|\^/| Maple 2016 (X86 64 LINUX)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2016
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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#BEGIN OUTFILE1
# before write maple top matter
# before write_ats library and user def block
#BEGIN ATS LIBRARY BLOCK
# Begin Function number 2
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s\n",str);
> fi;# end if 1;
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
# End Function number 2
# Begin Function number 3
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s",str);
> fi;# end if 1;
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
# End Function number 3
# Begin Function number 4
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> print(label,str);
> fi;# end if 1;
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
# End Function number 4
# Begin Function number 5
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 5
# Begin Function number 6
> omniout_complex := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> if vallen = 4 then
> printf("%-30s = %-20.4g %-20g %s \n",prelabel,Re(value), Im(value), postlabel);
> else
> printf("%-30s = %-20.12g %-20.12g %s \n",prelabel,Re(value),Im(value), postlabel);
> fi;# end if 0;
> fi;# end if -1;
> end;
omniout_complex := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then printf("%-30s = %-20.4g %-20g %s \n", prelabel,
Re(value), Im(value), postlabel)
else printf("%-30s = %-20.12g %-20.12g %s \n", prelabel, Re(value),
Im(value), postlabel)
end if
end if
end proc
# End Function number 6
# Begin Function number 7
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number -1
> if vallen = 5 then # if number 0
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;# end if 0;
> fi;# end if -1;
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 7
# Begin Function number 8
> logitem_time := proc(fd,secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> fprintf(fd,"
");
> if (secs_in >= 0) then # if number -1
> years_int := int_trunc(secs_in / glob_sec_in_year);
> sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
> days_int := int_trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := sec_temp mod int_trunc(glob_sec_in_day) ;
> hours_int := int_trunc(sec_temp / glob_sec_in_hour);
> sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
> minutes_int := int_trunc(sec_temp / glob_sec_in_minute);
> sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
> if (years_int > 0) then # if number 0
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 1
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 2
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 3
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 3
> else
> fprintf(fd," 0.0 Seconds");
> fi;# end if 2
> fprintf(fd," | \n");
> end;
logitem_time := proc(fd, secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
fprintf(fd, "");
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, " 0.0 Seconds")
end if;
fprintf(fd, " | \n")
end proc
# End Function number 8
# Begin Function number 9
> omniout_timestr := proc(secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> if (secs_in >= 0) then # if number 2
> years_int := int_trunc(secs_in / glob_sec_in_year);
> sec_temp := (int_trunc(secs_in) mod int_trunc(glob_sec_in_year));
> days_int := int_trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_day)) ;
> hours_int := int_trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_hour));
> minutes_int := int_trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod int_trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 3
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 4
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 5
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 6
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 6
> else
> printf(" 0.0 Seconds\n");
> fi;# end if 5
> end;
omniout_timestr := proc(secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" 0.0 Seconds\n")
end if
end proc
# End Function number 9
# Begin Function number 10
> zero_ats_ar := proc(arr_a)
> global ATS_MAX_TERMS;
> local iii;
> iii := 1;
> while (iii <= ATS_MAX_TERMS) do # do number 1
> arr_a [iii] := glob__0;
> iii := iii + 1;
> od;# end do number 1
> end;
zero_ats_ar := proc(arr_a)
local iii;
global ATS_MAX_TERMS;
iii := 1;
while iii <= ATS_MAX_TERMS do arr_a[iii] := glob__0; iii := iii + 1
end do
end proc
# End Function number 10
# Begin Function number 11
> ats := proc(mmm_ats,arr_a,arr_b,jjj_ats)
> global ATS_MAX_TERMS;
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := glob__0;
> if (jjj_ats <= mmm_ats) then # if number 5
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> if ((lll_ats <= ATS_MAX_TERMS and (iii_ats <= ATS_MAX_TERMS) )) then # if number 6
> ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]);
> fi;# end if 6;
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 5;
> ret_ats;
> end;
ats := proc(mmm_ats, arr_a, arr_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
global ATS_MAX_TERMS;
ret_ats := glob__0;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
if lll_ats <= ATS_MAX_TERMS and iii_ats <= ATS_MAX_TERMS then
ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats])
end if;
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
# End Function number 11
# Begin Function number 12
> att := proc(mmm_att,arr_aa,arr_bb,jjj_att)
> global ATS_MAX_TERMS;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := glob__0;
> if (jjj_att < mmm_att) then # if number 5
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while ((iii_att < mmm_att) and (iii_att <= ATS_MAX_TERMS) ) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if ((lll_att <= ATS_MAX_TERMS and (iii_att <= ATS_MAX_TERMS) )) then # if number 6
> ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att);
> fi;# end if 6;
> iii_att := iii_att + 1;
> od;# end do number 1;
> ret_att := ret_att / c(mmm_att) ;
> fi;# end if 5;
> ret_att;
> end;
att := proc(mmm_att, arr_aa, arr_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global ATS_MAX_TERMS;
ret_att := glob__0;
if jjj_att < mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att < mmm_att and iii_att <= ATS_MAX_TERMS do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= ATS_MAX_TERMS and iii_att <= ATS_MAX_TERMS then
ret_att :=
ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])*c(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/c(mmm_att)
end if;
ret_att
end proc
# End Function number 12
# Begin Function number 13
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
# End Function number 13
# Begin Function number 14
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
# End Function number 14
# Begin Function number 15
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
# End Function number 15
# Begin Function number 16
> logitem_good_digits := proc(file,rel_error)
> global glob_small_float,glob_prec;
> local good_digits;
> fprintf(file,"");
> fprintf(file,"%d",glob_min_good_digits);
> fprintf(file," | ");
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float, glob_prec;
fprintf(file, "");
fprintf(file, "%d", glob_min_good_digits);
fprintf(file, " | ")
end proc
# End Function number 16
# Begin Function number 17
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
# End Function number 17
# Begin Function number 18
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
# End Function number 18
# Begin Function number 19
> logitem_complex := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g + %g I",Re(x),Im(x));
> fprintf(file," | ");
> end;
logitem_complex := proc(file, x)
fprintf(file, "");
fprintf(file, "%g + %g I", Re(x), Im(x));
fprintf(file, " | ")
end proc
# End Function number 19
# Begin Function number 20
> logitem_h_reason := proc(file)
> global glob_h_reason;
> fprintf(file,"");
> if (glob_h_reason = 1) then # if number 5
> fprintf(file,"Max H");
> elif
> (glob_h_reason = 2) then # if number 6
> fprintf(file,"Display Interval");
> elif
> (glob_h_reason = 3) then # if number 7
> fprintf(file,"Optimal");
> elif
> (glob_h_reason = 4) then # if number 8
> fprintf(file,"Pole Accuracy");
> elif
> (glob_h_reason = 5) then # if number 9
> fprintf(file,"Min H (Pole)");
> elif
> (glob_h_reason = 6) then # if number 10
> fprintf(file,"Pole");
> elif
> (glob_h_reason = 7) then # if number 11
> fprintf(file,"Opt Iter");
> else
> fprintf(file,"Impossible");
> fi;# end if 11
> fprintf(file," | ");
> end;
logitem_h_reason := proc(file)
global glob_h_reason;
fprintf(file, "");
if glob_h_reason = 1 then fprintf(file, "Max H")
elif glob_h_reason = 2 then fprintf(file, "Display Interval")
elif glob_h_reason = 3 then fprintf(file, "Optimal")
elif glob_h_reason = 4 then fprintf(file, "Pole Accuracy")
elif glob_h_reason = 5 then fprintf(file, "Min H (Pole)")
elif glob_h_reason = 6 then fprintf(file, "Pole")
elif glob_h_reason = 7 then fprintf(file, "Opt Iter")
else fprintf(file, "Impossible")
end if;
fprintf(file, " | ")
end proc
# End Function number 20
# Begin Function number 21
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
# End Function number 21
# Begin Function number 22
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file) fprintf(file, "\n") end proc
# End Function number 22
# Begin Function number 23
> chk_data := proc()
> global glob_max_iter,ALWAYS, ATS_MAX_TERMS;
> local errflag;
> errflag := false;
> if (glob_max_iter < 2) then # if number 11
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 11;
> if (errflag) then # if number 11
> quit;
> fi;# end if 11
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, ATS_MAX_TERMS;
errflag := false;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
# End Function number 23
# Begin Function number 24
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := c(clock_sec2);
> sub1 := c(t_end2-t_start2);
> sub2 := c(t2-t_start2);
> if (sub1 = glob__0) then # if number 11
> sec_left := glob__0;
> else
> if (sub2 > glob__0) then # if number 12
> rrr := (sub1/sub2);
> sec_left := rrr * c(ms2) - c(ms2);
> else
> sec_left := glob__0;
> fi;# end if 12
> fi;# end if 11;
> sec_left;
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := c(clock_sec2);
sub1 := c(t_end2 - t_start2);
sub2 := c(t2 - t_start2);
if sub1 = glob__0 then sec_left := glob__0
else
if glob__0 < sub2 then
rrr := sub1/sub2; sec_left := rrr*c(ms2) - c(ms2)
else sec_left := glob__0
end if
end if;
sec_left
end proc
# End Function number 24
# Begin Function number 25
> comp_percent := proc(t_end2,t_start2, t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub2 > glob_small_float) then # if number 11
> rrr := (glob__100*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 11;
> rrr;
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < sub2 then rrr := glob__100*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
# End Function number 25
# Begin Function number 26
> comp_rad_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 11
> ret := float_abs(term1 * glob_h / term2);
> else
> ret := glob_larger_float;
> fi;# end if 11;
> ret;
> #BOTTOM TWO TERM RADIUS ANALYSIS
> end;
comp_rad_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := float_abs(term1*glob_h/term2)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 26
# Begin Function number 27
> comp_ord_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM ORDER ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 11
> ret := glob__1 + float_abs(term2) * c(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(c(last_no));
> else
> ret := glob_larger_float;
> fi;# end if 11;
> ret;
> #BOTTOM TWO TERM ORDER ANALYSIS
> end;
comp_ord_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := glob__1 + float_abs(term2)*
c(last_no)*ln(float_abs(term1*glob_h/term2))/ln(c(last_no))
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 27
# Begin Function number 28
> c := proc(in_val)
> #To Force Conversion when needed
> local ret;
> ret := evalc(in_val);
> ret;
> #End Conversion
> end;
c := proc(in_val) local ret; ret := evalc(in_val); ret end proc
# End Function number 28
# Begin Function number 29
> comp_rad_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret,temp;
> temp := float_abs(term2*term2*c(last_no)+glob__m2*term2*term2-term1*term3*c(last_no)+term1*term3);
> if (float_abs(temp) > glob__0) then # if number 11
> ret := float_abs((term2*glob_h*term1)/(temp));
> else
> ret := glob_larger_float;
> fi;# end if 11;
> ret;
> #BOTTOM THREE TERM RADIUS ANALYSIS
> end;
comp_rad_from_three_terms := proc(term1, term2, term3, last_no)
local ret, temp;
global glob_h, glob_larger_float;
temp := float_abs(term2*term2*c(last_no) + glob__m2*term2*term2
- term1*term3*c(last_no) + term1*term3);
if glob__0 < float_abs(temp) then
ret := float_abs(term2*glob_h*term1/temp)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 29
# Begin Function number 30
> comp_ord_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM ORDER ANALYSIS
> local ret;
> ret := float_abs((glob__4*term1*term3*c(last_no)-glob__3*term1*term3-glob__4*term2*term2*c(last_no)+glob__4*term2*term2+term2*term2*c(last_no*last_no)-term1*term3*c(last_no*last_no))/(term2*term2*c(last_no)-glob__2*term2*term2-term1*term3*c(last_no)+term1*term3));
> ret;
> #TOP THREE TERM ORDER ANALYSIS
> end;
comp_ord_from_three_terms := proc(term1, term2, term3, last_no)
local ret;
ret := float_abs((glob__4*term1*term3*c(last_no) - glob__3*term1*term3
- glob__4*term2*term2*c(last_no) + glob__4*term2*term2
+ term2*term2*c(last_no*last_no) - term1*term3*c(last_no*last_no))
/(term2*term2*c(last_no) - glob__2*term2*term2
- term1*term3*c(last_no) + term1*term3));
ret
end proc
# End Function number 30
# Begin Function number 31
> comp_rad_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> #TOP SIX TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float,glob_six_term_ord_save;
> local ret,rm0,rm1,rm2,rm3,rm4,nr1,nr2,dr1,dr2,ds2,rad_c,ord_no,ds1,rcs;
> if ((term5 <> glob__0) and (term4 <> glob__0) and (term3 <> glob__0) and (term2 <> glob__0) and (term1 <> glob__0)) then # if number 11
> rm0 := term6/term5;
> rm1 := term5/term4;
> rm2 := term4/term3;
> rm3 := term3/term2;
> rm4 := term2/term1;
> nr1 := c(last_no-1)*rm0 - glob__2*c(last_no-2)*rm1 + c(last_no-3)*rm2;
> nr2 := c(last_no-2)*rm1 - glob__2*c(last_no-3)*rm2 + c(last_no-4)*rm3;
> dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
> dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
> ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
> ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
> if ((float_abs(nr1 * dr2 - nr2 * dr1) = glob__0) or (float_abs(dr1) = glob__0)) then # if number 12
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> else
> if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0) then # if number 13
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) -c(last_no)/glob__2;
> if (float_abs(rcs) <> glob__0) then # if number 14
> if (rcs > glob__0) then # if number 15
> rad_c := float_abs( sqrt(rcs) * float_abs(glob_h));
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 15
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 14
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 13
> fi;# end if 12
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 11;
> glob_six_term_ord_save := ord_no;
> rad_c;
> #BOTTOM SIX TERM RADIUS ANALYSIS
> end;
comp_rad_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
local ret, rm0, rm1, rm2, rm3, rm4, nr1, nr2, dr1, dr2, ds2, rad_c, ord_no,
ds1, rcs;
global glob_h, glob_larger_float, glob_six_term_ord_save;
if term5 <> glob__0 and term4 <> glob__0 and term3 <> glob__0 and
term2 <> glob__0 and term1 <> glob__0 then
rm0 := term6/term5;
rm1 := term5/term4;
rm2 := term4/term3;
rm3 := term3/term2;
rm4 := term2/term1;
nr1 := c(last_no - 1)*rm0 - glob__2*c(last_no - 2)*rm1
+ c(last_no - 3)*rm2;
nr2 := c(last_no - 2)*rm1 - glob__2*c(last_no - 3)*rm2
+ c(last_no - 4)*rm3;
dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
if
float_abs(nr1*dr2 - nr2*dr1) = glob__0 or float_abs(dr1) = glob__0
then rad_c := glob_larger_float; ord_no := glob_larger_float
else
if glob__0 < float_abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no :=
(rcs*nr1 - ds1)/(glob__2*dr1) - c(last_no)/glob__2;
if float_abs(rcs) <> glob__0 then
if glob__0 < rcs then
rad_c := float_abs(sqrt(rcs)*float_abs(glob_h))
else
rad_c := glob_larger_float;
ord_no := glob_larger_float
end if
else
rad_c := glob_larger_float; ord_no := glob_larger_float
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if;
glob_six_term_ord_save := ord_no;
rad_c
end proc
# End Function number 31
# Begin Function number 32
> comp_ord_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> global glob_six_term_ord_save;
> #TOP SIX TERM ORDER ANALYSIS
> #TOP SAVED FROM SIX TERM RADIUS ANALYSIS
> glob_six_term_ord_save;
> #BOTTOM SIX TERM ORDER ANALYSIS
> end;
comp_ord_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
global glob_six_term_ord_save;
glob_six_term_ord_save
end proc
# End Function number 32
# Begin Function number 33
> factorial_2 := proc(nnn)
> ret := nnn!;
> ret;;
> end;
Warning, `ret` is implicitly declared local to procedure `factorial_2`
factorial_2 := proc(nnn) local ret; ret := nnn!; ret end proc
# End Function number 33
# Begin Function number 34
> factorial_1 := proc(nnn)
> global ATS_MAX_TERMS,array_fact_1;
> local ret;
> if (nnn <= ATS_MAX_TERMS) then # if number 11
> if (array_fact_1[nnn] = 0) then # if number 12
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 12;
> else
> ret := factorial_2(nnn);
> fi;# end if 11;
> ret;
> end;
factorial_1 := proc(nnn)
local ret;
global ATS_MAX_TERMS, array_fact_1;
if nnn <= ATS_MAX_TERMS then
if array_fact_1[nnn] = 0 then
ret := factorial_2(nnn); array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := factorial_2(nnn)
end if;
ret
end proc
# End Function number 34
# Begin Function number 35
> factorial_3 := proc(mmm,nnn)
> global ATS_MAX_TERMS,array_fact_2;
> local ret;
> if ((nnn <= ATS_MAX_TERMS) and (mmm <= ATS_MAX_TERMS)) then # if number 11
> if (array_fact_2[mmm,nnn] = 0) then # if number 12
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 12;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 11;
> ret;
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global ATS_MAX_TERMS, array_fact_2;
if nnn <= ATS_MAX_TERMS and mmm <= ATS_MAX_TERMS then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := factorial_2(mmm)/factorial_2(nnn)
end if;
ret
end proc
# End Function number 35
# Begin Function number 36
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
# End Function number 36
# Begin Function number 37
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
# End Function number 37
# Begin Function number 38
> float_abs := proc(x)
> abs(x);
> end;
float_abs := proc(x) abs(x) end proc
# End Function number 38
# Begin Function number 39
> expt := proc(x,y)
> x^y;
> end;
expt := proc(x, y) x^y end proc
# End Function number 39
# Begin Function number 40
> neg := proc(x)
> -x;
> end;
neg := proc(x) -x end proc
# End Function number 40
# Begin Function number 41
> int_trunc := proc(x)
> trunc(x);
> end;
int_trunc := proc(x) trunc(x) end proc
# End Function number 41
# Begin Function number 42
> estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer)
> local desired_abs_gbl_error,range,estimated_steps,step_error;
> global glob_desired_digits_correct,ALWAYS,ATS_MAX_TERMS;
> omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
> desired_abs_gbl_error := expt(glob__10,c( -glob_desired_digits_correct)) * c(float_abs(c(estimated_answer)));
> omniout_float(ALWAYS,"estimated_h",32,estimated_h,32,"");
> omniout_float(ALWAYS,"estimated_answer",32,estimated_answer,32,"");
> omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,"");
> range := (x_end - x_start);
> omniout_float(ALWAYS,"range",32,range,32,"");
> estimated_steps := range / estimated_h;
> omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,"");
> step_error := (c(float_abs(desired_abs_gbl_error) /sqrt(c( estimated_steps))/c(ATS_MAX_TERMS)));
> omniout_float(ALWAYS,"step_error",32,step_error,32,"");
> (step_error);;
> end;
estimated_needed_step_error := proc(
x_start, x_end, estimated_h, estimated_answer)
local desired_abs_gbl_error, range, estimated_steps, step_error;
global glob_desired_digits_correct, ALWAYS, ATS_MAX_TERMS;
omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, "");
desired_abs_gbl_error :=
expt(glob__10, c(-glob_desired_digits_correct))*
c(float_abs(c(estimated_answer)));
omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, "");
omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, "")
;
omniout_float(ALWAYS, "desired_abs_gbl_error", 32,
desired_abs_gbl_error, 32, "");
range := x_end - x_start;
omniout_float(ALWAYS, "range", 32, range, 32, "");
estimated_steps := range/estimated_h;
omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, "");
step_error := c(float_abs(desired_abs_gbl_error)/(
sqrt(c(estimated_steps))*c(ATS_MAX_TERMS)));
omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
step_error
end proc
# End Function number 42
#END ATS LIBRARY BLOCK
#BEGIN USER FUNCTION BLOCK
#BEGIN BLOCK 3
#BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return(c(20.0) * sqrt(c(0.1) * c(x) + c(0.2)) * sinh( sqrt(c(0.1) * c(x) + c(0.2))) - c(20.0) * cosh( sqrt(c(0.1) * c(x) + c(0.2))));
> end;
exact_soln_y := proc(x)
return
c(20.0)*sqrt(c(0.1)*c(x) + c(0.2))*sinh(sqrt(c(0.1)*c(x) + c(0.2)))
- c(20.0)*cosh(sqrt(c(0.1)*c(x) + c(0.2)))
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_0D1,
> array_const_0D2,
#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_g,
> array_tmp4,
> array_tmp5,
> 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_0D1,
array_const_0D2, 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_g, array_tmp4, array_tmp5,
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_0D1,
> array_const_0D2,
#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_g,
> array_tmp4,
> array_tmp5,
> 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_0D1,
array_const_0D2, 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_g, array_tmp4, array_tmp5,
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_0D1,
> array_const_0D2,
#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_g,
> array_tmp4,
> array_tmp5,
> 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_0D1,
array_const_0D2, 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_g, array_tmp4, array_tmp5,
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_0D1,
> array_const_0D2,
#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_g,
> array_tmp4,
> array_tmp5,
> 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_0D1,
array_const_0D2, 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_g, array_tmp4, array_tmp5,
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_0D1,
> array_const_0D2,
#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_g,
> array_tmp4,
> array_tmp5,
> 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_0D1,
array_const_0D2, 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_g, array_tmp4, array_tmp5,
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_0D1,
> array_const_0D2,
#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_g,
> array_tmp4,
> array_tmp5,
> 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_0D1,
array_const_0D2, 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_g, array_tmp4, array_tmp5,
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_0D1,
> array_const_0D2,
#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_g,
> array_tmp4,
> array_tmp5,
> 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_0D1,
array_const_0D2, 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_g, array_tmp4, array_tmp5,
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_0D1,
> array_const_0D2,
#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_g,
> array_tmp4,
> array_tmp5,
> 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 CONST - LINEAR $eq_no = 1 i = 1
> array_tmp1[1] := array_const_0D1[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp2[1] := array_tmp1[1] + array_const_0D2[1];
> #emit pre sqrt 1 $eq_no = 1
> array_tmp3[1] := sqrt(array_tmp2[1]);
> #emit pre cosh $eq_no = 1
> array_tmp4_g[1] := sinh(array_tmp3[1]);
> array_tmp4[1] := cosh(array_tmp3[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp5[1] := array_const_0D0[1] + array_tmp4[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_tmp5[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
> if (2 <= ATS_MAX_TERMS) then # if number 3
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(1);
> array_y_higher[2,1] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
> array_tmp1[2] := array_const_0D1[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre sqrt 2 $eq_no = 1
> array_tmp3[2] := array_tmp2[2] / array_tmp3[1]/glob__2;
> #emit pre cosh $eq_no = 1
> array_tmp4_g[2] := att(1,array_tmp4,array_tmp3,1);
> array_tmp4[2] := att(1,array_tmp4_g,array_tmp3,1);
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp5[2] := array_tmp4[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_tmp5[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 sqrt ID_LINEAR iii = 3 $eq_no = 1
> array_tmp3[3] := 0;
> array_tmp3[3] := neg(ats(3,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2;
> #emit pre cosh $eq_no = 1
> array_tmp4_g[3] := att(2,array_tmp4,array_tmp3,1);
> array_tmp4[3] := att(2,array_tmp4_g,array_tmp3,1);
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp5[3] := array_tmp4[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_tmp5[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 sqrt ID_LINEAR iii = 4 $eq_no = 1
> array_tmp3[4] := 0;
> array_tmp3[4] := neg(ats(4,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2;
> #emit pre cosh $eq_no = 1
> array_tmp4_g[4] := att(3,array_tmp4,array_tmp3,1);
> array_tmp4[4] := att(3,array_tmp4_g,array_tmp3,1);
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp5[4] := array_tmp4[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_tmp5[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 sqrt ID_LINEAR iii = 5 $eq_no = 1
> array_tmp3[5] := 0;
> array_tmp3[5] := neg(ats(5,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2;
> #emit pre cosh $eq_no = 1
> array_tmp4_g[5] := att(4,array_tmp4,array_tmp3,1);
> array_tmp4[5] := att(4,array_tmp4_g,array_tmp3,1);
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp5[5] := array_tmp4[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_tmp5[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 sqrt LINEAR $eq_no = 1
> array_tmp3[kkk] := 0;
> array_tmp3[kkk] := neg(ats(kkk,array_tmp3,array_tmp3,2)) /array_tmp3[1] / glob__2;
> #emit cosh $eq_no = 1
> array_tmp4_g[kkk] := att(kkk-1,array_tmp4,array_tmp3,1);
> array_tmp4[kkk] := att(kkk-1,array_tmp4_g,array_tmp3,1);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp5[kkk] := array_tmp4[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_tmp5[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_0D1,
array_const_0D2, 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_g, array_tmp4, array_tmp5,
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_const_0D1[1]*array_x[1];
array_tmp2[1] := array_tmp1[1] + array_const_0D2[1];
array_tmp3[1] := sqrt(array_tmp2[1]);
array_tmp4_g[1] := sinh(array_tmp3[1]);
array_tmp4[1] := cosh(array_tmp3[1]);
array_tmp5[1] := array_const_0D0[1] + array_tmp4[1];
if not array_y_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
if 2 <= ATS_MAX_TERMS then
array_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_const_0D1[1]*array_x[2];
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := array_tmp2[2]/(array_tmp3[1]*glob__2);
array_tmp4_g[2] := att(1, array_tmp4, array_tmp3, 1);
array_tmp4[2] := att(1, array_tmp4_g, array_tmp3, 1);
array_tmp5[2] := array_tmp4[2];
if not array_y_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
if 3 <= ATS_MAX_TERMS then
array_y[3] := temporary; array_y_higher[1, 3] := temporary
end if;
temporary := c(temporary)*c(2)/c(glob_h);
array_y_higher[2, 2] := c(temporary)
end if
end if;
kkk := 3;
array_tmp3[3] := 0;
array_tmp3[3] :=
neg(ats(3, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2);
array_tmp4_g[3] := att(2, array_tmp4, array_tmp3, 1);
array_tmp4[3] := att(2, array_tmp4_g, array_tmp3, 1);
array_tmp5[3] := array_tmp4[3];
if not array_y_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[3])*expt(glob_h, c(1))*c(factorial_3(2, 3));
if 4 <= ATS_MAX_TERMS then
array_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_tmp3[4] := 0;
array_tmp3[4] :=
neg(ats(4, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2);
array_tmp4_g[4] := att(3, array_tmp4, array_tmp3, 1);
array_tmp4[4] := att(3, array_tmp4_g, array_tmp3, 1);
array_tmp5[4] := array_tmp4[4];
if not array_y_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[4])*expt(glob_h, c(1))*c(factorial_3(3, 4));
if 5 <= ATS_MAX_TERMS then
array_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_tmp3[5] := 0;
array_tmp3[5] :=
neg(ats(5, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2);
array_tmp4_g[5] := att(4, array_tmp4, array_tmp3, 1);
array_tmp4[5] := att(4, array_tmp4_g, array_tmp3, 1);
array_tmp5[5] := array_tmp4[5];
if not array_y_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[5])*expt(glob_h, c(1))*c(factorial_3(4, 5));
if 6 <= ATS_MAX_TERMS then
array_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_tmp3[kkk] := 0;
array_tmp3[kkk] := neg(ats(kkk, array_tmp3, array_tmp3, 2))/(
array_tmp3[1]*glob__2);
array_tmp4_g[kkk] := att(kkk - 1, array_tmp4, array_tmp3, 1);
array_tmp4[kkk] := att(kkk - 1, array_tmp4_g, array_tmp3, 1);
array_tmp5[kkk] := array_tmp4[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_tmp5[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_0D1,
> array_const_0D2,
> #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_g,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> ATS_MAX_TERMS := 30;
> # before first input block
> #BEGIN FIRST INPUT BLOCK
> #BEGIN BLOCK 1
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=30;
> #END BLOCK 1
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> # before generate arrays
> array_y_init:= Array(0..(30),[]);
> array_norms:= Array(0..(30),[]);
> array_fact_1:= Array(0..(30),[]);
> array_1st_rel_error:= Array(0..(2),[]);
> array_last_rel_error:= Array(0..(2),[]);
> array_est_rel_error:= Array(0..(2),[]);
> array_max_est_error:= Array(0..(2),[]);
> array_type_pole:= Array(0..(2),[]);
> array_type_real_pole:= Array(0..(2),[]);
> array_type_complex_pole:= Array(0..(2),[]);
> array_est_digits:= Array(0..(2),[]);
> array_y:= Array(0..(30),[]);
> array_x:= Array(0..(30),[]);
> array_tmp0:= Array(0..(30),[]);
> array_tmp1:= Array(0..(30),[]);
> array_tmp2:= Array(0..(30),[]);
> array_tmp3:= Array(0..(30),[]);
> array_tmp4_g:= Array(0..(30),[]);
> array_tmp4:= Array(0..(30),[]);
> array_tmp5:= Array(0..(30),[]);
> array_m1:= Array(0..(30),[]);
> array_y_higher := Array(0..(2) ,(0..30+ 1),[]);
> array_y_higher_work := Array(0..(2) ,(0..30+ 1),[]);
> array_y_higher_work2 := Array(0..(2) ,(0..30+ 1),[]);
> array_y_set_initial := Array(0..(2) ,(0..30+ 1),[]);
> array_given_rad_poles := Array(0..(2) ,(0..3+ 1),[]);
> array_given_ord_poles := Array(0..(2) ,(0..3+ 1),[]);
> array_rad_test_poles := Array(0..(2) ,(0..4+ 1),[]);
> array_ord_test_poles := Array(0..(2) ,(0..4+ 1),[]);
> array_fact_2 := Array(0..(30) ,(0..30+ 1),[]);
> # before generate constants
> # before generate globals definition
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> # before generate const definition
> # before arrays initialized
> term := 1;
> while (term <= 30) do # do number 1
> array_y_init[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_norms[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_fact_1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_1st_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_last_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_est_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_max_est_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_real_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_complex_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_est_digits[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_y[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_x[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp0[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp3[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp4_g[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp4[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp5[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_m1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y_higher[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y_higher_work[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y_higher_work2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_y_set_initial[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_rad_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_ord_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_rad_test_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_ord_test_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=30) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_fact_2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> # before symbols initialized
> #BEGIN SYMBOLS INITIALIZATED
> zero_ats_ar(array_y);
> zero_ats_ar(array_x);
> zero_ats_ar(array_tmp0);
> zero_ats_ar(array_tmp1);
> zero_ats_ar(array_tmp2);
> zero_ats_ar(array_tmp3);
> zero_ats_ar(array_tmp4_g);
> zero_ats_ar(array_tmp4);
> zero_ats_ar(array_tmp5);
> 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_0D1);
> array_const_0D1[1] := c(0.1);
> zero_ats_ar(array_const_0D2);
> array_const_0D2[1] := c(0.2);
> zero_ats_ar(array_m1);
> array_m1[1] := glob__m1;
> #END SYMBOLS INITIALIZATED
> # before generate factorials init
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= ATS_MAX_TERMS) do # do number 1
> jjjf := 0;
> while (jjjf <= ATS_MAX_TERMS) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Table
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> glob_yes_pole := 4;
> glob_no_pole := 3;
> glob_not_given := 0;
> glob_no_sing_tests := 4;
> glob_ratio_test := 1;
> glob_three_term_test := 2;
> glob_six_term_test := 3;
> glob_log_10 := log(c(10.0));
> MAX_UNCHANGED := 10;
> glob__small := c(0.1e-50);
> glob_small_float := c(0.1e-50);
> glob_smallish_float := c(0.1e-60);
> glob_large_float := c(1.0e100);
> glob_larger_float := c(1.1e100);
> glob__m2 := c(-2);
> glob__m1 := c(-1);
> glob__0 := c(0);
> glob__1 := c(1);
> glob__2 := c(2);
> glob__3 := c(3);
> glob__4 := c(4);
> glob__5 := c(5);
> glob__8 := c(8);
> glob__10 := c(10);
> glob__100 := c(100);
> glob__pi := c(0.0);
> glob__0_5 := c(0.5);
> glob__0_8 := c(0.8);
> glob__m0_8 := c(-0.8);
> glob__0_25 := c(0.25);
> glob__0_125 := c(0.125);
> glob_h := 0.1;
> glob_nxt := 1;
> glob_prec := c(1.0e-16);
> glob_check_sign := c(1.0);
> glob_desired_digits_correct := c(8.0);
> glob_max_estimated_step_error := c(0.0);
> glob_ratio_of_radius := c(0.1);
> glob_percent_done := c(0.0);
> glob_total_exp_sec := c(0.1);
> glob_optimal_expect_sec := c(0.1);
> glob_estimated_size_answer := c(100.0);
> glob_almost_1 := c(0.9990);
> glob_clock_sec := c(0.0);
> glob_clock_start_sec := c(0.0);
> glob_disp_incr := c(0.1);
> glob_diff_rc_fm := c(0.1);
> glob_diff_rc_fmm1 := c(0.1);
> glob_diff_rc_fmm2 := c(0.1);
> glob_diff_ord_fm := c(0.1);
> glob_diff_ord_fmm1 := c(0.1);
> glob_diff_ord_fmm2 := c(0.1);
> glob_six_term_ord_save := c(0.1);
> glob_guess_error_rc := c(0.1);
> glob_guess_error_ord := c(0.1);
> glob_least_given_sing := c(9.9e200);
> glob_least_ratio_sing := c(9.9e200);
> glob_least_3_sing := c(9.9e100);
> glob_least_6_sing := c(9.9e100);
> glob_last_good_h := c(0.1);
> glob_max_h := c(0.1);
> glob_min_h := c(0.000001);
> glob_display_interval := c(0.1);
> glob_abserr := c(0.1e-10);
> glob_relerr := c(0.1e-10);
> glob_min_pole_est := c(0.1e+10);
> glob_max_rel_trunc_err := c(0.1e-10);
> glob_max_trunc_err := c(0.1e-10);
> glob_max_hours := c(0.0);
> glob_optimal_clock_start_sec := c(0.0);
> glob_optimal_start := c(0.0);
> glob_upper_ratio_limit := c(1.0001);
> glob_lower_ratio_limit := c(0.9999);
> glob_max_sec := c(10000.0);
> glob_orig_start_sec := c(0.0);
> glob_normmax := c(0.0);
> glob_max_minutes := c(0.0);
> glob_next_display := c(0.0);
> glob_est_digits := 1;
> glob_subiter_method := 3;
> glob_html_log := true;
> glob_min_good_digits := 99999;
> glob_good_digits := 0;
> glob_min_apfp_est_good_digits := 99999;
> glob_apfp_est_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> glob_h_reason := 0;
> glob_sec_in_minute := 60 ;
> glob_min_in_hour := 60;
> glob_hours_in_day := 24;
> glob_days_in_year := 365;
> glob_sec_in_hour := 3600;
> glob_sec_in_day := 86400;
> glob_sec_in_year := 31536000;
> glob_not_yet_finished := true;
> glob_initial_pass := true;
> glob_not_yet_start_msg := true;
> glob_reached_optimal_h := false;
> glob_optimal_done := false;
> glob_type_given_pole := 0;
> glob_optimize := false;
> glob_look_poles := false;
> glob_dump_closed_form := false;
> glob_max_iter := 10000;
> glob_no_eqs := 0;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_start := 0;
> glob_iter := 0;
> # before generate set diff initial
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> # before generate init omniout const
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> ATS_MAX_TERMS := 30;
> glob_iolevel := INFO;
> # set default block
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> glob_display_flag := true;
> glob_no_eqs := 1;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 10000;
> glob_max_hours := (0.0);
> glob_max_minutes := (15.0);
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/cosh_sqrtpostcpx.cpx#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = cosh ( sqrt ( 0.1 * x + 0.2 ) ) ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := -1.7 + 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 := 0.01;");
> omniout_str(ALWAYS,"glob_upper_ratio_limit := c(1.001);");
> omniout_str(ALWAYS,"glob_lower_ratio_limit := c(0.999);");
> 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 := 1;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_rad_poles[1,1] := c(-2.0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_rad_poles[1,2] := c(0.0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_ord_poles[1,1] := c(0.5);");
> 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,"");
> omniout_str(ALWAYS,"return(c(20.0) * sqrt(c(0.1) * c(x) + c(0.2)) * sinh( sqrt(c(0.1) * c(x) + c(0.2))) - c(20.0) * cosh( sqrt(c(0.1) * c(x) + c(0.2))));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"next_delta := proc()");
> omniout_str(ALWAYS,"global glob_nxt, x_delta;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"x_delta := [ 0.001 + 0.00004 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.000 + 0.000 * I ];");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_nxt := glob_nxt + 1;");
> omniout_str(ALWAYS,"it := x_delta[glob_nxt];");
> omniout_str(ALWAYS,"return it;");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := glob__0;
> glob_smallish_float := glob__0;
> glob_large_float := c(1.0e100);
> glob_larger_float := c( 1.1e100);
> glob_almost_1 := c( 0.99);
> # before second block
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #BEGIN BLOCK 2
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := -1.7 + 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 := 0.01;
> glob_upper_ratio_limit := c(1.001);
> glob_lower_ratio_limit := c(0.999);
> glob_type_given_pole := 1;
> array_given_rad_poles[1,1] := c(-2.0);
> array_given_rad_poles[1,2] := c(0.0);
> array_given_ord_poles[1,1] := c(0.5);
> 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 ) = cosh ( sqrt ( 0.1 * x + 0.2 ) ) ; ");
> 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,"2017-11-26T14:40:19-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"cosh_sqrt")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = cosh ( sqrt ( 0.1 * x + 0.2 ) ) ; ")
> ;
> 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,"cosh_sqrt diffeq.mxt")
> ;
> logitem_str(html_log_file,"cosh_sqrt 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_0D1,
array_const_0D2, 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_g, array_tmp4, array_tmp5,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
ATS_MAX_TERMS := 30;
Digits := 32;
max_terms := 30;
glob_html_log := true;
array_y_init := Array(0 .. 30, []);
array_norms := Array(0 .. 30, []);
array_fact_1 := Array(0 .. 30, []);
array_1st_rel_error := Array(0 .. 2, []);
array_last_rel_error := Array(0 .. 2, []);
array_est_rel_error := Array(0 .. 2, []);
array_max_est_error := Array(0 .. 2, []);
array_type_pole := Array(0 .. 2, []);
array_type_real_pole := Array(0 .. 2, []);
array_type_complex_pole := Array(0 .. 2, []);
array_est_digits := Array(0 .. 2, []);
array_y := Array(0 .. 30, []);
array_x := Array(0 .. 30, []);
array_tmp0 := Array(0 .. 30, []);
array_tmp1 := Array(0 .. 30, []);
array_tmp2 := Array(0 .. 30, []);
array_tmp3 := Array(0 .. 30, []);
array_tmp4_g := Array(0 .. 30, []);
array_tmp4 := Array(0 .. 30, []);
array_tmp5 := Array(0 .. 30, []);
array_m1 := Array(0 .. 30, []);
array_y_higher := Array(0 .. 2, 0 .. 31, []);
array_y_higher_work := Array(0 .. 2, 0 .. 31, []);
array_y_higher_work2 := Array(0 .. 2, 0 .. 31, []);
array_y_set_initial := Array(0 .. 2, 0 .. 31, []);
array_given_rad_poles := Array(0 .. 2, 0 .. 4, []);
array_given_ord_poles := Array(0 .. 2, 0 .. 4, []);
array_rad_test_poles := Array(0 .. 2, 0 .. 5, []);
array_ord_test_poles := Array(0 .. 2, 0 .. 5, []);
array_fact_2 := Array(0 .. 30, 0 .. 31, []);
term := 1;
while term <= 30 do array_y_init[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 30 do array_norms[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 30 do array_fact_1[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_1st_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do
array_last_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_est_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_max_est_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_type_pole[term] := 0; term := term + 1 end do;
term := 1;
while term <= 2 do array_type_real_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 2 do array_type_complex_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 2 do array_est_digits[term] := 0; term := term + 1 end do
;
term := 1;
while term <= 30 do array_y[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_x[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp0[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp1[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp3[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp4_g[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 30 do array_tmp4[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp5[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_m1[term] := c(0.); term := term + 1 end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 do
array_y_higher[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 do
array_y_higher_work[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 do
array_y_higher_work2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 do
array_y_set_initial[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_rad_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_ord_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 4 do
array_rad_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 4 do
array_ord_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 30 do
term := 1;
while term <= 30 do
array_fact_2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
zero_ats_ar(array_y);
zero_ats_ar(array_x);
zero_ats_ar(array_tmp0);
zero_ats_ar(array_tmp1);
zero_ats_ar(array_tmp2);
zero_ats_ar(array_tmp3);
zero_ats_ar(array_tmp4_g);
zero_ats_ar(array_tmp4);
zero_ats_ar(array_tmp5);
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_0D1);
array_const_0D1[1] := c(0.1);
zero_ats_ar(array_const_0D2);
array_const_0D2[1] := c(0.2);
zero_ats_ar(array_m1);
array_m1[1] := glob__m1;
iiif := 0;
while iiif <= ATS_MAX_TERMS do
jjjf := 0;
while jjjf <= ATS_MAX_TERMS do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
glob_yes_pole := 4;
glob_no_pole := 3;
glob_not_given := 0;
glob_no_sing_tests := 4;
glob_ratio_test := 1;
glob_three_term_test := 2;
glob_six_term_test := 3;
glob_log_10 := log(c(10.0));
MAX_UNCHANGED := 10;
glob__small := c(0.1*10^(-50));
glob_small_float := c(0.1*10^(-50));
glob_smallish_float := c(0.1*10^(-60));
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob__m2 := c(-2);
glob__m1 := c(-1);
glob__0 := c(0);
glob__1 := c(1);
glob__2 := c(2);
glob__3 := c(3);
glob__4 := c(4);
glob__5 := c(5);
glob__8 := c(8);
glob__10 := c(10);
glob__100 := c(100);
glob__pi := c(0.);
glob__0_5 := c(0.5);
glob__0_8 := c(0.8);
glob__m0_8 := c(-0.8);
glob__0_25 := c(0.25);
glob__0_125 := c(0.125);
glob_h := 0.1;
glob_nxt := 1;
glob_prec := c(0.10*10^(-15));
glob_check_sign := c(1.0);
glob_desired_digits_correct := c(8.0);
glob_max_estimated_step_error := c(0.);
glob_ratio_of_radius := c(0.1);
glob_percent_done := c(0.);
glob_total_exp_sec := c(0.1);
glob_optimal_expect_sec := c(0.1);
glob_estimated_size_answer := c(100.0);
glob_almost_1 := c(0.9990);
glob_clock_sec := c(0.);
glob_clock_start_sec := c(0.);
glob_disp_incr := c(0.1);
glob_diff_rc_fm := c(0.1);
glob_diff_rc_fmm1 := c(0.1);
glob_diff_rc_fmm2 := c(0.1);
glob_diff_ord_fm := c(0.1);
glob_diff_ord_fmm1 := c(0.1);
glob_diff_ord_fmm2 := c(0.1);
glob_six_term_ord_save := c(0.1);
glob_guess_error_rc := c(0.1);
glob_guess_error_ord := c(0.1);
glob_least_given_sing := c(0.99*10^201);
glob_least_ratio_sing := c(0.99*10^201);
glob_least_3_sing := c(0.99*10^101);
glob_least_6_sing := c(0.99*10^101);
glob_last_good_h := c(0.1);
glob_max_h := c(0.1);
glob_min_h := c(0.1*10^(-5));
glob_display_interval := c(0.1);
glob_abserr := c(0.1*10^(-10));
glob_relerr := c(0.1*10^(-10));
glob_min_pole_est := c(0.1*10^10);
glob_max_rel_trunc_err := c(0.1*10^(-10));
glob_max_trunc_err := c(0.1*10^(-10));
glob_max_hours := c(0.);
glob_optimal_clock_start_sec := c(0.);
glob_optimal_start := c(0.);
glob_upper_ratio_limit := c(1.0001);
glob_lower_ratio_limit := c(0.9999);
glob_max_sec := c(10000.0);
glob_orig_start_sec := c(0.);
glob_normmax := c(0.);
glob_max_minutes := c(0.);
glob_next_display := c(0.);
glob_est_digits := 1;
glob_subiter_method := 3;
glob_html_log := true;
glob_min_good_digits := 99999;
glob_good_digits := 0;
glob_min_apfp_est_good_digits := 99999;
glob_apfp_est_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
glob_h_reason := 0;
glob_sec_in_minute := 60;
glob_min_in_hour := 60;
glob_hours_in_day := 24;
glob_days_in_year := 365;
glob_sec_in_hour := 3600;
glob_sec_in_day := 86400;
glob_sec_in_year := 31536000;
glob_not_yet_finished := true;
glob_initial_pass := true;
glob_not_yet_start_msg := true;
glob_reached_optimal_h := false;
glob_optimal_done := false;
glob_type_given_pole := 0;
glob_optimize := false;
glob_look_poles := false;
glob_dump_closed_form := false;
glob_max_iter := 10000;
glob_no_eqs := 0;
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_start := 0;
glob_iter := 0;
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
ATS_MAX_TERMS := 30;
glob_iolevel := INFO;
glob_orig_start_sec := elapsed_time_seconds();
glob_display_flag := true;
glob_no_eqs := 1;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 10000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/cosh_sqrtpostcpx.cpx#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = cosh ( sqrt ( 0.1\
* x + 0.2 ) ) ; ");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := -1.7 + 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 := 0.01;");
omniout_str(ALWAYS, "glob_upper_ratio_limit := c(1.001);");
omniout_str(ALWAYS, "glob_lower_ratio_limit := c(0.999);");
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 := 1;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_rad_poles[1,1] := c(-2.0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_rad_poles[1,2] := c(0.0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_ord_poles[1,1] := c(0.5);");
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, "");
omniout_str(ALWAYS, "return(c(20.0) * sqrt(c(0.1) * c(x) + c(0.2)) * \
sinh( sqrt(c(0.1) * c(x) + c(0.2))) - c(20.0) * cosh( sqrt(c(0.1\
) * c(x) + c(0.2))));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "next_delta := proc()");
omniout_str(ALWAYS, "global glob_nxt, x_delta;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "x_delta := [ 0.001 + 0.00004 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
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omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.000 + 0.000 * I ];");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_nxt := glob_nxt + 1;");
omniout_str(ALWAYS, "it := x_delta[glob_nxt];");
omniout_str(ALWAYS, "return it;");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := glob__0;
glob_smallish_float := glob__0;
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob_almost_1 := c(0.99);
x_start := -1.7 + 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 := 0.01;
glob_upper_ratio_limit := c(1.001);
glob_lower_ratio_limit := c(0.999);
glob_type_given_pole := 1;
array_given_rad_poles[1, 1] := c(-2.0);
array_given_rad_poles[1, 2] := c(0.);
array_given_ord_poles[1, 1] := c(0.5);
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 ) = cosh ( sqrt ( 0\
.1 * x + 0.2 ) ) ; ");
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, "2017-11-26T14:40:19-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"cosh_sqrt");
logitem_str(html_log_file, "diff ( y , x , 1 ) = co\
sh ( sqrt ( 0.1 * x + 0.2 ) ) ; ");
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, "cosh_sqrt diffeq.mxt");
logitem_str(html_log_file, "cosh_sqrt 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/cosh_sqrtpostcpx.cpx#################
diff ( y , x , 1 ) = cosh ( sqrt ( 0.1 * x + 0.2 ) ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := -1.7 + 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 := 0.01;
glob_upper_ratio_limit := c(1.001);
glob_lower_ratio_limit := c(0.999);
glob_type_given_pole := 1;
array_given_rad_poles[1,1] := c(-2.0);
array_given_rad_poles[1,2] := c(0.0);
array_given_ord_poles[1,1] := c(0.5);
array_given_ord_poles[1,2] := c(0.0);
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=8;
glob_max_minutes:=(3.0);
glob_subiter_method:=3;
glob_max_iter:=10000;
glob_upper_ratio_limit:=c(1.000001);
glob_lower_ratio_limit:=c(0.999999);
glob_look_poles:=true;
glob_h:=c(0.001);
glob_display_interval:=c(0.01);
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return(c(20.0) * sqrt(c(0.1) * c(x) + c(0.2)) * sinh( sqrt(c(0.1) * c(x) + c(0.2))) - c(20.0) * cosh( sqrt(c(0.1) * c(x) + c(0.2))));
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] = -1.7 0.1
h = 0.0001 0.005
y[1] (numeric) = -19.697997499 0.101503614446
y[1] (closed_form) = -19.697997499 0.101503614446
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 0.3162
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6999 0.105
h = 0.0001 0.003
y[1] (numeric) = -19.6979211205 0.106579284719
y[1] (closed_form) = -19.6979217488 0.106579307805
absolute error = 6.288e-07
relative error = 3.192e-06 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 0.3179
Order of pole (given) = 0.5 0
NO 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=30.8MB, alloc=40.3MB, time=0.40
x[1] = -1.6998 0.108
h = 0.001 0.001
y[1] (numeric) = -19.6978354452 0.109624927117
y[1] (closed_form) = -19.6978362998 0.109624963976
absolute error = 8.554e-07
relative error = 4.343e-06 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 0.319
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6988 0.109
h = 0.001 0.003
y[1] (numeric) = -19.6968258294 0.110645396947
y[1] (closed_form) = -19.6968266842 0.110645483997
absolute error = 8.593e-07
relative error = 4.363e-06 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 0.3203
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6978 0.112
h = 0.0001 0.004
y[1] (numeric) = -19.6958271686 0.113696152914
y[1] (closed_form) = -19.6958282248 0.113696390402
absolute error = 1.083e-06
relative error = 5.496e-06 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 0.3223
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6977 0.116
h = 0.003 0.006
y[1] (numeric) = -19.6957481669 0.1177572874
y[1] (closed_form) = -19.6957496253 0.117757543962
absolute error = 1.481e-06
relative error = 7.519e-06 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 0.3238
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6947 0.122
h = 0.0001 0.005
y[1] (numeric) = -19.6927376989 0.123865661026
y[1] (closed_form) = -19.6927398386 0.12386681993
absolute error = 2.433e-06
relative error = 1.236e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 0.3288
Order of pole (given) = 0.5 0
NO 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=76.4MB, alloc=52.3MB, time=0.99
x[1] = -1.6946 0.127
h = 0.0001 0.003
y[1] (numeric) = -19.6926668218 0.128942763091
y[1] (closed_form) = -19.6926695923 0.128943945153
absolute error = 3.012e-06
relative error = 1.530e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 0.3308
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6945 0.13
h = 0.001 0.001
y[1] (numeric) = -19.6925844382 0.131989308655
y[1] (closed_form) = -19.6925874351 0.131990504467
absolute error = 3.227e-06
relative error = 1.638e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 0.332
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6935 0.131
h = 0.001 0.003
y[1] (numeric) = -19.6915756644 0.133011148712
y[1] (closed_form) = -19.6915786615 0.13301239473
absolute error = 3.246e-06
relative error = 1.648e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 0.3333
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6925 0.134
h = 0.0001 0.004
y[1] (numeric) = -19.6905800578 0.136063803198
y[1] (closed_form) = -19.6905832563 0.136065199595
absolute error = 3.490e-06
relative error = 1.772e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 0.3354
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6924 0.138
h = 0.003 0.006
y[1] (numeric) = -19.6905054542 0.140126104608
y[1] (closed_form) = -19.690509055 0.140127519969
absolute error = 3.869e-06
relative error = 1.965e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 0.3371
Order of pole (given) = 0.5 0
NO 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=122.1MB, alloc=52.3MB, time=1.55
x[1] = -1.6894 0.144
h = 0.0001 0.005
y[1] (numeric) = -19.6875008312 0.146239380702
y[1] (closed_form) = -19.6875051137 0.146241698328
absolute error = 4.869e-06
relative error = 2.473e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 0.3424
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6893 0.149
h = 0.0001 0.003
y[1] (numeric) = -19.687435459 0.151317912802
y[1] (closed_form) = -19.6874403722 0.151320253527
absolute error = 5.442e-06
relative error = 2.764e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 0.3446
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6892 0.152
h = 0.001 0.001
y[1] (numeric) = -19.6873563678 0.154365360409
y[1] (closed_form) = -19.6873615074 0.15436771486
absolute error = 5.653e-06
relative error = 2.871e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 0.346
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6882 0.153
h = 0.001 0.003
y[1] (numeric) = -19.6863484365 0.155388570508
y[1] (closed_form) = -19.6863535764 0.155390975178
absolute error = 5.675e-06
relative error = 2.882e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 0.3473
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6872 0.156
h = 0.0001 0.004
y[1] (numeric) = -19.6853558851 0.158443122564
y[1] (closed_form) = -19.6853612265 0.158445677553
absolute error = 5.921e-06
relative error = 3.008e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 0.3495
Order of pole (given) = 0.5 0
NO 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=167.7MB, alloc=52.3MB, time=2.12
x[1] = -1.6871 0.16
h = 0.003 0.006
y[1] (numeric) = -19.6852856805 0.162506589396
y[1] (closed_form) = -19.6852914242 0.162509163235
absolute error = 6.294e-06
relative error = 3.197e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.3514
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6841 0.166
h = 0.0001 0.005
y[1] (numeric) = -19.6822869047 0.168624766259
y[1] (closed_form) = -19.6822933304 0.16862824228
absolute error = 7.306e-06
relative error = 3.712e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.3569
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.684 0.171
h = 0.0001 0.003
y[1] (numeric) = -19.6822270384 0.173704726529
y[1] (closed_form) = -19.6822340948 0.173708225568
absolute error = 7.876e-06
relative error = 4.002e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.3593
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6839 0.174
h = 0.001 0.001
y[1] (numeric) = -19.6821512403 0.176753075057
y[1] (closed_form) = -19.6821585231 0.176756587795
absolute error = 8.086e-06
relative error = 4.108e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.3608
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6829 0.175
h = 0.001 0.003
y[1] (numeric) = -19.681144152 0.17777765501
y[1] (closed_form) = -19.6811514352 0.17778121798
absolute error = 8.108e-06
relative error = 4.120e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.3622
Order of pole (given) = 0.5 0
NO 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=213.3MB, alloc=52.3MB, time=2.67
x[1] = -1.6819 0.178
h = 0.0001 0.004
y[1] (numeric) = -19.6801546567 0.180834103687
y[1] (closed_form) = -19.6801621415 0.180837816916
absolute error = 8.355e-06
relative error = 4.245e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.3645
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6818 0.182
h = 0.003 0.006
y[1] (numeric) = -19.6800888519 0.184898734438
y[1] (closed_form) = -19.680096739 0.184902466399
absolute error = 8.725e-06
relative error = 4.433e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.3666
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6788 0.188
h = 0.0001 0.005
y[1] (numeric) = -19.6770959257 0.191021810374
y[1] (closed_form) = -19.6771044952 0.191026444425
absolute error = 9.742e-06
relative error = 4.951e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.3722
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6787 0.193
h = 0.0001 0.003
y[1] (numeric) = -19.6770415663 0.196103196945
y[1] (closed_form) = -19.6770507665 0.196107853914
absolute error = 1.031e-05
relative error = 5.240e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.3748
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6786 0.196
h = 0.001 0.001
y[1] (numeric) = -19.6769690618 0.199152445272
y[1] (closed_form) = -19.6769784885 0.199157115909
absolute error = 1.052e-05
relative error = 5.346e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.3764
Order of pole (given) = 0.5 0
NO 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=259.0MB, alloc=52.3MB, time=3.24
x[1] = -1.6776 0.197
h = 0.0001 0.004
y[1] (numeric) = -19.6759628172 0.200178394895
y[1] (closed_form) = -19.6759722442 0.200183115776
absolute error = 1.054e-05
relative error = 5.358e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.3778
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6775 0.201
h = 0.003 0.006
y[1] (numeric) = -19.6759008144 0.204243973679
y[1] (closed_form) = -19.6759106435 0.20424871339
absolute error = 1.091e-05
relative error = 5.546e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.38
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6745 0.207
h = 0.0001 0.005
y[1] (numeric) = -19.6729129835 0.210371195496
y[1] (closed_form) = -19.6729234952 0.210376837207
absolute error = 1.193e-05
relative error = 6.064e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.3857
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6744 0.212
h = 0.0001 0.003
y[1] (numeric) = -19.6728633821 0.215453742667
y[1] (closed_form) = -19.6728745245 0.215459407195
absolute error = 1.250e-05
relative error = 6.353e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.3885
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6743 0.215
h = 0.001 0.001
y[1] (numeric) = -19.6727937238 0.21850372537
y[1] (closed_form) = -19.6728050928 0.218509403536
absolute error = 1.271e-05
relative error = 6.459e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.3903
Order of pole (given) = 0.5 0
NO 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=304.5MB, alloc=52.3MB, time=3.80
x[1] = -1.6733 0.216
h = 0.001 0.003
y[1] (numeric) = -19.6717882222 0.219530843749
y[1] (closed_form) = -19.6717995915 0.219536572169
absolute error = 1.273e-05
relative error = 6.471e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.3916
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6723 0.219
h = 0.0001 0.004
y[1] (numeric) = -19.6708044388 0.222590782635
y[1] (closed_form) = -19.6708160097 0.222596661201
absolute error = 1.298e-05
relative error = 6.597e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.3941
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6722 0.223
h = 0.003 0.006
y[1] (numeric) = -19.670746837 0.226657522732
y[1] (closed_form) = -19.6707588103 0.226663419803
absolute error = 1.335e-05
relative error = 6.785e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.3965
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6692 0.229
h = 0.0001 0.005
y[1] (numeric) = -19.6677648599 0.232789640433
y[1] (closed_form) = -19.6677775163 0.232796439397
absolute error = 1.437e-05
relative error = 7.304e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.4023
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6691 0.234
h = 0.0001 0.003
y[1] (numeric) = -19.6677207673 0.237873610412
y[1] (closed_form) = -19.6677340543 0.237880432061
absolute error = 1.494e-05
relative error = 7.594e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.4053
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.669 0.237
h = 0.001 0.001
y[1] (numeric) = -19.6676544038 0.240924490819
y[1] (closed_form) = -19.6676679174 0.24093132607
absolute error = 1.514e-05
relative error = 7.699e-05 %
Correct digits = 6
memory used=350.1MB, alloc=52.3MB, time=4.36
Radius of convergence (given) for eq 1 = 0.4071
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.668 0.238
h = 0.001 0.003
y[1] (numeric) = -19.666649747 0.241952978514
y[1] (closed_form) = -19.6666632609 0.241959864028
absolute error = 1.517e-05
relative error = 7.711e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.4085
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.667 0.241
h = 0.0001 0.004
y[1] (numeric) = -19.6656690224 0.245014811291
y[1] (closed_form) = -19.6656827381 0.24502184689
absolute error = 1.541e-05
relative error = 7.838e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.4111
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6669 0.245
h = 0.003 0.006
y[1] (numeric) = -19.6656158227 0.249082710996
y[1] (closed_form) = -19.6656299408 0.249089764974
absolute error = 1.578e-05
relative error = 8.025e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.4135
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6639 0.251
h = 0.0001 0.005
y[1] (numeric) = -19.6626397018 0.255219722879
y[1] (closed_form) = -19.6626545034 0.255227678638
absolute error = 1.680e-05
relative error = 8.546e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.4195
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6638 0.256
h = 0.0001 0.003
y[1] (numeric) = -19.6626011189 0.260305113792
y[1] (closed_form) = -19.6626165511 0.260313092088
absolute error = 1.737e-05
relative error = 8.835e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.4226
Order of pole (given) = 0.5 0
NO 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=395.7MB, alloc=52.3MB, time=4.92
x[1] = -1.6637 0.259
h = 0.001 0.001
y[1] (numeric) = -19.6625380509 0.263356890782
y[1] (closed_form) = -19.6625537097 0.263364882639
absolute error = 1.758e-05
relative error = 8.940e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.4245
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6627 0.26
h = 0.001 0.003
y[1] (numeric) = -19.6615342394 0.264386747605
y[1] (closed_form) = -19.6615498984 0.264394789735
absolute error = 1.760e-05
relative error = 8.952e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.4259
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6617 0.263
h = 0.0001 0.004
y[1] (numeric) = -19.6605565747 0.267450473323
y[1] (closed_form) = -19.6605724356 0.267458665476
absolute error = 1.785e-05
relative error = 9.079e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.4285
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6616 0.267
h = 0.003 0.006
y[1] (numeric) = -19.6605077779 0.271519531129
y[1] (closed_form) = -19.6605240413 0.271527741534
absolute error = 1.822e-05
relative error = 9.266e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.431
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6586 0.273
h = 0.0001 0.005
y[1] (numeric) = -19.6575375154 0.277661435495
y[1] (closed_form) = -19.6575544626 0.27767054756
absolute error = 1.924e-05
relative error = 9.787e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.4371
Order of pole (given) = 0.5 0
NO 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=441.5MB, alloc=52.3MB, time=5.48
x[1] = -1.6585 0.278
h = 0.0001 0.003
y[1] (numeric) = -19.6575044434 0.282748245465
y[1] (closed_form) = -19.6575220211 0.282757379908
absolute error = 1.981e-05
relative error = 0.0001008 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.4403
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6584 0.281
h = 0.001 0.001
y[1] (numeric) = -19.6574446714 0.285800917914
y[1] (closed_form) = -19.6574624758 0.285810065875
absolute error = 2.002e-05
relative error = 0.0001018 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.4423
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6574 0.282
h = 0.001 0.003
y[1] (numeric) = -19.6564417057 0.286832143679
y[1] (closed_form) = -19.6564595104 0.286841341921
absolute error = 2.004e-05
relative error = 0.0001019 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.4437
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6564 0.285
h = 0.0001 0.004
y[1] (numeric) = -19.6554671018 0.289897761387
y[1] (closed_form) = -19.6554851084 0.28990710959
absolute error = 2.029e-05
relative error = 0.0001032 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.4464
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6563 0.289
h = 0.003 0.006
y[1] (numeric) = -19.6554227088 0.29396797579
y[1] (closed_form) = -19.6554411179 0.293977342115
absolute error = 2.065e-05
relative error = 0.0001051 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.4491
Order of pole (given) = 0.5 0
NO 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=487.3MB, alloc=52.3MB, time=6.04
x[1] = -1.6533 0.295
h = 0.0001 0.005
y[1] (numeric) = -19.6524583071 0.300114770934
y[1] (closed_form) = -19.6524774004 0.300125038794
absolute error = 2.168e-05
relative error = 0.0001103 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.4552
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6532 0.3
h = 0.0001 0.003
y[1] (numeric) = -19.6524307469 0.305202998083
y[1] (closed_form) = -19.6524504707 0.30521328815
absolute error = 2.225e-05
relative error = 0.0001132 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.4586
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6531 0.303
h = 0.001 0.001
y[1] (numeric) = -19.6523742716 0.30825656487
y[1] (closed_form) = -19.652394222 0.308266868408
absolute error = 2.245e-05
relative error = 0.0001142 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.4606
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6521 0.304
h = 0.0001 0.004
y[1] (numeric) = -19.6513721523 0.309289159389
y[1] (closed_form) = -19.6513921032 0.309299513216
absolute error = 2.248e-05
relative error = 0.0001144 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.462
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.652 0.308
h = 0.003 0.006
y[1] (numeric) = -19.6513315646 0.31336031556
y[1] (closed_form) = -19.6513519176 0.31337068751
absolute error = 2.284e-05
relative error = 0.0001162 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.4647
Order of pole (given) = 0.5 0
NO 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=532.9MB, alloc=52.3MB, time=6.60
x[1] = -1.649 0.314
h = 0.0001 0.005
y[1] (numeric) = -19.6483722677 0.319511249308
y[1] (closed_form) = -19.6483933053 0.319522522677
absolute error = 2.387e-05
relative error = 0.0001215 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.471
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6489 0.319
h = 0.0001 0.003
y[1] (numeric) = -19.6483494696 0.324600629138
y[1] (closed_form) = -19.6483711376 0.324611924561
absolute error = 2.444e-05
relative error = 0.0001243 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.4744
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6488 0.322
h = 0.001 0.001
y[1] (numeric) = -19.648295843 0.327654925561
y[1] (closed_form) = -19.6483177377 0.327666234412
absolute error = 2.464e-05
relative error = 0.0001254 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.4765
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6478 0.323
h = 0.001 0.003
y[1] (numeric) = -19.6472944692 0.328688688016
y[1] (closed_form) = -19.6473163643 0.328700047162
absolute error = 2.467e-05
relative error = 0.0001255 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.4779
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6468 0.326
h = 0.0001 0.004
y[1] (numeric) = -19.6463255858 0.331757787255
y[1] (closed_form) = -19.6463476829 0.331769296247
absolute error = 2.491e-05
relative error = 0.0001268 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.4807
Order of pole (given) = 0.5 0
NO 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=578.7MB, alloc=52.3MB, time=7.17
x[1] = -1.6467 0.33
h = 0.003 0.006
y[1] (numeric) = -19.646289403 0.335830097328
y[1] (closed_form) = -19.6463119026 0.335841624193
absolute error = 2.528e-05
relative error = 0.0001287 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.4834
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6437 0.336
h = 0.0001 0.005
y[1] (numeric) = -19.6433359712 0.341985918655
y[1] (closed_form) = -19.6433591557 0.341998346805
absolute error = 2.631e-05
relative error = 0.0001339 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.4897
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6436 0.341
h = 0.0001 0.003
y[1] (numeric) = -19.6433186867 0.347076712152
y[1] (closed_form) = -19.6433425017 0.347089162168
absolute error = 2.687e-05
relative error = 0.0001368 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.4933
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6435 0.344
h = 0.001 0.001
y[1] (numeric) = -19.643268358 0.350131900815
y[1] (closed_form) = -19.6432923996 0.350144364207
absolute error = 2.708e-05
relative error = 0.0001378 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.4954
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6425 0.345
h = 0.001 0.003
y[1] (numeric) = -19.6422678316 0.351167031668
y[1] (closed_form) = -19.6422918737 0.351179545362
absolute error = 2.710e-05
relative error = 0.000138 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.4968
Order of pole (given) = 0.5 0
NO 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=624.5MB, alloc=52.3MB, time=7.73
x[1] = -1.6415 0.348
h = 0.0001 0.004
y[1] (numeric) = -19.6413020118 0.354238020163
y[1] (closed_form) = -19.6413262559 0.354250683642
absolute error = 2.735e-05
relative error = 0.0001392 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.4996
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6414 0.352
h = 0.003 0.006
y[1] (numeric) = -19.641270235 0.358311482514
y[1] (closed_form) = -19.6412948818 0.35832416373
absolute error = 2.772e-05
relative error = 0.0001411 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.5025
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6384 0.358
h = 0.0001 0.005
y[1] (numeric) = -19.6383226706 0.364472189714
y[1] (closed_form) = -19.6383480025 0.364485772077
absolute error = 2.874e-05
relative error = 0.0001463 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.5088
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6383 0.363
h = 0.0001 0.003
y[1] (numeric) = -19.6383109007 0.369564394994
y[1] (closed_form) = -19.6383368632 0.369577999029
absolute error = 2.931e-05
relative error = 0.0001492 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.5124
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6382 0.366
h = 0.001 0.001
y[1] (numeric) = -19.6382638704 0.372620474773
y[1] (closed_form) = -19.6382900595 0.372634092129
absolute error = 2.952e-05
relative error = 0.0001503 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.5146
Order of pole (given) = 0.5 0
NO 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=670.1MB, alloc=52.3MB, time=8.29
x[1] = -1.6372 0.367
h = 0.001 0.003
y[1] (numeric) = -19.6372641922 0.373656973836
y[1] (closed_form) = -19.6372903817 0.373670641501
absolute error = 2.954e-05
relative error = 0.0001504 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.5161
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6362 0.37
h = 0.0001 0.004
y[1] (numeric) = -19.6363014369 0.376729850635
y[1] (closed_form) = -19.6363278286 0.376743668023
absolute error = 2.979e-05
relative error = 0.0001517 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.5189
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6361 0.374
h = 0.003 0.006
y[1] (numeric) = -19.636274067 0.380804463757
y[1] (closed_form) = -19.6363008613 0.380818298746
absolute error = 3.016e-05
relative error = 0.0001535 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.5218
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6331 0.38
h = 0.0001 0.005
y[1] (numeric) = -19.6333323722 0.386970055123
y[1] (closed_form) = -19.6333598521 0.386984791117
absolute error = 3.118e-05
relative error = 0.0001588 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.5282
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.633 0.385
h = 0.0001 0.003
y[1] (numeric) = -19.633326118 0.392063670301
y[1] (closed_form) = -19.6333542284 0.392078427767
absolute error = 3.175e-05
relative error = 0.0001617 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.5319
Order of pole (given) = 0.5 0
NO 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=715.8MB, alloc=52.3MB, time=8.85
x[1] = -1.6329 0.388
h = 0.001 0.001
y[1] (numeric) = -19.6332823867 0.395120640071
y[1] (closed_form) = -19.6333107238 0.395135410801
absolute error = 3.196e-05
relative error = 0.0001627 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.5341
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6319 0.389
h = 0.001 0.003
y[1] (numeric) = -19.6322835572 0.396158507157
y[1] (closed_form) = -19.6323118947 0.396173328203
absolute error = 3.198e-05
relative error = 0.0001629 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.5356
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6309 0.392
h = 0.0001 0.004
y[1] (numeric) = -19.6313238673 0.399233271308
y[1] (closed_form) = -19.631352407 0.399248242014
absolute error = 3.223e-05
relative error = 0.0001641 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.5384
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6308 0.396
h = 0.003 0.006
y[1] (numeric) = -19.6313009051 0.403309033692
y[1] (closed_form) = -19.6313298475 0.403324021862
absolute error = 3.259e-05
relative error = 0.000166 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.5414
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6278 0.402
h = 0.0001 0.005
y[1] (numeric) = -19.6283650823 0.409479507517
y[1] (closed_form) = -19.6283947106 0.409495396546
absolute error = 3.362e-05
relative error = 0.0001712 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.5478
Order of pole (given) = 0.5 0
NO 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=761.5MB, alloc=52.3MB, time=9.42
x[1] = -1.6277 0.407
h = 0.0001 0.003
y[1] (numeric) = -19.6283643448 0.414574530707
y[1] (closed_form) = -19.6283946035 0.414590441004
absolute error = 3.419e-05
relative error = 0.0001741 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.5516
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6276 0.41
h = 0.001 0.001
y[1] (numeric) = -19.6283239132 0.417632389344
y[1] (closed_form) = -19.6283543987 0.417648312846
absolute error = 3.439e-05
relative error = 0.0001752 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.5539
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6266 0.411
h = 0.0001 0.004
y[1] (numeric) = -19.6273259329 0.418671624264
y[1] (closed_form) = -19.6273564188 0.418687598087
absolute error = 3.442e-05
relative error = 0.0001753 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.5553
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6265 0.415
h = 0.003 0.006
y[1] (numeric) = -19.6273067793 0.422748322103
y[1] (closed_form) = -19.6273376676 0.422764313338
absolute error = 3.478e-05
relative error = 0.0001772 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.5583
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6235 0.421
h = 0.0001 0.005
y[1] (numeric) = -19.6243760708 0.428922927232
y[1] (closed_form) = -19.6244076454 0.428939819194
absolute error = 3.581e-05
relative error = 0.0001824 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.5648
Order of pole (given) = 0.5 0
NO 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=807.2MB, alloc=52.3MB, time=9.98
x[1] = -1.6234 0.426
h = 0.0001 0.003
y[1] (numeric) = -19.6243800994 0.43401909515
y[1] (closed_form) = -19.6244123045 0.434036008201
absolute error = 3.638e-05
relative error = 0.0001853 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.5686
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6233 0.429
h = 0.001 0.001
y[1] (numeric) = -19.6243425191 0.437077678677
y[1] (closed_form) = -19.6243749509 0.43709460488
absolute error = 3.658e-05
relative error = 0.0001864 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.5709
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6223 0.43
h = 0.001 0.003
y[1] (numeric) = -19.6233452866 0.438118080707
y[1] (closed_form) = -19.6233777189 0.438135057236
absolute error = 3.661e-05
relative error = 0.0001865 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.5723
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6213 0.433
h = 0.0001 0.004
y[1] (numeric) = -19.6223913259 0.4411963177
y[1] (closed_form) = -19.6224239605 0.441213443774
absolute error = 3.686e-05
relative error = 0.0001878 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.5752
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6212 0.437
h = 0.003 0.006
y[1] (numeric) = -19.6223765811 0.445274162054
y[1] (closed_form) = -19.6224096184 0.445291305333
absolute error = 3.722e-05
relative error = 0.0001896 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.5783
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6182 0.443
h = 0.0001 0.005
y[1] (numeric) = -19.6194517489 0.451453646432
y[1] (closed_form) = -19.6194854729 0.451471690288
absolute error = 3.825e-05
relative error = 0.0001949 %
Correct digits = 6
memory used=852.9MB, alloc=52.3MB, time=10.54
Radius of convergence (given) for eq 1 = 0.5848
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6181 0.448
h = 0.0001 0.003
y[1] (numeric) = -19.619461296 0.456551218838
y[1] (closed_form) = -19.6194956504 0.45656928357
absolute error = 3.881e-05
relative error = 0.0001978 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.5887
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.618 0.451
h = 0.001 0.001
y[1] (numeric) = -19.6194270165 0.459610689131
y[1] (closed_form) = -19.6194615977 0.459628766953
absolute error = 3.902e-05
relative error = 0.0001988 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.591
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.617 0.452
h = 0.001 0.003
y[1] (numeric) = -19.6184306343 0.460652458637
y[1] (closed_form) = -19.618465216 0.460670586791
absolute error = 3.905e-05
relative error = 0.000199 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.5924
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.616 0.455
h = 0.0001 0.004
y[1] (numeric) = -19.6174797418 0.463732580244
y[1] (closed_form) = -19.6175145259 0.46375085788
absolute error = 3.929e-05
relative error = 0.0002002 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.5954
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6159 0.459
h = 0.003 0.006
y[1] (numeric) = -19.617469407 0.467811569536
y[1] (closed_form) = -19.6175045938 0.467829864238
absolute error = 3.966e-05
relative error = 0.0002021 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.5985
Order of pole (given) = 0.5 0
NO 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=898.7MB, alloc=52.3MB, time=11.10
x[1] = -1.6129 0.465
h = 0.0001 0.005
y[1] (numeric) = -19.6145504534 0.473995931452
y[1] (closed_form) = -19.6145863272 0.474015126578
absolute error = 4.069e-05
relative error = 0.0002074 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.605
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6128 0.47
h = 0.0001 0.003
y[1] (numeric) = -19.61456552 0.479094906458
y[1] (closed_form) = -19.6146020242 0.479114122245
absolute error = 4.125e-05
relative error = 0.0002103 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.609
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6127 0.473
h = 0.001 0.001
y[1] (numeric) = -19.6145345419 0.48215526239
y[1] (closed_form) = -19.6145712729 0.482174491202
absolute error = 4.146e-05
relative error = 0.0002113 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.6113
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6117 0.474
h = 0.001 0.003
y[1] (numeric) = -19.6135390107 0.483198399185
y[1] (closed_form) = -19.6135757421 0.483217678334
absolute error = 4.148e-05
relative error = 0.0002114 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.6127
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6107 0.477
h = 0.0001 0.004
y[1] (numeric) = -19.6125911873 0.486280404451
y[1] (closed_form) = -19.6126281213 0.486299833022
absolute error = 4.173e-05
relative error = 0.0002127 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.6157
Order of pole (given) = 0.5 0
NO 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=944.5MB, alloc=52.3MB, time=11.66
x[1] = -1.6106 0.481
h = 0.003 0.006
y[1] (numeric) = -19.6125852633 0.490360537173
y[1] (closed_form) = -19.6126226001 0.490379982668
absolute error = 4.210e-05
relative error = 0.0002146 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.6189
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6076 0.487
h = 0.0001 0.005
y[1] (numeric) = -19.6096721905 0.496549774916
y[1] (closed_form) = -19.6097102147 0.49657012068
absolute error = 4.313e-05
relative error = 0.0002198 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.6254
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6075 0.492
h = 0.0001 0.003
y[1] (numeric) = -19.6096927776 0.501650150631
y[1] (closed_form) = -19.6097314322 0.501670516839
absolute error = 4.369e-05
relative error = 0.0002227 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.6294
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6074 0.495
h = 0.001 0.001
y[1] (numeric) = -19.6096651016 0.504711391076
y[1] (closed_form) = -19.609703983 0.504731770244
absolute error = 4.390e-05
relative error = 0.0002238 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.6318
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6064 0.496
h = 0.001 0.003
y[1] (numeric) = -19.6086704218 0.50575589497
y[1] (closed_form) = -19.6087093037 0.50577632448
absolute error = 4.392e-05
relative error = 0.0002239 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.6332
Order of pole (given) = 0.5 0
NO 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=990.3MB, alloc=52.3MB, time=12.23
x[1] = -1.6054 0.499
h = 0.0001 0.004
y[1] (numeric) = -19.6077256686 0.508839782943
y[1] (closed_form) = -19.607764753 0.508860361813
absolute error = 4.417e-05
relative error = 0.0002252 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.6362
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6053 0.503
h = 0.003 0.006
y[1] (numeric) = -19.6077241562 0.512921057585
y[1] (closed_form) = -19.6077636434 0.512941653237
absolute error = 4.454e-05
relative error = 0.0002271 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.6394
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6023 0.509
h = 0.0001 0.005
y[1] (numeric) = -19.6048169666 0.519115169442
y[1] (closed_form) = -19.6048571416 0.519136665207
absolute error = 4.556e-05
relative error = 0.0002323 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.6459
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6022 0.514
h = 0.0001 0.003
y[1] (numeric) = -19.6048430751 0.524216943976
y[1] (closed_form) = -19.6048838806 0.524238459966
absolute error = 4.613e-05
relative error = 0.0002352 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.65
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.6021 0.517
h = 0.001 0.001
y[1] (numeric) = -19.6048187018 0.527279067808
y[1] (closed_form) = -19.6048597341 0.527300596691
absolute error = 4.634e-05
relative error = 0.0002363 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.6524
Order of pole (given) = 0.5 0
NO 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=1036.0MB, alloc=52.3MB, time=12.79
x[1] = -1.6011 0.518
h = 0.0001 0.004
y[1] (numeric) = -19.6038248741 0.528324938613
y[1] (closed_form) = -19.6038659068 0.528346517842
absolute error = 4.636e-05
relative error = 0.0002364 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.6538
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.601 0.522
h = 0.003 0.006
y[1] (numeric) = -19.6038271735 0.532407142368
y[1] (closed_form) = -19.6038686089 0.532428738297
absolute error = 4.673e-05
relative error = 0.0002383 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.657
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.598 0.528
h = 0.0001 0.005
y[1] (numeric) = -19.6009251078 0.53860537821
y[1] (closed_form) = -19.6009672312 0.538627874112
absolute error = 4.775e-05
relative error = 0.0002435 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.6636
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5979 0.533
h = 0.0001 0.003
y[1] (numeric) = -19.6009559865 0.543708289499
y[1] (closed_form) = -19.6009987405 0.543730805434
absolute error = 4.832e-05
relative error = 0.0002464 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.6677
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5978 0.536
h = 0.001 0.001
y[1] (numeric) = -19.600934467 0.546771133468
y[1] (closed_form) = -19.6009774477 0.546793662237
absolute error = 4.853e-05
relative error = 0.0002475 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.6701
Order of pole (given) = 0.5 0
NO 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=1081.8MB, alloc=52.3MB, time=13.36
x[1] = -1.5968 0.537
h = 0.001 0.003
y[1] (numeric) = -19.5999413894 0.547818170552
y[1] (closed_form) = -19.5999843707 0.547840749672
absolute error = 4.855e-05
relative error = 0.0002476 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.6715
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5958 0.54
h = 0.0001 0.004
y[1] (numeric) = -19.5990023739 0.550905522665
y[1] (closed_form) = -19.5990455579 0.550928251029
absolute error = 4.880e-05
relative error = 0.0002489 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.6745
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5957 0.544
h = 0.003 0.006
y[1] (numeric) = -19.5990090862 0.554988865562
y[1] (closed_form) = -19.5990526731 0.555011610443
absolute error = 4.916e-05
relative error = 0.0002508 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.6778
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5927 0.55
h = 0.0001 0.005
y[1] (numeric) = -19.596112908 0.561191972301
y[1] (closed_form) = -19.5961571833 0.561215616996
absolute error = 5.019e-05
relative error = 0.000256 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.6844
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5926 0.555
h = 0.0001 0.003
y[1] (numeric) = -19.59614931 0.566296278878
y[1] (closed_form) = -19.5961942158 0.566319943384
absolute error = 5.076e-05
relative error = 0.0002589 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.6885
Order of pole (given) = 0.5 0
NO 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=1127.7MB, alloc=52.3MB, time=13.92
x[1] = -1.5925 0.558
h = 0.001 0.001
y[1] (numeric) = -19.5961310943 0.56936000413
y[1] (closed_form) = -19.5961762269 0.5693836814
absolute error = 5.097e-05
relative error = 0.00026 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.691
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5915 0.559
h = 0.001 0.003
y[1] (numeric) = -19.5951388699 0.570408407765
y[1] (closed_form) = -19.595184003 0.570432135391
absolute error = 5.099e-05
relative error = 0.0002601 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.6924
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5905 0.562
h = 0.0001 0.004
y[1] (numeric) = -19.5942029273 0.573497639844
y[1] (closed_form) = -19.5942482632 0.573521516652
absolute error = 5.124e-05
relative error = 0.0002614 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.6954
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5904 0.566
h = 0.003 0.006
y[1] (numeric) = -19.5942140535 0.57758212033
y[1] (closed_form) = -19.5942597923 0.577606013513
absolute error = 5.160e-05
relative error = 0.0002632 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.6987
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5874 0.572
h = 0.0001 0.005
y[1] (numeric) = -19.5913237649 0.583790096252
y[1] (closed_form) = -19.5913701926 0.583814889089
absolute error = 5.263e-05
relative error = 0.0002685 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.7053
Order of pole (given) = 0.5 0
NO 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=1173.5MB, alloc=52.3MB, time=14.48
x[1] = -1.5873 0.577
h = 0.0001 0.003
y[1] (numeric) = -19.5913656913 0.588895796226
y[1] (closed_form) = -19.5914127495 0.588920608648
absolute error = 5.320e-05
relative error = 0.0002714 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.7094
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5872 0.58
h = 0.001 0.001
y[1] (numeric) = -19.59135078 0.591960401632
y[1] (closed_form) = -19.591398065 0.591985226749
absolute error = 5.341e-05
relative error = 0.0002725 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.7119
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5862 0.581
h = 0.001 0.003
y[1] (numeric) = -19.5903594093 0.59301017163
y[1] (closed_form) = -19.5904066948 0.593035047107
absolute error = 5.343e-05
relative error = 0.0002726 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.7133
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5852 0.584
h = 0.0001 0.004
y[1] (numeric) = -19.5894265405 0.596101282719
y[1] (closed_form) = -19.5894740289 0.596126307316
absolute error = 5.368e-05
relative error = 0.0002739 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.7163
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5851 0.588
h = 0.003 0.006
y[1] (numeric) = -19.5894420814 0.600186899285
y[1] (closed_form) = -19.5894899728 0.600211940114
absolute error = 5.404e-05
relative error = 0.0002757 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.7196
Order of pole (given) = 0.5 0
NO 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=1219.3MB, alloc=52.3MB, time=15.04
x[1] = -1.5821 0.594
h = 0.0001 0.005
y[1] (numeric) = -19.5865576849 0.606399742674
y[1] (closed_form) = -19.5866062654 0.606425682995
absolute error = 5.507e-05
relative error = 0.000281 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.7263
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.582 0.599
h = 0.0001 0.003
y[1] (numeric) = -19.5866051367 0.611506834152
y[1] (closed_form) = -19.5866543478 0.611532793832
absolute error = 5.564e-05
relative error = 0.0002839 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.7304
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5819 0.602
h = 0.001 0.001
y[1] (numeric) = -19.5865935304 0.614572318586
y[1] (closed_form) = -19.5866429683 0.61459829089
absolute error = 5.585e-05
relative error = 0.000285 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.7329
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5809 0.603
h = 0.001 0.003
y[1] (numeric) = -19.5856030139 0.615623454755
y[1] (closed_form) = -19.5856524524 0.615649477425
absolute error = 5.587e-05
relative error = 0.0002851 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.7343
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5799 0.606
h = 0.0001 0.004
y[1] (numeric) = -19.58467322 0.618716443899
y[1] (closed_form) = -19.5847228614 0.618742615628
absolute error = 5.612e-05
relative error = 0.0002864 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.7374
Order of pole (given) = 0.5 0
NO 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=1265.2MB, alloc=52.3MB, time=15.61
x[1] = -1.5798 0.61
h = 0.003 0.006
y[1] (numeric) = -19.5846931764 0.622803195035
y[1] (closed_form) = -19.5847432208 0.622829382852
absolute error = 5.648e-05
relative error = 0.0002883 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.7407
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5768 0.616
h = 0.0001 0.005
y[1] (numeric) = -19.5818146742 0.629020904175
y[1] (closed_form) = -19.5818654082 0.629047991321
absolute error = 5.751e-05
relative error = 0.0002935 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.7474
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5767 0.621
h = 0.0001 0.003
y[1] (numeric) = -19.5818676523 0.634129385263
y[1] (closed_form) = -19.5819190169 0.634156491542
absolute error = 5.808e-05
relative error = 0.0002964 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.7515
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5766 0.624
h = 0.001 0.001
y[1] (numeric) = -19.5818593517 0.637195747596
y[1] (closed_form) = -19.5819109431 0.637222866428
absolute error = 5.828e-05
relative error = 0.0002975 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.7541
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5756 0.625
h = 0.0001 0.004
y[1] (numeric) = -19.5808696901 0.638248249748
y[1] (closed_form) = -19.580921282 0.638275418949
absolute error = 5.831e-05
relative error = 0.0002976 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.7555
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5755 0.629
h = 0.003 0.006
y[1] (numeric) = -19.5808934615 0.642335923638
y[1] (closed_form) = -19.5809454563 0.642363108826
absolute error = 5.867e-05
relative error = 0.0002995 %
Correct digits = 6
memory used=1311.0MB, alloc=52.3MB, time=16.17
Radius of convergence (given) for eq 1 = 0.7588
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5725 0.635
h = 0.0001 0.005
y[1] (numeric) = -19.5780200929 0.648557749428
y[1] (closed_form) = -19.5780727775 0.648585833801
absolute error = 5.970e-05
relative error = 0.0003048 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.7655
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5724 0.64
h = 0.0001 0.003
y[1] (numeric) = -19.5780778452 0.653667359286
y[1] (closed_form) = -19.5781311604 0.653695462594
absolute error = 6.027e-05
relative error = 0.0003077 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.7697
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5723 0.643
h = 0.001 0.001
y[1] (numeric) = -19.5780724009 0.656734436995
y[1] (closed_form) = -19.578125943 0.656762552794
absolute error = 6.048e-05
relative error = 0.0003087 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.7723
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5713 0.644
h = 0.001 0.003
y[1] (numeric) = -19.5770834918 0.657788104594
y[1] (closed_form) = -19.5771370345 0.657816270766
absolute error = 6.050e-05
relative error = 0.0003089 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.7736
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5703 0.647
h = 0.0001 0.004
y[1] (numeric) = -19.5761594442 0.660884549165
y[1] (closed_form) = -19.57621319 0.660912864281
absolute error = 6.075e-05
relative error = 0.0003101 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.7767
Order of pole (given) = 0.5 0
NO 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=1356.9MB, alloc=52.3MB, time=16.73
x[1] = -1.5702 0.651
h = 0.003 0.006
y[1] (numeric) = -19.5761876325 0.664973354826
y[1] (closed_form) = -19.5762417813 0.665001685761
absolute error = 6.111e-05
relative error = 0.000312 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.7801
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5672 0.657
h = 0.0001 0.005
y[1] (numeric) = -19.5733201624 0.671200043144
y[1] (closed_form) = -19.5733750015 0.6712292731
absolute error = 6.214e-05
relative error = 0.0003173 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.7867
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5671 0.662
h = 0.0001 0.003
y[1] (numeric) = -19.5733834429 0.676311039077
y[1] (closed_form) = -19.5734389126 0.676340287739
absolute error = 6.271e-05
relative error = 0.0003202 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.791
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.567 0.665
h = 0.001 0.001
y[1] (numeric) = -19.5733813054 0.679378992579
y[1] (closed_form) = -19.573437002 0.679408253659
absolute error = 6.292e-05
relative error = 0.0003212 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.7935
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.566 0.666
h = 0.001 0.003
y[1] (numeric) = -19.5723932522 0.6804340258
y[1] (closed_form) = -19.5724489494 0.680463337258
absolute error = 6.294e-05
relative error = 0.0003214 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.7949
Order of pole (given) = 0.5 0
NO 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=1402.6MB, alloc=52.3MB, time=17.30
x[1] = -1.565 0.669
h = 0.0001 0.004
y[1] (numeric) = -19.5714722822 0.683532345682
y[1] (closed_form) = -19.5715281825 0.683561806021
absolute error = 6.319e-05
relative error = 0.0003227 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.798
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5649 0.673
h = 0.003 0.006
y[1] (numeric) = -19.5715048883 0.687622281577
y[1] (closed_form) = -19.5715611917 0.687651757592
absolute error = 6.355e-05
relative error = 0.0003245 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.8014
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5619 0.679
h = 0.0001 0.005
y[1] (numeric) = -19.5686433191 0.693853830705
y[1] (closed_form) = -19.5687003131 0.693884205576
absolute error = 6.458e-05
relative error = 0.0003298 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.8081
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5618 0.684
h = 0.0001 0.003
y[1] (numeric) = -19.5687121288 0.698966210819
y[1] (closed_form) = -19.5687697535 0.698996604167
absolute error = 6.515e-05
relative error = 0.0003327 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.8123
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5617 0.687
h = 0.001 0.001
y[1] (numeric) = -19.5687132987 0.702035038984
y[1] (closed_form) = -19.5687711503 0.702065444677
absolute error = 6.536e-05
relative error = 0.0003338 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.8149
Order of pole (given) = 0.5 0
NO 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=1448.5MB, alloc=52.3MB, time=17.86
x[1] = -1.5607 0.688
h = 0.001 0.003
y[1] (numeric) = -19.567726102 0.703091437637
y[1] (closed_form) = -19.5677839542 0.703121893712
absolute error = 6.538e-05
relative error = 0.0003339 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.8163
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5597 0.691
h = 0.0001 0.004
y[1] (numeric) = -19.5668082104 0.706191631874
y[1] (closed_form) = -19.5668662659 0.706222236768
absolute error = 6.563e-05
relative error = 0.0003352 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.8194
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5596 0.695
h = 0.003 0.006
y[1] (numeric) = -19.5668452352 0.710282696492
y[1] (closed_form) = -19.5669036937 0.710313316918
absolute error = 6.599e-05
relative error = 0.000337 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.8228
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5566 0.701
h = 0.0001 0.005
y[1] (numeric) = -19.5639895692 0.716519104711
y[1] (closed_form) = -19.5640487188 0.716550623827
absolute error = 6.702e-05
relative error = 0.0003424 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.8295
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5565 0.706
h = 0.0001 0.003
y[1] (numeric) = -19.5640639091 0.721632867111
y[1] (closed_form) = -19.5641236894 0.721664404475
absolute error = 6.759e-05
relative error = 0.0003452 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.8337
Order of pole (given) = 0.5 0
NO 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=1494.3MB, alloc=52.3MB, time=18.44
x[1] = -1.5564 0.709
h = 0.001 0.001
y[1] (numeric) = -19.564068387 0.724702568811
y[1] (closed_form) = -19.5641283941 0.724734118445
absolute error = 6.780e-05
relative error = 0.0003463 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.8363
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5554 0.71
h = 0.001 0.003
y[1] (numeric) = -19.5630820474 0.725760332705
y[1] (closed_form) = -19.5631420552 0.725791932726
absolute error = 6.782e-05
relative error = 0.0003464 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.8377
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5544 0.713
h = 0.0001 0.004
y[1] (numeric) = -19.5621672353 0.72886240034
y[1] (closed_form) = -19.5622274464 0.728894149119
absolute error = 6.807e-05
relative error = 0.0003477 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.8408
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5543 0.717
h = 0.003 0.006
y[1] (numeric) = -19.5622086794 0.732954592169
y[1] (closed_form) = -19.5622692937 0.732986356335
absolute error = 6.843e-05
relative error = 0.0003496 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.8442
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5513 0.723
h = 0.0001 0.005
y[1] (numeric) = -19.559358919 0.73919585776
y[1] (closed_form) = -19.5594202246 0.739228520449
absolute error = 6.946e-05
relative error = 0.0003549 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.8509
Order of pole (given) = 0.5 0
NO 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=1540.3MB, alloc=52.3MB, time=19.02
x[1] = -1.5512 0.728
h = 0.0001 0.003
y[1] (numeric) = -19.5594387901 0.744311000551
y[1] (closed_form) = -19.5595007264 0.744343681258
absolute error = 7.003e-05
relative error = 0.0003578 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.8552
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5511 0.731
h = 0.001 0.001
y[1] (numeric) = -19.5594465766 0.747381574656
y[1] (closed_form) = -19.5595087399 0.747414267559
absolute error = 7.024e-05
relative error = 0.0003588 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.8578
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5501 0.732
h = 0.0001 0.004
y[1] (numeric) = -19.5584610946 0.748440703601
y[1] (closed_form) = -19.5585232586 0.748473446895
absolute error = 7.026e-05
relative error = 0.000359 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.8592
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.55 0.736
h = 0.003 0.006
y[1] (numeric) = -19.5585063571 0.752533811814
y[1] (closed_form) = -19.5585689241 0.752566570382
absolute error = 7.062e-05
relative error = 0.0003608 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.8627
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.547 0.742
h = 0.0001 0.005
y[1] (numeric) = -19.5556617396 0.758779186707
y[1] (closed_form) = -19.5557249983 0.758812843651
absolute error = 7.166e-05
relative error = 0.0003661 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.8694
Order of pole (given) = 0.5 0
NO 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=1586.3MB, alloc=52.3MB, time=19.60
x[1] = -1.5469 0.747
h = 0.0001 0.003
y[1] (numeric) = -19.555746389 0.763895450271
y[1] (closed_form) = -19.5558102784 0.763929125033
absolute error = 7.222e-05
relative error = 0.000369 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.8737
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5468 0.75
h = 0.001 0.001
y[1] (numeric) = -19.5557570343 0.766966734988
y[1] (closed_form) = -19.5558211507 0.767000421881
absolute error = 7.243e-05
relative error = 0.0003701 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.8763
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5458 0.751
h = 0.001 0.003
y[1] (numeric) = -19.5547723073 0.768027028545
y[1] (closed_form) = -19.5548364243 0.768060765832
absolute error = 7.245e-05
relative error = 0.0003702 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.8777
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5448 0.754
h = 0.0001 0.004
y[1] (numeric) = -19.5538632502 0.771132542882
y[1] (closed_form) = -19.5539275706 0.771166428812
absolute error = 7.270e-05
relative error = 0.0003715 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.8808
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5447 0.758
h = 0.0001 0.004
y[1] (numeric) = -19.5539129334 0.775226775493
y[1] (closed_form) = -19.5539776571 0.775260676541
absolute error = 7.306e-05
relative error = 0.0003734 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.8842
Order of pole (given) = 0.5 0
NO 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=1632.1MB, alloc=52.3MB, time=20.16
x[1] = -1.5446 0.762
h = 0.003 0.006
y[1] (numeric) = -19.5539634226 0.779321038449
y[1] (closed_form) = -19.5540285496 0.779354954426
absolute error = 7.343e-05
relative error = 0.0003752 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.8877
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5416 0.768
h = 0.0001 0.005
y[1] (numeric) = -19.5511259169 0.785571887167
y[1] (closed_form) = -19.551191736 0.785606701309
absolute error = 7.446e-05
relative error = 0.0003805 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.8944
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5415 0.773
h = 0.0001 0.003
y[1] (numeric) = -19.551217107 0.790689560105
y[1] (closed_form) = -19.5512835569 0.790724391794
absolute error = 7.503e-05
relative error = 0.0003834 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.8987
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5414 0.776
h = 0.001 0.001
y[1] (numeric) = -19.5512316666 0.793761742644
y[1] (closed_form) = -19.5512983434 0.793796586375
absolute error = 7.523e-05
relative error = 0.0003845 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9014
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5404 0.777
h = 0.001 0.003
y[1] (numeric) = -19.5502479974 0.794823604924
y[1] (closed_form) = -19.5503146749 0.794858499053
absolute error = 7.526e-05
relative error = 0.0003846 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9028
Order of pole (given) = 0.5 0
NO 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=1678.0MB, alloc=52.3MB, time=20.73
x[1] = -1.5394 0.78
h = 0.0001 0.004
y[1] (numeric) = -19.5493426248 0.79793119883
y[1] (closed_form) = -19.5494095059 0.797966241527
absolute error = 7.551e-05
relative error = 0.0003859 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9058
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5393 0.784
h = 0.003 0.006
y[1] (numeric) = -19.5493975359 0.802026584205
y[1] (closed_form) = -19.5494648202 0.802061641848
absolute error = 7.587e-05
relative error = 0.0003878 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9093
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5363 0.79
h = 0.0001 0.005
y[1] (numeric) = -19.5465659426 0.808282284961
y[1] (closed_form) = -19.5466339195 0.808318240601
absolute error = 7.690e-05
relative error = 0.0003931 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.916
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5362 0.795
h = 0.0001 0.003
y[1] (numeric) = -19.5466626668 0.81340133249
y[1] (closed_form) = -19.5467312744 0.813437305445
absolute error = 7.747e-05
relative error = 0.000396 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9204
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5361 0.798
h = 0.001 0.001
y[1] (numeric) = -19.5466805368 0.816474383978
y[1] (closed_form) = -19.5467493715 0.816510368899
absolute error = 7.767e-05
relative error = 0.000397 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.923
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5351 0.799
h = 0.001 0.003
y[1] (numeric) = -19.545697727 0.817537610701
y[1] (closed_form) = -19.5457665624 0.817573646025
absolute error = 7.770e-05
relative error = 0.0003972 %
Correct digits = 5
memory used=1723.9MB, alloc=52.3MB, time=21.30
Radius of convergence (given) for eq 1 = 0.9244
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5341 0.802
h = 0.0001 0.004
y[1] (numeric) = -19.5447954377 0.820647074099
y[1] (closed_form) = -19.5448644766 0.820683257929
absolute error = 7.795e-05
relative error = 0.0003985 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9275
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.534 0.806
h = 0.003 0.006
y[1] (numeric) = -19.5448547715 0.824743580542
y[1] (closed_form) = -19.5449242137 0.824779779173
absolute error = 7.831e-05
relative error = 0.0004003 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.931
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.531 0.812
h = 0.0001 0.005
y[1] (numeric) = -19.5420290929 0.831004131614
y[1] (closed_form) = -19.542099228 0.831041228074
absolute error = 7.934e-05
relative error = 0.0004056 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9377
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5309 0.817
h = 0.0001 0.003
y[1] (numeric) = -19.5421313522 0.836124551837
y[1] (closed_form) = -19.5422021182 0.83616166538
absolute error = 7.991e-05
relative error = 0.0004085 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9421
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5308 0.82
h = 0.001 0.001
y[1] (numeric) = -19.5421525333 0.839198471142
y[1] (closed_form) = -19.5422235262 0.839235596575
absolute error = 8.011e-05
relative error = 0.0004096 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9447
Order of pole (given) = 0.5 0
NO 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=1770.0MB, alloc=52.3MB, time=21.86
x[1] = -1.5298 0.821
h = 0.001 0.003
y[1] (numeric) = -19.5411705834 0.840263062119
y[1] (closed_form) = -19.5412415771 0.840300237959
absolute error = 8.014e-05
relative error = 0.0004097 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9461
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5288 0.824
h = 0.0001 0.004
y[1] (numeric) = -19.5402713784 0.84337439405
y[1] (closed_form) = -19.5403425757 0.843411718336
absolute error = 8.039e-05
relative error = 0.000411 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9492
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5287 0.828
h = 0.003 0.006
y[1] (numeric) = -19.5403351355 0.847472020048
y[1] (closed_form) = -19.5404067362 0.847509358989
absolute error = 8.075e-05
relative error = 0.0004129 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9527
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5257 0.834
h = 0.0001 0.005
y[1] (numeric) = -19.537515374 0.853737419713
y[1] (closed_form) = -19.5375876679 0.853775656314
absolute error = 8.178e-05
relative error = 0.0004182 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9594
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5256 0.839
h = 0.0001 0.003
y[1] (numeric) = -19.5376231694 0.858859210733
y[1] (closed_form) = -19.5376960943 0.858897464185
absolute error = 8.235e-05
relative error = 0.0004211 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9638
Order of pole (given) = 0.5 0
NO 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=1815.9MB, alloc=52.3MB, time=22.43
x[1] = -1.5255 0.842
h = 0.001 0.001
y[1] (numeric) = -19.5376476621 0.861933996726
y[1] (closed_form) = -19.537720814 0.861972261992
absolute error = 8.256e-05
relative error = 0.0004221 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9665
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5245 0.843
h = 0.001 0.003
y[1] (numeric) = -19.5366665728 0.862999951765
y[1] (closed_form) = -19.5367397255 0.863038267442
absolute error = 8.258e-05
relative error = 0.0004223 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9679
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5235 0.846
h = 0.0001 0.004
y[1] (numeric) = -19.535770453 0.866113151272
y[1] (closed_form) = -19.5358438093 0.866151615333
absolute error = 8.283e-05
relative error = 0.0004236 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.971
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5234 0.85
h = 0.003 0.006
y[1] (numeric) = -19.5358386344 0.87021189531
y[1] (closed_form) = -19.535912394 0.870250373881
absolute error = 8.319e-05
relative error = 0.0004254 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9745
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5204 0.856
h = 0.0001 0.005
y[1] (numeric) = -19.5330247922 0.876482141845
y[1] (closed_form) = -19.5330992455 0.876521517906
absolute error = 8.422e-05
relative error = 0.0004308 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9812
Order of pole (given) = 0.5 0
NO 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=1861.8MB, alloc=52.3MB, time=22.99
x[1] = -1.5203 0.861
h = 0.0001 0.003
y[1] (numeric) = -19.5331381247 0.881605301764
y[1] (closed_form) = -19.533213209 0.881644694445
absolute error = 8.479e-05
relative error = 0.0004336 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9856
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5202 0.864
h = 0.001 0.001
y[1] (numeric) = -19.5331659297 0.884680953315
y[1] (closed_form) = -19.533241241 0.884720357732
absolute error = 8.500e-05
relative error = 0.0004347 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9883
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5192 0.865
h = 0.0001 0.004
y[1] (numeric) = -19.5321857015 0.885748272224
y[1] (closed_form) = -19.5322610136 0.885787727057
absolute error = 8.502e-05
relative error = 0.0004348 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9896
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5191 0.869
h = 0.003 0.006
y[1] (numeric) = -19.5322577052 0.889847924702
y[1] (closed_form) = -19.5323334206 0.889887393925
absolute error = 8.539e-05
relative error = 0.0004367 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9932
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5161 0.875
h = 0.0001 0.005
y[1] (numeric) = -19.5294490178 0.896122271332
y[1] (closed_form) = -19.5295254271 0.896162637895
absolute error = 8.642e-05
relative error = 0.000442 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9999
Order of pole (given) = 0.5 0
NO 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=1907.6MB, alloc=52.3MB, time=23.56
x[1] = -1.516 0.88
h = 0.0001 0.003
y[1] (numeric) = -19.5295671335 0.90124654206
y[1] (closed_form) = -19.5296441738 0.901286925042
absolute error = 8.698e-05
relative error = 0.0004449 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.004
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5159 0.883
h = 0.001 0.001
y[1] (numeric) = -19.5295978004 0.904322898283
y[1] (closed_form) = -19.5296750678 0.904363292935
absolute error = 8.719e-05
relative error = 0.000446 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.007
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5149 0.884
h = 0.001 0.003
y[1] (numeric) = -19.5286183301 0.905391380747
y[1] (closed_form) = -19.5286955983 0.905431825817
absolute error = 8.721e-05
relative error = 0.0004461 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.008
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5139 0.887
h = 0.0001 0.004
y[1] (numeric) = -19.5277279759 0.908508016049
y[1] (closed_form) = -19.5278054479 0.908548609388
absolute error = 8.746e-05
relative error = 0.0004474 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.011
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5138 0.891
h = 0.003 0.006
y[1] (numeric) = -19.5278044051 0.912608783745
y[1] (closed_form) = -19.5278822805 0.912649391323
absolute error = 8.783e-05
relative error = 0.0004493 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.015
Order of pole (given) = 0.5 0
NO 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=1953.5MB, alloc=52.3MB, time=24.12
x[1] = -1.5108 0.897
h = 0.0001 0.005
y[1] (numeric) = -19.5250016413 0.918887974009
y[1] (closed_form) = -19.525080211 0.918929478758
absolute error = 8.886e-05
relative error = 0.0004546 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.022
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5107 0.902
h = 0.0001 0.003
y[1] (numeric) = -19.525125296 0.924013610093
y[1] (closed_form) = -19.5252044968 0.924055131029
absolute error = 8.942e-05
relative error = 0.0004575 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.026
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5106 0.905
h = 0.001 0.001
y[1] (numeric) = -19.5251592763 0.927090829762
y[1] (closed_form) = -19.5252387042 0.92713236229
absolute error = 8.963e-05
relative error = 0.0004585 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.029
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5096 0.906
h = 0.001 0.003
y[1] (numeric) = -19.5241806681 0.928160675733
y[1] (closed_form) = -19.5242600968 0.928202258684
absolute error = 8.966e-05
relative error = 0.0004587 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.03
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5086 0.909
h = 0.0001 0.004
y[1] (numeric) = -19.5232934018 0.931279175858
y[1] (closed_form) = -19.5233730344 0.931320907016
absolute error = 8.990e-05
relative error = 0.00046 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.033
Order of pole (given) = 0.5 0
NO 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=1999.4MB, alloc=52.3MB, time=24.69
x[1] = -1.5085 0.913
h = 0.003 0.006
y[1] (numeric) = -19.5233742576 0.935381057252
y[1] (closed_form) = -19.5234542937 0.935422802503
absolute error = 9.027e-05
relative error = 0.0004618 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.037
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5055 0.919
h = 0.0001 0.005
y[1] (numeric) = -19.5205774197 0.941665089425
y[1] (closed_form) = -19.5206581505 0.941707731677
absolute error = 9.130e-05
relative error = 0.0004672 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.044
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5054 0.924
h = 0.0001 0.003
y[1] (numeric) = -19.5207066143 0.946792088966
y[1] (closed_form) = -19.5207879762 0.946834747173
absolute error = 9.187e-05
relative error = 0.0004701 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.048
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5053 0.927
h = 0.001 0.001
y[1] (numeric) = -19.5207439086 0.94987017095
y[1] (closed_form) = -19.5208254976 0.949912840671
absolute error = 9.207e-05
relative error = 0.0004711 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.051
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5043 0.928
h = 0.001 0.003
y[1] (numeric) = -19.5197661633 0.950941380236
y[1] (closed_form) = -19.5198477531 0.950984100385
absolute error = 9.210e-05
relative error = 0.0004713 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.052
Order of pole (given) = 0.5 0
NO 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=2045.4MB, alloc=52.3MB, time=25.26
x[1] = -1.5033 0.931
h = 0.0001 0.004
y[1] (numeric) = -19.5188819858 0.954061744226
y[1] (closed_form) = -19.5189637796 0.95410461252
absolute error = 9.235e-05
relative error = 0.0004725 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.055
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5032 0.935
h = 0.003 0.006
y[1] (numeric) = -19.5189672689 0.958164737803
y[1] (closed_form) = -19.5190494662 0.958207620045
absolute error = 9.271e-05
relative error = 0.0004744 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.059
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5002 0.941
h = 0.0001 0.005
y[1] (numeric) = -19.5161763592 0.964453610159
y[1] (closed_form) = -19.5162592516 0.964497389231
absolute error = 9.374e-05
relative error = 0.0004797 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.065
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5001 0.946
h = 0.0001 0.003
y[1] (numeric) = -19.5163110948 0.969581971259
y[1] (closed_form) = -19.5163946183 0.969625766053
absolute error = 9.431e-05
relative error = 0.0004826 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.07
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.5 0.949
h = 0.001 0.001
y[1] (numeric) = -19.5163517037 0.972660914425
y[1] (closed_form) = -19.5164354544 0.972704720657
absolute error = 9.452e-05
relative error = 0.0004837 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.073
Order of pole (given) = 0.5 0
NO 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=2091.2MB, alloc=52.3MB, time=25.82
x[1] = -1.499 0.95
h = 0.001 0.003
y[1] (numeric) = -19.5153748217 0.973733486836
y[1] (closed_form) = -19.5154585732 0.973777343498
absolute error = 9.454e-05
relative error = 0.0004838 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.074
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.498 0.953
h = 0.0001 0.004
y[1] (numeric) = -19.5144937341 0.976855713731
y[1] (closed_form) = -19.5145776897 0.976899718477
absolute error = 9.479e-05
relative error = 0.0004851 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.077
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4979 0.957
h = 0.003 0.006
y[1] (numeric) = -19.5145834454 0.980959817976
y[1] (closed_form) = -19.5146678044 0.981003836524
absolute error = 9.515e-05
relative error = 0.000487 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.081
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4949 0.963
h = 0.0001 0.005
y[1] (numeric) = -19.5117984661 0.987253528788
y[1] (closed_form) = -19.5118835207 0.987298443996
absolute error = 9.619e-05
relative error = 0.0004923 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.087
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4948 0.968
h = 0.0001 0.003
y[1] (numeric) = -19.5119387436 0.992383249548
y[1] (closed_form) = -19.5120244294 0.992428180246
absolute error = 9.675e-05
relative error = 0.0004952 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.092
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4947 0.971
h = 0.001 0.001
y[1] (numeric) = -19.5119826678 0.995463052766
y[1] (closed_form) = -19.5120685807 0.995507994823
absolute error = 9.696e-05
relative error = 0.0004963 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.095
Order of pole (given) = 0.5 0
NO 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=2137.1MB, alloc=52.3MB, time=26.38
x[1] = -1.4937 0.972
h = 0.0001 0.004
y[1] (numeric) = -19.5110066497 0.996536988108
y[1] (closed_form) = -19.5110925634 0.996581980601
absolute error = 9.698e-05
relative error = 0.0004964 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.096
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4936 0.976
h = 0.003 0.006
y[1] (numeric) = -19.5111001865 1.0006419944
y[1] (closed_form) = -19.5111865037 1.00068700057
absolute error = 9.735e-05
relative error = 0.0004983 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.1
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4906 0.982
h = 0.0001 0.005
y[1] (numeric) = -19.5083203715 1.00693979793
y[1] (closed_form) = -19.5084073845 1.00698570061
absolute error = 9.838e-05
relative error = 0.0005036 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.106
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4905 0.987
h = 0.0001 0.003
y[1] (numeric) = -19.5084654363 1.01207062149
y[1] (closed_form) = -19.5085530804 1.01211653946
absolute error = 9.894e-05
relative error = 0.0005065 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.111
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4904 0.99
h = 0.001 0.001
y[1] (numeric) = -19.5085122248 1.01515112461
y[1] (closed_form) = -19.5086000962 1.01519705386
absolute error = 9.915e-05
relative error = 0.0005076 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.113
Order of pole (given) = 0.5 0
NO 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=2183.1MB, alloc=52.3MB, time=26.95
x[1] = -1.4894 0.991
h = 0.001 0.003
y[1] (numeric) = -19.507536967 1.01622622266
y[1] (closed_form) = -19.5076248392 1.01627220236
absolute error = 9.917e-05
relative error = 0.0005077 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.115
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4884 0.994
h = 0.0001 0.004
y[1] (numeric) = -19.5066616536 1.0193518766
y[1] (closed_form) = -19.5067497301 1.01939800427
absolute error = 9.942e-05
relative error = 0.000509 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.118
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4883 0.998
h = 0.003 0.006
y[1] (numeric) = -19.5067596199 1.02345799074
y[1] (closed_form) = -19.5068480999 1.02350413193
absolute error = 9.979e-05
relative error = 0.0005109 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.122
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4853 1.004
h = 0.0001 0.005
y[1] (numeric) = -19.5039857397 1.02976062948
y[1] (closed_form) = -19.5040749159 1.02980766701
absolute error = 0.0001008
relative error = 0.0005162 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.128
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4852 1.009
h = 0.0001 0.003
y[1] (numeric) = -19.5041363482 1.03489280915
y[1] (closed_form) = -19.5042261557 1.03493986174
absolute error = 0.0001014
relative error = 0.0005191 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.133
Order of pole (given) = 0.5 0
NO 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=2229.0MB, alloc=52.3MB, time=27.52
x[1] = -1.4851 1.012
h = 0.001 0.001
y[1] (numeric) = -19.5041864532 1.0379741702
y[1] (closed_form) = -19.5042764878 1.03802123401
absolute error = 0.0001016
relative error = 0.0005201 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.135
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4841 1.013
h = 0.001 0.003
y[1] (numeric) = -19.5032120603 1.03905063083
y[1] (closed_form) = -19.5033020958 1.03909774507
absolute error = 0.0001016
relative error = 0.0005203 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.137
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4831 1.016
h = 0.0001 0.004
y[1] (numeric) = -19.5023398395 1.04217814491
y[1] (closed_form) = -19.5024300793 1.04222540707
absolute error = 0.0001019
relative error = 0.0005216 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.14
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.483 1.02
h = 0.003 0.006
y[1] (numeric) = -19.5024422362 1.04628536537
y[1] (closed_form) = -19.5025328797 1.04633264091
absolute error = 0.0001022
relative error = 0.0005234 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.144
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.48 1.026
h = 0.0001 0.005
y[1] (numeric) = -19.499674293 1.0525928376
y[1] (closed_form) = -19.4997656331 1.05264100931
absolute error = 0.0001033
relative error = 0.0005288 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.15
Order of pole (given) = 0.5 0
NO 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=2275.0MB, alloc=52.3MB, time=28.08
x[1] = -1.4799 1.031
h = 0.0001 0.003
y[1] (numeric) = -19.4998304463 1.05772637149
y[1] (closed_form) = -19.4999224177 1.05777455801
absolute error = 0.0001038
relative error = 0.0005317 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.155
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4798 1.034
h = 0.001 0.001
y[1] (numeric) = -19.4998838683 1.06080858935
y[1] (closed_form) = -19.4999760668 1.06085678701
absolute error = 0.000104
relative error = 0.0005327 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.157
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4788 1.035
h = 0.001 0.003
y[1] (numeric) = -19.498910341 1.06188641234
y[1] (closed_form) = -19.4990025404 1.06193466045
absolute error = 0.0001041
relative error = 0.0005329 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.159
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4778 1.038
h = 0.0001 0.004
y[1] (numeric) = -19.4980412137 1.06501578562
y[1] (closed_form) = -19.4981336175 1.06506418157
absolute error = 0.0001043
relative error = 0.0005342 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.162
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4777 1.042
h = 0.003 0.006
y[1] (numeric) = -19.4981480416 1.06912411088
y[1] (closed_form) = -19.4982408491 1.06917252007
absolute error = 0.0001047
relative error = 0.000536 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.166
Order of pole (given) = 0.5 0
NO 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=2321.0MB, alloc=52.3MB, time=28.65
x[1] = -1.4747 1.048
h = 0.0001 0.005
y[1] (numeric) = -19.4953860378 1.07543641487
y[1] (closed_form) = -19.4954795422 1.07548572006
absolute error = 0.0001057
relative error = 0.0005414 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.172
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4746 1.053
h = 0.0001 0.003
y[1] (numeric) = -19.4955477369 1.08057130107
y[1] (closed_form) = -19.4956418726 1.08062062085
absolute error = 0.0001063
relative error = 0.0005443 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.177
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4745 1.056
h = 0.001 0.001
y[1] (numeric) = -19.4956044764 1.0836543746
y[1] (closed_form) = -19.4956988394 1.08370370543
absolute error = 0.0001065
relative error = 0.0005453 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.18
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4735 1.057
h = 0.001 0.003
y[1] (numeric) = -19.4946318152 1.08473355978
y[1] (closed_form) = -19.4947261791 1.08478294106
absolute error = 0.0001065
relative error = 0.0005455 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.181
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4725 1.06
h = 0.0001 0.004
y[1] (numeric) = -19.4937657825 1.08786479129
y[1] (closed_form) = -19.4938603508 1.08791432035
absolute error = 0.0001068
relative error = 0.0005468 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.184
Order of pole (given) = 0.5 0
NO 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=2366.9MB, alloc=52.3MB, time=29.22
x[1] = -1.4724 1.064
h = 0.003 0.006
y[1] (numeric) = -19.4938770424 1.09197421984
y[1] (closed_form) = -19.4939720144 1.092023762
absolute error = 0.0001071
relative error = 0.0005486 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.188
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4694 1.07
h = 0.0001 0.005
y[1] (numeric) = -19.4911209802 1.09829135386
y[1] (closed_form) = -19.4912166496 1.09834179184
absolute error = 0.0001082
relative error = 0.000554 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.194
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4693 1.075
h = 0.0001 0.003
y[1] (numeric) = -19.4912882261 1.10342759047
y[1] (closed_form) = -19.4913845268 1.10347804281
absolute error = 0.0001087
relative error = 0.0005569 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.199
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4692 1.078
h = 0.001 0.001
y[1] (numeric) = -19.4913482838 1.10651151854
y[1] (closed_form) = -19.4914448118 1.10656198186
absolute error = 0.0001089
relative error = 0.0005579 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.202
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4682 1.079
h = 0.0001 0.004
y[1] (numeric) = -19.4903764893 1.10759206571
y[1] (closed_form) = -19.4904730183 1.10764257948
absolute error = 0.0001089
relative error = 0.0005581 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.203
Order of pole (given) = 0.5 0
NO 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=2412.9MB, alloc=52.3MB, time=29.79
x[1] = -1.4681 1.083
h = 0.003 0.006
y[1] (numeric) = -19.490491578 1.11170238992
y[1] (closed_form) = -19.4905885106 1.11175291665
absolute error = 0.0001093
relative error = 0.0005599 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.207
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4651 1.089
h = 0.0001 0.005
y[1] (numeric) = -19.4877406896 1.11802360926
y[1] (closed_form) = -19.4878383199 1.11807503167
absolute error = 0.0001103
relative error = 0.0005653 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.213
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.465 1.094
h = 0.0001 0.003
y[1] (numeric) = -19.4879127267 1.12316094065
y[1] (closed_form) = -19.4880109884 1.12321237722
absolute error = 0.0001109
relative error = 0.0005682 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.218
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4649 1.097
h = 0.001 0.001
y[1] (numeric) = -19.4879756514 1.12624556384
y[1] (closed_form) = -19.4880741403 1.12629701132
absolute error = 0.0001111
relative error = 0.0005692 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.221
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4639 1.098
h = 0.001 0.003
y[1] (numeric) = -19.4870046195 1.12732727288
y[1] (closed_form) = -19.4871031094 1.12737877081
absolute error = 0.0001111
relative error = 0.0005694 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.222
Order of pole (given) = 0.5 0
NO 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=2458.8MB, alloc=52.3MB, time=30.35
x[1] = -1.4629 1.101
h = 0.0001 0.004
y[1] (numeric) = -19.4861443696 1.13046192267
y[1] (closed_form) = -19.4862430641 1.13051356827
absolute error = 0.0001114
relative error = 0.0005707 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.225
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4628 1.105
h = 0.003 0.006
y[1] (numeric) = -19.4862638917 1.13457334733
y[1] (closed_form) = -19.48636299 1.13462500575
absolute error = 0.0001118
relative error = 0.0005725 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.229
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4598 1.111
h = 0.0001 0.005
y[1] (numeric) = -19.4835189492 1.14089939346
y[1] (closed_form) = -19.4836187455 1.14095194738
absolute error = 0.0001128
relative error = 0.0005779 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.235
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4597 1.116
h = 0.0001 0.003
y[1] (numeric) = -19.4836965349 1.14603807171
y[1] (closed_form) = -19.4837969627 1.14609063955
absolute error = 0.0001134
relative error = 0.0005808 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.24
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4596 1.119
h = 0.001 0.001
y[1] (numeric) = -19.4837627789 1.14912354733
y[1] (closed_form) = -19.4838634339 1.149176126
absolute error = 0.0001136
relative error = 0.0005818 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.243
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4586 1.12
h = 0.001 0.003
y[1] (numeric) = -19.4827926148 1.15020661799
y[1] (closed_form) = -19.4828932709 1.15025924712
absolute error = 0.0001136
relative error = 0.000582 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.244
Order of pole (given) = 0.5 0
NO 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=2504.8MB, alloc=52.3MB, time=30.92
x[1] = -1.4576 1.123
h = 0.0001 0.004
y[1] (numeric) = -19.4819354621 1.15334312324
y[1] (closed_form) = -19.4820363228 1.15339589999
absolute error = 0.0001138
relative error = 0.0005833 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.247
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4575 1.127
h = 0.003 0.006
y[1] (numeric) = -19.4820594185 1.15745564685
y[1] (closed_form) = -19.482160683 1.15750843626
absolute error = 0.0001142
relative error = 0.0005851 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.251
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4545 1.133
h = 0.0001 0.005
y[1] (numeric) = -19.4793204242 1.16378651803
y[1] (closed_form) = -19.4794223872 1.16384020277
absolute error = 0.0001152
relative error = 0.0005905 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.257
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4544 1.138
h = 0.0001 0.003
y[1] (numeric) = -19.4795035595 1.16892654124
y[1] (closed_form) = -19.479606154 1.16898023967
absolute error = 0.0001158
relative error = 0.0005934 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.262
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4543 1.141
h = 0.001 0.001
y[1] (numeric) = -19.4795731234 1.17201286815
y[1] (closed_form) = -19.4796759452 1.17206657733
absolute error = 0.000116
relative error = 0.0005944 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.265
Order of pole (given) = 0.5 0
NO 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=2550.7MB, alloc=52.3MB, time=31.48
x[1] = -1.4533 1.142
h = 0.001 0.003
y[1] (numeric) = -19.4786038277 1.17309730024
y[1] (closed_form) = -19.4787066504 1.17315105989
absolute error = 0.000116
relative error = 0.0005946 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.266
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4523 1.145
h = 0.0001 0.004
y[1] (numeric) = -19.4777497732 1.17623566
y[1] (closed_form) = -19.4778528006 1.1762895672
absolute error = 0.0001163
relative error = 0.0005959 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.269
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4522 1.149
h = 0.003 0.006
y[1] (numeric) = -19.4778781647 1.18034928103
y[1] (closed_form) = -19.477981596 1.18040320075
absolute error = 0.0001166
relative error = 0.0005977 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.273
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4492 1.155
h = 0.0001 0.005
y[1] (numeric) = -19.4751451209 1.18668497552
y[1] (closed_form) = -19.475249251 1.1867397904
absolute error = 0.0001177
relative error = 0.0006031 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.28
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4491 1.16
h = 0.0001 0.003
y[1] (numeric) = -19.4753338068 1.1918263418
y[1] (closed_form) = -19.4754385685 1.19188117014
absolute error = 0.0001182
relative error = 0.000606 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.284
Order of pole (given) = 0.5 0
NO 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=2596.8MB, alloc=52.3MB, time=32.05
x[1] = -1.449 1.163
h = 0.001 0.001
y[1] (numeric) = -19.4754066913 1.19491351886
y[1] (closed_form) = -19.4755116803 1.19496835787
absolute error = 0.0001184
relative error = 0.000607 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.287
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.448 1.164
h = 0.001 0.003
y[1] (numeric) = -19.4744382645 1.19599931219
y[1] (closed_form) = -19.4745432545 1.19605420167
absolute error = 0.0001185
relative error = 0.0006072 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.288
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.447 1.167
h = 0.0001 0.004
y[1] (numeric) = -19.4735873091 1.1991395255
y[1] (closed_form) = -19.4736925038 1.19919456247
absolute error = 0.0001187
relative error = 0.0006085 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.291
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4469 1.171
h = 0.003 0.006
y[1] (numeric) = -19.4737201365 1.20325424243
y[1] (closed_form) = -19.4738257352 1.20330929178
absolute error = 0.0001191
relative error = 0.0006104 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.295
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4439 1.177
h = 0.0001 0.005
y[1] (numeric) = -19.4709930455 1.20959475852
y[1] (closed_form) = -19.4710993434 1.20965070284
absolute error = 0.0001201
relative error = 0.0006157 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.302
Order of pole (given) = 0.5 0
NO 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=2642.5MB, alloc=52.3MB, time=32.61
x[1] = -1.4438 1.182
h = 0.0001 0.003
y[1] (numeric) = -19.4711872829 1.21473746595
y[1] (closed_form) = -19.4712942125 1.2147934235
absolute error = 0.0001207
relative error = 0.0006186 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.306
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4437 1.185
h = 0.001 0.001
y[1] (numeric) = -19.4712634886 1.21782549204
y[1] (closed_form) = -19.4713706454 1.21788146018
absolute error = 0.0001209
relative error = 0.0006197 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.309
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4427 1.186
h = 0.0001 0.004
y[1] (numeric) = -19.4702959313 1.21891264641
y[1] (closed_form) = -19.4704030892 1.21896866503
absolute error = 0.0001209
relative error = 0.0006198 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.31
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4426 1.19
h = 0.003 0.006
y[1] (numeric) = -19.4704325908 1.22302825259
y[1] (closed_form) = -19.4705401525 1.22308428347
absolute error = 0.0001213
relative error = 0.0006217 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.314
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4396 1.196
h = 0.0001 0.005
y[1] (numeric) = -19.467710683 1.22937284661
y[1] (closed_form) = -19.4678189443 1.22942977231
absolute error = 0.0001223
relative error = 0.000627 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.321
Order of pole (given) = 0.5 0
NO 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=2688.5MB, alloc=52.3MB, time=33.18
x[1] = -1.4395 1.201
h = 0.0001 0.003
y[1] (numeric) = -19.4679097158 1.23451664079
y[1] (closed_form) = -19.4680186087 1.23457357952
absolute error = 0.0001229
relative error = 0.0006299 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.325
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4394 1.204
h = 0.001 0.001
y[1] (numeric) = -19.4679887908 1.23760535722
y[1] (closed_form) = -19.468097911 1.23766230646
absolute error = 0.0001231
relative error = 0.000631 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.328
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4384 1.205
h = 0.001 0.003
y[1] (numeric) = -19.4670219985 1.23869367261
y[1] (closed_form) = -19.4671311199 1.23875067234
absolute error = 0.0001231
relative error = 0.0006311 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.329
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4374 1.208
h = 0.0001 0.004
y[1] (numeric) = -19.4661768345 1.24183729543
y[1] (closed_form) = -19.4662861607 1.24189444252
absolute error = 0.0001234
relative error = 0.0006324 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.333
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4373 1.212
h = 0.003 0.006
y[1] (numeric) = -19.4663179313 1.24595399468
y[1] (closed_form) = -19.4664276615 1.24601115388
absolute error = 0.0001237
relative error = 0.0006343 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.336
Order of pole (given) = 0.5 0
NO 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=2734.4MB, alloc=52.3MB, time=33.74
x[1] = -1.4343 1.218
h = 0.0001 0.005
y[1] (numeric) = -19.4636019806 1.25230340702
y[1] (closed_form) = -19.4637124107 1.25236146088
absolute error = 0.0001248
relative error = 0.0006397 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.343
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4342 1.223
h = 0.0001 0.003
y[1] (numeric) = -19.4638065668 1.25744853881
y[1] (closed_form) = -19.4639176286 1.25750660547
absolute error = 0.0001253
relative error = 0.0006425 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.348
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4341 1.226
h = 0.001 0.001
y[1] (numeric) = -19.463888964 1.26053810215
y[1] (closed_form) = -19.4640002532 1.26059617924
absolute error = 0.0001255
relative error = 0.0006436 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.35
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4331 1.227
h = 0.001 0.003
y[1] (numeric) = -19.4629230424 1.26162777822
y[1] (closed_form) = -19.4630343326 1.2616859058
absolute error = 0.0001256
relative error = 0.0006437 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.352
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4321 1.23
h = 0.0001 0.004
y[1] (numeric) = -19.4620809802 1.26477325182
y[1] (closed_form) = -19.4621924755 1.2648315267
absolute error = 0.0001258
relative error = 0.0006451 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.355
Order of pole (given) = 0.5 0
NO 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=2780.4MB, alloc=52.3MB, time=34.31
x[1] = -1.432 1.234
h = 0.003 0.006
y[1] (numeric) = -19.4622265152 1.26889104262
y[1] (closed_form) = -19.4623384144 1.26894932946
absolute error = 0.0001262
relative error = 0.0006469 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.358
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.429 1.24
h = 0.0001 0.005
y[1] (numeric) = -19.4595165239 1.27524527157
y[1] (closed_form) = -19.4596291234 1.27530445289
absolute error = 0.0001272
relative error = 0.0006523 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.365
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4289 1.245
h = 0.0001 0.003
y[1] (numeric) = -19.4597266644 1.28039173906
y[1] (closed_form) = -19.4598398957 1.28045093295
absolute error = 0.0001278
relative error = 0.0006552 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.37
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4288 1.248
h = 0.001 0.001
y[1] (numeric) = -19.4598123846 1.28348214816
y[1] (closed_form) = -19.4599258433 1.28354135242
absolute error = 0.000128
relative error = 0.0006562 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.373
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4278 1.249
h = 0.001 0.003
y[1] (numeric) = -19.458847334 1.28457318472
y[1] (closed_form) = -19.4589607938 1.28463243946
absolute error = 0.000128
relative error = 0.0006564 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.374
Order of pole (given) = 0.5 0
NO 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=2826.4MB, alloc=52.3MB, time=34.88
x[1] = -1.4268 1.252
h = 0.0001 0.004
y[1] (numeric) = -19.4580083747 1.28772050814
y[1] (closed_form) = -19.4581220396 1.28777991012
absolute error = 0.0001283
relative error = 0.0006577 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.377
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4267 1.256
h = 0.003 0.006
y[1] (numeric) = -19.4581583487 1.29183938897
y[1] (closed_form) = -19.4582724176 1.29189880277
absolute error = 0.0001286
relative error = 0.0006595 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.381
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4237 1.262
h = 0.0001 0.005
y[1] (numeric) = -19.455454319 1.29819843278
y[1] (closed_form) = -19.4555690886 1.29825874089
absolute error = 0.0001297
relative error = 0.0006649 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.387
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4236 1.267
h = 0.0001 0.003
y[1] (numeric) = -19.4556700149 1.30334623407
y[1] (closed_form) = -19.4557854163 1.30340655451
absolute error = 0.0001302
relative error = 0.0006678 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.392
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4235 1.27
h = 0.001 0.001
y[1] (numeric) = -19.4557590586 1.30643748782
y[1] (closed_form) = -19.4558746874 1.30649781854
absolute error = 0.0001304
relative error = 0.0006688 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.395
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4225 1.271
h = 0.001 0.003
y[1] (numeric) = -19.4547948798 1.30752988467
y[1] (closed_form) = -19.4549105097 1.30759026588
absolute error = 0.0001304
relative error = 0.000669 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.396
Order of pole (given) = 0.5 0
NO 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=2872.4MB, alloc=52.3MB, time=35.44
x[1] = -1.4215 1.274
h = 0.0001 0.004
y[1] (numeric) = -19.4539590242 1.31067905694
y[1] (closed_form) = -19.4540748593 1.31073958533
absolute error = 0.0001307
relative error = 0.0006703 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.399
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4214 1.278
h = 0.003 0.006
y[1] (numeric) = -19.454113438 1.31479902629
y[1] (closed_form) = -19.4542296771 1.31485956635
absolute error = 0.0001311
relative error = 0.0006721 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.403
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4184 1.284
h = 0.0001 0.005
y[1] (numeric) = -19.4514153723 1.32116288323
y[1] (closed_form) = -19.4515323125 1.32122431743
absolute error = 0.0001321
relative error = 0.0006775 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.41
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4183 1.289
h = 0.0001 0.003
y[1] (numeric) = -19.4516366245 1.32631201642
y[1] (closed_form) = -19.4517541966 1.32637346271
absolute error = 0.0001327
relative error = 0.0006804 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.414
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4182 1.292
h = 0.001 0.001
y[1] (numeric) = -19.4517289923 1.32940411367
y[1] (closed_form) = -19.4518467919 1.32946557016
absolute error = 0.0001329
relative error = 0.0006815 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.417
Order of pole (given) = 0.5 0
NO 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=2918.3MB, alloc=52.3MB, time=36.00
x[1] = -1.4172 1.293
h = 0.0001 0.004
y[1] (numeric) = -19.4507656858 1.33049787061
y[1] (closed_form) = -19.4508834864 1.3305593776
absolute error = 0.0001329
relative error = 0.0006816 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.418
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4171 1.297
h = 0.003 0.006
y[1] (numeric) = -19.4509239348 1.3346187228
y[1] (closed_form) = -19.4510421395 1.33468024133
absolute error = 0.0001333
relative error = 0.0006835 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.422
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4141 1.303
h = 0.0001 0.005
y[1] (numeric) = -19.4482310619 1.34098665026
y[1] (closed_form) = -19.4483499679 1.34104906277
absolute error = 0.0001343
relative error = 0.0006889 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.429
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.414 1.308
h = 0.0001 0.003
y[1] (numeric) = -19.4484571135 1.34613686216
y[1] (closed_form) = -19.4485766514 1.34619928657
absolute error = 0.0001349
relative error = 0.0006917 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.433
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4139 1.311
h = 0.001 0.001
y[1] (numeric) = -19.4485523531 1.34922964496
y[1] (closed_form) = -19.4486721185 1.3492920795
absolute error = 0.0001351
relative error = 0.0006928 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.436
Order of pole (given) = 0.5 0
NO 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=2964.2MB, alloc=52.3MB, time=36.57
x[1] = -1.4129 1.312
h = 0.001 0.003
y[1] (numeric) = -19.447589814 1.35032456207
y[1] (closed_form) = -19.4477095806 1.35038704711
absolute error = 0.0001351
relative error = 0.0006929 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.437
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4119 1.315
h = 0.0001 0.004
y[1] (numeric) = -19.4467597585 1.35347713507
y[1] (closed_form) = -19.4468797303 1.35353976718
absolute error = 0.0001353
relative error = 0.0006943 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.441
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4118 1.319
h = 0.003 0.006
y[1] (numeric) = -19.4469224486 1.35759907294
y[1] (closed_form) = -19.4470428246 1.35766171644
absolute error = 0.0001357
relative error = 0.0006961 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.444
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4088 1.325
h = 0.0001 0.005
y[1] (numeric) = -19.4442355439 1.36397181027
y[1] (closed_form) = -19.4443566217 1.36403534758
absolute error = 0.0001367
relative error = 0.0007015 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.451
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4087 1.33
h = 0.0001 0.003
y[1] (numeric) = -19.4444671537 1.36912335051
y[1] (closed_form) = -19.4445888634 1.36918689949
absolute error = 0.0001373
relative error = 0.0007044 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.456
Order of pole (given) = 0.5 0
NO 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=3010.1MB, alloc=52.3MB, time=37.13
x[1] = -1.4086 1.333
h = 0.001 0.001
y[1] (numeric) = -19.4445657186 1.37221697469
y[1] (closed_form) = -19.4446876558 1.37228053372
absolute error = 0.0001375
relative error = 0.0007054 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.458
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4076 1.334
h = 0.001 0.003
y[1] (numeric) = -19.4436040529 1.37331325154
y[1] (closed_form) = -19.4437259912 1.37337686107
absolute error = 0.0001375
relative error = 0.0007056 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.46
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4066 1.337
h = 0.0001 0.004
y[1] (numeric) = -19.4427771038 1.37646767062
y[1] (closed_form) = -19.4428992475 1.37653142716
absolute error = 0.0001378
relative error = 0.0007069 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.463
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4065 1.341
h = 0.003 0.006
y[1] (numeric) = -19.442944236 1.38059069264
y[1] (closed_form) = -19.4430667839 1.38065446043
absolute error = 0.0001381
relative error = 0.0007087 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.466
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4035 1.347
h = 0.0001 0.005
y[1] (numeric) = -19.4402633018 1.38696823811
y[1] (closed_form) = -19.4403865519 1.38703289953
absolute error = 0.0001392
relative error = 0.0007141 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.473
Order of pole (given) = 0.5 0
NO 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=3056.0MB, alloc=52.3MB, time=37.70
x[1] = -1.4034 1.352
h = 0.0001 0.003
y[1] (numeric) = -19.4405004707 1.39212110479
y[1] (closed_form) = -19.4406243528 1.39218577764
absolute error = 0.0001397
relative error = 0.000717 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.478
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4033 1.355
h = 0.001 0.001
y[1] (numeric) = -19.4406023615 1.39521556922
y[1] (closed_form) = -19.4407264711 1.39528025205
absolute error = 0.00014
relative error = 0.0007181 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.481
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4023 1.356
h = 0.001 0.003
y[1] (numeric) = -19.4396415697 1.3963132056
y[1] (closed_form) = -19.4397656804 1.39637793893
absolute error = 0.00014
relative error = 0.0007182 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.482
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4013 1.359
h = 0.0001 0.004
y[1] (numeric) = -19.4388177281 1.39946946981
y[1] (closed_form) = -19.4389420442 1.39953435009
absolute error = 0.0001402
relative error = 0.0007195 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.485
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.4012 1.363
h = 0.003 0.006
y[1] (numeric) = -19.4389893032 1.40359357447
y[1] (closed_form) = -19.4391140236 1.40365846585
absolute error = 0.0001406
relative error = 0.0007214 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.489
Order of pole (given) = 0.5 0
NO 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=3101.9MB, alloc=52.3MB, time=38.27
x[1] = -1.3982 1.369
h = 0.0001 0.005
y[1] (numeric) = -19.4363143418 1.40997592633
y[1] (closed_form) = -19.4364397647 1.41004171117
absolute error = 0.0001416
relative error = 0.0007268 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.495
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3981 1.374
h = 0.0001 0.003
y[1] (numeric) = -19.4365570709 1.41513011754
y[1] (closed_form) = -19.4366831259 1.41519591358
absolute error = 0.0001422
relative error = 0.0007296 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.5
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.398 1.377
h = 0.001 0.001
y[1] (numeric) = -19.4366622881 1.41822542109
y[1] (closed_form) = -19.4367885706 1.41829122702
absolute error = 0.0001424
relative error = 0.0007307 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.503
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.397 1.378
h = 0.001 0.003
y[1] (numeric) = -19.4357023708 1.41932441681
y[1] (closed_form) = -19.4358286545 1.41939027325
absolute error = 0.0001424
relative error = 0.0007308 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.504
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.396 1.381
h = 0.0001 0.004
y[1] (numeric) = -19.4348816376 1.42248252518
y[1] (closed_form) = -19.4350081268 1.4225485285
absolute error = 0.0001427
relative error = 0.0007322 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.507
Order of pole (given) = 0.5 0
NO 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=3148.0MB, alloc=52.3MB, time=38.84
x[1] = -1.3959 1.385
h = 0.003 0.006
y[1] (numeric) = -19.4350576563 1.42660771095
y[1] (closed_form) = -19.4351845498 1.42667372523
absolute error = 0.000143
relative error = 0.000734 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.511
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3929 1.391
h = 0.0001 0.005
y[1] (numeric) = -19.43238867 1.43299486748
y[1] (closed_form) = -19.4325162665 1.43306177504
absolute error = 0.0001441
relative error = 0.0007394 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.518
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3928 1.396
h = 0.0001 0.003
y[1] (numeric) = -19.4326369603 1.43815038131
y[1] (closed_form) = -19.4327651888 1.43821729984
absolute error = 0.0001446
relative error = 0.0007423 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.522
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3927 1.399
h = 0.001 0.001
y[1] (numeric) = -19.4327455046 1.44124652284
y[1] (closed_form) = -19.4328739607 1.44131345119
absolute error = 0.0001448
relative error = 0.0007433 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.525
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3917 1.4
h = 0.003 0.006
y[1] (numeric) = -19.4317864624 1.4423468777
y[1] (closed_form) = -19.4319149196 1.44241385656
absolute error = 0.0001449
relative error = 0.0007435 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.526
Order of pole (given) = 0.5 0
NO 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=3193.9MB, alloc=52.3MB, time=39.40
x[1] = -1.3887 1.406
h = 0.0001 0.005
y[1] (numeric) = -19.4291214669 1.44873748885
y[1] (closed_form) = -19.4292506271 1.4488053609
absolute error = 0.0001459
relative error = 0.0007489 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.533
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3886 1.411
h = 0.0001 0.003
y[1] (numeric) = -19.4293735499 1.45389405152
y[1] (closed_form) = -19.4295033423 1.45396193437
absolute error = 0.0001465
relative error = 0.0007518 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.538
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3885 1.414
h = 0.001 0.001
y[1] (numeric) = -19.4294843621 1.45699085265
y[1] (closed_form) = -19.4296143821 1.45705874526
absolute error = 0.0001467
relative error = 0.0007528 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.541
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3875 1.415
h = 0.001 0.003
y[1] (numeric) = -19.428525888 1.4580921644
y[1] (closed_form) = -19.4286559091 1.45816010753
absolute error = 0.0001467
relative error = 0.000753 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.542
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3865 1.418
h = 0.0001 0.004
y[1] (numeric) = -19.4277103572 1.46125346167
y[1] (closed_form) = -19.4278405839 1.46132155158
absolute error = 0.000147
relative error = 0.0007543 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.545
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3864 1.422
h = 0.003 0.006
y[1] (numeric) = -19.427893851 1.46538058078
y[1] (closed_form) = -19.4280244821 1.46544868141
absolute error = 0.0001473
relative error = 0.0007561 %
Correct digits = 5
memory used=3239.9MB, alloc=52.3MB, time=39.97
Radius of convergence (given) for eq 1 = 1.549
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3834 1.428
h = 0.0001 0.005
y[1] (numeric) = -19.4252348343 1.47177599373
y[1] (closed_form) = -19.4253661689 1.47184498735
absolute error = 0.0001484
relative error = 0.0007615 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.555
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3833 1.433
h = 0.0001 0.003
y[1] (numeric) = -19.4254924801 1.47693387583
y[1] (closed_form) = -19.425624447 1.47700288003
absolute error = 0.0001489
relative error = 0.0007644 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.56
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3832 1.436
h = 0.001 0.001
y[1] (numeric) = -19.4256066205 1.48003151304
y[1] (closed_form) = -19.425738815 1.48010052692
absolute error = 0.0001491
relative error = 0.0007654 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.563
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3822 1.437
h = 0.001 0.003
y[1] (numeric) = -19.4246490224 1.48113418362
y[1] (closed_form) = -19.4247812181 1.48120324801
absolute error = 0.0001491
relative error = 0.0007656 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.564
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3812 1.44
h = 0.0001 0.004
y[1] (numeric) = -19.4238366026 1.48429732248
y[1] (closed_form) = -19.423969004 1.4843665336
absolute error = 0.0001494
relative error = 0.0007669 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.567
Order of pole (given) = 0.5 0
NO 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=3285.8MB, alloc=52.3MB, time=40.53
x[1] = -1.3811 1.444
h = 0.003 0.006
y[1] (numeric) = -19.4240245423 1.48842551864
y[1] (closed_form) = -19.424157348 1.48849474033
absolute error = 0.0001498
relative error = 0.0007688 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.571
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3781 1.45
h = 0.0001 0.005
y[1] (numeric) = -19.4213715068 1.49482573163
y[1] (closed_form) = -19.4215050166 1.49489584614
absolute error = 0.0001508
relative error = 0.0007742 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.578
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.378 1.455
h = 0.0001 0.003
y[1] (numeric) = -19.4216347166 1.49998493126
y[1] (closed_form) = -19.4217688586 1.50005505611
absolute error = 0.0001514
relative error = 0.000777 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.582
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3779 1.458
h = 0.001 0.001
y[1] (numeric) = -19.4217521857 1.50308340342
y[1] (closed_form) = -19.4218865553 1.50315353786
absolute error = 0.0001516
relative error = 0.0007781 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.585
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3769 1.459
h = 0.001 0.003
y[1] (numeric) = -19.4207954642 1.50418743263
y[1] (closed_form) = -19.420929835 1.5042576176
absolute error = 0.0001516
relative error = 0.0007783 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.586
Order of pole (given) = 0.5 0
NO 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=3331.7MB, alloc=52.3MB, time=41.10
x[1] = -1.3759 1.462
h = 0.0001 0.004
y[1] (numeric) = -19.4199861564 1.50735241212
y[1] (closed_form) = -19.420120733 1.50742274375
absolute error = 0.0001518
relative error = 0.0007796 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.59
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3758 1.466
h = 0.003 0.006
y[1] (numeric) = -19.4201785427 1.51148168381
y[1] (closed_form) = -19.4203135237 1.51155202586
absolute error = 0.0001522
relative error = 0.0007814 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.593
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3728 1.472
h = 0.0001 0.005
y[1] (numeric) = -19.4175314909 1.5178866951
y[1] (closed_form) = -19.4176671763 1.5179579298
absolute error = 0.0001532
relative error = 0.0007868 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.6
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3727 1.477
h = 0.0001 0.003
y[1] (numeric) = -19.4178002654 1.52304721034
y[1] (closed_form) = -19.4179365832 1.52311845515
absolute error = 0.0001538
relative error = 0.0007897 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.605
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3726 1.48
h = 0.001 0.001
y[1] (numeric) = -19.4179210639 1.52614651631
y[1] (closed_form) = -19.4180576092 1.52621777063
absolute error = 0.000154
relative error = 0.0007907 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.607
Order of pole (given) = 0.5 0
NO 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=3377.8MB, alloc=52.3MB, time=41.67
x[1] = -1.3716 1.481
h = 0.0001 0.004
y[1] (numeric) = -19.4169652196 1.52725190396
y[1] (closed_form) = -19.4171017662 1.52732320881
absolute error = 0.000154
relative error = 0.0007909 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.609
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3715 1.485
h = 0.003 0.006
y[1] (numeric) = -19.4171614469 1.53138204723
y[1] (closed_form) = -19.4172983979 1.53145336237
absolute error = 0.0001544
relative error = 0.0007927 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.613
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3685 1.491
h = 0.0001 0.005
y[1] (numeric) = -19.4145196046 1.53779111603
y[1] (closed_form) = -19.4146572603 1.53786332367
absolute error = 0.0001554
relative error = 0.0007982 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.619
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3684 1.496
h = 0.0001 0.003
y[1] (numeric) = -19.4147931856 1.54295269589
y[1] (closed_form) = -19.4149314737 1.54302491344
absolute error = 0.000156
relative error = 0.000801 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.624
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3683 1.499
h = 0.001 0.001
y[1] (numeric) = -19.4149168602 1.54605267899
y[1] (closed_form) = -19.4150553759 1.54612490598
absolute error = 0.0001562
relative error = 0.0008021 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.627
Order of pole (given) = 0.5 0
NO 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=3423.8MB, alloc=52.3MB, time=42.24
x[1] = -1.3673 1.5
h = 0.001 0.003
y[1] (numeric) = -19.4139617876 1.54715922532
y[1] (closed_form) = -19.4141003046 1.54723150285
absolute error = 0.0001562
relative error = 0.0008022 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.628
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3663 1.503
h = 0.0001 0.004
y[1] (numeric) = -19.4131582949 1.55032759012
y[1] (closed_form) = -19.4132970178 1.55040001419
absolute error = 0.0001565
relative error = 0.0008035 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.631
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3662 1.507
h = 0.003 0.006
y[1] (numeric) = -19.4133589703 1.55445880608
y[1] (closed_form) = -19.4134980976 1.55453124029
absolute error = 0.0001569
relative error = 0.0008054 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.635
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3632 1.513
h = 0.0001 0.005
y[1] (numeric) = -19.4107231158 1.56087266992
y[1] (closed_form) = -19.4108629483 1.56094599645
absolute error = 0.0001579
relative error = 0.0008108 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.642
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3631 1.518
h = 0.0001 0.003
y[1] (numeric) = -19.4110022635 1.56603556183
y[1] (closed_form) = -19.4111427284 1.56610889805
absolute error = 0.0001585
relative error = 0.0008137 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.646
Order of pole (given) = 0.5 0
NO 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=3469.9MB, alloc=52.3MB, time=42.80
x[1] = -1.363 1.521
h = 0.001 0.001
y[1] (numeric) = -19.4111292686 1.56913637661
y[1] (closed_form) = -19.4112699611 1.56920972219
absolute error = 0.0001587
relative error = 0.0008147 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.649
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.362 1.522
h = 0.001 0.003
y[1] (numeric) = -19.4101750743 1.57024428102
y[1] (closed_form) = -19.4103157681 1.57031767713
absolute error = 0.0001587
relative error = 0.0008149 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.65
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.361 1.525
h = 0.0001 0.004
y[1] (numeric) = -19.4093746963 1.57341448367
y[1] (closed_form) = -19.409515596 1.57348802627
absolute error = 0.0001589
relative error = 0.0008162 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.653
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3609 1.529
h = 0.003 0.006
y[1] (numeric) = -19.4095798205 1.57754677079
y[1] (closed_form) = -19.4097211248 1.57762032339
absolute error = 0.0001593
relative error = 0.000818 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.657
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3579 1.535
h = 0.0001 0.005
y[1] (numeric) = -19.4069499562 1.58396542792
y[1] (closed_form) = -19.407091966 1.58403987267
absolute error = 0.0001603
relative error = 0.0008235 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.664
Order of pole (given) = 0.5 0
NO 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=3515.7MB, alloc=52.3MB, time=43.37
x[1] = -1.3578 1.54
h = 0.0001 0.003
y[1] (numeric) = -19.4072346715 1.58912962999
y[1] (closed_form) = -19.4073773138 1.58920408418
absolute error = 0.0001609
relative error = 0.0008263 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.669
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3577 1.543
h = 0.001 0.001
y[1] (numeric) = -19.4073650077 1.59223127532
y[1] (closed_form) = -19.4075078776 1.59230573879
absolute error = 0.0001611
relative error = 0.0008274 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.671
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3567 1.544
h = 0.001 0.003
y[1] (numeric) = -19.4064116922 1.5933405376
y[1] (closed_form) = -19.4065545635 1.59341505161
absolute error = 0.0001611
relative error = 0.0008275 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.673
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3557 1.547
h = 0.0001 0.004
y[1] (numeric) = -19.4056144298 1.59651257714
y[1] (closed_form) = -19.4057575071 1.59658723757
absolute error = 0.0001614
relative error = 0.0008288 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.676
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3556 1.551
h = 0.003 0.006
y[1] (numeric) = -19.4058240038 1.6006459339
y[1] (closed_form) = -19.4059674856 1.60072060419
absolute error = 0.0001617
relative error = 0.0008307 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.68
Order of pole (given) = 0.5 0
NO 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=3561.8MB, alloc=52.3MB, time=43.93
x[1] = -1.3526 1.557
h = 0.0001 0.005
y[1] (numeric) = -19.4032001319 1.60706938258
y[1] (closed_form) = -19.4033443196 1.60714494484
absolute error = 0.0001628
relative error = 0.0008361 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.686
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3525 1.562
h = 0.0001 0.003
y[1] (numeric) = -19.4034904159 1.61223489289
y[1] (closed_form) = -19.4036352361 1.61231046437
absolute error = 0.0001634
relative error = 0.000839 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.691
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3524 1.565
h = 0.001 0.001
y[1] (numeric) = -19.4036240837 1.61533736763
y[1] (closed_form) = -19.4037691317 1.61541294831
absolute error = 0.0001636
relative error = 0.00084 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.694
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3514 1.566
h = 0.001 0.003
y[1] (numeric) = -19.4026716477 1.61644798759
y[1] (closed_form) = -19.402816697 1.61652361881
absolute error = 0.0001636
relative error = 0.0008402 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.695
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3504 1.569
h = 0.0001 0.004
y[1] (numeric) = -19.4018775019 1.61962186305
y[1] (closed_form) = -19.4020227573 1.61969764062
absolute error = 0.0001638
relative error = 0.0008415 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.698
Order of pole (given) = 0.5 0
NO 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=3607.7MB, alloc=52.3MB, time=44.50
x[1] = -1.3503 1.573
h = 0.003 0.006
y[1] (numeric) = -19.4020915263 1.62375628793
y[1] (closed_form) = -19.4022371863 1.62383207522
absolute error = 0.0001642
relative error = 0.0008433 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.702
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3473 1.579
h = 0.0001 0.005
y[1] (numeric) = -19.3994736492 1.63018452642
y[1] (closed_form) = -19.3996200155 1.6302612055
absolute error = 0.0001652
relative error = 0.0008488 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.709
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3472 1.584
h = 0.0001 0.003
y[1] (numeric) = -19.3997695028 1.63535134307
y[1] (closed_form) = -19.3999165016 1.63542803113
absolute error = 0.0001658
relative error = 0.0008516 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.713
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3471 1.587
h = 0.001 0.001
y[1] (numeric) = -19.399906503 1.63845464608
y[1] (closed_form) = -19.4000537295 1.63853134326
absolute error = 0.000166
relative error = 0.0008527 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.716
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3461 1.588
h = 0.0001 0.004
y[1] (numeric) = -19.3989549469 1.63956662352
y[1] (closed_form) = -19.3991021748 1.63964337125
absolute error = 0.000166
relative error = 0.0008528 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.717
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.346 1.592
h = 0.003 0.006
y[1] (numeric) = -19.3991728156 1.64370191357
y[1] (closed_form) = -19.3993204481 1.64377867087
absolute error = 0.0001664
relative error = 0.0008547 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.721
Order of pole (given) = 0.5 0
NO 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=3653.7MB, alloc=52.3MB, time=45.06
x[1] = -1.343 1.598
h = 0.0001 0.005
y[1] (numeric) = -19.3965601574 1.65013420212
y[1] (closed_form) = -19.3967084965 1.65021185107
absolute error = 0.0001674
relative error = 0.0008601 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.728
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3429 1.603
h = 0.0001 0.003
y[1] (numeric) = -19.3968608215 1.65530207533
y[1] (closed_form) = -19.3970097932 1.65537973306
absolute error = 0.000168
relative error = 0.000863 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.732
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3428 1.606
h = 0.001 0.001
y[1] (numeric) = -19.3970007003 1.65840605067
y[1] (closed_form) = -19.3971498997 1.65848371746
absolute error = 0.0001682
relative error = 0.000864 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.735
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3418 1.607
h = 0.001 0.003
y[1] (numeric) = -19.3960499183 1.65951918594
y[1] (closed_form) = -19.3961991191 1.65959690328
absolute error = 0.0001682
relative error = 0.0008642 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.737
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3408 1.61
h = 0.0001 0.004
y[1] (numeric) = -19.3952615962 1.66269643789
y[1] (closed_form) = -19.3954110032 1.66277430147
absolute error = 0.0001685
relative error = 0.0008655 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.74
Order of pole (given) = 0.5 0
NO 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=3699.6MB, alloc=52.3MB, time=45.62
x[1] = -1.3407 1.614
h = 0.003 0.006
y[1] (numeric) = -19.3954839167 1.66683279321
y[1] (closed_form) = -19.3956337285 1.66691066622
absolute error = 0.0001688
relative error = 0.0008673 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.743
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3377 1.62
h = 0.0001 0.005
y[1] (numeric) = -19.3928772576 1.6732698683
y[1] (closed_form) = -19.3930277763 1.67334863277
absolute error = 0.0001699
relative error = 0.0008727 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.75
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3376 1.625
h = 0.0001 0.003
y[1] (numeric) = -19.393183493 1.67843904428
y[1] (closed_form) = -19.3933346444 1.67851781731
absolute error = 0.0001704
relative error = 0.0008756 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.755
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3375 1.628
h = 0.001 0.001
y[1] (numeric) = -19.3933267053 1.68154384578
y[1] (closed_form) = -19.3934780844 1.68162262777
absolute error = 0.0001707
relative error = 0.0008767 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.758
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3365 1.629
h = 0.001 0.003
y[1] (numeric) = -19.3923768044 1.68265833815
y[1] (closed_form) = -19.3925281849 1.68273717071
absolute error = 0.0001707
relative error = 0.0008768 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.759
Order of pole (given) = 0.5 0
NO 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=3745.6MB, alloc=52.3MB, time=46.19
x[1] = -1.3355 1.632
h = 0.0001 0.004
y[1] (numeric) = -19.3915916015 1.68583742325
y[1] (closed_form) = -19.3917431883 1.68591640198
absolute error = 0.0001709
relative error = 0.0008781 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.762
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3354 1.636
h = 0.003 0.006
y[1] (numeric) = -19.3918183748 1.68997484232
y[1] (closed_form) = -19.3919703664 1.69005383034
absolute error = 0.0001713
relative error = 0.00088 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.766
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3324 1.642
h = 0.0001 0.005
y[1] (numeric) = -19.389217717 1.6964167022
y[1] (closed_form) = -19.3893704159 1.69649658151
absolute error = 0.0001723
relative error = 0.0008854 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.773
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3323 1.647
h = 0.0001 0.003
y[1] (numeric) = -19.3895295249 1.70158717905
y[1] (closed_form) = -19.3896828565 1.70166706667
absolute error = 0.0001729
relative error = 0.0008883 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.777
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3322 1.65
h = 0.001 0.001
y[1] (numeric) = -19.3896760711 1.70469280555
y[1] (closed_form) = -19.3898296305 1.70477270207
absolute error = 0.0001731
relative error = 0.0008893 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.78
Order of pole (given) = 0.5 0
NO 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=3791.5MB, alloc=52.3MB, time=46.76
x[1] = -1.3312 1.651
h = 0.001 0.003
y[1] (numeric) = -19.3887270518 1.70580865484
y[1] (closed_form) = -19.3888806127 1.70588860192
absolute error = 0.0001731
relative error = 0.0008895 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.781
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3302 1.654
h = 0.0001 0.004
y[1] (numeric) = -19.3879449693 1.70898957212
y[1] (closed_form) = -19.3880987365 1.70906966531
absolute error = 0.0001734
relative error = 0.0008908 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.784
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3301 1.658
h = 0.003 0.006
y[1] (numeric) = -19.3881761961 1.71312805342
y[1] (closed_form) = -19.3883303681 1.71320815575
absolute error = 0.0001737
relative error = 0.0008926 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.788
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3271 1.664
h = 0.0001 0.005
y[1] (numeric) = -19.3855815418 1.71957469634
y[1] (closed_form) = -19.3857364216 1.71965568979
absolute error = 0.0001748
relative error = 0.0008981 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.795
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.327 1.669
h = 0.0001 0.003
y[1] (numeric) = -19.3858989231 1.72474647214
y[1] (closed_form) = -19.3860544356 1.72482747367
absolute error = 0.0001753
relative error = 0.0009009 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.8
Order of pole (given) = 0.5 0
NO 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=3837.4MB, alloc=52.3MB, time=47.32
x[1] = -1.3269 1.672
h = 0.001 0.001
y[1] (numeric) = -19.386048804 1.72785292252
y[1] (closed_form) = -19.3862045443 1.72793393286
absolute error = 0.0001755
relative error = 0.000902 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.802
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3259 1.673
h = 0.001 0.003
y[1] (numeric) = -19.3851006669 1.72897012853
y[1] (closed_form) = -19.3852564087 1.72905118944
absolute error = 0.0001756
relative error = 0.0009021 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.804
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3249 1.676
h = 0.0001 0.004
y[1] (numeric) = -19.3843217056 1.73215287701
y[1] (closed_form) = -19.3844776538 1.73223408397
absolute error = 0.0001758
relative error = 0.0009034 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.807
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3248 1.68
h = 0.003 0.006
y[1] (numeric) = -19.3845573868 1.73629241902
y[1] (closed_form) = -19.3847137398 1.73637363497
absolute error = 0.0001762
relative error = 0.0009053 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.811
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3218 1.686
h = 0.0001 0.005
y[1] (numeric) = -19.3819687384 1.74274384324
y[1] (closed_form) = -19.3821257995 1.74282595013
absolute error = 0.0001772
relative error = 0.0009107 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.817
Order of pole (given) = 0.5 0
NO 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=3883.3MB, alloc=52.3MB, time=47.88
x[1] = -1.3217 1.691
h = 0.0001 0.003
y[1] (numeric) = -19.3822916941 1.74791691609
y[1] (closed_form) = -19.382449388 1.74799903083
absolute error = 0.0001778
relative error = 0.0009136 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.822
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3216 1.694
h = 0.001 0.001
y[1] (numeric) = -19.3824449101 1.7510241892
y[1] (closed_form) = -19.3826028319 1.75110631267
absolute error = 0.000178
relative error = 0.0009146 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.825
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3206 1.695
h = 0.0001 0.004
y[1] (numeric) = -19.3814976559 1.75214275173
y[1] (closed_form) = -19.3816555791 1.75222492578
absolute error = 0.000178
relative error = 0.0009148 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.826
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3205 1.699
h = 0.003 0.006
y[1] (numeric) = -19.3817371846 1.75628315247
y[1] (closed_form) = -19.3818955126 1.75636533538
absolute error = 0.0001784
relative error = 0.0009166 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.83
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3175 1.705
h = 0.0001 0.005
y[1] (numeric) = -19.3791537646 1.7627386193
y[1] (closed_form) = -19.379312801 1.76282169299
absolute error = 0.0001794
relative error = 0.0009221 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.837
Order of pole (given) = 0.5 0
NO 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=3929.1MB, alloc=52.3MB, time=48.45
x[1] = -1.3174 1.71
h = 0.0001 0.003
y[1] (numeric) = -19.3794815347 1.76791274065
y[1] (closed_form) = -19.3796412041 1.76799582199
absolute error = 0.00018
relative error = 0.0009249 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.841
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3173 1.713
h = 0.001 0.001
y[1] (numeric) = -19.3796376319 1.7710206813
y[1] (closed_form) = -19.3797975291 1.7711037713
absolute error = 0.0001802
relative error = 0.000926 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.844
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3163 1.714
h = 0.001 0.003
y[1] (numeric) = -19.3786911541 1.7721404008
y[1] (closed_form) = -19.3788510528 1.77222354137
absolute error = 0.0001802
relative error = 0.0009261 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.845
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3153 1.717
h = 0.0001 0.004
y[1] (numeric) = -19.377918025 1.77532651694
y[1] (closed_form) = -19.3780781302 1.77540980345
absolute error = 0.0001805
relative error = 0.0009274 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.848
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3152 1.721
h = 0.003 0.006
y[1] (numeric) = -19.3781620094 1.77946797554
y[1] (closed_form) = -19.3783225195 1.77955127077
absolute error = 0.0001808
relative error = 0.0009293 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.852
Order of pole (given) = 0.5 0
NO 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=3975.1MB, alloc=52.3MB, time=49.01
x[1] = -1.3122 1.727
h = 0.0001 0.005
y[1] (numeric) = -19.3755845995 1.78592822038
y[1] (closed_form) = -19.3757458185 1.78601240622
absolute error = 0.0001819
relative error = 0.0009347 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.859
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3121 1.732
h = 0.0001 0.003
y[1] (numeric) = -19.3759179458 1.79110363522
y[1] (closed_form) = -19.3760797978 1.79118782848
absolute error = 0.0001824
relative error = 0.0009376 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.864
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.312 1.735
h = 0.001 0.001
y[1] (numeric) = -19.3760773794 1.79421239647
y[1] (closed_form) = -19.3762394592 1.79429659831
absolute error = 0.0001826
relative error = 0.0009386 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.866
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.311 1.736
h = 0.001 0.003
y[1] (numeric) = -19.3751317854 1.79533347212
y[1] (closed_form) = -19.3752938667 1.79541772453
absolute error = 0.0001827
relative error = 0.0009388 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.868
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.31 1.739
h = 0.0001 0.004
y[1] (numeric) = -19.3743617802 1.79852141669
y[1] (closed_form) = -19.3745240681 1.79860581498
absolute error = 0.0001829
relative error = 0.0009401 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.871
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3099 1.743
h = 0.003 0.006
y[1] (numeric) = -19.3746102213 1.80266393163
y[1] (closed_form) = -19.3747729141 1.80274833849
absolute error = 0.0001833
relative error = 0.0009419 %
Correct digits = 5
memory used=4021.1MB, alloc=52.3MB, time=49.58
Radius of convergence (given) for eq 1 = 1.875
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3069 1.749
h = 0.0001 0.005
y[1] (numeric) = -19.3720388238 1.80912895274
y[1] (closed_form) = -19.3722022259 1.80921425003
absolute error = 0.0001843
relative error = 0.0009474 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.881
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3068 1.754
h = 0.0001 0.003
y[1] (numeric) = -19.3723777473 1.81430565915
y[1] (closed_form) = -19.3725417824 1.81439096363
absolute error = 0.0001849
relative error = 0.0009502 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.886
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3067 1.757
h = 0.001 0.001
y[1] (numeric) = -19.3725405178 1.81741523987
y[1] (closed_form) = -19.3727047808 1.81750055285
absolute error = 0.0001851
relative error = 0.0009513 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.889
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3057 1.758
h = 0.001 0.003
y[1] (numeric) = -19.3715958083 1.81853767147
y[1] (closed_form) = -19.3717600727 1.81862303503
absolute error = 0.0001851
relative error = 0.0009514 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.89
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3047 1.761
h = 0.0001 0.004
y[1] (numeric) = -19.3708289279 1.8217274435
y[1] (closed_form) = -19.3709933991 1.82181295287
absolute error = 0.0001854
relative error = 0.0009527 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.893
Order of pole (given) = 0.5 0
NO 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=4067.0MB, alloc=52.3MB, time=50.14
x[1] = -1.3046 1.765
h = 0.003 0.006
y[1] (numeric) = -19.3710818264 1.82587101325
y[1] (closed_form) = -19.3712467025 1.82595653104
absolute error = 0.0001857
relative error = 0.0009546 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.897
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3016 1.771
h = 0.0001 0.005
y[1] (numeric) = -19.3685164436 1.83234080889
y[1] (closed_form) = -19.3686820294 1.83242721694
absolute error = 0.0001868
relative error = 0.00096 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.904
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3015 1.776
h = 0.0001 0.003
y[1] (numeric) = -19.3688609453 1.83751880495
y[1] (closed_form) = -19.3690271641 1.83760521996
absolute error = 0.0001873
relative error = 0.0009629 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.908
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3014 1.779
h = 0.001 0.001
y[1] (numeric) = -19.3690270533 1.840629204
y[1] (closed_form) = -19.3691935001 1.84071562743
absolute error = 0.0001875
relative error = 0.0009639 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.911
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3004 1.78
h = 0.001 0.003
y[1] (numeric) = -19.3680832288 1.84175299136
y[1] (closed_form) = -19.3682496771 1.84183946537
absolute error = 0.0001876
relative error = 0.0009641 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.913
Order of pole (given) = 0.5 0
NO 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=4112.9MB, alloc=52.3MB, time=50.70
x[1] = -1.2994 1.783
h = 0.0001 0.004
y[1] (numeric) = -19.3673194743 1.84494458988
y[1] (closed_form) = -19.3674861293 1.84503120964
absolute error = 0.0001878
relative error = 0.0009654 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.916
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2993 1.787
h = 0.003 0.006
y[1] (numeric) = -19.367576831 1.84908921291
y[1] (closed_form) = -19.367743891 1.84917584095
absolute error = 0.0001882
relative error = 0.0009672 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.919
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2963 1.793
h = 0.0001 0.005
y[1] (numeric) = -19.3650174652 1.85556378132
y[1] (closed_form) = -19.3651852352 1.85565129945
absolute error = 0.0001892
relative error = 0.0009727 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.926
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2962 1.798
h = 0.0001 0.003
y[1] (numeric) = -19.365367546 1.86074306513
y[1] (closed_form) = -19.3655359491 1.86083058998
absolute error = 0.0001898
relative error = 0.0009755 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.931
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2961 1.801
h = 0.001 0.001
y[1] (numeric) = -19.3655369922 1.86385428138
y[1] (closed_form) = -19.3657056233 1.86394181456
absolute error = 0.00019
relative error = 0.0009766 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.934
Order of pole (given) = 0.5 0
NO 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=4158.8MB, alloc=52.3MB, time=51.27
x[1] = -1.2951 1.802
h = 0.0001 0.004
y[1] (numeric) = -19.3645940533 1.8649794243
y[1] (closed_form) = -19.3647626859 1.86506700807
absolute error = 0.00019
relative error = 0.0009768 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.935
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.295 1.806
h = 0.003 0.006
y[1] (numeric) = -19.3648552606 1.86912489963
y[1] (closed_form) = -19.3650242982 1.86921249155
absolute error = 0.0001904
relative error = 0.0009786 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.939
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.292 1.812
h = 0.0001 0.005
y[1] (numeric) = -19.3623011327 1.87560350318
y[1] (closed_form) = -19.3624708806 1.87569198502
absolute error = 0.0001914
relative error = 0.000984 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.945
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2919 1.817
h = 0.0001 0.003
y[1] (numeric) = -19.362656032 1.88078382743
y[1] (closed_form) = -19.362826413 1.88087231579
absolute error = 0.000192
relative error = 0.0009869 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.95
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2918 1.82
h = 0.001 0.001
y[1] (numeric) = -19.3628283618 1.88389570641
y[1] (closed_form) = -19.3629989708 1.88398420303
absolute error = 0.0001922
relative error = 0.0009879 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.953
Order of pole (given) = 0.5 0
NO 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=4204.7MB, alloc=52.3MB, time=51.84
x[1] = -1.2908 1.821
h = 0.001 0.003
y[1] (numeric) = -19.3618862017 1.88502200543
y[1] (closed_form) = -19.3620568123 1.88511055264
absolute error = 0.0001922
relative error = 0.0009881 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.954
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2898 1.824
h = 0.0001 0.004
y[1] (numeric) = -19.3611282879 1.88821696277
y[1] (closed_form) = -19.3612991054 1.88830565562
absolute error = 0.0001925
relative error = 0.0009894 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.957
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2897 1.828
h = 0.003 0.006
y[1] (numeric) = -19.3613939549 1.89236348854
y[1] (closed_form) = -19.3615651774 1.8924521894
absolute error = 0.0001928
relative error = 0.0009912 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.961
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2867 1.834
h = 0.0001 0.005
y[1] (numeric) = -19.3588458482 1.89884686157
y[1] (closed_form) = -19.3590177815 1.89893645218
absolute error = 0.0001939
relative error = 0.0009967 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.968
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2866 1.839
h = 0.0001 0.003
y[1] (numeric) = -19.3592063284 1.90402847001
y[1] (closed_form) = -19.3593788949 1.9041180669
absolute error = 0.0001944
relative error = 0.0009995 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.973
Order of pole (given) = 0.5 0
NO 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=4250.7MB, alloc=52.3MB, time=52.40
x[1] = -1.2865 1.842
h = 0.001 0.001
y[1] (numeric) = -19.3593819975 1.90714116405
y[1] (closed_form) = -19.3595547919 1.90723076913
absolute error = 0.0001946
relative error = 0.001001 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.975
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2855 1.843
h = 0.001 0.003
y[1] (numeric) = -19.358440724 1.90826881825
y[1] (closed_form) = -19.3586135201 1.90835847392
absolute error = 0.0001947
relative error = 0.001001 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.977
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2845 1.846
h = 0.0001 0.004
y[1] (numeric) = -19.3576859388 1.9114655993
y[1] (closed_form) = -19.3578589418 1.91155540055
absolute error = 0.0001949
relative error = 0.001002 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.98
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2844 1.85
h = 0.003 0.006
y[1] (numeric) = -19.3579560662 1.91561317398
y[1] (closed_form) = -19.3581294744 1.91570298309
absolute error = 0.0001953
relative error = 0.001004 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.984
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2814 1.856
h = 0.0001 0.005
y[1] (numeric) = -19.3554139831 1.92210131475
y[1] (closed_form) = -19.3555881023 1.92219201343
absolute error = 0.0001963
relative error = 0.001009 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.99
Order of pole (given) = 0.5 0
NO 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=4296.6MB, alloc=52.3MB, time=52.96
x[1] = -1.2813 1.861
h = 0.0001 0.003
y[1] (numeric) = -19.3557800452 1.92728420545
y[1] (closed_form) = -19.3559547977 1.92737491019
absolute error = 0.0001969
relative error = 0.001012 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.995
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2812 1.864
h = 0.001 0.001
y[1] (numeric) = -19.3559590541 1.93039771342
y[1] (closed_form) = -19.3561340346 1.93048842626
absolute error = 0.0001971
relative error = 0.001013 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.998
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2802 1.865
h = 0.001 0.003
y[1] (numeric) = -19.3550186679 1.93152672261
y[1] (closed_form) = -19.35519365 1.93161748605
absolute error = 0.0001971
relative error = 0.001013 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.999
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2792 1.868
h = 0.0001 0.004
y[1] (numeric) = -19.3542670122 1.93472532639
y[1] (closed_form) = -19.3544422014 1.93481623534
absolute error = 0.0001974
relative error = 0.001015 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.002
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2791 1.872
h = 0.003 0.006
y[1] (numeric) = -19.3545416009 1.93887394846
y[1] (closed_form) = -19.3547171952 1.93896486512
absolute error = 0.0001977
relative error = 0.001017 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.006
Order of pole (given) = 0.5 0
NO 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=4342.4MB, alloc=52.3MB, time=53.53
x[1] = -1.2761 1.878
h = 0.0001 0.005
y[1] (numeric) = -19.3520055436 1.94536685522
y[1] (closed_form) = -19.3521818493 1.94545866128
absolute error = 0.0001988
relative error = 0.001022 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.013
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.276 1.883
h = 0.0001 0.003
y[1] (numeric) = -19.3523771886 1.95055102628
y[1] (closed_form) = -19.3525541277 1.95064283816
absolute error = 0.0001993
relative error = 0.001025 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.017
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2759 1.886
h = 0.001 0.001
y[1] (numeric) = -19.352559538 1.95366534703
y[1] (closed_form) = -19.3527367051 1.95375716693
absolute error = 0.0001995
relative error = 0.001026 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.02
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2749 1.887
h = 0.001 0.003
y[1] (numeric) = -19.3516200396 1.95479571101
y[1] (closed_form) = -19.3517972083 1.95488758152
absolute error = 0.0001996
relative error = 0.001026 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.022
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2739 1.89
h = 0.0001 0.004
y[1] (numeric) = -19.3508715143 1.95799613655
y[1] (closed_form) = -19.3510488902 1.95808815251
absolute error = 0.0001998
relative error = 0.001027 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.025
Order of pole (given) = 0.5 0
NO 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=4388.2MB, alloc=52.3MB, time=54.09
x[1] = -1.2738 1.894
h = 0.003 0.006
y[1] (numeric) = -19.351150565 1.96214580448
y[1] (closed_form) = -19.3513283461 1.96223782801
absolute error = 0.0002002
relative error = 0.001029 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.028
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2708 1.9
h = 0.0001 0.005
y[1] (numeric) = -19.3486205358 1.96864347549
y[1] (closed_form) = -19.3487990288 1.96873638823
absolute error = 0.0002012
relative error = 0.001035 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.035
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2707 1.905
h = 0.0001 0.003
y[1] (numeric) = -19.3489977647 1.97382892498
y[1] (closed_form) = -19.3491768911 1.97392184332
absolute error = 0.0002018
relative error = 0.001038 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.04
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2706 1.908
h = 0.001 0.001
y[1] (numeric) = -19.3491834552 1.97694405738
y[1] (closed_form) = -19.3493628096 1.97703698365
absolute error = 0.000202
relative error = 0.001039 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.043
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2696 1.909
h = 0.0001 0.004
y[1] (numeric) = -19.3482448452 1.97807577595
y[1] (closed_form) = -19.3484242012 1.97816875283
absolute error = 0.000202
relative error = 0.001039 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.044
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2695 1.913
h = 0.003 0.006
y[1] (numeric) = -19.3485277498 1.98222628974
y[1] (closed_form) = -19.3487075109 1.98231927405
absolute error = 0.0002024
relative error = 0.001041 %
Correct digits = 5
memory used=4434.1MB, alloc=52.3MB, time=54.66
Radius of convergence (given) for eq 1 = 2.048
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2665 1.919
h = 0.0001 0.005
y[1] (numeric) = -19.3460029679 1.98872798839
y[1] (closed_form) = -19.3461834413 1.98882186176
absolute error = 0.0002034
relative error = 0.001046 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.054
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2664 1.924
h = 0.0001 0.003
y[1] (numeric) = -19.3463850193 1.99391447026
y[1] (closed_form) = -19.3465661261 1.99400834903
absolute error = 0.000204
relative error = 0.001049 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.059
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2663 1.927
h = 0.001 0.001
y[1] (numeric) = -19.3465735958 1.99703026057
y[1] (closed_form) = -19.3467549306 1.99712414721
absolute error = 0.0002042
relative error = 0.00105 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.062
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2653 1.928
h = 0.001 0.003
y[1] (numeric) = -19.345635767 1.99816313438
y[1] (closed_form) = -19.3458171035 1.99825707163
absolute error = 0.0002042
relative error = 0.00105 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.063
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2643 1.931
h = 0.0001 0.004
y[1] (numeric) = -19.344893091 2.0013669099
y[1] (closed_form) = -19.3450746348 2.00146099249
absolute error = 0.0002045
relative error = 0.001051 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.066
Order of pole (given) = 0.5 0
NO 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=4480.0MB, alloc=52.3MB, time=55.22
x[1] = -1.2642 1.935
h = 0.003 0.006
y[1] (numeric) = -19.345180459 2.0055184667
y[1] (closed_form) = -19.3453624081 2.00561255658
absolute error = 0.0002048
relative error = 0.001053 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.07
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2612 1.941
h = 0.0001 0.005
y[1] (numeric) = -19.3426617095 2.0120249263
y[1] (closed_form) = -19.3428443711 2.01211990506
absolute error = 0.0002059
relative error = 0.001059 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.077
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2611 1.946
h = 0.0001 0.003
y[1] (numeric) = -19.3430493466 2.01721268304
y[1] (closed_form) = -19.3432326417 2.01730766696
absolute error = 0.0002064
relative error = 0.001062 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.082
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.261 1.949
h = 0.001 0.001
y[1] (numeric) = -19.3432412653 2.02032928287
y[1] (closed_form) = -19.3434247884 2.02042427458
absolute error = 0.0002066
relative error = 0.001063 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.084
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.26 1.95
h = 0.001 0.003
y[1] (numeric) = -19.3423043259 2.02146351089
y[1] (closed_form) = -19.3424878508 2.02155855321
absolute error = 0.0002067
relative error = 0.001063 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.086
Order of pole (given) = 0.5 0
NO 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=4526.0MB, alloc=52.3MB, time=55.78
x[1] = -1.259 1.953
h = 0.0001 0.004
y[1] (numeric) = -19.3415647831 2.02466910539
y[1] (closed_form) = -19.3417485153 2.02476429298
absolute error = 0.0002069
relative error = 0.001064 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.089
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2589 1.957
h = 0.003 0.006
y[1] (numeric) = -19.3418566154 2.02882170367
y[1] (closed_form) = -19.3420407529 2.02891689841
absolute error = 0.0002073
relative error = 0.001066 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.093
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2559 1.963
h = 0.0001 0.005
y[1] (numeric) = -19.3393439005 2.03533292246
y[1] (closed_form) = -19.339528751 2.03542900591
absolute error = 0.0002083
relative error = 0.001071 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.099
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2558 1.968
h = 0.0001 0.003
y[1] (numeric) = -19.3397371242 2.04052195216
y[1] (closed_form) = -19.3399226083 2.04061804054
absolute error = 0.0002089
relative error = 0.001074 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.104
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2557 1.971
h = 0.001 0.001
y[1] (numeric) = -19.3399323857 2.04363936037
y[1] (closed_form) = -19.3401180979 2.04373545645
absolute error = 0.0002091
relative error = 0.001075 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.107
Order of pole (given) = 0.5 0
NO 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=4571.9MB, alloc=52.3MB, time=56.35
x[1] = -1.2547 1.972
h = 0.001 0.003
y[1] (numeric) = -19.3389963364 2.04477494241
y[1] (closed_form) = -19.3391820502 2.04487108911
absolute error = 0.0002091
relative error = 0.001075 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.108
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2537 1.975
h = 0.0001 0.004
y[1] (numeric) = -19.3382599277 2.04798235491
y[1] (closed_form) = -19.3384458489 2.04807864682
absolute error = 0.0002094
relative error = 0.001077 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.111
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2536 1.979
h = 0.003 0.006
y[1] (numeric) = -19.3385562251 2.05213599315
y[1] (closed_form) = -19.3387425516 2.05223229206
absolute error = 0.0002097
relative error = 0.001079 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.115
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2506 1.985
h = 0.0001 0.005
y[1] (numeric) = -19.3360495471 2.05865196938
y[1] (closed_form) = -19.336236587 2.05874915682
absolute error = 0.0002108
relative error = 0.001084 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.122
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2505 1.99
h = 0.0001 0.003
y[1] (numeric) = -19.3364483585 2.06384227012
y[1] (closed_form) = -19.336636032 2.06393946226
absolute error = 0.0002113
relative error = 0.001087 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.126
Order of pole (given) = 0.5 0
NO 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=4617.9MB, alloc=52.3MB, time=56.92
x[1] = -1.2504 1.993
h = 0.001 0.001
y[1] (numeric) = -19.3366469634 2.06696048556
y[1] (closed_form) = -19.336834865 2.06705768532
absolute error = 0.0002116
relative error = 0.001088 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.129
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2494 1.994
h = 0.001 0.003
y[1] (numeric) = -19.3357118047 2.06809742142
y[1] (closed_form) = -19.335899708 2.0681946718
absolute error = 0.0002116
relative error = 0.001088 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.131
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2484 1.997
h = 0.0001 0.004
y[1] (numeric) = -19.334978531 2.07130665096
y[1] (closed_form) = -19.3351666419 2.07140404649
absolute error = 0.0002118
relative error = 0.001089 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.134
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2483 2.001
h = 0.003 0.006
y[1] (numeric) = -19.3352792943 2.07546132762
y[1] (closed_form) = -19.3354678105 2.07555873001
absolute error = 0.0002122
relative error = 0.001091 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.138
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2453 2.007
h = 0.0001 0.005
y[1] (numeric) = -19.3327786555 2.08198205954
y[1] (closed_form) = -19.3329678855 2.08208035028
absolute error = 0.0002132
relative error = 0.001097 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.144
Order of pole (given) = 0.5 0
NO 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=4663.8MB, alloc=52.3MB, time=57.48
x[1] = -1.2452 2.012
h = 0.0001 0.003
y[1] (numeric) = -19.3331830556 2.08717362941
y[1] (closed_form) = -19.3333729192 2.08727192461
absolute error = 0.0002138
relative error = 0.001099 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.149
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2451 2.015
h = 0.001 0.001
y[1] (numeric) = -19.3333850045 2.09029265094
y[1] (closed_form) = -19.3335750962 2.09039095369
absolute error = 0.000214
relative error = 0.0011 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.152
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2441 2.016
h = 0.0001 0.004
y[1] (numeric) = -19.3324507369 2.09143094042
y[1] (closed_form) = -19.3326408304 2.09152929379
absolute error = 0.000214
relative error = 0.001101 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.153
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.244 2.02
h = 0.003 0.006
y[1] (numeric) = -19.3327553573 2.09558645651
y[1] (closed_form) = -19.3329458561 2.0956848166
absolute error = 0.0002144
relative error = 0.001102 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.157
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.241 2.026
h = 0.0001 0.005
y[1] (numeric) = -19.3302599753 2.10211120858
y[1] (closed_form) = -19.3304511882 2.10221045687
absolute error = 0.0002154
relative error = 0.001108 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.164
Order of pole (given) = 0.5 0
NO 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=4709.6MB, alloc=52.3MB, time=58.04
x[1] = -1.2409 2.031
h = 0.0001 0.003
y[1] (numeric) = -19.3306692017 2.10730380275
y[1] (closed_form) = -19.3308610483 2.1074030553
absolute error = 0.000216
relative error = 0.001111 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.168
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2408 2.034
h = 0.001 0.001
y[1] (numeric) = -19.3308740391 2.11042347738
y[1] (closed_form) = -19.3310661139 2.11052273741
absolute error = 0.0002162
relative error = 0.001112 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.171
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2398 2.035
h = 0.001 0.003
y[1] (numeric) = -19.3299405552 2.11156292123
y[1] (closed_form) = -19.3301326317 2.11166223189
absolute error = 0.0002162
relative error = 0.001112 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.172
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2388 2.038
h = 0.0001 0.004
y[1] (numeric) = -19.3292131393 2.11477549189
y[1] (closed_form) = -19.3294054234 2.11487494757
absolute error = 0.0002165
relative error = 0.001113 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.176
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2387 2.042
h = 0.003 0.006
y[1] (numeric) = -19.329522227 2.11893204354
y[1] (closed_form) = -19.3297149165 2.11903150581
absolute error = 0.0002168
relative error = 0.001115 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.179
Order of pole (given) = 0.5 0
NO 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=4755.6MB, alloc=52.3MB, time=58.61
x[1] = -1.2357 2.048
h = 0.0001 0.005
y[1] (numeric) = -19.3270328885 2.125461548
y[1] (closed_form) = -19.3272262925 2.12556189829
absolute error = 0.0002179
relative error = 0.001121 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.186
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2356 2.053
h = 0.0001 0.003
y[1] (numeric) = -19.3274477053 2.13065540773
y[1] (closed_form) = -19.3276417431 2.13075576204
absolute error = 0.0002185
relative error = 0.001123 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.191
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2355 2.056
h = 0.001 0.001
y[1] (numeric) = -19.3276558878 2.13377588633
y[1] (closed_form) = -19.3278501538 2.13387624803
absolute error = 0.0002187
relative error = 0.001124 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.194
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2345 2.057
h = 0.001 0.003
y[1] (numeric) = -19.3267232961 2.13491668342
y[1] (closed_form) = -19.3269175638 2.13501709576
absolute error = 0.0002187
relative error = 0.001125 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.195
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2335 2.06
h = 0.0001 0.004
y[1] (numeric) = -19.325999018 2.13813106831
y[1] (closed_form) = -19.3261934935 2.13823162562
absolute error = 0.0002189
relative error = 0.001126 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.198
Order of pole (given) = 0.5 0
NO 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=4801.6MB, alloc=52.3MB, time=59.18
x[1] = -1.2334 2.064
h = 0.003 0.006
y[1] (numeric) = -19.3263125738 2.14228865402
y[1] (closed_form) = -19.3265074547 2.14238921776
absolute error = 0.0002193
relative error = 0.001128 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.202
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2304 2.07
h = 0.0001 0.005
y[1] (numeric) = -19.323829281 2.14882290911
y[1] (closed_form) = -19.3240248768 2.1489243607
absolute error = 0.0002203
relative error = 0.001133 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.208
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2303 2.075
h = 0.0001 0.003
y[1] (numeric) = -19.3242496893 2.15401803247
y[1] (closed_form) = -19.3244459189 2.15411948786
absolute error = 0.0002209
relative error = 0.001136 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.213
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2302 2.078
h = 0.001 0.001
y[1] (numeric) = -19.3244612175 2.1571393139
y[1] (closed_form) = -19.3246576753 2.15724077659
absolute error = 0.0002211
relative error = 0.001137 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.216
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2292 2.079
h = 0.001 0.003
y[1] (numeric) = -19.3235295186 2.15828146404
y[1] (closed_form) = -19.3237259782 2.15838297737
absolute error = 0.0002211
relative error = 0.001137 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.217
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2282 2.082
h = 0.0001 0.004
y[1] (numeric) = -19.3228083792 2.1614976622
y[1] (closed_form) = -19.3230050466 2.16159932043
absolute error = 0.0002214
relative error = 0.001139 %
Correct digits = 5
memory used=4847.4MB, alloc=52.3MB, time=59.75
Radius of convergence (given) for eq 1 = 2.22
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2281 2.086
h = 0.003 0.006
y[1] (numeric) = -19.3231264039 2.16565628042
y[1] (closed_form) = -19.3233234767 2.16575794495
absolute error = 0.0002218
relative error = 0.00114 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.224
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2251 2.092
h = 0.0001 0.005
y[1] (numeric) = -19.3206491592 2.17219528439
y[1] (closed_form) = -19.3208469473 2.17229783658
absolute error = 0.0002228
relative error = 0.001146 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.231
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.225 2.097
h = 0.0001 0.003
y[1] (numeric) = -19.3210751598 2.17739166948
y[1] (closed_form) = -19.3212735818 2.17749422524
absolute error = 0.0002234
relative error = 0.001149 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.236
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2249 2.1
h = 0.001 0.001
y[1] (numeric) = -19.3212900343 2.18051375258
y[1] (closed_form) = -19.3214886845 2.18061631556
absolute error = 0.0002236
relative error = 0.00115 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.238
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2239 2.101
h = 0.001 0.003
y[1] (numeric) = -19.3203592288 2.18165725557
y[1] (closed_form) = -19.3205578808 2.18175986919
absolute error = 0.0002236
relative error = 0.00115 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.24
Order of pole (given) = 0.5 0
NO 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=4893.3MB, alloc=52.3MB, time=60.31
x[1] = -1.2229 2.104
h = 0.0001 0.004
y[1] (numeric) = -19.3196412292 2.18487526602
y[1] (closed_form) = -19.319840089 2.18497802449
absolute error = 0.0002238
relative error = 0.001151 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.243
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2228 2.108
h = 0.003 0.006
y[1] (numeric) = -19.3199637235 2.18903491524
y[1] (closed_form) = -19.3201629889 2.18913767985
absolute error = 0.0002242
relative error = 0.001153 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.247
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2198 2.114
h = 0.0001 0.005
y[1] (numeric) = -19.3174925291 2.19557866633
y[1] (closed_form) = -19.3176925101 2.19568231842
absolute error = 0.0002252
relative error = 0.001159 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.253
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2197 2.119
h = 0.0001 0.003
y[1] (numeric) = -19.3179241231 2.20077631122
y[1] (closed_form) = -19.3181247381 2.20087996665
absolute error = 0.0002258
relative error = 0.001161 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.258
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2196 2.122
h = 0.001 0.001
y[1] (numeric) = -19.3181423445 2.20389919486
y[1] (closed_form) = -19.3183431877 2.20400285744
absolute error = 0.000226
relative error = 0.001162 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.261
Order of pole (given) = 0.5 0
NO 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=4939.2MB, alloc=52.3MB, time=60.88
x[1] = -1.2186 2.123
h = 0.0001 0.004
y[1] (numeric) = -19.317212433 2.2050440505
y[1] (closed_form) = -19.317413278 2.20514776372
absolute error = 0.000226
relative error = 0.001163 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.262
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2185 2.127
h = 0.003 0.006
y[1] (numeric) = -19.3175387876 2.20920453269
y[1] (closed_form) = -19.3177400382 2.20930825191
absolute error = 0.0002264
relative error = 0.001164 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.266
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2155 2.133
h = 0.0001 0.005
y[1] (numeric) = -19.3150728595 2.21575229642
y[1] (closed_form) = -19.315274826 2.21585690298
absolute error = 0.0002274
relative error = 0.00117 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.273
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2154 2.138
h = 0.0001 0.003
y[1] (numeric) = -19.3155092838 2.22095095753
y[1] (closed_form) = -19.3157118843 2.22105556723
absolute error = 0.000228
relative error = 0.001173 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.277
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2153 2.141
h = 0.001 0.001
y[1] (numeric) = -19.3157303962 2.22407448946
y[1] (closed_form) = -19.3159332249 2.22417910622
absolute error = 0.0002282
relative error = 0.001174 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.28
Order of pole (given) = 0.5 0
NO 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=4985.1MB, alloc=52.3MB, time=61.44
x[1] = -1.2143 2.142
h = 0.001 0.003
y[1] (numeric) = -19.3148012707 2.22522049859
y[1] (closed_form) = -19.3150041013 2.225325166
absolute error = 0.0002282
relative error = 0.001174 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.282
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2133 2.145
h = 0.0001 0.004
y[1] (numeric) = -19.3140891373 2.22844184129
y[1] (closed_form) = -19.3142921759 2.22854665343
absolute error = 0.0002285
relative error = 0.001175 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.285
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2132 2.149
h = 0.003 0.006
y[1] (numeric) = -19.314419963 2.23260335161
y[1] (closed_form) = -19.3146234072 2.23270816961
absolute error = 0.0002289
relative error = 0.001177 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.289
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2102 2.155
h = 0.0001 0.005
y[1] (numeric) = -19.3119600895 2.23915585916
y[1] (closed_form) = -19.31216425 2.23926156432
absolute error = 0.0002299
relative error = 0.001183 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.295
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2101 2.16
h = 0.0001 0.003
y[1] (numeric) = -19.312402109 2.2443557765
y[1] (closed_form) = -19.3126069036 2.24446148457
absolute error = 0.0002305
relative error = 0.001185 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.3
Order of pole (given) = 0.5 0
NO 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=5031.1MB, alloc=52.3MB, time=62.01
x[1] = -1.21 2.163
h = 0.001 0.001
y[1] (numeric) = -19.3126265693 2.24748010683
y[1] (closed_form) = -19.3128315922 2.24758582189
absolute error = 0.0002307
relative error = 0.001186 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.303
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.209 2.164
h = 0.001 0.003
y[1] (numeric) = -19.3116983389 2.24862746823
y[1] (closed_form) = -19.3119033636 2.24873323394
absolute error = 0.0002307
relative error = 0.001187 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.304
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.208 2.167
h = 0.0001 0.004
y[1] (numeric) = -19.3109893479 2.25185062043
y[1] (closed_form) = -19.3111945806 2.25195653081
absolute error = 0.0002309
relative error = 0.001188 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.307
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2079 2.171
h = 0.003 0.006
y[1] (numeric) = -19.3113246456 2.25601315736
y[1] (closed_form) = -19.311530284 2.25611907345
absolute error = 0.0002313
relative error = 0.00119 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.311
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2049 2.177
h = 0.0001 0.005
y[1] (numeric) = -19.3088708288 2.26257040697
y[1] (closed_form) = -19.309077184 2.26267721004
absolute error = 0.0002324
relative error = 0.001195 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.318
Order of pole (given) = 0.5 0
NO 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=5077.1MB, alloc=52.3MB, time=62.57
x[1] = -1.2048 2.182
h = 0.0001 0.003
y[1] (numeric) = -19.3093184445 2.26777157863
y[1] (closed_form) = -19.3095254337 2.26787838437
absolute error = 0.0002329
relative error = 0.001198 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.322
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2047 2.185
h = 0.001 0.001
y[1] (numeric) = -19.3095462535 2.27089670622
y[1] (closed_form) = -19.309753471 2.27100351887
absolute error = 0.0002331
relative error = 0.001199 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.325
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2037 2.186
h = 0.001 0.003
y[1] (numeric) = -19.3086189186 2.27204541969
y[1] (closed_form) = -19.308826138 2.272152283
absolute error = 0.0002332
relative error = 0.001199 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.327
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2027 2.189
h = 0.0001 0.004
y[1] (numeric) = -19.307913071 2.27527038042
y[1] (closed_form) = -19.3081204985 2.27537738833
absolute error = 0.0002334
relative error = 0.001201 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.33
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2026 2.193
h = 0.003 0.006
y[1] (numeric) = -19.3082528413 2.27943394242
y[1] (closed_form) = -19.3084606746 2.2795409559
absolute error = 0.0002338
relative error = 0.001202 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.333
Order of pole (given) = 0.5 0
NO 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=5123.1MB, alloc=52.3MB, time=63.15
x[1] = -1.1996 2.199
h = 0.0001 0.005
y[1] (numeric) = -19.3058050837 2.28599593234
y[1] (closed_form) = -19.3060136341 2.28610383261
absolute error = 0.0002348
relative error = 0.001208 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.34
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1995 2.204
h = 0.0001 0.003
y[1] (numeric) = -19.3062582965 2.29119835639
y[1] (closed_form) = -19.306467481 2.29130625911
absolute error = 0.0002354
relative error = 0.001211 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.345
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1994 2.207
h = 0.001 0.001
y[1] (numeric) = -19.3064894547 2.2943242801
y[1] (closed_form) = -19.3066988676 2.29443218965
absolute error = 0.0002356
relative error = 0.001212 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.348
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1984 2.208
h = 0.001 0.003
y[1] (numeric) = -19.305563016 2.29547434544
y[1] (closed_form) = -19.3057724307 2.29558230565
absolute error = 0.0002356
relative error = 0.001212 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.349
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1974 2.211
h = 0.0001 0.004
y[1] (numeric) = -19.3048603126 2.29870111372
y[1] (closed_form) = -19.3050699356 2.29880921847
absolute error = 0.0002359
relative error = 0.001213 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.352
Order of pole (given) = 0.5 0
NO 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=5169.0MB, alloc=52.3MB, time=63.71
x[1] = -1.1973 2.215
h = 0.003 0.006
y[1] (numeric) = -19.3052045565 2.30286569928
y[1] (closed_form) = -19.3054145852 2.30297380945
absolute error = 0.0002362
relative error = 0.001215 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.356
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1943 2.221
h = 0.0001 0.005
y[1] (numeric) = -19.3027628603 2.30943242773
y[1] (closed_form) = -19.3029736065 2.30954142452
absolute error = 0.0002373
relative error = 0.00122 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.363
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1942 2.226
h = 0.0001 0.003
y[1] (numeric) = -19.3032216712 2.31463610226
y[1] (closed_form) = -19.3034330516 2.31474510126
absolute error = 0.0002378
relative error = 0.001223 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.367
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1941 2.229
h = 0.001 0.001
y[1] (numeric) = -19.3034561792 2.31776282095
y[1] (closed_form) = -19.303667788 2.31787182669
absolute error = 0.000238
relative error = 0.001224 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.37
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1931 2.23
h = 0.0001 0.004
y[1] (numeric) = -19.3025306373 2.31891423796
y[1] (closed_form) = -19.3027422479 2.31902329437
absolute error = 0.0002381
relative error = 0.001224 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.371
Order of pole (given) = 0.5 0
NO 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=5215.0MB, alloc=52.3MB, time=64.28
x[1] = -1.193 2.234
h = 0.003 0.006
y[1] (numeric) = -19.3028787447 2.32307965003
y[1] (closed_form) = -19.303090761 2.32318871173
absolute error = 0.0002384
relative error = 0.001226 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.375
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.19 2.24
h = 0.0001 0.005
y[1] (numeric) = -19.3004423242 2.32965038361
y[1] (closed_form) = -19.3006550584 2.32976033177
absolute error = 0.0002395
relative error = 0.001232 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.382
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1899 2.245
h = 0.0001 0.003
y[1] (numeric) = -19.3009059693 2.33485506627
y[1] (closed_form) = -19.3011193378 2.33496501645
absolute error = 0.00024
relative error = 0.001235 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.387
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1898 2.248
h = 0.001 0.001
y[1] (numeric) = -19.3011433707 2.33798242843
y[1] (closed_form) = -19.3013569676 2.33809238527
absolute error = 0.0002402
relative error = 0.001236 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.39
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1888 2.249
h = 0.001 0.003
y[1] (numeric) = -19.3002186172 2.33913499806
y[1] (closed_form) = -19.3004322159 2.33924500557
absolute error = 0.0002403
relative error = 0.001236 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.391
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1878 2.252
h = 0.0001 0.004
y[1] (numeric) = -19.2995217887 2.3423650897
y[1] (closed_form) = -19.2997355957 2.34247524163
absolute error = 0.0002405
relative error = 0.001237 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.394
Order of pole (given) = 0.5 0
NO 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=5261.0MB, alloc=52.3MB, time=64.84
x[1] = -1.1877 2.256
h = 0.003 0.006
y[1] (numeric) = -19.299874371 2.34653152245
y[1] (closed_form) = -19.3000885839 2.34664167954
absolute error = 0.0002409
relative error = 0.001239 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.398
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1847 2.262
h = 0.0001 0.005
y[1] (numeric) = -19.2974440161 2.35310699127
y[1] (closed_form) = -19.2976589472 2.35321803463
absolute error = 0.0002419
relative error = 0.001244 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.404
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1846 2.267
h = 0.0001 0.003
y[1] (numeric) = -19.2979132612 2.35831292083
y[1] (closed_form) = -19.2981288266 2.35842396598
absolute error = 0.0002425
relative error = 0.001247 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.409
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1845 2.27
h = 0.001 0.001
y[1] (numeric) = -19.2981540135 2.36144107582
y[1] (closed_form) = -19.2983698073 2.36155212756
absolute error = 0.0002427
relative error = 0.001248 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.412
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1835 2.271
h = 0.001 0.003
y[1] (numeric) = -19.2972301578 2.36259499675
y[1] (closed_form) = -19.2974459535 2.36270609916
absolute error = 0.0002427
relative error = 0.001248 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.413
Order of pole (given) = 0.5 0
NO 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=5306.9MB, alloc=52.3MB, time=65.40
x[1] = -1.1825 2.274
h = 0.0001 0.004
y[1] (numeric) = -19.2965364762 2.36582689314
y[1] (closed_form) = -19.2967524804 2.36593813991
absolute error = 0.000243
relative error = 0.00125 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.416
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1824 2.278
h = 0.003 0.006
y[1] (numeric) = -19.2968935343 2.36999434505
y[1] (closed_form) = -19.2971099443 2.37010559683
absolute error = 0.0002433
relative error = 0.001252 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.42
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1794 2.284
h = 0.0001 0.005
y[1] (numeric) = -19.2944692474 2.37657454734
y[1] (closed_form) = -19.294686376 2.37668668522
absolute error = 0.0002444
relative error = 0.001257 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.427
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1793 2.289
h = 0.0001 0.003
y[1] (numeric) = -19.2949440933 2.38178172188
y[1] (closed_form) = -19.2951618563 2.38189386131
absolute error = 0.0002449
relative error = 0.00126 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.432
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1792 2.292
h = 0.001 0.001
y[1] (numeric) = -19.2951881971 2.38491066858
y[1] (closed_form) = -19.2954061885 2.38502281452
absolute error = 0.0002451
relative error = 0.001261 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.435
Order of pole (given) = 0.5 0
NO 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=5352.9MB, alloc=52.3MB, time=65.97
x[1] = -1.1782 2.293
h = 0.001 0.003
y[1] (numeric) = -19.2942652398 2.38606594059
y[1] (closed_form) = -19.2944832332 2.38617813721
absolute error = 0.0002452
relative error = 0.001261 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.436
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1772 2.296
h = 0.0001 0.004
y[1] (numeric) = -19.2935747062 2.38929964076
y[1] (closed_form) = -19.293792908 2.38941198168
absolute error = 0.0002454
relative error = 0.001262 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.439
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1771 2.3
h = 0.003 0.006
y[1] (numeric) = -19.2939362408 2.39346811031
y[1] (closed_form) = -19.2941548485 2.39358045608
absolute error = 0.0002458
relative error = 0.001264 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.443
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1741 2.306
h = 0.0001 0.005
y[1] (numeric) = -19.2915180241 2.4000530443
y[1] (closed_form) = -19.2917373508 2.40016627599
absolute error = 0.0002468
relative error = 0.00127 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.449
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.174 2.311
h = 0.0001 0.003
y[1] (numeric) = -19.2919984718 2.40526146191
y[1] (closed_form) = -19.292218433 2.40537469492
absolute error = 0.0002474
relative error = 0.001273 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.454
Order of pole (given) = 0.5 0
NO 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=5398.8MB, alloc=52.3MB, time=66.54
x[1] = -1.1739 2.314
h = 0.001 0.001
y[1] (numeric) = -19.2922459278 2.40839119916
y[1] (closed_form) = -19.2924661174 2.4085044386
absolute error = 0.0002476
relative error = 0.001274 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.457
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1729 2.315
h = 0.001 0.003
y[1] (numeric) = -19.2913238694 2.40954782207
y[1] (closed_form) = -19.291544061 2.40966111218
absolute error = 0.0002476
relative error = 0.001274 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.458
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1719 2.318
h = 0.0001 0.004
y[1] (numeric) = -19.2906364847 2.41278332504
y[1] (closed_form) = -19.2908568848 2.41289675939
absolute error = 0.0002479
relative error = 0.001275 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.461
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1718 2.322
h = 0.003 0.006
y[1] (numeric) = -19.2910024966 2.41695281068
y[1] (closed_form) = -19.2912233027 2.41706624974
absolute error = 0.0002482
relative error = 0.001277 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.465
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1688 2.328
h = 0.0001 0.005
y[1] (numeric) = -19.2885903524 2.42354247462
y[1] (closed_form) = -19.2888118779 2.42365679943
absolute error = 0.0002493
relative error = 0.001282 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.472
Order of pole (given) = 0.5 0
NO 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=5444.8MB, alloc=52.3MB, time=67.12
x[1] = -1.1687 2.333
h = 0.0001 0.003
y[1] (numeric) = -19.289076403 2.42875213337
y[1] (closed_form) = -19.2892985629 2.42886645926
absolute error = 0.0002499
relative error = 0.001285 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.477
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1686 2.336
h = 0.001 0.001
y[1] (numeric) = -19.2893272117 2.43188266003
y[1] (closed_form) = -19.2895496001 2.43199699227
absolute error = 0.0002501
relative error = 0.001286 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.48
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1676 2.337
h = 0.0001 0.004
y[1] (numeric) = -19.2884060529 2.43304063363
y[1] (closed_form) = -19.2886284432 2.43315501655
absolute error = 0.0002501
relative error = 0.001286 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.481
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1675 2.341
h = 0.003 0.006
y[1] (numeric) = -19.2887759315 2.43721093933
y[1] (closed_form) = -19.2889987277 2.43732532683
absolute error = 0.0002504
relative error = 0.001288 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.485
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1645 2.347
h = 0.0001 0.005
y[1] (numeric) = -19.2863690724 2.44380460087
y[1] (closed_form) = -19.2865925884 2.44391987395
absolute error = 0.0002515
relative error = 0.001294 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.491
Order of pole (given) = 0.5 0
NO 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=5490.7MB, alloc=52.3MB, time=67.68
x[1] = -1.1644 2.352
h = 0.0001 0.003
y[1] (numeric) = -19.2868599612 2.44901525966
y[1] (closed_form) = -19.2870841117 2.44913053362
absolute error = 0.0002521
relative error = 0.001296 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.496
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1643 2.355
h = 0.001 0.001
y[1] (numeric) = -19.2871136657 2.45214642495
y[1] (closed_form) = -19.2873380447 2.4522617052
absolute error = 0.0002523
relative error = 0.001297 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.499
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1633 2.356
h = 0.001 0.003
y[1] (numeric) = -19.2861932977 2.4533055503
y[1] (closed_form) = -19.2864176787 2.45342088123
absolute error = 0.0002523
relative error = 0.001298 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.5
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1623 2.359
h = 0.0001 0.004
y[1] (numeric) = -19.2855117963 2.45654436773
y[1] (closed_form) = -19.285736386 2.45665984278
absolute error = 0.0002525
relative error = 0.001299 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.503
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1622 2.363
h = 0.003 0.006
y[1] (numeric) = -19.2858861536 2.46071568667
y[1] (closed_form) = -19.2861111493 2.46083116615
absolute error = 0.0002529
relative error = 0.001301 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.507
Order of pole (given) = 0.5 0
NO 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=5536.7MB, alloc=52.3MB, time=68.25
x[1] = -1.1592 2.369
h = 0.0001 0.005
y[1] (numeric) = -19.2834853713 2.46731407483
y[1] (closed_form) = -19.2837110871 2.46743043973
absolute error = 0.0002539
relative error = 0.001306 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.514
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1591 2.374
h = 0.0001 0.003
y[1] (numeric) = -19.2839818647 2.47252597118
y[1] (closed_form) = -19.2842082151 2.47264233673
absolute error = 0.0002545
relative error = 0.001309 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.519
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.159 2.377
h = 0.001 0.001
y[1] (numeric) = -19.284238923 2.47565792376
y[1] (closed_form) = -19.2844655019 2.4757742955
absolute error = 0.0002547
relative error = 0.00131 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.521
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.158 2.378
h = 0.001 0.003
y[1] (numeric) = -19.2833194556 2.47681839941
y[1] (closed_form) = -19.2835460365 2.47693482184
absolute error = 0.0002547
relative error = 0.00131 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.523
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.157 2.381
h = 0.0001 0.004
y[1] (numeric) = -19.2826411058 2.48005901685
y[1] (closed_form) = -19.2828678955 2.48017558333
absolute error = 0.000255
relative error = 0.001312 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.526
Order of pole (given) = 0.5 0
NO 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=5582.6MB, alloc=52.3MB, time=68.81
x[1] = -1.1569 2.385
h = 0.003 0.006
y[1] (numeric) = -19.2830199427 2.48423134749
y[1] (closed_form) = -19.2832471384 2.48434791826
absolute error = 0.0002554
relative error = 0.001313 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.53
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1539 2.391
h = 0.0001 0.005
y[1] (numeric) = -19.2806252394 2.49083446053
y[1] (closed_form) = -19.2808531556 2.49095191653
absolute error = 0.0002564
relative error = 0.001319 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.536
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1538 2.396
h = 0.0001 0.003
y[1] (numeric) = -19.2811273384 2.49604759252
y[1] (closed_form) = -19.2813558892 2.49616504894
absolute error = 0.000257
relative error = 0.001322 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.541
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1537 2.399
h = 0.001 0.001
y[1] (numeric) = -19.2813877511 2.49918033122
y[1] (closed_form) = -19.2816165305 2.49929779376
absolute error = 0.0002572
relative error = 0.001323 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.544
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1527 2.4
h = 0.001 0.003
y[1] (numeric) = -19.2804691849 2.50034215698
y[1] (closed_form) = -19.2806979663 2.50045967022
absolute error = 0.0002572
relative error = 0.001323 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.545
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1517 2.403
h = 0.0001 0.004
y[1] (numeric) = -19.2797939877 2.50358457344
y[1] (closed_form) = -19.2800229778 2.50370223067
absolute error = 0.0002574
relative error = 0.001324 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.548
Order of pole (given) = 0.5 0
NO 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=5628.5MB, alloc=52.3MB, time=69.38
x[1] = -1.1516 2.407
h = 0.003 0.006
y[1] (numeric) = -19.2801773049 2.50775791426
y[1] (closed_form) = -19.2804067012 2.50787557563
absolute error = 0.0002578
relative error = 0.001326 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.552
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1486 2.413
h = 0.0001 0.005
y[1] (numeric) = -19.2777886828 2.5143657504
y[1] (closed_form) = -19.2780188 2.51448429682
absolute error = 0.0002589
relative error = 0.001331 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.559
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1485 2.418
h = 0.0001 0.003
y[1] (numeric) = -19.2782963884 2.51958011611
y[1] (closed_form) = -19.2785271402 2.51969866272
absolute error = 0.0002594
relative error = 0.001334 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.564
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1484 2.421
h = 0.001 0.001
y[1] (numeric) = -19.2785601562 2.52271363981
y[1] (closed_form) = -19.2787911366 2.52283219244
absolute error = 0.0002596
relative error = 0.001335 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.566
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1474 2.422
h = 0.001 0.003
y[1] (numeric) = -19.2776424917 2.52387681548
y[1] (closed_form) = -19.2778734741 2.52399541881
absolute error = 0.0002597
relative error = 0.001335 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.568
Order of pole (given) = 0.5 0
NO 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=5674.4MB, alloc=52.3MB, time=69.94
x[1] = -1.1464 2.425
h = 0.0001 0.004
y[1] (numeric) = -19.2769704479 2.52712102998
y[1] (closed_form) = -19.2772016393 2.52723977725
absolute error = 0.0002599
relative error = 0.001337 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.571
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1463 2.429
h = 0.003 0.006
y[1] (numeric) = -19.2773582463 2.53129537944
y[1] (closed_form) = -19.2775898437 2.5314141307
absolute error = 0.0002603
relative error = 0.001339 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.575
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1433 2.435
h = 0.0001 0.005
y[1] (numeric) = -19.2749757078 2.53790793692
y[1] (closed_form) = -19.2752080266 2.53802757305
absolute error = 0.0002613
relative error = 0.001344 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.581
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1432 2.44
h = 0.0001 0.003
y[1] (numeric) = -19.2754890209 2.54312353443
y[1] (closed_form) = -19.2757219743 2.54324317052
absolute error = 0.0002619
relative error = 0.001347 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.586
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1431 2.443
h = 0.001 0.001
y[1] (numeric) = -19.2757561443 2.54625784197
y[1] (closed_form) = -19.2759893264 2.546377484
absolute error = 0.0002621
relative error = 0.001348 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.589
Order of pole (given) = 0.5 0
NO 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=5720.4MB, alloc=52.3MB, time=70.50
x[1] = -1.1421 2.444
h = 0.0001 0.004
y[1] (numeric) = -19.2748393821 2.54742236735
y[1] (closed_form) = -19.2750725663 2.54754206009
absolute error = 0.0002621
relative error = 0.001348 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.59
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.142 2.448
h = 0.003 0.006
y[1] (numeric) = -19.2752310503 2.5515975304
y[1] (closed_form) = -19.2754646406 2.551717227
absolute error = 0.0002625
relative error = 0.00135 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.594
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.139 2.454
h = 0.0001 0.005
y[1] (numeric) = -19.2728538065 2.55821407793
y[1] (closed_form) = -19.2730881183 2.55833465924
absolute error = 0.0002635
relative error = 0.001355 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.601
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1389 2.459
h = 0.0001 0.003
y[1] (numeric) = -19.2733719617 2.56343066738
y[1] (closed_form) = -19.2736069084 2.56355124845
absolute error = 0.0002641
relative error = 0.001358 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.605
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1388 2.462
h = 0.001 0.001
y[1] (numeric) = -19.2736419833 2.56656560872
y[1] (closed_form) = -19.2738771586 2.56668619567
absolute error = 0.0002643
relative error = 0.001359 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.608
Order of pole (given) = 0.5 0
NO 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=5766.4MB, alloc=52.3MB, time=71.07
x[1] = -1.1378 2.463
h = 0.001 0.003
y[1] (numeric) = -19.2727260144 2.56773128497
y[1] (closed_form) = -19.2729611917 2.56785192262
absolute error = 0.0002643
relative error = 0.001359 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.61
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1368 2.466
h = 0.0001 0.004
y[1] (numeric) = -19.2720598625 2.57097880503
y[1] (closed_form) = -19.2722952488 2.57109958649
absolute error = 0.0002646
relative error = 0.001361 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.613
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1367 2.47
h = 0.003 0.006
y[1] (numeric) = -19.2724560132 2.57515497386
y[1] (closed_form) = -19.2726918058 2.57527575904
absolute error = 0.0002649
relative error = 0.001363 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.617
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1337 2.476
h = 0.0001 0.005
y[1] (numeric) = -19.2700848571 2.58177623941
y[1] (closed_form) = -19.2703213717 2.58189790912
absolute error = 0.000266
relative error = 0.001368 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.623
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1336 2.481
h = 0.0001 0.003
y[1] (numeric) = -19.2706086217 2.58699405707
y[1] (closed_form) = -19.2708457711 2.58711572631
absolute error = 0.0002665
relative error = 0.001371 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.628
Order of pole (given) = 0.5 0
NO 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=5812.2MB, alloc=52.3MB, time=71.64
x[1] = -1.1335 2.484
h = 0.001 0.001
y[1] (numeric) = -19.270882 2.59012978012
y[1] (closed_form) = -19.2711193781 2.59025145516
absolute error = 0.0002667
relative error = 0.001372 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.631
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1325 2.485
h = 0.001 0.003
y[1] (numeric) = -19.2699669345 2.59129680569
y[1] (closed_form) = -19.2702043146 2.59141853144
absolute error = 0.0002668
relative error = 0.001372 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.632
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1315 2.488
h = 0.0001 0.004
y[1] (numeric) = -19.2693039388 2.59454612099
y[1] (closed_form) = -19.269541528 2.59466799049
absolute error = 0.000267
relative error = 0.001373 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.635
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1314 2.492
h = 0.003 0.006
y[1] (numeric) = -19.2697045728 2.59872329407
y[1] (closed_form) = -19.2699425683 2.59884516714
absolute error = 0.0002674
relative error = 0.001375 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.639
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1284 2.498
h = 0.0001 0.005
y[1] (numeric) = -19.2673395069 2.60534927587
y[1] (closed_form) = -19.2675782247 2.6054720333
absolute error = 0.0002684
relative error = 0.001381 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.646
Order of pole (given) = 0.5 0
NO 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=5858.2MB, alloc=52.3MB, time=72.20
x[1] = -1.1283 2.503
h = 0.0001 0.003
y[1] (numeric) = -19.2678688817 2.61056831983
y[1] (closed_form) = -19.2681082344 2.61069107655
absolute error = 0.000269
relative error = 0.001383 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.65
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1282 2.506
h = 0.001 0.001
y[1] (numeric) = -19.2681456174 2.61370482344
y[1] (closed_form) = -19.2683851988 2.61382758587
absolute error = 0.0002692
relative error = 0.001384 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.653
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1272 2.507
h = 0.001 0.003
y[1] (numeric) = -19.2672314558 2.61487319813
y[1] (closed_form) = -19.2674710393 2.61499601128
absolute error = 0.0002692
relative error = 0.001385 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.655
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1262 2.51
h = 0.0001 0.004
y[1] (numeric) = -19.2665716172 2.6181243077
y[1] (closed_form) = -19.2668114098 2.61824726453
absolute error = 0.0002695
relative error = 0.001386 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.658
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1261 2.514
h = 0.003 0.006
y[1] (numeric) = -19.2669767354 2.62230248349
y[1] (closed_form) = -19.2672169344 2.62242544375
absolute error = 0.0002698
relative error = 0.001388 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.662
Order of pole (given) = 0.5 0
NO 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=5904.3MB, alloc=52.3MB, time=72.77
x[1] = -1.1231 2.52
h = 0.0001 0.005
y[1] (numeric) = -19.2646177618 2.62893317978
y[1] (closed_form) = -19.2648586835 2.62905702421
absolute error = 0.0002709
relative error = 0.001393 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.668
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.123 2.525
h = 0.0001 0.003
y[1] (numeric) = -19.2651527479 2.63415344811
y[1] (closed_form) = -19.2653943045 2.6342772916
absolute error = 0.0002715
relative error = 0.001396 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.673
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1229 2.528
h = 0.001 0.001
y[1] (numeric) = -19.2654328415 2.63729073113
y[1] (closed_form) = -19.2656746268 2.63741458025
absolute error = 0.0002717
relative error = 0.001397 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.676
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1219 2.529
h = 0.001 0.003
y[1] (numeric) = -19.2645195845 2.63846045474
y[1] (closed_form) = -19.2647613719 2.63858435459
absolute error = 0.0002717
relative error = 0.001397 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.677
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1209 2.532
h = 0.0001 0.004
y[1] (numeric) = -19.2638629039 2.6417133576
y[1] (closed_form) = -19.2641049006 2.64183740107
absolute error = 0.0002719
relative error = 0.001399 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.68
Order of pole (given) = 0.5 0
NO 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=5950.1MB, alloc=52.3MB, time=73.33
x[1] = -1.1208 2.536
h = 0.003 0.006
y[1] (numeric) = -19.2642725071 2.64589253457
y[1] (closed_form) = -19.2645149101 2.64601658131
absolute error = 0.0002723
relative error = 0.0014 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.684
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1178 2.542
h = 0.0001 0.005
y[1] (numeric) = -19.2619196282 2.65252794357
y[1] (closed_form) = -19.2621627543 2.65265287431
absolute error = 0.0002733
relative error = 0.001406 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.691
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1177 2.547
h = 0.0001 0.003
y[1] (numeric) = -19.2624602264 2.65774943435
y[1] (closed_form) = -19.2627039876 2.65787436392
absolute error = 0.0002739
relative error = 0.001409 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.695
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1176 2.55
h = 0.001 0.001
y[1] (numeric) = -19.2627436786 2.66088749564
y[1] (closed_form) = -19.2629876685 2.66101243076
absolute error = 0.0002741
relative error = 0.00141 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.698
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1166 2.551
h = 0.0001 0.004
y[1] (numeric) = -19.2618313266 2.66205856797
y[1] (closed_form) = -19.2620753187 2.66218355382
absolute error = 0.0002741
relative error = 0.00141 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.7
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1165 2.555
h = 0.003 0.006
y[1] (numeric) = -19.2622448028 2.66623855207
y[1] (closed_form) = -19.2624892012 2.66636354105
absolute error = 0.0002745
relative error = 0.001412 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.703
Order of pole (given) = 0.5 0
NO 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=5996.0MB, alloc=52.3MB, time=73.89
x[1] = -1.1135 2.561
h = 0.0001 0.005
y[1] (numeric) = -19.2598972279 2.67287794357
y[1] (closed_form) = -19.2601423498 2.67300381639
absolute error = 0.0002756
relative error = 0.001417 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.71
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1134 2.566
h = 0.0001 0.003
y[1] (numeric) = -19.2604426723 2.67810041818
y[1] (closed_form) = -19.2606884292 2.67822628963
absolute error = 0.0002761
relative error = 0.00142 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.715
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1133 2.569
h = 0.001 0.001
y[1] (numeric) = -19.2607290251 2.68123910844
y[1] (closed_form) = -19.2609750107 2.68136498537
absolute error = 0.0002763
relative error = 0.001421 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.718
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1123 2.57
h = 0.001 0.003
y[1] (numeric) = -19.2598174688 2.68241133076
y[1] (closed_form) = -19.2600634566 2.68253725842
absolute error = 0.0002763
relative error = 0.001421 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.719
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1113 2.573
h = 0.0001 0.004
y[1] (numeric) = -19.2591666886 2.68566753025
y[1] (closed_form) = -19.2594128857 2.68579360142
absolute error = 0.0002766
relative error = 0.001422 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.722
Order of pole (given) = 0.5 0
NO 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=6041.8MB, alloc=52.3MB, time=74.46
x[1] = -1.1112 2.577
h = 0.003 0.006
y[1] (numeric) = -19.2595846511 2.68984851266
y[1] (closed_form) = -19.2598312546 2.68997458682
absolute error = 0.000277
relative error = 0.001424 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.726
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1082 2.583
h = 0.0001 0.005
y[1] (numeric) = -19.2572431751 2.69649261355
y[1] (closed_form) = -19.2574905025 2.69661957137
absolute error = 0.000278
relative error = 0.00143 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.733
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1081 2.588
h = 0.0001 0.003
y[1] (numeric) = -19.2577942334 2.70171630703
y[1] (closed_form) = -19.2580421959 2.70184326325
absolute error = 0.0002786
relative error = 0.001433 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.737
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.108 2.591
h = 0.001 0.001
y[1] (numeric) = -19.2580839458 2.70485577342
y[1] (closed_form) = -19.2583321371 2.70498273503
absolute error = 0.0002788
relative error = 0.001434 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.74
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.107 2.592
h = 0.001 0.003
y[1] (numeric) = -19.2571732957 2.70602934407
y[1] (closed_form) = -19.2574214891 2.70615635642
absolute error = 0.0002788
relative error = 0.001434 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.742
Order of pole (given) = 0.5 0
NO 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=6087.8MB, alloc=52.3MB, time=75.02
x[1] = -1.106 2.595
h = 0.0001 0.004
y[1] (numeric) = -19.2565256763 2.70928733404
y[1] (closed_form) = -19.2567740791 2.70941448983
absolute error = 0.0002791
relative error = 0.001435 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.745
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1059 2.599
h = 0.003 0.006
y[1] (numeric) = -19.2569481259 2.71346931323
y[1] (closed_form) = -19.2571969352 2.71359647187
absolute error = 0.0002794
relative error = 0.001437 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.748
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1029 2.605
h = 0.0001 0.005
y[1] (numeric) = -19.2546127511 2.72011812174
y[1] (closed_form) = -19.2548622846 2.72024616387
absolute error = 0.0002805
relative error = 0.001442 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.755
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1028 2.61
h = 0.0001 0.003
y[1] (numeric) = -19.2551694244 2.72534303216
y[1] (closed_form) = -19.2554195932 2.72547107245
absolute error = 0.000281
relative error = 0.001445 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.76
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1027 2.613
h = 0.001 0.001
y[1] (numeric) = -19.2554624971 2.72848327353
y[1] (closed_form) = -19.2557128945 2.72861131913
absolute error = 0.0002812
relative error = 0.001446 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.763
Order of pole (given) = 0.5 0
NO 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=6133.7MB, alloc=52.3MB, time=75.59
x[1] = -1.1017 2.614
h = 0.001 0.003
y[1] (numeric) = -19.2545527537 2.72965819232
y[1] (closed_form) = -19.2548031534 2.72978628866
absolute error = 0.0002813
relative error = 0.001446 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.764
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1007 2.617
h = 0.0001 0.004
y[1] (numeric) = -19.253908296 2.73291797179
y[1] (closed_form) = -19.2541589052 2.73304621151
absolute error = 0.0002815
relative error = 0.001448 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.767
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1006 2.621
h = 0.003 0.006
y[1] (numeric) = -19.2543352336 2.73710094622
y[1] (closed_form) = -19.2545862492 2.73722918865
absolute error = 0.0002819
relative error = 0.001449 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.771
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0976 2.627
h = 0.0001 0.005
y[1] (numeric) = -19.2520059621 2.74375446059
y[1] (closed_form) = -19.2522577025 2.74388358631
absolute error = 0.0002829
relative error = 0.001455 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.778
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0975 2.632
h = 0.0001 0.003
y[1] (numeric) = -19.2525682514 2.74898058602
y[1] (closed_form) = -19.252820627 2.74910970967
absolute error = 0.0002835
relative error = 0.001458 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.782
Order of pole (given) = 0.5 0
NO 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=6179.7MB, alloc=52.3MB, time=76.15
x[1] = -1.0974 2.635
h = 0.001 0.001
y[1] (numeric) = -19.2528646849 2.75212160122
y[1] (closed_form) = -19.2531172892 2.75225073011
absolute error = 0.0002837
relative error = 0.001459 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.785
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0964 2.636
h = 0.001 0.003
y[1] (numeric) = -19.2519558488 2.75329786795
y[1] (closed_form) = -19.2522084554 2.75342704758
absolute error = 0.0002837
relative error = 0.001459 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.787
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0954 2.639
h = 0.0001 0.004
y[1] (numeric) = -19.2513145538 2.75655943593
y[1] (closed_form) = -19.2515673699 2.75668875888
absolute error = 0.000284
relative error = 0.00146 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.79
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0953 2.643
h = 0.003 0.006
y[1] (numeric) = -19.2517459801 2.76074340408
y[1] (closed_form) = -19.2519992027 2.76087272959
absolute error = 0.0002843
relative error = 0.001462 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.794
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0923 2.649
h = 0.0001 0.005
y[1] (numeric) = -19.2494228144 2.76740162253
y[1] (closed_form) = -19.2496767621 2.76753183115
absolute error = 0.0002854
relative error = 0.001467 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.8
Order of pole (given) = 0.5 0
NO 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=6225.7MB, alloc=52.3MB, time=76.72
x[1] = -1.0922 2.654
h = 0.0001 0.003
y[1] (numeric) = -19.2499907206 2.77262896105
y[1] (closed_form) = -19.2502453036 2.77275916737
absolute error = 0.0002859
relative error = 0.00147 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.805
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0921 2.657
h = 0.001 0.001
y[1] (numeric) = -19.2502905155 2.77577074894
y[1] (closed_form) = -19.2505453272 2.77590096042
absolute error = 0.0002862
relative error = 0.001471 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.808
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0911 2.658
h = 0.0001 0.004
y[1] (numeric) = -19.2493825873 2.7769483634
y[1] (closed_form) = -19.2496374013 2.77707862562
absolute error = 0.0002862
relative error = 0.001471 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.809
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.091 2.662
h = 0.003 0.006
y[1] (numeric) = -19.2498178899 2.7811331322
y[1] (closed_form) = -19.2500731104 2.78126339684
absolute error = 0.0002865
relative error = 0.001473 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.813
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.088 2.668
h = 0.0001 0.005
y[1] (numeric) = -19.2475000376 2.78779532557
y[1] (closed_form) = -19.2477559835 2.78792647317
absolute error = 0.0002876
relative error = 0.001479 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.82
Order of pole (given) = 0.5 0
NO 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=6271.5MB, alloc=52.3MB, time=77.29
x[1] = -1.0879 2.673
h = 0.0001 0.003
y[1] (numeric) = -19.2480727938 2.79302363982
y[1] (closed_form) = -19.248329375 2.79315478492
absolute error = 0.0002882
relative error = 0.001482 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.824
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0878 2.676
h = 0.001 0.001
y[1] (numeric) = -19.2483754917 2.79616605185
y[1] (closed_form) = -19.2486323018 2.79629720203
absolute error = 0.0002884
relative error = 0.001483 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.827
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0868 2.677
h = 0.001 0.003
y[1] (numeric) = -19.2474683616 2.7973448154
y[1] (closed_form) = -19.2477251739 2.79747601633
absolute error = 0.0002884
relative error = 0.001483 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.828
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0858 2.68
h = 0.0001 0.004
y[1] (numeric) = -19.2468329754 2.80060967109
y[1] (closed_form) = -19.2470899973 2.80074101522
absolute error = 0.0002886
relative error = 0.001484 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.832
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0857 2.684
h = 0.003 0.006
y[1] (numeric) = -19.247272768 2.80479543073
y[1] (closed_form) = -19.2475301966 2.80492677715
absolute error = 0.000289
relative error = 0.001486 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.835
Order of pole (given) = 0.5 0
NO 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=6317.5MB, alloc=52.3MB, time=77.86
x[1] = -1.0827 2.69
h = 0.0001 0.005
y[1] (numeric) = -19.2449610257 2.81146232486
y[1] (closed_form) = -19.24521918 2.81159455405
absolute error = 0.00029
relative error = 0.001491 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.842
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0826 2.695
h = 0.0001 0.003
y[1] (numeric) = -19.2455394006 2.8166918486
y[1] (closed_form) = -19.2457981903 2.81682407506
absolute error = 0.0002906
relative error = 0.001494 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.847
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0825 2.698
h = 0.001 0.001
y[1] (numeric) = -19.245845461 2.81983503118
y[1] (closed_form) = -19.2461044796 2.81996726264
absolute error = 0.0002908
relative error = 0.001495 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.85
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0815 2.699
h = 0.001 0.003
y[1] (numeric) = -19.2449392399 2.82101514208
y[1] (closed_form) = -19.2451982607 2.82114742429
absolute error = 0.0002908
relative error = 0.001495 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.851
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0805 2.702
h = 0.0001 0.004
y[1] (numeric) = -19.244307019 2.82428178348
y[1] (closed_form) = -19.2445662496 2.82441420882
absolute error = 0.0002911
relative error = 0.001497 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.854
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0804 2.706
h = 0.003 0.006
y[1] (numeric) = -19.2447513026 2.82846853243
y[1] (closed_form) = -19.2450109398 2.82860095991
absolute error = 0.0002915
relative error = 0.001498 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.858
Order of pole (given) = 0.5 0
NO 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=6363.5MB, alloc=52.3MB, time=78.42
x[1] = -1.0774 2.712
h = 0.0001 0.005
y[1] (numeric) = -19.2424456725 2.83514012553
y[1] (closed_form) = -19.2427060359 2.83527343561
absolute error = 0.0002925
relative error = 0.001504 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.865
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0773 2.717
h = 0.0001 0.003
y[1] (numeric) = -19.2430296671 2.84037085685
y[1] (closed_form) = -19.2432906659 2.84050416397
absolute error = 0.0002931
relative error = 0.001507 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.869
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0772 2.72
h = 0.001 0.001
y[1] (numeric) = -19.2433390906 2.84351480883
y[1] (closed_form) = -19.2436003183 2.84364812086
absolute error = 0.0002933
relative error = 0.001508 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.872
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0762 2.721
h = 0.001 0.003
y[1] (numeric) = -19.242433779 2.84469626688
y[1] (closed_form) = -19.2426950089 2.84482962966
absolute error = 0.0002933
relative error = 0.001508 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.874
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0752 2.724
h = 0.0001 0.004
y[1] (numeric) = -19.2418047244 2.84796469299
y[1] (closed_form) = -19.2420661642 2.84809819886
absolute error = 0.0002936
relative error = 0.001509 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.877
Order of pole (given) = 0.5 0
NO 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=6409.5MB, alloc=52.3MB, time=78.98
x[1] = -1.0751 2.728
h = 0.003 0.006
y[1] (numeric) = -19.2422534997 2.85215242972
y[1] (closed_form) = -19.2425153462 2.85228593758
absolute error = 0.0002939
relative error = 0.001511 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.881
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0721 2.734
h = 0.0001 0.005
y[1] (numeric) = -19.2399539841 2.85882872003
y[1] (closed_form) = -19.2402165571 2.8589631103
absolute error = 0.000295
relative error = 0.001516 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.887
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.072 2.739
h = 0.0001 0.003
y[1] (numeric) = -19.2405435993 2.864060657
y[1] (closed_form) = -19.2408068078 2.86419504407
absolute error = 0.0002955
relative error = 0.001519 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.892
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0719 2.742
h = 0.001 0.001
y[1] (numeric) = -19.2408563866 2.86720537723
y[1] (closed_form) = -19.241119824 2.86733976914
absolute error = 0.0002957
relative error = 0.00152 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.895
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0709 2.743
h = 0.001 0.003
y[1] (numeric) = -19.239951985 2.86838818222
y[1] (closed_form) = -19.2402154248 2.86852262488
absolute error = 0.0002958
relative error = 0.00152 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.896
Order of pole (given) = 0.5 0
NO 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=6455.4MB, alloc=52.3MB, time=79.55
x[1] = -1.0699 2.746
h = 0.0001 0.004
y[1] (numeric) = -19.2393260977 2.87165839208
y[1] (closed_form) = -19.2395897474 2.87179297776
absolute error = 0.000296
relative error = 0.001522 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.899
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0698 2.75
h = 0.003 0.006
y[1] (numeric) = -19.2397793655 2.87584711505
y[1] (closed_form) = -19.2400434219 2.87598170257
absolute error = 0.0002964
relative error = 0.001523 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.903
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0668 2.756
h = 0.0001 0.005
y[1] (numeric) = -19.2374859668 2.88252810078
y[1] (closed_form) = -19.23775075 2.88266357054
absolute error = 0.0002974
relative error = 0.001529 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.91
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0667 2.761
h = 0.0001 0.003
y[1] (numeric) = -19.2380812035 2.88776124148
y[1] (closed_form) = -19.2383466223 2.88789670781
absolute error = 0.000298
relative error = 0.001532 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.914
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0666 2.764
h = 0.001 0.001
y[1] (numeric) = -19.2383973551 2.89090672882
y[1] (closed_form) = -19.2386630028 2.8910421999
absolute error = 0.0002982
relative error = 0.001533 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.917
Order of pole (given) = 0.5 0
NO 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=6501.4MB, alloc=52.3MB, time=80.12
x[1] = -1.0656 2.765
h = 0.0001 0.004
y[1] (numeric) = -19.2374938642 2.89209088054
y[1] (closed_form) = -19.2377595143 2.89222640239
absolute error = 0.0002982
relative error = 0.001533 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.919
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0655 2.769
h = 0.003 0.006
y[1] (numeric) = -19.2379510114 2.89628039768
y[1] (closed_form) = -19.2382170682 2.89641592123
absolute error = 0.0002986
relative error = 0.001535 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.922
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0625 2.775
h = 0.0001 0.005
y[1] (numeric) = -19.2356629355 2.90296535076
y[1] (closed_form) = -19.2359297195 2.90310175639
absolute error = 0.0002996
relative error = 0.00154 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.929
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0624 2.78
h = 0.0001 0.003
y[1] (numeric) = -19.2362630262 2.90819945906
y[1] (closed_form) = -19.2365304458 2.90833586106
absolute error = 0.0003002
relative error = 0.001543 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.934
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0623 2.783
h = 0.001 0.001
y[1] (numeric) = -19.2365820832 2.9113455657
y[1] (closed_form) = -19.2368497318 2.91148197238
absolute error = 0.0003004
relative error = 0.001544 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.937
Order of pole (given) = 0.5 0
NO 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=6547.4MB, alloc=52.3MB, time=80.68
x[1] = -1.0613 2.784
h = 0.001 0.003
y[1] (numeric) = -19.2356793928 2.91253086563
y[1] (closed_form) = -19.2359470437 2.91266732307
absolute error = 0.0003004
relative error = 0.001544 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.938
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0603 2.787
h = 0.0001 0.004
y[1] (numeric) = -19.2350594228 2.91580435426
y[1] (closed_form) = -19.2353272837 2.9159409546
absolute error = 0.0003007
relative error = 0.001546 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.941
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0602 2.791
h = 0.003 0.006
y[1] (numeric) = -19.2355210639 2.91999485476
y[1] (closed_form) = -19.2357893315 2.92013145667
absolute error = 0.000301
relative error = 0.001547 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.945
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0572 2.797
h = 0.0001 0.005
y[1] (numeric) = -19.233239109 2.92668449994
y[1] (closed_form) = -19.2335081043 2.92682198375
absolute error = 0.0003021
relative error = 0.001553 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.952
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0571 2.802
h = 0.0001 0.003
y[1] (numeric) = -19.233844823 2.93191980837
y[1] (closed_form) = -19.234114454 2.93205728832
absolute error = 0.0003027
relative error = 0.001556 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.956
Order of pole (given) = 0.5 0
NO 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=6593.4MB, alloc=52.3MB, time=81.25
x[1] = -1.057 2.805
h = 0.001 0.001
y[1] (numeric) = -19.2341672454 2.93506667997
y[1] (closed_form) = -19.2344371054 2.93520416451
absolute error = 0.0003029
relative error = 0.001557 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.959
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.056 2.806
h = 0.001 0.003
y[1] (numeric) = -19.2332654668 2.93625332626
y[1] (closed_form) = -19.2335353291 2.93639086157
absolute error = 0.0003029
relative error = 0.001557 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.961
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.055 2.809
h = 0.0001 0.004
y[1] (numeric) = -19.2326486667 2.93952859581
y[1] (closed_form) = -19.2329187391 2.93966627396
absolute error = 0.0003031
relative error = 0.001558 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.964
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0549 2.813
h = 0.003 0.006
y[1] (numeric) = -19.2331148025 2.94372007815
y[1] (closed_form) = -19.2333852817 2.94385775772
absolute error = 0.0003035
relative error = 0.00156 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.968
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0519 2.819
h = 0.0001 0.005
y[1] (numeric) = -19.2308389709 2.95041441365
y[1] (closed_form) = -19.2311101781 2.95055297493
absolute error = 0.0003046
relative error = 0.001565 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.974
Order of pole (given) = 0.5 0
NO 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=6639.4MB, alloc=52.3MB, time=81.82
x[1] = -1.0518 2.824
h = 0.0001 0.003
y[1] (numeric) = -19.2314503093 2.95565092029
y[1] (closed_form) = -19.2317221522 2.95578947748
absolute error = 0.0003051
relative error = 0.001568 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.979
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0517 2.827
h = 0.001 0.001
y[1] (numeric) = -19.2317760977 2.95879855569
y[1] (closed_form) = -19.2320481696 2.9589371174
absolute error = 0.0003053
relative error = 0.001569 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.982
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0507 2.828
h = 0.001 0.003
y[1] (numeric) = -19.2308752313 2.95998654813
y[1] (closed_form) = -19.2311473057 2.96012516061
absolute error = 0.0003053
relative error = 0.001569 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.983
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0497 2.831
h = 0.0001 0.004
y[1] (numeric) = -19.2302616022 2.96326359763
y[1] (closed_form) = -19.2305338867 2.96340235288
absolute error = 0.0003056
relative error = 0.001571 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.986
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0496 2.835
h = 0.003 0.006
y[1] (numeric) = -19.2307322334 2.96745606027
y[1] (closed_form) = -19.2310049248 2.96759481679
absolute error = 0.000306
relative error = 0.001572 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.99
Order of pole (given) = 0.5 0
NO 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=6685.3MB, alloc=52.3MB, time=82.38
x[1] = -1.0466 2.841
h = 0.0001 0.005
y[1] (numeric) = -19.2284625274 2.97415508431
y[1] (closed_form) = -19.2287359472 2.97429472237
absolute error = 0.000307
relative error = 0.001578 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.997
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0465 2.846
h = 0.0001 0.003
y[1] (numeric) = -19.2290794911 2.97939278723
y[1] (closed_form) = -19.2293535466 2.97953242096
absolute error = 0.0003076
relative error = 0.001581 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.001
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0464 2.849
h = 0.001 0.001
y[1] (numeric) = -19.2294086461 2.9825411853
y[1] (closed_form) = -19.2296829306 2.98268082347
absolute error = 0.0003078
relative error = 0.001582 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.004
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0454 2.85
h = 0.001 0.003
y[1] (numeric) = -19.2285086926 2.98373052369
y[1] (closed_form) = -19.2287829796 2.98387021263
absolute error = 0.0003078
relative error = 0.001582 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.006
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0444 2.853
h = 0.0001 0.004
y[1] (numeric) = -19.2278982353 2.98700935215
y[1] (closed_form) = -19.2281727325 2.9871491838
absolute error = 0.0003081
relative error = 0.001583 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.009
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0443 2.857
h = 0.003 0.006
y[1] (numeric) = -19.2283733629 2.99120279354
y[1] (closed_form) = -19.228648267 2.99134262632
absolute error = 0.0003084
relative error = 0.001585 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.013
Order of pole (given) = 0.5 0
NO 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=6731.1MB, alloc=52.3MB, time=82.94
x[1] = -1.0413 2.863
h = 0.0001 0.005
y[1] (numeric) = -19.2261097847 2.99790650435
y[1] (closed_form) = -19.2263854176 2.99804721848
absolute error = 0.0003095
relative error = 0.00159 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.019
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0412 2.868
h = 0.0001 0.003
y[1] (numeric) = -19.2267323746 3.00314540162
y[1] (closed_form) = -19.2270086434 3.00328611119
absolute error = 0.00031
relative error = 0.001593 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.024
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0411 2.871
h = 0.001 0.001
y[1] (numeric) = -19.2270648968 3.00629456121
y[1] (closed_form) = -19.2273413945 3.00643527514
absolute error = 0.0003102
relative error = 0.001594 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.027
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0401 2.872
h = 0.001 0.003
y[1] (numeric) = -19.2261658568 3.00748524534
y[1] (closed_form) = -19.226442357 3.00762601004
absolute error = 0.0003103
relative error = 0.001594 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.028
Order of pole (given) = 0.5 0
NO 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 ) = cosh ( sqrt ( 0.1 * x + 0.2 ) ) ;
Iterations = 754
Total Elapsed Time = 1 Minutes 23 Seconds
Expected Time Remaining = 0 Seconds
Optimized Time Remaining = 0 Seconds
Expected Total Time = 1 Minutes 23 Seconds
> quit
memory used=6775.8MB, alloc=52.3MB, time=83.47