|\^/| 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(arctan(c(x)));
> end;
exact_soln_y := proc(x) return arctan(c(x)) end proc
> next_delta := proc()
> global glob_nxt, x_delta;
> x_delta := [ 0.001 + 0.00004 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.000 + 0.000 * I ];
> glob_nxt := glob_nxt + 1;
> it := x_delta[glob_nxt];
> return it;
> end;
Warning, `it` is implicitly declared local to procedure `next_delta`
next_delta := proc()
local it;
global glob_nxt, x_delta;
x_delta := [0.001 + 0.00004*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0. + 0.*I];
glob_nxt := glob_nxt + 1;
it := x_delta[glob_nxt];
return it
end proc
#END USER DEF BLOCK
#END BLOCK 3
#END USER FUNCTION BLOCK
# before write_aux functions
# Begin Function number 2
> display_poles := proc()
> local rad_given;
> global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ;
> if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1
> rad_given := float_abs(array_x[1] - (array_given_rad_poles[1,1] + array_given_rad_poles[1,2] * I ));
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," ");
> omniout_complex(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," ");
> if ((float_abs(rad_given) < float_abs(glob_least_given_sing)) and
> (float_abs(rad_given) > 0.0)) then # if number 2
> glob_least_given_sing := rad_given;
> fi;# end if 2;
> elif
> (glob_type_given_pole = 3) then # if number 2
> omniout_str(ALWAYS,"NO POLE (given) for Equation 1");
> elif
> (glob_type_given_pole = 5) then # if number 3
> omniout_str(ALWAYS,"SOME POLE (given) for Equation 1");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 1");
> fi;# end if 3;
> if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," ");
> if ((float_abs(array_rad_test_poles[1,1]) < glob_least_ratio_sing)) then # if number 4
> glob_least_ratio_sing := array_rad_test_poles[1,1];
> fi;# end if 4;
> omniout_complex(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," ");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," ");
> if ((float_abs(array_rad_test_poles[1,2]) < glob_least_3_sing)) then # if number 4
> glob_least_3_sing := array_rad_test_poles[1,2];
> fi;# end if 4;
> omniout_complex(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," ");
> if ((float_abs(array_rad_test_poles[1,3]) < glob_least_6_sing)) then # if number 4
> glob_least_6_sing := array_rad_test_poles[1,3];
> fi;# end if 4;
> omniout_complex(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1");
> fi;# end if 3
> ;
> 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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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_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 mult LINEAR - LINEAR $eq_no = 1 i = 1
> array_tmp1[1] := array_x[1] * array_x[1];
> #emit pre add FULL - CONST $eq_no = 1 i = 1
> array_tmp2[1] := array_tmp1[1] + array_const_1D0[1];
> #emit pre div CONST FULL $eq_no = 1 i = 1
> array_tmp3[1] := array_const_1D0[1] / array_tmp2[1];
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp4[1] := array_const_0D0[1] + array_tmp3[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_tmp4[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 LINEAR - LINEAR $eq_no = 1 i = 2
> array_tmp1[2] := array_x[1] * array_x[2] + array_x[2] * array_x[1];
> #emit pre add FULL CONST $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre div CONST FULL $eq_no = 1 i = 2
> array_tmp3[2] := neg(ats(2,array_tmp2,array_tmp3,2)) / array_tmp2[1];
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp4[2] := array_tmp3[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_tmp4[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_tmp1[3] := array_x[2] * array_x[2];
> #emit pre add FULL CONST $eq_no = 1 i = 3
> array_tmp2[3] := array_tmp1[3];
> #emit pre div CONST FULL $eq_no = 1 i = 3
> array_tmp3[3] := neg(ats(3,array_tmp2,array_tmp3,2)) / array_tmp2[1];
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp4[3] := array_tmp3[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_tmp4[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_tmp2[4] := array_tmp1[4];
> #emit pre div CONST FULL $eq_no = 1 i = 4
> array_tmp3[4] := neg(ats(4,array_tmp2,array_tmp3,2)) / array_tmp2[1];
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp4[4] := array_tmp3[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_tmp4[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_tmp2[5] := array_tmp1[5];
> #emit pre div CONST FULL $eq_no = 1 i = 5
> array_tmp3[5] := neg(ats(5,array_tmp2,array_tmp3,2)) / array_tmp2[1];
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp4[5] := array_tmp3[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_tmp4[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_tmp2[kkk] := array_tmp1[kkk];
> #emit div CONST FULL $eq_no = 1 i = 1
> array_tmp3[kkk] := neg(ats(kkk,array_tmp2,array_tmp3,2)) / array_tmp2[1];
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp4[kkk] := array_tmp3[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_tmp4[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_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_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] := array_x[1]*array_x[1];
array_tmp2[1] := array_tmp1[1] + array_const_1D0[1];
array_tmp3[1] := array_const_1D0[1]/array_tmp2[1];
array_tmp4[1] := array_const_0D0[1] + array_tmp3[1];
if not array_y_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[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_tmp1[2] := array_x[1]*array_x[2] + array_x[1]*array_x[2];
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := neg(ats(2, array_tmp2, array_tmp3, 2))/array_tmp2[1];
array_tmp4[2] := array_tmp3[2];
if not array_y_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[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_tmp1[3] := array_x[2]*array_x[2];
array_tmp2[3] := array_tmp1[3];
array_tmp3[3] := neg(ats(3, array_tmp2, array_tmp3, 2))/array_tmp2[1];
array_tmp4[3] := array_tmp3[3];
if not array_y_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[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_tmp2[4] := array_tmp1[4];
array_tmp3[4] := neg(ats(4, array_tmp2, array_tmp3, 2))/array_tmp2[1];
array_tmp4[4] := array_tmp3[4];
if not array_y_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[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_tmp2[5] := array_tmp1[5];
array_tmp3[5] := neg(ats(5, array_tmp2, array_tmp3, 2))/array_tmp2[1];
array_tmp4[5] := array_tmp3[5];
if not array_y_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[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_tmp2[kkk] := array_tmp1[kkk];
array_tmp3[kkk] :=
neg(ats(kkk, array_tmp2, array_tmp3, 2))/array_tmp2[1];
array_tmp4[kkk] := array_tmp3[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_tmp4[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_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_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 := 20;
> # before first input block
> #BEGIN FIRST INPUT BLOCK
> #BEGIN BLOCK 1
> #BEGIN FIRST INPUT BLOCK
> Digits:=16;
> max_terms:=20;
> #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..(20),[]);
> array_norms:= Array(0..(20),[]);
> array_fact_1:= Array(0..(20),[]);
> 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..(20),[]);
> array_x:= Array(0..(20),[]);
> array_tmp0:= Array(0..(20),[]);
> array_tmp1:= Array(0..(20),[]);
> array_tmp2:= Array(0..(20),[]);
> array_tmp3:= Array(0..(20),[]);
> array_tmp4:= Array(0..(20),[]);
> array_m1:= Array(0..(20),[]);
> array_y_higher := Array(0..(2) ,(0..20+ 1),[]);
> array_y_higher_work := Array(0..(2) ,(0..20+ 1),[]);
> array_y_higher_work2 := Array(0..(2) ,(0..20+ 1),[]);
> array_y_set_initial := Array(0..(2) ,(0..20+ 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..(20) ,(0..20+ 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 <= 20) do # do number 1
> array_y_init[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_norms[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) 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 <= 20) do # do number 1
> array_y[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_x[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp0[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp3[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp4[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) 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 <= 20) 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 <= 20) 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 <= 20) 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 <= 20) 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 <=20) do # do number 1
> term := 1;
> while (term <= 20) 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_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_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;
> # before generate init omniout const
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> ATS_MAX_TERMS := 20;
> 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/sing2postcpx.cpx#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = 1.0 / ( x * x + 1.0 ) ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=16;");
> omniout_str(ALWAYS,"max_terms:=20;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := -2.1 + 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(0.001);");
> 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,"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,"#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(arctan(c(x)));");
> 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 := -2.1 + 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(0.001);
> 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 ) = 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,"2017-11-26T16:22:53-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"sing2")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = 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,"sing2 diffeq.mxt")
> ;
> logitem_str(html_log_file,"sing2 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_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_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 := 20;
Digits := 16;
max_terms := 20;
glob_html_log := true;
array_y_init := Array(0 .. 20, []);
array_norms := Array(0 .. 20, []);
array_fact_1 := Array(0 .. 20, []);
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 .. 20, []);
array_x := Array(0 .. 20, []);
array_tmp0 := Array(0 .. 20, []);
array_tmp1 := Array(0 .. 20, []);
array_tmp2 := Array(0 .. 20, []);
array_tmp3 := Array(0 .. 20, []);
array_tmp4 := Array(0 .. 20, []);
array_m1 := Array(0 .. 20, []);
array_y_higher := Array(0 .. 2, 0 .. 21, []);
array_y_higher_work := Array(0 .. 2, 0 .. 21, []);
array_y_higher_work2 := Array(0 .. 2, 0 .. 21, []);
array_y_set_initial := Array(0 .. 2, 0 .. 21, []);
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 .. 20, 0 .. 21, []);
term := 1;
while term <= 20 do array_y_init[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 20 do array_norms[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 20 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 <= 20 do array_y[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_x[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_tmp0[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_tmp1[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_tmp2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_tmp3[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_tmp4[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_m1[term] := c(0.); term := term + 1 end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 20 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 <= 20 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 <= 20 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 <= 20 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 <= 20 do
term := 1;
while term <= 20 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_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_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;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
ATS_MAX_TERMS := 20;
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/sing2postcpx.cpx#################");
omniout_str(ALWAYS,
"diff ( y , x , 1 ) = 1.0 / ( x * x + 1.0 ) ; ")
;
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=16;");
omniout_str(ALWAYS, "max_terms:=20;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := -2.1 + 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(0.001);");
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, "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, "#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(arctan(c(x)));");
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,");
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omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 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 := -2.1 + 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(0.001);
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 ) = 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, "2017-11-26T16:22:53-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"sing2");
logitem_str(html_log_file, "diff ( y , x , 1 ) = 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,
"sing2 diffeq.mxt");
logitem_str(html_log_file,
"sing2 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=3.9MB, alloc=40.3MB, time=0.08
##############ECHO OF PROBLEM#################
##############temp/sing2postcpx.cpx#################
diff ( y , x , 1 ) = 1.0 / ( x * x + 1.0 ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=16;
max_terms:=20;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := -2.1 + 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(0.001);
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(arctan(c(x)));
end;
next_delta := proc()
global glob_nxt, x_delta;
x_delta := [ 0.001 + 0.00004 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.000 + 0.000 * I ];
glob_nxt := glob_nxt + 1;
it := x_delta[glob_nxt];
return it;
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = -2.1 0.1
h = 0.0001 0.005
y[1] (numeric) = -1.12709378614 0.0184585655028
y[1] (closed_form) = -1.12709378614 0.0184585655028
absolute error = 0
relative error = 0 %
Correct digits = 14
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] = -2.0999 0.105
h = 0.0001 0.003
y[1] (numeric) = -1.12714839348 0.0193802636328
y[1] (closed_form) = -1.1271487504 0.0193802311016
absolute error = 3.584e-07
relative error = 3.179e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.283
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0998 0.108
h = 0.001 0.001
y[1] (numeric) = -1.12717615814 0.0199337215076
y[1] (closed_form) = -1.1271760863 0.0199337244718
absolute error = 7.190e-08
relative error = 6.378e-06 %
Correct digits = 7
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] = -2.0988 0.109
h = 0.001 0.003
y[1] (numeric) = -1.12700787787 0.0201333491884
y[1] (closed_form) = -1.1270075903 0.0201332982571
absolute error = 2.920e-07
relative error = 2.591e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 2.28
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0978 0.112
h = 0.0001 0.004
y[1] (numeric) = -1.12687081187 0.0207015291265
y[1] (closed_form) = -1.12687096902 0.0207015696951
absolute error = 1.623e-07
relative error = 1.440e-05 %
Correct digits = 7
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] = -2.0977 0.116
h = 0.003 0.006
y[1] (numeric) = -1.12691753159 0.0214400948446
y[1] (closed_form) = -1.12691794945 0.0214398497944
absolute error = 4.844e-07
relative error = 4.298e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.276
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0947 0.122
h = 0.0001 0.005
y[1] (numeric) = -1.12646674544 0.0225954813746
y[1] (closed_form) = -1.12646761424 0.022596874147
absolute error = 1.642e-06
relative error = 0.0001457 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.271
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0946 0.127
h = 0.0001 0.003
y[1] (numeric) = -1.12653830402 0.0235203186318
y[1] (closed_form) = -1.12653869412 0.0235207141924
absolute error = 5.556e-07
relative error = 4.930e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.269
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0945 0.13
h = 0.001 0.001
y[1] (numeric) = -1.12657573052 0.0240751582866
y[1] (closed_form) = -1.12657569065 0.0240755997942
absolute error = 4.433e-07
relative error = 3.934e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.268
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0935 0.131
h = 0.001 0.003
y[1] (numeric) = -1.12641033766 0.024278365152
y[1] (closed_form) = -1.12641007973 0.024278757679
absolute error = 4.697e-07
relative error = 4.169e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.267
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0925 0.134
h = 0.0001 0.004
y[1] (numeric) = -1.12628264047 0.0248508223397
y[1] (closed_form) = -1.1262828316 0.0248512961364
absolute error = 5.109e-07
relative error = 4.535e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.265
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0924 0.138
h = 0.003 0.006
y[1] (numeric) = -1.12634229876 0.0255910425433
y[1] (closed_form) = -1.12634274498 0.0255912230995
absolute error = 4.814e-07
relative error = 4.273e-05 %
Correct digits = 6
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] = -2.0894 0.144
h = 0.0001 0.005
y[1] (numeric) = -1.1259100197 0.0267580577271
y[1] (closed_form) = -1.12591095834 0.0267598730626
absolute error = 2.044e-06
relative error = 0.0001815 %
Correct digits = 6
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] = -2.0893 0.149
h = 0.0001 0.003
y[1] (numeric) = -1.1259978494 0.027684686269
y[1] (closed_form) = -1.1259982831 0.0276855111889
absolute error = 9.320e-07
relative error = 8.274e-05 %
Correct digits = 6
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] = -2.0892 0.152
h = 0.001 0.001
y[1] (numeric) = -1.12604501687 0.0282406823268
y[1] (closed_form) = -1.12604501969 0.0282415637444
absolute error = 8.814e-07
relative error = 7.825e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.255
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0882 0.153
h = 0.001 0.003
y[1] (numeric) = -1.12588261106 0.0284474160367
y[1] (closed_form) = -1.12588239362 0.0284482534862
absolute error = 8.652e-07
relative error = 7.682e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.253
Order of pole (given) = 1 0
NO 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=35.4MB, alloc=40.3MB, time=0.46
x[1] = -2.0872 0.156
h = 0.0001 0.004
y[1] (numeric) = -1.1257644299 0.0290239457638
y[1] (closed_form) = -1.12576466557 0.0290248540646
absolute error = 9.384e-07
relative error = 8.333e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.251
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0871 0.16
h = 0.003 0.006
y[1] (numeric) = -1.12583712768 0.0297655173794
y[1] (closed_form) = -1.12583761257 0.029766124934
absolute error = 7.773e-07
relative error = 6.902e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.25
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0841 0.166
h = 0.0001 0.005
y[1] (numeric) = -1.12542372222 0.0309437711302
y[1] (closed_form) = -1.12542474117 0.0309460092006
absolute error = 2.459e-06
relative error = 0.0002184 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.245
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.084 0.171
h = 0.0001 0.003
y[1] (numeric) = -1.12552794216 0.0318718077378
y[1] (closed_form) = -1.12552842999 0.0318730629906
absolute error = 1.347e-06
relative error = 0.0001196 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.243
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0839 0.174
h = 0.001 0.001
y[1] (numeric) = -1.12558492369 0.0324287311502
y[1] (closed_form) = -1.12558498002 0.0324300535425
absolute error = 1.324e-06
relative error = 0.0001175 %
Correct digits = 6
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] = -2.0829 0.175
h = 0.001 0.003
y[1] (numeric) = -1.12542560366 0.0326389361573
y[1] (closed_form) = -1.12542543766 0.0326402196883
absolute error = 1.294e-06
relative error = 0.000115 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.24
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0819 0.178
h = 0.0001 0.004
y[1] (numeric) = -1.1253170807 0.0332193281953
y[1] (closed_form) = -1.1253173716 0.0332206719779
absolute error = 1.375e-06
relative error = 0.0001221 %
Correct digits = 6
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] = -2.0818 0.182
h = 0.003 0.006
y[1] (numeric) = -1.12540291073 0.0339619433733
y[1] (closed_form) = -1.12540344473 0.0339629790285
absolute error = 1.165e-06
relative error = 0.0001035 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.237
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0788 0.188
h = 0.0001 0.005
y[1] (numeric) = -1.12500873631 0.0351510325985
y[1] (closed_form) = -1.12500984613 0.0351536932711
absolute error = 2.883e-06
relative error = 0.0002561 %
Correct digits = 6
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] = -2.0787 0.193
h = 0.0001 0.003
y[1] (numeric) = -1.12512945522 0.0360800882639
y[1] (closed_form) = -1.12513000778 0.0360817745243
absolute error = 1.774e-06
relative error = 0.0001576 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.23
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0786 0.196
h = 0.001 0.001
y[1] (numeric) = -1.12519631767 0.0366377064714
y[1] (closed_form) = -1.12519643843 0.0366394705951
absolute error = 1.768e-06
relative error = 0.0001571 %
Correct digits = 6
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] = -2.0776 0.197
h = 0.0001 0.004
y[1] (numeric) = -1.12504018114 0.0368513240242
y[1] (closed_form) = -1.12504007763 0.0368530544844
absolute error = 1.734e-06
relative error = 0.000154 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.227
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0775 0.201
h = 0.003 0.006
y[1] (numeric) = -1.12513681481 0.0375945401607
y[1] (closed_form) = -1.12513752424 0.0375958458464
absolute error = 1.486e-06
relative error = 0.000132 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.226
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0745 0.207
h = 0.0001 0.005
y[1] (numeric) = -1.12475959507 0.0387923889239
y[1] (closed_form) = -1.12476091625 0.0387953133958
absolute error = 3.209e-06
relative error = 0.0002851 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.221
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0744 0.212
h = 0.0001 0.003
y[1] (numeric) = -1.12489460039 0.0397218079406
y[1] (closed_form) = -1.12489534201 0.0397237661951
absolute error = 2.094e-06
relative error = 0.000186 %
Correct digits = 6
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
x[1] = -2.0743 0.215
h = 0.001 0.001
y[1] (numeric) = -1.12497002116 0.0402797167518
y[1] (closed_form) = -1.12497033108 0.0402817621581
absolute error = 2.069e-06
relative error = 0.0001838 %
Correct digits = 6
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] = -2.0733 0.216
h = 0.001 0.003
y[1] (numeric) = -1.12481674191 0.0404961827376
y[1] (closed_form) = -1.12481682608 0.0404981990453
absolute error = 2.018e-06
relative error = 0.0001793 %
Correct digits = 6
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] = -2.0723 0.219
h = 0.0001 0.004
y[1] (numeric) = -1.12472659077 0.041083064885
y[1] (closed_form) = -1.12472713797 0.0410851212268
absolute error = 2.128e-06
relative error = 0.0001891 %
Correct digits = 6
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] = -2.0722 0.223
h = 0.003 0.006
y[1] (numeric) = -1.1248370784 0.0418266284429
y[1] (closed_form) = -1.12483785657 0.0418283633645
absolute error = 1.901e-06
relative error = 0.0001689 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.213
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0692 0.229
h = 0.0001 0.005
y[1] (numeric) = -1.12447972382 0.0430345246551
y[1] (closed_form) = -1.12448115564 0.04303787053
absolute error = 3.639e-06
relative error = 0.0003234 %
Correct digits = 5
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] = -2.0691 0.234
h = 0.0001 0.003
y[1] (numeric) = -1.12463139706 0.0439642234418
y[1] (closed_form) = -1.12463222338 0.0439666130167
absolute error = 2.528e-06
relative error = 0.0002246 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.206
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.069 0.237
h = 0.001 0.001
y[1] (numeric) = -1.12471680328 0.0445223849216
y[1] (closed_form) = -1.12471719817 0.0445248724974
absolute error = 2.519e-06
relative error = 0.0002238 %
Correct digits = 6
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] = -2.068 0.238
h = 0.001 0.003
y[1] (numeric) = -1.12456688549 0.0447421444966
y[1] (closed_form) = -1.12456705296 0.0447446083297
absolute error = 2.470e-06
relative error = 0.0002194 %
Correct digits = 6
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] = -2.067 0.241
h = 0.0001 0.004
y[1] (numeric) = -1.1244867669 0.0453322566408
y[1] (closed_form) = -1.12448740035 0.0453347494346
absolute error = 2.572e-06
relative error = 0.0002285 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.202
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0669 0.245
h = 0.003 0.006
y[1] (numeric) = -1.12461060127 0.0460759579173
y[1] (closed_form) = -1.12461145887 0.0460781223183
absolute error = 2.328e-06
relative error = 0.0002068 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.2
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0639 0.251
h = 0.0001 0.005
y[1] (numeric) = -1.12427344054 0.0472934624592
y[1] (closed_form) = -1.12427499368 0.0472972287091
absolute error = 4.074e-06
relative error = 0.000362 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.196
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0638 0.256
h = 0.0001 0.003
y[1] (numeric) = -1.12444185917 0.0482230371573
y[1] (closed_form) = -1.12444278101 0.0482258578427
absolute error = 2.967e-06
relative error = 0.0002637 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.194
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0637 0.259
h = 0.001 0.001
y[1] (numeric) = -1.12453729905 0.0487812097195
y[1] (closed_form) = -1.12453779005 0.0487841393109
absolute error = 2.970e-06
relative error = 0.0002639 %
Correct digits = 6
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
memory used=81.5MB, alloc=44.3MB, time=1.05
x[1] = -2.0627 0.26
h = 0.001 0.003
y[1] (numeric) = -1.12439083689 0.0490041950283
y[1] (closed_form) = -1.12439109896 0.0490071063133
absolute error = 2.923e-06
relative error = 0.0002597 %
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] = -2.0617 0.263
h = 0.0001 0.004
y[1] (numeric) = -1.12432087158 0.049597306839
y[1] (closed_form) = -1.12432160226 0.0496002358598
absolute error = 3.019e-06
relative error = 0.0002682 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.189
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0616 0.267
h = 0.003 0.006
y[1] (numeric) = -1.12445811189 0.0503408217656
y[1] (closed_form) = -1.12445905964 0.0503434155803
absolute error = 2.762e-06
relative error = 0.0002453 %
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] = -2.0586 0.273
h = 0.0001 0.005
y[1] (numeric) = -1.12414146275 0.051567483303
y[1] (closed_form) = -1.12414314794 0.0515716685792
absolute error = 4.512e-06
relative error = 0.0004009 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.183
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0585 0.278
h = 0.0001 0.003
y[1] (numeric) = -1.12432669286 0.052496525403
y[1] (closed_form) = -1.12432772111 0.0524997766708
absolute error = 3.410e-06
relative error = 0.000303 %
Correct digits = 6
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] = -2.0584 0.281
h = 0.001 0.001
y[1] (numeric) = -1.12443220781 0.0530544646285
y[1] (closed_form) = -1.12443280614 0.0530578357538
absolute error = 3.424e-06
relative error = 0.0003042 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 2.18
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0574 0.282
h = 0.001 0.003
y[1] (numeric) = -1.12428929403 0.0532806046549
y[1] (closed_form) = -1.12428966205 0.0532839629865
absolute error = 3.378e-06
relative error = 0.0003002 %
Correct digits = 6
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] = -2.0564 0.285
h = 0.0001 0.004
y[1] (numeric) = -1.12422959665 0.053876480907
y[1] (closed_form) = -1.12423043561 0.0538798456063
absolute error = 3.468e-06
relative error = 0.0003081 %
Correct digits = 6
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] = -2.0563 0.289
h = 0.003 0.006
y[1] (numeric) = -1.12438029294 0.0546194817774
y[1] (closed_form) = -1.12438134165 0.0546225046255
absolute error = 3.200e-06
relative error = 0.0002842 %
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] = -2.0533 0.295
h = 0.0001 0.005
y[1] (numeric) = -1.12408446175 0.0558548370035
y[1] (closed_form) = -1.12408628971 0.055859439633
absolute error = 4.952e-06
relative error = 0.00044 %
Correct digits = 5
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] = -2.0532 0.3
h = 0.0001 0.003
y[1] (numeric) = -1.1242865578 0.0567829336661
y[1] (closed_form) = -1.12428770339 0.0567866146654
absolute error = 3.855e-06
relative error = 0.0003425 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.169
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0531 0.303
h = 0.001 0.001
y[1] (numeric) = -1.12440218229 0.057340392494
y[1] (closed_form) = -1.12440289919 0.057344204339
absolute error = 3.879e-06
relative error = 0.0003445 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.168
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0521 0.304
h = 0.0001 0.004
y[1] (numeric) = -1.12426290807 0.0575696130794
y[1] (closed_form) = -1.12426339345 0.0575734177158
absolute error = 3.835e-06
relative error = 0.0003407 %
Correct digits = 5
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] = -2.052 0.308
h = 0.003 0.006
y[1] (numeric) = -1.12442463788 0.0583119267396
y[1] (closed_form) = -1.12442589681 0.0583152028372
absolute error = 3.510e-06
relative error = 0.0003117 %
Correct digits = 6
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] = -2.049 0.314
h = 0.0001 0.005
y[1] (numeric) = -1.12414705818 0.0595541325235
y[1] (closed_form) = -1.12414913212 0.0595589768098
absolute error = 5.270e-06
relative error = 0.0004681 %
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
x[1] = -2.0489 0.319
h = 0.0001 0.003
y[1] (numeric) = -1.12436368841 0.0604808801652
y[1] (closed_form) = -1.1243650584 0.0604848144349
absolute error = 4.166e-06
relative error = 0.00037 %
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] = -2.0488 0.322
h = 0.001 0.001
y[1] (numeric) = -1.12448802726 0.0610376049222
y[1] (closed_form) = -1.12448897004 0.0610416794969
absolute error = 4.182e-06
relative error = 0.0003714 %
Correct digits = 5
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] = -2.0478 0.323
h = 0.001 0.003
y[1] (numeric) = -1.12435199304 0.0612693705822
y[1] (closed_form) = -1.12435270345 0.0612734428223
absolute error = 4.134e-06
relative error = 0.0003671 %
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] = -2.0468 0.326
h = 0.0001 0.004
y[1] (numeric) = -1.12431171159 0.061869623382
y[1] (closed_form) = -1.12431289626 0.0618736804675
absolute error = 4.227e-06
relative error = 0.0003754 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.155
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0467 0.33
h = 0.003 0.006
y[1] (numeric) = -1.12448753179 0.0626106228848
y[1] (closed_form) = -1.12448891188 0.062614326327
absolute error = 3.952e-06
relative error = 0.0003509 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.154
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0437 0.336
h = 0.0001 0.005
y[1] (numeric) = -1.12423130227 0.0638606259837
y[1] (closed_form) = -1.12423353896 0.063865883507
absolute error = 5.714e-06
relative error = 0.0005074 %
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] = -2.0436 0.341
h = 0.0001 0.003
y[1] (numeric) = -1.12446486301 0.0647856493018
y[1] (closed_form) = -1.12446637075 0.0647900107159
absolute error = 4.615e-06
relative error = 0.0004097 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.147
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0435 0.344
h = 0.001 0.001
y[1] (numeric) = -1.12459935352 0.0653414273851
y[1] (closed_form) = -1.12460043592 0.065345940129
absolute error = 4.641e-06
relative error = 0.000412 %
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] = -2.0425 0.345
h = 0.001 0.003
y[1] (numeric) = -1.12446712306 0.0655761262915
y[1] (closed_form) = -1.12446797216 0.0655806424069
absolute error = 4.595e-06
relative error = 0.000408 %
Correct digits = 5
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] = -2.0415 0.348
h = 0.0001 0.004
y[1] (numeric) = -1.12443739934 0.0661784438518
y[1] (closed_form) = -1.12443872409 0.0661829330888
absolute error = 4.681e-06
relative error = 0.0004155 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.143
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0414 0.352
h = 0.003 0.006
y[1] (numeric) = -1.12462676229 0.066917973867
y[1] (closed_form) = -1.12462827447 0.0669221033502
absolute error = 4.398e-06
relative error = 0.0003903 %
Correct digits = 5
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] = -2.0384 0.358
h = 0.0001 0.005
y[1] (numeric) = -1.12439215393 0.0681752783756
y[1] (closed_form) = -1.12439456411 0.0681809465165
absolute error = 6.159e-06
relative error = 0.0005468 %
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
memory used=127.6MB, alloc=44.3MB, time=1.63
x[1] = -2.0383 0.363
h = 0.0001 0.003
y[1] (numeric) = -1.12464266506 0.0690981541679
y[1] (closed_form) = -1.12464432156 0.0691029409298
absolute error = 5.065e-06
relative error = 0.0004495 %
Correct digits = 5
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] = -2.0382 0.366
h = 0.001 0.001
y[1] (numeric) = -1.12478732101 0.0696527321693
y[1] (closed_form) = -1.12478855436 0.0696576812924
absolute error = 5.100e-06
relative error = 0.0004526 %
Correct digits = 5
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] = -2.0372 0.367
h = 0.001 0.003
y[1] (numeric) = -1.12465898038 0.069890281334
y[1] (closed_form) = -1.12465997969 0.0698952395943
absolute error = 5.058e-06
relative error = 0.0004489 %
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] = -2.0362 0.37
h = 0.0001 0.004
y[1] (numeric) = -1.12463990374 0.0704944110992
y[1] (closed_form) = -1.12464137973 0.07049933065
absolute error = 5.136e-06
relative error = 0.0004558 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.131
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0361 0.374
h = 0.003 0.006
y[1] (numeric) = -1.12484282228 0.0712321325158
y[1] (closed_form) = -1.1248444775 0.071236686406
absolute error = 4.845e-06
relative error = 0.0004299 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.13
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0331 0.38
h = 0.0001 0.005
y[1] (numeric) = -1.12463009283 0.0724962316656
y[1] (closed_form) = -1.12463268721 0.0725023074688
absolute error = 6.607e-06
relative error = 0.0005862 %
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] = -2.033 0.385
h = 0.0001 0.003
y[1] (numeric) = -1.12489756171 0.073416533753
y[1] (closed_form) = -1.12489937799 0.0734217437284
absolute error = 5.517e-06
relative error = 0.0004894 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.124
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0329 0.388
h = 0.001 0.001
y[1] (numeric) = -1.1250523894 0.0739696564313
y[1] (closed_form) = -1.12505378507 0.0739750397952
absolute error = 5.561e-06
relative error = 0.0004933 %
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] = -2.0319 0.389
h = 0.001 0.003
y[1] (numeric) = -1.1249280227 0.0742099698328
y[1] (closed_form) = -1.12492918374 0.0742153681541
absolute error = 5.522e-06
relative error = 0.0004898 %
Correct digits = 5
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] = -2.0309 0.392
h = 0.0001 0.004
y[1] (numeric) = -1.12491967543 0.074815655164
y[1] (closed_form) = -1.12492131385 0.0748210028477
absolute error = 5.593e-06
relative error = 0.0004961 %
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] = -2.0308 0.396
h = 0.003 0.006
y[1] (numeric) = -1.12513615235 0.0755512265883
y[1] (closed_form) = -1.12513796157 0.0755562029174
absolute error = 5.295e-06
relative error = 0.0004696 %
Correct digits = 5
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] = -2.0278 0.402
h = 0.0001 0.005
y[1] (numeric) = -1.12494554586 0.0768216030805
y[1] (closed_form) = -1.12494833513 0.0768280832518
absolute error = 7.055e-06
relative error = 0.0006257 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.114
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0277 0.407
h = 0.0001 0.003
y[1] (numeric) = -1.12522996715 0.0777389026869
y[1] (closed_form) = -1.12523195422 0.0777445334006
absolute error = 5.971e-06
relative error = 0.0005294 %
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
x[1] = -2.0276 0.41
h = 0.001 0.001
y[1] (numeric) = -1.12539496526 0.0782903131954
y[1] (closed_form) = -1.12539653462 0.0782961283093
absolute error = 6.023e-06
relative error = 0.0005339 %
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] = -2.0266 0.411
h = 0.0001 0.004
y[1] (numeric) = -1.12527465447 0.0785333018162
y[1] (closed_form) = -1.12527598879 0.0785391377574
absolute error = 5.987e-06
relative error = 0.0005307 %
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] = -2.0265 0.415
h = 0.003 0.006
y[1] (numeric) = -1.1255022104 0.079266838904
y[1] (closed_form) = -1.12550426286 0.0792720463091
absolute error = 5.597e-06
relative error = 0.0004961 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.109
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0235 0.421
h = 0.0001 0.005
y[1] (numeric) = -1.12533089743 0.0805419294849
y[1] (closed_form) = -1.12533396466 0.0805486236313
absolute error = 7.363e-06
relative error = 0.0006527 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.105
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0234 0.426
h = 0.0001 0.003
y[1] (numeric) = -1.12562985389 0.081456098002
y[1] (closed_form) = -1.12563209867 0.0814619577159
absolute error = 6.275e-06
relative error = 0.000556 %
Correct digits = 5
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] = -2.0233 0.429
h = 0.001 0.001
y[1] (numeric) = -1.12580357483 0.0820057070193
y[1] (closed_form) = -1.12580540479 0.0820117605506
absolute error = 6.324e-06
relative error = 0.0005603 %
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] = -2.0223 0.43
h = 0.001 0.003
y[1] (numeric) = -1.12568684955 0.0822508752393
y[1] (closed_form) = -1.12568844432 0.0822569546885
absolute error = 6.285e-06
relative error = 0.0005569 %
Correct digits = 5
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] = -2.0213 0.433
h = 0.0001 0.004
y[1] (numeric) = -1.12569867242 0.0828586291052
y[1] (closed_form) = -1.12570074476 0.082864635501
absolute error = 6.354e-06
relative error = 0.0005629 %
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] = -2.0212 0.437
h = 0.003 0.006
y[1] (numeric) = -1.12594031533 0.083589123628
y[1] (closed_form) = -1.12594254213 0.0835947487788
absolute error = 6.050e-06
relative error = 0.0005358 %
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] = -2.0182 0.443
h = 0.0001 0.005
y[1] (numeric) = -1.12579153491 0.0848694996753
y[1] (closed_form) = -1.12579481673 0.0848765910265
absolute error = 7.814e-06
relative error = 0.0006921 %
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
x[1] = -2.0181 0.448
h = 0.0001 0.003
y[1] (numeric) = -1.12610739415 0.0857798627357
y[1] (closed_form) = -1.12610983013 0.0857861375337
absolute error = 6.731e-06
relative error = 0.000596 %
Correct digits = 5
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] = -2.018 0.451
h = 0.001 0.001
y[1] (numeric) = -1.1262912593 0.0863272784252
y[1] (closed_form) = -1.12629328401 0.0863337579884
absolute error = 6.789e-06
relative error = 0.000601 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.091
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.017 0.452
h = 0.001 0.003
y[1] (numeric) = -1.12617873532 0.0865749474855
y[1] (closed_form) = -1.12618052475 0.0865814589128
absolute error = 6.753e-06
relative error = 0.0005979 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.09
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.016 0.455
h = 0.0001 0.004
y[1] (numeric) = -1.12620147921 0.0871835012673
y[1] (closed_form) = -1.12620374587 0.0871899274989
absolute error = 6.814e-06
relative error = 0.0006033 %
Correct digits = 5
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] = -2.0159 0.459
h = 0.003 0.006
y[1] (numeric) = -1.12645662737 0.087910859725
y[1] (closed_form) = -1.12645903945 0.0879168996802
absolute error = 6.504e-06
relative error = 0.0005756 %
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
memory used=173.8MB, alloc=44.3MB, time=2.21
x[1] = -2.0129 0.465
h = 0.0001 0.005
y[1] (numeric) = -1.12633058165 0.0891959760175
y[1] (closed_form) = -1.12633408859 0.0892034603015
absolute error = 8.265e-06
relative error = 0.0007315 %
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] = -2.0128 0.47
h = 0.0001 0.003
y[1] (numeric) = -1.12666330085 0.090102099794
y[1] (closed_form) = -1.12666593897 0.09010878621
absolute error = 7.188e-06
relative error = 0.000636 %
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] = -2.0127 0.473
h = 0.001 0.001
y[1] (numeric) = -1.12685728648 0.0906470621386
y[1] (closed_form) = -1.12685951722 0.0906539642185
absolute error = 7.254e-06
relative error = 0.0006416 %
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] = -2.0117 0.474
h = 0.001 0.003
y[1] (numeric) = -1.12674903905 0.0908971347288
y[1] (closed_form) = -1.12675103461 0.0909040746531
absolute error = 7.221e-06
relative error = 0.0006388 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.079
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0107 0.477
h = 0.0001 0.004
y[1] (numeric) = -1.12678275724 0.0915062180115
y[1] (closed_form) = -1.12678522932 0.0915130605438
absolute error = 7.275e-06
relative error = 0.0006436 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.078
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0106 0.481
h = 0.003 0.006
y[1] (numeric) = -1.12705137312 0.0922300933088
y[1] (closed_form) = -1.12705398138 0.0922365447816
absolute error = 6.959e-06
relative error = 0.0006154 %
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] = -2.0076 0.487
h = 0.0001 0.005
y[1] (numeric) = -1.12694824876 0.0935193955818
y[1] (closed_form) = -1.12695199127 0.0935272681825
absolute error = 8.717e-06
relative error = 0.0007708 %
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
x[1] = -2.0075 0.492
h = 0.0001 0.003
y[1] (numeric) = -1.12729777168 0.0944208452458
y[1] (closed_form) = -1.12730062284 0.0944279394634
absolute error = 7.646e-06
relative error = 0.0006759 %
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] = -2.0074 0.495
h = 0.001 0.001
y[1] (numeric) = -1.12750184599 0.0949630935779
y[1] (closed_form) = -1.12750429402 0.0949704142962
absolute error = 7.719e-06
relative error = 0.0006822 %
Correct digits = 5
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] = -2.0064 0.496
h = 0.001 0.003
y[1] (numeric) = -1.1273979478 0.0952154695811
y[1] (closed_form) = -1.12740016092 0.0952228341527
absolute error = 7.690e-06
relative error = 0.0006797 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.069
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0054 0.499
h = 0.0001 0.004
y[1] (numeric) = -1.12744268562 0.0958248088976
y[1] (closed_form) = -1.12744537418 0.0958320638384
absolute error = 7.737e-06
relative error = 0.0006838 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.067
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -2.0053 0.503
h = 0.003 0.006
y[1] (numeric) = -1.12772472089 0.0965448532556
y[1] (closed_form) = -1.1277275362 0.0965517126116
absolute error = 7.415e-06
relative error = 0.0006551 %
Correct digits = 5
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] = -2.0023 0.509
h = 0.0001 0.005
y[1] (numeric) = -1.12764468862 0.0978377786396
y[1] (closed_form) = -1.12764867705 0.097846034596
absolute error = 9.169e-06
relative error = 0.0008101 %
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] = -2.0022 0.514
h = 0.0001 0.003
y[1] (numeric) = -1.12801094541 0.0987341188073
y[1] (closed_form) = -1.12801402045 0.0987416166572
absolute error = 8.104e-06
relative error = 0.0007157 %
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] = -2.0021 0.517
h = 0.001 0.001
y[1] (numeric) = -1.12822506848 0.0992733920759
y[1] (closed_form) = -1.12822774498 0.0992811271892
absolute error = 8.185e-06
relative error = 0.0007227 %
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] = -2.0011 0.518
h = 0.0001 0.004
y[1] (numeric) = -1.12812558952 0.0995279686297
y[1] (closed_form) = -1.12812803158 0.0995357536276
absolute error = 8.159e-06
relative error = 0.0007204 %
Correct digits = 5
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] = -2.001 0.522
h = 0.003 0.006
y[1] (numeric) = -1.12841854908 0.100244600695
y[1] (closed_form) = -1.12842163796 0.100251663677
absolute error = 7.709e-06
relative error = 0.0006805 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.057
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.998 0.528
h = 0.0001 0.005
y[1] (numeric) = -1.12835855179 0.101539910239
y[1] (closed_form) = -1.12836284651 0.101548347196
absolute error = 9.467e-06
relative error = 0.0008356 %
Correct digits = 5
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] = -1.9979 0.533
h = 0.0001 0.003
y[1] (numeric) = -1.12873907819 0.10243130565
y[1] (closed_form) = -1.12874244121 0.102439002835
absolute error = 8.400e-06
relative error = 0.0007411 %
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] = -1.9978 0.536
h = 0.001 0.001
y[1] (numeric) = -1.12896177296 0.102967690051
y[1] (closed_form) = -1.12896474181 0.102975633634
absolute error = 8.480e-06
relative error = 0.000748 %
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
x[1] = -1.9968 0.537
h = 0.001 0.003
y[1] (numeric) = -1.12886617635 0.103224022625
y[1] (closed_form) = -1.12886891138 0.103232021288
absolute error = 8.453e-06
relative error = 0.0007457 %
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] = -1.9958 0.54
h = 0.0001 0.004
y[1] (numeric) = -1.12893150697 0.103832968921
y[1] (closed_form) = -1.12893471425 0.103840835135
absolute error = 8.495e-06
relative error = 0.0007493 %
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] = -1.9957 0.544
h = 0.003 0.006
y[1] (numeric) = -1.12923829114 0.104544800356
y[1] (closed_form) = -1.12924160707 0.104552263399
absolute error = 8.167e-06
relative error = 0.0007201 %
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] = -1.9927 0.55
h = 0.0001 0.005
y[1] (numeric) = -1.12920165274 0.105842662778
y[1] (closed_form) = -1.1292062123 0.105851472821
absolute error = 9.920e-06
relative error = 0.0008747 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.043
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9926 0.555
h = 0.0001 0.003
y[1] (numeric) = -1.12959874119 0.106728139874
y[1] (closed_form) = -1.12960234799 0.106736231865
absolute error = 8.859e-06
relative error = 0.0007808 %
Correct digits = 5
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] = -1.9925 0.558
h = 0.001 0.001
y[1] (numeric) = -1.12983138532 0.107261064096
y[1] (closed_form) = -1.1298346032 0.10726941307
absolute error = 8.948e-06
relative error = 0.0007884 %
Correct digits = 5
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] = -1.9915 0.559
h = 0.001 0.003
y[1] (numeric) = -1.12974032934 0.107519397988
y[1] (closed_form) = -1.12974331422 0.107527808097
absolute error = 8.924e-06
relative error = 0.0007864 %
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] = -1.9905 0.562
h = 0.0001 0.004
y[1] (numeric) = -1.12981676034 0.108127803139
y[1] (closed_form) = -1.12982021528 0.108136068514
absolute error = 8.958e-06
relative error = 0.0007893 %
Correct digits = 5
memory used=219.9MB, alloc=44.3MB, time=2.80
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] = -1.9904 0.566
h = 0.003 0.006
y[1] (numeric) = -1.13013676091 0.108834809239
y[1] (closed_form) = -1.13014031455 0.108842667706
absolute error = 8.625e-06
relative error = 0.0007596 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.037
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9874 0.572
h = 0.0001 0.005
y[1] (numeric) = -1.130123604 0.110134639899
y[1] (closed_form) = -1.13012843841 0.110143817086
absolute error = 1.037e-05
relative error = 0.0009135 %
Correct digits = 5
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] = -1.9873 0.577
h = 0.0001 0.003
y[1] (numeric) = -1.13053714501 0.111013764466
y[1] (closed_form) = -1.13054100618 0.11102224608
absolute error = 9.319e-06
relative error = 0.0008204 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.032
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9872 0.58
h = 0.001 0.001
y[1] (numeric) = -1.13077967481 0.111542968011
y[1] (closed_form) = -1.13078315267 0.111551717082
absolute error = 9.415e-06
relative error = 0.0008286 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.031
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9862 0.581
h = 0.001 0.003
y[1] (numeric) = -1.13069322108 0.111803192927
y[1] (closed_form) = -1.13069646695 0.111812009191
absolute error = 9.395e-06
relative error = 0.0008269 %
Correct digits = 5
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] = -1.9852 0.584
h = 0.0001 0.004
y[1] (numeric) = -1.1307807654 0.112410774153
y[1] (closed_form) = -1.13078447875 0.112419433407
absolute error = 9.422e-06
relative error = 0.0008291 %
Correct digits = 5
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] = -1.9851 0.588
h = 0.003 0.006
y[1] (numeric) = -1.13111389134 0.11311260812
y[1] (closed_form) = -1.13111769328 0.113120857022
absolute error = 9.083e-06
relative error = 0.000799 %
Correct digits = 5
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] = -1.9821 0.594
h = 0.0001 0.005
y[1] (numeric) = -1.13112432094 0.114413815703
y[1] (closed_form) = -1.13112944008 0.114423353747
absolute error = 1.082e-05
relative error = 0.0009521 %
Correct digits = 5
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] = -1.982 0.599
h = 0.0001 0.003
y[1] (numeric) = -1.13155419092 0.115286154823
y[1] (closed_form) = -1.13155831695 0.115295020524
absolute error = 9.779e-06
relative error = 0.0008597 %
Correct digits = 5
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
x[1] = -1.9819 0.602
h = 0.001 0.001
y[1] (numeric) = -1.13180653426 0.115811377924
y[1] (closed_form) = -1.13181028294 0.115820521431
absolute error = 9.882e-06
relative error = 0.0008686 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.021
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9809 0.603
h = 0.001 0.003
y[1] (numeric) = -1.13172474125 0.116073381113
y[1] (closed_form) = -1.13172825915 0.116082597868
absolute error = 9.865e-06
relative error = 0.0008672 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.02
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9799 0.606
h = 0.0001 0.004
y[1] (numeric) = -1.13182340306 0.116679853862
y[1] (closed_form) = -1.13182738545 0.116688901352
absolute error = 9.885e-06
relative error = 0.0008688 %
Correct digits = 5
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] = -1.9798 0.61
h = 0.003 0.006
y[1] (numeric) = -1.13216955207 0.117376170074
y[1] (closed_form) = -1.13217361278 0.117384804069
absolute error = 9.541e-06
relative error = 0.0008382 %
Correct digits = 5
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] = -1.9768 0.616
h = 0.0001 0.005
y[1] (numeric) = -1.13220365517 0.11867815715
y[1] (closed_form) = -1.13220906876 0.118688049426
absolute error = 1.128e-05
relative error = 0.0009906 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.014
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9767 0.621
h = 0.0001 0.003
y[1] (numeric) = -1.1326497164 0.119543279721
y[1] (closed_form) = -1.13265411763 0.119552523617
absolute error = 1.024e-05
relative error = 0.0008989 %
Correct digits = 5
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] = -1.9766 0.624
h = 0.001 0.001
y[1] (numeric) = -1.13291179263 0.120064263645
y[1] (closed_form) = -1.13291582285 0.120073795556
absolute error = 1.035e-05
relative error = 0.0009084 %
Correct digits = 5
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] = -1.9756 0.625
h = 0.0001 0.004
y[1] (numeric) = -1.13283471556 0.120327929987
y[1] (closed_form) = -1.13283851639 0.120337541192
absolute error = 1.034e-05
relative error = 0.0009072 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.011
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9755 0.629
h = 0.003 0.006
y[1] (numeric) = -1.1331914217 0.121019458085
y[1] (closed_form) = -1.13319578266 0.121028263255
absolute error = 9.826e-06
relative error = 0.0008622 %
Correct digits = 5
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] = -1.9725 0.635
h = 0.0001 0.005
y[1] (numeric) = -1.13324595731 0.122321350414
y[1] (closed_form) = -1.13325170083 0.122331385872
absolute error = 1.156e-05
relative error = 0.001014 %
Correct digits = 5
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] = -1.9724 0.64
h = 0.0001 0.003
y[1] (numeric) = -1.13370574134 0.123179727405
y[1] (closed_form) = -1.13371045677 0.123189135906
absolute error = 1.052e-05
relative error = 0.0009228 %
Correct digits = 5
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] = -1.9723 0.643
h = 0.001 0.001
y[1] (numeric) = -1.13397606959 0.123696741753
y[1] (closed_form) = -1.13398041984 0.123706446852
absolute error = 1.064e-05
relative error = 0.0009324 %
Correct digits = 5
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
x[1] = -1.9713 0.644
h = 0.001 0.003
y[1] (numeric) = -1.13390311138 0.123961688752
y[1] (closed_form) = -1.13390723368 0.123971478316
absolute error = 1.062e-05
relative error = 0.0009312 %
Correct digits = 5
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] = -1.9703 0.647
h = 0.0001 0.004
y[1] (numeric) = -1.1340224194 0.124565204584
y[1] (closed_form) = -1.13402699943 0.124574802237
absolute error = 1.063e-05
relative error = 0.0009322 %
Correct digits = 5
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] = -1.9702 0.651
h = 0.003 0.006
y[1] (numeric) = -1.13439241473 0.125250187699
y[1] (closed_form) = -1.13439705356 0.125259366963
absolute error = 1.028e-05
relative error = 0.0009012 %
Correct digits = 5
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] = -1.9672 0.657
h = 0.0001 0.005
y[1] (numeric) = -1.13447072924 0.126551733083
y[1] (closed_form) = -1.13447678475 0.126562109438
absolute error = 1.201e-05
relative error = 0.001052 %
Correct digits = 5
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] = -1.9671 0.662
h = 0.0001 0.003
y[1] (numeric) = -1.13494640521 0.127402100022
y[1] (closed_form) = -1.13495141467 0.127411874698
absolute error = 1.098e-05
relative error = 0.0009617 %
Correct digits = 5
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] = -1.967 0.665
h = 0.001 0.001
y[1] (numeric) = -1.13522629056 0.127914398798
y[1] (closed_form) = -1.13523094181 0.127924479979
absolute error = 1.110e-05
relative error = 0.0009718 %
Correct digits = 5
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
memory used=266.0MB, alloc=44.3MB, time=3.38
x[1] = -1.966 0.666
h = 0.001 0.003
y[1] (numeric) = -1.13515814049 0.12818078821
y[1] (closed_form) = -1.13516256556 0.128190959862
absolute error = 1.109e-05
relative error = 0.000971 %
Correct digits = 5
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] = -1.965 0.669
h = 0.0001 0.004
y[1] (numeric) = -1.13528852476 0.128782374757
y[1] (closed_form) = -1.13529340344 0.128792342394
absolute error = 1.110e-05
relative error = 0.0009713 %
Correct digits = 5
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] = -1.9649 0.673
h = 0.003 0.006
y[1] (numeric) = -1.13567118362 0.1294608633
y[1] (closed_form) = -1.13567611044 0.129470410312
absolute error = 1.074e-05
relative error = 0.0009399 %
Correct digits = 5
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
x[1] = -1.9619 0.679
h = 0.0001 0.005
y[1] (numeric) = -1.13577331041 0.130761450377
y[1] (closed_form) = -1.13577968711 0.13077216005
absolute error = 1.246e-05
relative error = 0.00109 %
Correct digits = 5
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] = -1.9618 0.684
h = 0.0001 0.003
y[1] (numeric) = -1.13626469977 0.13160338447
y[1] (closed_form) = -1.13627001318 0.131613518425
absolute error = 1.144e-05
relative error = 0.001 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.987
Order of pole (given) = 1 0
NO POLE (ratio test) 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 0.687
h = 0.001 0.001
y[1] (numeric) = -1.13655403711 0.132110713776
y[1] (closed_form) = -1.13655899964 0.132121163963
absolute error = 1.157e-05
relative error = 0.001011 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.987
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9607 0.688
h = 0.001 0.003
y[1] (numeric) = -1.1364907404 0.132378424299
y[1] (closed_form) = -1.13649547872 0.132388970933
absolute error = 1.156e-05
relative error = 0.001011 %
Correct digits = 5
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] = -1.9597 0.691
h = 0.0001 0.004
y[1] (numeric) = -1.13663216993 0.132977793165
y[1] (closed_form) = -1.13663735732 0.13298812376
absolute error = 1.156e-05
relative error = 0.00101 %
Correct digits = 5
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] = -1.9596 0.695
h = 0.003 0.006
y[1] (numeric) = -1.13702734602 0.133649450174
y[1] (closed_form) = -1.13703257077 0.133659358241
absolute error = 1.120e-05
relative error = 0.0009784 %
Correct digits = 5
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] = -1.9566 0.701
h = 0.0001 0.005
y[1] (numeric) = -1.13715329904 0.134948463883
y[1] (closed_form) = -1.13716000591 0.134959498969
absolute error = 1.291e-05
relative error = 0.001128 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.979
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9565 0.706
h = 0.0001 0.003
y[1] (numeric) = -1.13766020893 0.135781546249
y[1] (closed_form) = -1.13766583605 0.135792032242
absolute error = 1.190e-05
relative error = 0.001039 %
Correct digits = 5
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] = -1.9564 0.709
h = 0.001 0.001
y[1] (numeric) = -1.13795888459 0.136283654484
y[1] (closed_form) = -1.13796416848 0.136294466241
absolute error = 1.203e-05
relative error = 0.00105 %
Correct digits = 5
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] = -1.9554 0.71
h = 0.001 0.003
y[1] (numeric) = -1.13790048275 0.136552562858
y[1] (closed_form) = -1.13790554459 0.136563476998
absolute error = 1.203e-05
relative error = 0.00105 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.977
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9544 0.713
h = 0.0001 0.004
y[1] (numeric) = -1.13805291715 0.137149425419
y[1] (closed_form) = -1.13805842313 0.137160111593
absolute error = 1.202e-05
relative error = 0.001049 %
Correct digits = 5
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] = -1.9543 0.717
h = 0.003 0.006
y[1] (numeric) = -1.13846045272 0.137813917219
y[1] (closed_form) = -1.13846598519 0.1378241793
absolute error = 1.166e-05
relative error = 0.001017 %
Correct digits = 5
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] = -1.9513 0.723
h = 0.0001 0.005
y[1] (numeric) = -1.13861022621 0.139110739492
y[1] (closed_form) = -1.13861727202 0.139122091765
absolute error = 1.336e-05
relative error = 0.001165 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.971
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9512 0.728
h = 0.0001 0.003
y[1] (numeric) = -1.13913244949 0.139934555737
y[1] (closed_form) = -1.13913839986 0.139945386182
absolute error = 1.236e-05
relative error = 0.001077 %
Correct digits = 5
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] = -1.9511 0.731
h = 0.001 0.001
y[1] (numeric) = -1.13944034119 0.140431193939
y[1] (closed_form) = -1.13944595634 0.140442359471
absolute error = 1.250e-05
relative error = 0.001089 %
Correct digits = 5
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] = -1.9501 0.732
h = 0.0001 0.004
y[1] (numeric) = -1.13938687192 0.14070117506
y[1] (closed_form) = -1.1393922674 0.140712448866
absolute error = 1.250e-05
relative error = 0.001089 %
Correct digits = 5
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] = -1.95 0.736
h = 0.003 0.006
y[1] (numeric) = -1.13980437819 0.141359542968
y[1] (closed_form) = -1.1398102329 0.141369939254
absolute error = 1.193e-05
relative error = 0.001039 %
Correct digits = 5
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] = -1.947 0.742
h = 0.0001 0.005
y[1] (numeric) = -1.1399745995 0.142653698944
y[1] (closed_form) = -1.13998199312 0.142665152439
absolute error = 1.363e-05
relative error = 0.001187 %
Correct digits = 5
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] = -1.9469 0.747
h = 0.0001 0.003
y[1] (numeric) = -1.14050971024 0.143469032452
y[1] (closed_form) = -1.14051599594 0.143479988255
absolute error = 1.263e-05
relative error = 0.001099 %
Correct digits = 5
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] = -1.9468 0.75
h = 0.001 0.001
y[1] (numeric) = -1.14082536123 0.143960657501
y[1] (closed_form) = -1.14083131897 0.143971956136
absolute error = 1.277e-05
relative error = 0.001111 %
Correct digits = 5
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] = -1.9458 0.751
h = 0.001 0.003
y[1] (numeric) = -1.14077617568 0.144231401222
y[1] (closed_form) = -1.14078191601 0.144242813126
absolute error = 1.277e-05
relative error = 0.001111 %
Correct digits = 5
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] = -1.9448 0.754
h = 0.0001 0.004
y[1] (numeric) = -1.14094890962 0.144822703149
y[1] (closed_form) = -1.14095508367 0.144833865272
absolute error = 1.276e-05
relative error = 0.001109 %
Correct digits = 5
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] = -1.9447 0.758
h = 0.0001 0.004
y[1] (numeric) = -1.14137888985 0.14547284499
y[1] (closed_form) = -1.14138506988 0.145483581169
absolute error = 1.239e-05
relative error = 0.001077 %
Correct digits = 5
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] = -1.9446 0.762
h = 0.003 0.006
y[1] (numeric) = -1.14181063884 0.146120743037
y[1] (closed_form) = -1.14181681888 0.146131479217
absolute error = 1.239e-05
relative error = 0.001076 %
Correct digits = 5
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] = -1.9416 0.768
h = 0.0001 0.005
y[1] (numeric) = -1.14200856921 0.147410031738
y[1] (closed_form) = -1.14201632078 0.147421778287
absolute error = 1.407e-05
relative error = 0.001222 %
Correct digits = 5
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=312.1MB, alloc=44.3MB, time=3.97
x[1] = -1.9415 0.773
h = 0.0001 0.003
y[1] (numeric) = -1.14256073222 0.148213026064
y[1] (closed_form) = -1.14256736046 0.148224308766
absolute error = 1.309e-05
relative error = 0.001136 %
Correct digits = 5
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] = -1.9414 0.776
h = 0.001 0.001
y[1] (numeric) = -1.14288665535 0.148697350557
y[1] (closed_form) = -1.1428929661 0.148708986163
absolute error = 1.324e-05
relative error = 0.001149 %
Correct digits = 5
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] = -1.9404 0.777
h = 0.001 0.003
y[1] (numeric) = -1.1428433538 0.148968874971
y[1] (closed_form) = -1.14284945059 0.148980630512
absolute error = 1.324e-05
relative error = 0.001149 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.953
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9394 0.78
h = 0.0001 0.004
y[1] (numeric) = -1.14302865574 0.149555843267
y[1] (closed_form) = -1.14303517864 0.149567335724
absolute error = 1.321e-05
relative error = 0.001146 %
Correct digits = 5
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] = -1.9393 0.784
h = 0.003 0.006
y[1] (numeric) = -1.14347219638 0.15019602406
y[1] (closed_form) = -1.14347871221 0.150207090372
absolute error = 1.284e-05
relative error = 0.001114 %
Correct digits = 5
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] = -1.9363 0.79
h = 0.0001 0.005
y[1] (numeric) = -1.14369377575 0.151481239212
y[1] (closed_form) = -1.14370189086 0.151493275713
absolute error = 1.452e-05
relative error = 0.001258 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.948
Order of pole (given) = 1 0
NO POLE (ratio test) 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 0.795
h = 0.0001 0.003
y[1] (numeric) = -1.14426051748 0.152273756359
y[1] (closed_form) = -1.14426749622 0.152285358017
absolute error = 1.354e-05
relative error = 0.001173 %
Correct digits = 5
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] = -1.9361 0.798
h = 0.001 0.001
y[1] (numeric) = -1.14459522199 0.152751882768
y[1] (closed_form) = -1.14460189221 0.152763845911
absolute error = 1.370e-05
relative error = 0.001186 %
Correct digits = 5
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] = -1.9351 0.799
h = 0.001 0.003
y[1] (numeric) = -1.14455693664 0.153024089352
y[1] (closed_form) = -1.14456339588 0.15303617812
absolute error = 1.371e-05
relative error = 0.001187 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.946
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9341 0.802
h = 0.0001 0.004
y[1] (numeric) = -1.14475296962 0.1536073963
y[1] (closed_form) = -1.1447598484 0.15361921063
absolute error = 1.367e-05
relative error = 0.001184 %
Correct digits = 5
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] = -1.934 0.806
h = 0.003 0.006
y[1] (numeric) = -1.14520810274 0.154239119052
y[1] (closed_form) = -1.14521496329 0.154250507112
absolute error = 1.329e-05
relative error = 0.001151 %
Correct digits = 5
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] = -1.931 0.812
h = 0.0001 0.005
y[1] (numeric) = -1.14545324317 0.155519639007
y[1] (closed_form) = -1.14546172952 0.155531956022
absolute error = 1.496e-05
relative error = 0.001294 %
Correct digits = 5
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
x[1] = -1.9309 0.817
h = 0.0001 0.003
y[1] (numeric) = -1.14603429981 0.156301289346
y[1] (closed_form) = -1.14604163766 0.156313201053
absolute error = 1.399e-05
relative error = 0.00121 %
Correct digits = 5
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
x[1] = -1.9308 0.82
h = 0.001 0.001
y[1] (numeric) = -1.14637762945 0.156772983355
y[1] (closed_form) = -1.14638466808 0.156785264857
absolute error = 1.416e-05
relative error = 0.001223 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.939
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9298 0.821
h = 0.001 0.003
y[1] (numeric) = -1.14634438158 0.15704574116
y[1] (closed_form) = -1.14635121239 0.157058153897
absolute error = 1.417e-05
relative error = 0.001224 %
Correct digits = 5
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] = -1.9288 0.824
h = 0.0001 0.004
y[1] (numeric) = -1.14655105691 0.157625103016
y[1] (closed_form) = -1.14655830031 0.157637230142
absolute error = 1.413e-05
relative error = 0.001221 %
Correct digits = 5
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] = -1.9287 0.828
h = 0.003 0.006
y[1] (numeric) = -1.14701756822 0.158248058257
y[1] (closed_form) = -1.14702478218 0.158259759357
absolute error = 1.375e-05
relative error = 0.001187 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.936
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9257 0.834
h = 0.0001 0.005
y[1] (numeric) = -1.1472861609 0.159523262224
y[1] (closed_form) = -1.1472950259 0.159535850034
absolute error = 1.540e-05
relative error = 0.001329 %
Correct digits = 5
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] = -1.9256 0.839
h = 0.0001 0.003
y[1] (numeric) = -1.1478812549 0.160293663611
y[1] (closed_form) = -1.14788896021 0.160305876142
absolute error = 1.444e-05
relative error = 0.001246 %
Correct digits = 5
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] = -1.9255 0.842
h = 0.001 0.001
y[1] (numeric) = -1.14823304513 0.160758695335
y[1] (closed_form) = -1.14824046082 0.16077128569
absolute error = 1.461e-05
relative error = 0.00126 %
Correct digits = 5
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] = -1.9245 0.843
h = 0.001 0.003
y[1] (numeric) = -1.14820485171 0.161031872289
y[1] (closed_form) = -1.14821206295 0.161044599401
absolute error = 1.463e-05
relative error = 0.001262 %
Correct digits = 5
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] = -1.9235 0.846
h = 0.0001 0.004
y[1] (numeric) = -1.14842207103 0.161607007351
y[1] (closed_form) = -1.14842968751 0.161619437875
absolute error = 1.458e-05
relative error = 0.001257 %
Correct digits = 5
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] = -1.9234 0.85
h = 0.003 0.006
y[1] (numeric) = -1.14889973526 0.162220891759
y[1] (closed_form) = -1.14890731107 0.162232896877
absolute error = 1.420e-05
relative error = 0.001223 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.929
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9204 0.856
h = 0.0001 0.005
y[1] (numeric) = -1.1491916504 0.16349016064
y[1] (closed_form) = -1.14920090115 0.163503009254
absolute error = 1.583e-05
relative error = 0.001364 %
Correct digits = 5
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] = -1.9203 0.861
h = 0.0001 0.003
y[1] (numeric) = -1.14980049058 0.164248939019
y[1] (closed_form) = -1.14980857142 0.164261442847
absolute error = 1.489e-05
relative error = 0.001282 %
Correct digits = 5
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] = -1.9202 0.864
h = 0.001 0.001
y[1] (numeric) = -1.15016056871 0.164707083377
y[1] (closed_form) = -1.15016836982 0.164719972758
absolute error = 1.507e-05
relative error = 0.001297 %
Correct digits = 5
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] = -1.9192 0.865
h = 0.0001 0.004
y[1] (numeric) = -1.15013744238 0.164980546448
y[1] (closed_form) = -1.15014504261 0.164993578011
absolute error = 1.509e-05
relative error = 0.001298 %
Correct digits = 5
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
memory used=358.3MB, alloc=44.3MB, time=4.57
x[1] = -1.9191 0.869
h = 0.003 0.006
y[1] (numeric) = -1.15062403794 0.165586775113
y[1] (closed_form) = -1.15063195509 0.165598863273
absolute error = 1.445e-05
relative error = 0.001243 %
Correct digits = 5
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] = -1.9161 0.875
h = 0.0001 0.005
y[1] (numeric) = -1.15093582756 0.166850166116
y[1] (closed_form) = -1.15094543858 0.166863059573
absolute error = 1.608e-05
relative error = 0.001383 %
Correct digits = 5
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] = -1.916 0.88
h = 0.0001 0.003
y[1] (numeric) = -1.15155611227 0.167598488117
y[1] (closed_form) = -1.15156454575 0.167611063483
absolute error = 1.514e-05
relative error = 0.001301 %
Correct digits = 5
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] = -1.9159 0.883
h = 0.001 0.001
y[1] (numeric) = -1.15192309432 0.168050431977
y[1] (closed_form) = -1.15193125692 0.168063399179
absolute error = 1.532e-05
relative error = 0.001316 %
Correct digits = 5
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] = -1.9149 0.884
h = 0.001 0.003
y[1] (numeric) = -1.15190433755 0.16832397371
y[1] (closed_form) = -1.15191230255 0.168337087633
absolute error = 1.534e-05
relative error = 0.001318 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.918
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9139 0.887
h = 0.0001 0.004
y[1] (numeric) = -1.15214082357 0.168890380223
y[1] (closed_form) = -1.15214917897 0.168903177817
absolute error = 1.528e-05
relative error = 0.001313 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.917
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9138 0.891
h = 0.003 0.006
y[1] (numeric) = -1.15263848811 0.169486475698
y[1] (closed_form) = -1.15264678194 0.169498850179
absolute error = 1.490e-05
relative error = 0.001279 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.917
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9108 0.897
h = 0.0001 0.005
y[1] (numeric) = -1.15297329522 0.170742789206
y[1] (closed_form) = -1.15298330421 0.170755924109
absolute error = 1.651e-05
relative error = 0.001417 %
Correct digits = 5
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] = -1.9107 0.902
h = 0.0001 0.003
y[1] (numeric) = -1.15360674471 0.171478819633
y[1] (closed_form) = -1.15361556782 0.171491667692
absolute error = 1.559e-05
relative error = 0.001336 %
Correct digits = 5
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] = -1.9106 0.905
h = 0.001 0.001
y[1] (numeric) = -1.15398166952 0.17192347361
y[1] (closed_form) = -1.15399023216 0.171936720639
absolute error = 1.577e-05
relative error = 0.001352 %
Correct digits = 5
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] = -1.9096 0.906
h = 0.001 0.003
y[1] (numeric) = -1.1539679899 0.172197051919
y[1] (closed_form) = -1.15397635886 0.172210450888
absolute error = 1.580e-05
relative error = 0.001354 %
Correct digits = 5
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] = -1.9086 0.909
h = 0.0001 0.004
y[1] (numeric) = -1.15421468176 0.172758442215
y[1] (closed_form) = -1.15422343267 0.172771514544
absolute error = 1.573e-05
relative error = 0.001348 %
Correct digits = 5
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] = -1.9085 0.913
h = 0.003 0.006
y[1] (numeric) = -1.15472279245 0.173344640546
y[1] (closed_form) = -1.15473147059 0.173357291471
absolute error = 1.534e-05
relative error = 0.001314 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.91
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.9055 0.919
h = 0.0001 0.005
y[1] (numeric) = -1.15508042688 0.174593267336
y[1] (closed_form) = -1.15509083997 0.174606632983
absolute error = 1.694e-05
relative error = 0.00145 %
Correct digits = 5
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] = -1.9054 0.924
h = 0.0001 0.003
y[1] (numeric) = -1.15572671255 0.175316658798
y[1] (closed_form) = -1.15573593247 0.175329769199
absolute error = 1.603e-05
relative error = 0.001371 %
Correct digits = 5
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] = -1.9053 0.927
h = 0.001 0.001
y[1] (numeric) = -1.15610938492 0.175753813652
y[1] (closed_form) = -1.15611835506 0.175767329819
absolute error = 1.622e-05
relative error = 0.001387 %
Correct digits = 5
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] = -1.9043 0.928
h = 0.001 0.003
y[1] (numeric) = -1.15610078224 0.176027293762
y[1] (closed_form) = -1.1561095628 0.176040966967
absolute error = 1.625e-05
relative error = 0.00139 %
Correct digits = 5
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] = -1.9033 0.931
h = 0.0001 0.004
y[1] (numeric) = -1.15635754435 0.176583397969
y[1] (closed_form) = -1.15636669805 0.176596734488
absolute error = 1.618e-05
relative error = 0.001383 %
Correct digits = 5
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
x[1] = -1.9032 0.935
h = 0.003 0.006
y[1] (numeric) = -1.15687583545 0.177159424261
y[1] (closed_form) = -1.15688490518 0.17717234147
absolute error = 1.578e-05
relative error = 0.001349 %
Correct digits = 5
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] = -1.9002 0.941
h = 0.0001 0.005
y[1] (numeric) = -1.15725608589 0.178399760196
y[1] (closed_form) = -1.15726690887 0.178413345653
absolute error = 1.737e-05
relative error = 0.001483 %
Correct digits = 5
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] = -1.9001 0.946
h = 0.0001 0.003
y[1] (numeric) = -1.15791486657 0.179110175729
y[1] (closed_form) = -1.15792449014 0.179123537856
absolute error = 1.647e-05
relative error = 0.001405 %
Correct digits = 5
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] = -1.9 0.949
h = 0.001 0.001
y[1] (numeric) = -1.15830508377 0.179539628422
y[1] (closed_form) = -1.15831446851 0.179553402759
absolute error = 1.667e-05
relative error = 0.001422 %
Correct digits = 5
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] = -1.899 0.95
h = 0.001 0.003
y[1] (numeric) = -1.15830155322 0.179812875282
y[1] (closed_form) = -1.15831075266 0.179826811626
absolute error = 1.670e-05
relative error = 0.001425 %
Correct digits = 5
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] = -1.898 0.953
h = 0.0001 0.004
y[1] (numeric) = -1.15856824051 0.18036342758
y[1] (closed_form) = -1.15857780391 0.180377017473
absolute error = 1.662e-05
relative error = 0.001417 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.899
Order of pole (given) = 1 0
NO POLE (ratio test) 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 0.957
h = 0.003 0.006
y[1] (numeric) = -1.15909643632 0.180929015437
y[1] (closed_form) = -1.15910590462 0.1809421885
absolute error = 1.622e-05
relative error = 0.001383 %
Correct digits = 5
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] = -1.8949 0.963
h = 0.0001 0.005
y[1] (numeric) = -1.15949907042 0.182160462377
y[1] (closed_form) = -1.1595103087 0.182174256501
absolute error = 1.779e-05
relative error = 0.001516 %
Correct digits = 5
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] = -1.8948 0.968
h = 0.0001 0.003
y[1] (numeric) = -1.16016999274 0.182857576042
y[1] (closed_form) = -1.16018002647 0.182871179022
absolute error = 1.690e-05
relative error = 0.001439 %
Correct digits = 5
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] = -1.8947 0.971
h = 0.001 0.001
y[1] (numeric) = -1.16056754471 0.183279130095
y[1] (closed_form) = -1.16057735078 0.183293151366
absolute error = 1.711e-05
relative error = 0.001456 %
Correct digits = 5
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
memory used=404.6MB, alloc=44.3MB, time=5.16
x[1] = -1.8937 0.972
h = 0.0001 0.004
y[1] (numeric) = -1.16056907685 0.183552008566
y[1] (closed_form) = -1.16057870209 0.183566196673
absolute error = 1.714e-05
relative error = 0.001459 %
Correct digits = 5
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] = -1.8936 0.976
h = 0.003 0.006
y[1] (numeric) = -1.16110514449 0.184108853343
y[1] (closed_form) = -1.16111496231 0.184122065397
absolute error = 1.646e-05
relative error = 0.0014 %
Correct digits = 5
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] = -1.8906 0.982
h = 0.0001 0.005
y[1] (numeric) = -1.1615267282 0.185331912742
y[1] (closed_form) = -1.16153832855 0.18534570454
absolute error = 1.802e-05
relative error = 0.001532 %
Correct digits = 5
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] = -1.8905 0.987
h = 0.0001 0.003
y[1] (numeric) = -1.16220764612 0.186017185761
y[1] (closed_form) = -1.16221803877 0.186030814348
absolute error = 1.714e-05
relative error = 0.001456 %
Correct digits = 5
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] = -1.8904 0.99
h = 0.001 0.001
y[1] (numeric) = -1.16261124082 0.186431705023
y[1] (closed_form) = -1.16262141567 0.186445756698
absolute error = 1.735e-05
relative error = 0.001473 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.89
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8894 0.991
h = 0.001 0.003
y[1] (numeric) = -1.16261711305 0.186704098193
y[1] (closed_form) = -1.16262711111 0.186718320687
absolute error = 1.739e-05
relative error = 0.001476 %
Correct digits = 5
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] = -1.8884 0.994
h = 0.0001 0.004
y[1] (numeric) = -1.16290177724 0.18724351412
y[1] (closed_form) = -1.16291212115 0.187257372917
absolute error = 1.729e-05
relative error = 0.001468 %
Correct digits = 5
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] = -1.8883 0.998
h = 0.003 0.006
y[1] (numeric) = -1.16344750544 0.187788890738
y[1] (closed_form) = -1.16345773376 0.187802338483
absolute error = 1.690e-05
relative error = 0.001434 %
Correct digits = 5
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] = -1.8853 1.004
h = 0.0001 0.005
y[1] (numeric) = -1.16389097792 0.189001970618
y[1] (closed_form) = -1.1639030025 0.189015949777
absolute error = 1.844e-05
relative error = 0.001564 %
Correct digits = 5
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] = -1.8852 1.009
h = 0.0001 0.003
y[1] (numeric) = -1.16458334529 0.189673371131
y[1] (closed_form) = -1.16459415908 0.189687219638
absolute error = 1.757e-05
relative error = 0.001489 %
Correct digits = 5
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] = -1.8851 1.012
h = 0.001 0.001
y[1] (numeric) = -1.164993863 0.190079647497
y[1] (closed_form) = -1.16500447058 0.19009392446
absolute error = 1.779e-05
relative error = 0.001507 %
Correct digits = 5
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] = -1.8841 1.013
h = 0.001 0.003
y[1] (numeric) = -1.16500476632 0.190351421499
y[1] (closed_form) = -1.16501520188 0.190365873829
absolute error = 1.783e-05
relative error = 0.00151 %
Correct digits = 5
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] = -1.8831 1.016
h = 0.0001 0.004
y[1] (numeric) = -1.16529888636 0.190884553325
y[1] (closed_form) = -1.16530965762 0.190898633095
absolute error = 1.773e-05
relative error = 0.001501 %
Correct digits = 5
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
x[1] = -1.883 1.02
h = 0.003 0.006
y[1] (numeric) = -1.16585367565 0.19141878418
y[1] (closed_form) = -1.16586432044 0.191432456482
absolute error = 1.733e-05
relative error = 0.001467 %
Correct digits = 5
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
x[1] = -1.88 1.026
h = 0.0001 0.005
y[1] (numeric) = -1.16631874524 0.192621308907
y[1] (closed_form) = -1.16633119835 0.192635463761
absolute error = 1.885e-05
relative error = 0.001595 %
Correct digits = 5
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] = -1.8799 1.031
h = 0.0001 0.003
y[1] (numeric) = -1.16702217619 0.193278545812
y[1] (closed_form) = -1.16703341656 0.193292602716
absolute error = 1.800e-05
relative error = 0.001522 %
Correct digits = 5
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] = -1.8798 1.034
h = 0.001 0.001
y[1] (numeric) = -1.1674393873 0.193676403547
y[1] (closed_form) = -1.16745043324 0.193690893877
absolute error = 1.822e-05
relative error = 0.00154 %
Correct digits = 5
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] = -1.8788 1.035
h = 0.001 0.003
y[1] (numeric) = -1.16745529886 0.19394742414
y[1] (closed_form) = -1.16746617772 0.193962094222
absolute error = 1.826e-05
relative error = 0.001543 %
Correct digits = 5
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] = -1.8778 1.038
h = 0.0001 0.004
y[1] (numeric) = -1.16775869433 0.194474025757
y[1] (closed_form) = -1.16776989843 0.194488314761
absolute error = 1.816e-05
relative error = 0.001534 %
Correct digits = 5
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] = -1.8777 1.042
h = 0.003 0.006
y[1] (numeric) = -1.16832223379 0.194996881702
y[1] (closed_form) = -1.16833330063 0.195010767206
absolute error = 1.776e-05
relative error = 0.001499 %
Correct digits = 5
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] = -1.8747 1.048
h = 0.0001 0.005
y[1] (numeric) = -1.1688085885 0.196188285214
y[1] (closed_form) = -1.16882147403 0.196202603946
absolute error = 1.926e-05
relative error = 0.001625 %
Correct digits = 5
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] = -1.8746 1.053
h = 0.0001 0.003
y[1] (numeric) = -1.16952268666 0.1968310806
y[1] (closed_form) = -1.16953435864 0.196845334176
absolute error = 1.842e-05
relative error = 0.001553 %
Correct digits = 5
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] = -1.8745 1.056
h = 0.001 0.001
y[1] (numeric) = -1.16994635524 0.197220351828
y[1] (closed_form) = -1.16995784475 0.197235043392
absolute error = 1.865e-05
relative error = 0.001572 %
Correct digits = 5
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] = -1.8735 1.057
h = 0.001 0.003
y[1] (numeric) = -1.16996724749 0.197490485455
y[1] (closed_form) = -1.16997857502 0.197505360987
absolute error = 1.870e-05
relative error = 0.001576 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.874
Order of pole (given) = 1 0
NO POLE (ratio test) 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 1.06
h = 0.0001 0.004
y[1] (numeric) = -1.17027972923 0.19801031685
y[1] (closed_form) = -1.17029137123 0.198024803146
absolute error = 1.858e-05
relative error = 0.001566 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.873
Order of pole (given) = 1 0
NO POLE (ratio test) 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 1.064
h = 0.003 0.006
y[1] (numeric) = -1.17085169969 0.198521579422
y[1] (closed_form) = -1.17086319378 0.198535666566
absolute error = 1.818e-05
relative error = 0.001531 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.873
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8694 1.07
h = 0.0001 0.005
y[1] (numeric) = -1.17135900752 0.199701306156
y[1] (closed_form) = -1.17137232895 0.199715776813
absolute error = 1.967e-05
relative error = 0.001655 %
Correct digits = 5
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] = -1.8693 1.075
h = 0.0001 0.003
y[1] (numeric) = -1.17208336654 0.200329395823
y[1] (closed_form) = -1.17209547476 0.200343834163
absolute error = 1.884e-05
relative error = 0.001585 %
Correct digits = 5
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
memory used=450.8MB, alloc=44.3MB, time=5.76
x[1] = -1.8692 1.078
h = 0.001 0.001
y[1] (numeric) = -1.17251325062 0.200709920837
y[1] (closed_form) = -1.1725251885 0.200724801309
absolute error = 1.908e-05
relative error = 0.001604 %
Correct digits = 5
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] = -1.8682 1.079
h = 0.0001 0.004
y[1] (numeric) = -1.17253909133 0.200979034836
y[1] (closed_form) = -1.17255087249 0.200994103314
absolute error = 1.913e-05
relative error = 0.001608 %
Correct digits = 5
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
x[1] = -1.8681 1.083
h = 0.003 0.006
y[1] (numeric) = -1.17311769568 0.201480649279
y[1] (closed_form) = -1.17312954016 0.201494730124
absolute error = 1.840e-05
relative error = 0.001546 %
Correct digits = 5
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
x[1] = -1.8651 1.089
h = 0.0001 0.005
y[1] (numeric) = -1.17364261053 0.202649644999
y[1] (closed_form) = -1.17365628779 0.202664066232
absolute error = 1.988e-05
relative error = 0.001669 %
Correct digits = 5
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] = -1.865 1.094
h = 0.0001 0.003
y[1] (numeric) = -1.17437528994 0.203264760279
y[1] (closed_form) = -1.1743877556 0.203279177436
absolute error = 1.906e-05
relative error = 0.001599 %
Correct digits = 5
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] = -1.8649 1.097
h = 0.001 0.001
y[1] (numeric) = -1.1748102194 0.203637565405
y[1] (closed_form) = -1.17482252533 0.203652427772
absolute error = 1.930e-05
relative error = 0.001618 %
Correct digits = 5
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] = -1.8639 1.098
h = 0.001 0.003
y[1] (numeric) = -1.17484027592 0.203905638009
y[1] (closed_form) = -1.1748524298 0.203920691646
absolute error = 1.935e-05
relative error = 0.001623 %
Correct digits = 5
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] = -1.8629 1.101
h = 0.0001 0.004
y[1] (numeric) = -1.17516904557 0.204412152836
y[1] (closed_form) = -1.17518149302 0.204426803203
absolute error = 1.922e-05
relative error = 0.001612 %
Correct digits = 5
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] = -1.8628 1.105
h = 0.003 0.006
y[1] (numeric) = -1.17575568446 0.204901208585
y[1] (closed_form) = -1.17576796466 0.204915469009
absolute error = 1.882e-05
relative error = 0.001577 %
Correct digits = 5
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] = -1.8598 1.111
h = 0.0001 0.005
y[1] (numeric) = -1.17630087644 0.206057529332
y[1] (closed_form) = -1.1763149948 0.206072079922
absolute error = 2.027e-05
relative error = 0.001698 %
Correct digits = 5
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] = -1.8597 1.116
h = 0.0001 0.003
y[1] (numeric) = -1.17704303317 0.206657490551
y[1] (closed_form) = -1.17705594243 0.206672069837
absolute error = 1.947e-05
relative error = 0.001629 %
Correct digits = 5
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] = -1.8596 1.119
h = 0.001 0.001
y[1] (numeric) = -1.1774837114 0.207021278082
y[1] (closed_form) = -1.17749647331 0.207036305919
absolute error = 1.972e-05
relative error = 0.001649 %
Correct digits = 5
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] = -1.8586 1.12
h = 0.001 0.003
y[1] (numeric) = -1.17751864244 0.207288087813
y[1] (closed_form) = -1.17753125781 0.207303310607
absolute error = 1.977e-05
relative error = 0.001654 %
Correct digits = 5
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] = -1.8576 1.123
h = 0.0001 0.004
y[1] (numeric) = -1.17785590847 0.207787185649
y[1] (closed_form) = -1.17786880584 0.207801998129
absolute error = 1.964e-05
relative error = 0.001642 %
Correct digits = 5
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] = -1.8575 1.127
h = 0.003 0.006
y[1] (numeric) = -1.17845002149 0.208264089724
y[1] (closed_form) = -1.17846274146 0.208278517668
absolute error = 1.923e-05
relative error = 0.001607 %
Correct digits = 5
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] = -1.8545 1.133
h = 0.0001 0.005
y[1] (numeric) = -1.17901510376 0.209407215226
y[1] (closed_form) = -1.17902966547 0.209421882938
absolute error = 2.067e-05
relative error = 0.001726 %
Correct digits = 5
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] = -1.8544 1.138
h = 0.0001 0.003
y[1] (numeric) = -1.17976630623 0.209991800161
y[1] (closed_form) = -1.1797796625 0.21000652924
absolute error = 1.988e-05
relative error = 0.001659 %
Correct digits = 5
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] = -1.8543 1.141
h = 0.001 0.001
y[1] (numeric) = -1.18021247607 0.210346435418
y[1] (closed_form) = -1.18022569749 0.210361615948
absolute error = 2.013e-05
relative error = 0.001679 %
Correct digits = 5
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] = -1.8533 1.142
h = 0.001 0.003
y[1] (numeric) = -1.18025223611 0.210611853382
y[1] (closed_form) = -1.18026531663 0.210627232359
absolute error = 2.019e-05
relative error = 0.001684 %
Correct digits = 5
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] = -1.8523 1.145
h = 0.0001 0.004
y[1] (numeric) = -1.18059777803 0.211103321584
y[1] (closed_form) = -1.18061112874 0.211118283619
absolute error = 2.005e-05
relative error = 0.001672 %
Correct digits = 5
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] = -1.8522 1.149
h = 0.003 0.006
y[1] (numeric) = -1.18119901855 0.211567900504
y[1] (closed_form) = -1.18121218189 0.211582483766
absolute error = 1.965e-05
relative error = 0.001637 %
Correct digits = 5
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] = -1.8492 1.155
h = 0.0001 0.005
y[1] (numeric) = -1.18178358595 0.212697324455
y[1] (closed_form) = -1.18179859283 0.212712096992
absolute error = 2.106e-05
relative error = 0.001754 %
Correct digits = 5
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] = -1.8491 1.16
h = 0.0001 0.003
y[1] (numeric) = -1.18254339494 0.213266326361
y[1] (closed_form) = -1.1825572012 0.21328119278
absolute error = 2.029e-05
relative error = 0.001688 %
Correct digits = 5
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] = -1.849 1.163
h = 0.001 0.001
y[1] (numeric) = -1.1829947946 0.213611683893
y[1] (closed_form) = -1.1830084786 0.213627004217
absolute error = 2.054e-05
relative error = 0.001709 %
Correct digits = 5
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] = -1.848 1.164
h = 0.001 0.003
y[1] (numeric) = -1.1830393336 0.213875582898
y[1] (closed_form) = -1.18305288245 0.213891104955
absolute error = 2.060e-05
relative error = 0.001714 %
Correct digits = 5
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] = -1.847 1.167
h = 0.0001 0.004
y[1] (numeric) = -1.18339292347 0.214359216812
y[1] (closed_form) = -1.18340673049 0.214374315724
absolute error = 2.046e-05
relative error = 0.001701 %
Correct digits = 5
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] = -1.8469 1.171
h = 0.003 0.006
y[1] (numeric) = -1.18400093893 0.214811309559
y[1] (closed_form) = -1.18401454881 0.214826035814
absolute error = 2.005e-05
relative error = 0.001666 %
Correct digits = 5
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] = -1.8439 1.177
h = 0.0001 0.005
y[1] (numeric) = -1.1846045686 0.215926540482
y[1] (closed_form) = -1.18462002203 0.215941405502
absolute error = 2.144e-05
relative error = 0.001781 %
Correct digits = 5
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
memory used=497.1MB, alloc=44.3MB, time=6.34
x[1] = -1.8438 1.182
h = 0.0001 0.003
y[1] (numeric) = -1.18537253787 0.216479768471
y[1] (closed_form) = -1.18538679665 0.216494759683
absolute error = 2.069e-05
relative error = 0.001717 %
Correct digits = 5
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] = -1.8437 1.185
h = 0.001 0.001
y[1] (numeric) = -1.18582890134 0.21681573229
y[1] (closed_form) = -1.18584305053 0.216831179406
absolute error = 2.095e-05
relative error = 0.001738 %
Correct digits = 5
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] = -1.8427 1.186
h = 0.0001 0.004
y[1] (numeric) = -1.18587816475 0.217077987056
y[1] (closed_form) = -1.18589218464 0.217093638983
absolute error = 2.101e-05
relative error = 0.001743 %
Correct digits = 5
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] = -1.8426 1.19
h = 0.003 0.006
y[1] (numeric) = -1.18649143539 0.217519748015
y[1] (closed_form) = -1.1865053889 0.217534422956
absolute error = 2.025e-05
relative error = 0.001679 %
Correct digits = 5
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] = -1.8396 1.196
h = 0.0001 0.005
y[1] (numeric) = -1.18711094482 0.218622160522
y[1] (closed_form) = -1.18712673981 0.218636930832
absolute error = 2.163e-05
relative error = 0.001792 %
Correct digits = 5
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] = -1.8395 1.201
h = 0.0001 0.003
y[1] (numeric) = -1.18788538534 0.219161580508
y[1] (closed_form) = -1.18789999214 0.219176504525
absolute error = 2.088e-05
relative error = 0.001729 %
Correct digits = 5
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] = -1.8394 1.204
h = 0.001 0.001
y[1] (numeric) = -1.18834569196 0.219489318284
y[1] (closed_form) = -1.18836020012 0.219504699408
absolute error = 2.114e-05
relative error = 0.00175 %
Correct digits = 5
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] = -1.8384 1.205
h = 0.001 0.003
y[1] (numeric) = -1.18839895334 0.219750003724
y[1] (closed_form) = -1.18841333739 0.219765592064
absolute error = 2.121e-05
relative error = 0.001755 %
Correct digits = 5
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] = -1.8374 1.208
h = 0.0001 0.004
y[1] (numeric) = -1.18876678929 0.220218454836
y[1] (closed_form) = -1.18878140852 0.22023360981
absolute error = 2.106e-05
relative error = 0.001742 %
Correct digits = 5
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] = -1.8373 1.212
h = 0.003 0.006
y[1] (numeric) = -1.18938630225 0.220646858552
y[1] (closed_form) = -1.1894007069 0.22066165326
absolute error = 2.065e-05
relative error = 0.001707 %
Correct digits = 5
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] = -1.8343 1.218
h = 0.0001 0.005
y[1] (numeric) = -1.19002403673 0.221734211287
y[1] (closed_form) = -1.19004027949 0.221749051064
absolute error = 2.200e-05
relative error = 0.001817 %
Correct digits = 5
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] = -1.8342 1.223
h = 0.0001 0.003
y[1] (numeric) = -1.19080578918 0.222257551029
y[1] (closed_form) = -1.19082085186 0.222272576285
absolute error = 2.128e-05
relative error = 0.001756 %
Correct digits = 5
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] = -1.8341 1.226
h = 0.001 0.001
y[1] (numeric) = -1.19127055371 0.222575708414
y[1] (closed_form) = -1.19128553049 0.222591191924
absolute error = 2.154e-05
relative error = 0.001778 %
Correct digits = 5
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] = -1.8331 1.227
h = 0.001 0.003
y[1] (numeric) = -1.1913284249 0.222834523062
y[1] (closed_form) = -1.1913432836 0.22285021646
absolute error = 2.161e-05
relative error = 0.001783 %
Correct digits = 5
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] = -1.8321 1.23
h = 0.0001 0.004
y[1] (numeric) = -1.19170361681 0.22329460459
y[1] (closed_form) = -1.19171869814 0.223309859698
absolute error = 2.145e-05
relative error = 0.001769 %
Correct digits = 5
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] = -1.832 1.234
h = 0.003 0.006
y[1] (numeric) = -1.1923288669 0.223710137285
y[1] (closed_form) = -1.19234372459 0.22372503919
absolute error = 2.104e-05
relative error = 0.001735 %
Correct digits = 5
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] = -1.829 1.24
h = 0.0001 0.005
y[1] (numeric) = -1.19298435672 0.224781985845
y[1] (closed_form) = -1.19300104735 0.224796882739
absolute error = 2.237e-05
relative error = 0.001843 %
Correct digits = 5
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] = -1.8289 1.245
h = 0.0001 0.003
y[1] (numeric) = -1.19377295901 0.225289101694
y[1] (closed_form) = -1.1937884788 0.22530421548
absolute error = 2.166e-05
relative error = 0.001783 %
Correct digits = 5
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] = -1.8288 1.248
h = 0.001 0.001
y[1] (numeric) = -1.19424190582 0.225597590883
y[1] (closed_form) = -1.19425735246 0.225613163608
absolute error = 2.193e-05
relative error = 0.001805 %
Correct digits = 5
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] = -1.8278 1.249
h = 0.001 0.003
y[1] (numeric) = -1.19430431991 0.225854416104
y[1] (closed_form) = -1.1943196546 0.225870201165
absolute error = 2.201e-05
relative error = 0.001811 %
Correct digits = 5
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] = -1.8268 1.252
h = 0.0001 0.004
y[1] (numeric) = -1.19468661469 0.226305957455
y[1] (closed_form) = -1.19470215929 0.226321299768
absolute error = 2.184e-05
relative error = 0.001796 %
Correct digits = 5
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] = -1.8267 1.256
h = 0.003 0.006
y[1] (numeric) = -1.19531723188 0.226708508816
y[1] (closed_form) = -1.19533254407 0.226723505299
absolute error = 2.143e-05
relative error = 0.001762 %
Correct digits = 5
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] = -1.8237 1.262
h = 0.0001 0.005
y[1] (numeric) = -1.19598999231 0.227764426646
y[1] (closed_form) = -1.19600713046 0.227779368339
absolute error = 2.274e-05
relative error = 0.001868 %
Correct digits = 5
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] = -1.8236 1.267
h = 0.0001 0.003
y[1] (numeric) = -1.19678497818 0.228255191945
y[1] (closed_form) = -1.19680095584 0.228270381535
absolute error = 2.205e-05
relative error = 0.001809 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.843
Order of pole (given) = 1 0
NO POLE (ratio test) 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 1.27
h = 0.001 0.001
y[1] (numeric) = -1.19725782908 0.228553935272
y[1] (closed_form) = -1.19727374635 0.228569584024
absolute error = 2.232e-05
relative error = 0.001831 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.843
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8225 1.271
h = 0.001 0.003
y[1] (numeric) = -1.19732471506 0.228808655119
y[1] (closed_form) = -1.19734052657 0.228824518429
absolute error = 2.240e-05
relative error = 0.001837 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.843
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8215 1.274
h = 0.0001 0.004
y[1] (numeric) = -1.19771385405 0.229251495229
y[1] (closed_form) = -1.19772986262 0.229266911802
absolute error = 2.222e-05
relative error = 0.001822 %
Correct digits = 5
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] = -1.8214 1.278
h = 0.003 0.006
y[1] (numeric) = -1.19834946522 0.229640968565
y[1] (closed_form) = -1.1983652329 0.22965604698
absolute error = 2.182e-05
relative error = 0.001788 %
Correct digits = 5
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
memory used=543.4MB, alloc=44.3MB, time=6.93
x[1] = -1.8184 1.284
h = 0.0001 0.005
y[1] (numeric) = -1.19903899728 0.230680547652
y[1] (closed_form) = -1.19905658218 0.230695521881
absolute error = 2.310e-05
relative error = 0.001892 %
Correct digits = 5
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] = -1.8183 1.289
h = 0.0001 0.003
y[1] (numeric) = -1.19983989709 0.231154852934
y[1] (closed_form) = -1.19985633293 0.231170105606
absolute error = 2.242e-05
relative error = 0.001835 %
Correct digits = 5
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] = -1.8182 1.292
h = 0.001 0.001
y[1] (numeric) = -1.20031637184 0.231443782994
y[1] (closed_form) = -1.20033276001 0.231459494589
absolute error = 2.270e-05
relative error = 0.001857 %
Correct digits = 5
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] = -1.8172 1.293
h = 0.0001 0.004
y[1] (numeric) = -1.20038765468 0.231696284394
y[1] (closed_form) = -1.20040394336 0.231712212538
absolute error = 2.278e-05
relative error = 0.001863 %
Correct digits = 5
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] = -1.8171 1.297
h = 0.003 0.006
y[1] (numeric) = -1.20102705053 0.232074993208
y[1] (closed_form) = -1.20104314753 0.232089977202
absolute error = 2.199e-05
relative error = 0.001798 %
Correct digits = 5
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] = -1.8141 1.303
h = 0.0001 0.005
y[1] (numeric) = -1.20173040841 0.233100004916
y[1] (closed_form) = -1.2017483131 0.233114842708
absolute error = 2.325e-05
relative error = 0.0019 %
Correct digits = 5
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] = -1.814 1.308
h = 0.0001 0.003
y[1] (numeric) = -1.20253582312 0.233560004758
y[1] (closed_form) = -1.20255258981 0.233575146725
absolute error = 2.259e-05
relative error = 0.001844 %
Correct digits = 5
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] = -1.8139 1.311
h = 0.001 0.001
y[1] (numeric) = -1.20301507371 0.233840403215
y[1] (closed_form) = -1.20303180364 0.233856003381
absolute error = 2.287e-05
relative error = 0.001866 %
Correct digits = 5
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] = -1.8129 1.312
h = 0.001 0.003
y[1] (numeric) = -1.20309004998 0.234090855749
y[1] (closed_form) = -1.20310668587 0.234106673914
absolute error = 2.296e-05
relative error = 0.001873 %
Correct digits = 5
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] = -1.8119 1.315
h = 0.0001 0.004
y[1] (numeric) = -1.20349111099 0.234517035867
y[1] (closed_form) = -1.20350791973 0.234532401301
absolute error = 2.277e-05
relative error = 0.001857 %
Correct digits = 5
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] = -1.8118 1.319
h = 0.003 0.006
y[1] (numeric) = -1.20413485582 0.234881915042
y[1] (closed_form) = -1.20415140879 0.234896957433
absolute error = 2.237e-05
relative error = 0.001823 %
Correct digits = 5
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] = -1.8088 1.325
h = 0.0001 0.005
y[1] (numeric) = -1.2048540177 0.235889886642
y[1] (closed_form) = -1.20487236636 0.235904734386
absolute error = 2.360e-05
relative error = 0.001923 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.838
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8087 1.33
h = 0.0001 0.003
y[1] (numeric) = -1.20566446531 0.236333274665
y[1] (closed_form) = -1.20568168938 0.236348456131
absolute error = 2.296e-05
relative error = 0.001869 %
Correct digits = 5
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] = -1.8086 1.333
h = 0.001 0.001
y[1] (numeric) = -1.20614681386 0.236603765407
y[1] (closed_form) = -1.20616401377 0.236619403979
absolute error = 2.325e-05
relative error = 0.001891 %
Correct digits = 5
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] = -1.8076 1.334
h = 0.001 0.003
y[1] (numeric) = -1.20622603594 0.23685179837
y[1] (closed_form) = -1.20624314818 0.236867656494
absolute error = 2.333e-05
relative error = 0.001898 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.838
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8066 1.337
h = 0.0001 0.004
y[1] (numeric) = -1.20663317283 0.237268874564
y[1] (closed_form) = -1.20665044482 0.237284277343
absolute error = 2.314e-05
relative error = 0.001882 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.838
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8065 1.341
h = 0.003 0.006
y[1] (numeric) = -1.20728083211 0.237620479981
y[1] (closed_form) = -1.20729784074 0.237635568164
absolute error = 2.274e-05
relative error = 0.001848 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.838
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8035 1.347
h = 0.0001 0.005
y[1] (numeric) = -1.20801526345 0.238611060073
y[1] (closed_form) = -1.20803405405 0.238625905779
absolute error = 2.395e-05
relative error = 0.001945 %
Correct digits = 5
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] = -1.8034 1.352
h = 0.0001 0.003
y[1] (numeric) = -1.20883026922 0.239037776681
y[1] (closed_form) = -1.20884794968 0.239052985053
absolute error = 2.332e-05
relative error = 0.001893 %
Correct digits = 5
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] = -1.8033 1.355
h = 0.001 0.001
y[1] (numeric) = -1.20931543229 0.239298322076
y[1] (closed_form) = -1.20933310111 0.239313986007
absolute error = 2.361e-05
relative error = 0.001915 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.838
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.8023 1.356
h = 0.001 0.003
y[1] (numeric) = -1.20939881454 0.23954383165
y[1] (closed_form) = -1.20941640205 0.23955971645
absolute error = 2.370e-05
relative error = 0.001922 %
Correct digits = 5
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] = -1.8013 1.359
h = 0.0001 0.004
y[1] (numeric) = -1.20981175148 0.239951681875
y[1] (closed_form) = -1.20982948561 0.239967109204
absolute error = 2.351e-05
relative error = 0.001906 %
Correct digits = 5
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] = -1.8012 1.363
h = 0.003 0.006
y[1] (numeric) = -1.21046294618 0.240289970467
y[1] (closed_form) = -1.21048040972 0.240305091886
absolute error = 2.310e-05
relative error = 0.001872 %
Correct digits = 5
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] = -1.7982 1.369
h = 0.0001 0.005
y[1] (numeric) = -1.21121210174 0.241262828427
y[1] (closed_form) = -1.21123133183 0.241277660234
absolute error = 2.429e-05
relative error = 0.001966 %
Correct digits = 5
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] = -1.7981 1.374
h = 0.0001 0.003
y[1] (numeric) = -1.21203119066 0.241672831538
y[1] (closed_form) = -1.21204932604 0.241688054309
absolute error = 2.368e-05
relative error = 0.001916 %
Correct digits = 5
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] = -1.798 1.377
h = 0.001 0.001
y[1] (numeric) = -1.2125188846 0.241923404412
y[1] (closed_form) = -1.21253702075 0.241939080747
absolute error = 2.397e-05
relative error = 0.001939 %
Correct digits = 5
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] = -1.797 1.378
h = 0.001 0.003
y[1] (numeric) = -1.21260633793 0.242166290318
y[1] (closed_form) = -1.21262439917 0.242182188601
absolute error = 2.406e-05
relative error = 0.001946 %
Correct digits = 5
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] = -1.796 1.381
h = 0.0001 0.004
y[1] (numeric) = -1.21302479576 0.242564803065
y[1] (closed_form) = -1.21304299047 0.242580242238
absolute error = 2.386e-05
relative error = 0.001929 %
Correct digits = 5
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
memory used=589.7MB, alloc=44.3MB, time=7.51
x[1] = -1.7959 1.385
h = 0.003 0.006
y[1] (numeric) = -1.21367914691 0.242889745734
y[1] (closed_form) = -1.21369706412 0.24290488791
absolute error = 2.346e-05
relative error = 0.001895 %
Correct digits = 5
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] = -1.7929 1.391
h = 0.0001 0.005
y[1] (numeric) = -1.2144424717 0.243844572171
y[1] (closed_form) = -1.21446213841 0.243859378367
absolute error = 2.462e-05
relative error = 0.001987 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.835
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7928 1.396
h = 0.0001 0.003
y[1] (numeric) = -1.21526516929 0.244237837191
y[1] (closed_form) = -1.21528375768 0.244253061959
absolute error = 2.403e-05
relative error = 0.001938 %
Correct digits = 5
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] = -1.7927 1.399
h = 0.001 0.001
y[1] (numeric) = -1.21575511071 0.244478420815
y[1] (closed_form) = -1.21577371214 0.244494096709
absolute error = 2.433e-05
relative error = 0.001962 %
Correct digits = 5
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] = -1.7917 1.4
h = 0.003 0.006
y[1] (numeric) = -1.21584654278 0.244718586461
y[1] (closed_form) = -1.21586507573 0.244734485145
absolute error = 2.442e-05
relative error = 0.001969 %
Correct digits = 5
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] = -1.7887 1.406
h = 0.0001 0.005
y[1] (numeric) = -1.21661958366 0.245662751779
y[1] (closed_form) = -1.21664002156 0.245676711828
absolute error = 2.475e-05
relative error = 0.001994 %
Correct digits = 5
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] = -1.7886 1.411
h = 0.0001 0.003
y[1] (numeric) = -1.21744491081 0.246044574418
y[1] (closed_form) = -1.21746428152 0.246058972048
absolute error = 2.414e-05
relative error = 0.001943 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.835
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7885 1.414
h = 0.001 0.001
y[1] (numeric) = -1.21793648598 0.246278330429
y[1] (closed_form) = -1.21795587818 0.246293177559
absolute error = 2.442e-05
relative error = 0.001965 %
Correct digits = 5
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] = -1.7875 1.415
h = 0.001 0.003
y[1] (numeric) = -1.2180306711 0.246516668152
y[1] (closed_form) = -1.2180499992 0.246531738675
absolute error = 2.451e-05
relative error = 0.001972 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.835
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7865 1.418
h = 0.0001 0.004
y[1] (numeric) = -1.21845804727 0.246899320615
y[1] (closed_form) = -1.21847748667 0.246913930033
absolute error = 2.432e-05
relative error = 0.001956 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.835
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7864 1.422
h = 0.003 0.006
y[1] (numeric) = -1.21911720524 0.247201768397
y[1] (closed_form) = -1.21913635607 0.247216096174
absolute error = 2.392e-05
relative error = 0.001923 %
Correct digits = 5
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] = -1.7834 1.428
h = 0.0001 0.005
y[1] (numeric) = -1.21990363295 0.248125844004
y[1] (closed_form) = -1.21992450201 0.248139758976
absolute error = 2.508e-05
relative error = 0.002015 %
Correct digits = 5
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] = -1.7833 1.433
h = 0.0001 0.003
y[1] (numeric) = -1.22073177105 0.248490914623
y[1] (closed_form) = -1.22075159086 0.248505293544
absolute error = 2.449e-05
relative error = 0.001966 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.835
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7832 1.436
h = 0.001 0.001
y[1] (numeric) = -1.22122511717 0.24871466962
y[1] (closed_form) = -1.22124497049 0.248729494869
absolute error = 2.478e-05
relative error = 0.001988 %
Correct digits = 5
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] = -1.7822 1.437
h = 0.001 0.003
y[1] (numeric) = -1.22132312054 0.248950130314
y[1] (closed_form) = -1.22134291617 0.248965179395
absolute error = 2.487e-05
relative error = 0.001995 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.835
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7812 1.44
h = 0.0001 0.004
y[1] (numeric) = -1.22175525668 0.249323191468
y[1] (closed_form) = -1.2217751505 0.249337779111
absolute error = 2.467e-05
relative error = 0.001978 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.835
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7811 1.444
h = 0.003 0.006
y[1] (numeric) = -1.22241655706 0.249612274521
y[1] (closed_form) = -1.22243615638 0.249626589967
absolute error = 2.427e-05
relative error = 0.001945 %
Correct digits = 5
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] = -1.7781 1.45
h = 0.0001 0.005
y[1] (numeric) = -1.22321562805 0.250517580493
y[1] (closed_form) = -1.22323692431 0.250531439163
absolute error = 2.541e-05
relative error = 0.002035 %
Correct digits = 5
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] = -1.778 1.455
h = 0.0001 0.003
y[1] (numeric) = -1.22404610764 0.250865921083
y[1] (closed_form) = -1.22406637347 0.250880269267
absolute error = 2.483e-05
relative error = 0.001987 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.835
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7779 1.458
h = 0.001 0.001
y[1] (numeric) = -1.22454094417 0.251079686163
y[1] (closed_form) = -1.22456125535 0.251094477083
absolute error = 2.513e-05
relative error = 0.00201 %
Correct digits = 5
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] = -1.7769 1.459
h = 0.001 0.003
y[1] (numeric) = -1.22464266552 0.25131218375
y[1] (closed_form) = -1.2246629254 0.251327198707
absolute error = 2.522e-05
relative error = 0.002017 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.835
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7759 1.462
h = 0.0001 0.004
y[1] (numeric) = -1.22507927435 0.251675581791
y[1] (closed_form) = -1.22509961937 0.251690135454
absolute error = 2.501e-05
relative error = 0.002 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.835
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7758 1.466
h = 0.003 0.006
y[1] (numeric) = -1.2257423434 0.251951322008
y[1] (closed_form) = -1.22576238838 0.251965613082
absolute error = 2.462e-05
relative error = 0.001967 %
Correct digits = 5
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] = -1.7728 1.472
h = 0.0001 0.005
y[1] (numeric) = -1.2265534752 0.252837630073
y[1] (closed_form) = -1.22657519433 0.252851421431
absolute error = 2.573e-05
relative error = 0.002054 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.835
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7727 1.477
h = 0.0001 0.003
y[1] (numeric) = -1.22738583032 0.253169279623
y[1] (closed_form) = -1.22740653866 0.253183585224
absolute error = 2.517e-05
relative error = 0.002008 %
Correct digits = 5
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] = -1.7726 1.48
h = 0.001 0.001
y[1] (numeric) = -1.22788187876 0.253373076042
y[1] (closed_form) = -1.22790264409 0.253387820376
absolute error = 2.547e-05
relative error = 0.002031 %
Correct digits = 5
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] = -1.7716 1.481
h = 0.0001 0.004
y[1] (numeric) = -1.22798721529 0.253602528603
y[1] (closed_form) = -1.22800793568 0.253617496943
absolute error = 2.556e-05
relative error = 0.002039 %
Correct digits = 5
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] = -1.7715 1.485
h = 0.003 0.006
y[1] (numeric) = -1.22865143457 0.253867380641
y[1] (closed_form) = -1.22867176745 0.253881510721
absolute error = 2.476e-05
relative error = 0.001974 %
Correct digits = 5
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
memory used=635.9MB, alloc=44.3MB, time=8.10
x[1] = -1.7685 1.491
h = 0.0001 0.005
y[1] (numeric) = -1.22947224818 0.254737036254
y[1] (closed_form) = -1.22949423398 0.254750630827
absolute error = 2.585e-05
relative error = 0.002059 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.835
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7684 1.496
h = 0.0001 0.003
y[1] (numeric) = -1.23030564994 0.255054347864
y[1] (closed_form) = -1.23032664275 0.255068477021
absolute error = 2.530e-05
relative error = 0.002014 %
Correct digits = 5
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] = -1.7683 1.499
h = 0.001 0.001
y[1] (numeric) = -1.23080240223 0.255249578293
y[1] (closed_form) = -1.23082346182 0.255264142284
absolute error = 2.561e-05
relative error = 0.002037 %
Correct digits = 5
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] = -1.7673 1.5
h = 0.001 0.003
y[1] (numeric) = -1.23091072895 0.25547630609
y[1] (closed_form) = -1.23093174903 0.255491093801
absolute error = 2.570e-05
relative error = 0.002044 %
Correct digits = 5
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] = -1.7663 1.503
h = 0.0001 0.004
y[1] (numeric) = -1.23135477635 0.255821524357
y[1] (closed_form) = -1.23137585754 0.255835852458
absolute error = 2.549e-05
relative error = 0.002027 %
Correct digits = 5
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] = -1.7662 1.507
h = 0.003 0.006
y[1] (numeric) = -1.2320199949 0.256072530294
y[1] (closed_form) = -1.23204076687 0.256086614104
absolute error = 2.510e-05
relative error = 0.001994 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.838
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7632 1.513
h = 0.0001 0.005
y[1] (numeric) = -1.23285177138 0.2569228305
y[1] (closed_form) = -1.23287417092 0.256936337969
absolute error = 2.616e-05
relative error = 0.002077 %
Correct digits = 5
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] = -1.7631 1.518
h = 0.0001 0.003
y[1] (numeric) = -1.23368619456 0.257223573403
y[1] (closed_form) = -1.23370762214 0.257237638527
absolute error = 2.563e-05
relative error = 0.002034 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.838
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.763 1.521
h = 0.001 0.001
y[1] (numeric) = -1.23418364809 0.257408904476
y[1] (closed_form) = -1.23420515366 0.257423399703
absolute error = 2.593e-05
relative error = 0.002057 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.838
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.762 1.522
h = 0.001 0.003
y[1] (numeric) = -1.23429539177 0.257632447492
y[1] (closed_form) = -1.2343168641 0.257647165982
absolute error = 2.603e-05
relative error = 0.002065 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.838
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.761 1.525
h = 0.0001 0.004
y[1] (numeric) = -1.23474308618 0.257967860764
y[1] (closed_form) = -1.23476460687 0.257982121128
absolute error = 2.582e-05
relative error = 0.002047 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.838
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7609 1.529
h = 0.003 0.006
y[1] (numeric) = -1.23540902381 0.258205664573
y[1] (closed_form) = -1.23543023086 0.258219690607
absolute error = 2.543e-05
relative error = 0.002015 %
Correct digits = 5
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] = -1.7579 1.535
h = 0.0001 0.005
y[1] (numeric) = -1.23625117006 0.259036445987
y[1] (closed_form) = -1.236273978 0.259049856053
absolute error = 2.646e-05
relative error = 0.002095 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.838
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7578 1.54
h = 0.0001 0.003
y[1] (numeric) = -1.23708616318 0.259320706215
y[1] (closed_form) = -1.23710802088 0.259334696078
absolute error = 2.595e-05
relative error = 0.002053 %
Correct digits = 5
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] = -1.7577 1.543
h = 0.001 0.001
y[1] (numeric) = -1.23758404792 0.259496187308
y[1] (closed_form) = -1.23760599457 0.259510602171
absolute error = 2.626e-05
relative error = 0.002076 %
Correct digits = 5
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] = -1.7567 1.544
h = 0.001 0.003
y[1] (numeric) = -1.23769909967 0.259716476037
y[1] (closed_form) = -1.23772101929 0.259731113481
absolute error = 2.636e-05
relative error = 0.002084 %
Correct digits = 5
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] = -1.7557 1.547
h = 0.0001 0.004
y[1] (numeric) = -1.23815015317 0.260042054395
y[1] (closed_form) = -1.23817210855 0.26005623565
absolute error = 2.614e-05
relative error = 0.002066 %
Correct digits = 5
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] = -1.7556 1.551
h = 0.003 0.006
y[1] (numeric) = -1.23881645131 0.260266728724
y[1] (closed_form) = -1.23883808901 0.2602806857
absolute error = 2.575e-05
relative error = 0.002034 %
Correct digits = 5
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] = -1.7526 1.557
h = 0.0001 0.005
y[1] (numeric) = -1.23966837251 0.261077850675
y[1] (closed_form) = -1.23969158319 0.261091153314
absolute error = 2.675e-05
relative error = 0.002112 %
Correct digits = 5
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] = -1.7525 1.562
h = 0.0001 0.003
y[1] (numeric) = -1.24050349047 0.261345730056
y[1] (closed_form) = -1.24052577328 0.261359633681
absolute error = 2.626e-05
relative error = 0.002072 %
Correct digits = 5
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] = -1.7524 1.565
h = 0.001 0.001
y[1] (numeric) = -1.24100154018 0.261511419989
y[1] (closed_form) = -1.24102392263 0.26152574315
absolute error = 2.657e-05
relative error = 0.002095 %
Correct digits = 5
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] = -1.7514 1.566
h = 0.001 0.003
y[1] (numeric) = -1.2411197894 0.26172838939
y[1] (closed_form) = -1.24114215095 0.26174293423
absolute error = 2.668e-05
relative error = 0.002103 %
Correct digits = 5
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] = -1.7504 1.569
h = 0.0001 0.004
y[1] (numeric) = -1.24157391509 0.262044113596
y[1] (closed_form) = -1.24159629997 0.262058204627
absolute error = 2.645e-05
relative error = 0.002084 %
Correct digits = 5
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] = -1.7503 1.573
h = 0.003 0.006
y[1] (numeric) = -1.24224022046 0.262255743577
y[1] (closed_form) = -1.24226228401 0.262269620449
absolute error = 2.606e-05
relative error = 0.002053 %
Correct digits = 5
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] = -1.7473 1.579
h = 0.0001 0.005
y[1] (numeric) = -1.24310132115 0.263047088033
y[1] (closed_form) = -1.2431249286 0.263060273508
absolute error = 2.704e-05
relative error = 0.002128 %
Correct digits = 5
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] = -1.7472 1.584
h = 0.0001 0.003
y[1] (numeric) = -1.24393612596 0.263298703779
y[1] (closed_form) = -1.2439588285 0.26331251045
absolute error = 2.657e-05
relative error = 0.00209 %
Correct digits = 5
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] = -1.7471 1.587
h = 0.001 0.001
y[1] (numeric) = -1.24443407857 0.263454670572
y[1] (closed_form) = -1.24445689116 0.263468890972
absolute error = 2.688e-05
relative error = 0.002113 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.843
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7461 1.588
h = 0.0001 0.004
y[1] (numeric) = -1.24455541316 0.263668260116
y[1] (closed_form) = -1.2445782109 0.263682701079
absolute error = 2.699e-05
relative error = 0.002121 %
Correct digits = 5
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
memory used=682.2MB, alloc=44.3MB, time=8.69
x[1] = -1.746 1.592
h = 0.003 0.006
y[1] (numeric) = -1.24522144599 0.26386929475
y[1] (closed_form) = -1.24524376625 0.263882980535
absolute error = 2.618e-05
relative error = 0.002057 %
Correct digits = 5
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] = -1.743 1.598
h = 0.0001 0.005
y[1] (numeric) = -1.24608973446 0.264643438362
y[1] (closed_form) = -1.24611357227 0.264656402296
absolute error = 2.713e-05
relative error = 0.00213 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.843
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7429 1.603
h = 0.0001 0.003
y[1] (numeric) = -1.24692373336 0.264881170872
y[1] (closed_form) = -1.24694668667 0.26489477232
absolute error = 2.668e-05
relative error = 0.002093 %
Correct digits = 5
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] = -1.7428 1.606
h = 0.001 0.001
y[1] (numeric) = -1.24742128147 0.26502883493
y[1] (closed_form) = -1.24744435348 0.265042844724
absolute error = 2.699e-05
relative error = 0.002117 %
Correct digits = 5
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] = -1.7418 1.607
h = 0.001 0.003
y[1] (numeric) = -1.24754513991 0.265239435295
y[1] (closed_form) = -1.24756820221 0.265253664452
absolute error = 2.710e-05
relative error = 0.002125 %
Correct digits = 5
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] = -1.7408 1.61
h = 0.0001 0.004
y[1] (numeric) = -1.24800410679 0.265536779454
y[1] (closed_form) = -1.24802716982 0.265550560512
absolute error = 2.687e-05
relative error = 0.002106 %
Correct digits = 5
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] = -1.7407 1.614
h = 0.003 0.006
y[1] (numeric) = -1.24866935335 0.26572441442
y[1] (closed_form) = -1.24869208945 0.265738000303
absolute error = 2.649e-05
relative error = 0.002075 %
Correct digits = 5
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] = -1.7377 1.62
h = 0.0001 0.005
y[1] (numeric) = -1.24954571442 0.266478627706
y[1] (closed_form) = -1.249569937 0.266491457241
absolute error = 2.741e-05
relative error = 0.002145 %
Correct digits = 5
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] = -1.7376 1.625
h = 0.0001 0.003
y[1] (numeric) = -1.25037860814 0.266700359053
y[1] (closed_form) = -1.25040197014 0.266713844437
absolute error = 2.697e-05
relative error = 0.00211 %
Correct digits = 5
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] = -1.7375 1.628
h = 0.001 0.001
y[1] (numeric) = -1.25087558505 0.266838453092
y[1] (closed_form) = -1.25089907559 0.266852340421
absolute error = 2.729e-05
relative error = 0.002134 %
Correct digits = 5
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] = -1.7365 1.629
h = 0.001 0.003
y[1] (numeric) = -1.25100231642 0.267045574458
y[1] (closed_form) = -1.25102580311 0.26705967965
absolute error = 2.740e-05
relative error = 0.002142 %
Correct digits = 5
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] = -1.7355 1.632
h = 0.0001 0.004
y[1] (numeric) = -1.25146354498 0.26733307051
y[1] (closed_form) = -1.25148702057 0.267346731182
absolute error = 2.716e-05
relative error = 0.002122 %
Correct digits = 5
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] = -1.7354 1.636
h = 0.003 0.006
y[1] (numeric) = -1.25212782368 0.267507974406
y[1] (closed_form) = -1.25215096982 0.267521450114
absolute error = 2.678e-05
relative error = 0.002092 %
Correct digits = 5
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] = -1.7324 1.642
h = 0.0001 0.005
y[1] (numeric) = -1.25301166613 0.268242203097
y[1] (closed_form) = -1.25303626671 0.268254889382
absolute error = 2.768e-05
relative error = 0.00216 %
Correct digits = 5
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] = -1.7323 1.647
h = 0.0001 0.003
y[1] (numeric) = -1.25384304071 0.268448091794
y[1] (closed_form) = -1.25386680507 0.26846145124
absolute error = 2.726e-05
relative error = 0.002126 %
Correct digits = 5
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] = -1.7322 1.65
h = 0.001 0.001
y[1] (numeric) = -1.25433919855 0.268576708553
y[1] (closed_form) = -1.25436310099 0.268590463245
absolute error = 2.758e-05
relative error = 0.00215 %
Correct digits = 5
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] = -1.7312 1.651
h = 0.001 0.003
y[1] (numeric) = -1.25446868772 0.268780303458
y[1] (closed_form) = -1.25449259207 0.268794274315
absolute error = 2.769e-05
relative error = 0.002158 %
Correct digits = 5
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] = -1.7302 1.654
h = 0.0001 0.004
y[1] (numeric) = -1.25493189969 0.269057971945
y[1] (closed_form) = -1.25495578132 0.269071502254
absolute error = 2.745e-05
relative error = 0.002139 %
Correct digits = 5
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] = -1.7301 1.658
h = 0.003 0.006
y[1] (numeric) = -1.25559488276 0.269220274575
y[1] (closed_form) = -1.25561843282 0.269233630129
absolute error = 2.707e-05
relative error = 0.002108 %
Correct digits = 5
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] = -1.7271 1.664
h = 0.0001 0.005
y[1] (numeric) = -1.2564856187 0.269934486167
y[1] (closed_form) = -1.25651059027 0.26994702068
absolute error = 2.794e-05
relative error = 0.002174 %
Correct digits = 5
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] = -1.727 1.669
h = 0.0001 0.003
y[1] (numeric) = -1.25731506968 0.270124704186
y[1] (closed_form) = -1.25733922978 0.270137928133
absolute error = 2.754e-05
relative error = 0.002142 %
Correct digits = 5
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] = -1.7269 1.672
h = 0.001 0.001
y[1] (numeric) = -1.25781016618 0.270243944462
y[1] (closed_form) = -1.25783447356 0.270257556677
absolute error = 2.786e-05
relative error = 0.002165 %
Correct digits = 5
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] = -1.7259 1.673
h = 0.001 0.003
y[1] (numeric) = -1.25794229739 0.270443970018
y[1] (closed_form) = -1.25796661233 0.270457796509
absolute error = 2.797e-05
relative error = 0.002174 %
Correct digits = 5
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] = -1.7249 1.676
h = 0.0001 0.004
y[1] (numeric) = -1.25840721779 0.270711841296
y[1] (closed_form) = -1.25843149866 0.270725231591
absolute error = 2.773e-05
relative error = 0.002154 %
Correct digits = 5
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] = -1.7248 1.68
h = 0.003 0.006
y[1] (numeric) = -1.25906858516 0.270861683036
y[1] (closed_form) = -1.25909253271 0.270874908763
absolute error = 2.736e-05
relative error = 0.002124 %
Correct digits = 5
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] = -1.7218 1.686
h = 0.0001 0.005
y[1] (numeric) = -1.25996563105 0.271555866429
y[1] (closed_form) = -1.25999096636 0.271568240981
absolute error = 2.820e-05
relative error = 0.002188 %
Correct digits = 5
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] = -1.7217 1.691
h = 0.0001 0.003
y[1] (numeric) = -1.26079276396 0.271730598627
y[1] (closed_form) = -1.26081731291 0.271743677842
absolute error = 2.782e-05
relative error = 0.002157 %
Correct digits = 5
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] = -1.7216 1.694
h = 0.001 0.001
y[1] (numeric) = -1.2612865628 0.271840570936
y[1] (closed_form) = -1.26131126787 0.271854031181
absolute error = 2.813e-05
relative error = 0.00218 %
Correct digits = 5
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
memory used=728.6MB, alloc=44.3MB, time=9.29
x[1] = -1.7206 1.695
h = 0.0001 0.004
y[1] (numeric) = -1.26142121984 0.272036988814
y[1] (closed_form) = -1.26144593801 0.272050661261
absolute error = 2.825e-05
relative error = 0.002189 %
Correct digits = 5
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] = -1.7205 1.699
h = 0.003 0.006
y[1] (numeric) = -1.2620810147 0.272176754433
y[1] (closed_form) = -1.26210518418 0.272189765691
absolute error = 2.745e-05
relative error = 0.002126 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.857
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7175 1.705
h = 0.0001 0.005
y[1] (numeric) = -1.26298279033 0.272853639563
y[1] (closed_form) = -1.26300831759 0.272865775326
absolute error = 2.827e-05
relative error = 0.002187 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.857
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7174 1.71
h = 0.0001 0.003
y[1] (numeric) = -1.26380743883 0.273015233323
y[1] (closed_form) = -1.26383220173 0.273028085713
absolute error = 2.790e-05
relative error = 0.002158 %
Correct digits = 5
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] = -1.7173 1.713
h = 0.001 0.001
y[1] (numeric) = -1.26429982768 0.273117339778
y[1] (closed_form) = -1.26432475395 0.273130566673
absolute error = 2.822e-05
relative error = 0.002182 %
Correct digits = 5
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] = -1.7163 1.714
h = 0.001 0.003
y[1] (numeric) = -1.26443652215 0.273310596853
y[1] (closed_form) = -1.26446146615 0.273324033959
absolute error = 2.833e-05
relative error = 0.00219 %
Correct digits = 5
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] = -1.7153 1.717
h = 0.0001 0.004
y[1] (numeric) = -1.26490378734 0.273560338365
y[1] (closed_form) = -1.26492867691 0.273573348459
absolute error = 2.808e-05
relative error = 0.00217 %
Correct digits = 5
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] = -1.7152 1.721
h = 0.003 0.006
y[1] (numeric) = -1.26556118048 0.273687429046
y[1] (closed_form) = -1.26558573462 0.273700293423
absolute error = 2.772e-05
relative error = 0.002141 %
Correct digits = 5
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] = -1.7122 1.727
h = 0.0001 0.005
y[1] (numeric) = -1.26646819541 0.274344327613
y[1] (closed_form) = -1.26649407228 0.274356289183
absolute error = 2.851e-05
relative error = 0.0022 %
Correct digits = 5
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] = -1.7121 1.732
h = 0.0001 0.003
y[1] (numeric) = -1.26728982271 0.274490816165
y[1] (closed_form) = -1.26731496081 0.274503507634
absolute error = 2.816e-05
relative error = 0.002172 %
Correct digits = 5
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] = -1.712 1.735
h = 0.001 0.001
y[1] (numeric) = -1.26778049238 0.274583878537
y[1] (closed_form) = -1.26780580207 0.27459693684
absolute error = 2.848e-05
relative error = 0.002195 %
Correct digits = 5
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] = -1.711 1.736
h = 0.001 0.003
y[1] (numeric) = -1.26791949575 0.274773470024
y[1] (closed_form) = -1.26794482844 0.274786736146
absolute error = 2.860e-05
relative error = 0.002204 %
Correct digits = 5
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] = -1.71 1.739
h = 0.0001 0.004
y[1] (numeric) = -1.26838770542 0.275013556153
y[1] (closed_form) = -1.26841297311 0.275026400609
absolute error = 2.834e-05
relative error = 0.002184 %
Correct digits = 5
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] = -1.7099 1.743
h = 0.003 0.006
y[1] (numeric) = -1.2690426154 0.275128645167
y[1] (closed_form) = -1.26906754701 0.275141353934
absolute error = 2.798e-05
relative error = 0.002155 %
Correct digits = 5
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] = -1.7069 1.749
h = 0.0001 0.005
y[1] (numeric) = -1.26995430382 0.275765604748
y[1] (closed_form) = -1.26998052252 0.27577738493
absolute error = 2.874e-05
relative error = 0.002212 %
Correct digits = 5
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] = -1.7068 1.754
h = 0.0001 0.003
y[1] (numeric) = -1.27077254684 0.275897206314
y[1] (closed_form) = -1.27079805254 0.275909728616
absolute error = 2.841e-05
relative error = 0.002185 %
Correct digits = 5
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] = -1.7067 1.757
h = 0.001 0.001
y[1] (numeric) = -1.2712612796 0.275981353125
y[1] (closed_form) = -1.27128696472 0.275994234383
absolute error = 2.873e-05
relative error = 0.002209 %
Correct digits = 5
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] = -1.7057 1.758
h = 0.001 0.003
y[1] (numeric) = -1.27140247566 0.276167253539
y[1] (closed_form) = -1.27142818894 0.276180340062
absolute error = 2.885e-05
relative error = 0.002218 %
Correct digits = 5
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] = -1.7047 1.761
h = 0.0001 0.004
y[1] (numeric) = -1.27187137148 0.276397749942
y[1] (closed_form) = -1.2718970095 0.276410420461
absolute error = 2.860e-05
relative error = 0.002197 %
Correct digits = 5
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] = -1.7046 1.765
h = 0.003 0.006
y[1] (numeric) = -1.2725235117 0.276501013872
y[1] (closed_form) = -1.27254881333 0.276513558645
absolute error = 2.824e-05
relative error = 0.002169 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.868
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7016 1.771
h = 0.0001 0.005
y[1] (numeric) = -1.2734393156 0.277118101566
y[1] (closed_form) = -1.27346586815 0.277129693519
absolute error = 2.897e-05
relative error = 0.002223 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.868
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.7015 1.776
h = 0.0001 0.003
y[1] (numeric) = -1.27425382293 0.27723504484
y[1] (closed_form) = -1.27427968842 0.277247390088
absolute error = 2.866e-05
relative error = 0.002198 %
Correct digits = 5
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
x[1] = -1.7014 1.779
h = 0.001 0.001
y[1] (numeric) = -1.27474040795 0.277310410897
y[1] (closed_form) = -1.27476646034 0.277323107034
absolute error = 2.898e-05
relative error = 0.002222 %
Correct digits = 5
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] = -1.7004 1.78
h = 0.001 0.003
y[1] (numeric) = -1.27488368091 0.277492599135
y[1] (closed_form) = -1.27490976644 0.27750549783
absolute error = 2.910e-05
relative error = 0.00223 %
Correct digits = 5
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] = -1.6994 1.783
h = 0.0001 0.004
y[1] (numeric) = -1.27535300971 0.277713579875
y[1] (closed_form) = -1.27537901005 0.277726068527
absolute error = 2.884e-05
relative error = 0.00221 %
Correct digits = 5
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] = -1.6993 1.787
h = 0.003 0.006
y[1] (numeric) = -1.27600210297 0.277805203471
y[1] (closed_form) = -1.27602776697 0.277817576217
absolute error = 2.849e-05
relative error = 0.002182 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.873
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6963 1.793
h = 0.0001 0.005
y[1] (numeric) = -1.2769214729 0.278402505308
y[1] (closed_form) = -1.27694835122 0.278413902547
absolute error = 2.919e-05
relative error = 0.002234 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.873
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6962 1.798
h = 0.0001 0.003
y[1] (numeric) = -1.27773190518 0.278505028792
y[1] (closed_form) = -1.27775812245 0.278517189462
absolute error = 2.890e-05
relative error = 0.00221 %
Correct digits = 5
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
memory used=774.9MB, alloc=44.3MB, time=9.88
x[1] = -1.6961 1.801
h = 0.001 0.001
y[1] (numeric) = -1.27821613878 0.278571754793
y[1] (closed_form) = -1.27824255006 0.278584258114
absolute error = 2.922e-05
relative error = 0.002234 %
Correct digits = 5
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] = -1.6951 1.802
h = 0.0001 0.004
y[1] (numeric) = -1.27836137339 0.278750214066
y[1] (closed_form) = -1.27838782265 0.278762917096
absolute error = 2.934e-05
relative error = 0.002243 %
Correct digits = 5
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] = -1.695 1.806
h = 0.003 0.006
y[1] (numeric) = -1.27900775793 0.278832465966
y[1] (closed_form) = -1.27903360716 0.278844607939
absolute error = 2.856e-05
relative error = 0.002182 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.877
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.692 1.812
h = 0.0001 0.005
y[1] (numeric) = -1.27992953056 0.279412785933
y[1] (closed_form) = -1.27995656206 0.279423934551
absolute error = 2.924e-05
relative error = 0.002232 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.877
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6919 1.817
h = 0.0001 0.003
y[1] (numeric) = -1.28073602509 0.279503149133
y[1] (closed_form) = -1.28076241809 0.279515068769
absolute error = 2.896e-05
relative error = 0.002209 %
Correct digits = 5
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] = -1.6918 1.82
h = 0.001 0.001
y[1] (numeric) = -1.28121797659 0.279562586108
y[1] (closed_form) = -1.28124456932 0.279574841106
absolute error = 2.928e-05
relative error = 0.002233 %
Correct digits = 5
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] = -1.6908 1.821
h = 0.001 0.003
y[1] (numeric) = -1.2813647634 0.279737803888
y[1] (closed_form) = -1.28139139811 0.279750255977
absolute error = 2.940e-05
relative error = 0.002242 %
Correct digits = 5
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] = -1.6898 1.824
h = 0.0001 0.004
y[1] (numeric) = -1.2818341322 0.27994130439
y[1] (closed_form) = -1.28186066417 0.279953358366
absolute error = 2.914e-05
relative error = 0.002221 %
Correct digits = 5
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] = -1.6897 1.828
h = 0.003 0.006
y[1] (numeric) = -1.28247671816 0.280011829138
y[1] (closed_form) = -1.28250291492 0.280023785191
absolute error = 2.880e-05
relative error = 0.002194 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.882
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6867 1.834
h = 0.0001 0.005
y[1] (numeric) = -1.28340106138 0.280572577806
y[1] (closed_form) = -1.28342840318 0.280583520697
absolute error = 2.945e-05
relative error = 0.002242 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.882
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6866 1.839
h = 0.0001 0.003
y[1] (numeric) = -1.28420288543 0.280648992497
y[1] (closed_form) = -1.2842296148 0.280660714634
absolute error = 2.919e-05
relative error = 0.00222 %
Correct digits = 5
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] = -1.6865 1.842
h = 0.001 0.001
y[1] (numeric) = -1.28468212789 0.280700067749
y[1] (closed_form) = -1.2847090634 0.28071211675
absolute error = 2.951e-05
relative error = 0.002244 %
Correct digits = 5
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] = -1.6855 1.843
h = 0.001 0.003
y[1] (numeric) = -1.284830664 0.280871537863
y[1] (closed_form) = -1.28485764603 0.280883780862
absolute error = 2.963e-05
relative error = 0.002253 %
Correct digits = 5
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] = -1.6845 1.846
h = 0.0001 0.004
y[1] (numeric) = -1.28529977403 0.281065780689
y[1] (closed_form) = -1.28532664433 0.281077632283
absolute error = 2.937e-05
relative error = 0.002232 %
Correct digits = 5
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] = -1.6844 1.85
h = 0.003 0.006
y[1] (numeric) = -1.28593857663 0.281125236839
y[1] (closed_form) = -1.28596511272 0.281136999978
absolute error = 2.903e-05
relative error = 0.002205 %
Correct digits = 5
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] = -1.6814 1.856
h = 0.0001 0.005
y[1] (numeric) = -1.28686496974 0.281666550679
y[1] (closed_form) = -1.28689261344 0.281677282385
absolute error = 2.965e-05
relative error = 0.002251 %
Correct digits = 5
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] = -1.6813 1.861
h = 0.0001 0.003
y[1] (numeric) = -1.28766181992 0.281729279531
y[1] (closed_form) = -1.28768887721 0.281740797703
absolute error = 2.941e-05
relative error = 0.002231 %
Correct digits = 5
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] = -1.6812 1.864
h = 0.001 0.001
y[1] (numeric) = -1.28813817099 0.281772148299
y[1] (closed_form) = -1.28816544046 0.281783984722
absolute error = 2.973e-05
relative error = 0.002254 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.89
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6802 1.865
h = 0.001 0.003
y[1] (numeric) = -1.28828834387 0.2819398658
y[1] (closed_form) = -1.28831566423 0.28195189301
absolute error = 2.985e-05
relative error = 0.002263 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.89
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6792 1.868
h = 0.0001 0.004
y[1] (numeric) = -1.28875696478 0.28212495409
y[1] (closed_form) = -1.28878416477 0.28213659683
absolute error = 2.959e-05
relative error = 0.002243 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.89
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6791 1.872
h = 0.003 0.006
y[1] (numeric) = -1.28939174531 0.282173552754
y[1] (closed_form) = -1.28941861242 0.282185116352
absolute error = 2.925e-05
relative error = 0.002216 %
Correct digits = 5
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] = -1.6761 1.878
h = 0.0001 0.005
y[1] (numeric) = -1.29031967885 0.282695584559
y[1] (closed_form) = -1.29034761598 0.282706099978
absolute error = 2.985e-05
relative error = 0.00226 %
Correct digits = 5
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] = -1.676 1.883
h = 0.0001 0.003
y[1] (numeric) = -1.29111126469 0.282744897421
y[1] (closed_form) = -1.29113864134 0.282756205537
absolute error = 2.962e-05
relative error = 0.002241 %
Correct digits = 5
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] = -1.6759 1.886
h = 0.001 0.001
y[1] (numeric) = -1.2915845497 0.282779719276
y[1] (closed_form) = -1.29161214419 0.282791336932
absolute error = 2.994e-05
relative error = 0.002264 %
Correct digits = 5
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] = -1.6749 1.887
h = 0.001 0.003
y[1] (numeric) = -1.29173624806 0.282943683162
y[1] (closed_form) = -1.29176389766 0.282955488283
absolute error = 3.006e-05
relative error = 0.002273 %
Correct digits = 5
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] = -1.6739 1.89
h = 0.0001 0.004
y[1] (numeric) = -1.29220415599 0.283119726697
y[1] (closed_form) = -1.29223167693 0.283131154493
absolute error = 2.980e-05
relative error = 0.002253 %
Correct digits = 5
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] = -1.6738 1.894
h = 0.003 0.006
y[1] (numeric) = -1.29283468609 0.283157684524
y[1] (closed_form) = -1.29286187577 0.283169042325
absolute error = 2.947e-05
relative error = 0.002226 %
Correct digits = 5
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] = -1.6708 1.9
h = 0.0001 0.005
y[1] (numeric) = -1.2937636624 0.283660602669
y[1] (closed_form) = -1.29379188441 0.283670897053
absolute error = 3.004e-05
relative error = 0.002268 %
Correct digits = 5
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=821.3MB, alloc=44.3MB, time=10.47
x[1] = -1.6707 1.905
h = 0.0001 0.003
y[1] (numeric) = -1.29454970645 0.283696775889
y[1] (closed_form) = -1.2945773938 0.28370786823
absolute error = 2.983e-05
relative error = 0.002251 %
Correct digits = 5
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] = -1.6706 1.908
h = 0.001 0.001
y[1] (numeric) = -1.29501975848 0.283723714325
y[1] (closed_form) = -1.29504766896 0.283735107416
absolute error = 3.015e-05
relative error = 0.002274 %
Correct digits = 5
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] = -1.6696 1.909
h = 0.0001 0.004
y[1] (numeric) = -1.29517287246 0.283883927425
y[1] (closed_form) = -1.29520084209 0.28389550456
absolute error = 3.027e-05
relative error = 0.002283 %
Correct digits = 5
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] = -1.6695 1.913
h = 0.003 0.006
y[1] (numeric) = -1.29579974804 0.283913354579
y[1] (closed_form) = -1.29582708597 0.283924472277
absolute error = 2.951e-05
relative error = 0.002225 %
Correct digits = 5
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] = -1.6665 1.919
h = 0.0001 0.005
y[1] (numeric) = -1.29672900812 0.284399961909
y[1] (closed_form) = -1.29675734578 0.284410004716
absolute error = 3.006e-05
relative error = 0.002265 %
Correct digits = 5
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] = -1.6664 1.924
h = 0.0001 0.003
y[1] (numeric) = -1.29750991793 0.284425120982
y[1] (closed_form) = -1.29753774306 0.284435965206
absolute error = 2.986e-05
relative error = 0.002248 %
Correct digits = 5
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
x[1] = -1.6663 1.927
h = 0.001 0.001
y[1] (numeric) = -1.29797696821 0.284445448324
y[1] (closed_form) = -1.29800502062 0.284456585626
absolute error = 3.018e-05
relative error = 0.002271 %
Correct digits = 5
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] = -1.6653 1.928
h = 0.001 0.003
y[1] (numeric) = -1.29813116936 0.284602422864
y[1] (closed_form) = -1.29815928422 0.284613741147
absolute error = 3.031e-05
relative error = 0.00228 %
Correct digits = 5
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] = -1.6643 1.931
h = 0.0001 0.004
y[1] (numeric) = -1.29859707344 0.284761964015
y[1] (closed_form) = -1.29862504524 0.284772918842
absolute error = 3.004e-05
relative error = 0.00226 %
Correct digits = 5
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] = -1.6642 1.935
h = 0.003 0.006
y[1] (numeric) = -1.29921900196 0.284780771622
y[1] (closed_form) = -1.2992466464 0.284791672969
absolute error = 2.972e-05
relative error = 0.002234 %
Correct digits = 5
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] = -1.6612 1.941
h = 0.0001 0.005
y[1] (numeric) = -1.3001484143 0.285248623045
y[1] (closed_form) = -1.30017702082 0.285258437017
absolute error = 3.024e-05
relative error = 0.002272 %
Correct digits = 5
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] = -1.6611 1.946
h = 0.0001 0.003
y[1] (numeric) = -1.30092330455 0.285261174604
y[1] (closed_form) = -1.30095142399 0.285271793504
absolute error = 3.006e-05
relative error = 0.002257 %
Correct digits = 5
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] = -1.661 1.949
h = 0.001 0.001
y[1] (numeric) = -1.30138683408 0.285273933583
y[1] (closed_form) = -1.3014151854 0.285284836674
absolute error = 3.038e-05
relative error = 0.00228 %
Correct digits = 5
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] = -1.66 1.95
h = 0.001 0.003
y[1] (numeric) = -1.30154225082 0.285427173644
y[1] (closed_form) = -1.30157066831 0.285438254134
absolute error = 3.050e-05
relative error = 0.002289 %
Correct digits = 5
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] = -1.659 1.953
h = 0.0001 0.004
y[1] (numeric) = -1.30200684056 0.285578019685
y[1] (closed_form) = -1.30203510773 0.285588744351
absolute error = 3.023e-05
relative error = 0.002268 %
Correct digits = 5
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] = -1.6589 1.957
h = 0.003 0.006
y[1] (numeric) = -1.30262392582 0.285586834279
y[1] (closed_form) = -1.30265186805 0.285597514078
absolute error = 2.991e-05
relative error = 0.002243 %
Correct digits = 5
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] = -1.6559 1.963
h = 0.0001 0.005
y[1] (numeric) = -1.30355302932 0.28603613836
y[1] (closed_form) = -1.3035818961 0.286045719742
absolute error = 3.042e-05
relative error = 0.002279 %
Correct digits = 5
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] = -1.6558 1.968
h = 0.0001 0.003
y[1] (numeric) = -1.30432166032 0.286036373463
y[1] (closed_form) = -1.30435006524 0.286046762377
absolute error = 3.025e-05
relative error = 0.002265 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.918
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6557 1.971
h = 0.001 0.001
y[1] (numeric) = -1.30478152461 0.286041736492
y[1] (closed_form) = -1.30481016565 0.286052400681
absolute error = 3.056e-05
relative error = 0.002288 %
Correct digits = 5
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] = -1.6547 1.972
h = 0.001 0.003
y[1] (numeric) = -1.30493805195 0.286191255153
y[1] (closed_form) = -1.30496676271 0.286202093086
absolute error = 3.069e-05
relative error = 0.002297 %
Correct digits = 5
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] = -1.6537 1.975
h = 0.0001 0.004
y[1] (numeric) = -1.30540113025 0.286333537754
y[1] (closed_form) = -1.30542968378 0.286344027629
absolute error = 3.042e-05
relative error = 0.002276 %
Correct digits = 5
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] = -1.6536 1.979
h = 0.003 0.006
y[1] (numeric) = -1.3060131844 0.286332592192
y[1] (closed_form) = -1.30604141566 0.286343045609
absolute error = 3.010e-05
relative error = 0.002252 %
Correct digits = 5
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
x[1] = -1.6506 1.985
h = 0.0001 0.005
y[1] (numeric) = -1.30694153147 0.286763570077
y[1] (closed_form) = -1.3069706499 0.286772915452
absolute error = 3.058e-05
relative error = 0.002285 %
Correct digits = 5
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
x[1] = -1.6505 1.99
h = 0.0001 0.003
y[1] (numeric) = -1.30770367672 0.286751783707
y[1] (closed_form) = -1.30773235824 0.286761938336
absolute error = 3.043e-05
relative error = 0.002273 %
Correct digits = 5
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] = -1.6504 1.993
h = 0.001 0.001
y[1] (numeric) = -1.30815973912 0.286749925592
y[1] (closed_form) = -1.30818866063 0.286760346567
absolute error = 3.074e-05
relative error = 0.002295 %
Correct digits = 5
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] = -1.6494 1.994
h = 0.001 0.003
y[1] (numeric) = -1.30831727401 0.286895739266
y[1] (closed_form) = -1.30834626862 0.286906330262
absolute error = 3.087e-05
relative error = 0.002305 %
Correct digits = 5
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] = -1.6484 1.997
h = 0.0001 0.004
y[1] (numeric) = -1.30877865099 0.287029594825
y[1] (closed_form) = -1.30880748182 0.287039845652
absolute error = 3.060e-05
relative error = 0.002284 %
Correct digits = 5
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] = -1.6483 2.001
h = 0.003 0.006
y[1] (numeric) = -1.30938549665 0.287019124921
y[1] (closed_form) = -1.30941400813 0.287029347485
absolute error = 3.029e-05
relative error = 0.00226 %
Correct digits = 5
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
memory used=867.6MB, alloc=44.3MB, time=11.05
x[1] = -1.6453 2.007
h = 0.0001 0.005
y[1] (numeric) = -1.31031265352 0.287432009543
y[1] (closed_form) = -1.31034201501 0.287441115826
absolute error = 3.074e-05
relative error = 0.002292 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.929
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6452 2.012
h = 0.0001 0.003
y[1] (numeric) = -1.31106809966 0.287408499969
y[1] (closed_form) = -1.31109704887 0.287418416373
absolute error = 3.060e-05
relative error = 0.00228 %
Correct digits = 5
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] = -1.6451 2.015
h = 0.001 0.001
y[1] (numeric) = -1.31152023131 0.28739959753
y[1] (closed_form) = -1.31154942405 0.287409771352
absolute error = 3.091e-05
relative error = 0.002302 %
Correct digits = 5
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] = -1.6441 2.016
h = 0.0001 0.004
y[1] (numeric) = -1.31167867274 0.287541725821
y[1] (closed_form) = -1.31170794178 0.287552065885
absolute error = 3.104e-05
relative error = 0.002312 %
Correct digits = 5
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] = -1.644 2.02
h = 0.003 0.006
y[1] (numeric) = -1.31228112003 0.287523652167
y[1] (closed_form) = -1.31230974393 0.287533631766
absolute error = 3.031e-05
relative error = 0.002256 %
Correct digits = 5
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] = -1.641 2.026
h = 0.0001 0.005
y[1] (numeric) = -1.31320670427 0.287921178594
y[1] (closed_form) = -1.31323614635 0.287930036341
absolute error = 3.075e-05
relative error = 0.002287 %
Correct digits = 5
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] = -1.6409 2.031
h = 0.0001 0.003
y[1] (numeric) = -1.31395608837 0.287887901987
y[1] (closed_form) = -1.3139851391 0.287897569651
absolute error = 3.062e-05
relative error = 0.002276 %
Correct digits = 5
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] = -1.6408 2.034
h = 0.001 0.001
y[1] (numeric) = -1.3144046583 0.287873127653
y[1] (closed_form) = -1.31443395522 0.287883045028
absolute error = 3.093e-05
relative error = 0.002299 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.939
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6398 2.035
h = 0.001 0.003
y[1] (numeric) = -1.31456375727 0.288012092517
y[1] (closed_form) = -1.31459313306 0.288022172805
absolute error = 3.106e-05
relative error = 0.002308 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.939
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6388 2.038
h = 0.0001 0.004
y[1] (numeric) = -1.31502139189 0.288130670182
y[1] (closed_form) = -1.31505059275 0.288140425301
absolute error = 3.079e-05
relative error = 0.002287 %
Correct digits = 5
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
x[1] = -1.6387 2.042
h = 0.003 0.006
y[1] (numeric) = -1.31561800265 0.288103179905
y[1] (closed_form) = -1.31564689028 0.288112921389
absolute error = 3.049e-05
relative error = 0.002264 %
Correct digits = 5
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] = -1.6357 2.048
h = 0.0001 0.005
y[1] (numeric) = -1.31654163028 0.288483079903
y[1] (closed_form) = -1.31657129952 0.288491693778
absolute error = 3.089e-05
relative error = 0.002292 %
Correct digits = 5
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] = -1.6356 2.053
h = 0.0001 0.003
y[1] (numeric) = -1.31728395649 0.288438643905
y[1] (closed_form) = -1.31731325835 0.288448067052
absolute error = 3.078e-05
relative error = 0.002282 %
Correct digits = 5
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] = -1.6355 2.056
h = 0.001 0.001
y[1] (numeric) = -1.31772837868 0.288417159682
y[1] (closed_form) = -1.31775792961 0.288426823661
absolute error = 3.109e-05
relative error = 0.002305 %
Correct digits = 5
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] = -1.6345 2.057
h = 0.001 0.003
y[1] (numeric) = -1.31788820234 0.288552484784
y[1] (closed_form) = -1.31791783501 0.288562307816
absolute error = 3.122e-05
relative error = 0.002314 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.946
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6335 2.06
h = 0.0001 0.004
y[1] (numeric) = -1.31834363479 0.288663050201
y[1] (closed_form) = -1.318373087 0.28867255619
absolute error = 3.095e-05
relative error = 0.002293 %
Correct digits = 5
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] = -1.6334 2.064
h = 0.003 0.006
y[1] (numeric) = -1.31893458987 0.288626723758
y[1] (closed_form) = -1.3189637324 0.288636223669
absolute error = 3.065e-05
relative error = 0.00227 %
Correct digits = 5
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
x[1] = -1.6304 2.07
h = 0.0001 0.005
y[1] (numeric) = -1.31985586811 0.288989259402
y[1] (closed_form) = -1.31988575604 0.288997627227
absolute error = 3.104e-05
relative error = 0.002297 %
Correct digits = 5
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] = -1.6303 2.075
h = 0.0001 0.003
y[1] (numeric) = -1.32059096007 0.28893396815
y[1] (closed_form) = -1.3206205042 0.288943143834
absolute error = 3.094e-05
relative error = 0.002288 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.953
Order of pole (given) = 1 0
NO POLE (ratio test) 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 2.078
h = 0.001 0.001
y[1] (numeric) = -1.32103112768 0.288905954516
y[1] (closed_form) = -1.32106092343 0.288915362196
absolute error = 3.125e-05
relative error = 0.002311 %
Correct digits = 5
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] = -1.6292 2.079
h = 0.001 0.003
y[1] (numeric) = -1.32119158142 0.289037667765
y[1] (closed_form) = -1.32122146163 0.289047230601
absolute error = 3.137e-05
relative error = 0.00232 %
Correct digits = 5
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] = -1.6282 2.082
h = 0.0001 0.004
y[1] (numeric) = -1.32164465034 0.289140371854
y[1] (closed_form) = -1.32167434491 0.289149625829
absolute error = 3.110e-05
relative error = 0.002299 %
Correct digits = 5
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] = -1.6281 2.086
h = 0.003 0.006
y[1] (numeric) = -1.32222981217 0.289095451743
y[1] (closed_form) = -1.32225920078 0.289104706964
absolute error = 3.081e-05
relative error = 0.002276 %
Correct digits = 5
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] = -1.6251 2.092
h = 0.0001 0.005
y[1] (numeric) = -1.32314836285 0.289440893827
y[1] (closed_form) = -1.32317846107 0.289449013729
absolute error = 3.117e-05
relative error = 0.002302 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.958
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.625 2.097
h = 0.0001 0.003
y[1] (numeric) = -1.3238760568 0.289375052443
y[1] (closed_form) = -1.32390583439 0.289383978049
absolute error = 3.109e-05
relative error = 0.002294 %
Correct digits = 5
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] = -1.6249 2.1
h = 0.001 0.001
y[1] (numeric) = -1.32431187052 0.289340690518
y[1] (closed_form) = -1.32434190196 0.289349839341
absolute error = 3.139e-05
relative error = 0.002316 %
Correct digits = 5
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] = -1.6239 2.101
h = 0.001 0.003
y[1] (numeric) = -1.32447286213 0.289468822447
y[1] (closed_form) = -1.32450298058 0.289478122505
absolute error = 3.152e-05
relative error = 0.002325 %
Correct digits = 5
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] = -1.6229 2.104
h = 0.0001 0.004
y[1] (numeric) = -1.32492341358 0.289563818991
y[1] (closed_form) = -1.32495334154 0.289572818406
absolute error = 3.125e-05
relative error = 0.002304 %
Correct digits = 5
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
memory used=914.0MB, alloc=44.3MB, time=11.64
x[1] = -1.6228 2.108
h = 0.003 0.006
y[1] (numeric) = -1.32550265459 0.289510548351
y[1] (closed_form) = -1.32553228049 0.2895195561
absolute error = 3.097e-05
relative error = 0.002282 %
Correct digits = 5
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] = -1.6198 2.114
h = 0.0001 0.005
y[1] (numeric) = -1.3264181142 0.289839175613
y[1] (closed_form) = -1.32644841441 0.289847046012
absolute error = 3.131e-05
relative error = 0.002306 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.966
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6197 2.119
h = 0.0001 0.003
y[1] (numeric) = -1.32713825885 0.289763089655
y[1] (closed_form) = -1.32716826114 0.289771762894
absolute error = 3.123e-05
relative error = 0.002299 %
Correct digits = 5
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] = -1.6196 2.122
h = 0.001 0.001
y[1] (numeric) = -1.32756962677 0.289722560873
y[1] (closed_form) = -1.32759988482 0.28973144862
absolute error = 3.154e-05
relative error = 0.002321 %
Correct digits = 5
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] = -1.6186 2.123
h = 0.0001 0.004
y[1] (numeric) = -1.32773106649 0.289847144493
y[1] (closed_form) = -1.32776141392 0.289856179535
absolute error = 3.166e-05
relative error = 0.00233 %
Correct digits = 5
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] = -1.6185 2.127
h = 0.003 0.006
y[1] (numeric) = -1.328305365 0.289787234943
y[1] (closed_form) = -1.32833506984 0.289796002516
absolute error = 3.097e-05
relative error = 0.002278 %
Correct digits = 5
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] = -1.6155 2.133
h = 0.0001 0.005
y[1] (numeric) = -1.32921768848 0.290101659713
y[1] (closed_form) = -1.32924803762 0.29010928953
absolute error = 3.129e-05
relative error = 0.0023 %
Correct digits = 5
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] = -1.6154 2.138
h = 0.0001 0.003
y[1] (numeric) = -1.32993110602 0.290017092344
y[1] (closed_form) = -1.32996117639 0.290025521731
absolute error = 3.123e-05
relative error = 0.002294 %
Correct digits = 5
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] = -1.6153 2.141
h = 0.001 0.001
y[1] (numeric) = -1.33035850858 0.289971454949
y[1] (closed_form) = -1.330388836 0.289980091394
absolute error = 3.153e-05
relative error = 0.002316 %
Correct digits = 5
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] = -1.6143 2.142
h = 0.001 0.003
y[1] (numeric) = -1.33052022235 0.290093008589
y[1] (closed_form) = -1.33055064102 0.290101788902
absolute error = 3.166e-05
relative error = 0.002325 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.977
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6133 2.145
h = 0.0001 0.004
y[1] (numeric) = -1.33096561752 0.290174114759
y[1] (closed_form) = -1.33099583771 0.29018260982
absolute error = 3.139e-05
relative error = 0.002304 %
Correct digits = 5
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] = -1.6132 2.149
h = 0.003 0.006
y[1] (numeric) = -1.33153344268 0.290106026931
y[1] (closed_form) = -1.33156336858 0.290114542826
absolute error = 3.111e-05
relative error = 0.002283 %
Correct digits = 5
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] = -1.6102 2.155
h = 0.0001 0.005
y[1] (numeric) = -1.3324420415 0.290404178001
y[1] (closed_form) = -1.33247257737 0.290411556224
absolute error = 3.141e-05
relative error = 0.002304 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.982
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6101 2.16
h = 0.0001 0.003
y[1] (numeric) = -1.33314766414 0.290309935466
y[1] (closed_form) = -1.33317794308 0.290318109167
absolute error = 3.136e-05
relative error = 0.002299 %
Correct digits = 5
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] = -1.61 2.163
h = 0.001 0.001
y[1] (numeric) = -1.33357047126 0.290258469493
y[1] (closed_form) = -1.33360100861 0.290266841706
absolute error = 3.166e-05
relative error = 0.00232 %
Correct digits = 5
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] = -1.609 2.164
h = 0.001 0.003
y[1] (numeric) = -1.33373247326 0.290376543329
y[1] (closed_form) = -1.33376310393 0.290385055457
absolute error = 3.179e-05
relative error = 0.002329 %
Correct digits = 5
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] = -1.608 2.167
h = 0.0001 0.004
y[1] (numeric) = -1.33417495314 0.290450396022
y[1] (closed_form) = -1.33420538145 0.290458631139
absolute error = 3.152e-05
relative error = 0.002309 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.987
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6079 2.171
h = 0.003 0.006
y[1] (numeric) = -1.33473654913 0.290374654126
y[1] (closed_form) = -1.33476668748 0.290382916475
absolute error = 3.125e-05
relative error = 0.002288 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.989
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6049 2.177
h = 0.0001 0.005
y[1] (numeric) = -1.33564110206 0.290656828619
y[1] (closed_form) = -1.33567181663 0.290663954458
absolute error = 3.153e-05
relative error = 0.002307 %
Correct digits = 5
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] = -1.6048 2.182
h = 0.0001 0.003
y[1] (numeric) = -1.33633881274 0.290553214757
y[1] (closed_form) = -1.33636929173 0.290561131367
absolute error = 3.149e-05
relative error = 0.002303 %
Correct digits = 5
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] = -1.6047 2.185
h = 0.001 0.001
y[1] (numeric) = -1.33675695293 0.290496100779
y[1] (closed_form) = -1.33678769138 0.290504207455
absolute error = 3.179e-05
relative error = 0.002324 %
Correct digits = 5
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] = -1.6037 2.186
h = 0.001 0.003
y[1] (numeric) = -1.3369191607 0.290610734055
y[1] (closed_form) = -1.33694999438 0.290618976694
absolute error = 3.192e-05
relative error = 0.002333 %
Correct digits = 5
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] = -1.6027 2.189
h = 0.0001 0.004
y[1] (numeric) = -1.33735859963 0.290677494689
y[1] (closed_form) = -1.3373892274 0.290685468542
absolute error = 3.165e-05
relative error = 0.002312 %
Correct digits = 5
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] = -1.6026 2.193
h = 0.003 0.006
y[1] (numeric) = -1.3379138758 0.290594340355
y[1] (closed_form) = -1.33794421807 0.290602347594
absolute error = 3.138e-05
relative error = 0.002292 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.998
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5996 2.199
h = 0.0001 0.005
y[1] (numeric) = -1.33881407628 0.290860840479
y[1] (closed_form) = -1.33884496162 0.290867713401
absolute error = 3.164e-05
relative error = 0.002309 %
Correct digits = 5
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] = -1.5995 2.204
h = 0.0001 0.003
y[1] (numeric) = -1.33950376941 0.290748157672
y[1] (closed_form) = -1.33953444001 0.290755816074
absolute error = 3.161e-05
relative error = 0.002306 %
Correct digits = 5
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] = -1.5994 2.207
h = 0.001 0.001
y[1] (numeric) = -1.339917178 0.290685575447
y[1] (closed_form) = -1.33994810883 0.29069341558
absolute error = 3.191e-05
relative error = 0.002327 %
Correct digits = 5
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
x[1] = -1.5984 2.208
h = 0.001 0.003
y[1] (numeric) = -1.34007951168 0.290796809311
y[1] (closed_form) = -1.34011053951 0.290804781464
absolute error = 3.204e-05
relative error = 0.002336 %
Correct digits = 5
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=960.6MB, alloc=44.3MB, time=12.26
x[1] = -1.5974 2.211
h = 0.0001 0.004
y[1] (numeric) = -1.34051579115 0.290856640493
y[1] (closed_form) = -1.34054660983 0.290864352055
absolute error = 3.177e-05
relative error = 0.002316 %
Correct digits = 5
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] = -1.5973 2.215
h = 0.003 0.006
y[1] (numeric) = -1.3410646659 0.290766314079
y[1] (closed_form) = -1.34109520366 0.290774064939
absolute error = 3.151e-05
relative error = 0.002296 %
Correct digits = 5
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] = -1.5943 2.221
h = 0.0001 0.005
y[1] (numeric) = -1.34196022196 0.291017446429
y[1] (closed_form) = -1.34199127026 0.291024066152
absolute error = 3.175e-05
relative error = 0.002312 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.008
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5942 2.226
h = 0.0001 0.003
y[1] (numeric) = -1.34264180311 0.290895995167
y[1] (closed_form) = -1.342672657 0.290903394526
absolute error = 3.173e-05
relative error = 0.00231 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.011
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5941 2.229
h = 0.001 0.001
y[1] (numeric) = -1.34305042208 0.290828123379
y[1] (closed_form) = -1.34308153671 0.290835696254
absolute error = 3.202e-05
relative error = 0.00233 %
Correct digits = 5
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] = -1.5931 2.23
h = 0.0001 0.004
y[1] (numeric) = -1.34321280445 0.290936000743
y[1] (closed_form) = -1.34324401769 0.290943701706
absolute error = 3.215e-05
relative error = 0.002339 %
Correct digits = 5
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] = -1.593 2.234
h = 0.003 0.006
y[1] (numeric) = -1.34375637893 0.290839996483
y[1] (closed_form) = -1.34378696531 0.290847514606
absolute error = 3.150e-05
relative error = 0.002291 %
Correct digits = 5
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] = -1.59 2.24
h = 0.0001 0.005
y[1] (numeric) = -1.34464753641 0.291078208921
y[1] (closed_form) = -1.34467860592 0.291084599775
absolute error = 3.172e-05
relative error = 0.002306 %
Correct digits = 5
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] = -1.5899 2.245
h = 0.0001 0.003
y[1] (numeric) = -1.34532196811 0.290949546901
y[1] (closed_form) = -1.34535286019 0.290956711712
absolute error = 3.171e-05
relative error = 0.002304 %
Correct digits = 5
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] = -1.5898 2.248
h = 0.001 0.001
y[1] (numeric) = -1.34572636269 0.290877321994
y[1] (closed_form) = -1.34575751565 0.29088465335
absolute error = 3.200e-05
relative error = 0.002324 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.021
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5888 2.249
h = 0.001 0.003
y[1] (numeric) = -1.34588868792 0.290982346418
y[1] (closed_form) = -1.34591994071 0.290989802477
absolute error = 3.213e-05
relative error = 0.002333 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.021
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5878 2.252
h = 0.0001 0.004
y[1] (numeric) = -1.34631871909 0.291029759707
y[1] (closed_form) = -1.3463497576 0.291036970335
absolute error = 3.187e-05
relative error = 0.002313 %
Correct digits = 5
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
x[1] = -1.5877 2.256
h = 0.003 0.006
y[1] (numeric) = -1.34685541636 0.290926799845
y[1] (closed_form) = -1.34688618279 0.290934060069
absolute error = 3.161e-05
relative error = 0.002294 %
Correct digits = 5
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] = -1.5847 2.262
h = 0.0001 0.005
y[1] (numeric) = -1.34774142817 0.291150227472
y[1] (closed_form) = -1.34777264647 0.291156365313
absolute error = 3.182e-05
relative error = 0.002307 %
Correct digits = 5
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] = -1.5846 2.267
h = 0.0001 0.003
y[1] (numeric) = -1.34840760435 0.291013350551
y[1] (closed_form) = -1.34843866454 0.291020255572
absolute error = 3.182e-05
relative error = 0.002307 %
Correct digits = 5
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] = -1.5845 2.27
h = 0.001 0.001
y[1] (numeric) = -1.34880712055 0.290936165408
y[1] (closed_form) = -1.34883844165 0.290943229005
absolute error = 3.211e-05
relative error = 0.002327 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.031
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5835 2.271
h = 0.001 0.003
y[1] (numeric) = -1.34896935841 0.291037918226
y[1] (closed_form) = -1.34900078068 0.291045102639
absolute error = 3.223e-05
relative error = 0.002336 %
Correct digits = 5
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] = -1.5825 2.274
h = 0.0001 0.004
y[1] (numeric) = -1.34939593159 0.291078872197
y[1] (closed_form) = -1.3494271372 0.29108581922
absolute error = 3.197e-05
relative error = 0.002316 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.032
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5824 2.278
h = 0.003 0.006
y[1] (numeric) = -1.34992604458 0.290969418539
y[1] (closed_form) = -1.34995698294 0.29097642038
absolute error = 3.172e-05
relative error = 0.002297 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.034
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5794 2.284
h = 0.0001 0.005
y[1] (numeric) = -1.35080665967 0.29117837669
y[1] (closed_form) = -1.35083801935 0.291184261887
absolute error = 3.191e-05
relative error = 0.002309 %
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] = -1.5793 2.289
h = 0.0001 0.003
y[1] (numeric) = -1.35146451607 0.291033577665
y[1] (closed_form) = -1.3514957364 0.291040222807
absolute error = 3.192e-05
relative error = 0.002309 %
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] = -1.5792 2.292
h = 0.001 0.001
y[1] (numeric) = -1.35185911386 0.290951606539
y[1] (closed_form) = -1.3518905949 0.290958402429
absolute error = 3.221e-05
relative error = 0.002329 %
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] = -1.5782 2.293
h = 0.001 0.003
y[1] (numeric) = -1.35202119475 0.291050134895
y[1] (closed_form) = -1.35205277816 0.291057047741
absolute error = 3.233e-05
relative error = 0.002338 %
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] = -1.5772 2.296
h = 0.0001 0.004
y[1] (numeric) = -1.35244421798 0.291084793848
y[1] (closed_form) = -1.35247558263 0.291091477274
absolute error = 3.207e-05
relative error = 0.002318 %
Correct digits = 5
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] = -1.5771 2.3
h = 0.003 0.006
y[1] (numeric) = -1.35296769768 0.290969078766
y[1] (closed_form) = -1.35299879999 0.290975821992
absolute error = 3.182e-05
relative error = 0.0023 %
Correct digits = 5
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
x[1] = -1.5741 2.306
h = 0.0001 0.005
y[1] (numeric) = -1.35384267891 0.291163884692
y[1] (closed_form) = -1.35387417269 0.291169517824
absolute error = 3.199e-05
relative error = 0.00231 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.045
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.574 2.311
h = 0.0001 0.003
y[1] (numeric) = -1.35449216117 0.291011453044
y[1] (closed_form) = -1.35452353382 0.291017838455
absolute error = 3.202e-05
relative error = 0.002311 %
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] = -1.5739 2.314
h = 0.001 0.001
y[1] (numeric) = -1.35488180645 0.290924868262
y[1] (closed_form) = -1.35491343938 0.290931396739
absolute error = 3.230e-05
relative error = 0.002331 %
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] = -1.5729 2.315
h = 0.001 0.003
y[1] (numeric) = -1.35504366343 0.29102022053
y[1] (closed_form) = -1.35507539978 0.291026862139
memory used=1007.0MB, alloc=44.3MB, time=12.85
absolute error = 3.242e-05
relative error = 0.002339 %
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] = -1.5719 2.318
h = 0.0001 0.004
y[1] (numeric) = -1.3554630513 0.291048748559
y[1] (closed_form) = -1.35549456707 0.291055168638
absolute error = 3.216e-05
relative error = 0.00232 %
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
x[1] = -1.5718 2.322
h = 0.003 0.006
y[1] (numeric) = -1.35597985649 0.290927001707
y[1] (closed_form) = -1.35601111488 0.290933486333
absolute error = 3.192e-05
relative error = 0.002302 %
Correct digits = 5
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] = -1.5688 2.328
h = 0.0001 0.005
y[1] (numeric) = -1.35684898041 0.291107973996
y[1] (closed_form) = -1.35688060117 0.291113355839
absolute error = 3.208e-05
relative error = 0.002311 %
Correct digits = 5
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] = -1.5687 2.333
h = 0.0001 0.003
y[1] (numeric) = -1.35749004374 0.290948195574
y[1] (closed_form) = -1.35752156103 0.290954321634
absolute error = 3.211e-05
relative error = 0.002313 %
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] = -1.5686 2.336
h = 0.001 0.001
y[1] (numeric) = -1.35787470813 0.290857167353
y[1] (closed_form) = -1.35790648504 0.290863428951
absolute error = 3.239e-05
relative error = 0.002332 %
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] = -1.5676 2.337
h = 0.0001 0.004
y[1] (numeric) = -1.35803627689 0.290949393008
y[1] (closed_form) = -1.35806815816 0.290955763952
absolute error = 3.251e-05
relative error = 0.002341 %
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] = -1.5675 2.341
h = 0.003 0.006
y[1] (numeric) = -1.35854758931 0.290822892318
y[1] (closed_form) = -1.35857886968 0.290829155225
absolute error = 3.190e-05
relative error = 0.002296 %
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] = -1.5645 2.347
h = 0.0001 0.005
y[1] (numeric) = -1.35941134319 0.290992285945
y[1] (closed_form) = -1.35944296158 0.290997453273
absolute error = 3.204e-05
relative error = 0.002304 %
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] = -1.5644 2.352
h = 0.0001 0.003
y[1] (numeric) = -1.360045048 0.290826510428
y[1] (closed_form) = -1.36007657758 0.290832414537
absolute error = 3.208e-05
relative error = 0.002306 %
Correct digits = 5
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] = -1.5643 2.355
h = 0.001 0.001
y[1] (numeric) = -1.36042535627 0.290731851697
y[1] (closed_form) = -1.36045714465 0.290737885002
absolute error = 3.236e-05
relative error = 0.002326 %
Correct digits = 5
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] = -1.5633 2.356
h = 0.001 0.003
y[1] (numeric) = -1.36058659102 0.290821430864
y[1] (closed_form) = -1.36061848441 0.290827570279
absolute error = 3.248e-05
relative error = 0.002334 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.069
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5623 2.359
h = 0.0001 0.004
y[1] (numeric) = -1.36099894038 0.29083903111
y[1] (closed_form) = -1.36103061059 0.290844963441
absolute error = 3.222e-05
relative error = 0.002315 %
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] = -1.5622 2.363
h = 0.003 0.006
y[1] (numeric) = -1.36150317617 0.290706741804
y[1] (closed_form) = -1.36153459839 0.290712746841
absolute error = 3.199e-05
relative error = 0.002298 %
Correct digits = 5
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] = -1.5592 2.369
h = 0.0001 0.005
y[1] (numeric) = -1.36236069635 0.290862898575
y[1] (closed_form) = -1.36239242889 0.290867816638
absolute error = 3.211e-05
relative error = 0.002305 %
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] = -1.5591 2.374
h = 0.0001 0.003
y[1] (numeric) = -1.36298592641 0.290690297857
y[1] (closed_form) = -1.36301758675 0.290695943984
absolute error = 3.216e-05
relative error = 0.002308 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.078
Order of pole (given) = 1 0
NO POLE (ratio test) 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 2.377
h = 0.001 0.001
y[1] (numeric) = -1.36336121742 0.290591506412
y[1] (closed_form) = -1.36339313553 0.290597274504
absolute error = 3.244e-05
relative error = 0.002327 %
Correct digits = 5
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] = -1.558 2.378
h = 0.001 0.003
y[1] (numeric) = -1.36352205187 0.290678054226
y[1] (closed_form) = -1.36355407568 0.290683924727
absolute error = 3.256e-05
relative error = 0.002335 %
Correct digits = 5
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] = -1.557 2.381
h = 0.0001 0.004
y[1] (numeric) = -1.36393055825 0.290689990469
y[1] (closed_form) = -1.36396235778 0.290695661493
absolute error = 3.230e-05
relative error = 0.002316 %
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] = -1.5569 2.385
h = 0.003 0.006
y[1] (numeric) = -1.36442804478 0.290552309514
y[1] (closed_form) = -1.36445960141 0.290558057335
absolute error = 3.208e-05
relative error = 0.002299 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.084
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5539 2.391
h = 0.0001 0.005
y[1] (numeric) = -1.36527914552 0.290695548719
y[1] (closed_form) = -1.36531098553 0.290700218805
absolute error = 3.218e-05
relative error = 0.002305 %
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] = -1.5538 2.396
h = 0.0001 0.003
y[1] (numeric) = -1.36589588139 0.290516396682
y[1] (closed_form) = -1.36592766525 0.290521785804
absolute error = 3.224e-05
relative error = 0.002308 %
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] = -1.5537 2.399
h = 0.001 0.001
y[1] (numeric) = -1.3662661419 0.290413635746
y[1] (closed_form) = -1.36629818232 0.290419139768
absolute error = 3.251e-05
relative error = 0.002327 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.091
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5527 2.4
h = 0.001 0.003
y[1] (numeric) = -1.3664265192 0.290497204128
y[1] (closed_form) = -1.3664586659 0.290502806904
absolute error = 3.263e-05
relative error = 0.002336 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.091
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5517 2.403
h = 0.0001 0.004
y[1] (numeric) = -1.36683112096 0.290503637403
y[1] (closed_form) = -1.36686304254 0.290509048198
absolute error = 3.238e-05
relative error = 0.002317 %
Correct digits = 5
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] = -1.5516 2.407
h = 0.003 0.006
y[1] (numeric) = -1.36732184447 0.29036078181
y[1] (closed_form) = -1.36735352823 0.290366273272
absolute error = 3.216e-05
relative error = 0.0023 %
Correct digits = 5
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] = -1.5486 2.413
h = 0.0001 0.005
y[1] (numeric) = -1.36816635265 0.290491422082
y[1] (closed_form) = -1.36819829362 0.290495845644
absolute error = 3.225e-05
relative error = 0.002305 %
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] = -1.5485 2.418
h = 0.0001 0.003
y[1] (numeric) = -1.36877458307 0.290305988021
y[1] (closed_form) = -1.36880648338 0.290311121303
absolute error = 3.231e-05
relative error = 0.002309 %
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] = -1.5484 2.421
h = 0.001 0.001
y[1] (numeric) = -1.36913980474 0.290199418126
y[1] (closed_form) = -1.36917196023 0.290204659411
absolute error = 3.258e-05
relative error = 0.002328 %
Correct digits = 5
memory used=1053.4MB, alloc=44.3MB, time=13.44
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] = -1.5474 2.422
h = 0.001 0.003
y[1] (numeric) = -1.36929967058 0.290280059635
y[1] (closed_form) = -1.3693319328 0.290285396074
absolute error = 3.270e-05
relative error = 0.002336 %
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] = -1.5464 2.425
h = 0.0001 0.004
y[1] (numeric) = -1.36970031185 0.290281149704
y[1] (closed_form) = -1.36973234832 0.290286301539
absolute error = 3.245e-05
relative error = 0.002317 %
Correct digits = 5
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] = -1.5463 2.429
h = 0.003 0.006
y[1] (numeric) = -1.37018426497 0.290133332783
y[1] (closed_form) = -1.37021606873 0.290138568938
absolute error = 3.223e-05
relative error = 0.002301 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.105
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5433 2.435
h = 0.0001 0.005
y[1] (numeric) = -1.37102201978 0.290251691657
y[1] (closed_form) = -1.37105405536 0.290255870295
absolute error = 3.231e-05
relative error = 0.002305 %
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] = -1.5432 2.44
h = 0.0001 0.003
y[1] (numeric) = -1.37162174131 0.29006024008
y[1] (closed_form) = -1.37165375117 0.290065118865
absolute error = 3.238e-05
relative error = 0.00231 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.111
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5431 2.443
h = 0.001 0.001
y[1] (numeric) = -1.3719819205 0.289950018951
y[1] (closed_form) = -1.37201418397 0.289954999012
absolute error = 3.265e-05
relative error = 0.002328 %
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
x[1] = -1.5421 2.444
h = 0.0001 0.004
y[1] (numeric) = -1.37214122308 0.290027786682
y[1] (closed_form) = -1.37217359365 0.290032858352
absolute error = 3.277e-05
relative error = 0.002336 %
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
x[1] = -1.542 2.448
h = 0.003 0.006
y[1] (numeric) = -1.37261963084 0.289876078661
y[1] (closed_form) = -1.37265143387 0.289881106653
absolute error = 3.220e-05
relative error = 0.002295 %
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] = -1.539 2.454
h = 0.0001 0.005
y[1] (numeric) = -1.37345131176 0.289984202063
y[1] (closed_form) = -1.3734833255 0.289988182176
absolute error = 3.226e-05
relative error = 0.002298 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.117
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5389 2.459
h = 0.0001 0.003
y[1] (numeric) = -1.3740436446 0.289787880112
y[1] (closed_form) = -1.37407564492 0.289792551776
absolute error = 3.234e-05
relative error = 0.002303 %
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] = -1.5388 2.462
h = 0.001 0.001
y[1] (numeric) = -1.3743994429 0.289674700247
y[1] (closed_form) = -1.37443169528 0.289679467556
absolute error = 3.260e-05
relative error = 0.002321 %
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] = -1.5378 2.463
h = 0.001 0.003
y[1] (numeric) = -1.37455818769 0.289750044675
y[1] (closed_form) = -1.37459054734 0.289754900586
absolute error = 3.272e-05
relative error = 0.002329 %
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] = -1.5368 2.466
h = 0.0001 0.004
y[1] (numeric) = -1.37495127036 0.289741660867
y[1] (closed_form) = -1.37498340375 0.289746345572
absolute error = 3.247e-05
relative error = 0.002311 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.124
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5367 2.47
h = 0.003 0.006
y[1] (numeric) = -1.37542257333 0.289585247108
y[1] (closed_form) = -1.37545448356 0.289590022307
absolute error = 3.227e-05
relative error = 0.002295 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.127
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5337 2.476
h = 0.0001 0.005
y[1] (numeric) = -1.37624723696 0.289681677184
y[1] (closed_form) = -1.37627933396 0.289685415799
absolute error = 3.231e-05
relative error = 0.002298 %
Correct digits = 5
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] = -1.5336 2.481
h = 0.0001 0.003
y[1] (numeric) = -1.37683107714 0.28947981643
y[1] (closed_form) = -1.37686317463 0.289484236616
absolute error = 3.240e-05
relative error = 0.002303 %
Correct digits = 5
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] = -1.5335 2.484
h = 0.001 0.001
y[1] (numeric) = -1.37718183971 0.289363270924
y[1] (closed_form) = -1.37721418742 0.289367780351
absolute error = 3.266e-05
relative error = 0.002321 %
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] = -1.5325 2.485
h = 0.001 0.003
y[1] (numeric) = -1.37733993205 0.289435841986
y[1] (closed_form) = -1.37737238719 0.289440436582
absolute error = 3.278e-05
relative error = 0.002329 %
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] = -1.5315 2.488
h = 0.0001 0.004
y[1] (numeric) = -1.37772892627 0.289422563846
y[1] (closed_form) = -1.37776115513 0.289426994247
absolute error = 3.253e-05
relative error = 0.002311 %
Correct digits = 5
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] = -1.5314 2.492
h = 0.003 0.006
y[1] (numeric) = -1.37819347314 0.289261777159
y[1] (closed_form) = -1.37822548393 0.289266301112
absolute error = 3.233e-05
relative error = 0.002296 %
Correct digits = 5
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] = -1.5284 2.498
h = 0.0001 0.005
y[1] (numeric) = -1.37901099197 0.289346825908
y[1] (closed_form) = -1.37904316636 0.289350325006
absolute error = 3.236e-05
relative error = 0.002297 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.14
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5283 2.503
h = 0.0001 0.003
y[1] (numeric) = -1.37958635642 0.289139676206
y[1] (closed_form) = -1.37961854465 0.289143846712
absolute error = 3.246e-05
relative error = 0.002303 %
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] = -1.5282 2.506
h = 0.001 0.001
y[1] (numeric) = -1.37993209181 0.289019914172
y[1] (closed_form) = -1.37996452828 0.28902416769
absolute error = 3.271e-05
relative error = 0.00232 %
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] = -1.5272 2.507
h = 0.001 0.003
y[1] (numeric) = -1.38008948684 0.289089765905
y[1] (closed_form) = -1.38012203082 0.28909410122
absolute error = 3.283e-05
relative error = 0.002328 %
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] = -1.5262 2.51
h = 0.0001 0.004
y[1] (numeric) = -1.38047435718 0.289071746625
y[1] (closed_form) = -1.38050667503 0.28907592462
absolute error = 3.259e-05
relative error = 0.00231 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.147
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5261 2.514
h = 0.003 0.006
y[1] (numeric) = -1.38093216268 0.288906784731
y[1] (closed_form) = -1.38096426755 0.288911059139
absolute error = 3.239e-05
relative error = 0.002296 %
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] = -1.5231 2.52
h = 0.0001 0.005
y[1] (numeric) = -1.38174242018 0.288980761562
y[1] (closed_form) = -1.38177466626 0.288984023243
absolute error = 3.241e-05
relative error = 0.002296 %
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] = -1.523 2.525
h = 0.0001 0.003
y[1] (numeric) = -1.38230933228 0.288768567434
y[1] (closed_form) = -1.38234160503 0.288772490196
absolute error = 3.251e-05
relative error = 0.002302 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.155
Order of pole (given) = 1 0
NO 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=1099.9MB, alloc=44.3MB, time=14.04
x[1] = -1.5229 2.528
h = 0.001 0.001
y[1] (numeric) = -1.38265005292 0.288645734845
y[1] (closed_form) = -1.3826825718 0.288649734566
absolute error = 3.276e-05
relative error = 0.00232 %
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] = -1.5219 2.529
h = 0.001 0.003
y[1] (numeric) = -1.38280670816 0.288712921444
y[1] (closed_form) = -1.38283933451 0.288716999655
absolute error = 3.288e-05
relative error = 0.002328 %
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] = -1.5209 2.532
h = 0.0001 0.004
y[1] (numeric) = -1.38318742398 0.288690312185
y[1] (closed_form) = -1.38321982456 0.288694239812
absolute error = 3.264e-05
relative error = 0.00231 %
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] = -1.5208 2.536
h = 0.003 0.006
y[1] (numeric) = -1.38363850792 0.288521368539
y[1] (closed_form) = -1.38367070057 0.288525395245
absolute error = 3.244e-05
relative error = 0.002295 %
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] = -1.5178 2.542
h = 0.0001 0.005
y[1] (numeric) = -1.3844413982 0.288584579951
y[1] (closed_form) = -1.38447371042 0.288587606421
absolute error = 3.245e-05
relative error = 0.002295 %
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] = -1.5177 2.547
h = 0.0001 0.003
y[1] (numeric) = -1.38499988745 0.288367580485
y[1] (closed_form) = -1.38503223864 0.288371257571
absolute error = 3.256e-05
relative error = 0.002301 %
Correct digits = 5
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] = -1.5176 2.55
h = 0.001 0.001
y[1] (numeric) = -1.38533560943 0.288241820112
y[1] (closed_form) = -1.38536820453 0.288245568279
absolute error = 3.281e-05
relative error = 0.002319 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.169
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5166 2.551
h = 0.0001 0.004
y[1] (numeric) = -1.38549148465 0.288306395848
y[1] (closed_form) = -1.38552418711 0.288310219264
absolute error = 3.293e-05
relative error = 0.002327 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.169
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5165 2.555
h = 0.003 0.006
y[1] (numeric) = -1.38593708386 0.288134346986
y[1] (closed_form) = -1.38596925692 0.288138180683
absolute error = 3.240e-05
relative error = 0.002289 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.172
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5135 2.561
h = 0.0001 0.005
y[1] (numeric) = -1.38673343241 0.288188624162
y[1] (closed_form) = -1.38676570716 0.288191468884
absolute error = 3.240e-05
relative error = 0.002287 %
Correct digits = 5
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] = -1.5134 2.566
h = 0.0001 0.003
y[1] (numeric) = -1.38728464612 0.287967775417
y[1] (closed_form) = -1.3873169699 0.287971261512
absolute error = 3.251e-05
relative error = 0.002295 %
Correct digits = 5
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] = -1.5133 2.569
h = 0.001 0.001
y[1] (numeric) = -1.38761604836 0.287839665973
y[1] (closed_form) = -1.38764861396 0.287843218259
absolute error = 3.276e-05
relative error = 0.002312 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.18
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5123 2.57
h = 0.001 0.003
y[1] (numeric) = -1.38777119145 0.287902047723
y[1] (closed_form) = -1.38780386421 0.287905672525
absolute error = 3.287e-05
relative error = 0.002319 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.18
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5113 2.573
h = 0.0001 0.004
y[1] (numeric) = -1.38814406052 0.28787134259
y[1] (closed_form) = -1.38817650867 0.287874828951
absolute error = 3.263e-05
relative error = 0.002302 %
Correct digits = 5
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] = -1.5112 2.577
h = 0.003 0.006
y[1] (numeric) = -1.38858266387 0.287695569108
y[1] (closed_form) = -1.38861491347 0.287699158958
absolute error = 3.245e-05
relative error = 0.002288 %
Correct digits = 5
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] = -1.5082 2.583
h = 0.0001 0.005
y[1] (numeric) = -1.38937147875 0.287739643418
y[1] (closed_form) = -1.38940380982 0.287742257356
absolute error = 3.244e-05
relative error = 0.002286 %
Correct digits = 5
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] = -1.5081 2.588
h = 0.0001 0.003
y[1] (numeric) = -1.38991434233 0.287514418998
y[1] (closed_form) = -1.38994673376 0.287517663646
absolute error = 3.255e-05
relative error = 0.002294 %
Correct digits = 5
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] = -1.508 2.591
h = 0.001 0.001
y[1] (numeric) = -1.39024078657 0.287383638475
y[1] (closed_form) = -1.3902734174 0.287386943763
absolute error = 3.280e-05
relative error = 0.00231 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.192
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.507 2.592
h = 0.001 0.003
y[1] (numeric) = -1.39039508136 0.287443510689
y[1] (closed_form) = -1.39042781908 0.287446885379
absolute error = 3.291e-05
relative error = 0.002318 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.192
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.506 2.595
h = 0.0001 0.004
y[1] (numeric) = -1.39076373512 0.287408635954
y[1] (closed_form) = -1.39079624905 0.287411878525
absolute error = 3.268e-05
relative error = 0.002301 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.194
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5059 2.599
h = 0.003 0.006
y[1] (numeric) = -1.3911957012 0.287229409586
y[1] (closed_form) = -1.39122802152 0.287232757792
absolute error = 3.249e-05
relative error = 0.002287 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.196
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5029 2.605
h = 0.0001 0.005
y[1] (numeric) = -1.39197690487 0.287263577523
y[1] (closed_form) = -1.39200928718 0.287265963147
absolute error = 3.247e-05
relative error = 0.002284 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.199
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5028 2.61
h = 0.0001 0.003
y[1] (numeric) = -1.39251146341 0.287034200536
y[1] (closed_form) = -1.39254391691 0.287037206127
absolute error = 3.259e-05
relative error = 0.002292 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.202
Order of pole (given) = 1 0
NO POLE (ratio test) 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 2.613
h = 0.001 0.001
y[1] (numeric) = -1.39283297513 0.286900882281
y[1] (closed_form) = -1.39286566551 0.286903943134
absolute error = 3.283e-05
relative error = 0.002309 %
Correct digits = 5
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] = -1.5017 2.614
h = 0.001 0.003
y[1] (numeric) = -1.39298638764 0.286958298989
y[1] (closed_form) = -1.39301918457 0.2869614262
absolute error = 3.295e-05
relative error = 0.002316 %
Correct digits = 5
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] = -1.5007 2.617
h = 0.0001 0.004
y[1] (numeric) = -1.39335081238 0.286919396898
y[1] (closed_form) = -1.39338338649 0.286922398163
absolute error = 3.271e-05
relative error = 0.002299 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.206
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5006 2.621
h = 0.003 0.006
y[1] (numeric) = -1.39377617795 0.286736894023
y[1] (closed_form) = -1.39380856336 0.286740002899
absolute error = 3.253e-05
relative error = 0.002286 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.209
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4976 2.627
h = 0.0001 0.005
y[1] (numeric) = -1.39454970211 0.286761448156
y[1] (closed_form) = -1.39458213077 0.286763608012
absolute error = 3.250e-05
relative error = 0.002283 %
Correct digits = 5
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
memory used=1146.3MB, alloc=44.3MB, time=14.64
x[1] = -1.4975 2.632
h = 0.0001 0.003
y[1] (numeric) = -1.39507600554 0.286528136064
y[1] (closed_form) = -1.39510851573 0.286530905083
absolute error = 3.263e-05
relative error = 0.002291 %
Correct digits = 5
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] = -1.4974 2.635
h = 0.001 0.001
y[1] (numeric) = -1.39539261313 0.286392410091
y[1] (closed_form) = -1.39542535759 0.286395229168
absolute error = 3.287e-05
relative error = 0.002307 %
Correct digits = 5
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] = -1.4964 2.636
h = 0.001 0.003
y[1] (numeric) = -1.39554511147 0.28644742511
y[1] (closed_form) = -1.39557796207 0.28645030757
absolute error = 3.298e-05
relative error = 0.002315 %
Correct digits = 5
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] = -1.4954 2.639
h = 0.0001 0.004
y[1] (numeric) = -1.39590529742 0.286404635404
y[1] (closed_form) = -1.39593792629 0.286407397942
absolute error = 3.275e-05
relative error = 0.002298 %
Correct digits = 5
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
x[1] = -1.4953 2.643
h = 0.003 0.006
y[1] (numeric) = -1.39632410304 0.28621902791
y[1] (closed_form) = -1.39635654808 0.28622189987
absolute error = 3.257e-05
relative error = 0.002285 %
Correct digits = 5
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] = -1.4923 2.649
h = 0.0001 0.005
y[1] (numeric) = -1.39708988824 0.286234256669
y[1] (closed_form) = -1.39712235851 0.286236193374
absolute error = 3.253e-05
relative error = 0.002281 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.224
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4922 2.654
h = 0.0001 0.003
y[1] (numeric) = -1.39760799106 0.285997221271
y[1] (closed_form) = -1.39764055271 0.28599975629
absolute error = 3.266e-05
relative error = 0.002289 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.228
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4921 2.657
h = 0.001 0.001
y[1] (numeric) = -1.39791972566 0.285859214247
y[1] (closed_form) = -1.39795251889 0.285861794292
absolute error = 3.289e-05
relative error = 0.002305 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.23
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4911 2.658
h = 0.0001 0.004
y[1] (numeric) = -1.39807127992 0.285911881121
y[1] (closed_form) = -1.39810417882 0.285914521644
absolute error = 3.300e-05
relative error = 0.002313 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.23
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.491 2.662
h = 0.003 0.006
y[1] (numeric) = -1.39848474885 0.285723869309
y[1] (closed_form) = -1.39851715909 0.285726564215
absolute error = 3.252e-05
relative error = 0.002278 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.233
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.488 2.668
h = 0.0001 0.005
y[1] (numeric) = -1.39924372504 0.285731391759
y[1] (closed_form) = -1.39927614573 0.285733163603
absolute error = 3.247e-05
relative error = 0.002274 %
Correct digits = 5
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] = -1.4879 2.673
h = 0.0001 0.003
y[1] (numeric) = -1.3997547749 0.285491413458
y[1] (closed_form) = -1.39978729494 0.285493774146
absolute error = 3.261e-05
relative error = 0.002282 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.239
Order of pole (given) = 1 0
NO POLE (ratio test) 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 2.676
h = 0.001 0.001
y[1] (numeric) = -1.4000623167 0.28535159935
y[1] (closed_form) = -1.40009506589 0.285354000901
absolute error = 3.284e-05
relative error = 0.002298 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.241
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4868 2.677
h = 0.001 0.003
y[1] (numeric) = -1.40021300878 0.285402299335
y[1] (closed_form) = -1.40024586314 0.285404758929
absolute error = 3.295e-05
relative error = 0.002305 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.241
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4858 2.68
h = 0.0001 0.004
y[1] (numeric) = -1.40056525155 0.285352689345
y[1] (closed_form) = -1.40059788664 0.285355039811
absolute error = 3.272e-05
relative error = 0.002289 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.243
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4857 2.684
h = 0.003 0.006
y[1] (numeric) = -1.40097193817 0.285161823774
y[1] (closed_form) = -1.40100439836 0.285164286554
absolute error = 3.255e-05
relative error = 0.002277 %
Correct digits = 5
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] = -1.4827 2.69
h = 0.0001 0.005
y[1] (numeric) = -1.40172309049 0.285160546387
y[1] (closed_form) = -1.40175554442 0.285162100166
absolute error = 3.249e-05
relative error = 0.002271 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.248
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4826 2.695
h = 0.0001 0.003
y[1] (numeric) = -1.40222605455 0.284917223034
y[1] (closed_form) = -1.40225861682 0.284919354776
absolute error = 3.263e-05
relative error = 0.002281 %
Correct digits = 5
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] = -1.4825 2.698
h = 0.001 0.001
y[1] (numeric) = -1.40252878937 0.284775354215
y[1] (closed_form) = -1.40256157799 0.284777522103
absolute error = 3.286e-05
relative error = 0.002296 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.254
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4815 2.699
h = 0.001 0.003
y[1] (numeric) = -1.40267848755 0.284823805061
y[1] (closed_form) = -1.40271138074 0.284826028219
absolute error = 3.297e-05
relative error = 0.002303 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.254
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4805 2.702
h = 0.0001 0.004
y[1] (numeric) = -1.40302648525 0.284770692789
y[1] (closed_form) = -1.40305916062 0.284772812413
absolute error = 3.274e-05
relative error = 0.002287 %
Correct digits = 5
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] = -1.4804 2.706
h = 0.003 0.006
y[1] (numeric) = -1.40342674858 0.284577188838
y[1] (closed_form) = -1.40345925375 0.284579422146
absolute error = 3.258e-05
relative error = 0.002275 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.259
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4774 2.712
h = 0.0001 0.005
y[1] (numeric) = -1.40417004092 0.284567387147
y[1] (closed_form) = -1.40420252382 0.28456872564
absolute error = 3.251e-05
relative error = 0.002269 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.261
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4773 2.717
h = 0.0001 0.003
y[1] (numeric) = -1.40466498497 0.284320914297
y[1] (closed_form) = -1.40469758474 0.284322819875
absolute error = 3.266e-05
relative error = 0.002279 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.265
Order of pole (given) = 1 0
NO POLE (ratio test) 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 2.72
h = 0.001 0.001
y[1] (numeric) = -1.40496295079 0.284177107832
y[1] (closed_form) = -1.40499577403 0.284179045003
absolute error = 3.288e-05
relative error = 0.002294 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.267
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4762 2.721
h = 0.001 0.003
y[1] (numeric) = -1.40511163059 0.284223361963
y[1] (closed_form) = -1.40514455776 0.284225351705
absolute error = 3.299e-05
relative error = 0.002301 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.267
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4752 2.724
h = 0.0001 0.004
y[1] (numeric) = -1.40545538692 0.284166876885
y[1] (closed_form) = -1.40548809782 0.284168768535
absolute error = 3.277e-05
relative error = 0.002285 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.269
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4751 2.728
h = 0.003 0.006
y[1] (numeric) = -1.40584927986 0.283970889037
y[1] (closed_form) = -1.40588182521 0.2839728956
absolute error = 3.261e-05
relative error = 0.002273 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.272
Order of pole (given) = 1 0
NO 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=1192.8MB, alloc=44.3MB, time=15.22
x[1] = -1.4721 2.734
h = 0.0001 0.005
y[1] (numeric) = -1.40658468364 0.283952833824
y[1] (closed_form) = -1.40661719136 0.283953959857
absolute error = 3.253e-05
relative error = 0.002267 %
Correct digits = 5
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] = -1.472 2.739
h = 0.0001 0.003
y[1] (numeric) = -1.40707167689 0.283703401412
y[1] (closed_form) = -1.40710430958 0.283705083666
absolute error = 3.268e-05
relative error = 0.002276 %
Correct digits = 5
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] = -1.4719 2.742
h = 0.001 0.001
y[1] (numeric) = -1.40736491374 0.283557771039
y[1] (closed_form) = -1.40739776698 0.283559480496
absolute error = 3.290e-05
relative error = 0.002291 %
Correct digits = 5
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] = -1.4709 2.743
h = 0.001 0.003
y[1] (numeric) = -1.40751255248 0.283601880402
y[1] (closed_form) = -1.40754550894 0.283603639802
absolute error = 3.300e-05
relative error = 0.002299 %
Correct digits = 5
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] = -1.4699 2.746
h = 0.0001 0.004
y[1] (numeric) = -1.40785207423 0.283542149245
y[1] (closed_form) = -1.40788481608 0.283543815847
absolute error = 3.278e-05
relative error = 0.002283 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.282
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4698 2.75
h = 0.003 0.006
y[1] (numeric) = -1.40823965237 0.283343827525
y[1] (closed_form) = -1.40827223324 0.283345610129
absolute error = 3.263e-05
relative error = 0.002271 %
Correct digits = 5
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] = -1.4668 2.756
h = 0.0001 0.005
y[1] (numeric) = -1.40896714614 0.283317784706
y[1] (closed_form) = -1.40899967471 0.283318701141
absolute error = 3.254e-05
relative error = 0.002264 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.288
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4667 2.761
h = 0.0001 0.003
y[1] (numeric) = -1.40944626099 0.283065577078
y[1] (closed_form) = -1.40947892219 0.283067038902
absolute error = 3.269e-05
relative error = 0.002274 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.292
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4666 2.764
h = 0.001 0.001
y[1] (numeric) = -1.40973481082 0.282918233227
y[1] (closed_form) = -1.40976768961 0.282919718026
absolute error = 3.291e-05
relative error = 0.002289 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.294
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4656 2.765
h = 0.0001 0.004
y[1] (numeric) = -1.40988138753 0.282960249248
y[1] (closed_form) = -1.40991436879 0.282961781431
absolute error = 3.302e-05
relative error = 0.002296 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.294
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4655 2.769
h = 0.003 0.006
y[1] (numeric) = -1.41026384103 0.282760136935
y[1] (closed_form) = -1.41029637521 0.282761758598
absolute error = 3.257e-05
relative error = 0.002265 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.297
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4625 2.775
h = 0.0001 0.005
y[1] (numeric) = -1.41098442326 0.282727522244
y[1] (closed_form) = -1.41101689318 0.282728290308
absolute error = 3.248e-05
relative error = 0.002257 %
Correct digits = 5
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] = -1.4624 2.78
h = 0.0001 0.003
y[1] (numeric) = -1.41145678666 0.282473161813
y[1] (closed_form) = -1.41148939536 0.28247446589
absolute error = 3.263e-05
relative error = 0.002267 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.304
Order of pole (given) = 1 0
NO POLE (ratio test) 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 2.783
h = 0.001 0.001
y[1] (numeric) = -1.41174131834 0.282324484101
y[1] (closed_form) = -1.41177414199 0.282325807674
absolute error = 3.285e-05
relative error = 0.002282 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.306
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4613 2.784
h = 0.001 0.003
y[1] (numeric) = -1.41188694125 0.282364751954
y[1] (closed_form) = -1.41191986666 0.282366120777
absolute error = 3.295e-05
relative error = 0.002289 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.306
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4603 2.787
h = 0.0001 0.004
y[1] (numeric) = -1.41221857613 0.282299358498
y[1] (closed_form) = -1.41225129031 0.282300643955
absolute error = 3.274e-05
relative error = 0.002273 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.308
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4602 2.791
h = 0.003 0.006
y[1] (numeric) = -1.41259453632 0.282097151682
y[1] (closed_form) = -1.41262709786 0.28209855477
absolute error = 3.259e-05
relative error = 0.002263 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.311
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4572 2.797
h = 0.0001 0.005
y[1] (numeric) = -1.4133071896 0.282057030983
y[1] (closed_form) = -1.41333967339 0.282057594908
absolute error = 3.249e-05
relative error = 0.002254 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.314
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4571 2.802
h = 0.0001 0.003
y[1] (numeric) = -1.41377181891 0.281800222722
y[1] (closed_form) = -1.41380444837 0.281801311918
absolute error = 3.265e-05
relative error = 0.002265 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.317
Order of pole (given) = 1 0
NO POLE (ratio test) 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 2.805
h = 0.001 0.001
y[1] (numeric) = -1.41405174747 0.28165002776
y[1] (closed_form) = -1.41408458885 0.281651132517
absolute error = 3.286e-05
relative error = 0.002279 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.32
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.456 2.806
h = 0.001 0.003
y[1] (numeric) = -1.41419627429 0.281688296642
y[1] (closed_form) = -1.41422921661 0.281689444222
absolute error = 3.296e-05
relative error = 0.002286 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.32
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.455 2.809
h = 0.0001 0.004
y[1] (numeric) = -1.41452371096 0.28162000408
y[1] (closed_form) = -1.41455644395 0.281621073164
absolute error = 3.275e-05
relative error = 0.002271 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.322
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4549 2.813
h = 0.003 0.006
y[1] (numeric) = -1.41489352988 0.281415867496
y[1] (closed_form) = -1.4149261146 0.281417054938
absolute error = 3.261e-05
relative error = 0.00226 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.325
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4519 2.819
h = 0.0001 0.005
y[1] (numeric) = -1.41559825137 0.28136849222
y[1] (closed_form) = -1.41563074546 0.281368854952
absolute error = 3.250e-05
relative error = 0.002251 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.327
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4518 2.824
h = 0.0001 0.003
y[1] (numeric) = -1.41605522659 0.281109404747
y[1] (closed_form) = -1.41608787287 0.281110282072
absolute error = 3.266e-05
relative error = 0.002262 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.331
Order of pole (given) = 1 0
NO POLE (ratio test) 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 2.827
h = 0.001 0.001
y[1] (numeric) = -1.41633059863 0.280957793649
y[1] (closed_form) = -1.41636345376 0.280958682749
absolute error = 3.287e-05
relative error = 0.002276 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.334
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4507 2.828
h = 0.001 0.003
y[1] (numeric) = -1.41647401297 0.280994113265
y[1] (closed_form) = -1.41650696817 0.280995042832
absolute error = 3.297e-05
relative error = 0.002283 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.334
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4497 2.831
h = 0.0001 0.004
y[1] (numeric) = -1.41679726856 0.280923037505
y[1] (closed_form) = -1.4168300164 0.2809238933
absolute error = 3.276e-05
relative error = 0.002268 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.335
Order of pole (given) = 1 0
NO 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=1239.2MB, alloc=44.3MB, time=15.83
x[1] = -1.4496 2.835
h = 0.003 0.006
y[1] (numeric) = -1.41716101018 0.280717104287
y[1] (closed_form) = -1.41719361405 0.280718079051
absolute error = 3.262e-05
relative error = 0.002258 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.338
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4466 2.841
h = 0.0001 0.005
y[1] (numeric) = -1.41785780293 0.280662720706
y[1] (closed_form) = -1.41789030389 0.280662885209
absolute error = 3.250e-05
relative error = 0.002249 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.341
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4465 2.846
h = 0.0001 0.003
y[1] (numeric) = -1.41830720632 0.280401517276
y[1] (closed_form) = -1.4183398656 0.280402185766
absolute error = 3.267e-05
relative error = 0.002259 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.345
Order of pole (given) = 1 0
NO POLE (ratio test) 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 2.849
h = 0.001 0.001
y[1] (numeric) = -1.4185780698 0.280248587972
y[1] (closed_form) = -1.41861093484 0.280249264602
absolute error = 3.287e-05
relative error = 0.002273 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.348
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4454 2.85
h = 0.001 0.003
y[1] (numeric) = -1.41872035676 0.280283007373
y[1] (closed_form) = -1.41875332097 0.280283722182
absolute error = 3.297e-05
relative error = 0.00228 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.348
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4444 2.853
h = 0.0001 0.004
y[1] (numeric) = -1.41903945072 0.280209261514
y[1] (closed_form) = -1.41907220962 0.280209907131
absolute error = 3.277e-05
relative error = 0.002265 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.349
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4443 2.857
h = 0.003 0.006
y[1] (numeric) = -1.41939718073 0.280001660546
y[1] (closed_form) = -1.41942979988 0.280002425633
absolute error = 3.263e-05
relative error = 0.002255 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.353
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4413 2.863
h = 0.0001 0.005
y[1] (numeric) = -1.4200860534 0.279940509734
y[1] (closed_form) = -1.42011855796 0.279940478988
absolute error = 3.250e-05
relative error = 0.002246 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.355
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4412 2.868
h = 0.0001 0.003
y[1] (numeric) = -1.42052796923 0.279677348311
y[1] (closed_form) = -1.42056063786 0.279677811027
absolute error = 3.267e-05
relative error = 0.002257 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.359
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4411 2.871
h = 0.001 0.001
y[1] (numeric) = -1.42079437335 0.279523195594
y[1] (closed_form) = -1.42082724464 0.279523662961
absolute error = 3.287e-05
relative error = 0.00227 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.362
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4401 2.872
h = 0.001 0.003
y[1] (numeric) = -1.42093551946 0.279555763145
y[1] (closed_form) = -1.42096848898 0.279556266472
absolute error = 3.297e-05
relative error = 0.002277 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.362
Order of pole (given) = 1 0
NO 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 ) = 1.0 / ( x * x + 1.0 ) ;
Iterations = 754
Total Elapsed Time = 15 Seconds
Expected Time Remaining = 0 Seconds
Optimized Time Remaining = 0 Seconds
Expected Total Time = 15 Seconds
> quit
memory used=1258.4MB, alloc=44.3MB, time=16.06