = 1.555e-05
relative error = 0.007367 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.871
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8511 0.731
h = 0.001 0.001
y[1] (numeric) = 0.173200351363 0.120409413754
y[1] (closed_form) = 0.173191837875 0.120422707337
absolute error = 1.579e-05
relative error = 0.007484 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.871
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8501 0.732
h = 0.0001 0.004
y[1] (numeric) = 0.173186483125 0.120659449423
y[1] (closed_form) = 0.173178228928 0.120672939635
absolute error = 1.582e-05
relative error = 0.007493 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.869
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.85 0.736
h = 0.003 0.006
y[1] (numeric) = 0.172669467075 0.12114565142
y[1] (closed_form) = 0.172660835293 0.121157880344
absolute error = 1.497e-05
relative error = 0.007096 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.869
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.847 0.742
h = 0.0001 0.005
y[1] (numeric) = 0.172224603197 0.122247267258
y[1] (closed_form) = 0.172213692315 0.122260483268
absolute error = 1.714e-05
relative error = 0.008115 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.865
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8469 0.747
h = 0.0001 0.003
y[1] (numeric) = 0.171564639394 0.122842950383
y[1] (closed_form) = 0.171555305234 0.122855802304
absolute error = 1.588e-05
relative error = 0.007528 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.864
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8468 0.75
h = 0.001 0.001
y[1] (numeric) = 0.171172502124 0.123202875441
y[1] (closed_form) = 0.171163507188 0.123216260727
absolute error = 1.613e-05
relative error = 0.007647 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.864
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8458 0.751
h = 0.001 0.003
y[1] (numeric) = 0.171152845555 0.123452806883
y[1] (closed_form) = 0.171144105133 0.123466396991
absolute error = 1.616e-05
relative error = 0.007657 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.863
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8448 0.754
h = 0.0001 0.004
y[1] (numeric) = 0.17086296428 0.123933740851
y[1] (closed_form) = 0.170853722165 0.123946890855
absolute error = 1.607e-05
relative error = 0.007615 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.861
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=833.7MB, alloc=44.3MB, time=10.72
x[1] = -1.8447 0.758
h = 0.0001 0.004
y[1] (numeric) = 0.170331771157 0.124405980824
y[1] (closed_form) = 0.170322633546 0.124418572198
absolute error = 1.556e-05
relative error = 0.007376 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.861
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8446 0.762
h = 0.003 0.006
y[1] (numeric) = 0.169798858269 0.124874818689
y[1] (closed_form) = 0.169789720658 0.124887410063
absolute error = 1.556e-05
relative error = 0.007381 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.86
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8416 0.768
h = 0.0001 0.005
y[1] (numeric) = 0.169319067179 0.125962840418
y[1] (closed_form) = 0.169307602692 0.125976332179
absolute error = 1.770e-05
relative error = 0.00839 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.856
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8415 0.773
h = 0.0001 0.003
y[1] (numeric) = 0.168640053644 0.12653786554
y[1] (closed_form) = 0.168630186235 0.126551054564
absolute error = 1.647e-05
relative error = 0.007813 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.855
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8414 0.776
h = 0.001 0.001
y[1] (numeric) = 0.168236428947 0.126885501751
y[1] (closed_form) = 0.16822688078 0.126899239596
absolute error = 1.673e-05
relative error = 0.007939 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.855
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8404 0.777
h = 0.001 0.003
y[1] (numeric) = 0.16820886729 0.127134878772
y[1] (closed_form) = 0.168199566412 0.127148832322
absolute error = 1.677e-05
relative error = 0.007953 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.854
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8394 0.78
h = 0.0001 0.004
y[1] (numeric) = 0.167903698952 0.127606776114
y[1] (closed_form) = 0.167893912084 0.127620267964
absolute error = 1.667e-05
relative error = 0.007903 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.853
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8393 0.784
h = 0.003 0.006
y[1] (numeric) = 0.167357439989 0.128062317407
y[1] (closed_form) = 0.167347780284 0.128075252781
absolute error = 1.614e-05
relative error = 0.007661 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.852
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8363 0.79
h = 0.0001 0.005
y[1] (numeric) = 0.166847804192 0.129138550929
y[1] (closed_form) = 0.166835777326 0.129152311489
absolute error = 1.828e-05
relative error = 0.008662 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.848
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8362 0.795
h = 0.0001 0.003
y[1] (numeric) = 0.166152572335 0.12969580698
y[1] (closed_form) = 0.166142159453 0.129709317882
absolute error = 1.706e-05
relative error = 0.008093 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.848
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=880.6MB, alloc=44.3MB, time=11.33
x[1] = -1.8361 0.798
h = 0.001 0.001
y[1] (numeric) = 0.16573916775 0.130032872632
y[1] (closed_form) = 0.165729056732 0.130046945464
absolute error = 1.733e-05
relative error = 0.008226 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.847
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8351 0.799
h = 0.001 0.003
y[1] (numeric) = 0.165704841443 0.130281740141
y[1] (closed_form) = 0.165694971374 0.130296037978
absolute error = 1.737e-05
relative error = 0.008242 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.846
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8341 0.802
h = 0.0001 0.004
y[1] (numeric) = 0.165386626581 0.130745833922
y[1] (closed_form) = 0.165376284278 0.130759651618
absolute error = 1.726e-05
relative error = 0.008187 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.845
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.834 0.806
h = 0.003 0.006
y[1] (numeric) = 0.164827545558 0.131187013437
y[1] (closed_form) = 0.164817349918 0.131200276752
absolute error = 1.673e-05
relative error = 0.007941 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.844
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.831 0.812
h = 0.0001 0.005
y[1] (numeric) = 0.164288344181 0.132250394948
y[1] (closed_form) = 0.164275743762 0.132264405858
absolute error = 1.884e-05
relative error = 0.008935 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.841
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8309 0.817
h = 0.0001 0.003
y[1] (numeric) = 0.163577434904 0.132789256439
y[1] (closed_form) = 0.163566463367 0.132803071985
absolute error = 1.764e-05
relative error = 0.008373 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.84
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8308 0.82
h = 0.001 0.001
y[1] (numeric) = 0.163154572478 0.133115375381
y[1] (closed_form) = 0.163143884719 0.133129765385
absolute error = 1.792e-05
relative error = 0.008513 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.84
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8298 0.821
h = 0.001 0.003
y[1] (numeric) = 0.163113472115 0.133363500205
y[1] (closed_form) = 0.163103018521 0.133378124346
absolute error = 1.798e-05
relative error = 0.008532 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.839
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8288 0.824
h = 0.0001 0.004
y[1] (numeric) = 0.162782425644 0.133819313385
y[1] (closed_form) = 0.162771514466 0.133833439326
absolute error = 1.785e-05
relative error = 0.00847 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.837
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8287 0.828
h = 0.003 0.006
y[1] (numeric) = 0.162210963663 0.134245635677
y[1] (closed_form) = 0.162200218751 0.134259210157
absolute error = 1.731e-05
relative error = 0.008222 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.837
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8257 0.834
h = 0.0001 0.005
y[1] (numeric) = 0.161642522185 0.135295102344
y[1] (closed_form) = 0.161629337712 0.135309344518
absolute error = 1.941e-05
relative error = 0.009207 %
Correct digits = 4
memory used=927.5MB, alloc=44.3MB, time=11.94
Radius of convergence (given) for eq 1 = 1.833
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8256 0.839
h = 0.0001 0.003
y[1] (numeric) = 0.160916507458 0.135814959924
y[1] (closed_form) = 0.16090496466 0.135829062174
absolute error = 1.822e-05
relative error = 0.008655 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.833
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8255 0.842
h = 0.001 0.001
y[1] (numeric) = 0.160484527879 0.136129765636
y[1] (closed_form) = 0.16047325008 0.136144454239
absolute error = 1.852e-05
relative error = 0.0088 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.832
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8245 0.843
h = 0.001 0.003
y[1] (numeric) = 0.160436653592 0.136376911959
y[1] (closed_form) = 0.16042560273 0.136391843635
absolute error = 1.858e-05
relative error = 0.008822 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.831
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8235 0.846
h = 0.0001 0.004
y[1] (numeric) = 0.160093012218 0.136823971744
y[1] (closed_form) = 0.160081519313 0.136838387599
absolute error = 1.844e-05
relative error = 0.008754 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.83
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8234 0.85
h = 0.003 0.006
y[1] (numeric) = 0.159509635149 0.137234954845
y[1] (closed_form) = 0.159498328178 0.137248823001
absolute error = 1.789e-05
relative error = 0.008504 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.83
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8204 0.856
h = 0.0001 0.005
y[1] (numeric) = 0.158912326241 0.138269447154
y[1] (closed_form) = 0.158898547934 0.138283900901
absolute error = 1.997e-05
relative error = 0.00948 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.826
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8203 0.861
h = 0.0001 0.003
y[1] (numeric) = 0.158171808876 0.138769709503
y[1] (closed_form) = 0.158159682835 0.13878407982
absolute error = 1.880e-05
relative error = 0.008936 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.826
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8202 0.864
h = 0.001 0.001
y[1] (numeric) = 0.157731071338 0.139072846224
y[1] (closed_form) = 0.157719190843 0.139087814112
absolute error = 1.911e-05
relative error = 0.009087 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.825
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8192 0.865
h = 0.0001 0.004
y[1] (numeric) = 0.157676433106 0.13931877602
y[1] (closed_form) = 0.157664771878 0.139333995697
absolute error = 1.917e-05
relative error = 0.009112 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.824
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8191 0.869
h = 0.003 0.006
y[1] (numeric) = 0.157083699788 0.139716849547
y[1] (closed_form) = 0.157071923579 0.139730723337
absolute error = 1.820e-05
relative error = 0.008656 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.824
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=974.2MB, alloc=44.3MB, time=12.54
x[1] = -1.8161 0.875
h = 0.0001 0.005
y[1] (numeric) = 0.156462073174 0.140737271431
y[1] (closed_form) = 0.156447801828 0.140751658135
absolute error = 2.026e-05
relative error = 0.009629 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.82
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.816 0.88
h = 0.0001 0.003
y[1] (numeric) = 0.155709821053 0.141220046111
y[1] (closed_form) = 0.155697208563 0.141234398874
absolute error = 1.911e-05
relative error = 0.009089 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.82
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8159 0.883
h = 0.001 0.001
y[1] (numeric) = 0.155261991101 0.141512764576
y[1] (closed_form) = 0.15524960677 0.141527723744
absolute error = 1.942e-05
relative error = 0.009244 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.82
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8149 0.884
h = 0.001 0.003
y[1] (numeric) = 0.155201564802 0.141757375058
y[1] (closed_form) = 0.155189392684 0.141772593222
absolute error = 1.949e-05
relative error = 0.009271 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.819
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8139 0.887
h = 0.0001 0.004
y[1] (numeric) = 0.15483530994 0.142186765655
y[1] (closed_form) = 0.154822727238 0.142201436765
absolute error = 1.933e-05
relative error = 0.009194 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.817
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8138 0.891
h = 0.003 0.006
y[1] (numeric) = 0.154231280969 0.142567848133
y[1] (closed_form) = 0.154218920755 0.14258198109
absolute error = 1.878e-05
relative error = 0.008939 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.817
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8108 0.897
h = 0.0001 0.005
y[1] (numeric) = 0.153581620703 0.143571347381
y[1] (closed_form) = 0.153566739646 0.143585907403
absolute error = 2.082e-05
relative error = 0.009903 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.814
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8107 0.902
h = 0.0001 0.003
y[1] (numeric) = 0.152816074838 0.144033489144
y[1] (closed_form) = 0.152802858865 0.144048073393
absolute error = 1.968e-05
relative error = 0.009372 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.813
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8106 0.905
h = 0.001 0.001
y[1] (numeric) = 0.152360207627 0.14431391402
y[1] (closed_form) = 0.152347199182 0.144329114498
absolute error = 2.001e-05
relative error = 0.009533 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.813
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8096 0.906
h = 0.001 0.003
y[1] (numeric) = 0.152293066032 0.144556861223
y[1] (closed_form) = 0.152280261322 0.144572328925
absolute error = 2.008e-05
relative error = 0.009563 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.812
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1021.1MB, alloc=44.3MB, time=13.14
x[1] = -1.8086 0.909
h = 0.0001 0.004
y[1] (numeric) = 0.151915020554 0.144976183884
y[1] (closed_form) = 0.151901823295 0.144991088469
absolute error = 1.991e-05
relative error = 0.00948 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.811
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8085 0.913
h = 0.003 0.006
y[1] (numeric) = 0.151300548627 0.145340643008
y[1] (closed_form) = 0.151287593457 0.145355015713
absolute error = 1.935e-05
relative error = 0.009223 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.811
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8055 0.919
h = 0.0001 0.005
y[1] (numeric) = 0.150623365631 0.146326184289
y[1] (closed_form) = 0.150607867391 0.146340896376
absolute error = 2.137e-05
relative error = 0.01018 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.807
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8054 0.924
h = 0.0001 0.003
y[1] (numeric) = 0.149845214301 0.146767164453
y[1] (closed_form) = 0.149831384913 0.146781959691
absolute error = 2.025e-05
relative error = 0.009655 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.807
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8053 0.927
h = 0.001 0.001
y[1] (numeric) = 0.149381720297 0.147034977391
y[1] (closed_form) = 0.149368077208 0.147050397871
absolute error = 2.059e-05
relative error = 0.009823 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.807
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8043 0.928
h = 0.001 0.003
y[1] (numeric) = 0.149307903107 0.147276019799
y[1] (closed_form) = 0.149294454848 0.14729171543
absolute error = 2.067e-05
relative error = 0.009855 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.806
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8033 0.931
h = 0.0001 0.004
y[1] (numeric) = 0.148918388871 0.147684829964
y[1] (closed_form) = 0.148904566943 0.147699947067
absolute error = 2.048e-05
relative error = 0.009766 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.805
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8032 0.935
h = 0.003 0.006
y[1] (numeric) = 0.148294032145 0.148032250535
y[1] (closed_form) = 0.148280471794 0.148046842933
absolute error = 1.992e-05
relative error = 0.009507 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.804
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8002 0.941
h = 0.0001 0.005
y[1] (numeric) = 0.147589886367 0.14899881203
y[1] (closed_form) = 0.147573764357 0.149013654449
absolute error = 2.191e-05
relative error = 0.01045 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.801
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8001 0.946
h = 0.0001 0.003
y[1] (numeric) = 0.146799846485 0.149418127478
y[1] (closed_form) = 0.14678539455 0.14943311261
absolute error = 2.082e-05
relative error = 0.009939 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.801
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1067.8MB, alloc=44.3MB, time=13.73
x[1] = -1.8 0.949
h = 0.001 0.001
y[1] (numeric) = 0.146329153326 0.149673025403
y[1] (closed_form) = 0.146314865899 0.149688643932
absolute error = 2.117e-05
relative error = 0.01011 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.801
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.799 0.95
h = 0.001 0.003
y[1] (numeric) = 0.146248711076 0.149911921278
y[1] (closed_form) = 0.146234609158 0.149927822561
absolute error = 2.125e-05
relative error = 0.01015 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.8
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.798 0.953
h = 0.0001 0.004
y[1] (numeric) = 0.145848071906 0.150309784817
y[1] (closed_form) = 0.145833616023 0.150325092863
absolute error = 2.105e-05
relative error = 0.01005 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.799
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7979 0.957
h = 0.003 0.006
y[1] (numeric) = 0.145214411131 0.150639772663
y[1] (closed_form) = 0.145200236151 0.150654564091
absolute error = 2.049e-05
relative error = 0.009791 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.798
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7949 0.963
h = 0.0001 0.005
y[1] (numeric) = 0.144483911604 0.151586348936
y[1] (closed_form) = 0.144467160159 0.151601299518
absolute error = 2.245e-05
relative error = 0.01072 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.795
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7948 0.968
h = 0.0001 0.003
y[1] (numeric) = 0.143682727781 0.151983524082
y[1] (closed_form) = 0.143667645016 0.151998677445
absolute error = 2.138e-05
relative error = 0.01022 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.795
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7947 0.971
h = 0.001 0.001
y[1] (numeric) = 0.143205279718 0.152225220369
y[1] (closed_form) = 0.143190339148 0.152241014385
absolute error = 2.174e-05
relative error = 0.0104 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.795
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7937 0.972
h = 0.0001 0.004
y[1] (numeric) = 0.143118273957 0.152461728343
y[1] (closed_form) = 0.143103509169 0.152477812358
absolute error = 2.183e-05
relative error = 0.01044 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.794
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7936 0.976
h = 0.003 0.006
y[1] (numeric) = 0.14247747874 0.152777169311
y[1] (closed_form) = 0.142462832375 0.152791886556
absolute error = 2.076e-05
relative error = 0.009939 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.794
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7906 0.982
h = 0.0001 0.005
y[1] (numeric) = 0.141725073855 0.153705449377
y[1] (closed_form) = 0.141707842523 0.153720246385
absolute error = 2.271e-05
relative error = 0.01086 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.791
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1114.7MB, alloc=44.3MB, time=14.34
x[1] = -1.7905 0.987
h = 0.0001 0.003
y[1] (numeric) = 0.1409151852 0.154083088327
y[1] (closed_form) = 0.140899618477 0.154098140063
absolute error = 2.165e-05
relative error = 0.01037 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.791
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7904 0.99
h = 0.001 0.001
y[1] (numeric) = 0.14043245226 0.154313132013
y[1] (closed_form) = 0.140417008068 0.154328829618
absolute error = 2.202e-05
relative error = 0.01055 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.79
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7894 0.991
h = 0.001 0.003
y[1] (numeric) = 0.140339886992 0.154547315033
y[1] (closed_form) = 0.140324609813 0.154563308448
absolute error = 2.212e-05
relative error = 0.01059 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.789
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7884 0.994
h = 0.0001 0.004
y[1] (numeric) = 0.13991967828 0.154923573541
y[1] (closed_form) = 0.139904086053 0.154938948678
absolute error = 2.190e-05
relative error = 0.01049 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.788
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7883 0.998
h = 0.003 0.006
y[1] (numeric) = 0.13927054216 0.155220059077
y[1] (closed_form) = 0.139255266061 0.155234935305
absolute error = 2.132e-05
relative error = 0.01022 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.788
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7853 1.004
h = 0.0001 0.005
y[1] (numeric) = 0.138493058175 0.156126545373
y[1] (closed_form) = 0.138475189724 0.156141408251
absolute error = 2.324e-05
relative error = 0.01114 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.785
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7852 1.009
h = 0.0001 0.003
y[1] (numeric) = 0.137673485778 0.156481248575
y[1] (closed_form) = 0.137657275495 0.156496426787
absolute error = 2.221e-05
relative error = 0.01065 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.785
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7851 1.012
h = 0.001 0.001
y[1] (numeric) = 0.137184869375 0.156697610755
y[1] (closed_form) = 0.137168758463 0.1567134403
absolute error = 2.259e-05
relative error = 0.01084 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.785
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7841 1.013
h = 0.001 0.003
y[1] (numeric) = 0.137085887745 0.156928960888
y[1] (closed_form) = 0.137069933407 0.156945092749
absolute error = 2.269e-05
relative error = 0.01089 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.784
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7831 1.016
h = 0.0001 0.004
y[1] (numeric) = 0.136655661222 0.157293105583
y[1] (closed_form) = 0.136639413726 0.157308606794
absolute error = 2.246e-05
relative error = 0.01078 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.783
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.783 1.02
h = 0.003 0.006
y[1] (numeric) = 0.13599900326 0.157571168533
y[1] (closed_form) = 0.135983090447 0.157586181537
absolute error = 2.188e-05
relative error = 0.01051 %
Correct digits = 4
memory used=1161.6MB, alloc=44.3MB, time=14.94
Radius of convergence (given) for eq 1 = 1.783
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.78 1.026
h = 0.0001 0.005
y[1] (numeric) = 0.135197187807 0.158454919469
y[1] (closed_form) = 0.135178679409 0.158469825075
absolute error = 2.376e-05
relative error = 0.01141 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.78
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7799 1.031
h = 0.0001 0.003
y[1] (numeric) = 0.134368748514 0.158786300984
y[1] (closed_form) = 0.13435188906 0.158801582625
absolute error = 2.275e-05
relative error = 0.01094 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.78
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7798 1.034
h = 0.001 0.001
y[1] (numeric) = 0.133874736225 0.1589887486
y[1] (closed_form) = 0.133857952589 0.159004686022
absolute error = 2.315e-05
relative error = 0.01114 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.78
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7788 1.035
h = 0.001 0.003
y[1] (numeric) = 0.133769431921 0.159217029127
y[1] (closed_form) = 0.133752794061 0.159233274939
absolute error = 2.325e-05
relative error = 0.01118 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.779
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7778 1.038
h = 0.0001 0.004
y[1] (numeric) = 0.133329613009 0.159568679249
y[1] (closed_form) = 0.133312704578 0.159584282954
absolute error = 2.301e-05
relative error = 0.01106 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.778
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7777 1.042
h = 0.003 0.006
y[1] (numeric) = 0.13266609222 0.159828021277
y[1] (closed_form) = 0.132649536652 0.159843148387
absolute error = 2.243e-05
relative error = 0.0108 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.778
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7747 1.048
h = 0.0001 0.005
y[1] (numeric) = 0.131840740236 0.160688123228
y[1] (closed_form) = 0.131821590113 0.16070304818
absolute error = 2.428e-05
relative error = 0.01168 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.775
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7746 1.053
h = 0.0001 0.003
y[1] (numeric) = 0.131004273452 0.160995831891
y[1] (closed_form) = 0.130986760223 0.161011193515
absolute error = 2.330e-05
relative error = 0.01122 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.775
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7745 1.056
h = 0.001 0.001
y[1] (numeric) = 0.130505366386 0.161184152664
y[1] (closed_form) = 0.130487905082 0.161200173465
absolute error = 2.370e-05
relative error = 0.01143 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.775
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7735 1.057
h = 0.001 0.003
y[1] (numeric) = 0.130393844429 0.161409129717
y[1] (closed_form) = 0.130376517763 0.161425464526
absolute error = 2.381e-05
relative error = 0.01148 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.774
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1208.3MB, alloc=44.3MB, time=15.54
x[1] = -1.7725 1.06
h = 0.0001 0.004
y[1] (numeric) = 0.129944878434 0.161747921606
y[1] (closed_form) = 0.129927304438 0.161763603818
absolute error = 2.355e-05
relative error = 0.01135 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.774
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7724 1.064
h = 0.003 0.006
y[1] (numeric) = 0.129275171321 0.161988272678
y[1] (closed_form) = 0.12925796794 0.162003490804
absolute error = 2.297e-05
relative error = 0.01108 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.774
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7694 1.07
h = 0.0001 0.005
y[1] (numeric) = 0.12842712405 0.162823843035
y[1] (closed_form) = 0.128407331497 0.162838763769
absolute error = 2.479e-05
relative error = 0.01195 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.771
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7693 1.075
h = 0.0001 0.003
y[1] (numeric) = 0.127583490022 0.163107564176
y[1] (closed_form) = 0.127565319456 0.163122981989
absolute error = 2.383e-05
relative error = 0.01151 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.771
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7692 1.078
h = 0.001 0.001
y[1] (numeric) = 0.127080201788 0.163281567629
y[1] (closed_form) = 0.127062058974 0.163297646935
absolute error = 2.424e-05
relative error = 0.01172 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.771
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7682 1.079
h = 0.0001 0.004
y[1] (numeric) = 0.126962578504 0.163503010879
y[1] (closed_form) = 0.126944558872 0.163519409326
absolute error = 2.436e-05
relative error = 0.01177 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.77
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7681 1.083
h = 0.003 0.006
y[1] (numeric) = 0.12628835594 0.163727642903
y[1] (closed_form) = 0.126270696202 0.16374270515
absolute error = 2.321e-05
relative error = 0.01123 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.77
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7651 1.089
h = 0.0001 0.005
y[1] (numeric) = 0.125421787297 0.164541160556
y[1] (closed_form) = 0.125401547703 0.164555843379
absolute error = 2.500e-05
relative error = 0.01209 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.767
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.765 1.094
h = 0.0001 0.003
y[1] (numeric) = 0.12457297747 0.16480394004
y[1] (closed_form) = 0.124554344018 0.164819171405
absolute error = 2.407e-05
relative error = 0.01165 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.768
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7649 1.097
h = 0.001 0.001
y[1] (numeric) = 0.124066511292 0.164965440806
y[1] (closed_form) = 0.124047884593 0.164981334477
absolute error = 2.449e-05
relative error = 0.01186 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.768
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1255.1MB, alloc=44.3MB, time=16.14
x[1] = -1.7639 1.098
h = 0.001 0.003
y[1] (numeric) = 0.123943783661 0.165183590463
y[1] (closed_form) = 0.123925269997 0.165199807147
absolute error = 2.461e-05
relative error = 0.01192 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.767
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7629 1.101
h = 0.0001 0.004
y[1] (numeric) = 0.123479209725 0.165497456881
y[1] (closed_form) = 0.123460493642 0.165513004484
absolute error = 2.433e-05
relative error = 0.01178 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.766
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7628 1.105
h = 0.003 0.006
y[1] (numeric) = 0.122800078164 0.165701800042
y[1] (closed_form) = 0.122781764216 0.165716909371
absolute error = 2.374e-05
relative error = 0.01151 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.766
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7598 1.111
h = 0.0001 0.005
y[1] (numeric) = 0.121912507899 0.166489247925
y[1] (closed_form) = 0.121891627768 0.166503882429
absolute error = 2.550e-05
relative error = 0.01236 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.763
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7597 1.116
h = 0.0001 0.003
y[1] (numeric) = 0.121058183146 0.166727567717
y[1] (closed_form) = 0.121038888906 0.16674281026
absolute error = 2.459e-05
relative error = 0.01193 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.764
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7596 1.119
h = 0.001 0.001
y[1] (numeric) = 0.120548322499 0.166874464455
y[1] (closed_form) = 0.120529010487 0.166890369534
absolute error = 2.502e-05
relative error = 0.01215 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.764
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7586 1.12
h = 0.001 0.003
y[1] (numeric) = 0.12041974239 0.167088665215
y[1] (closed_form) = 0.120400531441 0.167104897473
absolute error = 2.515e-05
relative error = 0.01221 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.763
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7576 1.123
h = 0.0001 0.004
y[1] (numeric) = 0.119947401532 0.167388745436
y[1] (closed_form) = 0.119928012979 0.167404301159
absolute error = 2.486e-05
relative error = 0.01207 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.762
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7575 1.127
h = 0.003 0.006
y[1] (numeric) = 0.119264104324 0.167573501739
y[1] (closed_form) = 0.119245134107 0.167588634164
absolute error = 2.427e-05
relative error = 0.0118 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.762
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7545 1.133
h = 0.0001 0.005
y[1] (numeric) = 0.118356497967 0.168334103035
y[1] (closed_form) = 0.118334979762 0.168348665489
absolute error = 2.598e-05
relative error = 0.01263 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.76
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1301.9MB, alloc=44.3MB, time=16.74
x[1] = -1.7544 1.138
h = 0.0001 0.003
y[1] (numeric) = 0.117497566826 0.168547761615
y[1] (closed_form) = 0.117477611387 0.168562990887
absolute error = 2.510e-05
relative error = 0.01222 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.76
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7543 1.141
h = 0.001 0.001
y[1] (numeric) = 0.11698485431 0.16867993145
y[1] (closed_form) = 0.116964856472 0.168695822335
absolute error = 2.554e-05
relative error = 0.01244 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.76
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7533 1.142
h = 0.001 0.003
y[1] (numeric) = 0.116850569708 0.168889967078
y[1] (closed_form) = 0.116830660721 0.168906188763
absolute error = 2.568e-05
relative error = 0.0125 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.759
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7523 1.145
h = 0.0001 0.004
y[1] (numeric) = 0.116370975783 0.169175975973
y[1] (closed_form) = 0.11635091445 0.169191514809
absolute error = 2.538e-05
relative error = 0.01236 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.758
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7522 1.149
h = 0.003 0.006
y[1] (numeric) = 0.115684242173 0.169340996607
y[1] (closed_form) = 0.115664614729 0.169356127938
absolute error = 2.478e-05
relative error = 0.01208 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.759
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7492 1.155
h = 0.0001 0.005
y[1] (numeric) = 0.114757605393 0.170074016882
y[1] (closed_form) = 0.114735452706 0.17008848362
absolute error = 2.646e-05
relative error = 0.0129 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.756
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7491 1.16
h = 0.0001 0.003
y[1] (numeric) = 0.113894989207 0.170262854808
y[1] (closed_form) = 0.113874373306 0.170278046247
absolute error = 2.561e-05
relative error = 0.0125 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.756
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.749 1.163
h = 0.001 0.001
y[1] (numeric) = 0.113379975118 0.170380199998
y[1] (closed_form) = 0.113359292153 0.170396050961
absolute error = 2.606e-05
relative error = 0.01273 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.757
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.748 1.164
h = 0.001 0.003
y[1] (numeric) = 0.113240144714 0.170585860486
y[1] (closed_form) = 0.113219538177 0.170602045303
absolute error = 2.620e-05
relative error = 0.0128 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.756
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.747 1.167
h = 0.0001 0.004
y[1] (numeric) = 0.112753826811 0.170857536178
y[1] (closed_form) = 0.112733093566 0.170873033006
absolute error = 2.588e-05
relative error = 0.01264 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.755
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1348.8MB, alloc=44.3MB, time=17.34
x[1] = -1.7469 1.171
h = 0.003 0.006
y[1] (numeric) = 0.112064395529 0.171002706269
y[1] (closed_form) = 0.112044111026 0.171017812171
absolute error = 2.529e-05
relative error = 0.01237 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.755
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7439 1.177
h = 0.0001 0.005
y[1] (numeric) = 0.111119771963 0.171707456215
y[1] (closed_form) = 0.111096989516 0.171721803703
absolute error = 2.692e-05
relative error = 0.01316 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.753
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7438 1.182
h = 0.0001 0.003
y[1] (numeric) = 0.110254402482 0.171871357235
y[1] (closed_form) = 0.110233128017 0.171886486233
absolute error = 2.611e-05
relative error = 0.01278 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.753
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7437 1.185
h = 0.001 0.001
y[1] (numeric) = 0.10973764338 0.171973805833
y[1] (closed_form) = 0.109716277219 0.171989591087
absolute error = 2.656e-05
relative error = 0.01302 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.753
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7427 1.186
h = 0.0001 0.004
y[1] (numeric) = 0.109592436283 0.172174888086
y[1] (closed_form) = 0.109571133951 0.172191009668
absolute error = 2.672e-05
relative error = 0.01309 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.753
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7426 1.19
h = 0.003 0.006
y[1] (numeric) = 0.108901383879 0.172303760518
y[1] (closed_form) = 0.108880676355 0.172318631704
absolute error = 2.549e-05
relative error = 0.01251 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.753
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7396 1.196
h = 0.0001 0.005
y[1] (numeric) = 0.107942487863 0.172983464035
y[1] (closed_form) = 0.10791931063 0.172997497299
absolute error = 2.709e-05
relative error = 0.01329 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.751
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7395 1.201
h = 0.0001 0.003
y[1] (numeric) = 0.107075798766 0.17312582323
y[1] (closed_form) = 0.107054101836 0.173140685522
absolute error = 2.630e-05
relative error = 0.01292 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.751
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7394 1.204
h = 0.001 0.001
y[1] (numeric) = 0.106558165091 0.173215400161
y[1] (closed_form) = 0.106536355403 0.173230914656
absolute error = 2.676e-05
relative error = 0.01316 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.751
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7384 1.205
h = 0.001 0.003
y[1] (numeric) = 0.106408530728 0.173412323649
y[1] (closed_form) = 0.106386773885 0.173428175968
absolute error = 2.692e-05
relative error = 0.01323 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.75
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1395.6MB, alloc=44.3MB, time=17.94
x[1] = -1.7374 1.208
h = 0.0001 0.004
y[1] (numeric) = 0.105911333061 0.173656651134
y[1] (closed_form) = 0.105889498018 0.173671809446
absolute error = 2.658e-05
relative error = 0.01307 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.75
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7373 1.212
h = 0.003 0.006
y[1] (numeric) = 0.105219110571 0.173764686821
y[1] (closed_form) = 0.105197749649 0.173779487175
absolute error = 2.599e-05
relative error = 0.01279 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.75
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7343 1.218
h = 0.0001 0.005
y[1] (numeric) = 0.104244269227 0.174414979705
y[1] (closed_form) = 0.104220474295 0.174428850602
absolute error = 2.754e-05
relative error = 0.01355 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.748
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7342 1.223
h = 0.0001 0.003
y[1] (numeric) = 0.103376579767 0.174532315005
y[1] (closed_form) = 0.103354231226 0.174547069238
absolute error = 2.678e-05
relative error = 0.0132 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.748
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7341 1.226
h = 0.001 0.001
y[1] (numeric) = 0.102858248305 0.174606938711
y[1] (closed_form) = 0.10283576264 0.174622339677
absolute error = 2.725e-05
relative error = 0.01345 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.749
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7331 1.227
h = 0.001 0.003
y[1] (numeric) = 0.102703580649 0.17479892904
y[1] (closed_form) = 0.102681134996 0.17481466918
absolute error = 2.741e-05
relative error = 0.01352 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.748
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7321 1.23
h = 0.0001 0.004
y[1] (numeric) = 0.102201247139 0.175028318787
y[1] (closed_form) = 0.10217874961 0.175043363304
absolute error = 2.706e-05
relative error = 0.01335 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.747
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.732 1.234
h = 0.003 0.006
y[1] (numeric) = 0.101508474865 0.175116378613
y[1] (closed_form) = 0.101486464018 0.175131083772
absolute error = 2.647e-05
relative error = 0.01308 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.748
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.729 1.24
h = 0.0001 0.005
y[1] (numeric) = 0.100518825807 0.17573671491
y[1] (closed_form) = 0.100494421105 0.175750400676
absolute error = 2.798e-05
relative error = 0.01382 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.746
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7289 1.245
h = 0.0001 0.003
y[1] (numeric) = 0.0996510827826 0.17582903824
y[1] (closed_form) = 0.099628087899 0.175843660076
absolute error = 2.725e-05
relative error = 0.01348 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.746
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7288 1.248
h = 0.001 0.001
y[1] (numeric) = 0.0991326192159 0.175888713322
y[1] (closed_form) = 0.0991094630821 0.175903975241
absolute error = 2.773e-05
relative error = 0.01374 %
Correct digits = 4
memory used=1442.2MB, alloc=44.3MB, time=18.54
Radius of convergence (given) for eq 1 = 1.746
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7278 1.249
h = 0.001 0.003
y[1] (numeric) = 0.0989731150201 0.176075590939
y[1] (closed_form) = 0.0989499859882 0.176091192763
absolute error = 2.790e-05
relative error = 0.01381 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.746
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7268 1.252
h = 0.0001 0.004
y[1] (numeric) = 0.0984662205649 0.176289880444
y[1] (closed_form) = 0.0984430660842 0.176304786297
absolute error = 2.754e-05
relative error = 0.01364 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.745
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7267 1.256
h = 0.003 0.006
y[1] (numeric) = 0.0977736544304 0.176357987133
y[1] (closed_form) = 0.0977509983046 0.176372572853
absolute error = 2.695e-05
relative error = 0.01336 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.746
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7237 1.262
h = 0.0001 0.005
y[1] (numeric) = 0.096770362769 0.176947875162
y[1] (closed_form) = 0.0967453573161 0.17696135343
absolute error = 2.841e-05
relative error = 0.01408 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.743
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7236 1.267
h = 0.0001 0.003
y[1] (numeric) = 0.0959035132076 0.177015244237
y[1] (closed_form) = 0.0958798784285 0.177029709566
absolute error = 2.771e-05
relative error = 0.01376 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.744
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7235 1.27
h = 0.001 0.001
y[1] (numeric) = 0.0953854834052 0.177060002635
y[1] (closed_form) = 0.0953616635614 0.177075100226
absolute error = 2.820e-05
relative error = 0.01402 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.745
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7225 1.271
h = 0.001 0.003
y[1] (numeric) = 0.0952213482327 0.177241597378
y[1] (closed_form) = 0.0951975425398 0.17725703498
absolute error = 2.837e-05
relative error = 0.0141 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.744
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7215 1.274
h = 0.0001 0.004
y[1] (numeric) = 0.0947104759764 0.177440651835
y[1] (closed_form) = 0.094686671288 0.177455394398
absolute error = 2.800e-05
relative error = 0.01392 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.743
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7214 1.278
h = 0.003 0.006
y[1] (numeric) = 0.0940188712302 0.177488864721
y[1] (closed_form) = 0.0939955756401 0.177503306946
absolute error = 2.741e-05
relative error = 0.01365 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.744
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7184 1.284
h = 0.0001 0.005
y[1] (numeric) = 0.0930031263853 0.178047868992
y[1] (closed_form) = 0.0929775302758 0.178061117858
absolute error = 2.882e-05
relative error = 0.01435 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.742
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1489.1MB, alloc=44.3MB, time=19.14
x[1] = -1.7183 1.289
h = 0.0001 0.003
y[1] (numeric) = 0.0921381147494 0.178090387516
y[1] (closed_form) = 0.0921138476913 0.178104672528
absolute error = 2.816e-05
relative error = 0.01404 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.742
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7182 1.292
h = 0.001 0.001
y[1] (numeric) = 0.0916210830995 0.178120288631
y[1] (closed_form) = 0.0915966075471 0.178135196926
absolute error = 2.866e-05
relative error = 0.01431 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.743
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7172 1.293
h = 0.0001 0.004
y[1] (numeric) = 0.0914525307842 0.1782964403
y[1] (closed_form) = 0.0914280564293 0.178311688083
absolute error = 2.884e-05
relative error = 0.01439 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.742
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7171 1.297
h = 0.003 0.006
y[1] (numeric) = 0.0907623020106 0.178328456605
y[1] (closed_form) = 0.0907386344874 0.178342593446
absolute error = 2.757e-05
relative error = 0.01378 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.743
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7141 1.303
h = 0.0001 0.005
y[1] (numeric) = 0.0897371802975 0.178860443908
y[1] (closed_form) = 0.0897112585864 0.178873316024
absolute error = 2.894e-05
relative error = 0.01446 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.741
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.714 1.308
h = 0.0001 0.003
y[1] (numeric) = 0.0888747964247 0.178881727163
y[1] (closed_form) = 0.0888501654874 0.178895675493
absolute error = 2.831e-05
relative error = 0.01417 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.741
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7139 1.311
h = 0.001 0.001
y[1] (numeric) = 0.0883592490299 0.17889892913
y[1] (closed_form) = 0.088334389919 0.178913491833
absolute error = 2.881e-05
relative error = 0.01444 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.742
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7129 1.312
h = 0.001 0.003
y[1] (numeric) = 0.0881871389397 0.179070226294
y[1] (closed_form) = 0.0881622699208 0.179085127375
absolute error = 2.899e-05
relative error = 0.01452 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.741
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7119 1.315
h = 0.0001 0.004
y[1] (numeric) = 0.0876706222174 0.17924063971
y[1] (closed_form) = 0.0876458031801 0.179254851227
absolute error = 2.860e-05
relative error = 0.01433 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.741
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7118 1.319
h = 0.003 0.006
y[1] (numeric) = 0.0869830384568 0.179252150949
y[1] (closed_form) = 0.0869587456575 0.179266100389
absolute error = 2.801e-05
relative error = 0.01406 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.741
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1535.9MB, alloc=44.3MB, time=19.74
x[1] = -1.7088 1.325
h = 0.0001 0.005
y[1] (numeric) = 0.0859477334563 0.179752613975
y[1] (closed_form) = 0.0859212428729 0.179765217545
absolute error = 2.934e-05
relative error = 0.01472 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.739
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7087 1.33
h = 0.0001 0.003
y[1] (numeric) = 0.0850889258865 0.179749372918
y[1] (closed_form) = 0.0850636801755 0.179763097798
absolute error = 2.874e-05
relative error = 0.01445 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.74
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7086 1.333
h = 0.001 0.001
y[1] (numeric) = 0.0845754156404 0.179751907699
y[1] (closed_form) = 0.0845499192454 0.179766235888
absolute error = 2.925e-05
relative error = 0.01472 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.741
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7076 1.334
h = 0.001 0.003
y[1] (numeric) = 0.084399307881 0.179917494771
y[1] (closed_form) = 0.0843737887313 0.179932159641
absolute error = 2.943e-05
relative error = 0.01481 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.74
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7066 1.337
h = 0.0001 0.004
y[1] (numeric) = 0.0838805125123 0.180072452542
y[1] (closed_form) = 0.0838550694219 0.180086432457
absolute error = 2.903e-05
relative error = 0.01461 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.74
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7065 1.341
h = 0.003 0.006
y[1] (numeric) = 0.0831960247208 0.180064450782
y[1] (closed_form) = 0.0831711157519 0.18007818972
absolute error = 2.845e-05
relative error = 0.01434 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.74
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7035 1.347
h = 0.0001 0.005
y[1] (numeric) = 0.0821517757037 0.180533123382
y[1] (closed_form) = 0.0821247292346 0.180545438203
absolute error = 2.972e-05
relative error = 0.01498 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.738
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7034 1.352
h = 0.0001 0.003
y[1] (numeric) = 0.0812974653778 0.180505592361
y[1] (closed_form) = 0.0812716157524 0.180519071252
absolute error = 2.915e-05
relative error = 0.01473 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.739
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7033 1.355
h = 0.001 0.001
y[1] (numeric) = 0.0807865427834 0.18049359735
y[1] (closed_form) = 0.0807604205498 0.180507667404
absolute error = 2.967e-05
relative error = 0.015 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.74
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7023 1.356
h = 0.001 0.003
y[1] (numeric) = 0.0806066713316 0.180653345521
y[1] (closed_form) = 0.0805805136053 0.180667749934
absolute error = 2.986e-05
relative error = 0.0151 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.739
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1582.7MB, alloc=44.3MB, time=20.34
x[1] = -1.7013 1.359
h = 0.0001 0.004
y[1] (numeric) = 0.0800861959183 0.180792824406
y[1] (closed_form) = 0.0800601400502 0.180806549742
absolute error = 2.945e-05
relative error = 0.01489 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.739
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7012 1.363
h = 0.003 0.006
y[1] (numeric) = 0.0794055351829 0.180765509547
y[1] (closed_form) = 0.0793800202673 0.180779015348
absolute error = 2.887e-05
relative error = 0.01462 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.739
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6982 1.369
h = 0.0001 0.005
y[1] (numeric) = 0.0783535920666 0.181202186814
y[1] (closed_form) = 0.0783260036381 0.181214193389
absolute error = 3.009e-05
relative error = 0.01524 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.738
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6981 1.374
h = 0.0001 0.003
y[1] (numeric) = 0.0775046864467 0.181150644913
y[1] (closed_form) = 0.0774782448494 0.181163855852
absolute error = 2.956e-05
relative error = 0.015 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.739
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.698 1.377
h = 0.001 0.001
y[1] (numeric) = 0.0769968940204 0.181124284205
y[1] (closed_form) = 0.0769701585441 0.181138073117
absolute error = 3.008e-05
relative error = 0.01528 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.739
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.697 1.378
h = 0.001 0.003
y[1] (numeric) = 0.0768134986315 0.181278076448
y[1] (closed_form) = 0.0767867150722 0.181292196775
absolute error = 3.028e-05
relative error = 0.01538 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.739
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.696 1.381
h = 0.0001 0.004
y[1] (numeric) = 0.0762919415284 0.18140208266
y[1] (closed_form) = 0.0762652852685 0.18141553104
absolute error = 2.986e-05
relative error = 0.01517 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.738
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6959 1.385
h = 0.003 0.006
y[1] (numeric) = 0.0756158273354 0.181355690033
y[1] (closed_form) = 0.0755897177855 0.181368940598
absolute error = 2.928e-05
relative error = 0.0149 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.739
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6929 1.391
h = 0.0001 0.005
y[1] (numeric) = 0.074557446902 0.181760228972
y[1] (closed_form) = 0.0745293313345 0.181771908567
absolute error = 3.045e-05
relative error = 0.0155 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.737
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6928 1.396
h = 0.0001 0.003
y[1] (numeric) = 0.073714837204 0.181684999165
y[1] (closed_form) = 0.0736878166258 0.18169792083
absolute error = 2.995e-05
relative error = 0.01528 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.739
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1629.3MB, alloc=44.3MB, time=20.94
x[1] = -1.6927 1.399
h = 0.001 0.001
y[1] (numeric) = 0.0732107078269 0.181644463058
y[1] (closed_form) = 0.0731833728161 0.1816579485
absolute error = 3.048e-05
relative error = 0.01556 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.739
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6917 1.4
h = 0.003 0.006
y[1] (numeric) = 0.073024033304 0.181792194477
y[1] (closed_form) = 0.0729966378058 0.181806007781
absolute error = 3.068e-05
relative error = 0.01566 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.738
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6887 1.406
h = 0.0001 0.005
y[1] (numeric) = 0.0719603147895 0.182176802497
y[1] (closed_form) = 0.0719317889068 0.182186892981
absolute error = 3.026e-05
relative error = 0.01545 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.737
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6886 1.411
h = 0.0001 0.003
y[1] (numeric) = 0.0711219576376 0.182085303128
y[1] (closed_form) = 0.0710944909747 0.182096661416
absolute error = 2.972e-05
relative error = 0.0152 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.738
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6885 1.414
h = 0.001 0.001
y[1] (numeric) = 0.0706203008464 0.182035031818
y[1] (closed_form) = 0.0705925056743 0.182046944053
absolute error = 3.024e-05
relative error = 0.01549 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.739
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6875 1.415
h = 0.001 0.003
y[1] (numeric) = 0.0704313595283 0.182178614803
y[1] (closed_form) = 0.070403495356 0.182190852414
absolute error = 3.043e-05
relative error = 0.01558 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.738
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6865 1.418
h = 0.0001 0.004
y[1] (numeric) = 0.0699089402655 0.182276595442
y[1] (closed_form) = 0.0698812455554 0.182288175303
absolute error = 3.002e-05
relative error = 0.01538 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.738
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6864 1.422
h = 0.003 0.006
y[1] (numeric) = 0.0692416279016 0.182198478828
y[1] (closed_form) = 0.0692144876993 0.182209897888
absolute error = 2.944e-05
relative error = 0.01511 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.738
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6834 1.428
h = 0.0001 0.005
y[1] (numeric) = 0.0681744270498 0.182548714023
y[1] (closed_form) = 0.0681454005053 0.182558447364
absolute error = 3.061e-05
relative error = 0.01571 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.737
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6833 1.433
h = 0.0001 0.003
y[1] (numeric) = 0.0673438361983 0.182434147086
y[1] (closed_form) = 0.0673158142475 0.182445181365
absolute error = 3.012e-05
relative error = 0.01549 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.738
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6832 1.436
h = 0.001 0.001
y[1] (numeric) = 0.0668467217567 0.182370066438
y[1] (closed_form) = 0.0668183520682 0.182381638858
absolute error = 3.064e-05
relative error = 0.01577 %
Correct digits = 4
memory used=1676.2MB, alloc=44.3MB, time=21.54
Radius of convergence (given) for eq 1 = 1.739
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6822 1.437
h = 0.001 0.003
y[1] (numeric) = 0.0666549218807 0.182507433485
y[1] (closed_form) = 0.0666264711711 0.182519326722
absolute error = 3.084e-05
relative error = 0.01587 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.738
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6812 1.44
h = 0.0001 0.004
y[1] (numeric) = 0.0661330164091 0.182590088696
y[1] (closed_form) = 0.0661047592933 0.182601334564
absolute error = 3.041e-05
relative error = 0.01566 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.738
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6811 1.444
h = 0.003 0.006
y[1] (numeric) = 0.0654721188776 0.182493679367
y[1] (closed_form) = 0.0654444190784 0.18250478659
absolute error = 2.984e-05
relative error = 0.01539 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.739
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6781 1.45
h = 0.0001 0.005
y[1] (numeric) = 0.0644018644312 0.182811669107
y[1] (closed_form) = 0.0643723542148 0.182821028855
absolute error = 3.096e-05
relative error = 0.01597 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.737
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.678 1.455
h = 0.0001 0.003
y[1] (numeric) = 0.0635798752633 0.18267447038
y[1] (closed_form) = 0.06355131364 0.182685161341
absolute error = 3.050e-05
relative error = 0.01577 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.739
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6779 1.458
h = 0.001 0.001
y[1] (numeric) = 0.0630878029106 0.182596838031
y[1] (closed_form) = 0.0630588751956 0.182608050455
absolute error = 3.102e-05
relative error = 0.01606 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.739
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6769 1.459
h = 0.001 0.003
y[1] (numeric) = 0.0628933993577 0.182727918098
y[1] (closed_form) = 0.0628643788854 0.182739446209
absolute error = 3.123e-05
relative error = 0.01616 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.739
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6759 1.462
h = 0.0001 0.004
y[1] (numeric) = 0.0623725901342 0.182795361593
y[1] (closed_form) = 0.0623437867539 0.182806253857
absolute error = 3.079e-05
relative error = 0.01594 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.738
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6758 1.466
h = 0.003 0.006
y[1] (numeric) = 0.0617187665067 0.182681018406
y[1] (closed_form) = 0.0616905221433 0.182691794205
absolute error = 3.023e-05
relative error = 0.01568 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.739
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6728 1.472
h = 0.0001 0.005
y[1] (numeric) = 0.0606467088255 0.182966849243
y[1] (closed_form) = 0.0606167326211 0.182975819885
absolute error = 3.129e-05
relative error = 0.01623 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.738
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1723.0MB, alloc=44.3MB, time=22.14
x[1] = -1.6727 1.477
h = 0.0001 0.003
y[1] (numeric) = 0.0598341309179 0.182807493575
y[1] (closed_form) = 0.0598050461141 0.182817822773
absolute error = 3.086e-05
relative error = 0.01605 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.739
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6726 1.48
h = 0.001 0.001
y[1] (numeric) = 0.0593475850652 0.182716590487
y[1] (closed_form) = 0.0593181167409 0.182727423657
absolute error = 3.140e-05
relative error = 0.01634 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.74
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6716 1.481
h = 0.0001 0.004
y[1] (numeric) = 0.059150834878 0.182841325489
y[1] (closed_form) = 0.0591212623792 0.182852468665
absolute error = 3.160e-05
relative error = 0.01644 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.739
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6715 1.485
h = 0.003 0.006
y[1] (numeric) = 0.0585032981738 0.18271261611
y[1] (closed_form) = 0.058474805867 0.182722996537
absolute error = 3.032e-05
relative error = 0.01581 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.74
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6685 1.491
h = 0.0001 0.005
y[1] (numeric) = 0.0574310616807 0.182970880306
y[1] (closed_form) = 0.057400907708 0.182979410272
absolute error = 3.134e-05
relative error = 0.01634 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.739
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6684 1.496
h = 0.0001 0.003
y[1] (numeric) = 0.0566274670867 0.182792986158
y[1] (closed_form) = 0.0565981541973 0.182802895124
absolute error = 3.094e-05
relative error = 0.01617 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.741
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6683 1.499
h = 0.001 0.001
y[1] (numeric) = 0.0561462065547 0.182690975451
y[1] (closed_form) = 0.0561164961392 0.182701372536
absolute error = 3.148e-05
relative error = 0.01647 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.741
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6673 1.5
h = 0.001 0.003
y[1] (numeric) = 0.0559477196274 0.182810188506
y[1] (closed_form) = 0.0559178955662 0.182820890153
absolute error = 3.169e-05
relative error = 0.01657 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.741
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6663 1.503
h = 0.0001 0.004
y[1] (numeric) = 0.0554306461524 0.182849754191
y[1] (closed_form) = 0.0554010808247 0.182859844569
absolute error = 3.124e-05
relative error = 0.01635 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.741
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6662 1.507
h = 0.003 0.006
y[1] (numeric) = 0.0547918674458 0.182703200956
y[1] (closed_form) = 0.0547628611011 0.182713215966
absolute error = 3.069e-05
relative error = 0.01609 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.742
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1769.8MB, alloc=44.3MB, time=22.74
x[1] = -1.6632 1.513
h = 0.0001 0.005
y[1] (numeric) = 0.0537201190015 0.182929644069
y[1] (closed_form) = 0.0536895337358 0.182937758913
absolute error = 3.164e-05
relative error = 0.0166 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.741
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6631 1.518
h = 0.0001 0.003
y[1] (numeric) = 0.0529273589145 0.182730583167
y[1] (closed_form) = 0.0528975558614 0.182740098738
absolute error = 3.129e-05
relative error = 0.01644 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.742
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.663 1.521
h = 0.001 0.001
y[1] (numeric) = 0.0524524768486 0.182615888197
y[1] (closed_form) = 0.0524222606887 0.182625873061
absolute error = 3.182e-05
relative error = 0.01675 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.743
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.662 1.522
h = 0.001 0.003
y[1] (numeric) = 0.0522521248736 0.182728685882
y[1] (closed_form) = 0.0522217843354 0.182738968668
absolute error = 3.204e-05
relative error = 0.01686 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.742
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.661 1.525
h = 0.0001 0.004
y[1] (numeric) = 0.0517377576365 0.182753524857
y[1] (closed_form) = 0.0517076971431 0.182763210887
absolute error = 3.158e-05
relative error = 0.01663 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.742
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6609 1.529
h = 0.003 0.006
y[1] (numeric) = 0.0511078092146 0.182590235266
y[1] (closed_form) = 0.0510783062708 0.182599867791
absolute error = 3.104e-05
relative error = 0.01637 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.743
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6579 1.535
h = 0.0001 0.005
y[1] (numeric) = 0.0500377566108 0.182785115967
y[1] (closed_form) = 0.0500067593587 0.182792803053
absolute error = 3.194e-05
relative error = 0.01685 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.742
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6578 1.54
h = 0.0001 0.003
y[1] (numeric) = 0.0492565541022 0.182565464185
y[1] (closed_form) = 0.0492262795465 0.182574570664
absolute error = 3.161e-05
relative error = 0.01672 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.744
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6577 1.543
h = 0.001 0.001
y[1] (numeric) = 0.0487884835162 0.182438426249
y[1] (closed_form) = 0.0487577813157 0.182447982564
absolute error = 3.216e-05
relative error = 0.01703 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.744
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6567 1.544
h = 0.001 0.003
y[1] (numeric) = 0.0485865250702 0.18254478774
y[1] (closed_form) = 0.0485556881655 0.182554634857
absolute error = 3.237e-05
relative error = 0.01714 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.744
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1816.7MB, alloc=44.3MB, time=23.35
x[1] = -1.6557 1.547
h = 0.0001 0.004
y[1] (numeric) = 0.048075403419 0.182555118193
y[1] (closed_form) = 0.0480448669961 0.182564384011
absolute error = 3.191e-05
relative error = 0.0169 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.744
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6556 1.551
h = 0.003 0.006
y[1] (numeric) = 0.0474548523369 0.182375560474
y[1] (closed_form) = 0.0474248709629 0.182384794415
absolute error = 3.137e-05
relative error = 0.01665 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.745
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6526 1.557
h = 0.0001 0.005
y[1] (numeric) = 0.0463876817641 0.182539195068
y[1] (closed_form) = 0.046356292275 0.182546442814
absolute error = 3.222e-05
relative error = 0.0171 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.744
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6525 1.562
h = 0.0001 0.003
y[1] (numeric) = 0.0456187260278 0.182299559609
y[1] (closed_form) = 0.045587999268 0.182308242331
absolute error = 3.193e-05
relative error = 0.01699 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.745
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6524 1.565
h = 0.001 0.001
y[1] (numeric) = 0.0451578798036 0.182160538724
y[1] (closed_form) = 0.045126711935 0.182169651264
absolute error = 3.247e-05
relative error = 0.0173 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.746
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6514 1.566
h = 0.001 0.003
y[1] (numeric) = 0.0449545724943 0.182260456091
y[1] (closed_form) = 0.0449232600291 0.182269851863
absolute error = 3.269e-05
relative error = 0.01741 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.746
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6504 1.569
h = 0.0001 0.004
y[1] (numeric) = 0.0444472208548 0.182256521111
y[1] (closed_form) = 0.0444162283821 0.182265351922
absolute error = 3.223e-05
relative error = 0.01718 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.746
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6503 1.573
h = 0.003 0.006
y[1] (numeric) = 0.0438366066475 0.182061187764
y[1] (closed_form) = 0.0438061656788 0.182070008025
absolute error = 3.169e-05
relative error = 0.01692 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.747
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6473 1.579
h = 0.0001 0.005
y[1] (numeric) = 0.0427734792879 0.18219394843
y[1] (closed_form) = 0.0427417176861 0.182200746322
absolute error = 3.248e-05
relative error = 0.01736 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.746
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6472 1.584
h = 0.0001 0.003
y[1] (numeric) = 0.0420174239584 0.181934965491
y[1] (closed_form) = 0.0419862648619 0.181943210857
absolute error = 3.223e-05
relative error = 0.01726 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.748
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1863.6MB, alloc=44.3MB, time=23.96
x[1] = -1.6471 1.587
h = 0.001 0.001
y[1] (numeric) = 0.0415641938455 0.181784339001
y[1] (closed_form) = 0.0415325812759 0.181792993679
absolute error = 3.278e-05
relative error = 0.01758 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.749
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6461 1.588
h = 0.0001 0.004
y[1] (numeric) = 0.0413597935226 0.181877817051
y[1] (closed_form) = 0.0413280269216 0.181886746969
absolute error = 3.300e-05
relative error = 0.01769 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.748
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.646 1.592
h = 0.003 0.006
y[1] (numeric) = 0.040757709943 0.181669980248
y[1] (closed_form) = 0.0407271030404 0.181678380042
absolute error = 3.174e-05
relative error = 0.01705 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.749
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.643 1.598
h = 0.0001 0.005
y[1] (numeric) = 0.0396993319342 0.181776571348
y[1] (closed_form) = 0.0396674808638 0.18178292239
absolute error = 3.248e-05
relative error = 0.01746 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.748
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6429 1.603
h = 0.0001 0.003
y[1] (numeric) = 0.0389550956666 0.1815016281
y[1] (closed_form) = 0.038923795105 0.181509434196
absolute error = 3.226e-05
relative error = 0.01738 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.75
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6428 1.606
h = 0.001 0.001
y[1] (numeric) = 0.0385088499938 0.181341422885
y[1] (closed_form) = 0.0384770864637 0.181349620174
absolute error = 3.280e-05
relative error = 0.0177 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.751
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6418 1.607
h = 0.001 0.003
y[1] (numeric) = 0.0383037882025 0.181429362676
y[1] (closed_form) = 0.0382718630043 0.18143782791
absolute error = 3.303e-05
relative error = 0.01781 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.75
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6408 1.61
h = 0.0001 0.004
y[1] (numeric) = 0.0378049525001 0.181399669462
y[1] (closed_form) = 0.0377733807619 0.181407602466
absolute error = 3.255e-05
relative error = 0.01757 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.751
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6407 1.614
h = 0.003 0.006
y[1] (numeric) = 0.0372143380763 0.18117649952
y[1] (closed_form) = 0.0371833083202 0.181184460581
absolute error = 3.203e-05
relative error = 0.01732 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.752
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6377 1.62
h = 0.0001 0.005
y[1] (numeric) = 0.0361620805178 0.181253063919
y[1] (closed_form) = 0.0361298956372 0.181258948671
absolute error = 3.272e-05
relative error = 0.0177 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.751
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1910.3MB, alloc=44.3MB, time=24.56
x[1] = -1.6376 1.625
h = 0.0001 0.003
y[1] (numeric) = 0.035431853037 0.180960032455
y[1] (closed_form) = 0.0354001585098 0.180967379067
absolute error = 3.253e-05
relative error = 0.01764 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.753
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6375 1.628
h = 0.001 0.001
y[1] (numeric) = 0.0349938883184 0.18078896893
y[1] (closed_form) = 0.0349617205584 0.180796685524
absolute error = 3.308e-05
relative error = 0.01796 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.754
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6365 1.629
h = 0.001 0.003
y[1] (numeric) = 0.034788201887 0.180870514416
y[1] (closed_form) = 0.0347558639357 0.180878490271
absolute error = 3.331e-05
relative error = 0.01808 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.753
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6355 1.632
h = 0.0001 0.004
y[1] (numeric) = 0.0342945379436 0.180827383814
y[1] (closed_form) = 0.0342625700658 0.180834845923
absolute error = 3.283e-05
relative error = 0.01784 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.753
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6354 1.636
h = 0.003 0.006
y[1] (numeric) = 0.0337152344246 0.180589969159
y[1] (closed_form) = 0.0336838021679 0.18059747945
absolute error = 3.232e-05
relative error = 0.01759 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.755
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6324 1.642
h = 0.0001 0.005
y[1] (numeric) = 0.0326701690871 0.180637026669
y[1] (closed_form) = 0.0326376711991 0.180642437726
absolute error = 3.295e-05
relative error = 0.01795 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.754
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6323 1.647
h = 0.0001 0.003
y[1] (numeric) = 0.0319544945059 0.180326611875
y[1] (closed_form) = 0.0319224271011 0.180333488586
absolute error = 3.280e-05
relative error = 0.01791 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.756
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6322 1.65
h = 0.001 0.001
y[1] (numeric) = 0.0315251373946 0.180145108489
y[1] (closed_form) = 0.0314925876346 0.180152333688
absolute error = 3.334e-05
relative error = 0.01823 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.757
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6312 1.651
h = 0.001 0.003
y[1] (numeric) = 0.0313190728365 0.18022029946
y[1] (closed_form) = 0.0312863448746 0.180227774913
absolute error = 3.357e-05
relative error = 0.01835 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.756
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6302 1.654
h = 0.0001 0.004
y[1] (numeric) = 0.0308310347868 0.180164059126
y[1] (closed_form) = 0.0307986924357 0.180171039934
absolute error = 3.309e-05
relative error = 0.0181 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.756
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6301 1.658
h = 0.003 0.006
y[1] (numeric) = 0.0302634646623 0.179912967157
y[1] (closed_form) = 0.0302316506563 0.17992001575
absolute error = 3.259e-05
relative error = 0.01786 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.758
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1957.0MB, alloc=44.3MB, time=25.16
x[1] = -1.6271 1.664
h = 0.0001 0.005
y[1] (numeric) = 0.0292266268652 0.179931084539
y[1] (closed_form) = 0.029193836883 0.179936015581
absolute error = 3.316e-05
relative error = 0.01819 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.757
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.627 1.669
h = 0.0001 0.003
y[1] (numeric) = 0.0285260091243 0.179604010431
y[1] (closed_form) = 0.0284935902211 0.17961040796
absolute error = 3.304e-05
relative error = 0.01817 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.759
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6269 1.672
h = 0.001 0.001
y[1] (numeric) = 0.0281055623941 0.179412497098
y[1] (closed_form) = 0.0280726531595 0.179419221413
absolute error = 3.359e-05
relative error = 0.0185 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.76
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6259 1.673
h = 0.001 0.003
y[1] (numeric) = 0.0278993616452 0.179481384933
y[1] (closed_form) = 0.0278662667244 0.179488350203
absolute error = 3.382e-05
relative error = 0.01862 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.76
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6249 1.676
h = 0.0001 0.004
y[1] (numeric) = 0.0274173827774 0.179412381151
y[1] (closed_form) = 0.0273846879033 0.179418871424
absolute error = 3.333e-05
relative error = 0.01837 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.76
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6248 1.68
h = 0.003 0.006
y[1] (numeric) = 0.026861936308 0.179148193712
y[1] (closed_form) = 0.0268297616305 0.1791547708
absolute error = 3.284e-05
relative error = 0.01813 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.761
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6218 1.686
h = 0.0001 0.005
y[1] (numeric) = 0.025834322464 0.179137981915
y[1] (closed_form) = 0.0258012613441 0.179142427699
absolute error = 3.336e-05
relative error = 0.01843 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.761
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6217 1.691
h = 0.0001 0.003
y[1] (numeric) = 0.0251492246296 0.17879498896
y[1] (closed_form) = 0.0251164758256 0.178800899169
absolute error = 3.328e-05
relative error = 0.01843 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.763
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6216 1.694
h = 0.001 0.001
y[1] (numeric) = 0.0247379667559 0.17859390547
y[1] (closed_form) = 0.0247047207894 0.178600120627
absolute error = 3.382e-05
relative error = 0.01876 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.764
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6206 1.695
h = 0.0001 0.004
y[1] (numeric) = 0.0245318665221 0.178656552716
y[1] (closed_form) = 0.0244984279229 0.178662999274
absolute error = 3.405e-05
relative error = 0.01888 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.763
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2003.8MB, alloc=44.3MB, time=25.76
x[1] = -1.6205 1.699
h = 0.003 0.006
y[1] (numeric) = 0.0239866210874 0.178382116102
y[1] (closed_form) = 0.0239543632632 0.178388267793
absolute error = 3.284e-05
relative error = 0.01825 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.765
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6175 1.705
h = 0.0001 0.005
y[1] (numeric) = 0.0229680402557 0.178348165586
y[1] (closed_form) = 0.0229349728399 0.178352178799
absolute error = 3.331e-05
relative error = 0.01852 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.764
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6174 1.71
h = 0.0001 0.003
y[1] (numeric) = 0.0222968180423 0.177992265348
y[1] (closed_form) = 0.0222640130727 0.177997738264
absolute error = 3.326e-05
relative error = 0.01854 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.766
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6173 1.713
h = 0.001 0.001
y[1] (numeric) = 0.0218937805714 0.17778341623
y[1] (closed_form) = 0.0218604737321 0.177789175178
absolute error = 3.380e-05
relative error = 0.01887 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.767
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6163 1.714
h = 0.001 0.003
y[1] (numeric) = 0.0216880250846 0.177840754988
y[1] (closed_form) = 0.0216545201878 0.177846736864
absolute error = 3.403e-05
relative error = 0.019 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.767
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6153 1.717
h = 0.0001 0.004
y[1] (numeric) = 0.0212185406662 0.177749063961
y[1] (closed_form) = 0.0211854594369 0.177754608736
absolute error = 3.354e-05
relative error = 0.01874 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.767
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6152 1.721
h = 0.003 0.006
y[1] (numeric) = 0.020686718955 0.177462251931
y[1] (closed_form) = 0.0206541403878 0.177467917134
absolute error = 3.307e-05
relative error = 0.01851 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.769
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6122 1.727
h = 0.0001 0.005
y[1] (numeric) = 0.0196790968157 0.177401227326
y[1] (closed_form) = 0.0196457971853 0.177404748594
absolute error = 3.349e-05
relative error = 0.01876 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.769
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6121 1.732
h = 0.0001 0.003
y[1] (numeric) = 0.0190241366796 0.177030824992
y[1] (closed_form) = 0.0189910423974 0.177035798735
absolute error = 3.347e-05
relative error = 0.0188 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.771
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.612 1.735
h = 0.001 0.001
y[1] (numeric) = 0.0186307352084 0.176813247486
y[1] (closed_form) = 0.0185971343341 0.176818485374
absolute error = 3.401e-05
relative error = 0.01913 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.772
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2050.5MB, alloc=44.3MB, time=26.36
x[1] = -1.611 1.736
h = 0.001 0.003
y[1] (numeric) = 0.0184255036685 0.176864492819
y[1] (closed_form) = 0.0183916988134 0.176869943708
absolute error = 3.424e-05
relative error = 0.01926 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.771
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.61 1.739
h = 0.0001 0.004
y[1] (numeric) = 0.0179631906582 0.176761122602
y[1] (closed_form) = 0.0179298206626 0.176766157174
absolute error = 3.375e-05
relative error = 0.01899 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.772
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6099 1.743
h = 0.003 0.006
y[1] (numeric) = 0.0174444200041 0.176462943567
y[1] (closed_form) = 0.0174115422958 0.176468115712
absolute error = 3.328e-05
relative error = 0.01877 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.773
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6069 1.749
h = 0.0001 0.005
y[1] (numeric) = 0.0164486298556 0.176375565262
y[1] (closed_form) = 0.0164151187283 0.17637859234
absolute error = 3.365e-05
relative error = 0.01899 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.773
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6068 1.754
h = 0.0001 0.003
y[1] (numeric) = 0.0158102758148 0.175991433019
y[1] (closed_form) = 0.0157769140348 0.175995902697
absolute error = 3.366e-05
relative error = 0.01905 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.775
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6067 1.757
h = 0.001 0.001
y[1] (numeric) = 0.0154267180375 0.175765586048
y[1] (closed_form) = 0.015392846055 0.175770298043
absolute error = 3.420e-05
relative error = 0.01938 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.776
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6057 1.758
h = 0.001 0.003
y[1] (numeric) = 0.0152222288422 0.175810829715
y[1] (closed_form) = 0.0151881475099 0.175815744634
absolute error = 3.443e-05
relative error = 0.01951 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.776
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6047 1.761
h = 0.0001 0.004
y[1] (numeric) = 0.0147674326575 0.175696183882
y[1] (closed_form) = 0.0147337962312 0.175700703529
absolute error = 3.394e-05
relative error = 0.01925 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.776
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6046 1.765
h = 0.003 0.006
y[1] (numeric) = 0.0142619756553 0.175387254996
y[1] (closed_form) = 0.0142288204593 0.175391928634
absolute error = 3.348e-05
relative error = 0.01903 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.778
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6016 1.771
h = 0.0001 0.005
y[1] (numeric) = 0.0132788447387 0.17527427575
y[1] (closed_form) = 0.0132451426372 0.175276807395
absolute error = 3.380e-05
relative error = 0.01923 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.778
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2097.2MB, alloc=44.3MB, time=26.96
x[1] = -1.6015 1.776
h = 0.0001 0.003
y[1] (numeric) = 0.0126573991817 0.174877191917
y[1] (closed_form) = 0.0126237916662 0.174881153748
absolute error = 3.384e-05
relative error = 0.0193 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.78
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6014 1.779
h = 0.001 0.001
y[1] (numeric) = 0.0122838680373 0.174643538146
y[1] (closed_form) = 0.0122497478001 0.174647720595
absolute error = 3.438e-05
relative error = 0.01963 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.781
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6004 1.78
h = 0.001 0.003
y[1] (numeric) = 0.0120803322411 0.174682881106
y[1] (closed_form) = 0.0120459978402 0.174687256283
absolute error = 3.461e-05
relative error = 0.01977 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.78
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5994 1.783
h = 0.0001 0.004
y[1] (numeric) = 0.011633374309 0.174557374286
y[1] (closed_form) = 0.0115994937171 0.174561375424
absolute error = 3.412e-05
relative error = 0.0195 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.781
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5993 1.787
h = 0.003 0.006
y[1] (numeric) = 0.0111414604664 0.174238316825
y[1] (closed_form) = 0.0111080494196 0.174242487615
absolute error = 3.367e-05
relative error = 0.01928 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.782
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5963 1.793
h = 0.0001 0.005
y[1] (numeric) = 0.0101717687224 0.174100518517
y[1] (closed_form) = 0.0101378959192 0.174102554465
absolute error = 3.393e-05
relative error = 0.01946 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.782
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5962 1.798
h = 0.0001 0.003
y[1] (numeric) = 0.00956749268063 0.173691264965
y[1] (closed_form) = 0.00953366107368 0.173694716255
absolute error = 3.401e-05
relative error = 0.01955 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.785
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5961 1.801
h = 0.001 0.001
y[1] (numeric) = 0.00920414651211 0.173450269268
y[1] (closed_form) = 0.00916980073092 0.173453919668
absolute error = 3.454e-05
relative error = 0.01988 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.786
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5951 1.802
h = 0.0001 0.004
y[1] (numeric) = 0.00900176739169 0.173483821097
y[1] (closed_form) = 0.00896720318579 0.173487653949
absolute error = 3.478e-05
relative error = 0.02002 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.785
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.595 1.806
h = 0.003 0.006
y[1] (numeric) = 0.00852109131151 0.173156964846
y[1] (closed_form) = 0.00848767495907 0.173160724085
absolute error = 3.363e-05
relative error = 0.0194 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.787
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2144.0MB, alloc=44.3MB, time=27.56
x[1] = -1.592 1.812
h = 0.0001 0.005
y[1] (numeric) = 0.00756383775969 0.172998620877
y[1] (closed_form) = 0.00753003153503 0.173000255569
absolute error = 3.385e-05
relative error = 0.01955 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.787
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5919 1.817
h = 0.0001 0.003
y[1] (numeric) = 0.00697465072094 0.17257972698
y[1] (closed_form) = 0.00694084114165 0.172582761773
absolute error = 3.395e-05
relative error = 0.01965 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.789
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5918 1.82
h = 0.001 0.001
y[1] (numeric) = 0.00662025956182 0.172332907875
y[1] (closed_form) = 0.00658593564187 0.172336123465
absolute error = 3.447e-05
relative error = 0.01999 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.791
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5908 1.821
h = 0.001 0.003
y[1] (numeric) = 0.00641909968319 0.172361585697
y[1] (closed_form) = 0.00638455423372 0.17236497481
absolute error = 3.471e-05
relative error = 0.02012 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.79
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5898 1.824
h = 0.0001 0.004
y[1] (numeric) = 0.00598761643121 0.172217105117
y[1] (closed_form) = 0.0059535380867 0.172220160034
absolute error = 3.421e-05
relative error = 0.01986 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.791
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5897 1.828
h = 0.003 0.006
y[1] (numeric) = 0.0055215051278 0.171881026218
y[1] (closed_form) = 0.00548787293788 0.171884277676
absolute error = 3.379e-05
relative error = 0.01965 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.792
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5867 1.834
h = 0.0001 0.005
y[1] (numeric) = 0.00457900297417 0.171699392289
y[1] (closed_form) = 0.00454506290434 0.171700533511
absolute error = 3.396e-05
relative error = 0.01977 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.793
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5866 1.839
h = 0.0001 0.003
y[1] (numeric) = 0.00400735348236 0.1712697864
y[1] (closed_form) = 0.00397335956049 0.171272308709
absolute error = 3.409e-05
relative error = 0.0199 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.795
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5865 1.842
h = 0.001 0.001
y[1] (numeric) = 0.00366337193436 0.171016492388
y[1] (closed_form) = 0.00362886411978 0.171019174513
absolute error = 3.461e-05
relative error = 0.02023 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.796
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5855 1.843
h = 0.001 0.003
y[1] (numeric) = 0.00346372347996 0.171039606028
y[1] (closed_form) = 0.00342899089096 0.171042451343
absolute error = 3.485e-05
relative error = 0.02037 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.796
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5845 1.846
h = 0.0001 0.004
y[1] (numeric) = 0.00304085821812 0.170885500196
y[1] (closed_form) = 0.00300659842214 0.170888032684
absolute error = 3.435e-05
relative error = 0.0201 %
Correct digits = 4
memory used=2190.8MB, alloc=44.3MB, time=28.17
Radius of convergence (given) for eq 1 = 1.796
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5844 1.85
h = 0.003 0.006
y[1] (numeric) = 0.00258875956108 0.170541076256
y[1] (closed_form) = 0.00255493275338 0.170543818654
absolute error = 3.394e-05
relative error = 0.0199 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.798
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5814 1.856
h = 0.0001 0.005
y[1] (numeric) = 0.00166164863463 0.170336998865
y[1] (closed_form) = 0.00162759398803 0.170337648957
absolute error = 3.406e-05
relative error = 0.02 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.798
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5813 1.861
h = 0.0001 0.003
y[1] (numeric) = 0.00110768255423 0.169897458919
y[1] (closed_form) = 0.00107352524593 0.16989946902
absolute error = 3.422e-05
relative error = 0.02014 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.801
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5812 1.864
h = 0.001 0.001
y[1] (numeric) = 0.000774200447511 0.169638152823
y[1] (closed_form) = 0.000739530667792 0.16964030211
absolute error = 3.474e-05
relative error = 0.02048 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.802
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5802 1.865
h = 0.001 0.003
y[1] (numeric) = 0.000576242412205 0.169655833034
y[1] (closed_form) = 0.000541345147347 0.16965813519
absolute error = 3.497e-05
relative error = 0.02061 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.801
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5792 1.868
h = 0.0001 0.004
y[1] (numeric) = 0.000162222272808 0.169492544028
y[1] (closed_form) = 0.000127802400088 0.169494554654
absolute error = 3.448e-05
relative error = 0.02034 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.802
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5791 1.872
h = 0.003 0.006
y[1] (numeric) = -0.000275758123363 0.1691403933
y[1] (closed_form) = -0.000309758586803 0.169142626376
absolute error = 3.407e-05
relative error = 0.02014 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.804
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5761 1.878
h = 0.0001 0.005
y[1] (numeric) = -0.00118688767973 0.168914735437
y[1] (closed_form) = -0.00122103806801 0.168914897575
absolute error = 3.415e-05
relative error = 0.02022 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.804
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.576 1.883
h = 0.0001 0.003
y[1] (numeric) = -0.00172306314727 0.168466033694
y[1] (closed_form) = -0.00175736323 0.168467532836
absolute error = 3.433e-05
relative error = 0.02038 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.807
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5759 1.886
h = 0.001 0.001
y[1] (numeric) = -0.00204597899052 0.168201175064
y[1] (closed_form) = -0.00208078918867 0.168202793168
absolute error = 3.485e-05
relative error = 0.02072 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.808
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2237.5MB, alloc=44.3MB, time=28.77
x[1] = -1.5749 1.887
h = 0.001 0.003
y[1] (numeric) = -0.00224207658963 0.16821355882
y[1] (closed_form) = -0.00227711646008 0.168215319516
absolute error = 3.508e-05
relative error = 0.02085 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.808
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5739 1.89
h = 0.0001 0.004
y[1] (numeric) = -0.00264704874042 0.168041532149
y[1] (closed_form) = -0.00268160768395 0.168043022474
absolute error = 3.459e-05
relative error = 0.02058 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.808
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5738 1.894
h = 0.003 0.006
y[1] (numeric) = -0.00307083574548 0.167682267739
y[1] (closed_form) = -0.00310498921553 0.167683992216
absolute error = 3.420e-05
relative error = 0.02039 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.81
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5708 1.9
h = 0.0001 0.005
y[1] (numeric) = -0.00396544351538 0.167435905692
y[1] (closed_form) = -0.00399967128238 0.167435583851
absolute error = 3.423e-05
relative error = 0.02044 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.81
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5707 1.905
h = 0.0001 0.003
y[1] (numeric) = -0.00448375877596 0.166978806599
y[1] (closed_form) = -0.00451818141565 0.16697979697
absolute error = 3.444e-05
relative error = 0.02062 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.813
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5706 1.908
h = 0.001 0.001
y[1] (numeric) = -0.00479606391807 0.16670885044
y[1] (closed_form) = -0.00483099342373 0.166709939998
absolute error = 3.495e-05
relative error = 0.02095 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.814
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5696 1.909
h = 0.0001 0.004
y[1] (numeric) = -0.00499014023232 0.166716080299
y[1] (closed_form) = -0.00502530108649 0.166717302245
absolute error = 3.518e-05
relative error = 0.02109 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.814
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5695 1.913
h = 0.003 0.006
y[1] (numeric) = -0.0054022748045 0.166351471123
y[1] (closed_form) = -0.00543636532373 0.166352813535
absolute error = 3.412e-05
relative error = 0.0205 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.816
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5665 1.919
h = 0.0001 0.005
y[1] (numeric) = -0.00628203401913 0.166088201803
y[1] (closed_form) = -0.00631613601963 0.166087522403
absolute error = 3.411e-05
relative error = 0.02052 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.816
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5664 1.924
h = 0.0001 0.003
y[1] (numeric) = -0.00678486010203 0.165624692442
y[1] (closed_form) = -0.00681919400562 0.165625302083
absolute error = 3.434e-05
relative error = 0.02072 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.819
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2284.3MB, alloc=44.3MB, time=29.37
x[1] = -1.5663 1.927
h = 0.001 0.001
y[1] (numeric) = -0.00708795944507 0.165350835213
y[1] (closed_form) = -0.00712279650791 0.165351527466
absolute error = 3.484e-05
relative error = 0.02105 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.82
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5653 1.928
h = 0.001 0.003
y[1] (numeric) = -0.00728011521652 0.165353773229
y[1] (closed_form) = -0.00731518455259 0.165354589154
absolute error = 3.508e-05
relative error = 0.02119 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.82
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5643 1.931
h = 0.0001 0.004
y[1] (numeric) = -0.00766770170249 0.165166791562
y[1] (closed_form) = -0.00770228651248 0.165167375937
absolute error = 3.459e-05
relative error = 0.02092 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.82
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5642 1.935
h = 0.003 0.006
y[1] (numeric) = -0.00806491099351 0.164796067386
y[1] (closed_form) = -0.00809911713835 0.164796905277
absolute error = 3.422e-05
relative error = 0.02074 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.822
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5612 1.941
h = 0.0001 0.005
y[1] (numeric) = -0.00892728506092 0.164513754241
y[1] (closed_form) = -0.00896143171279 0.164512600435
absolute error = 3.417e-05
relative error = 0.02074 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.823
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5611 1.946
h = 0.0001 0.003
y[1] (numeric) = -0.00941222619451 0.164043242194
y[1] (closed_form) = -0.00944664629227 0.164043349713
absolute error = 3.442e-05
relative error = 0.02095 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.825
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.561 1.949
h = 0.001 0.001
y[1] (numeric) = -0.00970469452165 0.163765117882
y[1] (closed_form) = -0.00973961299057 0.163765289194
absolute error = 3.492e-05
relative error = 0.02128 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.827
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.56 1.95
h = 0.001 0.003
y[1] (numeric) = -0.00989455638532 0.163763181599
y[1] (closed_form) = -0.00992970789391 0.163763466594
absolute error = 3.515e-05
relative error = 0.02143 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.826
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.559 1.953
h = 0.0001 0.004
y[1] (numeric) = -0.0102726511232 0.163568744218
y[1] (closed_form) = -0.0103073174433 0.163568818106
absolute error = 3.467e-05
relative error = 0.02115 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.827
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5589 1.957
h = 0.003 0.006
y[1] (numeric) = -0.0106556191382 0.163192617159
y[1] (closed_form) = -0.0106899214384 0.163192953859
absolute error = 3.430e-05
relative error = 0.02098 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.829
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2331.1MB, alloc=44.3MB, time=29.98
x[1] = -1.5559 1.963
h = 0.0001 0.005
y[1] (numeric) = -0.0115002081961 0.162892156965
y[1] (closed_form) = -0.0115343826758 0.16289053476
absolute error = 3.421e-05
relative error = 0.02095 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.83
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5558 1.968
h = 0.0001 0.003
y[1] (numeric) = -0.0119672953 0.162415373222
y[1] (closed_form) = -0.0120017827564 0.162414983247
absolute error = 3.449e-05
relative error = 0.02118 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.832
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5557 1.971
h = 0.001 0.001
y[1] (numeric) = -0.0122491480315 0.162133417231
y[1] (closed_form) = -0.0122841283074 0.162133072791
absolute error = 3.498e-05
relative error = 0.02151 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.834
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5547 1.972
h = 0.001 0.003
y[1] (numeric) = -0.0124365820318 0.162126761569
y[1] (closed_form) = -0.0124717956482 0.16212652097
absolute error = 3.521e-05
relative error = 0.02166 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.834
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5537 1.975
h = 0.0001 0.004
y[1] (numeric) = -0.0128050725254 0.161925313626
y[1] (closed_form) = -0.012839801227 0.161924882019
absolute error = 3.473e-05
relative error = 0.02138 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.834
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5536 1.979
h = 0.003 0.006
y[1] (numeric) = -0.013173832623 0.16154436188
y[1] (closed_form) = -0.0132082121001 0.161544201547
absolute error = 3.438e-05
relative error = 0.02121 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.836
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5506 1.985
h = 0.0001 0.005
y[1] (numeric) = -0.0140002846562 0.161226653157
y[1] (closed_form) = -0.0140344707265 0.161224569184
absolute error = 3.425e-05
relative error = 0.02116 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.837
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5505 1.99
h = 0.0001 0.003
y[1] (numeric) = -0.0144495810975 0.160744313841
y[1] (closed_form) = -0.0144841176293 0.160743431769
absolute error = 3.455e-05
relative error = 0.02141 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.84
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5504 1.993
h = 0.001 0.001
y[1] (numeric) = -0.0147208529882 0.16045895284
y[1] (closed_form) = -0.0147558760719 0.160458098635
absolute error = 3.503e-05
relative error = 0.02174 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.841
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5494 1.994
h = 0.001 0.003
y[1] (numeric) = -0.0149057346233 0.160447735882
y[1] (closed_form) = -0.0149409909012 0.160446975847
absolute error = 3.526e-05
relative error = 0.02188 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.841
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2378.0MB, alloc=44.3MB, time=30.59
x[1] = -1.5484 1.997
h = 0.0001 0.004
y[1] (numeric) = -0.0152645305136 0.160239719347
y[1] (closed_form) = -0.0152993030471 0.160238788012
absolute error = 3.479e-05
relative error = 0.02161 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.842
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5483 2.001
h = 0.003 0.006
y[1] (numeric) = -0.0156191414417 0.159854508844
y[1] (closed_form) = -0.0156535796461 0.159853856425
absolute error = 3.444e-05
relative error = 0.02144 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.844
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5453 2.007
h = 0.0001 0.005
y[1] (numeric) = -0.0164271513485 0.159520449129
y[1] (closed_form) = -0.0164613333794 0.159517910598
absolute error = 3.428e-05
relative error = 0.02137 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.844
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5452 2.012
h = 0.0001 0.003
y[1] (numeric) = -0.0168587514 0.159033254006
y[1] (closed_form) = -0.0168933193073 0.159031885953
absolute error = 3.459e-05
relative error = 0.02163 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.847
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5451 2.015
h = 0.001 0.001
y[1] (numeric) = -0.0171194956271 0.158744905034
y[1] (closed_form) = -0.0171545431517 0.158743547797
absolute error = 3.507e-05
relative error = 0.02197 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.849
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5441 2.016
h = 0.0001 0.004
y[1] (numeric) = -0.0173017098186 0.158729287431
y[1] (closed_form) = -0.0173369899634 0.158728014885
absolute error = 3.530e-05
relative error = 0.02211 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.848
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.544 2.02
h = 0.003 0.006
y[1] (numeric) = -0.0176448044462 0.158341026957
y[1] (closed_form) = -0.0176791240763 0.158340033366
absolute error = 3.433e-05
relative error = 0.02155 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.85
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.541 2.026
h = 0.0001 0.005
y[1] (numeric) = -0.018436550391 0.157993832687
y[1] (closed_form) = -0.0184705626057 0.157990987643
absolute error = 3.413e-05
relative error = 0.02146 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.851
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5409 2.031
h = 0.0001 0.003
y[1] (numeric) = -0.0188529690574 0.157503213434
y[1] (closed_form) = -0.0188873955747 0.157501510663
absolute error = 3.447e-05
relative error = 0.02173 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.854
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5408 2.034
h = 0.001 0.001
y[1] (numeric) = -0.0191046783454 0.157212742742
y[1] (closed_form) = -0.0191395778219 0.157211036715
absolute error = 3.494e-05
relative error = 0.02206 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.856
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5398 2.035
h = 0.001 0.003
y[1] (numeric) = -0.0192844617031 0.15719350085
y[1] (closed_form) = -0.0193195928693 0.157191871538
absolute error = 3.517e-05
relative error = 0.02221 %
Correct digits = 4
memory used=2424.8MB, alloc=44.3MB, time=31.19
Radius of convergence (given) for eq 1 = 1.855
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5388 2.038
h = 0.0001 0.004
y[1] (numeric) = -0.0196249846777 0.156974539342
y[1] (closed_form) = -0.0196596367414 0.156972774189
absolute error = 3.470e-05
relative error = 0.02193 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.856
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5387 2.042
h = 0.003 0.006
y[1] (numeric) = -0.0199534699447 0.156583029622
y[1] (closed_form) = -0.0199878155688 0.156581555283
absolute error = 3.438e-05
relative error = 0.02178 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.858
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5357 2.048
h = 0.0001 0.005
y[1] (numeric) = -0.0207263375932 0.156221145442
y[1] (closed_form) = -0.0207603184566 0.156217860806
absolute error = 3.414e-05
relative error = 0.02166 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.859
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5356 2.053
h = 0.0001 0.003
y[1] (numeric) = -0.0211253198365 0.155726922493
y[1] (closed_form) = -0.0211597465276 0.155724747065
absolute error = 3.450e-05
relative error = 0.02195 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.862
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5355 2.056
h = 0.001 0.001
y[1] (numeric) = -0.0213666508359 0.155434210413
y[1] (closed_form) = -0.0214015424498 0.155432015893
absolute error = 3.496e-05
relative error = 0.02228 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.864
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5345 2.057
h = 0.001 0.003
y[1] (numeric) = -0.0215435793898 0.155410872775
y[1] (closed_form) = -0.0215787013812 0.155408745902
absolute error = 3.519e-05
relative error = 0.02243 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.863
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5335 2.06
h = 0.0001 0.004
y[1] (numeric) = -0.0218742703643 0.155186579584
y[1] (closed_form) = -0.0219089167465 0.15518433524
absolute error = 3.472e-05
relative error = 0.02215 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.864
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5334 2.064
h = 0.003 0.006
y[1] (numeric) = -0.0221889095717 0.154792350975
y[1] (closed_form) = -0.0222232644298 0.154790402814
absolute error = 3.441e-05
relative error = 0.022 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.866
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5304 2.07
h = 0.0001 0.005
y[1] (numeric) = -0.0229427213965 0.154416657272
y[1] (closed_form) = -0.022976657103 0.154412941645
absolute error = 3.414e-05
relative error = 0.02187 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.867
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5303 2.075
h = 0.0001 0.003
y[1] (numeric) = -0.0233244406557 0.153919476303
y[1] (closed_form) = -0.0233588516332 0.153916836117
absolute error = 3.451e-05
relative error = 0.02217 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.87
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2471.5MB, alloc=44.3MB, time=31.80
x[1] = -1.5302 2.078
h = 0.001 0.001
y[1] (numeric) = -0.0235554937752 0.153624907989
y[1] (closed_form) = -0.0235903611137 0.153622233547
absolute error = 3.497e-05
relative error = 0.0225 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.872
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5292 2.079
h = 0.001 0.003
y[1] (numeric) = -0.0237294789047 0.153597639354
y[1] (closed_form) = -0.0237645749408 0.153595023732
absolute error = 3.519e-05
relative error = 0.02264 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.872
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5282 2.082
h = 0.0001 0.004
y[1] (numeric) = -0.0240503261484 0.153368433656
y[1] (closed_form) = -0.0240849507962 0.153365718408
absolute error = 3.473e-05
relative error = 0.02237 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.872
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5281 2.086
h = 0.003 0.006
y[1] (numeric) = -0.0243512638309 0.152971994752
y[1] (closed_form) = -0.0243856117973 0.152969580298
absolute error = 3.443e-05
relative error = 0.02223 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.875
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5251 2.092
h = 0.0001 0.005
y[1] (numeric) = -0.0250858842233 0.152583361738
y[1] (closed_form) = -0.0251197616215 0.152579224124
absolute error = 3.413e-05
relative error = 0.02207 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.876
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.525 2.097
h = 0.0001 0.003
y[1] (numeric) = -0.0254505384239 0.152083847648
y[1] (closed_form) = -0.0254849184666 0.152080751135
absolute error = 3.452e-05
relative error = 0.02239 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.879
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5249 2.1
h = 0.001 0.001
y[1] (numeric) = -0.025671428696 0.15178779599
y[1] (closed_form) = -0.0257062560615 0.151784650739
absolute error = 3.497e-05
relative error = 0.02272 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.88
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5239 2.101
h = 0.001 0.003
y[1] (numeric) = -0.0258423907353 0.151756761553
y[1] (closed_form) = -0.0258774447729 0.151753666554
absolute error = 3.519e-05
relative error = 0.02286 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.88
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5229 2.104
h = 0.0001 0.004
y[1] (numeric) = -0.0261534009118 0.151523054396
y[1] (closed_form) = -0.0261879884632 0.15151987706
absolute error = 3.473e-05
relative error = 0.02259 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.881
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5228 2.108
h = 0.003 0.006
y[1] (numeric) = -0.0264408006057 0.151124897024
y[1] (closed_form) = -0.0264751262071 0.151122024359
absolute error = 3.445e-05
relative error = 0.02245 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.883
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2518.4MB, alloc=44.3MB, time=32.40
x[1] = -1.5198 2.114
h = 0.0001 0.005
y[1] (numeric) = -0.0271561343111 0.150724182726
y[1] (closed_form) = -0.027189940908 0.150719632486
absolute error = 3.411e-05
relative error = 0.02227 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.884
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5197 2.119
h = 0.0001 0.003
y[1] (numeric) = -0.0275039441469 0.150222938825
y[1] (closed_form) = -0.0275382787126 0.150219394897
absolute error = 3.452e-05
relative error = 0.0226 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.887
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5196 2.122
h = 0.001 0.001
y[1] (numeric) = -0.0277148002111 0.149925763964
y[1] (closed_form) = -0.0277495726331 0.149922157511
absolute error = 3.496e-05
relative error = 0.02293 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.889
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5186 2.123
h = 0.0001 0.004
y[1] (numeric) = -0.0278826682529 0.149891128877
y[1] (closed_form) = -0.0279176649984 0.149887564373
absolute error = 3.518e-05
relative error = 0.02307 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.889
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5185 2.127
h = 0.003 0.006
y[1] (numeric) = -0.028159128561 0.149491940038
y[1] (closed_form) = -0.0281932939248 0.149488773946
absolute error = 3.431e-05
relative error = 0.02256 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.891
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5155 2.133
h = 0.0001 0.005
y[1] (numeric) = -0.0288576839811 0.149081733547
y[1] (closed_form) = -0.0288912915898 0.149076930527
absolute error = 3.395e-05
relative error = 0.02236 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.892
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5154 2.138
h = 0.0001 0.003
y[1] (numeric) = -0.0291911763493 0.148579663498
y[1] (closed_form) = -0.0292253316862 0.148575836308
absolute error = 3.437e-05
relative error = 0.0227 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.895
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5153 2.141
h = 0.001 0.001
y[1] (numeric) = -0.0293935001638 0.148281917388
y[1] (closed_form) = -0.0294280847491 0.148278016481
absolute error = 3.480e-05
relative error = 0.02302 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.897
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5143 2.142
h = 0.001 0.003
y[1] (numeric) = -0.029558614516 0.148244352698
y[1] (closed_form) = -0.0295934210669 0.14824048685
absolute error = 3.502e-05
relative error = 0.02317 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.897
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5133 2.145
h = 0.0001 0.004
y[1] (numeric) = -0.029851354734 0.148003448527
y[1] (closed_form) = -0.0298857057635 0.14799953089
absolute error = 3.457e-05
relative error = 0.0229 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.898
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2565.2MB, alloc=44.3MB, time=33.00
x[1] = -1.5132 2.149
h = 0.003 0.006
y[1] (numeric) = -0.0301140505798 0.147603498512
y[1] (closed_form) = -0.0301481666781 0.147599890718
absolute error = 3.431e-05
relative error = 0.02277 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.9
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5102 2.155
h = 0.0001 0.005
y[1] (numeric) = -0.0307932535597 0.147182768726
y[1] (closed_form) = -0.0308267689955 0.147177571431
absolute error = 3.392e-05
relative error = 0.02255 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.901
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5101 2.16
h = 0.0001 0.003
y[1] (numeric) = -0.0311103734855 0.146680028626
y[1] (closed_form) = -0.0311444582385 0.146675771878
absolute error = 3.435e-05
relative error = 0.02291 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.904
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.51 2.163
h = 0.001 0.001
y[1] (numeric) = -0.0313029391033 0.146381792326
y[1] (closed_form) = -0.0313374429755 0.146377449376
absolute error = 3.478e-05
relative error = 0.02323 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.906
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.509 2.164
h = 0.001 0.003
y[1] (numeric) = -0.0314648519963 0.146340933212
y[1] (closed_form) = -0.0314995749468 0.146336617548
absolute error = 3.499e-05
relative error = 0.02338 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.906
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.508 2.167
h = 0.0001 0.004
y[1] (numeric) = -0.0317478722484 0.146096651156
y[1] (closed_form) = -0.0317821462642 0.14609229929
absolute error = 3.455e-05
relative error = 0.02311 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.907
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5079 2.171
h = 0.003 0.006
y[1] (numeric) = -0.0319975957982 0.145696289534
y[1] (closed_form) = -0.0320316490955 0.145692249428
absolute error = 3.429e-05
relative error = 0.02299 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.909
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5049 2.177
h = 0.0001 0.005
y[1] (numeric) = -0.0326574569705 0.145265849505
y[1] (closed_form) = -0.0326908696259 0.145260268076
absolute error = 3.388e-05
relative error = 0.02275 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.911
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5048 2.182
h = 0.0001 0.003
y[1] (numeric) = -0.0329584805382 0.144762977417
y[1] (closed_form) = -0.0329924821494 0.144758301132
absolute error = 3.432e-05
relative error = 0.02312 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.914
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5047 2.185
h = 0.001 0.001
y[1] (numeric) = -0.0331414497542 0.144464572502
y[1] (closed_form) = -0.0331758600599 0.144459798228
absolute error = 3.474e-05
relative error = 0.02344 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.915
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2612.0MB, alloc=44.3MB, time=33.61
x[1] = -1.5037 2.186
h = 0.001 0.003
y[1] (numeric) = -0.0333001140182 0.144420581424
y[1] (closed_form) = -0.0333347402556 0.144415826955
absolute error = 3.495e-05
relative error = 0.02358 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.915
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5027 2.189
h = 0.0001 0.004
y[1] (numeric) = -0.0335734833225 0.144173294302
y[1] (closed_form) = -0.0336076677139 0.144168518599
absolute error = 3.452e-05
relative error = 0.02332 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.916
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5026 2.193
h = 0.003 0.006
y[1] (numeric) = -0.0338104584659 0.143772943277
y[1] (closed_form) = -0.0338444361146 0.143768480617
absolute error = 3.427e-05
relative error = 0.0232 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.919
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4996 2.199
h = 0.0001 0.005
y[1] (numeric) = -0.0344510220903 0.143333587609
y[1] (closed_form) = -0.0344843220074 0.143327632385
absolute error = 3.383e-05
relative error = 0.02295 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.92
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4995 2.204
h = 0.0001 0.003
y[1] (numeric) = -0.0347362415823 0.142831098123
y[1] (closed_form) = -0.0347701481889 0.142826012621
absolute error = 3.429e-05
relative error = 0.02332 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.923
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4994 2.207
h = 0.001 0.001
y[1] (numeric) = -0.0349097859062 0.142532832282
y[1] (closed_form) = -0.0349440905313 0.142527637701
absolute error = 3.470e-05
relative error = 0.02364 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.925
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4984 2.208
h = 0.001 0.003
y[1] (numeric) = -0.0350651621527 0.142485870022
y[1] (closed_form) = -0.0350996793251 0.142480688062
absolute error = 3.490e-05
relative error = 0.02379 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.925
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4974 2.211
h = 0.0001 0.004
y[1] (numeric) = -0.0353289634245 0.14223593945
y[1] (closed_form) = -0.0353630462968 0.142230750595
absolute error = 3.448e-05
relative error = 0.02352 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.926
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4973 2.215
h = 0.003 0.006
y[1] (numeric) = -0.0355534264839 0.141836002492
y[1] (closed_form) = -0.0355873163256 0.141831127359
absolute error = 3.424e-05
relative error = 0.02341 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.928
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4943 2.221
h = 0.0001 0.005
y[1] (numeric) = -0.0361747686038 0.141388506101
y[1] (closed_form) = -0.0362079464665 0.141382187578
absolute error = 3.377e-05
relative error = 0.02314 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.93
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4942 2.226
h = 0.0001 0.003
y[1] (numeric) = -0.0364444908609 0.140886890123
y[1] (closed_form) = -0.0364782912926 0.140881405985
absolute error = 3.424e-05
relative error = 0.02353 %
Correct digits = 4
memory used=2659.0MB, alloc=44.3MB, time=34.22
Radius of convergence (given) for eq 1 = 1.933
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4941 2.229
h = 0.001 0.001
y[1] (numeric) = -0.0366087905459 0.140589057034
y[1] (closed_form) = -0.0366429781106 0.140583453416
absolute error = 3.464e-05
relative error = 0.02385 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.935
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4931 2.23
h = 0.0001 0.004
y[1] (numeric) = -0.0367608468724 0.140539282342
y[1] (closed_form) = -0.0367952433845 0.140533684464
absolute error = 3.485e-05
relative error = 0.02399 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.934
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.493 2.234
h = 0.003 0.006
y[1] (numeric) = -0.0369752622035 0.140139989511
y[1] (closed_form) = -0.0370089639021 0.140134871302
absolute error = 3.409e-05
relative error = 0.02352 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.937
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.49 2.24
h = 0.0001 0.005
y[1] (numeric) = -0.0375800580835 0.139686317725
y[1] (closed_form) = -0.0376130211466 0.139679799031
absolute error = 3.360e-05
relative error = 0.02323 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.938
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4899 2.245
h = 0.0001 0.003
y[1] (numeric) = -0.037836714402 0.139186007976
y[1] (closed_form) = -0.0378703118416 0.139180293224
absolute error = 3.408e-05
relative error = 0.02363 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.942
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4898 2.248
h = 0.001 0.001
y[1] (numeric) = -0.0379932165806 0.138888878865
y[1] (closed_form) = -0.0380271915339 0.138883036357
absolute error = 3.447e-05
relative error = 0.02394 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.943
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4888 2.249
h = 0.001 0.003
y[1] (numeric) = -0.0381423642019 0.138836848586
y[1] (closed_form) = -0.0381765447701 0.138831006186
absolute error = 3.468e-05
relative error = 0.02408 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.943
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4878 2.252
h = 0.0001 0.004
y[1] (numeric) = -0.0383886040738 0.138583032654
y[1] (closed_form) = -0.0384223655998 0.138577208241
absolute error = 3.426e-05
relative error = 0.02382 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.944
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4877 2.256
h = 0.003 0.006
y[1] (numeric) = -0.0385904666672 0.138185017285
y[1] (closed_form) = -0.0386240598909 0.138179506199
absolute error = 3.404e-05
relative error = 0.02373 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.947
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4847 2.262
h = 0.0001 0.005
y[1] (numeric) = -0.0391762693838 0.137724588969
y[1] (closed_form) = -0.039209094858 0.137717726907
absolute error = 3.354e-05
relative error = 0.02342 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.949
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2705.7MB, alloc=44.3MB, time=34.82
x[1] = -1.4846 2.267
h = 0.0001 0.003
y[1] (numeric) = -0.039418037905 0.13722599892
y[1] (closed_form) = -0.0394515103374 0.137219905874
absolute error = 3.402e-05
relative error = 0.02383 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.952
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4845 2.27
h = 0.001 0.001
y[1] (numeric) = -0.0395656539964 0.136929809213
y[1] (closed_form) = -0.0395994927818 0.136923579269
absolute error = 3.441e-05
relative error = 0.02414 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.954
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4835 2.271
h = 0.001 0.003
y[1] (numeric) = -0.0397114430217 0.136875255587
y[1] (closed_form) = -0.0397454834801 0.13686901944
absolute error = 3.461e-05
relative error = 0.02428 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.954
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4825 2.274
h = 0.0001 0.004
y[1] (numeric) = -0.0399484241888 0.136619763993
y[1] (closed_form) = -0.039982054208 0.13661355834
absolute error = 3.420e-05
relative error = 0.02402 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.955
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4824 2.278
h = 0.003 0.006
y[1] (numeric) = -0.0401385120438 0.136223209442
y[1] (closed_form) = -0.0401719865924 0.136217316238
absolute error = 3.399e-05
relative error = 0.02393 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.957
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4794 2.284
h = 0.0001 0.005
y[1] (numeric) = -0.0407054779992 0.135756737363
y[1] (closed_form) = -0.0407381583442 0.135749542687
absolute error = 3.346e-05
relative error = 0.02361 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.959
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4793 2.289
h = 0.0001 0.003
y[1] (numeric) = -0.0409326982521 0.135260289869
y[1] (closed_form) = -0.04096603645 0.13525382961
absolute error = 3.396e-05
relative error = 0.02403 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.962
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4792 2.292
h = 0.001 0.001
y[1] (numeric) = -0.0410716282088 0.134965292948
y[1] (closed_form) = -0.0411053215011 0.134958687307
absolute error = 3.433e-05
relative error = 0.02434 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.964
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4782 2.293
h = 0.001 0.003
y[1] (numeric) = -0.0412140463913 0.134908367143
y[1] (closed_form) = -0.0412479372577 0.134901749295
absolute error = 3.453e-05
relative error = 0.02448 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.964
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4772 2.296
h = 0.0001 0.004
y[1] (numeric) = -0.0414418964539 0.1346515149
y[1] (closed_form) = -0.0414753857756 0.134644939416
absolute error = 3.413e-05
relative error = 0.02422 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.965
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2752.4MB, alloc=44.3MB, time=35.43
x[1] = -1.4771 2.3
h = 0.003 0.006
y[1] (numeric) = -0.0416204818559 0.134256751718
y[1] (closed_form) = -0.0416538281989 0.134250487318
absolute error = 3.393e-05
relative error = 0.02414 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.968
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4741 2.306
h = 0.0001 0.005
y[1] (numeric) = -0.0421687920394 0.133784925567
y[1] (closed_form) = -0.0422013203089 0.133777409063
absolute error = 3.339e-05
relative error = 0.0238 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.969
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.474 2.311
h = 0.0001 0.003
y[1] (numeric) = -0.0423818122039 0.133291019977
y[1] (closed_form) = -0.0424150075985 0.133284203689
absolute error = 3.389e-05
relative error = 0.02423 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.973
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4739 2.314
h = 0.001 0.001
y[1] (numeric) = -0.0425122612185 0.132997455291
y[1] (closed_form) = -0.0425458003852 0.132990485785
absolute error = 3.426e-05
relative error = 0.02453 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.975
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4729 2.315
h = 0.001 0.003
y[1] (numeric) = -0.0426513025648 0.132938305358
y[1] (closed_form) = -0.0426850350695 0.132931317945
absolute error = 3.445e-05
relative error = 0.02467 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.975
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4719 2.318
h = 0.0001 0.004
y[1] (numeric) = -0.0428701585041 0.132680394925
y[1] (closed_form) = -0.0429034986107 0.132673461112
absolute error = 3.405e-05
relative error = 0.02442 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.976
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4718 2.322
h = 0.003 0.006
y[1] (numeric) = -0.0430375202409 0.132287735038
y[1] (closed_form) = -0.0430707295065 0.132281110487
absolute error = 3.386e-05
relative error = 0.02434 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.978
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4688 2.328
h = 0.0001 0.005
y[1] (numeric) = -0.0435673783975 0.131811220882
y[1] (closed_form) = -0.0435997482235 0.131803393336
absolute error = 3.330e-05
relative error = 0.02399 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.98
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4687 2.333
h = 0.0001 0.003
y[1] (numeric) = -0.0437665539081 0.131320233285
y[1] (closed_form) = -0.0437995985748 0.131313072223
absolute error = 3.381e-05
relative error = 0.02443 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.983
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4686 2.336
h = 0.001 0.001
y[1] (numeric) = -0.0438887315835 0.131028326499
y[1] (closed_form) = -0.0439221086698 0.131021005012
absolute error = 3.417e-05
relative error = 0.02473 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.985
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2799.3MB, alloc=44.3MB, time=36.04
x[1] = -1.4676 2.337
h = 0.0001 0.004
y[1] (numeric) = -0.0440243960224 0.130967097152
y[1] (closed_form) = -0.0440579620921 0.13095975236
absolute error = 3.436e-05
relative error = 0.02487 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.985
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4675 2.341
h = 0.003 0.006
y[1] (numeric) = -0.0441827936927 0.130576393092
y[1] (closed_form) = -0.0442157993293 0.130569574929
absolute error = 3.370e-05
relative error = 0.02445 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.988
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4645 2.347
h = 0.0001 0.005
y[1] (numeric) = -0.044696902665 0.130096574782
y[1] (closed_form) = -0.0447290529893 0.130088595818
absolute error = 3.313e-05
relative error = 0.02408 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.99
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4644 2.352
h = 0.0001 0.003
y[1] (numeric) = -0.0448844907636 0.129608541586
y[1] (closed_form) = -0.0449173209822 0.129601200423
absolute error = 3.364e-05
relative error = 0.02453 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.993
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4643 2.355
h = 0.001 0.001
y[1] (numeric) = -0.0449997425265 0.129318327248
y[1] (closed_form) = -0.0450328953166 0.129310820082
absolute error = 3.399e-05
relative error = 0.02482 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.995
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4633 2.356
h = 0.001 0.003
y[1] (numeric) = -0.045132481966 0.12925546133
y[1] (closed_form) = -0.0451658198505 0.129247926508
absolute error = 3.418e-05
relative error = 0.02496 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.995
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4623 2.359
h = 0.0001 0.004
y[1] (numeric) = -0.0453349903122 0.128996446414
y[1] (closed_form) = -0.0453679534763 0.128988984319
absolute error = 3.380e-05
relative error = 0.02472 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.996
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4622 2.363
h = 0.003 0.006
y[1] (numeric) = -0.0454822601605 0.128608593245
y[1] (closed_form) = -0.0455151140551 0.128601435779
absolute error = 3.362e-05
relative error = 0.02465 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.999
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4592 2.369
h = 0.0001 0.005
y[1] (numeric) = -0.0459783579051 0.128125259104
y[1] (closed_form) = -0.0460103395441 0.128116989143
absolute error = 3.303e-05
relative error = 0.02427 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.001
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4591 2.374
h = 0.0001 0.003
y[1] (numeric) = -0.0461527813563 0.127640778597
y[1] (closed_form) = -0.0461854478977 0.127633113749
absolute error = 3.355e-05
relative error = 0.02472 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.004
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2846.1MB, alloc=44.3MB, time=36.64
x[1] = -1.459 2.377
h = 0.001 0.001
y[1] (numeric) = -0.0462601631641 0.127352603465
y[1] (closed_form) = -0.0462931409565 0.127344766533
absolute error = 3.390e-05
relative error = 0.02502 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.006
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.458 2.378
h = 0.001 0.003
y[1] (numeric) = -0.0463895418096 0.127287917756
y[1] (closed_form) = -0.0464227001718 0.127280048326
absolute error = 3.408e-05
relative error = 0.02515 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.006
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.457 2.381
h = 0.0001 0.004
y[1] (numeric) = -0.0465834950269 0.12702863803
y[1] (closed_form) = -0.046616288325 0.127020850787
absolute error = 3.371e-05
relative error = 0.02491 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.007
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4569 2.385
h = 0.003 0.006
y[1] (numeric) = -0.0467203680889 0.126643676339
y[1] (closed_form) = -0.0467530631804 0.126636190771
absolute error = 3.354e-05
relative error = 0.02485 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.01
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4539 2.391
h = 0.0001 0.005
y[1] (numeric) = -0.0471987133425 0.126157422715
y[1] (closed_form) = -0.0472305214852 0.126148872401
absolute error = 3.294e-05
relative error = 0.02445 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.012
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4538 2.396
h = 0.0001 0.003
y[1] (numeric) = -0.0473603409239 0.125676806425
y[1] (closed_form) = -0.0473928376179 0.125668829161
absolute error = 3.346e-05
relative error = 0.02491 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.016
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4537 2.399
h = 0.001 0.001
y[1] (numeric) = -0.0474600705957 0.12539085787
y[1] (closed_form) = -0.0474928672734 0.125382703017
absolute error = 3.380e-05
relative error = 0.02521 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.018
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4527 2.4
h = 0.001 0.003
y[1] (numeric) = -0.0475861034393 0.12532448653
y[1] (closed_form) = -0.0476190760928 0.125316294628
absolute error = 3.398e-05
relative error = 0.02534 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.018
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4517 2.403
h = 0.0001 0.004
y[1] (numeric) = -0.0477716665412 0.125065195491
y[1] (closed_form) = -0.0478042839016 0.125057094638
absolute error = 3.361e-05
relative error = 0.0251 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.019
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4516 2.407
h = 0.003 0.006
y[1] (numeric) = -0.0478984367037 0.124683367803
y[1] (closed_form) = -0.0479309665327 0.124675565328
absolute error = 3.345e-05
relative error = 0.02504 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.022
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2892.8MB, alloc=44.3MB, time=37.25
x[1] = -1.4486 2.413
h = 0.0001 0.005
y[1] (numeric) = -0.0483593042303 0.124194766438
y[1] (closed_form) = -0.048390934574 0.12418594632
absolute error = 3.284e-05
relative error = 0.02464 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.024
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4485 2.418
h = 0.0001 0.003
y[1] (numeric) = -0.0485085071884 0.123718304237
y[1] (closed_form) = -0.0485408284432 0.123710025776
absolute error = 3.336e-05
relative error = 0.02511 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.027
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4484 2.421
h = 0.001 0.001
y[1] (numeric) = -0.0486008041103 0.123434756775
y[1] (closed_form) = -0.0486334141599 0.123426295781
absolute error = 3.369e-05
relative error = 0.0254 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.029
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4474 2.422
h = 0.001 0.003
y[1] (numeric) = -0.0487235107901 0.123366830043
y[1] (closed_form) = -0.0487562921677 0.123358327734
absolute error = 3.387e-05
relative error = 0.02553 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.029
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4464 2.425
h = 0.0001 0.004
y[1] (numeric) = -0.0489008541421 0.123107768652
y[1] (closed_form) = -0.0489332900811 0.123099365666
absolute error = 3.351e-05
relative error = 0.02529 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.03
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4463 2.429
h = 0.003 0.006
y[1] (numeric) = -0.0490178169706 0.122729300419
y[1] (closed_form) = -0.0490501756616 0.122721192201
absolute error = 3.336e-05
relative error = 0.02524 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.033
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4433 2.435
h = 0.0001 0.005
y[1] (numeric) = -0.0494614959368 0.122238898442
y[1] (closed_form) = -0.0494929446677 0.122229818958
absolute error = 3.273e-05
relative error = 0.02482 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.035
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4432 2.44
h = 0.0001 0.003
y[1] (numeric) = -0.0495986469095 0.121766859088
y[1] (closed_form) = -0.049630787692 0.121758290577
absolute error = 3.326e-05
relative error = 0.0253 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.039
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4431 2.443
h = 0.001 0.001
y[1] (numeric) = -0.0496837313938 0.121485874699
y[1] (closed_form) = -0.0497161498838 0.121477119246
absolute error = 3.358e-05
relative error = 0.02558 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.041
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4421 2.444
h = 0.0001 0.004
y[1] (numeric) = -0.0498031358728 0.121416518795
y[1] (closed_form) = -0.0498357210039 0.121407718042
absolute error = 3.375e-05
relative error = 0.02572 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.041
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.442 2.448
h = 0.003 0.006
y[1] (numeric) = -0.0499123039748 0.121040968466
y[1] (closed_form) = -0.0499444539541 0.121032712673
absolute error = 3.319e-05
relative error = 0.02535 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.044
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2939.7MB, alloc=44.3MB, time=37.85
x[1] = -1.439 2.454
h = 0.0001 0.005
y[1] (numeric) = -0.0503414159616 0.1205496358
y[1] (closed_form) = -0.0503726490813 0.120540448118
absolute error = 3.256e-05
relative error = 0.02492 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.046
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4389 2.459
h = 0.0001 0.003
y[1] (numeric) = -0.0504685483619 0.120081740519
y[1] (closed_form) = -0.0505004732385 0.120073037997
absolute error = 3.309e-05
relative error = 0.0254 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.049
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4388 2.462
h = 0.001 0.001
y[1] (numeric) = -0.0505476342339 0.119803165062
y[1] (closed_form) = -0.0505798273278 0.119794272349
absolute error = 3.340e-05
relative error = 0.02568 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.051
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4378 2.463
h = 0.001 0.003
y[1] (numeric) = -0.0506642034926 0.119732715797
y[1] (closed_form) = -0.0506965591295 0.119723774627
absolute error = 3.357e-05
relative error = 0.02582 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.051
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4368 2.466
h = 0.0001 0.004
y[1] (numeric) = -0.0508267294509 0.119474773617
y[1] (closed_form) = -0.0508587581916 0.119465945535
absolute error = 3.322e-05
relative error = 0.02559 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.053
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4367 2.47
h = 0.003 0.006
y[1] (numeric) = -0.0509262776726 0.119103208461
y[1] (closed_form) = -0.0509582472 0.119094667577
absolute error = 3.309e-05
relative error = 0.02555 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.055
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4337 2.476
h = 0.0001 0.005
y[1] (numeric) = -0.0513387780115 0.118611024328
y[1] (closed_form) = -0.0513698237744 0.118601596373
absolute error = 3.245e-05
relative error = 0.0251 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.058
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4336 2.481
h = 0.0001 0.003
y[1] (numeric) = -0.0514545547508 0.118147993365
y[1] (closed_form) = -0.0514862913364 0.118139021305
absolute error = 3.298e-05
relative error = 0.02559 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.061
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4335 2.484
h = 0.001 0.001
y[1] (numeric) = -0.0515268401648 0.117872247573
y[1] (closed_form) = -0.0515588341303 0.117863081858
absolute error = 3.328e-05
relative error = 0.02587 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.063
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4325 2.485
h = 0.001 0.003
y[1] (numeric) = -0.0516401636364 0.117800592675
y[1] (closed_form) = -0.0516723154249 0.117791375018
absolute error = 3.345e-05
relative error = 0.026 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.063
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2986.4MB, alloc=44.3MB, time=38.45
x[1] = -1.4315 2.488
h = 0.0001 0.004
y[1] (numeric) = -0.0517949826745 0.117543499399
y[1] (closed_form) = -0.0518268174976 0.117534401506
absolute error = 3.311e-05
relative error = 0.02578 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.065
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4314 2.492
h = 0.003 0.006
y[1] (numeric) = -0.051885573154 0.11717584492
y[1] (closed_form) = -0.0519173579155 0.117167029872
absolute error = 3.298e-05
relative error = 0.02574 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.068
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4284 2.498
h = 0.0001 0.005
y[1] (numeric) = -0.0522817834837 0.116683286669
y[1] (closed_form) = -0.0523126393613 0.116673628459
absolute error = 3.233e-05
relative error = 0.02529 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.07
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4283 2.503
h = 0.0001 0.003
y[1] (numeric) = -0.0523865756126 0.11622533171
y[1] (closed_form) = -0.0524181203568 0.11621610092
absolute error = 3.287e-05
relative error = 0.02578 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.073
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4282 2.506
h = 0.001 0.001
y[1] (numeric) = -0.0524522802144 0.11595254365
y[1] (closed_form) = -0.0524840716586 0.115943116216
absolute error = 3.316e-05
relative error = 0.02605 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.076
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4272 2.507
h = 0.001 0.003
y[1] (numeric) = -0.0525623924701 0.115879797458
y[1] (closed_form) = -0.0525943370153 0.115870314856
absolute error = 3.332e-05
relative error = 0.02619 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.076
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4262 2.51
h = 0.0001 0.004
y[1] (numeric) = -0.052709688835 0.115623747169
y[1] (closed_form) = -0.0527413263254 0.115614390481
absolute error = 3.299e-05
relative error = 0.02596 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.077
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4261 2.514
h = 0.003 0.006
y[1] (numeric) = -0.0527916160682 0.1152601673
y[1] (closed_form) = -0.0528232122564 0.115251088891
absolute error = 3.287e-05
relative error = 0.02593 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.08
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4231 2.52
h = 0.0001 0.005
y[1] (numeric) = -0.0531718667277 0.114767688441
y[1] (closed_form) = -0.0532025306024 0.114757809818
absolute error = 3.222e-05
relative error = 0.02547 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.082
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.423 2.525
h = 0.0001 0.003
y[1] (numeric) = -0.053266043172 0.11431500247
y[1] (closed_form) = -0.0532973930022 0.114305523605
absolute error = 3.275e-05
relative error = 0.02597 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.086
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3033.2MB, alloc=44.3MB, time=39.06
x[1] = -1.4229 2.528
h = 0.001 0.001
y[1] (numeric) = -0.053325385439 0.114045289089
y[1] (closed_form) = -0.0533569714622 0.114035611046
absolute error = 3.304e-05
relative error = 0.02624 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.088
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4219 2.529
h = 0.001 0.003
y[1] (numeric) = -0.0534323242014 0.113971561745
y[1] (closed_form) = -0.0534640586133 0.113961825559
absolute error = 3.319e-05
relative error = 0.02637 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.088
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4209 2.532
h = 0.0001 0.004
y[1] (numeric) = -0.0535722842194 0.113716736944
y[1] (closed_form) = -0.0536037214448 0.113707132312
absolute error = 3.287e-05
relative error = 0.02615 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.089
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4208 2.536
h = 0.003 0.006
y[1] (numeric) = -0.0536458408216 0.113357380932
y[1] (closed_form) = -0.0536772451147 0.113348049825
absolute error = 3.276e-05
relative error = 0.02612 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.092
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4178 2.542
h = 0.0001 0.005
y[1] (numeric) = -0.0540104695311 0.1128654115
y[1] (closed_form) = -0.0540409396758 0.112855322122
absolute error = 3.210e-05
relative error = 0.02565 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.095
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4177 2.547
h = 0.0001 0.003
y[1] (numeric) = -0.0540943963404 0.112418169481
y[1] (closed_form) = -0.0541255486396 0.112408453028
absolute error = 3.263e-05
relative error = 0.02616 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.098
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4176 2.55
h = 0.001 0.001
y[1] (numeric) = -0.0541475931321 0.112151637007
y[1] (closed_form) = -0.054178971305 0.112141719274
absolute error = 3.291e-05
relative error = 0.02642 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.1
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4166 2.551
h = 0.0001 0.004
y[1] (numeric) = -0.0542513989933 0.112077034449
y[1] (closed_form) = -0.0542829208628 0.11206705584
absolute error = 3.306e-05
relative error = 0.02655 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.101
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4165 2.555
h = 0.003 0.006
y[1] (numeric) = -0.054318332512 0.111721246167
y[1] (closed_form) = -0.0543495311335 0.111711808505
absolute error = 3.259e-05
relative error = 0.02624 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.103
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4135 2.561
h = 0.0001 0.005
y[1] (numeric) = -0.0546698021266 0.111230222476
y[1] (closed_form) = -0.0547000667084 0.11122006181
absolute error = 3.192e-05
relative error = 0.02576 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.106
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3080.0MB, alloc=44.3MB, time=39.67
x[1] = -1.4134 2.566
h = 0.0001 0.003
y[1] (numeric) = -0.0547452641716 0.110787909517
y[1] (closed_form) = -0.0547762066665 0.11077809941
absolute error = 3.246e-05
relative error = 0.02627 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.11
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4133 2.569
h = 0.001 0.001
y[1] (numeric) = -0.0547933826803 0.11052426197
y[1] (closed_form) = -0.0548245423079 0.110514249223
absolute error = 3.273e-05
relative error = 0.02653 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.112
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4123 2.57
h = 0.001 0.003
y[1] (numeric) = -0.0548945175538 0.110449024298
y[1] (closed_form) = -0.0549258168338 0.110438948565
absolute error = 3.288e-05
relative error = 0.02666 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.112
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4113 2.573
h = 0.0001 0.004
y[1] (numeric) = -0.055021346238 0.110197009153
y[1] (closed_form) = -0.0550523665651 0.110187074057
absolute error = 3.257e-05
relative error = 0.02644 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.113
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4112 2.577
h = 0.003 0.006
y[1] (numeric) = -0.0550801508971 0.109845953558
y[1] (closed_form) = -0.0551111527835 0.10983628263
absolute error = 3.248e-05
relative error = 0.02643 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.116
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4082 2.583
h = 0.0001 0.005
y[1] (numeric) = -0.0554166468719 0.109356174301
y[1] (closed_form) = -0.0554467155902 0.109345820333
absolute error = 3.180e-05
relative error = 0.02594 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.119
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4081 2.588
h = 0.0001 0.003
y[1] (numeric) = -0.055482532056 0.108919581039
y[1] (closed_form) = -0.0555132734094 0.108909552375
absolute error = 3.234e-05
relative error = 0.02645 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.122
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.408 2.591
h = 0.001 0.001
y[1] (numeric) = -0.0555249039102 0.108659282418
y[1] (closed_form) = -0.0555558524628 0.108649049757
absolute error = 3.260e-05
relative error = 0.02671 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.125
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.407 2.592
h = 0.001 0.003
y[1] (numeric) = -0.0556229892735 0.108583354957
y[1] (closed_form) = -0.0556540728519 0.108573057005
absolute error = 3.275e-05
relative error = 0.02684 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.125
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.406 2.595
h = 0.0001 0.004
y[1] (numeric) = -0.0557430229088 0.108333023706
y[1] (closed_form) = -0.0557738371669 0.108322870674
absolute error = 3.244e-05
relative error = 0.02663 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.126
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3126.9MB, alloc=44.3MB, time=40.27
x[1] = -1.4059 2.599
h = 0.003 0.006
y[1] (numeric) = -0.0557942799085 0.10798653937
y[1] (closed_form) = -0.0558250830065 0.10797664534
absolute error = 3.235e-05
relative error = 0.02662 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.129
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4029 2.605
h = 0.0001 0.005
y[1] (numeric) = -0.056116154141 0.107498369855
y[1] (closed_form) = -0.0561460262731 0.107487831656
absolute error = 3.168e-05
relative error = 0.02612 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.132
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4028 2.61
h = 0.0001 0.003
y[1] (numeric) = -0.0561728165049 0.107067623627
y[1] (closed_form) = -0.0562033552821 0.10705738633
absolute error = 3.221e-05
relative error = 0.02664 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.135
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4027 2.613
h = 0.001 0.001
y[1] (numeric) = -0.0562096516771 0.106810751801
y[1] (closed_form) = -0.0562403879393 0.106800309521
absolute error = 3.246e-05
relative error = 0.02689 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.138
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4017 2.614
h = 0.001 0.003
y[1] (numeric) = -0.0563047348177 0.106734228535
y[1] (closed_form) = -0.0563356015248 0.106723718874
absolute error = 3.261e-05
relative error = 0.02702 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.138
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4007 2.617
h = 0.0001 0.004
y[1] (numeric) = -0.0564181625984 0.106485721694
y[1] (closed_form) = -0.056448769505 0.106475360798
absolute error = 3.231e-05
relative error = 0.02681 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.139
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4006 2.621
h = 0.003 0.006
y[1] (numeric) = -0.0564621521428 0.106143906392
y[1] (closed_form) = -0.0564927548017 0.106133799227
absolute error = 3.223e-05
relative error = 0.02681 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.142
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3976 2.627
h = 0.0001 0.005
y[1] (numeric) = -0.0567697594625 0.105657690328
y[1] (closed_form) = -0.0567994346004 0.105646976752
absolute error = 3.155e-05
relative error = 0.0263 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.145
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3975 2.632
h = 0.0001 0.003
y[1] (numeric) = -0.0568175478522 0.105232903177
y[1] (closed_form) = -0.0568478829916 0.105222466953
absolute error = 3.208e-05
relative error = 0.02682 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.149
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3974 2.635
h = 0.001 0.001
y[1] (numeric) = -0.0568490533105 0.104979526901
y[1] (closed_form) = -0.0568795764481 0.104968885058
absolute error = 3.233e-05
relative error = 0.02708 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.151
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3964 2.636
h = 0.001 0.003
y[1] (numeric) = -0.0569411833961 0.104902497717
y[1] (closed_form) = -0.056971832451 0.104891786613
absolute error = 3.247e-05
relative error = 0.0272 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.151
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3173.7MB, alloc=44.3MB, time=40.87
x[1] = -1.3954 2.639
h = 0.0001 0.004
y[1] (numeric) = -0.0570481941551 0.104655945711
y[1] (closed_form) = -0.0570785928014 0.104645386797
absolute error = 3.218e-05
relative error = 0.027 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.153
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3953 2.643
h = 0.003 0.006
y[1] (numeric) = -0.0570851922068 0.104318885244
y[1] (closed_form) = -0.0571155931575 0.1043085747
absolute error = 3.210e-05
relative error = 0.02699 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.156
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3923 2.649
h = 0.0001 0.005
y[1] (numeric) = -0.0573788893856 0.103834945317
y[1] (closed_form) = -0.0574083674167 0.103824064991
absolute error = 3.142e-05
relative error = 0.02649 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.158
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3922 2.654
h = 0.0001 0.003
y[1] (numeric) = -0.0574181469893 0.103416214696
y[1] (closed_form) = -0.0574482777808 0.103405589027
absolute error = 3.195e-05
relative error = 0.02701 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.162
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3921 2.657
h = 0.001 0.001
y[1] (numeric) = -0.0574445264187 0.10316639403
y[1] (closed_form) = -0.057474835956 0.103155562434
absolute error = 3.219e-05
relative error = 0.02726 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.164
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3911 2.658
h = 0.0001 0.004
y[1] (numeric) = -0.0575337542681 0.103088944776
y[1] (closed_form) = -0.0575641852553 0.10307804224
absolute error = 3.233e-05
relative error = 0.02738 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.164
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.391 2.662
h = 0.003 0.006
y[1] (numeric) = -0.0575652439482 0.102755838947
y[1] (closed_form) = -0.0575954481612 0.102745457075
absolute error = 3.194e-05
relative error = 0.02712 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.167
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.388 2.668
h = 0.0001 0.005
y[1] (numeric) = -0.0578472862 0.102274260926
y[1] (closed_form) = -0.0578765727342 0.102263339818
absolute error = 3.126e-05
relative error = 0.0266 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.17
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3879 2.673
h = 0.0001 0.003
y[1] (numeric) = -0.0578795444459 0.101860907157
y[1] (closed_form) = -0.0579094768139 0.101850221945
absolute error = 3.178e-05
relative error = 0.02713 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.174
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3878 2.676
h = 0.001 0.001
y[1] (numeric) = -0.0579017151505 0.101614246624
y[1] (closed_form) = -0.0579318184937 0.101603355577
absolute error = 3.201e-05
relative error = 0.02737 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.176
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3220.5MB, alloc=44.3MB, time=41.48
x[1] = -1.3868 2.677
h = 0.001 0.003
y[1] (numeric) = -0.0579884829596 0.101536535217
y[1] (closed_form) = -0.0580187039431 0.101525571987
absolute error = 3.215e-05
relative error = 0.02749 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.176
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3858 2.68
h = 0.0001 0.004
y[1] (numeric) = -0.0580840793341 0.101294005867
y[1] (closed_form) = -0.058114067032 0.10128320004
absolute error = 3.188e-05
relative error = 0.0273 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.178
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3857 2.684
h = 0.003 0.006
y[1] (numeric) = -0.0581088448925 0.100966058462
y[1] (closed_form) = -0.0581388460899 0.100955490788
absolute error = 3.181e-05
relative error = 0.0273 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.181
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3827 2.69
h = 0.0001 0.005
y[1] (numeric) = -0.0583776462082 0.100487298875
y[1] (closed_form) = -0.0584067362465 0.100476226459
absolute error = 3.113e-05
relative error = 0.02678 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.184
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3826 2.695
h = 0.0001 0.003
y[1] (numeric) = -0.0584019966134 0.100080142652
y[1] (closed_form) = -0.0584317242848 0.100069285019
absolute error = 3.165e-05
relative error = 0.02731 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.187
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3825 2.698
h = 0.001 0.001
y[1] (numeric) = -0.0584194112272 0.0998371254353
y[1] (closed_form) = -0.0584493010752 0.0998260622154
absolute error = 3.187e-05
relative error = 0.02755 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.19
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3815 2.699
h = 0.001 0.003
y[1] (numeric) = -0.0585033759309 0.0997591425334
y[1] (closed_form) = -0.0585333790817 0.0997480057965
absolute error = 3.200e-05
relative error = 0.02767 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.19
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3805 2.702
h = 0.0001 0.004
y[1] (numeric) = -0.0585930911956 0.0995188862841
y[1] (closed_form) = -0.0586228700163 0.0995079092801
absolute error = 3.174e-05
relative error = 0.02748 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.191
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3804 2.706
h = 0.003 0.006
y[1] (numeric) = -0.0586116288946 0.0991958749559
y[1] (closed_form) = -0.0586414267818 0.0991851305919
absolute error = 3.168e-05
relative error = 0.02749 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.195
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3774 2.712
h = 0.0001 0.005
y[1] (numeric) = -0.0588675464969 0.0987201997444
y[1] (closed_form) = -0.0588964406698 0.098708983986
absolute error = 3.099e-05
relative error = 0.02696 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.197
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3267.4MB, alloc=44.3MB, time=42.08
x[1] = -1.3773 2.717
h = 0.0001 0.003
y[1] (numeric) = -0.0588843138154 0.0983193007425
y[1] (closed_form) = -0.0589138369716 0.0983082794893
absolute error = 3.151e-05
relative error = 0.0275 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.201
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3772 2.72
h = 0.001 0.001
y[1] (numeric) = -0.0588971652791 0.0980799643491
y[1] (closed_form) = -0.0589268420608 0.0980687380311
absolute error = 3.173e-05
relative error = 0.02773 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.203
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3762 2.721
h = 0.001 0.003
y[1] (numeric) = -0.0589783812111 0.0980017846117
y[1] (closed_form) = -0.0590081670335 0.0979904836166
absolute error = 3.186e-05
relative error = 0.02785 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.204
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3752 2.724
h = 0.0001 0.004
y[1] (numeric) = -0.0590623991973 0.0977638962032
y[1] (closed_form) = -0.0590919694753 0.0977527569235
absolute error = 3.160e-05
relative error = 0.02766 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.205
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3751 2.728
h = 0.003 0.006
y[1] (numeric) = -0.0590749655446 0.0974458658113
y[1] (closed_form) = -0.0591045601297 0.097434953632
absolute error = 3.154e-05
relative error = 0.02768 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.208
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3721 2.734
h = 0.0001 0.005
y[1] (numeric) = -0.0593183553911 0.0969735223266
y[1] (closed_form) = -0.0593470545565 0.0969621709563
absolute error = 3.086e-05
relative error = 0.02715 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.211
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.372 2.739
h = 0.0001 0.003
y[1] (numeric) = -0.0593278574058 0.096578928307
y[1] (closed_form) = -0.0593571765031 0.0965677519904
absolute error = 3.138e-05
relative error = 0.02768 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.215
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3719 2.742
h = 0.001 0.001
y[1] (numeric) = -0.0593363345857 0.0963433031293
y[1] (closed_form) = -0.0593657990072 0.0963319225241
absolute error = 3.159e-05
relative error = 0.02791 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.217
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3709 2.743
h = 0.001 0.003
y[1] (numeric) = -0.0594148569535 0.0962649974666
y[1] (closed_form) = -0.0594444262339 0.0962535411895
absolute error = 3.171e-05
relative error = 0.02803 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.218
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3699 2.746
h = 0.0001 0.004
y[1] (numeric) = -0.0594933594658 0.0960295632545
y[1] (closed_form) = -0.0595227218091 0.0960182703456
absolute error = 3.146e-05
relative error = 0.02785 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.219
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3314.3MB, alloc=44.3MB, time=42.70
x[1] = -1.3698 2.75
h = 0.003 0.006
y[1] (numeric) = -0.0595002053774 0.0957165493579
y[1] (closed_form) = -0.0595295969521 0.0957054779972
absolute error = 3.141e-05
relative error = 0.02787 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.222
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3668 2.756
h = 0.0001 0.005
y[1] (numeric) = -0.0597314214767 0.0952477670221
y[1] (closed_form) = -0.0597599267035 0.0952362875343
absolute error = 3.073e-05
relative error = 0.02733 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.225
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3667 2.761
h = 0.0001 0.003
y[1] (numeric) = -0.0597339687661 0.0948595144997
y[1] (closed_form) = -0.0597630845171 0.0948481914285
absolute error = 3.124e-05
relative error = 0.02787 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.229
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3666 2.764
h = 0.001 0.001
y[1] (numeric) = -0.0597382563117 0.0946276242059
y[1] (closed_form) = -0.0597675093371 0.0946160978585
absolute error = 3.144e-05
relative error = 0.0281 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.231
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3656 2.765
h = 0.0001 0.004
y[1] (numeric) = -0.0598141410234 0.0945492598684
y[1] (closed_form) = -0.0598434948094 0.0945376570108
absolute error = 3.156e-05
relative error = 0.02821 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.232
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3655 2.769
h = 0.003 0.006
y[1] (numeric) = -0.0598164989326 0.0942403771971
y[1] (closed_form) = -0.0598457066167 0.0942292638033
absolute error = 3.125e-05
relative error = 0.028 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.235
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3625 2.775
h = 0.0001 0.005
y[1] (numeric) = -0.060037563623 0.09377497002
y[1] (closed_form) = -0.0600658936893 0.0937634742117
absolute error = 3.057e-05
relative error = 0.02746 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.238
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3624 2.78
h = 0.0001 0.003
y[1] (numeric) = -0.0600344435104 0.0933922751266
y[1] (closed_form) = -0.0600633755413 0.0933809204516
absolute error = 3.108e-05
relative error = 0.02799 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.242
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3623 2.783
h = 0.001 0.001
y[1] (numeric) = -0.0600353140696 0.0931636607929
y[1] (closed_form) = -0.0600643766632 0.0931521039808
absolute error = 3.128e-05
relative error = 0.02822 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.244
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3613 2.784
h = 0.001 0.003
y[1] (numeric) = -0.0601089738834 0.0930853275808
y[1] (closed_form) = -0.060138133772 0.0930736937038
absolute error = 3.140e-05
relative error = 0.02833 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.244
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3361.0MB, alloc=44.3MB, time=43.30
x[1] = -1.3603 2.787
h = 0.0001 0.004
y[1] (numeric) = -0.0601777205613 0.0928547233505
y[1] (closed_form) = -0.0602066890445 0.0928432550036
absolute error = 3.116e-05
relative error = 0.02816 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.246
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3602 2.791
h = 0.003 0.006
y[1] (numeric) = -0.0601746304 0.0925511702978
y[1] (closed_form) = -0.060203636403 0.092539913127
absolute error = 3.111e-05
relative error = 0.02818 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.249
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3572 2.797
h = 0.0001 0.005
y[1] (numeric) = -0.0603841750352 0.0920897016035
y[1] (closed_form) = -0.0604123137433 0.0920780909773
absolute error = 3.044e-05
relative error = 0.02764 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.252
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3571 2.802
h = 0.0001 0.003
y[1] (numeric) = -0.0603746584506 0.0917133849407
y[1] (closed_form) = -0.0604033891741 0.0917018982925
absolute error = 3.094e-05
relative error = 0.02818 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.256
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.357 2.805
h = 0.001 0.001
y[1] (numeric) = -0.0603716714649 0.0914885308678
y[1] (closed_form) = -0.0604005251727 0.0914768434853
absolute error = 3.113e-05
relative error = 0.0284 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.258
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.356 2.806
h = 0.001 0.003
y[1] (numeric) = -0.0604427996695 0.0914102540246
y[1] (closed_form) = -0.0604717467395 0.0913984890076
absolute error = 3.125e-05
relative error = 0.02851 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.258
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.355 2.809
h = 0.0001 0.004
y[1] (numeric) = -0.060506538303 0.091182305834
y[1] (closed_form) = -0.0605353020287 0.0911707071563
absolute error = 3.101e-05
relative error = 0.02834 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.26
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3549 2.813
h = 0.003 0.006
y[1] (numeric) = -0.0604984132991 0.0908838215245
y[1] (closed_form) = -0.0605272186194 0.0908724285048
absolute error = 3.098e-05
relative error = 0.02837 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.263
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3519 2.819
h = 0.0001 0.005
y[1] (numeric) = -0.0606967828485 0.0904264731792
y[1] (closed_form) = -0.060724731784 0.0904147545544
absolute error = 3.031e-05
relative error = 0.02783 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.266
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3518 2.824
h = 0.0001 0.003
y[1] (numeric) = -0.0606811587088 0.090056542705
y[1] (closed_form) = -0.0607096894705 0.0900449316746
absolute error = 3.080e-05
relative error = 0.02836 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.27
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3517 2.827
h = 0.001 0.001
y[1] (numeric) = -0.0606744861219 0.0898354554658
y[1] (closed_form) = -0.0607031325404 0.0898236452923
absolute error = 3.099e-05
relative error = 0.02858 %
Correct digits = 4
memory used=3407.7MB, alloc=44.3MB, time=43.91
Radius of convergence (given) for eq 1 = 2.273
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3507 2.828
h = 0.001 0.003
y[1] (numeric) = -0.0607431397237 0.0897572923022
y[1] (closed_form) = -0.0607718756633 0.0897454040579
absolute error = 3.110e-05
relative error = 0.02869 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.273
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3497 2.831
h = 0.0001 0.004
y[1] (numeric) = -0.060802042019 0.0895320574794
y[1] (closed_form) = -0.060830602477 0.0895203361202
absolute error = 3.087e-05
relative error = 0.02852 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.275
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3496 2.835
h = 0.003 0.006
y[1] (numeric) = -0.060789110043 0.0892386464356
y[1] (closed_form) = -0.0608177158932 0.0892271252474
absolute error = 3.084e-05
relative error = 0.02856 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.278
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3466 2.841
h = 0.0001 0.005
y[1] (numeric) = -0.0609766454094 0.0887855849611
y[1] (closed_form) = -0.0610044063117 0.0887737649244
absolute error = 3.017e-05
relative error = 0.02801 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.281
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3465 2.846
h = 0.0001 0.003
y[1] (numeric) = -0.0609551948833 0.0884220397973
y[1] (closed_form) = -0.0609835272191 0.0884103117265
absolute error = 3.066e-05
relative error = 0.02855 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.285
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3464 2.849
h = 0.001 0.001
y[1] (numeric) = -0.0609450040872 0.088204720668
y[1] (closed_form) = -0.0609734450018 0.0881927952177
absolute error = 3.084e-05
relative error = 0.02876 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.287
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3454 2.85
h = 0.001 0.003
y[1] (numeric) = -0.0610112402217 0.0881267252184
y[1] (closed_form) = -0.0610397669096 0.0881147213866
absolute error = 3.095e-05
relative error = 0.02887 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.287
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3444 2.853
h = 0.0001 0.004
y[1] (numeric) = -0.0610654748439 0.087904254405
y[1] (closed_form) = -0.0610938337115 0.0878924177571
absolute error = 3.073e-05
relative error = 0.02871 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.289
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3443 2.857
h = 0.003 0.006
y[1] (numeric) = -0.0610479576012 0.0876159142687
y[1] (closed_form) = -0.0610763653919 0.0876042723446
absolute error = 3.070e-05
relative error = 0.02875 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.293
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3413 2.863
h = 0.0001 0.005
y[1] (numeric) = -0.0612249951923 0.0871672915032
y[1] (closed_form) = -0.0612525699415 0.087155376411
absolute error = 3.004e-05
relative error = 0.0282 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.296
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3454.6MB, alloc=44.3MB, time=44.51
x[1] = -1.3412 2.868
h = 0.0001 0.003
y[1] (numeric) = -0.0611979916365 0.0868101225146
y[1] (closed_form) = -0.0612261272571 0.0867982844969
absolute error = 3.052e-05
relative error = 0.02874 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.3
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3411 2.871
h = 0.001 0.001
y[1] (numeric) = -0.0611844454297 0.0865965678174
y[1] (closed_form) = -0.0612126827987 0.0865845343419
absolute error = 3.069e-05
relative error = 0.02895 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.302
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3401 2.872
h = 0.001 0.003
y[1] (numeric) = -0.0612483212382 0.0865187909445
y[1] (closed_form) = -0.0612766407273 0.0865066788946
absolute error = 3.080e-05
relative error = 0.02905 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.302
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff ( y , x , 1 ) = neg ( 2.0 ) * x / ( x * x + 1.0 ) / ( x * x + 1.0 ) ;
Iterations = 754
Total Elapsed Time = 44 Seconds
Expected Time Remaining = 0 Seconds
Optimized Time Remaining = 0 Seconds
Expected Total Time = 44 Seconds
> quit
memory used=3472.2MB, alloc=44.3MB, time=44.72