|\^/| 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(cos(c(x)) - sin(c(x))) ;
> end;
exact_soln_y := proc(x) return cos(c(x)) - sin(c(x)) end proc
> next_delta := proc()
> global glob_nxt, x_delta;
> x_delta := [ 0.001 + 0.00004 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.000 + 0.000 * I ];
> glob_nxt := glob_nxt + 1;
> it := x_delta[glob_nxt];
> return it;
> end;
Warning, `it` is implicitly declared local to procedure `next_delta`
next_delta := proc()
local it;
global glob_nxt, x_delta;
x_delta := [0.001 + 0.00004*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0. + 0.*I];
glob_nxt := glob_nxt + 1;
it := x_delta[glob_nxt];
return it
end proc
#END USER DEF BLOCK
#END BLOCK 3
#END USER FUNCTION BLOCK
# before write_aux functions
# Begin Function number 2
> display_poles := proc()
> local rad_given;
> global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ;
> if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1
> rad_given := float_abs(array_x[1] - (array_given_rad_poles[1,1] + array_given_rad_poles[1,2] * I ));
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," ");
> omniout_complex(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," ");
> if ((float_abs(rad_given) < float_abs(glob_least_given_sing)) and
> (float_abs(rad_given) > 0.0)) then # if number 2
> glob_least_given_sing := rad_given;
> fi;# end if 2;
> elif
> (glob_type_given_pole = 3) then # if number 2
> omniout_str(ALWAYS,"NO POLE (given) for Equation 1");
> elif
> (glob_type_given_pole = 5) then # if number 3
> omniout_str(ALWAYS,"SOME POLE (given) for Equation 1");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 1");
> fi;# end if 3;
> if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," ");
> if ((float_abs(array_rad_test_poles[1,1]) < glob_least_ratio_sing)) then # if number 4
> glob_least_ratio_sing := array_rad_test_poles[1,1];
> fi;# end if 4;
> omniout_complex(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," ");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," ");
> if ((float_abs(array_rad_test_poles[1,2]) < glob_least_3_sing)) then # if number 4
> glob_least_3_sing := array_rad_test_poles[1,2];
> fi;# end if 4;
> omniout_complex(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," ");
> if ((float_abs(array_rad_test_poles[1,3]) < glob_least_6_sing)) then # if number 4
> glob_least_6_sing := array_rad_test_poles[1,3];
> fi;# end if 4;
> omniout_complex(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1");
> fi;# end if 3
> ;
> end;
display_poles := proc()
local rad_given;
global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float,
glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord,
glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
glob_least_3_sing, glob_least_6_sing, glob_least_given_sing,
glob_least_ratio_sing, array_x;
if glob_type_given_pole = 1 or glob_type_given_pole = 2 then
rad_given := float_abs(array_x[1] - array_given_rad_poles[1, 1]
- array_given_rad_poles[1, 2]*I);
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 1 ", 4,
rad_given, 4, " ");
omniout_complex(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles[1, 1], 4, " ");
if float_abs(rad_given) < float_abs(glob_least_given_sing) and
0. < float_abs(rad_given) then glob_least_given_sing := rad_given
end if
elif glob_type_given_pole = 3 then
omniout_str(ALWAYS, "NO POLE (given) for Equation 1")
elif glob_type_given_pole = 5 then
omniout_str(ALWAYS, "SOME POLE (given) for Equation 1")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 1")
end if;
if array_rad_test_poles[1, 1] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (ratio test) for eq 1 ", 4,
array_rad_test_poles[1, 1], 4, " ");
if float_abs(array_rad_test_poles[1, 1]) < glob_least_ratio_sing
then glob_least_ratio_sing := array_rad_test_poles[1, 1]
end if;
omniout_complex(ALWAYS,
"Order of pole (ratio test) ", 4,
array_ord_test_poles[1, 1], 4, " ")
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 2] and
array_rad_test_poles[1, 2] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 1 ", 4,
array_rad_test_poles[1, 2], 4, " ");
if float_abs(array_rad_test_poles[1, 2]) < glob_least_3_sing then
glob_least_3_sing := array_rad_test_poles[1, 2]
end if;
omniout_complex(ALWAYS,
"Order of pole (three term test) ", 4,
array_ord_test_poles[1, 2], 4, " ")
else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 3] and
array_rad_test_poles[1, 3] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 1 ", 4,
array_rad_test_poles[1, 3], 4, " ");
if float_abs(array_rad_test_poles[1, 3]) < glob_least_6_sing then
glob_least_6_sing := array_rad_test_poles[1, 3]
end if;
omniout_complex(ALWAYS,
"Order of pole (six term test) ", 4,
array_ord_test_poles[1, 3], 4, " ")
else omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 1")
end if
end proc
# End Function number 2
# Begin Function number 3
> my_check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 3
> ret := glob__1;
> else
> ret := glob__m1;
> fi;# end if 3;
> ret;;
> end;
my_check_sign := proc(x0, xf)
local ret;
if x0 < xf then ret := glob__1 else ret := glob__m1 end if; ret
end proc
# End Function number 3
# Begin Function number 4
> est_size_answer := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#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_g,
> 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_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_g, 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,
#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_g,
> 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_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_g, 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,
#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_g,
> 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_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_g, 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,
#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_g,
> 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_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_g, 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,
#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_g,
> 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_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_g, 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,
#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_g,
> 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_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_g, 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,
#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_g,
> 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_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_g, 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,
#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_g,
> 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 sin 1 $eq_no = 1
> array_tmp1[1] := sin(array_x[1]);
> array_tmp1_g[1] := cos(array_x[1]);
> #emit pre neg FULL $eq_no = 1
> array_tmp2[1] := neg(array_tmp1[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
> #emit pre cos 1 $eq_no = 1
> array_tmp4[1] := cos(array_x[1]);
> array_tmp4_g[1] := sin(array_x[1]);
> #emit pre sub FULL FULL $eq_no = 1 i = 1
> array_tmp5[1] := array_tmp3[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 sin ID_LINEAR iii = 2 $eq_no = 1
> array_tmp1[2] := array_tmp1_g[1] * array_x[2] / c(1);
> array_tmp1_g[2] := neg(array_tmp1[1]) * array_x[2] / c(1);
> #emit pre neg FULL $eq_no = 1
> array_tmp2[2] := neg(array_tmp1[2]);
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp3[2] := array_tmp2[2];
> #emit pre cos ID_LINEAR iii = 2 $eq_no = 1
> array_tmp4[2] := neg(array_tmp4_g[1]) * array_x[2] / c(1);
> array_tmp4_g[2] := array_tmp4[1] * array_x[2] / c(1);
> #emit pre sub FULL FULL $eq_no = 1 i = 2
> array_tmp5[2] := array_tmp3[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 sin ID_LINEAR iii = 3 $eq_no = 1
> array_tmp1[3] := array_tmp1_g[2] * array_x[2] / c(2);
> array_tmp1_g[3] := neg(array_tmp1[2]) * array_x[2] / c(2);
> #emit pre neg FULL $eq_no = 1
> array_tmp2[3] := neg(array_tmp1[3]);
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp3[3] := array_tmp2[3];
> #emit pre cos ID_LINEAR iii = 3 $eq_no = 1
> array_tmp4[3] := neg(array_tmp4_g[2]) * array_x[2] / c(2);
> array_tmp4_g[3] := array_tmp4[2] * array_x[2] / c(2);
> #emit pre sub FULL FULL $eq_no = 1 i = 3
> array_tmp5[3] := array_tmp3[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 sin ID_LINEAR iii = 4 $eq_no = 1
> array_tmp1[4] := array_tmp1_g[3] * array_x[2] / c(3);
> array_tmp1_g[4] := neg(array_tmp1[3]) * array_x[2] / c(3);
> #emit pre neg FULL $eq_no = 1
> array_tmp2[4] := neg(array_tmp1[4]);
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp3[4] := array_tmp2[4];
> #emit pre cos ID_LINEAR iii = 4 $eq_no = 1
> array_tmp4[4] := neg(array_tmp4_g[3]) * array_x[2] / c(3);
> array_tmp4_g[4] := array_tmp4[3] * array_x[2] / c(3);
> #emit pre sub FULL FULL $eq_no = 1 i = 4
> array_tmp5[4] := array_tmp3[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 sin ID_LINEAR iii = 5 $eq_no = 1
> array_tmp1[5] := array_tmp1_g[4] * array_x[2] / c(4);
> array_tmp1_g[5] := neg(array_tmp1[4]) * array_x[2] / c(4);
> #emit pre neg FULL $eq_no = 1
> array_tmp2[5] := neg(array_tmp1[5]);
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp3[5] := array_tmp2[5];
> #emit pre cos ID_LINEAR iii = 5 $eq_no = 1
> array_tmp4[5] := neg(array_tmp4_g[4]) * array_x[2] / c(4);
> array_tmp4_g[5] := array_tmp4[4] * array_x[2] / c(4);
> #emit pre sub FULL FULL $eq_no = 1 i = 5
> array_tmp5[5] := array_tmp3[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 sin LINEAR $eq_no = 1
> array_tmp1[kkk] := array_tmp1_g[kkk - 1] * array_x[2] / c(kkk - 1);
> array_tmp1_g[kkk] := neg(array_tmp1[kkk - 1]) * array_x[2] / c(kkk - 1);
> #emit neg FULL $eq_no = 1
> array_tmp2[kkk] := neg(array_tmp1[kkk]);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp3[kkk] := array_tmp2[kkk];
> #emit cos LINEAR $eq_no = 1
> array_tmp4[kkk] := neg(array_tmp4_g[kkk - 1]) * array_x[2] / c(kkk - 1);
> array_tmp4_g[kkk] := array_tmp4[kkk - 1] * array_x[2] / c(kkk - 1);
> #emit FULL - FULL sub $eq_no = 1
> array_tmp5[kkk] := array_tmp3[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_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_g, 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] := sin(array_x[1]);
array_tmp1_g[1] := cos(array_x[1]);
array_tmp2[1] := neg(array_tmp1[1]);
array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
array_tmp4[1] := cos(array_x[1]);
array_tmp4_g[1] := sin(array_x[1]);
array_tmp5[1] := array_tmp3[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_tmp1_g[1]*array_x[2]/c(1);
array_tmp1_g[2] := neg(array_tmp1[1])*array_x[2]/c(1);
array_tmp2[2] := neg(array_tmp1[2]);
array_tmp3[2] := array_tmp2[2];
array_tmp4[2] := neg(array_tmp4_g[1])*array_x[2]/c(1);
array_tmp4_g[2] := array_tmp4[1]*array_x[2]/c(1);
array_tmp5[2] := array_tmp3[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_tmp1[3] := array_tmp1_g[2]*array_x[2]/c(2);
array_tmp1_g[3] := neg(array_tmp1[2])*array_x[2]/c(2);
array_tmp2[3] := neg(array_tmp1[3]);
array_tmp3[3] := array_tmp2[3];
array_tmp4[3] := neg(array_tmp4_g[2])*array_x[2]/c(2);
array_tmp4_g[3] := array_tmp4[2]*array_x[2]/c(2);
array_tmp5[3] := array_tmp3[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_tmp1[4] := array_tmp1_g[3]*array_x[2]/c(3);
array_tmp1_g[4] := neg(array_tmp1[3])*array_x[2]/c(3);
array_tmp2[4] := neg(array_tmp1[4]);
array_tmp3[4] := array_tmp2[4];
array_tmp4[4] := neg(array_tmp4_g[3])*array_x[2]/c(3);
array_tmp4_g[4] := array_tmp4[3]*array_x[2]/c(3);
array_tmp5[4] := array_tmp3[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_tmp1[5] := array_tmp1_g[4]*array_x[2]/c(4);
array_tmp1_g[5] := neg(array_tmp1[4])*array_x[2]/c(4);
array_tmp2[5] := neg(array_tmp1[5]);
array_tmp3[5] := array_tmp2[5];
array_tmp4[5] := neg(array_tmp4_g[4])*array_x[2]/c(4);
array_tmp4_g[5] := array_tmp4[4]*array_x[2]/c(4);
array_tmp5[5] := array_tmp3[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_tmp1[kkk] := array_tmp1_g[kkk - 1]*array_x[2]/c(kkk - 1);
array_tmp1_g[kkk] := neg(array_tmp1[kkk - 1])*array_x[2]/c(kkk - 1)
;
array_tmp2[kkk] := neg(array_tmp1[kkk]);
array_tmp3[kkk] := array_tmp2[kkk];
array_tmp4[kkk] := neg(array_tmp4_g[kkk - 1])*array_x[2]/c(kkk - 1)
;
array_tmp4_g[kkk] := array_tmp4[kkk - 1]*array_x[2]/c(kkk - 1);
array_tmp5[kkk] := array_tmp3[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,
> #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_g,
> 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 := 40;
> # before first input block
> #BEGIN FIRST INPUT BLOCK
> #BEGIN BLOCK 1
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=40;
> #END BLOCK 1
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> # before generate arrays
> array_y_init:= Array(0..(40),[]);
> array_norms:= Array(0..(40),[]);
> array_fact_1:= Array(0..(40),[]);
> 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..(40),[]);
> array_x:= Array(0..(40),[]);
> array_tmp0:= Array(0..(40),[]);
> array_tmp1_g:= Array(0..(40),[]);
> array_tmp1:= Array(0..(40),[]);
> array_tmp2:= Array(0..(40),[]);
> array_tmp3:= Array(0..(40),[]);
> array_tmp4_g:= Array(0..(40),[]);
> array_tmp4:= Array(0..(40),[]);
> array_tmp5:= Array(0..(40),[]);
> array_m1:= Array(0..(40),[]);
> array_y_higher := Array(0..(2) ,(0..40+ 1),[]);
> array_y_higher_work := Array(0..(2) ,(0..40+ 1),[]);
> array_y_higher_work2 := Array(0..(2) ,(0..40+ 1),[]);
> array_y_set_initial := Array(0..(2) ,(0..40+ 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..(40) ,(0..40+ 1),[]);
> # before generate constants
> # before generate globals definition
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> # before generate const definition
> # before arrays initialized
> term := 1;
> while (term <= 40) do # do number 1
> array_y_init[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_norms[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_fact_1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 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 <= 40) do # do number 1
> array_y[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_x[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp0[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp1_g[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp3[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp4_g[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp4[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp5[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_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 <= 40) 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 <= 40) 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 <= 40) 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 <= 40) 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 <=40) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_fact_2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> # before symbols initialized
> #BEGIN SYMBOLS INITIALIZATED
> zero_ats_ar(array_y);
> zero_ats_ar(array_x);
> zero_ats_ar(array_tmp0);
> zero_ats_ar(array_tmp1_g);
> 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_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;
> array_y_set_initial[1,31] := false;
> array_y_set_initial[1,32] := false;
> array_y_set_initial[1,33] := false;
> array_y_set_initial[1,34] := false;
> array_y_set_initial[1,35] := false;
> array_y_set_initial[1,36] := false;
> array_y_set_initial[1,37] := false;
> array_y_set_initial[1,38] := false;
> array_y_set_initial[1,39] := false;
> array_y_set_initial[1,40] := false;
> # before generate init omniout const
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> ATS_MAX_TERMS := 40;
> glob_iolevel := INFO;
> # set default block
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> glob_display_flag := true;
> glob_no_eqs := 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/sub_sin_cospostcpx.cpx#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = neg ( sin ( x ) ) - cos ( x ) ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=40;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := 0.1 + 0.1 * I;");
> omniout_str(ALWAYS,"x_end := 99.0 + 99.0 * I;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_type_given_pole := 3;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=8;");
> omniout_str(ALWAYS,"glob_max_minutes:=(3.0);");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"glob_max_iter:=10000;");
> omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);");
> omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);");
> omniout_str(ALWAYS,"glob_look_poles:=true;");
> omniout_str(ALWAYS,"glob_h:=c(0.001);");
> omniout_str(ALWAYS,"glob_display_interval:=c(0.01);");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"return(cos(c(x)) - sin(c(x))) ;");
> 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 := 0.1 + 0.1 * I;
> x_end := 99.0 + 99.0 * I;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_type_given_pole := 3;
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=8;
> glob_max_minutes:=(3.0);
> glob_subiter_method:=3;
> glob_max_iter:=10000;
> glob_upper_ratio_limit:=c(1.000001);
> glob_lower_ratio_limit:=c(0.999999);
> glob_look_poles:=true;
> glob_h:=c(0.001);
> glob_display_interval:=c(0.01);
> #END OVERRIDE BLOCK
> #END BLOCK 2
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_sec := (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours);
> # after second input block
> found_h := true;
> glob_h := next_delta();
> #START ADJUST ALL SERIES
> if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 9
> h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius;
> omniout_str(ALWAYS,"SETTING H FOR POLE");
> glob_h_reason := 6;
> if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> h_new := glob_min_h;
> glob_h_reason := 5;
> fi;# end if 10;
> term := 1;
> ratio := c(1.0);
> while (term <= ATS_MAX_TERMS) do # do number 1
> array_y[term] := array_y[term]* ratio;
> array_y_higher[1,term] := array_y_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / float_abs(glob_h);
> term := term + 1;
> od;# end do number 1;
> glob_h := h_new;
> fi;# end if 9;
> #BOTTOM ADJUST ALL SERIES
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 9
> html_log_file := fopen("entry.html",WRITE,TEXT);
> fi;# end if 9;
> #BEGIN SOLUTION CODE
> found_h := true;
> if (found_h) then # if number 9
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := c(x_start);
> array_x[2] := c(glob_h);
> glob_next_display := c(x_start);
> glob_min_pole_est := glob_larger_float;
> glob_least_given_sing := glob_larger_float;
> glob_least_ratio_sing := glob_larger_float;
> glob_least_3_sing := glob_larger_float;
> glob_least_6_sing := glob_larger_float;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 1
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1));
> term_no := term_no + 1;
> od;# end do number 1;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 1
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 2
> it := term_no + r_order - 1;
> if (term_no < ATS_MAX_TERMS) then # if number 10
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 10;
> term_no := term_no + 1;
> od;# end do number 2;
> r_order := r_order + 1;
> od;# end do number 1
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> glob_clock_sec := elapsed_time_seconds();
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> found_h := true;
> glob_h := next_delta();
> #START ADJUST ALL SERIES
> if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 10
> h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius;
> omniout_str(ALWAYS,"SETTING H FOR POLE");
> glob_h_reason := 6;
> if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 11
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> h_new := glob_min_h;
> glob_h_reason := 5;
> fi;# end if 11;
> term := 1;
> ratio := c(1.0);
> while (term <= ATS_MAX_TERMS) do # do number 1
> array_y[term] := array_y[term]* ratio;
> array_y_higher[1,term] := array_y_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / float_abs(glob_h);
> term := term + 1;
> od;# end do number 1;
> glob_h := h_new;
> fi;# end if 10;
> #BOTTOM ADJUST ALL SERIES
> #END OPTIMIZE CODE
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_iter < glob_max_iter) and ((glob_iter < 10) or ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0))))) do # do number 1
> #left paren 0001C
> if (true) then # if number 10
> omniout_str(INFO," ");
> fi;# end if 10;
> found_h := true;
> glob_h := next_delta();
> #START ADJUST ALL SERIES
> if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 10
> h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius;
> omniout_str(ALWAYS,"SETTING H FOR POLE");
> glob_h_reason := 6;
> if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 11
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> h_new := glob_min_h;
> glob_h_reason := 5;
> fi;# end if 11;
> term := 1;
> ratio := c(1.0);
> while (term <= ATS_MAX_TERMS) do # do number 2
> array_y[term] := array_y[term]* ratio;
> array_y_higher[1,term] := array_y_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / float_abs(glob_h);
> term := term + 1;
> od;# end do number 2;
> glob_h := h_new;
> fi;# end if 10;
> #BOTTOM ADJUST ALL SERIES
> #END OPTIMIZE CODE
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> atomall();
> if ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0))) then # if number 10
> display_alot(current_iter);
> fi;# end if 10;
> if ((glob_look_poles) and ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0)))) then # if number 10
> check_for_pole();
> fi;# end if 10;
> if (true) then # if number 10
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 10;
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y;
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := ATS_MAX_TERMS;
> while (term_no >= 1) do # do number 2
> array_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 3
> array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 3;
> term_no := term_no - 1;
> od;# end do number 2;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> ;
> od;# end do number 1;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 10
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 10;
> if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec )) then # if number 10
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 10;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 1 ) = neg ( sin ( x ) ) - cos ( x ) ; ");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 10
> logstart(html_log_file);
> logitem_str(html_log_file,"2017-11-26T16:39:03-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"sub_sin_cos")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = neg ( sin ( x ) ) - cos ( x ) ; ")
> ;
> 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,"sub_sin_cos diffeq.mxt")
> ;
> logitem_str(html_log_file,"sub_sin_cos 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_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_g, 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 := 40;
Digits := 32;
max_terms := 40;
glob_html_log := true;
array_y_init := Array(0 .. 40, []);
array_norms := Array(0 .. 40, []);
array_fact_1 := Array(0 .. 40, []);
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 .. 40, []);
array_x := Array(0 .. 40, []);
array_tmp0 := Array(0 .. 40, []);
array_tmp1_g := Array(0 .. 40, []);
array_tmp1 := Array(0 .. 40, []);
array_tmp2 := Array(0 .. 40, []);
array_tmp3 := Array(0 .. 40, []);
array_tmp4_g := Array(0 .. 40, []);
array_tmp4 := Array(0 .. 40, []);
array_tmp5 := Array(0 .. 40, []);
array_m1 := Array(0 .. 40, []);
array_y_higher := Array(0 .. 2, 0 .. 41, []);
array_y_higher_work := Array(0 .. 2, 0 .. 41, []);
array_y_higher_work2 := Array(0 .. 2, 0 .. 41, []);
array_y_set_initial := Array(0 .. 2, 0 .. 41, []);
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 .. 40, 0 .. 41, []);
term := 1;
while term <= 40 do array_y_init[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 40 do array_norms[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 40 do array_fact_1[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 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 <= 40 do array_y[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_x[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp0[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp1_g[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 40 do array_tmp1[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp3[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp4_g[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 40 do array_tmp4[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp5[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_m1[term] := c(0.); term := term + 1 end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 40 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 <= 40 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 <= 40 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 <= 40 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 <= 40 do
term := 1;
while term <= 40 do
array_fact_2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
zero_ats_ar(array_y);
zero_ats_ar(array_x);
zero_ats_ar(array_tmp0);
zero_ats_ar(array_tmp1_g);
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_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;
array_y_set_initial[1, 31] := false;
array_y_set_initial[1, 32] := false;
array_y_set_initial[1, 33] := false;
array_y_set_initial[1, 34] := false;
array_y_set_initial[1, 35] := false;
array_y_set_initial[1, 36] := false;
array_y_set_initial[1, 37] := false;
array_y_set_initial[1, 38] := false;
array_y_set_initial[1, 39] := false;
array_y_set_initial[1, 40] := false;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
ATS_MAX_TERMS := 40;
glob_iolevel := INFO;
glob_orig_start_sec := elapsed_time_seconds();
glob_display_flag := true;
glob_no_eqs := 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/sub_sin_cospostcpx.cpx#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = neg ( sin ( x ) \
) - cos ( x ) ; ");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=40;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := 0.1 + 0.1 * I;");
omniout_str(ALWAYS, "x_end := 99.0 + 99.0 * I;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_type_given_pole := 3;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=8;");
omniout_str(ALWAYS, "glob_max_minutes:=(3.0);");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "glob_max_iter:=10000;");
omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);");
omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);");
omniout_str(ALWAYS, "glob_look_poles:=true;");
omniout_str(ALWAYS, "glob_h:=c(0.001);");
omniout_str(ALWAYS, "glob_display_interval:=c(0.01);");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "return(cos(c(x)) - sin(c(x))) ;");
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,");
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omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.000 + 0.000 * I ];");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_nxt := glob_nxt + 1;");
omniout_str(ALWAYS, "it := x_delta[glob_nxt];");
omniout_str(ALWAYS, "return it;");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := glob__0;
glob_smallish_float := glob__0;
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob_almost_1 := c(0.99);
x_start := 0.1 + 0.1*I;
x_end := 99.0 + 99.0*I;
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_type_given_pole := 3;
glob_desired_digits_correct := 8;
glob_max_minutes := 3.0;
glob_subiter_method := 3;
glob_max_iter := 10000;
glob_upper_ratio_limit := c(1.000001);
glob_lower_ratio_limit := c(0.999999);
glob_look_poles := true;
glob_h := c(0.001);
glob_display_interval := c(0.01);
glob_last_good_h := glob_h;
glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours;
found_h := true;
glob_h := next_delta();
if
float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h)
then
h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius;
omniout_str(ALWAYS, "SETTING H FOR POLE");
glob_h_reason := 6;
if glob_check_sign*h_new < glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
h_new := glob_min_h;
glob_h_reason := 5
end if;
term := 1;
ratio := c(1.0);
while term <= ATS_MAX_TERMS do
array_y[term] := array_y[term]*ratio;
array_y_higher[1, term] := array_y_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/float_abs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT)
end if;
found_h := true;
if found_h then
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := c(x_start);
array_x[2] := c(glob_h);
glob_next_display := c(x_start);
glob_min_pole_est := glob_larger_float;
glob_least_given_sing := glob_larger_float;
glob_least_ratio_sing := glob_larger_float;
glob_least_3_sing := glob_larger_float;
glob_least_6_sing := glob_larger_float;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1));
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
if term_no < ATS_MAX_TERMS then
array_y_higher[r_order, term_no] := array_y_init[it]*
expt(glob_h, c(term_no - 1))/
c(factorial_1(term_no - 1))
end if;
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
glob_clock_sec := elapsed_time_seconds();
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
found_h := true;
glob_h := next_delta();
if float_abs(glob_min_pole_est)*glob_ratio_of_radius <
float_abs(glob_h) then
h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius
;
omniout_str(ALWAYS, "SETTING H FOR POLE");
glob_h_reason := 6;
if glob_check_sign*h_new < glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
h_new := glob_min_h;
glob_h_reason := 5
end if;
term := 1;
ratio := c(1.0);
while term <= ATS_MAX_TERMS do
array_y[term] := array_y[term]*ratio;
array_y_higher[1, term] := array_y_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/float_abs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_iter < glob_max_iter and
(glob_iter < 10 or not (Re(glob_h) = 0. and Im(glob_h) = 0.)) do
omniout_str(INFO, " ");
found_h := true;
glob_h := next_delta();
if float_abs(glob_min_pole_est)*glob_ratio_of_radius <
float_abs(glob_h) then
h_new :=
glob_check_sign*glob_min_pole_est*glob_ratio_of_radius;
omniout_str(ALWAYS, "SETTING H FOR POLE");
glob_h_reason := 6;
if glob_check_sign*h_new < glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
h_new := glob_min_h;
glob_h_reason := 5
end if;
term := 1;
ratio := c(1.0);
while term <= ATS_MAX_TERMS do
array_y[term] := array_y[term]*ratio;
array_y_higher[1, term] :=
array_y_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/float_abs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
atomall();
if not (Re(glob_h) = 0. and Im(glob_h) = 0.) then
display_alot(current_iter)
end if;
if
glob_look_poles and not (Re(glob_h) = 0. and Im(glob_h) = 0.)
then check_for_pole()
end if;
glob_next_display := glob_next_display + glob_display_interval;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
term_no := ATS_MAX_TERMS;
while 1 <= term_no do
array_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if glob_max_sec <= elapsed_time_seconds() - glob_orig_start_sec
then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff ( y , x , 1 ) = neg ( sin ( x )\
) - cos ( x ) ; ");
omniout_int(INFO, "Iterations ", 32, glob_iter,
4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2017-11-26T16:39:03-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"sub_sin_cos");
logitem_str(html_log_file, "diff ( y , x , 1 ) = ne\
g ( sin ( x ) ) - cos ( x ) ; ");
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, "sub_sin_cos diffeq.mxt");
logitem_str(html_log_file, "sub_sin_cos maple results");
logitem_str(html_log_file, "OK");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end if
end proc
# End Function number 12
> main();
memory used=3.8MB, alloc=40.3MB, time=0.08
##############ECHO OF PROBLEM#################
##############temp/sub_sin_cospostcpx.cpx#################
diff ( y , x , 1 ) = neg ( sin ( x ) ) - cos ( x ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=40;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.1 + 0.1 * I;
x_end := 99.0 + 99.0 * I;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_type_given_pole := 3;
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=8;
glob_max_minutes:=(3.0);
glob_subiter_method:=3;
glob_max_iter:=10000;
glob_upper_ratio_limit:=c(1.000001);
glob_lower_ratio_limit:=c(0.999999);
glob_look_poles:=true;
glob_h:=c(0.001);
glob_display_interval:=c(0.01);
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return(cos(c(x)) - sin(c(x))) ;
end;
next_delta := proc()
global glob_nxt, x_delta;
x_delta := [ 0.001 + 0.00004 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.000 + 0.000 * I ];
glob_nxt := glob_nxt + 1;
it := x_delta[glob_nxt];
return it;
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = 0.1 0.1
h = 0.0001 0.005
y[1] (numeric) = 0.899650333496 -0.109666322381
y[1] (closed_form) = 0.899650333496 -0.109666322381
absolute error = 0
relative error = 0 %
Correct digits = 30
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6253
Order of pole (three term test) = 32.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1001 0.105
h = 0.0001 0.003
y[1] (numeric) = 0.89999757642 -0.115178386372
y[1] (closed_form) = 0.899999820397 -0.1151787138
absolute error = 2.268e-06
relative error = 0.0002499 %
Correct digits = 6
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3009
Order of pole (three term test) = 32.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1002 0.108
h = 0.001 0.001
y[1] (numeric) = 0.900176641839 -0.118491944166
y[1] (closed_form) = 0.900176197085 -0.118491827211
absolute error = 4.599e-07
relative error = 5.065e-05 %
Correct digits = 6
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2365
Order of pole (three term test) = 32.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1012 0.109
h = 0.001 0.003
y[1] (numeric) = 0.899173195664 -0.119691764686
y[1] (closed_form) = 0.89917151205 -0.119690978789
absolute error = 1.858e-06
relative error = 0.0002048 %
Correct digits = 6
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.122
Order of pole (three term test) = 32.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1022 0.112
h = 0.0001 0.004
y[1] (numeric) = 0.898364296751 -0.123098588947
y[1] (closed_form) = 0.898365187613 -0.123099065299
absolute error = 1.010e-06
relative error = 0.0001114 %
Correct digits = 6
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6358
Order of pole (three term test) = 32.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1023 0.116
h = 0.003 0.006
y[1] (numeric) = 0.898659797414 -0.127526041523
y[1] (closed_form) = 0.898662745084 -0.127525203112
absolute error = 3.065e-06
relative error = 0.0003376 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8439
Order of pole (three term test) = 32.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1053 0.122
h = 0.0001 0.005
y[1] (numeric) = 0.89597946866 -0.134470262372
y[1] (closed_form) = 0.895982361401 -0.134480145739
absolute error = 1.030e-05
relative error = 0.001137 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3759
Order of pole (three term test) = 32.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1054 0.127
h = 0.0001 0.003
y[1] (numeric) = 0.896424771407 -0.140028951352
y[1] (closed_form) = 0.896426568065 -0.140031972909
absolute error = 3.515e-06
relative error = 0.0003875 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3034
Order of pole (three term test) = 32.61 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=30.5MB, alloc=40.3MB, time=0.38
x[1] = 0.1055 0.13
h = 0.001 0.001
y[1] (numeric) = 0.896660295028 -0.143367304052
y[1] (closed_form) = 0.896659416011 -0.143369806954
absolute error = 2.653e-06
relative error = 0.0002921 %
Correct digits = 6
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2385
Order of pole (three term test) = 32.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1065 0.131
h = 0.001 0.003
y[1] (numeric) = 0.895668234458 -0.144593867349
y[1] (closed_form) = 0.89566613534 -0.144595667134
absolute error = 2.765e-06
relative error = 0.0003048 %
Correct digits = 6
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.132
Order of pole (three term test) = 32.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1075 0.134
h = 0.0001 0.004
y[1] (numeric) = 0.894908746245 -0.148042740235
y[1] (closed_form) = 0.894909186218 -0.148045873567
absolute error = 3.164e-06
relative error = 0.0003488 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6415
Order of pole (three term test) = 32.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1076 0.138
h = 0.003 0.006
y[1] (numeric) = 0.895279427014 -0.152503171058
y[1] (closed_form) = 0.895281960515 -0.152505046669
absolute error = 3.152e-06
relative error = 0.0003471 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8518
Order of pole (three term test) = 32.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1106 0.144
h = 0.0001 0.005
y[1] (numeric) = 0.892689344647 -0.159551640853
y[1] (closed_form) = 0.89269152493 -0.159564240623
absolute error = 1.279e-05
relative error = 0.00141 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3796
Order of pole (three term test) = 32.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1107 0.149
h = 0.0001 0.003
y[1] (numeric) = 0.893228083819 -0.165152435996
y[1] (closed_form) = 0.893229359097 -0.165158138347
absolute error = 5.843e-06
relative error = 0.0006433 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3065
Order of pole (three term test) = 32.62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1108 0.152
h = 0.001 0.001
y[1] (numeric) = 0.893519394459 -0.168517160561
y[1] (closed_form) = 0.893518006019 -0.168522269125
absolute error = 5.294e-06
relative error = 0.0005822 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.241
Order of pole (three term test) = 32.62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1118 0.153
h = 0.001 0.003
y[1] (numeric) = 0.892537981135 -0.169770794487
y[1] (closed_form) = 0.89253539096 -0.169775165152
absolute error = 5.081e-06
relative error = 0.0005592 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.144
Order of pole (three term test) = 32.62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1128 0.156
h = 0.0001 0.004
y[1] (numeric) = 0.891826753015 -0.173263111293
y[1] (closed_form) = 0.891826667395 -0.173268888002
absolute error = 5.777e-06
relative error = 0.0006359 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6484
Order of pole (three term test) = 32.62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1129 0.16
h = 0.003 0.006
y[1] (numeric) = 0.892271742641 -0.177758640423
y[1] (closed_form) = 0.892273788515 -0.17776321637
absolute error = 5.012e-06
relative error = 0.0005509 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8613
Order of pole (three term test) = 32.62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1159 0.166
h = 0.0001 0.005
y[1] (numeric) = 0.889769081955 -0.184913968669
y[1] (closed_form) = 0.889770473661 -0.184929275964
absolute error = 1.537e-05
relative error = 0.001691 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3841
Order of pole (three term test) = 32.62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.116 0.171
h = 0.0001 0.003
y[1] (numeric) = 0.890400196971 -0.190559549149
y[1] (closed_form) = 0.890400875945 -0.190567920059
absolute error = 8.398e-06
relative error = 0.0009223 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3102
Order of pole (three term test) = 32.62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1161 0.174
h = 0.001 0.001
y[1] (numeric) = 0.890746642731 -0.193952247572
y[1] (closed_form) = 0.890744668869 -0.19395994867
absolute error = 7.950e-06
relative error = 0.0008721 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.244
Order of pole (three term test) = 32.62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1171 0.175
h = 0.001 0.003
y[1] (numeric) = 0.889775136835 -0.195233294805
y[1] (closed_form) = 0.889771979228 -0.195240222606
absolute error = 7.613e-06
relative error = 0.0008358 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.159
Order of pole (three term test) = 32.62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1181 0.178
h = 0.0001 0.004
y[1] (numeric) = 0.889111030073 -0.198770481886
y[1] (closed_form) = 0.889110343299 -0.198778889454
absolute error = 8.436e-06
relative error = 0.0009259 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6567
Order of pole (three term test) = 32.62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1182 0.182
h = 0.003 0.006
y[1] (numeric) = 0.889629482999 -0.203303262717
y[1] (closed_form) = 0.889630966937 -0.203310526431
absolute error = 7.414e-06
relative error = 0.0008124 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8726
Order of pole (three term test) = 32.63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1212 0.188
h = 0.0001 0.005
y[1] (numeric) = 0.887211434225 -0.210568128026
y[1] (closed_form) = 0.887211960244 -0.210586135017
absolute error = 1.801e-05
relative error = 0.001976 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3893
Order of pole (three term test) = 32.63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1213 0.193
h = 0.0001 0.003
y[1] (numeric) = 0.887933896176 -0.216261214979
y[1] (closed_form) = 0.887933903029 -0.21627224329
absolute error = 1.103e-05
relative error = 0.001207 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3146
Order of pole (three term test) = 32.63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1214 0.196
h = 0.001 0.001
y[1] (numeric) = 0.888334843772 -0.219683514867
y[1] (closed_form) = 0.888332207616 -0.219693796418
absolute error = 1.061e-05
relative error = 0.00116 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2475
Order of pole (three term test) = 32.63 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=74.1MB, alloc=44.3MB, time=0.90
x[1] = 0.1224 0.197
h = 0.0001 0.004
y[1] (numeric) = 0.887372503608 -0.220992332892
y[1] (closed_form) = 0.88736870134 -0.22100180512
absolute error = 1.021e-05
relative error = 0.001116 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.487
Order of pole (three term test) = 32.63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1225 0.201
h = 0.003 0.006
y[1] (numeric) = 0.887950487341 -0.225557088088
y[1] (closed_form) = 0.887952416328 -0.22556644416
absolute error = 9.553e-06
relative error = 0.001043 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8838
Order of pole (three term test) = 32.63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1255 0.207
h = 0.0001 0.005
y[1] (numeric) = 0.885604379216 -0.232917474801
y[1] (closed_form) = 0.885605086692 -0.23293759183
absolute error = 2.013e-05
relative error = 0.002198 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3944
Order of pole (three term test) = 32.64 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1256 0.212
h = 0.0001 0.003
y[1] (numeric) = 0.886405279815 -0.238652593516
y[1] (closed_form) = 0.886405635294 -0.238665690487
absolute error = 1.310e-05
relative error = 0.001427 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3189
Order of pole (three term test) = 32.64 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1257 0.215
h = 0.001 0.001
y[1] (numeric) = 0.88685302686 -0.242101057401
y[1] (closed_form) = 0.886850746032 -0.24211334051
absolute error = 1.249e-05
relative error = 0.001359 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2509
Order of pole (three term test) = 32.64 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1267 0.216
h = 0.001 0.003
y[1] (numeric) = 0.885898317458 -0.243433980047
y[1] (closed_form) = 0.885894884979 -0.243445422105
absolute error = 1.195e-05
relative error = 0.0013 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.191
Order of pole (three term test) = 32.64 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1277 0.219
h = 0.0001 0.004
y[1] (numeric) = 0.885319474955 -0.247058034762
y[1] (closed_form) = 0.885318453528 -0.247071097498
absolute error = 1.310e-05
relative error = 0.001426 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6757
Order of pole (three term test) = 32.64 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1278 0.223
h = 0.003 0.006
y[1] (numeric) = 0.885972965681 -0.251665128648
y[1] (closed_form) = 0.885974191967 -0.251677152904
absolute error = 1.209e-05
relative error = 0.001312 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8984
Order of pole (three term test) = 32.64 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1308 0.229
h = 0.0001 0.005
y[1] (numeric) = 0.883706308239 -0.259140255732
y[1] (closed_form) = 0.883706003727 -0.259163061559
absolute error = 2.281e-05
relative error = 0.002477 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4011
Order of pole (three term test) = 32.64 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1309 0.234
h = 0.0001 0.003
y[1] (numeric) = 0.884596755371 -0.264928070868
y[1] (closed_form) = 0.884596295056 -0.264943808198
absolute error = 1.574e-05
relative error = 0.001705 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3244
Order of pole (three term test) = 32.64 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.131 0.237
h = 0.001 0.001
y[1] (numeric) = 0.885097893246 -0.268409242079
y[1] (closed_form) = 0.885094804539 -0.268424086804
absolute error = 1.516e-05
relative error = 0.001639 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2553
Order of pole (three term test) = 32.65 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.132 0.238
h = 0.001 0.003
y[1] (numeric) = 0.88415096769 -0.269770649009
y[1] (closed_form) = 0.884146744331 -0.269784615457
absolute error = 1.459e-05
relative error = 0.001578 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.212
Order of pole (three term test) = 32.65 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.133 0.241
h = 0.0001 0.004
y[1] (numeric) = 0.883616065081 -0.27344384268
y[1] (closed_form) = 0.883614221216 -0.273459507171
absolute error = 1.577e-05
relative error = 0.001705 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6878
Order of pole (three term test) = 32.65 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1331 0.245
h = 0.003 0.006
y[1] (numeric) = 0.884340761183 -0.278094548925
y[1] (closed_form) = 0.884341207858 -0.278109231879
absolute error = 1.469e-05
relative error = 0.001585 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9147
Order of pole (three term test) = 32.65 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1361 0.251
h = 0.0001 0.005
y[1] (numeric) = 0.882150777671 -0.285687295837
y[1] (closed_form) = 0.88214938105 -0.285712785533
absolute error = 2.553e-05
relative error = 0.002753 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4086
Order of pole (three term test) = 32.65 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1362 0.256
h = 0.0001 0.003
y[1] (numeric) = 0.883129827489 -0.291530653858
y[1] (closed_form) = 0.883128472838 -0.29154902336
absolute error = 1.842e-05
relative error = 0.001981 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3306
Order of pole (three term test) = 32.65 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1363 0.259
h = 0.001 0.001
y[1] (numeric) = 0.883683772803 -0.295046236416
y[1] (closed_form) = 0.883679796685 -0.295063633549
absolute error = 1.785e-05
relative error = 0.001916 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2603
Order of pole (three term test) = 32.65 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1373 0.26
h = 0.001 0.003
y[1] (numeric) = 0.882743881864 -0.296436527486
y[1] (closed_form) = 0.88273878778 -0.296453008452
absolute error = 1.725e-05
relative error = 0.001853 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.236
Order of pole (three term test) = 32.66 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1383 0.263
h = 0.0001 0.004
y[1] (numeric) = 0.882251818621 -0.300160410058
y[1] (closed_form) = 0.882249073163 -0.30017866776
absolute error = 1.846e-05
relative error = 0.001981 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7012
Order of pole (three term test) = 32.66 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=117.8MB, alloc=44.3MB, time=1.42
x[1] = 0.1384 0.267
h = 0.003 0.006
y[1] (numeric) = 0.883046965877 -0.304857018036
y[1] (closed_form) = 0.883046555058 -0.304874351231
absolute error = 1.734e-05
relative error = 0.001856 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9329
Order of pole (three term test) = 32.66 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1414 0.273
h = 0.0001 0.005
y[1] (numeric) = 0.880930887069 -0.312570335739
y[1] (closed_form) = 0.880928317095 -0.312598505345
absolute error = 2.829e-05
relative error = 0.003026 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4169
Order of pole (three term test) = 32.66 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1415 0.278
h = 0.0001 0.003
y[1] (numeric) = 0.88199762317 -0.318472129097
y[1] (closed_form) = 0.881995294618 -0.318493123576
absolute error = 2.112e-05
relative error = 0.002253 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3375
Order of pole (three term test) = 32.66 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1416 0.281
h = 0.001 0.001
y[1] (numeric) = 0.882603808583 -0.322023855025
y[1] (closed_form) = 0.882598864521 -0.322043796316
absolute error = 2.055e-05
relative error = 0.002187 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2657
Order of pole (three term test) = 32.66 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1426 0.282
h = 0.001 0.003
y[1] (numeric) = 0.881670199502 -0.323443444902
y[1] (closed_form) = 0.881664153864 -0.323462431456
absolute error = 1.993e-05
relative error = 0.002122 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.262
Order of pole (three term test) = 32.66 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1436 0.285
h = 0.0001 0.004
y[1] (numeric) = 0.881219882807 -0.327219599421
y[1] (closed_form) = 0.881216155583 -0.327240442762
absolute error = 2.117e-05
relative error = 0.002253 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7162
Order of pole (three term test) = 32.67 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1437 0.289
h = 0.003 0.006
y[1] (numeric) = 0.88208474841 -0.331964435865
y[1] (closed_form) = 0.882083401206 -0.331984411852
absolute error = 2.002e-05
relative error = 0.002124 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9531
Order of pole (three term test) = 32.67 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1467 0.295
h = 0.0001 0.005
y[1] (numeric) = 0.880039810655 -0.339801347529
y[1] (closed_form) = 0.880035984925 -0.339832194034
absolute error = 3.108e-05
relative error = 0.003295 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4261
Order of pole (three term test) = 32.67 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1468 0.3
h = 0.0001 0.003
y[1] (numeric) = 0.881193342986 -0.345764515768
y[1] (closed_form) = 0.881189959913 -0.345788128996
absolute error = 2.385e-05
relative error = 0.00252 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.345
Order of pole (three term test) = 32.67 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1469 0.303
h = 0.001 0.001
y[1] (numeric) = 0.881851216546 -0.349354145752
y[1] (closed_form) = 0.881845222973 -0.349376623884
absolute error = 2.326e-05
relative error = 0.002453 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2717
Order of pole (three term test) = 32.67 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1479 0.304
h = 0.0001 0.004
y[1] (numeric) = 0.880923132597 -0.350803463925
y[1] (closed_form) = 0.880916053559 -0.350824948058
absolute error = 2.262e-05
relative error = 0.002386 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.633
Order of pole (three term test) = 32.67 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.148 0.308
h = 0.003 0.006
y[1] (numeric) = 0.881844564627 -0.355589388814
y[1] (closed_form) = 0.881843393007 -0.355611552741
absolute error = 2.219e-05
relative error = 0.002334 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9721
Order of pole (three term test) = 32.68 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.151 0.314
h = 0.0001 0.005
y[1] (numeric) = 0.879860175086 -0.363534359886
y[1] (closed_form) = 0.879856247583 -0.36356743106
absolute error = 3.330e-05
relative error = 0.003498 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4348
Order of pole (three term test) = 32.68 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1511 0.319
h = 0.0001 0.003
y[1] (numeric) = 0.881088504947 -0.369551728317
y[1] (closed_form) = 0.881085194082 -0.369577511175
absolute error = 2.599e-05
relative error = 0.002721 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3521
Order of pole (three term test) = 32.68 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1512 0.322
h = 0.001 0.001
y[1] (numeric) = 0.881790919815 -0.373174810104
y[1] (closed_form) = 0.881785001027 -0.373199386416
absolute error = 2.528e-05
relative error = 0.00264 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2774
Order of pole (three term test) = 32.68 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1522 0.323
h = 0.001 0.003
y[1] (numeric) = 0.880867343751 -0.374650019191
y[1] (closed_form) = 0.880860352675 -0.374673566957
absolute error = 2.456e-05
relative error = 0.002566 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.318
Order of pole (three term test) = 32.68 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1532 0.326
h = 0.0001 0.004
y[1] (numeric) = 0.880492490615 -0.378527301415
y[1] (closed_form) = 0.880487764363 -0.378552858983
absolute error = 2.599e-05
relative error = 0.002712 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.748
Order of pole (three term test) = 32.69 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1533 0.33
h = 0.003 0.006
y[1] (numeric) = 0.881485846835 -0.383367393328
y[1] (closed_form) = 0.881483589165 -0.383392189766
absolute error = 2.490e-05
relative error = 0.00259 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9959
Order of pole (three term test) = 32.69 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=161.4MB, alloc=44.3MB, time=1.94
x[1] = 0.1563 0.336
h = 0.0001 0.005
y[1] (numeric) = 0.879567502013 -0.391441811351
y[1] (closed_form) = 0.879562162194 -0.391477557289
absolute error = 3.614e-05
relative error = 0.003754 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4456
Order of pole (three term test) = 32.69 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1564 0.341
h = 0.0001 0.003
y[1] (numeric) = 0.880881074709 -0.397526163617
y[1] (closed_form) = 0.880876556326 -0.397554557137
absolute error = 2.875e-05
relative error = 0.002975 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.361
Order of pole (three term test) = 32.69 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1565 0.344
h = 0.001 0.001
y[1] (numeric) = 0.881634211169 -0.401190510465
y[1] (closed_form) = 0.881627088155 -0.401217613415
absolute error = 2.802e-05
relative error = 0.002893 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2845
Order of pole (three term test) = 32.69 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1575 0.345
h = 0.001 0.003
y[1] (numeric) = 0.880714745586 -0.402696295696
y[1] (closed_form) = 0.880706565909 -0.402722329517
absolute error = 2.729e-05
relative error = 0.002818 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.351
Order of pole (three term test) = 32.7 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1585 0.348
h = 0.0001 0.004
y[1] (numeric) = 0.880378567719 -0.406630578416
y[1] (closed_form) = 0.88037262437 -0.406658706132
absolute error = 2.875e-05
relative error = 0.002965 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7672
Order of pole (three term test) = 32.7 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1586 0.352
h = 0.003 0.006
y[1] (numeric) = 0.881439685607 -0.411525777341
y[1] (closed_form) = 0.881436259927 -0.41155320162
absolute error = 2.764e-05
relative error = 0.002841 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.022
Order of pole (three term test) = 32.7 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1616 0.358
h = 0.0001 0.005
y[1] (numeric) = 0.879584627789 -0.419732876235
y[1] (closed_form) = 0.879577789737 -0.41977129654
absolute error = 3.902e-05
relative error = 0.004004 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4574
Order of pole (three term test) = 32.7 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1617 0.363
h = 0.0001 0.003
y[1] (numeric) = 0.880982623229 -0.42588729268
y[1] (closed_form) = 0.8809768135 -0.425918293304
absolute error = 3.154e-05
relative error = 0.003223 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3707
Order of pole (three term test) = 32.7 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1618 0.366
h = 0.001 0.001
y[1] (numeric) = 0.881785970064 -0.429594750893
y[1] (closed_form) = 0.881777558107 -0.429624375728
absolute error = 3.080e-05
relative error = 0.00314 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2921
Order of pole (three term test) = 32.71 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1628 0.367
h = 0.001 0.003
y[1] (numeric) = 0.88086984458 -0.431131584354
y[1] (closed_form) = 0.880860391354 -0.431160098741
absolute error = 3.004e-05
relative error = 0.003063 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.388
Order of pole (three term test) = 32.71 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1638 0.37
h = 0.0001 0.004
y[1] (numeric) = 0.880571271166 -0.435124582895
y[1] (closed_form) = 0.880564026303 -0.435155276749
absolute error = 3.154e-05
relative error = 0.003211 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7881
Order of pole (three term test) = 32.71 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1639 0.374
h = 0.003 0.006
y[1] (numeric) = 0.881699492863 -0.440077368137
y[1] (closed_form) = 0.881694816068 -0.440107416513
absolute error = 3.041e-05
relative error = 0.003086 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.05
Order of pole (three term test) = 32.71 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1669 0.38
h = 0.0001 0.005
y[1] (numeric) = 0.879904962245 -0.448420457073
y[1] (closed_form) = 0.879896538734 -0.448461552217
absolute error = 4.195e-05
relative error = 0.004248 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4701
Order of pole (three term test) = 32.72 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.167 0.385
h = 0.0001 0.003
y[1] (numeric) = 0.881386582488 -0.454648069673
y[1] (closed_form) = 0.881379396386 -0.454681674732
absolute error = 3.436e-05
relative error = 0.003465 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3811
Order of pole (three term test) = 32.72 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1671 0.388
h = 0.001 0.001
y[1] (numeric) = 0.882239641316 -0.45840051692
y[1] (closed_form) = 0.882229854526 -0.458432659736
absolute error = 3.360e-05
relative error = 0.003379 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3004
Order of pole (three term test) = 32.72 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1681 0.389
h = 0.001 0.003
y[1] (numeric) = 0.881326079832 -0.459968885632
y[1] (closed_form) = 0.881315266951 -0.459999875933
absolute error = 3.282e-05
relative error = 0.003302 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.427
Order of pole (three term test) = 32.72 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1691 0.392
h = 0.0001 0.004
y[1] (numeric) = 0.881064043508 -0.464022350862
y[1] (closed_form) = 0.881055411521 -0.464055607708
absolute error = 3.436e-05
relative error = 0.00345 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8105
Order of pole (three term test) = 32.72 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1692 0.396
h = 0.003 0.006
y[1] (numeric) = 0.882258728317 -0.469035243629
y[1] (closed_form) = 0.88225271612 -0.469067913261
absolute error = 3.322e-05
relative error = 0.003324 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.08
Order of pole (three term test) = 32.72 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1722 0.402
h = 0.0001 0.005
y[1] (numeric) = 0.880521960976 -0.477517707894
y[1] (closed_form) = 0.880511863434 -0.477561479201
absolute error = 4.492e-05
relative error = 0.004485 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4838
Order of pole (three term test) = 32.73 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=204.9MB, alloc=44.3MB, time=2.46
x[1] = 0.1723 0.407
h = 0.0001 0.003
y[1] (numeric) = 0.882086429137 -0.4838217015
y[1] (closed_form) = 0.882077780402 -0.48385790919
absolute error = 3.723e-05
relative error = 0.0037 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3923
Order of pole (three term test) = 32.73 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1724 0.41
h = 0.001 0.001
y[1] (numeric) = 0.88298871375 -0.487621047556
y[1] (closed_form) = 0.882977465022 -0.487655705276
absolute error = 3.644e-05
relative error = 0.003612 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3092
Order of pole (three term test) = 32.73 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1734 0.411
h = 0.0001 0.004
y[1] (numeric) = 0.882076933981 -0.489221453515
y[1] (closed_form) = 0.88206467414 -0.489254915888
absolute error = 3.564e-05
relative error = 0.003533 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.859
Order of pole (three term test) = 32.73 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1735 0.415
h = 0.003 0.006
y[1] (numeric) = 0.883325607471 -0.494285302049
y[1] (closed_form) = 0.883319491329 -0.494320279805
absolute error = 3.551e-05
relative error = 0.003508 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.108
Order of pole (three term test) = 32.73 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1765 0.421
h = 0.0001 0.005
y[1] (numeric) = 0.88163805945 -0.50288986242
y[1] (closed_form) = 0.881627563645 -0.502935996512
absolute error = 4.731e-05
relative error = 0.004661 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4964
Order of pole (three term test) = 32.74 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1766 0.426
h = 0.0001 0.003
y[1] (numeric) = 0.883274195981 -0.509261219238
y[1] (closed_form) = 0.883265331957 -0.509299721369
absolute error = 3.951e-05
relative error = 0.003875 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4026
Order of pole (three term test) = 32.74 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1767 0.429
h = 0.001 0.001
y[1] (numeric) = 0.884219062198 -0.513101909882
y[1] (closed_form) = 0.884207597051 -0.513138785487
absolute error = 3.862e-05
relative error = 0.003777 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3174
Order of pole (three term test) = 32.74 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1777 0.43
h = 0.001 0.003
y[1] (numeric) = 0.88330857461 -0.51473029747
y[1] (closed_form) = 0.883296110573 -0.514765940059
absolute error = 3.776e-05
relative error = 0.003693 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.508
Order of pole (three term test) = 32.75 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1787 0.433
h = 0.0001 0.004
y[1] (numeric) = 0.883112463754 -0.518900655808
y[1] (closed_form) = 0.883102131799 -0.518938731421
absolute error = 3.945e-05
relative error = 0.003852 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.857
Order of pole (three term test) = 32.75 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1788 0.437
h = 0.003 0.006
y[1] (numeric) = 0.884429959722 -0.524031478224
y[1] (closed_form) = 0.884422348053 -0.524069075327
absolute error = 3.836e-05
relative error = 0.003731 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.142
Order of pole (three term test) = 32.75 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1818 0.443
h = 0.0001 0.005
y[1] (numeric) = 0.882795056469 -0.532781951984
y[1] (closed_form) = 0.882782718137 -0.532830767987
absolute error = 5.035e-05
relative error = 0.004883 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.512
Order of pole (three term test) = 32.76 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1819 0.448
h = 0.0001 0.003
y[1] (numeric) = 0.884512687082 -0.539235769886
y[1] (closed_form) = 0.884502196496 -0.539276874591
absolute error = 4.242e-05
relative error = 0.004095 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4153
Order of pole (three term test) = 32.76 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.182 0.451
h = 0.001 0.001
y[1] (numeric) = 0.885505928163 -0.543127006521
y[1] (closed_form) = 0.885492835615 -0.543166394506
absolute error = 4.151e-05
relative error = 0.003996 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3275
Order of pole (three term test) = 32.76 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.183 0.452
h = 0.001 0.003
y[1] (numeric) = 0.884595754953 -0.544788414991
y[1] (closed_form) = 0.884581678159 -0.544826525663
absolute error = 4.063e-05
relative error = 0.003911 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.556
Order of pole (three term test) = 32.76 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.184 0.455
h = 0.0001 0.004
y[1] (numeric) = 0.884433161054 -0.54902446274
y[1] (closed_form) = 0.884421190138 -0.549065098014
absolute error = 4.236e-05
relative error = 0.004069 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8844
Order of pole (three term test) = 32.76 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1841 0.459
h = 0.003 0.006
y[1] (numeric) = 0.885815405952 -0.554222852749
y[1] (closed_form) = 0.885806210886 -0.554263068847
absolute error = 4.125e-05
relative error = 0.003948 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.179
Order of pole (three term test) = 32.76 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1871 0.465
h = 0.0001 0.005
y[1] (numeric) = 0.884230361313 -0.56312284815
y[1] (closed_form) = 0.884216087812 -0.563174349726
absolute error = 5.344e-05
relative error = 0.005098 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5286
Order of pole (three term test) = 32.77 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1872 0.47
h = 0.0001 0.003
y[1] (numeric) = 0.886028763969 -0.569662470162
y[1] (closed_form) = 0.886016556819 -0.569706178015
absolute error = 4.538e-05
relative error = 0.004308 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4289
Order of pole (three term test) = 32.77 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1873 0.473
h = 0.001 0.001
y[1] (numeric) = 0.88706992525 -0.573606258532
y[1] (closed_form) = 0.887055114514 -0.573648158084
absolute error = 4.444e-05
relative error = 0.004207 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3383
Order of pole (three term test) = 32.78 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=248.4MB, alloc=44.3MB, time=2.97
x[1] = 0.1883 0.474
h = 0.001 0.003
y[1] (numeric) = 0.88615926398 -0.575301233088
y[1] (closed_form) = 0.88614348349 -0.575341810219
absolute error = 4.354e-05
relative error = 0.004121 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.607
Order of pole (three term test) = 32.78 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1893 0.477
h = 0.0001 0.004
y[1] (numeric) = 0.886029124985 -0.579604863639
y[1] (closed_form) = 0.886015424543 -0.579648058592
absolute error = 4.532e-05
relative error = 0.00428 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9136
Order of pole (three term test) = 32.78 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1894 0.481
h = 0.003 0.006
y[1] (numeric) = 0.887475536654 -0.584873513671
y[1] (closed_form) = 0.887464668988 -0.584916349237
absolute error = 4.419e-05
relative error = 0.004158 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.218
Order of pole (three term test) = 32.78 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1924 0.487
h = 0.0001 0.005
y[1] (numeric) = 0.885937552334 -0.593926718762
y[1] (closed_form) = 0.885921249514 -0.593980910344
absolute error = 5.659e-05
relative error = 0.005306 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5464
Order of pole (three term test) = 32.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1925 0.492
h = 0.0001 0.003
y[1] (numeric) = 0.887816021812 -0.600555545865
y[1] (closed_form) = 0.887802006707 -0.600601858231
absolute error = 4.839e-05
relative error = 0.004514 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4434
Order of pole (three term test) = 32.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1926 0.495
h = 0.001 0.001
y[1] (numeric) = 0.888904658221 -0.604553926852
y[1] (closed_form) = 0.88888803714 -0.604598337901
absolute error = 4.742e-05
relative error = 0.004411 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3497
Order of pole (three term test) = 32.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1936 0.496
h = 0.001 0.003
y[1] (numeric) = 0.8879926984 -0.606283027889
y[1] (closed_form) = 0.887975121925 -0.606326070581
absolute error = 4.649e-05
relative error = 0.004324 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.662
Order of pole (three term test) = 32.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1946 0.499
h = 0.0001 0.004
y[1] (numeric) = 0.887893951295 -0.610656173015
y[1] (closed_form) = 0.887878429373 -0.610701928427
absolute error = 4.832e-05
relative error = 0.004484 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9447
Order of pole (three term test) = 32.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1947 0.503
h = 0.003 0.006
y[1] (numeric) = 0.889403960444 -0.615997822495
y[1] (closed_form) = 0.889391329601 -0.616043278807
absolute error = 4.718e-05
relative error = 0.004361 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.26
Order of pole (three term test) = 32.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1977 0.509
h = 0.0001 0.005
y[1] (numeric) = 0.887910223873 -0.625208006154
y[1] (closed_form) = 0.887891796029 -0.62526489293
absolute error = 5.980e-05
relative error = 0.005506 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5652
Order of pole (three term test) = 32.81 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1978 0.514
h = 0.0001 0.003
y[1] (numeric) = 0.889868070649 -0.631929498675
y[1] (closed_form) = 0.889852154766 -0.631978417681
absolute error = 5.144e-05
relative error = 0.004713 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4588
Order of pole (three term test) = 32.81 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1979 0.517
h = 0.001 0.001
y[1] (numeric) = 0.891003746026 -0.63598454912
y[1] (closed_form) = 0.890985221034 -0.636031472321
absolute error = 5.045e-05
relative error = 0.004608 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3619
Order of pole (three term test) = 32.81 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1989 0.518
h = 0.0001 0.004
y[1] (numeric) = 0.890089668616 -0.63774835229
y[1] (closed_form) = 0.890070202471 -0.637793860349
absolute error = 4.950e-05
relative error = 0.00452 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.176
Order of pole (three term test) = 32.81 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.199 0.522
h = 0.003 0.006
y[1] (numeric) = 0.891651393535 -0.64315167063
y[1] (closed_form) = 0.891638365475 -0.643199579624
absolute error = 4.965e-05
relative error = 0.004516 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.298
Order of pole (three term test) = 32.81 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.202 0.528
h = 0.0001 0.005
y[1] (numeric) = 0.890195411775 -0.652499575537
y[1] (closed_form) = 0.890176271955 -0.652558986568
absolute error = 6.242e-05
relative error = 0.005655 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5825
Order of pole (three term test) = 32.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2021 0.533
h = 0.0001 0.003
y[1] (numeric) = 0.892222203945 -0.659302714015
y[1] (closed_form) = 0.892205770406 -0.65935407589
absolute error = 5.393e-05
relative error = 0.004861 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4729
Order of pole (three term test) = 32.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2022 0.536
h = 0.001 0.001
y[1] (numeric) = 0.893398735334 -0.663407681388
y[1] (closed_form) = 0.893379688255 -0.663456964961
absolute error = 5.284e-05
relative error = 0.004748 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3731
Order of pole (three term test) = 32.83 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2032 0.537
h = 0.001 0.003
y[1] (numeric) = 0.892482595393 -0.665201866335
y[1] (closed_form) = 0.892462618769 -0.665249693636
absolute error = 5.183e-05
relative error = 0.004656 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.773
Order of pole (three term test) = 32.83 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2042 0.54
h = 0.0001 0.004
y[1] (numeric) = 0.892440309022 -0.669709293521
y[1] (closed_form) = 0.892422341476 -0.669760015017
absolute error = 5.381e-05
relative error = 0.004823 %
Correct digits = 4
memory used=292.0MB, alloc=44.3MB, time=3.50
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.008
Order of pole (three term test) = 32.83 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2043 0.544
h = 0.003 0.006
y[1] (numeric) = 0.894068132265 -0.675193492562
y[1] (closed_form) = 0.894053168722 -0.675244027868
absolute error = 5.270e-05
relative error = 0.004704 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.345
Order of pole (three term test) = 32.83 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2073 0.55
h = 0.0001 0.005
y[1] (numeric) = 0.892651166519 -0.684705641833
y[1] (closed_form) = 0.892629719389 -0.684767760831
absolute error = 6.572e-05
relative error = 0.005841 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6035
Order of pole (three term test) = 32.84 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2074 0.555
h = 0.0001 0.003
y[1] (numeric) = 0.894756133841 -0.691608055232
y[1] (closed_form) = 0.89473762289 -0.691662030823
absolute error = 5.706e-05
relative error = 0.005046 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4901
Order of pole (three term test) = 32.84 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2075 0.558
h = 0.001 0.001
y[1] (numeric) = 0.895978939777 -0.695773660183
y[1] (closed_form) = 0.895957810803 -0.69582546013
absolute error = 5.594e-05
relative error = 0.004931 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3866
Order of pole (three term test) = 32.85 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2085 0.559
h = 0.001 0.003
y[1] (numeric) = 0.895059140989 -0.697603669289
y[1] (closed_form) = 0.895037096532 -0.697653964558
absolute error = 5.491e-05
relative error = 0.004839 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.838
Order of pole (three term test) = 32.85 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2095 0.562
h = 0.0001 0.004
y[1] (numeric) = 0.895045216333 -0.702186367873
y[1] (closed_form) = 0.895025156261 -0.702239657243
absolute error = 5.694e-05
relative error = 0.005005 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.045
Order of pole (three term test) = 32.85 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2096 0.566
h = 0.003 0.006
y[1] (numeric) = 0.896735106066 -0.707751679194
y[1] (closed_form) = 0.896718112312 -0.707804844294
absolute error = 5.582e-05
relative error = 0.004886 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.394
Order of pole (three term test) = 32.85 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2126 0.572
h = 0.0001 0.005
y[1] (numeric) = 0.895354291905 -0.717432079172
y[1] (closed_form) = 0.895330437079 -0.71749691339
absolute error = 6.908e-05
relative error = 0.006021 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6258
Order of pole (three term test) = 32.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2127 0.577
h = 0.0001 0.003
y[1] (numeric) = 0.897536784317 -0.724437405376
y[1] (closed_form) = 0.897516098805 -0.724493998907
absolute error = 6.026e-05
relative error = 0.005224 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5082
Order of pole (three term test) = 32.87 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2128 0.58
h = 0.001 0.001
y[1] (numeric) = 0.898805450813 -0.728665832278
y[1] (closed_form) = 0.898782142108 -0.728720151221
absolute error = 5.911e-05
relative error = 0.005108 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.401
Order of pole (three term test) = 32.87 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2138 0.581
h = 0.001 0.003
y[1] (numeric) = 0.897881147031 -0.730532285374
y[1] (closed_form) = 0.897856936837 -0.730585050332
absolute error = 5.805e-05
relative error = 0.005015 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.906
Order of pole (three term test) = 32.87 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2148 0.584
h = 0.0001 0.004
y[1] (numeric) = 0.897894508975 -0.735192341464
y[1] (closed_form) = 0.897872258679 -0.735248202258
absolute error = 6.013e-05
relative error = 0.005181 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.084
Order of pole (three term test) = 32.87 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2149 0.588
h = 0.003 0.006
y[1] (numeric) = 0.899645937727 -0.74084169653
y[1] (closed_form) = 0.899626817492 -0.740897495633
absolute error = 5.898e-05
relative error = 0.005061 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.446
Order of pole (three term test) = 32.88 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2179 0.594
h = 0.0001 0.005
y[1] (numeric) = 0.898298387966 -0.7506944387
y[1] (closed_form) = 0.898272023325 -0.750761996066
absolute error = 7.252e-05
relative error = 0.006195 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6494
Order of pole (three term test) = 32.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.218 0.599
h = 0.0001 0.003
y[1] (numeric) = 0.900557766749 -0.757806380593
y[1] (closed_form) = 0.900534807925 -0.757865596974
absolute error = 6.351e-05
relative error = 0.005396 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5275
Order of pole (three term test) = 32.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2181 0.602
h = 0.001 0.001
y[1] (numeric) = 0.901871886075 -0.762099853158
y[1] (closed_form) = 0.901846298221 -0.762156694358
absolute error = 6.234e-05
relative error = 0.005279 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4162
Order of pole (three term test) = 32.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2191 0.603
h = 0.001 0.003
y[1] (numeric) = 0.900942220597 -0.764003385638
y[1] (closed_form) = 0.900915745202 -0.764058622628
absolute error = 6.125e-05
relative error = 0.005185 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.978
Order of pole (three term test) = 32.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2201 0.606
h = 0.0001 0.004
y[1] (numeric) = 0.900981788426 -0.768742926977
y[1] (closed_form) = 0.900957248613 -0.768801363406
absolute error = 6.338e-05
relative error = 0.005351 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.125
Order of pole (three term test) = 32.9 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=335.7MB, alloc=44.3MB, time=4.02
x[1] = 0.2202 0.61
h = 0.003 0.006
y[1] (numeric) = 0.902794237185 -0.774479309922
y[1] (closed_form) = 0.902772892616 -0.77453774794
absolute error = 6.221e-05
relative error = 0.00523 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.501
Order of pole (three term test) = 32.9 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2232 0.616
h = 0.0001 0.005
y[1] (numeric) = 0.901477039611 -0.784508572101
y[1] (closed_form) = 0.901448061256 -0.784578861198
absolute error = 7.603e-05
relative error = 0.006362 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6743
Order of pole (three term test) = 32.91 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2233 0.621
h = 0.0001 0.003
y[1] (numeric) = 0.903812676236 -0.791730899106
y[1] (closed_form) = 0.903787343699 -0.791792743913
absolute error = 6.683e-05
relative error = 0.005562 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5478
Order of pole (three term test) = 32.91 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2234 0.624
h = 0.001 0.001
y[1] (numeric) = 0.905171846215 -0.796091681302
y[1] (closed_form) = 0.905143878168 -0.796151048639
absolute error = 6.563e-05
relative error = 0.005444 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4323
Order of pole (three term test) = 32.92 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2244 0.625
h = 0.0001 0.004
y[1] (numeric) = 0.904235951249 -0.798032944215
y[1] (closed_form) = 0.904207109577 -0.798090656178
absolute error = 6.452e-05
relative error = 0.00535 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.6
Order of pole (three term test) = 32.92 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2245 0.629
h = 0.003 0.006
y[1] (numeric) = 0.906098064574 -0.803842658228
y[1] (closed_form) = 0.906076011816 -0.803903717819
absolute error = 6.492e-05
relative error = 0.00536 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.552
Order of pole (three term test) = 32.92 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2275 0.635
h = 0.0001 0.005
y[1] (numeric) = 0.904806812382 -0.814026961411
y[1] (closed_form) = 0.904776786845 -0.814099959617
absolute error = 7.893e-05
relative error = 0.006485 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.697
Order of pole (three term test) = 32.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2276 0.64
h = 0.0001 0.003
y[1] (numeric) = 0.907208970104 -0.821346476295
y[1] (closed_form) = 0.907182798594 -0.821410935966
absolute error = 6.957e-05
relative error = 0.005685 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5662
Order of pole (three term test) = 32.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2277 0.643
h = 0.001 0.001
y[1] (numeric) = 0.908607439104 -0.825766510515
y[1] (closed_form) = 0.908578624759 -0.825828403363
absolute error = 6.827e-05
relative error = 0.00556 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4469
Order of pole (three term test) = 32.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2287 0.644
h = 0.001 0.003
y[1] (numeric) = 0.907665938516 -0.827740872382
y[1] (closed_form) = 0.907636261887 -0.827801064884
absolute error = 6.711e-05
relative error = 0.005463 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.124
Order of pole (three term test) = 32.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2297 0.647
h = 0.0001 0.004
y[1] (numeric) = 0.907752378362 -0.832633844443
y[1] (closed_form) = 0.907724593695 -0.832697434568
absolute error = 6.940e-05
relative error = 0.005634 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.208
Order of pole (three term test) = 32.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2298 0.651
h = 0.003 0.006
y[1] (numeric) = 0.909678137954 -0.838539581319
y[1] (closed_form) = 0.909653674487 -0.838603291985
absolute error = 6.825e-05
relative error = 0.005516 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.613
Order of pole (three term test) = 32.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2328 0.657
h = 0.0001 0.005
y[1] (numeric) = 0.908411796733 -0.848908447956
y[1] (closed_form) = 0.908378959367 -0.848984196834
absolute error = 8.256e-05
relative error = 0.00664 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7245
Order of pole (three term test) = 32.96 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2329 0.662
h = 0.0001 0.003
y[1] (numeric) = 0.910889112719 -0.856345551732
y[1] (closed_form) = 0.910860376211 -0.856412653149
absolute error = 7.300e-05
relative error = 0.005839 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5887
Order of pole (three term test) = 32.96 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.233 0.665
h = 0.001 0.001
y[1] (numeric) = 0.912331924497 -0.860837223339
y[1] (closed_form) = 0.912300537508 -0.860901652366
absolute error = 7.167e-05
relative error = 0.005713 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4646
Order of pole (three term test) = 32.96 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.234 0.666
h = 0.001 0.003
y[1] (numeric) = 0.911382556455 -0.862850579758
y[1] (closed_form) = 0.91135032108 -0.862913255476
absolute error = 7.048e-05
relative error = 0.005616 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.209
Order of pole (three term test) = 32.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.235 0.669
h = 0.0001 0.004
y[1] (numeric) = 0.911492097756 -0.867829373633
y[1] (closed_form) = 0.911461730346 -0.867895556154
absolute error = 7.282e-05
relative error = 0.005786 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.256
Order of pole (three term test) = 32.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2351 0.673
h = 0.003 0.006
y[1] (numeric) = 0.91347746866 -0.873830983281
y[1] (closed_form) = 0.91345049185 -0.873897351859
absolute error = 7.164e-05
relative error = 0.005667 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.677
Order of pole (three term test) = 32.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2381 0.679
h = 0.0001 0.005
y[1] (numeric) = 0.912233042852 -0.884388845442
y[1] (closed_form) = 0.9121972844 -0.884467355365
absolute error = 8.627e-05
relative error = 0.00679 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7535
Order of pole (three term test) = 32.98 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=379.2MB, alloc=44.3MB, time=4.54
x[1] = 0.2382 0.684
h = 0.0001 0.003
y[1] (numeric) = 0.914784912101 -0.891947506609
y[1] (closed_form) = 0.914753505225 -0.892017257158
absolute error = 7.650e-05
relative error = 0.005987 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6123
Order of pole (three term test) = 32.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2383 0.687
h = 0.001 0.001
y[1] (numeric) = 0.91627167693 -0.896513199948
y[1] (closed_form) = 0.916237611342 -0.896580170703
absolute error = 7.514e-05
relative error = 0.005861 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4833
Order of pole (three term test) = 32.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2393 0.688
h = 0.001 0.003
y[1] (numeric) = 0.915313539047 -0.898566247444
y[1] (closed_form) = 0.915278638991 -0.89863141093
absolute error = 7.392e-05
relative error = 0.005763 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.297
Order of pole (three term test) = 33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2403 0.691
h = 0.0001 0.004
y[1] (numeric) = 0.915445070601 -0.903633158626
y[1] (closed_form) = 0.915412014548 -0.90370194013
absolute error = 7.631e-05
relative error = 0.005933 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.307
Order of pole (three term test) = 33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2404 0.695
h = 0.003 0.006
y[1] (numeric) = 0.917489558311 -0.909733840341
y[1] (closed_form) = 0.917459963762 -0.909802874293
absolute error = 7.511e-05
relative error = 0.005813 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.745
Order of pole (three term test) = 33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2434 0.701
h = 0.0001 0.005
y[1] (numeric) = 0.916264018274 -0.920485221373
y[1] (closed_form) = 0.916225227503 -0.92056650329
absolute error = 9.006e-05
relative error = 0.006934 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.784
Order of pole (three term test) = 33.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2435 0.706
h = 0.0001 0.003
y[1] (numeric) = 0.918889841428 -0.928169481238
y[1] (closed_form) = 0.918855656978 -0.92824188889
absolute error = 8.007e-05
relative error = 0.006131 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6371
Order of pole (three term test) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2436 0.709
h = 0.001 0.001
y[1] (numeric) = 0.920420172358 -0.932811624653
y[1] (closed_form) = 0.920383320401 -0.932881143219
absolute error = 7.868e-05
relative error = 0.006004 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5029
Order of pole (three term test) = 33.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2446 0.71
h = 0.001 0.003
y[1] (numeric) = 0.919452348989 -0.934905075803
y[1] (closed_form) = 0.919414676523 -0.934972732121
absolute error = 7.744e-05
relative error = 0.005905 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.391
Order of pole (three term test) = 33.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2456 0.713
h = 0.0001 0.004
y[1] (numeric) = 0.919604749071 -0.940062445087
y[1] (closed_form) = 0.919568896643 -0.940133832718
absolute error = 7.988e-05
relative error = 0.006074 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.36
Order of pole (three term test) = 33.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2457 0.717
h = 0.003 0.006
y[1] (numeric) = 0.921707862929 -0.946265457118
y[1] (closed_form) = 0.921675544428 -0.946337164512
absolute error = 7.865e-05
relative error = 0.005954 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.816
Order of pole (three term test) = 33.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2487 0.723
h = 0.0001 0.005
y[1] (numeric) = 0.920498142498 -0.957214973004
y[1] (closed_form) = 0.920456206147 -0.957299038422
absolute error = 9.394e-05
relative error = 0.007074 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8161
Order of pole (three term test) = 33.05 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2488 0.728
h = 0.0001 0.003
y[1] (numeric) = 0.923197324624 -0.965028947385
y[1] (closed_form) = 0.923160253508 -0.965104020674
absolute error = 8.373e-05
relative error = 0.006269 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6632
Order of pole (three term test) = 33.05 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2489 0.731
h = 0.001 0.001
y[1] (numeric) = 0.924770836738 -0.969750014234
y[1] (closed_form) = 0.924731088777 -0.969822087208
absolute error = 8.231e-05
relative error = 0.006142 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5235
Order of pole (three term test) = 33.05 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2499 0.732
h = 0.0001 0.004
y[1] (numeric) = 0.9237923984 -0.971884597777
y[1] (closed_form) = 0.92375184395 -0.971954752482
absolute error = 8.103e-05
relative error = 0.006043 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.149
Order of pole (three term test) = 33.06 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.25 0.736
h = 0.003 0.006
y[1] (numeric) = 0.925943261406 -0.978173667007
y[1] (closed_form) = 0.92590990176 -0.97824818932
absolute error = 8.165e-05
relative error = 0.006062 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.88
Order of pole (three term test) = 33.06 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.253 0.742
h = 0.0001 0.005
y[1] (numeric) = 0.924747109711 -0.989297360861
y[1] (closed_form) = 0.924703764846 -0.989384343792
absolute error = 9.718e-05
relative error = 0.007176 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8452
Order of pole (three term test) = 33.07 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2531 0.747
h = 0.0001 0.003
y[1] (numeric) = 0.927510576155 -0.997225478913
y[1] (closed_form) = 0.927472321388 -0.997303362733
absolute error = 8.677e-05
relative error = 0.006371 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6869
Order of pole (three term test) = 33.08 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2532 0.75
h = 0.001 0.001
y[1] (numeric) = 0.929121931045 -1.002015988
y[1] (closed_form) = 0.92908098962 -1.00209077429
absolute error = 8.526e-05
relative error = 0.006239 %
Correct digits = 4
memory used=422.8MB, alloc=44.3MB, time=5.06
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5423
Order of pole (three term test) = 33.08 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2542 0.751
h = 0.001 0.003
y[1] (numeric) = 0.928134102473 -1.00418671469
y[1] (closed_form) = 0.928092366004 -1.00425953348
absolute error = 8.393e-05
relative error = 0.006138 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.578
Order of pole (three term test) = 33.09 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2552 0.754
h = 0.0001 0.004
y[1] (numeric) = 0.928323453575 -1.00951857758
y[1] (closed_form) = 0.928283493823 -1.00959534446
absolute error = 8.654e-05
relative error = 0.00631 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.467
Order of pole (three term test) = 33.09 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2553 0.758
h = 0.0001 0.004
y[1] (numeric) = 0.930535673612 -1.0159201974
y[1] (closed_form) = 0.930499387485 -1.01599741102
absolute error = 8.531e-05
relative error = 0.006193 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.168
Order of pole (three term test) = 33.1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2554 0.762
h = 0.003 0.006
y[1] (numeric) = 0.932765633178 -1.02233925417
y[1] (closed_form) = 0.932729347051 -1.02241646779
absolute error = 8.531e-05
relative error = 0.006165 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.973
Order of pole (three term test) = 33.1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2584 0.768
h = 0.0001 0.005
y[1] (numeric) = 0.93158877087 -1.03370594485
y[1] (closed_form) = 0.931541992617 -1.03379577231
absolute error = 0.0001013
relative error = 0.007278 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8871
Order of pole (three term test) = 33.11 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2585 0.773
h = 0.0001 0.003
y[1] (numeric) = 0.934442202472 -1.04179319924
y[1] (closed_form) = 0.934400823313 -1.04187377251
absolute error = 9.058e-05
relative error = 0.006472 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.721
Order of pole (three term test) = 33.12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2586 0.776
h = 0.001 0.001
y[1] (numeric) = 0.936106533152 -1.04668051807
y[1] (closed_form) = 0.936062450873 -1.04675785913
absolute error = 8.902e-05
relative error = 0.006339 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5692
Order of pole (three term test) = 33.12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2596 0.777
h = 0.001 0.003
y[1] (numeric) = 0.935105691376 -1.0489017039
y[1] (closed_form) = 0.935060828504 -1.04897700878
absolute error = 8.766e-05
relative error = 0.006238 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.706
Order of pole (three term test) = 33.13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2606 0.78
h = 0.0001 0.004
y[1] (numeric) = 0.935319270497 -1.05434746376
y[1] (closed_form) = 0.935276160486 -1.05442685803
absolute error = 9.034e-05
relative error = 0.00641 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.54
Order of pole (three term test) = 33.13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2607 0.784
h = 0.003 0.006
y[1] (numeric) = 0.937602862166 -1.06087867791
y[1] (closed_form) = 0.937563518743 -1.06095859846
absolute error = 8.908e-05
relative error = 0.006292 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.056
Order of pole (three term test) = 33.14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2637 0.79
h = 0.0001 0.005
y[1] (numeric) = 0.93643251165 -1.07245824538
y[1] (closed_form) = 0.936382231897 -1.07255090036
absolute error = 0.0001054
relative error = 0.007404 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9244
Order of pole (three term test) = 33.15 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2638 0.795
h = 0.0001 0.003
y[1] (numeric) = 0.939357727091 -1.08068820291
y[1] (closed_form) = 0.939313118753 -1.08077147662
absolute error = 9.447e-05
relative error = 0.006597 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7514
Order of pole (three term test) = 33.16 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2639 0.798
h = 0.001 0.001
y[1] (numeric) = 0.941064205357 -1.08566225341
y[1] (closed_form) = 0.941016882945 -1.0857421775
absolute error = 9.288e-05
relative error = 0.006465 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5932
Order of pole (three term test) = 33.16 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2649 0.799
h = 0.001 0.003
y[1] (numeric) = 0.940049876656 -1.08792693063
y[1] (closed_form) = 0.940001787919 -1.08800475922
absolute error = 9.149e-05
relative error = 0.006363 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.82
Order of pole (three term test) = 33.17 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2659 0.802
h = 0.0001 0.004
y[1] (numeric) = 0.940279796302 -1.09347312511
y[1] (closed_form) = 0.940233436176 -1.09355516526
absolute error = 9.423e-05
relative error = 0.006534 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.605
Order of pole (three term test) = 33.17 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.266 0.806
h = 0.003 0.006
y[1] (numeric) = 0.942620227414 -1.10012046288
y[1] (closed_form) = 0.942577712663 -1.10020310076
absolute error = 9.293e-05
relative error = 0.006415 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.143
Order of pole (three term test) = 33.18 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.269 0.812
h = 0.0001 0.005
y[1] (numeric) = 0.94145315454 -1.11191791359
y[1] (closed_form) = 0.9413992513 -1.11201340973
absolute error = 0.0001097
relative error = 0.007526 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9635
Order of pole (three term test) = 33.19 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2691 0.817
h = 0.0001 0.003
y[1] (numeric) = 0.944449568121 -1.1202950087
y[1] (closed_form) = 0.944401613391 -1.12038099355
absolute error = 9.845e-05
relative error = 0.006719 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7832
Order of pole (three term test) = 33.2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=466.5MB, alloc=44.3MB, time=5.57
x[1] = 0.2692 0.82
h = 0.001 0.001
y[1] (numeric) = 0.946197811958 -1.12535845663
y[1] (closed_form) = 0.946147131744 -1.12544097229
absolute error = 9.684e-05
relative error = 0.006586 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6184
Order of pole (three term test) = 33.2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2702 0.821
h = 0.001 0.003
y[1] (numeric) = 0.945169005713 -1.1276674212
y[1] (closed_form) = 0.945117573581 -1.1277477809
absolute error = 9.541e-05
relative error = 0.006484 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.94
Order of pole (three term test) = 33.21 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2712 0.824
h = 0.0001 0.004
y[1] (numeric) = 0.945414077239 -1.13331663255
y[1] (closed_form) = 0.945364349274 -1.1334013283
absolute error = 9.822e-05
relative error = 0.006655 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.673
Order of pole (three term test) = 33.21 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2713 0.828
h = 0.003 0.006
y[1] (numeric) = 0.947810864573 -1.14008367046
y[1] (closed_form) = 0.947765062385 -1.14016903656
absolute error = 9.688e-05
relative error = 0.006534 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.234
Order of pole (three term test) = 33.22 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2743 0.834
h = 0.0001 0.005
y[1] (numeric) = 0.94664378587 -1.15210411095
y[1] (closed_form) = 0.946586134844 -1.15220246235
absolute error = 0.000114
relative error = 0.007645 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.005
Order of pole (three term test) = 33.23 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2744 0.839
h = 0.0001 0.003
y[1] (numeric) = 0.949710810038 -1.16063286176
y[1] (closed_form) = 0.949659389546 -1.16072156889
absolute error = 0.0001025
relative error = 0.006837 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8167
Order of pole (three term test) = 33.24 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2745 0.842
h = 0.001 0.001
y[1] (numeric) = 0.951500435624 -1.16578842338
y[1] (closed_form) = 0.951446277805 -1.16587353953
absolute error = 0.0001009
relative error = 0.006704 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6448
Order of pole (three term test) = 33.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2755 0.843
h = 0.001 0.003
y[1] (numeric) = 0.950456144288 -1.16814248808
y[1] (closed_form) = 0.950401249118 -1.16822538665
absolute error = 9.943e-05
relative error = 0.006602 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.066
Order of pole (three term test) = 33.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2765 0.846
h = 0.0001 0.004
y[1] (numeric) = 0.950715161932 -1.17389734906
y[1] (closed_form) = 0.950661946249 -1.17398471056
absolute error = 0.0001023
relative error = 0.006772 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.745
Order of pole (three term test) = 33.26 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2766 0.85
h = 0.003 0.006
y[1] (numeric) = 0.953167820044 -1.18078773132
y[1] (closed_form) = 0.953118612175 -1.18087583701
absolute error = 0.0001009
relative error = 0.00665 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.33
Order of pole (three term test) = 33.26 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2796 0.856
h = 0.0001 0.005
y[1] (numeric) = 0.951997400036 -1.1930363698
y[1] (closed_form) = 0.951935874548 -1.19313759099
absolute error = 0.0001185
relative error = 0.007761 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.048
Order of pole (three term test) = 33.28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2797 0.861
h = 0.0001 0.003
y[1] (numeric) = 0.955134444061 -1.20172138005
y[1] (closed_form) = 0.955079436221 -1.20181282105
absolute error = 0.0001067
relative error = 0.006951 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8517
Order of pole (three term test) = 33.29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2798 0.864
h = 0.001 0.001
y[1] (numeric) = 0.956965064959 -1.20697182328
y[1] (closed_form) = 0.956907307538 -1.20705954923
absolute error = 0.000105
relative error = 0.006819 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6725
Order of pole (three term test) = 33.29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2808 0.865
h = 0.0001 0.004
y[1] (numeric) = 0.955904263406 -1.20937181783
y[1] (closed_form) = 0.955845783381 -1.2094572634
absolute error = 0.0001035
relative error = 0.006717 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.046
Order of pole (three term test) = 33.29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2809 0.869
h = 0.003 0.006
y[1] (numeric) = 0.958402450537 -1.21636573983
y[1] (closed_form) = 0.958351752271 -1.21645693757
absolute error = 0.0001043
relative error = 0.006738 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.416
Order of pole (three term test) = 33.3 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2839 0.875
h = 0.0001 0.005
y[1] (numeric) = 0.9572292464 -1.22881514781
y[1] (closed_form) = 0.957165821667 -1.22891958133
absolute error = 0.0001222
relative error = 0.007844 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.087
Order of pole (three term test) = 33.32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.284 0.88
h = 0.0001 0.003
y[1] (numeric) = 0.960428022345 -1.23763758991
y[1] (closed_form) = 0.960371364934 -1.23773212041
absolute error = 0.0001102
relative error = 0.007035 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8834
Order of pole (three term test) = 33.33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2841 0.883
h = 0.001 0.001
y[1] (numeric) = 0.96229479467 -1.24297147883
y[1] (closed_form) = 0.962235375302 -1.24306218576
absolute error = 0.0001084
relative error = 0.006898 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6975
Order of pole (three term test) = 33.33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2851 0.884
h = 0.001 0.003
y[1] (numeric) = 0.961219507755 -1.24541189935
y[1] (closed_form) = 0.961159377872 -1.2455002707
absolute error = 0.0001069
relative error = 0.006794 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.316
Order of pole (three term test) = 33.34 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=510.1MB, alloc=44.3MB, time=6.08
x[1] = 0.2861 0.887
h = 0.0001 0.004
y[1] (numeric) = 0.961502538155 -1.2513704023
y[1] (closed_form) = 0.961444042655 -1.25146347945
absolute error = 0.0001099
relative error = 0.006966 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.887
Order of pole (three term test) = 33.34 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2862 0.891
h = 0.003 0.006
y[1] (numeric) = 0.964059429666 -1.25849958556
y[1] (closed_form) = 0.964005099964 -1.2585935467
absolute error = 0.0001085
relative error = 0.006846 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.52
Order of pole (three term test) = 33.35 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2892 0.897
h = 0.0001 0.005
y[1] (numeric) = 0.962876594827 -1.27118720019
y[1] (closed_form) = 0.962809053573 -1.27129453317
absolute error = 0.0001268
relative error = 0.007952 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.134
Order of pole (three term test) = 33.37 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2893 0.902
h = 0.0001 0.003
y[1] (numeric) = 0.96614433569 -1.28017471001
y[1] (closed_form) = 0.966083858742 -1.2802719985
absolute error = 0.0001146
relative error = 0.007142 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9216
Order of pole (three term test) = 33.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2894 0.905
h = 0.001 0.001
y[1] (numeric) = 0.96805140895 -1.28560877718
y[1] (closed_form) = 0.967988157061 -1.28570211364
absolute error = 0.0001127
relative error = 0.007006 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7277
Order of pole (three term test) = 33.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2904 0.906
h = 0.001 0.003
y[1] (numeric) = 0.966957665608 -1.2880967298
y[1] (closed_form) = 0.966893718331 -1.28818766562
absolute error = 0.0001112
relative error = 0.006902 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.46
Order of pole (three term test) = 33.39 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2914 0.909
h = 0.0001 0.004
y[1] (numeric) = 0.967251121159 -1.29416871643
y[1] (closed_form) = 0.96718878272 -1.29426449201
absolute error = 0.0001143
relative error = 0.007073 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.969
Order of pole (three term test) = 33.39 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2915 0.913
h = 0.003 0.006
y[1] (numeric) = 0.969862519037 -1.30143206321
y[1] (closed_form) = 0.969804433233 -1.30152880038
absolute error = 0.0001128
relative error = 0.006952 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.63
Order of pole (three term test) = 33.4 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2945 0.919
h = 0.0001 0.005
y[1] (numeric) = 0.968666555238 -1.31436339321
y[1] (closed_form) = 0.968594763655 -1.31447364128
absolute error = 0.0001316
relative error = 0.008058 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.183
Order of pole (three term test) = 33.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2946 0.924
h = 0.0001 0.003
y[1] (numeric) = 0.972002654809 -1.32352083044
y[1] (closed_form) = 0.971938230081 -1.32362088965
absolute error = 0.000119
relative error = 0.007247 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9617
Order of pole (three term test) = 33.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2947 0.927
h = 0.001 0.001
y[1] (numeric) = 0.973949631162 -1.32905799814
y[1] (closed_form) = 0.973882418165 -1.32915397442
absolute error = 0.0001172
relative error = 0.007111 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7593
Order of pole (three term test) = 33.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2957 0.928
h = 0.001 0.003
y[1] (numeric) = 0.972836352494 -1.3315943621
y[1] (closed_form) = 0.97276845948 -1.33168787141
absolute error = 0.0001156
relative error = 0.007007 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.611
Order of pole (three term test) = 33.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2967 0.931
h = 0.0001 0.004
y[1] (numeric) = 0.973138950896 -1.33778266921
y[1] (closed_form) = 0.973072640778 -1.33788115481
absolute error = 0.0001187
relative error = 0.007177 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.055
Order of pole (three term test) = 33.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2968 0.935
h = 0.003 0.006
y[1] (numeric) = 0.975804351794 -1.34518410006
y[1] (closed_form) = 0.975742382865 -1.34528362629
absolute error = 0.0001172
relative error = 0.007055 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.744
Order of pole (three term test) = 33.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2998 0.941
h = 0.0001 0.005
y[1] (numeric) = 0.974591697953 -1.35836476219
y[1] (closed_form) = 0.974515519617 -1.35847794135
absolute error = 0.0001364
relative error = 0.00816 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.234
Order of pole (three term test) = 33.47 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2999 0.946
h = 0.0001 0.003
y[1] (numeric) = 0.977995541559 -1.36769707995
y[1] (closed_form) = 0.977927038363 -1.36779992295
absolute error = 0.0001236
relative error = 0.007349 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.004
Order of pole (three term test) = 33.48 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3 0.949
h = 0.001 0.001
y[1] (numeric) = 0.97998201731 -1.37334032678
y[1] (closed_form) = 0.979910712199 -1.37343895342
absolute error = 0.0001217
relative error = 0.007213 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7925
Order of pole (three term test) = 33.49 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.301 0.95
h = 0.001 0.003
y[1] (numeric) = 0.978848104224 -1.37592599882
y[1] (closed_form) = 0.978776134729 -1.37602209088
absolute error = 0.0001201
relative error = 0.00711 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.768
Order of pole (three term test) = 33.49 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.302 0.953
h = 0.0001 0.004
y[1] (numeric) = 0.979158540214 -1.38223351837
y[1] (closed_form) = 0.979088127236 -1.38233472589
absolute error = 0.0001233
relative error = 0.007278 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.145
Order of pole (three term test) = 33.5 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=553.4MB, alloc=44.3MB, time=6.60
x[1] = 0.3021 0.957
h = 0.003 0.006
y[1] (numeric) = 0.981877433205 -1.38977702939
y[1] (closed_form) = 0.981811451705 -1.38987935807
absolute error = 0.0001218
relative error = 0.007155 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.864
Order of pole (three term test) = 33.51 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3051 0.963
h = 0.0001 0.005
y[1] (numeric) = 0.980644462481 -1.4032127502
y[1] (closed_form) = 0.980563758286 -1.40332887676
absolute error = 0.0001414
relative error = 0.00826 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.288
Order of pole (three term test) = 33.53 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3052 0.968
h = 0.0001 0.003
y[1] (numeric) = 0.984115425551 -1.41272499716
y[1] (closed_form) = 0.984042710689 -1.41283063732
absolute error = 0.0001282
relative error = 0.007449 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.048
Order of pole (three term test) = 33.54 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3053 0.971
h = 0.001 0.001
y[1] (numeric) = 0.986140990274 -1.41847735927
y[1] (closed_form) = 0.986065459556 -1.41857864707
absolute error = 0.0001263
relative error = 0.007313 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8272
Order of pole (three term test) = 33.55 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3063 0.972
h = 0.0001 0.004
y[1] (numeric) = 0.984985322767 -1.42111325382
y[1] (closed_form) = 0.984909143589 -1.42121193813
absolute error = 0.0001247
relative error = 0.00721 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.977
Order of pole (three term test) = 33.55 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3064 0.976
h = 0.003 0.006
y[1] (numeric) = 0.987747806763 -1.42877589746
y[1] (closed_form) = 0.987679935267 -1.42888156777
absolute error = 0.0001256
relative error = 0.00723 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.973
Order of pole (three term test) = 33.56 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3094 0.982
h = 0.0001 0.005
y[1] (numeric) = 0.986497524418 -1.44243613717
y[1] (closed_form) = 0.986414482234 -1.44255573867
absolute error = 0.0001456
relative error = 0.008332 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.337
Order of pole (three term test) = 33.58 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3095 0.987
h = 0.0001 0.003
y[1] (numeric) = 0.99002797988 -1.45210658934
y[1] (closed_form) = 0.989953200509 -1.45221556896
absolute error = 0.0001322
relative error = 0.00752 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.087
Order of pole (three term test) = 33.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3096 0.99
h = 0.001 0.001
y[1] (numeric) = 0.992088206722 -1.45795489161
y[1] (closed_form) = 0.992010597616 -1.45805939987
absolute error = 0.0001302
relative error = 0.007381 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8585
Order of pole (three term test) = 33.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3106 0.991
h = 0.001 0.003
y[1] (numeric) = 0.990913513777 -1.46063503956
y[1] (closed_form) = 0.990835269323 -1.46073688373
absolute error = 0.0001284
relative error = 0.007276 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.082
Order of pole (three term test) = 33.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3116 0.994
h = 0.0001 0.004
y[1] (numeric) = 0.991236479778 -1.46717222039
y[1] (closed_form) = 0.991159743166 -1.46727944655
absolute error = 0.0001319
relative error = 0.007447 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.324
Order of pole (three term test) = 33.62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3117 0.998
h = 0.003 0.006
y[1] (numeric) = 0.99405532686 -1.4749903887
y[1] (closed_form) = 0.993983195438 -1.47509888888
absolute error = 0.0001303
relative error = 0.007325 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.103
Order of pole (three term test) = 33.63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3147 1.004
h = 0.0001 0.005
y[1] (numeric) = 0.992777865015 -1.48891668633
y[1] (closed_form) = 0.992690030953 -1.48903926804
absolute error = 0.0001508
relative error = 0.008427 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.396
Order of pole (three term test) = 33.65 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3148 1.009
h = 0.0001 0.003
y[1] (numeric) = 0.99637430931 -1.49877673152
y[1] (closed_form) = 0.996295063694 -1.49888853561
absolute error = 0.000137
relative error = 0.007614 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.135
Order of pole (three term test) = 33.66 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3149 1.012
h = 0.001 0.001
y[1] (numeric) = 0.998472878272 -1.50473996147
y[1] (closed_form) = 0.998390788467 -1.50484715324
absolute error = 0.000135
relative error = 0.007476 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8964
Order of pole (three term test) = 33.67 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3159 1.013
h = 0.001 0.003
y[1] (numeric) = 0.997274300107 -1.50747209496
y[1] (closed_form) = 0.99719159146 -1.50757655121
absolute error = 0.0001332
relative error = 0.007371 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.262
Order of pole (three term test) = 33.67 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3169 1.016
h = 0.0001 0.004
y[1] (numeric) = 0.997601268144 -1.51413709183
y[1] (closed_form) = 0.997520039489 -1.51424707712
absolute error = 0.0001367
relative error = 0.00754 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.426
Order of pole (three term test) = 33.68 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.317 1.02
h = 0.003 0.006
y[1] (numeric) = 1.00047214406 -1.5221092113
y[1] (closed_form) = 1.000395616 -1.52222055569
absolute error = 0.0001351
relative error = 0.007417 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.24
Order of pole (three term test) = 33.69 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.32 1.026
h = 0.0001 0.005
y[1] (numeric) = 0.999163672435 -1.53630761824
y[1] (closed_form) = 0.999070899337 -1.53643319725
absolute error = 0.0001561
relative error = 0.008519 %
Correct digits = 4
memory used=597.1MB, alloc=52.3MB, time=7.14
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.458
Order of pole (three term test) = 33.72 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3201 1.031
h = 0.0001 0.003
y[1] (numeric) = 1.00282544573 -1.54636259062
y[1] (closed_form) = 1.00274159314 -1.54647723337
absolute error = 0.000142
relative error = 0.007706 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.185
Order of pole (three term test) = 33.73 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3202 1.034
h = 0.001 0.001
y[1] (numeric) = 1.00496192286 -1.55244395644
y[1] (closed_form) = 1.00487521141 -1.55255384315
absolute error = 0.00014
relative error = 0.007569 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9359
Order of pole (three term test) = 33.74 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3212 1.035
h = 0.001 0.003
y[1] (numeric) = 1.00373827584 -1.55522904159
y[1] (closed_form) = 1.0036509624 -1.55533611995
absolute error = 0.0001382
relative error = 0.007464 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.451
Order of pole (three term test) = 33.74 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3222 1.038
h = 0.0001 0.004
y[1] (numeric) = 1.00406784059 -1.56202496949
y[1] (closed_form) = 1.00398197868 -1.56213772679
absolute error = 0.0001417
relative error = 0.007632 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.533
Order of pole (three term test) = 33.75 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3223 1.042
h = 0.003 0.006
y[1] (numeric) = 1.006990195 -1.57015534432
y[1] (closed_form) = 1.00690913092 -1.57026954752
absolute error = 0.00014
relative error = 0.007508 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.383
Order of pole (three term test) = 33.76 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3253 1.048
h = 0.0001 0.005
y[1] (numeric) = 1.00564680571 -1.58463202879
y[1] (closed_form) = 1.00554894347 -1.58476062241
absolute error = 0.0001616
relative error = 0.00861 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.522
Order of pole (three term test) = 33.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3254 1.053
h = 0.0001 0.003
y[1] (numeric) = 1.00937323248 -1.59488736664
y[1] (closed_form) = 1.00928462943 -1.59500486246
absolute error = 0.0001472
relative error = 0.007796 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.238
Order of pole (three term test) = 33.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3255 1.056
h = 0.001 0.001
y[1] (numeric) = 1.01154717358 -1.60109013924
y[1] (closed_form) = 1.01145569679 -1.60120273244
absolute error = 0.0001451
relative error = 0.00766 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9774
Order of pole (three term test) = 33.81 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3265 1.057
h = 0.001 0.003
y[1] (numeric) = 1.01029725027 -1.60392916045
y[1] (closed_form) = 1.01020518875 -1.60403887106
absolute error = 0.0001432
relative error = 0.007555 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.648
Order of pole (three term test) = 33.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3275 1.06
h = 0.0001 0.004
y[1] (numeric) = 1.01062797706 -1.61085919465
y[1] (closed_form) = 1.01053733794 -1.61097473705
absolute error = 0.0001469
relative error = 0.007722 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.645
Order of pole (three term test) = 33.83 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3276 1.064
h = 0.003 0.006
y[1] (numeric) = 1.01360124619 -1.61915221322
y[1] (closed_form) = 1.01351550397 -1.61926929008
absolute error = 0.0001451
relative error = 0.007597 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.533
Order of pole (three term test) = 33.84 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3306 1.07
h = 0.0001 0.005
y[1] (numeric) = 1.01221895053 -1.63391346216
y[1] (closed_form) = 1.01211584601 -1.63404508788
absolute error = 0.0001672
relative error = 0.008699 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.59
Order of pole (three term test) = 33.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3307 1.075
h = 0.0001 0.003
y[1] (numeric) = 1.01600933803 -1.6443747102
y[1] (closed_form) = 1.01591583819 -1.64449507367
absolute error = 0.0001524
relative error = 0.007885 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.293
Order of pole (three term test) = 33.88 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3308 1.078
h = 0.001 0.001
y[1] (numeric) = 1.01822028764 -1.65070222455
y[1] (closed_form) = 1.01812389903 -1.65081753594
absolute error = 0.0001503
relative error = 0.007749 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.021
Order of pole (three term test) = 33.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3318 1.079
h = 0.0001 0.004
y[1] (numeric) = 1.01694285607 -1.6535961847
y[1] (closed_form) = 1.01684590037 -1.6537085378
absolute error = 0.0001484
relative error = 0.007644 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.141
Order of pole (three term test) = 33.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3319 1.083
h = 0.003 0.006
y[1] (numeric) = 1.01995759796 -1.66202545444
y[1] (closed_form) = 1.01986952744 -1.66214614828
absolute error = 0.0001494
relative error = 0.007662 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.668
Order of pole (three term test) = 33.9 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3349 1.089
h = 0.0001 0.005
y[1] (numeric) = 1.01854204871 -1.67703730317
y[1] (closed_form) = 1.0184361232 -1.67717269122
absolute error = 0.0001719
relative error = 0.008761 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.65
Order of pole (three term test) = 33.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.335 1.094
h = 0.0001 0.003
y[1] (numeric) = 1.02238946706 -1.68767956457
y[1] (closed_form) = 1.02229344721 -1.68780354227
absolute error = 0.0001568
relative error = 0.007947 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.342
Order of pole (three term test) = 33.95 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=640.8MB, alloc=52.3MB, time=7.65
x[1] = 0.3351 1.097
h = 0.001 0.001
y[1] (numeric) = 1.02463343955 -1.69411673978
y[1] (closed_form) = 1.02453451605 -1.69423553454
absolute error = 0.0001546
relative error = 0.007808 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.06
Order of pole (three term test) = 33.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3361 1.098
h = 0.001 0.003
y[1] (numeric) = 1.02333199496 -1.69705915495
y[1] (closed_form) = 1.02323251898 -1.69717492486
absolute error = 0.0001526
relative error = 0.007702 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.039
Order of pole (three term test) = 33.96 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3371 1.101
h = 0.0001 0.004
y[1] (numeric) = 1.02366264889 -1.70424741995
y[1] (closed_form) = 1.02356454108 -1.70436931443
absolute error = 0.0001565
relative error = 0.00787 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.868
Order of pole (three term test) = 33.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3372 1.105
h = 0.003 0.006
y[1] (numeric) = 1.0267311714 -1.71285446649
y[1] (closed_form) = 1.02663815097 -1.71297806397
absolute error = 0.0001547
relative error = 0.007746 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.831
Order of pole (three term test) = 33.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3402 1.111
h = 0.0001 0.005
y[1] (numeric) = 1.02526914567 -1.72816295085
y[1] (closed_form) = 1.02515768485 -1.72830140587
absolute error = 0.0001777
relative error = 0.008845 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.724
Order of pole (three term test) = 34.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3403 1.116
h = 0.0001 0.003
y[1] (numeric) = 1.02917925337 -1.73902174006
y[1] (closed_form) = 1.02907805686 -1.73914861482
absolute error = 0.0001623
relative error = 0.008031 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.402
Order of pole (three term test) = 34.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3404 1.119
h = 0.001 0.001
y[1] (numeric) = 1.0314593952 -1.74559004389
y[1] (closed_form) = 1.03135527973 -1.74571158064
absolute error = 0.00016
relative error = 0.007893 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.107
Order of pole (three term test) = 34.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3414 1.12
h = 0.001 0.003
y[1] (numeric) = 1.03012809429 -1.74858932923
y[1] (closed_form) = 1.0300234448 -1.74870776265
absolute error = 0.000158
relative error = 0.007787 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.263
Order of pole (three term test) = 34.05 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3424 1.123
h = 0.0001 0.004
y[1] (numeric) = 1.03045567165 -1.7559211457
y[1] (closed_form) = 1.03035235907 -1.75604586526
absolute error = 0.000162
relative error = 0.007954 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.996
Order of pole (three term test) = 34.06 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3425 1.127
h = 0.003 0.006
y[1] (numeric) = 1.03357346606 -1.76470387905
y[1] (closed_form) = 1.0334753454 -1.76483039561
absolute error = 0.0001601
relative error = 0.007829 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.002
Order of pole (three term test) = 34.07 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3455 1.133
h = 0.0001 0.005
y[1] (numeric) = 1.03206072705 -1.78031563755
y[1] (closed_form) = 1.03194356873 -1.78045717746
absolute error = 0.0001837
relative error = 0.008928 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.801
Order of pole (three term test) = 34.1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3456 1.138
h = 0.0001 0.003
y[1] (numeric) = 1.03603277435 -1.79139681726
y[1] (closed_form) = 1.03592624637 -1.7915266041
absolute error = 0.0001679
relative error = 0.008114 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.464
Order of pole (three term test) = 34.12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3457 1.141
h = 0.001 0.001
y[1] (numeric) = 1.03834859324 -1.79809977611
y[1] (closed_form) = 1.03823913092 -1.79822406677
absolute error = 0.0001656
relative error = 0.007976 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.156
Order of pole (three term test) = 34.13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3467 1.142
h = 0.001 0.003
y[1] (numeric) = 1.03698612957 -1.80115698858
y[1] (closed_form) = 1.03687615215 -1.80127809588
absolute error = 0.0001636
relative error = 0.007871 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.498
Order of pole (three term test) = 34.14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3477 1.145
h = 0.0001 0.004
y[1] (numeric) = 1.03730906978 -1.80863577564
y[1] (closed_form) = 1.03720039716 -1.80876333385
absolute error = 0.0001676
relative error = 0.008037 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.13
Order of pole (three term test) = 34.15 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3478 1.149
h = 0.003 0.006
y[1] (numeric) = 1.04047550929 -1.81759892719
y[1] (closed_form) = 1.04037213506 -1.81772837841
absolute error = 0.0001657
relative error = 0.00791 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.18
Order of pole (three term test) = 34.16 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3508 1.155
h = 0.0001 0.005
y[1] (numeric) = 1.03890772638 -1.83352072479
y[1] (closed_form) = 1.03878470505 -1.83366536757
absolute error = 0.0001899
relative error = 0.00901 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.881
Order of pole (three term test) = 34.19 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3509 1.16
h = 0.0001 0.003
y[1] (numeric) = 1.04294093989 -1.8448302735
y[1] (closed_form) = 1.04282892252 -1.84496298754
absolute error = 0.0001737
relative error = 0.008195 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.529
Order of pole (three term test) = 34.21 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.351 1.163
h = 0.001 0.001
y[1] (numeric) = 1.04529192843 -1.8516714835
y[1] (closed_form) = 1.04517696126 -1.85179853999
absolute error = 0.0001713
relative error = 0.008058 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.208
Order of pole (three term test) = 34.22 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=684.5MB, alloc=52.3MB, time=8.16
x[1] = 0.352 1.164
h = 0.001 0.003
y[1] (numeric) = 1.04389696781 -1.8547876992
y[1] (closed_form) = 1.04378150499 -1.85491149074
absolute error = 0.0001693
relative error = 0.007953 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.743
Order of pole (three term test) = 34.23 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.353 1.167
h = 0.0001 0.004
y[1] (numeric) = 1.04421367394 -1.86241694193
y[1] (closed_form) = 1.04409948289 -1.86254735237
absolute error = 0.0001733
relative error = 0.008118 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.269
Order of pole (three term test) = 34.24 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3531 1.171
h = 0.003 0.006
y[1] (numeric) = 1.04742811182 -1.87156533664
y[1] (closed_form) = 1.04731932762 -1.87169773821
absolute error = 0.0001714
relative error = 0.00799 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.366
Order of pole (three term test) = 34.26 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3561 1.177
h = 0.0001 0.005
y[1] (numeric) = 1.04580085697 -1.88780406681
y[1] (closed_form) = 1.04567180372 -1.88795183052
absolute error = 0.0001962
relative error = 0.00909 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.965
Order of pole (three term test) = 34.29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3562 1.182
h = 0.0001 0.003
y[1] (numeric) = 1.04989443795 -1.89934808143
y[1] (closed_form) = 1.04977677008 -1.89948373784
absolute error = 0.0001796
relative error = 0.008274 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.598
Order of pole (three term test) = 34.31 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3563 1.185
h = 0.001 0.001
y[1] (numeric) = 1.05228007251 -1.90633120993
y[1] (closed_form) = 1.05215943937 -1.90646104415
absolute error = 0.0001772
relative error = 0.008139 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.262
Order of pole (three term test) = 34.32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3573 1.186
h = 0.0001 0.004
y[1] (numeric) = 1.0508512522 -1.90950752429
y[1] (closed_form) = 1.05073014338 -1.90963401036
absolute error = 0.0001751
relative error = 0.008034 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.591
Order of pole (three term test) = 34.33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3574 1.19
h = 0.003 0.006
y[1] (numeric) = 1.05410474788 -1.91881098777
y[1] (closed_form) = 1.05399315217 -1.91894730802
absolute error = 0.0001762
relative error = 0.008047 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.534
Order of pole (three term test) = 34.35 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3604 1.196
h = 0.0001 0.005
y[1] (numeric) = 1.05242656816 -1.93532892481
y[1] (closed_form) = 1.05229415986 -1.93548076345
absolute error = 0.0002015
relative error = 0.009145 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.04
Order of pole (three term test) = 34.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3605 1.201
h = 0.0001 0.003
y[1] (numeric) = 1.05657434516 -1.94707902874
y[1] (closed_form) = 1.05645365478 -1.94721859944
absolute error = 0.0001845
relative error = 0.008329 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.659
Order of pole (three term test) = 34.4 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3606 1.204
h = 0.001 0.001
y[1] (numeric) = 1.05899112072 -1.95418690432
y[1] (closed_form) = 1.05886744974 -1.95432050861
absolute error = 0.0001821
relative error = 0.008191 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.31
Order of pole (three term test) = 34.41 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3616 1.205
h = 0.001 0.003
y[1] (numeric) = 1.05753277541 -1.95741626765
y[1] (closed_form) = 1.05740864538 -1.95754645062
absolute error = 0.0001799
relative error = 0.008085 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.231
Order of pole (three term test) = 34.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3626 1.208
h = 0.0001 0.004
y[1] (numeric) = 1.05783539332 -1.96533510075
y[1] (closed_form) = 1.0577124731 -1.96547222454
absolute error = 0.0001842
relative error = 0.008251 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.547
Order of pole (three term test) = 34.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3627 1.212
h = 0.003 0.006
y[1] (numeric) = 1.06113969645 -1.97484080823
y[1] (closed_form) = 1.06102239146 -1.9749801102
absolute error = 0.0001821
relative error = 0.008123 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.737
Order of pole (three term test) = 34.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3657 1.218
h = 0.0001 0.005
y[1] (numeric) = 1.05939361936 -1.99168890996
y[1] (closed_form) = 1.05925485574 -1.99184390522
absolute error = 0.000208
relative error = 0.009222 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.132
Order of pole (three term test) = 34.49 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3658 1.223
h = 0.0001 0.003
y[1] (numeric) = 1.06360027993 -2.00368515902
y[1] (closed_form) = 1.06347363071 -2.00382770235
absolute error = 0.0001907
relative error = 0.008405 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.733
Order of pole (three term test) = 34.51 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3659 1.226
h = 0.001 0.001
y[1] (numeric) = 1.06605072603 -2.01094197886
y[1] (closed_form) = 1.06592108073 -2.01107838487
absolute error = 0.0001882
relative error = 0.008268 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.369
Order of pole (three term test) = 34.52 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3669 1.227
h = 0.001 0.003
y[1] (numeric) = 1.06455591979 -2.0142335483
y[1] (closed_form) = 1.06442583647 -2.01436644671
absolute error = 0.000186
relative error = 0.008163 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.509
Order of pole (three term test) = 34.53 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3679 1.23
h = 0.0001 0.004
y[1] (numeric) = 1.0648475645 -2.02231320268
y[1] (closed_form) = 1.06471865509 -2.02245321958
absolute error = 0.0001903
relative error = 0.008327 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.705
Order of pole (three term test) = 34.55 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=728.2MB, alloc=52.3MB, time=8.67
x[1] = 0.368 1.234
h = 0.003 0.006
y[1] (numeric) = 1.06819795458 -2.03201850047
y[1] (closed_form) = 1.06807477468 -2.03216080005
absolute error = 0.0001882
relative error = 0.008198 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.949
Order of pole (three term test) = 34.56 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.371 1.24
h = 0.0001 0.005
y[1] (numeric) = 1.06637925478 -2.0492040411
y[1] (closed_form) = 1.06623395676 -2.04936221103
absolute error = 0.0002148
relative error = 0.009297 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.227
Order of pole (three term test) = 34.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3711 1.245
h = 0.0001 0.003
y[1] (numeric) = 1.07064391909 -2.06145288571
y[1] (closed_form) = 1.07051114037 -2.06159841688
absolute error = 0.000197
relative error = 0.008481 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.811
Order of pole (three term test) = 34.62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3712 1.248
h = 0.001 0.001
y[1] (numeric) = 1.07312746053 -2.06886252985
y[1] (closed_form) = 1.07299167032 -2.06900174927
absolute error = 0.0001945
relative error = 0.008344 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.43
Order of pole (three term test) = 34.64 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3722 1.249
h = 0.001 0.003
y[1] (numeric) = 1.0715947442 -2.07221745749
y[1] (closed_form) = 1.07145853761 -2.07235308133
absolute error = 0.0001922
relative error = 0.008239 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.801
Order of pole (three term test) = 34.64 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3732 1.252
h = 0.0001 0.004
y[1] (numeric) = 1.07187366433 -2.08046168486
y[1] (closed_form) = 1.07173859465 -2.0806046084
absolute error = 0.0001966
relative error = 0.008402 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.871
Order of pole (three term test) = 34.66 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3733 1.256
h = 0.003 0.006
y[1] (numeric) = 1.07526940544 -2.0903717792
y[1] (closed_form) = 1.07514018163 -2.09051709228
absolute error = 0.0001945
relative error = 0.008272 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.17
Order of pole (three term test) = 34.68 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3763 1.262
h = 0.0001 0.005
y[1] (numeric) = 1.07337324577 -2.10790216986
y[1] (closed_form) = 1.07322123056 -2.10806353242
absolute error = 0.0002217
relative error = 0.009372 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.327
Order of pole (three term test) = 34.72 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3764 1.267
h = 0.0001 0.003
y[1] (numeric) = 1.07769500153 -2.12041018914
y[1] (closed_form) = 1.07755591917 -2.12055872328
absolute error = 0.0002035
relative error = 0.008555 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.892
Order of pole (three term test) = 34.74 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3765 1.27
h = 0.001 0.001
y[1] (numeric) = 1.08021104256 -2.12797661502
y[1] (closed_form) = 1.08006893339 -2.12811865939
absolute error = 0.0002009
relative error = 0.008419 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.494
Order of pole (three term test) = 34.76 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3775 1.271
h = 0.001 0.003
y[1] (numeric) = 1.0786389349 -2.13139607299
y[1] (closed_form) = 1.07849643165 -2.13153443207
absolute error = 0.0001986
relative error = 0.008315 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.105
Order of pole (three term test) = 34.77 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3785 1.274
h = 0.0001 0.004
y[1] (numeric) = 1.07890333494 -2.13980869713
y[1] (closed_form) = 1.07876193039 -2.1399545407
absolute error = 0.0002031
relative error = 0.008477 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.045
Order of pole (three term test) = 34.78 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3786 1.278
h = 0.003 0.006
y[1] (numeric) = 1.08234366406 -2.1499288982
y[1] (closed_form) = 1.08220822385 -2.15007724063
absolute error = 0.0002009
relative error = 0.008345 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.402
Order of pole (three term test) = 34.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3816 1.284
h = 0.0001 0.005
y[1] (numeric) = 1.08036509161 -2.16781168918
y[1] (closed_form) = 1.0802061726 -2.16797626222
absolute error = 0.0002288
relative error = 0.009445 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.431
Order of pole (three term test) = 34.85 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3817 1.289
h = 0.0001 0.003
y[1] (numeric) = 1.08474299212 -2.18058559374
y[1] (closed_form) = 1.08459742841 -2.18073714585
absolute error = 0.0002101
relative error = 0.008628 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.977
Order of pole (three term test) = 34.87 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3818 1.292
h = 0.001 0.001
y[1] (numeric) = 1.08729091523 -2.18831283784
y[1] (closed_form) = 1.08714230953 -2.18845771853
absolute error = 0.0002075
relative error = 0.008493 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.561
Order of pole (three term test) = 34.88 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3828 1.293
h = 0.0001 0.004
y[1] (numeric) = 1.085677902 -2.1917980185
y[1] (closed_form) = 1.0855289252 -2.1919391224
absolute error = 0.0002052
relative error = 0.008389 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.393
Order of pole (three term test) = 34.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3829 1.297
h = 0.003 0.006
y[1] (numeric) = 1.08915444829 -2.20209399513
y[1] (closed_form) = 1.08901566155 -2.20224658493
absolute error = 0.0002063
relative error = 0.008396 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.611
Order of pole (three term test) = 34.91 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3859 1.303
h = 0.0001 0.005
y[1] (numeric) = 1.08710520301 -2.22028733877
y[1] (closed_form) = 1.08694233636 -2.22045632506
absolute error = 0.0002347
relative error = 0.009493 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.525
Order of pole (three term test) = 34.96 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=772.0MB, alloc=52.3MB, time=9.18
x[1] = 0.386 1.308
h = 0.0001 0.003
y[1] (numeric) = 1.0915339237 -2.23329493189
y[1] (closed_form) = 1.09138478094 -2.23345072411
absolute error = 0.0002157
relative error = 0.008676 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.053
Order of pole (three term test) = 34.98 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3861 1.311
h = 0.001 0.001
y[1] (numeric) = 1.09411076046 -2.24116352754
y[1] (closed_form) = 1.09395856054 -2.24131248914
absolute error = 0.000213
relative error = 0.008539 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.621
Order of pole (three term test) = 35 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3871 1.312
h = 0.001 0.003
y[1] (numeric) = 1.0924621012 -2.24470676296
y[1] (closed_form) = 1.09230954941 -2.24485186728
absolute error = 0.0002105
relative error = 0.008433 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.71
Order of pole (three term test) = 35.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3881 1.315
h = 0.0001 0.004
y[1] (numeric) = 1.0926966623 -2.25344338932
y[1] (closed_form) = 1.09254513707 -2.25359633232
absolute error = 0.0002153
relative error = 0.008596 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.389
Order of pole (three term test) = 35.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3882 1.319
h = 0.003 0.006
y[1] (numeric) = 1.09622048624 -2.26396854035
y[1] (closed_form) = 1.09607515288 -2.26412419096
absolute error = 0.000213
relative error = 0.008466 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.862
Order of pole (three term test) = 35.05 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3912 1.325
h = 0.0001 0.005
y[1] (numeric) = 1.09407938407 -2.28252877432
y[1] (closed_form) = 1.09390925616 -2.28270100624
absolute error = 0.0002421
relative error = 0.009564 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.638
Order of pole (three term test) = 35.1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3913 1.33
h = 0.0001 0.003
y[1] (numeric) = 1.09856247322 -2.29581511161
y[1] (closed_form) = 1.09840650877 -2.29597395161
absolute error = 0.0002226
relative error = 0.008746 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.145
Order of pole (three term test) = 35.12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3914 1.333
h = 0.001 0.001
y[1] (numeric) = 1.10117003131 -2.30385226074
y[1] (closed_form) = 1.10101099483 -2.30400408139
absolute error = 0.0002199
relative error = 0.00861 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.694
Order of pole (three term test) = 35.14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3924 1.334
h = 0.001 0.003
y[1] (numeric) = 1.09947757244 -2.30746351108
y[1] (closed_form) = 1.09931820839 -2.30761137957
absolute error = 0.0002174
relative error = 0.008505 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.056
Order of pole (three term test) = 35.15 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3934 1.337
h = 0.0001 0.004
y[1] (numeric) = 1.09969226593 -2.31637990638
y[1] (closed_form) = 1.09953388657 -2.31653580905
absolute error = 0.0002222
relative error = 0.008667 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.586
Order of pole (three term test) = 35.17 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3935 1.341
h = 0.003 0.006
y[1] (numeric) = 1.10325839877 -2.32713095993
y[1] (closed_form) = 1.10310633596 -2.32728968696
absolute error = 0.0002198
relative error = 0.008535 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.125
Order of pole (three term test) = 35.19 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3965 1.347
h = 0.0001 0.005
y[1] (numeric) = 1.10102013497 -2.34606604691
y[1] (closed_form) = 1.1008425478 -2.34624154186
absolute error = 0.0002497
relative error = 0.009634 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.756
Order of pole (three term test) = 35.24 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3966 1.352
h = 0.0001 0.003
y[1] (numeric) = 1.10555653789 -2.35963823146
y[1] (closed_form) = 1.10539356336 -2.35980013382
absolute error = 0.0002297
relative error = 0.008816 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.242
Order of pole (three term test) = 35.27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3967 1.355
h = 0.001 0.001
y[1] (numeric) = 1.10819413177 -2.36784820651
y[1] (closed_form) = 1.10802807055 -2.36800289688
absolute error = 0.0002269
relative error = 0.008681 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.77
Order of pole (three term test) = 35.29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3977 1.356
h = 0.001 0.003
y[1] (numeric) = 1.10645625945 -2.37152872352
y[1] (closed_form) = 1.10628989574 -2.37167936496
absolute error = 0.0002244
relative error = 0.008576 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.418
Order of pole (three term test) = 35.3 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3987 1.359
h = 0.0001 0.004
y[1] (numeric) = 1.10664910376 -2.38062900301
y[1] (closed_form) = 1.10648368143 -2.38078787804
absolute error = 0.0002294
relative error = 0.008736 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.792
Order of pole (three term test) = 35.32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3988 1.363
h = 0.003 0.006
y[1] (numeric) = 1.11025666404 -2.39161169242
y[1] (closed_form) = 1.11009768517 -2.3917735113
absolute error = 0.0002268
relative error = 0.008603 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.4
Order of pole (three term test) = 35.34 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4018 1.369
h = 0.0001 0.005
y[1] (numeric) = 1.10791580213 -2.41092974334
y[1] (closed_form) = 1.10773055354 -2.41110851845
absolute error = 0.0002574
relative error = 0.009702 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.88
Order of pole (three term test) = 35.39 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4019 1.374
h = 0.0001 0.003
y[1] (numeric) = 1.11250442181 -2.42479502098
y[1] (closed_form) = 1.11233424485 -2.42496000006
absolute error = 0.000237
relative error = 0.008884 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.342
Order of pole (three term test) = 35.42 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=815.9MB, alloc=52.3MB, time=9.70
x[1] = 0.402 1.377
h = 0.001 0.001
y[1] (numeric) = 1.1151713393 -2.4331821802
y[1] (closed_form) = 1.11499806129 -2.43333975063
absolute error = 0.0002342
relative error = 0.00875 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.85
Order of pole (three term test) = 35.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.403 1.378
h = 0.001 0.003
y[1] (numeric) = 1.11338640283 -2.43693323661
y[1] (closed_form) = 1.1132128482 -2.43708665942
absolute error = 0.0002316
relative error = 0.008646 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.796
Order of pole (three term test) = 35.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.404 1.381
h = 0.0001 0.004
y[1] (numeric) = 1.11355536353 -2.44622159429
y[1] (closed_form) = 1.11338270549 -2.44638345408
absolute error = 0.0002367
relative error = 0.008805 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.007
Order of pole (three term test) = 35.48 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4041 1.385
h = 0.003 0.006
y[1] (numeric) = 1.11720343466 -2.45744176816
y[1] (closed_form) = 1.11703734925 -2.45760669415
absolute error = 0.0002341
relative error = 0.00867 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.688
Order of pole (three term test) = 35.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4071 1.391
h = 0.0001 0.005
y[1] (numeric) = 1.11475440208 -2.47715104465
y[1] (closed_form) = 1.11456128565 -2.47733311676
absolute error = 0.0002654
relative error = 0.00977 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.01
Order of pole (three term test) = 35.55 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4072 1.396
h = 0.0001 0.003
y[1] (numeric) = 1.11939409694 -2.49131680702
y[1] (closed_form) = 1.11921652123 -2.49148487688
absolute error = 0.0002445
relative error = 0.008952 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.447
Order of pole (three term test) = 35.59 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4073 1.399
h = 0.001 0.001
y[1] (numeric) = 1.12208959791 -2.49988559628
y[1] (closed_form) = 1.1219089071 -2.50004605674
absolute error = 0.0002417
relative error = 0.008819 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.933
Order of pole (three term test) = 35.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4083 1.4
h = 0.003 0.006
y[1] (numeric) = 1.12025590869 -2.503708486
y[1] (closed_form) = 1.12007496798 -2.5038646982
absolute error = 0.000239
relative error = 0.008715 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 19.5
Order of pole (three term test) = 35.62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4113 1.406
h = 0.0001 0.005
y[1] (numeric) = 1.11771197031 -2.52366087348
y[1] (closed_form) = 1.11751054368 -2.52386232848
absolute error = 0.0002849
relative error = 0.01032 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.101
Order of pole (three term test) = 35.67 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4114 1.411
h = 0.0001 0.003
y[1] (numeric) = 1.12237831716 -2.53803895238
y[1] (closed_form) = 1.1221927652 -2.53822627379
absolute error = 0.0002637
relative error = 0.009501 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.522
Order of pole (three term test) = 35.71 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4115 1.414
h = 0.001 0.001
y[1] (numeric) = 1.12508832442 -2.54673600552
y[1] (closed_form) = 1.12489965306 -2.54691557669
absolute error = 0.0002605
relative error = 0.009355 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.991
Order of pole (three term test) = 35.73 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4125 1.415
h = 0.001 0.003
y[1] (numeric) = 1.1232182499 -2.5506077904
y[1] (closed_form) = 1.12302935014 -2.55078304361
absolute error = 0.0002577
relative error = 0.009245 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.47
Order of pole (three term test) = 35.74 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4135 1.418
h = 0.0001 0.004
y[1] (numeric) = 1.12333715391 -2.56022262086
y[1] (closed_form) = 1.1231490662 -2.56040666235
absolute error = 0.0002632
relative error = 0.009412 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.391
Order of pole (three term test) = 35.76 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4136 1.422
h = 0.003 0.006
y[1] (numeric) = 1.12704510498 -2.571858203
y[1] (closed_form) = 1.12686380985 -2.57204552728
absolute error = 0.0002607
relative error = 0.009284 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.201
Order of pole (three term test) = 35.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4166 1.428
h = 0.0001 0.005
y[1] (numeric) = 1.12439013531 -2.59224394591
y[1] (closed_form) = 1.1241804821 -2.59244872014
absolute error = 0.0002931
relative error = 0.01037 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.24
Order of pole (three term test) = 35.85 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4167 1.433
h = 0.0001 0.003
y[1] (numeric) = 1.12910532867 -2.60693529377
y[1] (closed_form) = 1.1289120369 -2.60712572381
absolute error = 0.0002713
relative error = 0.009551 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.635
Order of pole (three term test) = 35.88 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4168 1.436
h = 0.001 0.001
y[1] (numeric) = 1.13184248593 -2.61582166469
y[1] (closed_form) = 1.13164606145 -2.6160041366
absolute error = 0.0002681
relative error = 0.009406 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.081
Order of pole (three term test) = 35.9 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4178 1.437
h = 0.001 0.003
y[1] (numeric) = 1.12992068572 -2.61976747074
y[1] (closed_form) = 1.12972406111 -2.61994552068
absolute error = 0.0002653
relative error = 0.009297 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.896
Order of pole (three term test) = 35.92 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4188 1.44
h = 0.0001 0.004
y[1] (numeric) = 1.1300098488 -2.62958199802
y[1] (closed_form) = 1.12981398699 -2.62976905067
absolute error = 0.0002708
relative error = 0.009462 %
Correct digits = 4
memory used=859.8MB, alloc=52.3MB, time=10.21
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.633
Order of pole (three term test) = 35.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4189 1.444
h = 0.003 0.006
y[1] (numeric) = 1.13375550197 -2.64147134921
y[1] (closed_form) = 1.13356656801 -2.64166181515
absolute error = 0.0002683
relative error = 0.009333 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.524
Order of pole (three term test) = 35.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4219 1.45
h = 0.0001 0.005
y[1] (numeric) = 1.13097645318 -2.66227113785
y[1] (closed_form) = 1.13075835504 -2.66247924705
absolute error = 0.0003015
relative error = 0.01042 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.386
Order of pole (three term test) = 36.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.422 1.455
h = 0.0001 0.003
y[1] (numeric) = 1.13573921653 -2.67728355247
y[1] (closed_form) = 1.13553797742 -2.67747710415
absolute error = 0.0002792
relative error = 0.0096 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.754
Order of pole (three term test) = 36.07 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4221 1.458
h = 0.001 0.001
y[1] (numeric) = 1.13850269927 -2.68636393102
y[1] (closed_form) = 1.13829831454 -2.68654931234
absolute error = 0.0002759
relative error = 0.009457 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.174
Order of pole (three term test) = 36.09 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4231 1.459
h = 0.001 0.003
y[1] (numeric) = 1.13652737694 -2.69038510902
y[1] (closed_form) = 1.13632282131 -2.69056596229
absolute error = 0.000273
relative error = 0.009349 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.34
Order of pole (three term test) = 36.1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4241 1.462
h = 0.0001 0.004
y[1] (numeric) = 1.13658455081 -2.70040382858
y[1] (closed_form) = 1.13638070697 -2.70059390328
absolute error = 0.0002787
relative error = 0.009513 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.887
Order of pole (three term test) = 36.13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4242 1.466
h = 0.003 0.006
y[1] (numeric) = 1.14036684099 -2.71255324301
y[1] (closed_form) = 1.14017006266 -2.71274686464
absolute error = 0.0002761
relative error = 0.009382 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.862
Order of pole (three term test) = 36.16 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4272 1.472
h = 0.0001 0.005
y[1] (numeric) = 1.13745759518 -2.73377591235
y[1] (closed_form) = 1.13723082914 -2.73398737181
absolute error = 0.0003101
relative error = 0.01047 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.538
Order of pole (three term test) = 36.22 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4273 1.477
h = 0.0001 0.003
y[1] (numeric) = 1.14226659881 -2.74911734899
y[1] (closed_form) = 1.14205720047 -2.7493140349
absolute error = 0.0002873
relative error = 0.00965 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.877
Order of pole (three term test) = 36.26 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4274 1.48
h = 0.001 0.001
y[1] (numeric) = 1.14505554925 -2.75839651961
y[1] (closed_form) = 1.14484299287 -2.75858481847
absolute error = 0.000284
relative error = 0.009508 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.272
Order of pole (three term test) = 36.29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4284 1.481
h = 0.0001 0.004
y[1] (numeric) = 1.14302486641 -2.76249444223
y[1] (closed_form) = 1.14281216931 -2.76267810486
absolute error = 0.000281
relative error = 0.0094 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.67
Order of pole (three term test) = 36.3 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4285 1.485
h = 0.003 0.006
y[1] (numeric) = 1.14683671657 -2.77486124524
y[1] (closed_form) = 1.14663549884 -2.77505975483
absolute error = 0.0002827
relative error = 0.009414 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.167
Order of pole (three term test) = 36.33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4315 1.491
h = 0.0001 0.005
y[1] (numeric) = 1.14381556553 -2.79645676798
y[1] (closed_form) = 1.14358363931 -2.79667329387
absolute error = 0.0003173
relative error = 0.0105 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.675
Order of pole (three term test) = 36.4 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4316 1.496
h = 0.0001 0.003
y[1] (numeric) = 1.14866731529 -2.81208738062
y[1] (closed_form) = 1.14845320108 -2.81228893861
absolute error = 0.0002941
relative error = 0.00968 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.989
Order of pole (three term test) = 36.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4317 1.499
h = 0.001 0.001
y[1] (numeric) = 1.15147992147 -2.82154128095
y[1] (closed_form) = 1.15126263627 -2.82173426186
absolute error = 0.0002906
relative error = 0.009536 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.36
Order of pole (three term test) = 36.46 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4327 1.5
h = 0.001 0.003
y[1] (numeric) = 1.14940101793 -2.82570706887
y[1] (closed_form) = 1.1491836175 -2.82589531835
absolute error = 0.0002876
relative error = 0.009427 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.22
Order of pole (three term test) = 36.48 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4337 1.503
h = 0.0001 0.004
y[1] (numeric) = 1.14939503166 -2.83611844915
y[1] (closed_form) = 1.14917824594 -2.83631633938
absolute error = 0.0002935
relative error = 0.009591 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.389
Order of pole (three term test) = 36.51 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4338 1.507
h = 0.003 0.006
y[1] (numeric) = 1.1532457889 -2.84876856574
y[1] (closed_form) = 1.15303633289 -2.84897025867
absolute error = 0.0002908
relative error = 0.009461 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.534
Order of pole (three term test) = 36.54 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4368 1.513
h = 0.0001 0.005
y[1] (numeric) = 1.15008274243 -2.87080392076
y[1] (closed_form) = 1.14984172089 -2.87102382682
absolute error = 0.0003263
relative error = 0.01055 %
Correct digits = 4
memory used=903.6MB, alloc=52.3MB, time=10.72
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.84
Order of pole (three term test) = 36.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4369 1.518
h = 0.0001 0.003
y[1] (numeric) = 1.15497820748 -2.88677880629
y[1] (closed_form) = 1.15475552798 -2.8869835233
absolute error = 0.0003025
relative error = 0.009728 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.123
Order of pole (three term test) = 36.65 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.437 1.521
h = 0.001 0.001
y[1] (numeric) = 1.15781465134 -2.89644067123
y[1] (closed_form) = 1.15758878936 -2.89663658588
absolute error = 0.000299
relative error = 0.009585 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.466
Order of pole (three term test) = 36.68 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.438 1.522
h = 0.001 0.003
y[1] (numeric) = 1.1556768677 -2.90068584003
y[1] (closed_form) = 1.15545092258 -2.90087691103
absolute error = 0.0002959
relative error = 0.009476 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.73
Order of pole (three term test) = 36.69 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.439 1.525
h = 0.0001 0.004
y[1] (numeric) = 1.15563216668 -2.91131478066
y[1] (closed_form) = 1.15540677989 -2.91151572389
absolute error = 0.000302
relative error = 0.00964 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.677
Order of pole (three term test) = 36.73 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4391 1.529
h = 0.003 0.006
y[1] (numeric) = 1.15951634459 -2.92424369233
y[1] (closed_form) = 1.15929843213 -2.9244485815
absolute error = 0.0002991
relative error = 0.009508 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.918
Order of pole (three term test) = 36.76 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4421 1.535
h = 0.0001 0.005
y[1] (numeric) = 1.15620482154 -2.94672818838
y[1] (closed_form) = 1.15595446789 -2.94695148843
absolute error = 0.0003355
relative error = 0.0106 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.013
Order of pole (three term test) = 36.83 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4422 1.54
h = 0.0001 0.003
y[1] (numeric) = 1.16114250823 -2.96305577183
y[1] (closed_form) = 1.16091103853 -2.96326365902
absolute error = 0.0003111
relative error = 0.009776 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.264
Order of pole (three term test) = 36.88 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4423 1.543
h = 0.001 0.001
y[1] (numeric) = 1.16400182964 -2.97293066794
y[1] (closed_form) = 1.16376716657 -2.97312952276
absolute error = 0.0003076
relative error = 0.009634 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.577
Order of pole (three term test) = 36.91 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4433 1.544
h = 0.001 0.003
y[1] (numeric) = 1.16180320118 -2.97725665452
y[1] (closed_form) = 1.16156848816 -2.97745055123
absolute error = 0.0003044
relative error = 0.009526 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.26
Order of pole (three term test) = 36.92 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4443 1.547
h = 0.0001 0.004
y[1] (numeric) = 1.16171728617 -2.98810799106
y[1] (closed_form) = 1.16148307306 -2.98831199611
absolute error = 0.0003106
relative error = 0.009688 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.977
Order of pole (three term test) = 36.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4444 1.551
h = 0.003 0.006
y[1] (numeric) = 1.16563364039 -3.00132249826
y[1] (closed_form) = 1.16540704872 -3.00153059601
absolute error = 0.0003076
relative error = 0.009555 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.319
Order of pole (three term test) = 36.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4474 1.557
h = 0.0001 0.005
y[1] (numeric) = 1.16216688718 -3.02426561423
y[1] (closed_form) = 1.16190695957 -3.02449232144
absolute error = 0.0003449
relative error = 0.01065 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.194
Order of pole (three term test) = 37.07 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4475 1.562
h = 0.0001 0.003
y[1] (numeric) = 1.16714523883 -3.04095449126
y[1] (closed_form) = 1.16690474929 -3.0411655592
absolute error = 0.00032
relative error = 0.009823 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.41
Order of pole (three term test) = 37.11 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4476 1.565
h = 0.001 0.001
y[1] (numeric) = 1.17002643842 -3.05104758759
y[1] (closed_form) = 1.16978274527 -3.05124938826
absolute error = 0.0003164
relative error = 0.009682 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.693
Order of pole (three term test) = 37.14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4486 1.566
h = 0.001 0.003
y[1] (numeric) = 1.16776495385 -3.0554558515
y[1] (closed_form) = 1.16752124506 -3.05565257735
absolute error = 0.0003132
relative error = 0.009575 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.81
Order of pole (three term test) = 37.16 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4496 1.569
h = 0.0001 0.004
y[1] (numeric) = 1.16763525495 -3.06653451127
y[1] (closed_form) = 1.16739198552 -3.0667415863
absolute error = 0.0003195
relative error = 0.009736 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.291
Order of pole (three term test) = 37.19 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4497 1.573
h = 0.003 0.006
y[1] (numeric) = 1.17158248917 -3.08004155217
y[1] (closed_form) = 1.17134699082 -3.0802528703
absolute error = 0.0003164
relative error = 0.009601 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.738
Order of pole (three term test) = 37.23 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4527 1.579
h = 0.0001 0.005
y[1] (numeric) = 1.1679535745 -3.10345293983
y[1] (closed_form) = 1.1676838259 -3.10368306673
absolute error = 0.0003546
relative error = 0.01069 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.382
Order of pole (three term test) = 37.31 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=947.3MB, alloc=52.3MB, time=11.23
x[1] = 0.4528 1.584
h = 0.0001 0.003
y[1] (numeric) = 1.1729709687 -3.12051188033
y[1] (closed_form) = 1.17272122481 -3.12072613893
absolute error = 0.0003291
relative error = 0.00987 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.564
Order of pole (three term test) = 37.36 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4529 1.587
h = 0.001 0.001
y[1] (numeric) = 1.17587300619 -3.13082845049
y[1] (closed_form) = 1.17562004916 -3.13103320197
absolute error = 0.0003254
relative error = 0.009731 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.814
Order of pole (three term test) = 37.39 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4539 1.588
h = 0.0001 0.004
y[1] (numeric) = 1.17354660635 -3.13532047414
y[1] (closed_form) = 1.17329366918 -3.13552003176
absolute error = 0.0003222
relative error = 0.009624 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.93
Order of pole (three term test) = 37.41 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.454 1.592
h = 0.003 0.006
y[1] (numeric) = 1.17751856571 -3.14907195521
y[1] (closed_form) = 1.17727790806 -3.14928856698
absolute error = 0.0003238
relative error = 0.00963 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.11
Order of pole (three term test) = 37.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.457 1.598
h = 0.0001 0.005
y[1] (numeric) = 1.17375011553 -3.17289632591
y[1] (closed_form) = 1.17347440703 -3.17313192968
absolute error = 0.0003627
relative error = 0.01072 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.552
Order of pole (three term test) = 37.53 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4571 1.603
h = 0.0001 0.003
y[1] (numeric) = 1.17880431852 -3.19028052556
y[1] (closed_form) = 1.17854910995 -3.19050005489
absolute error = 0.0003366
relative error = 0.009898 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.702
Order of pole (three term test) = 37.58 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4572 1.606
h = 0.001 0.001
y[1] (numeric) = 1.18172617653 -3.20079352841
y[1] (closed_form) = 1.18146774428 -3.20100334018
absolute error = 0.0003329
relative error = 0.009756 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.923
Order of pole (three term test) = 37.62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4582 1.607
h = 0.001 0.003
y[1] (numeric) = 1.17934323562 -3.20535966188
y[1] (closed_form) = 1.17908485329 -3.205564175
absolute error = 0.0003295
relative error = 0.009648 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.9
Order of pole (three term test) = 37.63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4592 1.61
h = 0.0001 0.004
y[1] (numeric) = 1.17912782439 -3.21687534998
y[1] (closed_form) = 1.17886976579 -3.21709067408
absolute error = 0.0003361
relative error = 0.009809 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.914
Order of pole (three term test) = 37.67 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4593 1.614
h = 0.003 0.006
y[1] (numeric) = 1.18313256821 -3.23094534879
y[1] (closed_form) = 1.18288256783 -3.23116520409
absolute error = 0.0003329
relative error = 0.009675 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.57
Order of pole (three term test) = 37.71 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4623 1.62
h = 0.0001 0.005
y[1] (numeric) = 1.1791886873 -3.25525650845
y[1] (closed_form) = 1.17890268418 -3.25549555628
absolute error = 0.0003727
relative error = 0.01077 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.757
Order of pole (three term test) = 37.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4624 1.625
h = 0.0001 0.003
y[1] (numeric) = 1.18427883897 -3.27302758768
y[1] (closed_form) = 1.1840139265 -3.27325032713
absolute error = 0.0003461
relative error = 0.009943 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.868
Order of pole (three term test) = 37.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4625 1.628
h = 0.001 0.001
y[1] (numeric) = 1.18721955025 -3.28377417674
y[1] (closed_form) = 1.18695140594 -3.28398694922
absolute error = 0.0003423
relative error = 0.009803 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.055
Order of pole (three term test) = 37.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4635 1.629
h = 0.001 0.003
y[1] (numeric) = 1.18476774903 -3.28842691581
y[1] (closed_form) = 1.18449969242 -3.28863426614
absolute error = 0.0003389
relative error = 0.009695 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 14.53
Order of pole (three term test) = 37.91 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4645 1.632
h = 0.0001 0.004
y[1] (numeric) = 1.18450085338 -3.30018457844
y[1] (closed_form) = 1.18423305343 -3.30040299468
absolute error = 0.0003456
relative error = 0.009855 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.27
Order of pole (three term test) = 37.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4646 1.636
h = 0.003 0.006
y[1] (numeric) = 1.18853255038 -3.31456776342
y[1] (closed_form) = 1.18827296573 -3.31479087223
absolute error = 0.0003423
relative error = 0.00972 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.05
Order of pole (three term test) = 37.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4676 1.642
h = 0.0001 0.005
y[1] (numeric) = 1.18440577084 -3.33937587627
y[1] (closed_form) = 1.18410921069 -3.33961837849
absolute error = 0.0003831
relative error = 0.01081 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.971
Order of pole (three term test) = 38.08 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4677 1.647
h = 0.0001 0.003
y[1] (numeric) = 1.18953004739 -3.35754312441
y[1] (closed_form) = 1.189255182 -3.35776908182
absolute error = 0.0003558
relative error = 0.009989 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.042
Order of pole (three term test) = 38.14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4678 1.65
h = 0.001 0.001
y[1] (numeric) = 1.19248844638 -3.36852888514
y[1] (closed_form) = 1.19221034185 -3.36874462085
absolute error = 0.000352
relative error = 0.00985 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.192
Order of pole (three term test) = 38.18 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=991.2MB, alloc=52.3MB, time=11.74
x[1] = 0.4688 1.651
h = 0.001 0.003
y[1] (numeric) = 1.18996558192 -3.37326977928
y[1] (closed_form) = 1.18968760417 -3.37347996691
absolute error = 0.0003485
relative error = 0.009742 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 15.18
Order of pole (three term test) = 38.19 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4698 1.654
h = 0.0001 0.004
y[1] (numeric) = 1.18964433805 -3.3852747148
y[1] (closed_form) = 1.18936654746 -3.38549622835
absolute error = 0.0003553
relative error = 0.009901 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.642
Order of pole (three term test) = 38.24 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4699 1.658
h = 0.003 0.006
y[1] (numeric) = 1.19370147197 -3.39997858383
y[1] (closed_form) = 1.19343205639 -3.40020495539
absolute error = 0.0003519
relative error = 0.009765 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.54
Order of pole (three term test) = 38.28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4729 1.664
h = 0.0001 0.005
y[1] (numeric) = 1.18938412663 -3.425293998
y[1] (closed_form) = 1.18907674138 -3.42553996408
absolute error = 0.0003937
relative error = 0.01086 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.195
Order of pole (three term test) = 38.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.473 1.669
h = 0.0001 0.003
y[1] (numeric) = 1.19454062739 -3.44386689301
y[1] (closed_form) = 1.19425555479 -3.44409607533
absolute error = 0.0003658
relative error = 0.01003 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.224
Order of pole (three term test) = 38.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4731 1.672
h = 0.001 0.001
y[1] (numeric) = 1.19751550082 -3.45509752401
y[1] (closed_form) = 1.19722718269 -3.4553162245
absolute error = 0.0003619
relative error = 0.009896 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.336
Order of pole (three term test) = 38.48 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4741 1.673
h = 0.001 0.003
y[1] (numeric) = 1.19491931722 -3.45992814633
y[1] (closed_form) = 1.1946311663 -3.4601411703
absolute error = 0.0003583
relative error = 0.009789 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 15.86
Order of pole (three term test) = 38.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4751 1.676
h = 0.0001 0.004
y[1] (numeric) = 1.19454077893 -3.47218575313
y[1] (closed_form) = 1.19425274308 -3.47241036825
absolute error = 0.0003653
relative error = 0.009947 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.031
Order of pole (three term test) = 38.54 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4752 1.68
h = 0.003 0.006
y[1] (numeric) = 1.1986217703 -3.48721795624
y[1] (closed_form) = 1.19834227188 -3.48744759897
absolute error = 0.0003617
relative error = 0.00981 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.06
Order of pole (three term test) = 38.59 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4782 1.686
h = 0.0001 0.005
y[1] (numeric) = 1.19410598677 -3.51305120673
y[1] (closed_form) = 1.19378750264 -3.51330064517
absolute error = 0.0004045
relative error = 0.0109 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.428
Order of pole (three term test) = 38.69 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4783 1.691
h = 0.0001 0.003
y[1] (numeric) = 1.19929273118 -3.532039419
y[1] (closed_form) = 1.19899719167 -3.5322718323
absolute error = 0.000376
relative error = 0.01008 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.414
Order of pole (three term test) = 38.75 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4784 1.694
h = 0.001 0.001
y[1] (numeric) = 1.20228281619 -3.54352073436
y[1] (closed_form) = 1.20198402571 -3.54374240016
absolute error = 0.000372
relative error = 0.009942 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.486
Order of pole (three term test) = 38.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4794 1.695
h = 0.0001 0.004
y[1] (numeric) = 1.19961100321 -3.54844268178
y[1] (closed_form) = 1.19931242176 -3.54865854006
absolute error = 0.0003684
relative error = 0.009836 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 20.98
Order of pole (three term test) = 38.81 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4795 1.699
h = 0.003 0.006
y[1] (numeric) = 1.20371081575 -3.56374915323
y[1] (closed_form) = 1.20342535345 -3.56398452428
absolute error = 0.00037
relative error = 0.009836 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.53
Order of pole (three term test) = 38.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4825 1.705
h = 0.0001 0.005
y[1] (numeric) = 1.19902410089 -3.59003921629
y[1] (closed_form) = 1.19869876279 -3.59029456863
absolute error = 0.0004136
relative error = 0.01093 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.639
Order of pole (three term test) = 38.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4826 1.71
h = 0.0001 0.003
y[1] (numeric) = 1.20424033638 -3.60939248683
y[1] (closed_form) = 1.20393849551 -3.60963059657
absolute error = 0.0003845
relative error = 0.0101 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.585
Order of pole (three term test) = 39.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4827 1.713
h = 0.001 0.001
y[1] (numeric) = 1.20724554702 -3.62109416885
y[1] (closed_form) = 1.20694044807 -3.62132129793
absolute error = 0.0003804
relative error = 0.009964 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.621
Order of pole (three term test) = 39.07 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4837 1.714
h = 0.001 0.003
y[1] (numeric) = 1.20450785645 -3.62609696233
y[1] (closed_form) = 1.20420300209 -3.62631816855
absolute error = 0.0003767
relative error = 0.009857 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.22
Order of pole (three term test) = 39.09 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4847 1.717
h = 0.0001 0.004
y[1] (numeric) = 1.20401773826 -3.638840219
y[1] (closed_form) = 1.20371286104 -3.63907352504
absolute error = 0.0003839
relative error = 0.01002 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.803
Order of pole (three term test) = 39.14 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1035.1MB, alloc=52.3MB, time=12.25
x[1] = 0.4848 1.721
h = 0.003 0.006
y[1] (numeric) = 1.20814282563 -3.65450403351
y[1] (closed_form) = 1.20784679745 -3.65474269224
absolute error = 0.0003803
relative error = 0.009879 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.09
Order of pole (three term test) = 39.2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4878 1.727
h = 0.0001 0.005
y[1] (numeric) = 1.20324258786 -3.68133214337
y[1] (closed_form) = 1.20290562577 -3.68159098461
absolute error = 0.0004249
relative error = 0.01097 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.892
Order of pole (three term test) = 39.3 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4879 1.732
h = 0.0001 0.003
y[1] (numeric) = 1.20848527886 -3.70111927731
y[1] (closed_form) = 1.20817247307 -3.70136062993
absolute error = 0.0003951
relative error = 0.01015 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.792
Order of pole (three term test) = 39.37 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.488 1.735
h = 0.001 0.001
y[1] (numeric) = 1.21150328513 -3.71308279436
y[1] (closed_form) = 1.21118721771 -3.71331289001
absolute error = 0.000391
relative error = 0.01001 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.784
Order of pole (three term test) = 39.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.489 1.736
h = 0.001 0.003
y[1] (numeric) = 1.20868553647 -3.71817997756
y[1] (closed_form) = 1.20836975819 -3.71840401446
absolute error = 0.0003872
relative error = 0.009903 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.99
Order of pole (three term test) = 39.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.49 1.739
h = 0.0001 0.004
y[1] (numeric) = 1.20812928501 -3.73119195627
y[1] (closed_form) = 1.20781340401 -3.73142837373
absolute error = 0.0003946
relative error = 0.01006 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.24
Order of pole (three term test) = 39.49 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4901 1.743
h = 0.003 0.006
y[1] (numeric) = 1.2122734372 -3.74720687966
y[1] (closed_form) = 1.21196657558 -3.74744883195
absolute error = 0.0003908
relative error = 0.009922 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.68
Order of pole (three term test) = 39.55 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4931 1.749
h = 0.0001 0.005
y[1] (numeric) = 1.20715118561 -3.77458412505
y[1] (closed_form) = 1.20680230858 -3.77484646073
absolute error = 0.0004365
relative error = 0.01101 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.157
Order of pole (three term test) = 39.66 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4932 1.754
h = 0.0001 0.003
y[1] (numeric) = 1.21241810768 -3.79481536648
y[1] (closed_form) = 1.21209406112 -3.79505996518
absolute error = 0.000406
relative error = 0.01019 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.007
Order of pole (three term test) = 39.73 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4933 1.757
h = 0.001 0.001
y[1] (numeric) = 1.21544749543 -3.80704687686
y[1] (closed_form) = 1.21512018484 -3.80727993638
absolute error = 0.0004018
relative error = 0.01005 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.954
Order of pole (three term test) = 39.78 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4943 1.758
h = 0.001 0.003
y[1] (numeric) = 1.21254721527 -3.81224011655
y[1] (closed_form) = 1.21222023989 -3.81246697874
absolute error = 0.000398
relative error = 0.009948 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 18.8
Order of pole (three term test) = 39.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4953 1.761
h = 0.0001 0.004
y[1] (numeric) = 1.2119215423 -3.82552662003
y[1] (closed_form) = 1.21159438143 -3.82576614915
absolute error = 0.0004055
relative error = 0.0101 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.7
Order of pole (three term test) = 39.85 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4954 1.765
h = 0.003 0.006
y[1] (numeric) = 1.21608291376 -3.84190092036
y[1] (closed_form) = 1.21576494542 -3.84214617107
absolute error = 0.0004016
relative error = 0.009965 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 14.3
Order of pole (three term test) = 39.92 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4984 1.771
h = 0.0001 0.005
y[1] (numeric) = 1.21072992813 -3.86983858859
y[1] (closed_form) = 1.21036883897 -3.87010442305
absolute error = 0.0004484
relative error = 0.01106 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.434
Order of pole (three term test) = 40.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4985 1.776
h = 0.0001 0.003
y[1] (numeric) = 1.21601876429 -3.89052438974
y[1] (closed_form) = 1.21568319523 -3.89077223657
absolute error = 0.0004172
relative error = 0.01023 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.233
Order of pole (three term test) = 40.11 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4986 1.779
h = 0.001 0.001
y[1] (numeric) = 1.21905806211 -3.90303017657
y[1] (closed_form) = 1.21871922781 -3.903266196
absolute error = 0.0004129
relative error = 0.0101 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.132
Order of pole (three term test) = 40.16 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4996 1.78
h = 0.001 0.003
y[1] (numeric) = 1.21607271698 -3.90832116407
y[1] (closed_form) = 1.21573426557 -3.90855084484
absolute error = 0.000409
relative error = 0.009993 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 19.65
Order of pole (three term test) = 40.18 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5006 1.783
h = 0.0001 0.004
y[1] (numeric) = 1.2153742386 -3.92188810403
y[1] (closed_form) = 1.21503551587 -3.92213074382
absolute error = 0.0004167
relative error = 0.01015 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.19
Order of pole (three term test) = 40.24 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5007 1.787
h = 0.003 0.006
y[1] (numeric) = 1.21955090782 -3.93863021722
y[1] (closed_form) = 1.21922155364 -3.93887877012
absolute error = 0.0004126
relative error = 0.01001 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 14.94
Order of pole (three term test) = 40.3 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1078.8MB, alloc=52.3MB, time=12.76
x[1] = 0.5037 1.793
h = 0.0001 0.005
y[1] (numeric) = 1.21395823204 -3.9671397973
y[1] (closed_form) = 1.21358462718 -3.96740913364
absolute error = 0.0004606
relative error = 0.0111 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.724
Order of pole (three term test) = 40.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5038 1.798
h = 0.0001 0.003
y[1] (numeric) = 1.2192665693 -3.98829082274
y[1] (closed_form) = 1.21891918999 -3.98854191855
absolute error = 0.0004286
relative error = 0.01028 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.468
Order of pole (three term test) = 40.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5039 1.801
h = 0.001 0.001
y[1] (numeric) = 1.22231424628 -4.00107729652
y[1] (closed_form) = 1.22196360181 -4.00131627055
absolute error = 0.0004243
relative error = 0.01014 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.318
Order of pole (three term test) = 40.55 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5049 1.802
h = 0.0001 0.004
y[1] (numeric) = 1.21924124114 -4.00646774787
y[1] (closed_form) = 1.21889102889 -4.00670023912
absolute error = 0.0004204
relative error = 0.01004 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.98
Order of pole (three term test) = 40.58 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.505 1.806
h = 0.003 0.006
y[1] (numeric) = 1.22342953157 -4.0235170242
y[1] (closed_form) = 1.22309331316 -4.0237717694
absolute error = 0.0004218
relative error = 0.01003 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 15.52
Order of pole (three term test) = 40.65 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.508 1.812
h = 0.0001 0.005
y[1] (numeric) = 1.21763018426 -4.05253124823
y[1] (closed_form) = 1.21724872497 -4.05280696195
absolute error = 0.0004707
relative error = 0.01112 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.985
Order of pole (three term test) = 40.77 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5081 1.817
h = 0.0001 0.003
y[1] (numeric) = 1.22295901784 -4.07409123711
y[1] (closed_form) = 1.22260440126 -4.07434848219
absolute error = 0.0004381
relative error = 0.0103 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.68
Order of pole (three term test) = 40.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5082 1.82
h = 0.001 0.001
y[1] (numeric) = 1.22601608431 -4.08712447549
y[1] (closed_form) = 1.22565820008 -4.08736934034
absolute error = 0.0004336
relative error = 0.01016 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.485
Order of pole (three term test) = 40.91 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5092 1.821
h = 0.001 0.003
y[1] (numeric) = 1.22286671123 -4.09260302263
y[1] (closed_form) = 1.22250930128 -4.09284127773
absolute error = 0.0004295
relative error = 0.01006 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 21.33
Order of pole (three term test) = 40.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5102 1.824
h = 0.0001 0.004
y[1] (numeric) = 1.22202692469 -4.10670887193
y[1] (closed_form) = 1.22166907891 -4.10696064633
absolute error = 0.0004375
relative error = 0.01021 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.14
Order of pole (three term test) = 41 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5103 1.828
h = 0.003 0.006
y[1] (numeric) = 1.2262312999 -4.12415831626
y[1] (closed_form) = 1.22588316034 -4.12441637105
absolute error = 0.0004334
relative error = 0.01007 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.22
Order of pole (three term test) = 41.07 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5133 1.834
h = 0.0001 0.005
y[1] (numeric) = 1.22017508876 -4.15376649177
y[1] (closed_form) = 1.21978053143 -4.15404571338
absolute error = 0.0004834
relative error = 0.01116 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.299
Order of pole (three term test) = 41.2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5134 1.839
h = 0.0001 0.003
y[1] (numeric) = 1.22551879872 -4.17581216083
y[1] (closed_form) = 1.22515181999 -4.17607265663
absolute error = 0.00045
relative error = 0.01034 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.935
Order of pole (three term test) = 41.29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5135 1.842
h = 0.001 0.001
y[1] (numeric) = 1.22858131003 -4.18913838239
y[1] (closed_form) = 1.22821106618 -4.18938619176
absolute error = 0.0004455
relative error = 0.01021 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.687
Order of pole (three term test) = 41.34 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5145 1.843
h = 0.001 0.003
y[1] (numeric) = 1.22533929997 -4.19471968567
y[1] (closed_form) = 1.22496958294 -4.1949607358
absolute error = 0.0004414
relative error = 0.0101 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.29
Order of pole (three term test) = 41.37 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5155 1.846
h = 0.0001 0.004
y[1] (numeric) = 1.22441654763 -4.2091235468
y[1] (closed_form) = 1.22404629971 -4.20937842537
absolute error = 0.0004495
relative error = 0.01025 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.69
Order of pole (three term test) = 41.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5156 1.85
h = 0.003 0.006
y[1] (numeric) = 1.22863038585 -4.22696592102
y[1] (closed_form) = 1.2282700286 -4.22722728579
absolute error = 0.0004452
relative error = 0.01011 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.95
Order of pole (three term test) = 41.51 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5186 1.856
h = 0.0001 0.005
y[1] (numeric) = 1.22230764457 -4.25718013465
y[1] (closed_form) = 1.22189966655 -4.25746286335
absolute error = 0.0004964
relative error = 0.01121 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.627
Order of pole (three term test) = 41.64 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5187 1.861
h = 0.0001 0.003
y[1] (numeric) = 1.22766352578 -4.27972278125
y[1] (closed_form) = 1.22728387921 -4.27998652488
absolute error = 0.0004623
relative error = 0.01038 %
Correct digits = 4
memory used=1122.6MB, alloc=52.3MB, time=13.27
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.203
Order of pole (three term test) = 41.74 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5188 1.864
h = 0.001 0.001
y[1] (numeric) = 1.23072977028 -4.29334877596
y[1] (closed_form) = 1.2303468626 -4.2935995204
absolute error = 0.0004577
relative error = 0.01025 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.898
Order of pole (three term test) = 41.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5198 1.865
h = 0.001 0.003
y[1] (numeric) = 1.22739234349 -4.29903462394
y[1] (closed_form) = 1.22701001696 -4.29927845668
absolute error = 0.0004535
relative error = 0.01014 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.29
Order of pole (three term test) = 41.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5208 1.868
h = 0.0001 0.004
y[1] (numeric) = 1.2263828454 -4.31374284873
y[1] (closed_form) = 1.22599988947 -4.31400082526
absolute error = 0.0004617
relative error = 0.0103 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.26
Order of pole (three term test) = 41.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5209 1.872
h = 0.003 0.006
y[1] (numeric) = 1.23060390667 -4.33198727033
y[1] (closed_form) = 1.23023102884 -4.33225194412
absolute error = 0.0004573
relative error = 0.01015 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.71
Order of pole (three term test) = 41.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5239 1.878
h = 0.0001 0.005
y[1] (numeric) = 1.22400470608 -4.36281982286
y[1] (closed_form) = 1.2235829778 -4.36310605631
absolute error = 0.0005097
relative error = 0.01125 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.97
Order of pole (three term test) = 42.11 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.524 1.883
h = 0.0001 0.003
y[1] (numeric) = 1.22936994305 -4.38587097379
y[1] (closed_form) = 1.22897731642 -4.38613796088
absolute error = 0.0004748
relative error = 0.01042 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.482
Order of pole (three term test) = 42.21 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5241 1.886
h = 0.001 0.001
y[1] (numeric) = 1.2324381409 -4.39980366914
y[1] (closed_form) = 1.2320422587 -4.4000573376
absolute error = 0.0004702
relative error = 0.01029 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.118
Order of pole (three term test) = 42.27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5251 1.887
h = 0.001 0.003
y[1] (numeric) = 1.22900244972 -4.40559587578
y[1] (closed_form) = 1.2286072049 -4.40584247706
absolute error = 0.0004659
relative error = 0.01019 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.34
Order of pole (three term test) = 42.3 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5261 1.89
h = 0.0001 0.004
y[1] (numeric) = 1.22790231541 -4.42061493462
y[1] (closed_form) = 1.22750633908 -4.42087600133
absolute error = 0.0004743
relative error = 0.01034 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.86
Order of pole (three term test) = 42.37 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5262 1.894
h = 0.003 0.006
y[1] (numeric) = 1.23212826928 -4.43927070608
y[1] (closed_form) = 1.23174256153 -4.43953868652
absolute error = 0.0004697
relative error = 0.01019 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 18.51
Order of pole (three term test) = 42.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5292 1.9
h = 0.0001 0.005
y[1] (numeric) = 1.22524240995 -4.47073411571
y[1] (closed_form) = 1.22480659477 -4.47102385
absolute error = 0.0005233
relative error = 0.01129 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.329
Order of pole (three term test) = 42.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5293 1.905
h = 0.0001 0.003
y[1] (numeric) = 1.2306140729 -4.49430553179
y[1] (closed_form) = 1.23020814731 -4.49457575642
absolute error = 0.0004876
relative error = 0.01046 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.773
Order of pole (three term test) = 42.7 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5294 1.908
h = 0.001 0.001
y[1] (numeric) = 1.23368237359 -4.50855199558
y[1] (closed_form) = 1.23327319961 -4.50880857531
absolute error = 0.000483
relative error = 0.01033 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.349
Order of pole (three term test) = 42.77 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5304 1.909
h = 0.0001 0.004
y[1] (numeric) = 1.23014550078 -4.51445240041
y[1] (closed_form) = 1.22973702232 -4.51470175441
absolute error = 0.0004786
relative error = 0.01023 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 32.18
Order of pole (three term test) = 42.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5305 1.913
h = 0.003 0.006
y[1] (numeric) = 1.23437432227 -4.53345161255
y[1] (closed_form) = 1.23398074192 -4.53372627866
absolute error = 0.0004799
relative error = 0.01021 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 19.22
Order of pole (three term test) = 42.88 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5335 1.919
h = 0.0001 0.005
y[1] (numeric) = 1.2272410591 -4.56547182085
y[1] (closed_form) = 1.22679626929 -4.56576842196
absolute error = 0.0005346
relative error = 0.01131 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.652
Order of pole (three term test) = 43.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5336 1.924
h = 0.0001 0.003
y[1] (numeric) = 1.23262220938 -4.58950063684
y[1] (closed_form) = 1.23220799878 -4.58977749044
absolute error = 0.0004982
relative error = 0.01048 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.036
Order of pole (three term test) = 43.15 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5337 1.927
h = 0.001 0.001
y[1] (numeric) = 1.23569291585 -4.60402298104
y[1] (closed_form) = 1.23527546039 -4.60428590319
absolute error = 0.0004934
relative error = 0.01035 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.556
Order of pole (three term test) = 43.21 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5347 1.928
h = 0.001 0.003
y[1] (numeric) = 1.23206787791 -4.61001926585
memory used=1166.4MB, alloc=52.3MB, time=13.78
y[1] (closed_form) = 1.23165116768 -4.61027482257
absolute error = 0.0004888
relative error = 0.01024 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.42
Order of pole (three term test) = 43.24 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5357 1.931
h = 0.0001 0.004
y[1] (numeric) = 1.23079223407 -4.62563554446
y[1] (closed_form) = 1.23037459642 -4.62590618363
absolute error = 0.0004977
relative error = 0.0104 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 15.04
Order of pole (three term test) = 43.32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5358 1.935
h = 0.003 0.006
y[1] (numeric) = 1.23502593646 -4.64508216165
y[1] (closed_form) = 1.23461893275 -4.64536012986
absolute error = 0.0004929
relative error = 0.01025 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 20.09
Order of pole (three term test) = 43.41 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5388 1.941
h = 0.0001 0.005
y[1] (numeric) = 1.22758644586 -4.67775724013
y[1] (closed_form) = 1.22712692322 -4.67805733442
absolute error = 0.0005488
relative error = 0.01135 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.041
Order of pole (three term test) = 43.57 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5389 1.946
h = 0.0001 0.003
y[1] (numeric) = 1.23296839898 -4.70232888264
y[1] (closed_form) = 1.23254027765 -4.70260896237
absolute error = 0.0005116
relative error = 0.01052 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.352
Order of pole (three term test) = 43.68 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.539 1.949
h = 0.001 0.001
y[1] (numeric) = 1.23603565666 -4.71717855392
y[1] (closed_form) = 1.23560430078 -4.7174443628
absolute error = 0.0005067
relative error = 0.01039 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.806
Order of pole (three term test) = 43.75 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.54 1.95
h = 0.001 0.003
y[1] (numeric) = 1.23230384007 -4.72328656527
y[1] (closed_form) = 1.23187329133 -4.72354484426
absolute error = 0.0005021
relative error = 0.01029 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.61
Order of pole (three term test) = 43.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.541 1.953
h = 0.0001 0.004
y[1] (numeric) = 1.23092587219 -4.73923291222
y[1] (closed_form) = 1.23049428305 -4.73950661407
absolute error = 0.0005111
relative error = 0.01044 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 15.72
Order of pole (three term test) = 43.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5411 1.957
h = 0.003 0.006
y[1] (numeric) = 1.23515738997 -4.75911857805
y[1] (closed_form) = 1.2347366342 -4.75939984163
absolute error = 0.0005061
relative error = 0.01029 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 20.99
Order of pole (three term test) = 43.96 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5441 1.963
h = 0.0001 0.005
y[1] (numeric) = 1.22740065968 -4.792461689
y[1] (closed_form) = 1.22692604642 -4.79276526756
absolute error = 0.0005634
relative error = 0.01139 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.448
Order of pole (three term test) = 44.13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5442 1.968
h = 0.0001 0.003
y[1] (numeric) = 1.23278013887 -4.81758861598
y[1] (closed_form) = 1.23233776798 -4.81787191114
absolute error = 0.0005253
relative error = 0.01056 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.683
Order of pole (three term test) = 44.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5443 1.971
h = 0.001 0.001
y[1] (numeric) = 1.23584188297 -4.83277309997
y[1] (closed_form) = 1.23539628971 -4.83304177761
absolute error = 0.0005203
relative error = 0.01043 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.067
Order of pole (three term test) = 44.32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5453 1.972
h = 0.001 0.003
y[1] (numeric) = 1.23200016182 -4.83899475231
y[1] (closed_form) = 1.23155543971 -4.83925573237
absolute error = 0.0005156
relative error = 0.01033 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.85
Order of pole (three term test) = 44.35 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5463 1.975
h = 0.0001 0.004
y[1] (numeric) = 1.23051552267 -4.85527811654
y[1] (closed_form) = 1.23006964313 -4.85555486665
absolute error = 0.0005248
relative error = 0.01048 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.43
Order of pole (three term test) = 44.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5464 1.979
h = 0.003 0.006
y[1] (numeric) = 1.2347421474 -4.8756128842
y[1] (closed_form) = 1.23430730383 -4.87589743471
absolute error = 0.0005197
relative error = 0.01033 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 21.94
Order of pole (three term test) = 44.53 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5494 1.985
h = 0.0001 0.005
y[1] (numeric) = 1.22665686476 -4.90963742051
y[1] (closed_form) = 1.22616679537 -4.90994447251
absolute error = 0.0005783
relative error = 0.01143 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.873
Order of pole (three term test) = 44.71 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5495 1.99
h = 0.0001 0.003
y[1] (numeric) = 1.23203046259 -4.93533234248
y[1] (closed_form) = 1.23157349609 -4.9356188405
absolute error = 0.0005394
relative error = 0.0106 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.029
Order of pole (three term test) = 44.84 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5496 1.993
h = 0.001 0.001
y[1] (numeric) = 1.23508454774 -4.95085927618
y[1] (closed_form) = 1.23462437298 -4.95113080263
absolute error = 0.0005343
relative error = 0.01047 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.34
Order of pole (three term test) = 44.91 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5506 1.994
h = 0.001 0.003
y[1] (numeric) = 1.23112971951 -4.95719651015
y[1] (closed_form) = 1.2306704821 -4.957460168
absolute error = 0.0005295
relative error = 0.01037 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.15
Order of pole (three term test) = 44.95 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1210.2MB, alloc=52.3MB, time=14.30
x[1] = 0.5516 1.997
h = 0.0001 0.004
y[1] (numeric) = 1.22953393463 -4.97382396938
y[1] (closed_form) = 1.22907341857 -4.97410375139
absolute error = 0.0005388
relative error = 0.01052 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.16
Order of pole (three term test) = 45.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5517 2.001
h = 0.003 0.006
y[1] (numeric) = 1.2337528509 -4.99461809568
y[1] (closed_form) = 1.23330357661 -4.99490592288
absolute error = 0.0005336
relative error = 0.01037 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.93
Order of pole (three term test) = 45.14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5547 2.007
h = 0.0001 0.005
y[1] (numeric) = 1.22532739452 -5.02933768427
y[1] (closed_form) = 1.22482149565 -5.02964819687
absolute error = 0.0005936
relative error = 0.01147 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.32
Order of pole (three term test) = 45.32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5548 2.012
h = 0.0001 0.003
y[1] (numeric) = 1.23069156843 -5.05561356934
y[1] (closed_form) = 1.23021965284 -5.05590325574
absolute error = 0.0005537
relative error = 0.01064 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.39
Order of pole (three term test) = 45.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5549 2.015
h = 0.001 0.001
y[1] (numeric) = 1.23373576591 -5.07149074412
y[1] (closed_form) = 1.2332606582 -5.07176509728
absolute error = 0.0005486
relative error = 0.01051 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.625
Order of pole (three term test) = 45.53 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5559 2.016
h = 0.0001 0.004
y[1] (numeric) = 1.22966454953 -5.07794552667
y[1] (closed_form) = 1.22919044766 -5.07821183687
absolute error = 0.0005438
relative error = 0.01041 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 39.87
Order of pole (three term test) = 45.57 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.556 2.02
h = 0.003 0.006
y[1] (numeric) = 1.23387573328 -5.09912309808
y[1] (closed_form) = 1.2334174564 -5.09941813352
absolute error = 0.000545
relative error = 0.01039 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.81
Order of pole (three term test) = 45.68 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.559 2.026
h = 0.0001 0.005
y[1] (numeric) = 1.2251564234 -5.13445630429
y[1] (closed_form) = 1.22464029519 -5.13477419831
absolute error = 0.0006062
relative error = 0.01148 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.72
Order of pole (three term test) = 45.87 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5591 2.031
h = 0.0001 0.003
y[1] (numeric) = 1.23051667764 -5.16124302027
y[1] (closed_form) = 1.23003530354 -5.16153984169
absolute error = 0.0005655
relative error = 0.01066 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.715
Order of pole (three term test) = 46 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5592 2.034
h = 0.001 0.001
y[1] (numeric) = 1.23355481499 -5.17742818557
y[1] (closed_form) = 1.23307025992 -5.17770935605
absolute error = 0.0005602
relative error = 0.01053 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.882
Order of pole (three term test) = 46.09 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5602 2.035
h = 0.001 0.003
y[1] (numeric) = 1.22938215943 -5.1839871864
y[1] (closed_form) = 1.22889866887 -5.18426016021
absolute error = 0.0005552
relative error = 0.01042 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 32.73
Order of pole (three term test) = 46.13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5612 2.038
h = 0.0001 0.004
y[1] (numeric) = 1.22757150223 -5.20127566989
y[1] (closed_form) = 1.22708650016 -5.20156544723
absolute error = 0.000565
relative error = 0.01057 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 18.63
Order of pole (three term test) = 46.22 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5613 2.042
h = 0.003 0.006
y[1] (numeric) = 1.23177396985 -5.22295274475
y[1] (closed_form) = 1.2313006043 -5.22325103711
absolute error = 0.0005595
relative error = 0.01043 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.88
Order of pole (three term test) = 46.33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5643 2.048
h = 0.0001 0.005
y[1] (numeric) = 1.22269217976 -5.25900714226
y[1] (closed_form) = 1.22215950566 -5.25932847194
absolute error = 0.0006221
relative error = 0.01152 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.2
Order of pole (three term test) = 46.53 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5644 2.053
h = 0.0001 0.003
y[1] (numeric) = 1.22803620447 -5.28639970129
y[1] (closed_form) = 1.22753920309 -5.28669968304
absolute error = 0.0005805
relative error = 0.0107 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.107
Order of pole (three term test) = 46.67 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5645 2.056
h = 0.001 0.001
y[1] (numeric) = 1.23106017268 -5.30295005579
y[1] (closed_form) = 1.2305600104 -5.30323401039
absolute error = 0.0005751
relative error = 0.01056 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.192
Order of pole (three term test) = 46.76 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5655 2.057
h = 0.001 0.003
y[1] (numeric) = 1.22676483216 -5.3096303771
y[1] (closed_form) = 1.22626580722 -5.30990595421
absolute error = 0.0005701
relative error = 0.01046 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 34.2
Order of pole (three term test) = 46.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5665 2.06
h = 0.0001 0.004
y[1] (numeric) = 1.22482958253 -5.32728399279
y[1] (closed_form) = 1.22432891213 -5.32757674814
absolute error = 0.00058
relative error = 0.01061 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 19.47
Order of pole (three term test) = 46.9 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5666 2.064
h = 0.003 0.006
y[1] (numeric) = 1.22901579411 -5.34945096745
y[1] (closed_form) = 1.22852697551 -5.349752501
absolute error = 0.0005743
relative error = 0.01046 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26
Order of pole (three term test) = 47.02 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1254.0MB, alloc=52.3MB, time=14.80
x[1] = 0.5696 2.07
h = 0.0001 0.005
y[1] (numeric) = 1.2195589747 -5.38624087625
y[1] (closed_form) = 1.2190093579 -5.38656562254
absolute error = 0.0006384
relative error = 0.01156 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.7
Order of pole (three term test) = 47.22 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5697 2.075
h = 0.0001 0.003
y[1] (numeric) = 1.2248828179 -5.41425301353
y[1] (closed_form) = 1.2243698137 -5.41455613515
absolute error = 0.0005959
relative error = 0.01073 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.517
Order of pole (three term test) = 47.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5698 2.078
h = 0.001 0.001
y[1] (numeric) = 1.22789013583 -5.43117680815
y[1] (closed_form) = 1.22737399309 -5.43146351838
absolute error = 0.0005904
relative error = 0.0106 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.515
Order of pole (three term test) = 47.47 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5708 2.079
h = 0.001 0.003
y[1] (numeric) = 1.22346859404 -5.43798049393
y[1] (closed_form) = 1.22295366395 -5.43825864227
absolute error = 0.0005853
relative error = 0.0105 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 35.74
Order of pole (three term test) = 47.51 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5718 2.082
h = 0.0001 0.004
y[1] (numeric) = 1.22140375251 -5.45600683916
y[1] (closed_form) = 1.22088703825 -5.4563025479
absolute error = 0.0005953
relative error = 0.01065 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 20.35
Order of pole (three term test) = 47.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5719 2.086
h = 0.003 0.006
y[1] (numeric) = 1.22557044691 -5.47867479634
y[1] (closed_form) = 1.22506580309 -5.47897955323
absolute error = 0.0005895
relative error = 0.0105 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.17
Order of pole (three term test) = 47.73 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5749 2.092
h = 0.0001 0.005
y[1] (numeric) = 1.21572570654 -5.51621478429
y[1] (closed_form) = 1.21515874173 -5.51654292574
absolute error = 0.0006551
relative error = 0.0116 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.23
Order of pole (three term test) = 47.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.575 2.097
h = 0.0001 0.003
y[1] (numeric) = 1.22102526258 -5.54486051281
y[1] (closed_form) = 1.22049587197 -5.54516675154
absolute error = 0.0006116
relative error = 0.01077 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.945
Order of pole (three term test) = 48.11 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5751 2.1
h = 0.001 0.001
y[1] (numeric) = 1.2240133544 -5.56216616486
y[1] (closed_form) = 1.22348085001 -5.56245559974
absolute error = 0.0006061
relative error = 0.01064 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.854
Order of pole (three term test) = 48.2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5761 2.101
h = 0.001 0.003
y[1] (numeric) = 1.21946200872 -5.56909528587
y[1] (closed_form) = 1.21893079484 -5.56937597084
absolute error = 0.0006008
relative error = 0.01054 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.35
Order of pole (three term test) = 48.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5771 2.104
h = 0.0001 0.004
y[1] (numeric) = 1.21726242982 -5.58750209772
y[1] (closed_form) = 1.21672928815 -5.58780073282
absolute error = 0.0006111
relative error = 0.01069 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 21.26
Order of pole (three term test) = 48.35 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5772 2.108
h = 0.003 0.006
y[1] (numeric) = 1.22140622016 -5.61068234401
y[1] (closed_form) = 1.22088537096 -5.61099030415
absolute error = 0.0006051
relative error = 0.01054 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.4
Order of pole (three term test) = 48.48 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5802 2.114
h = 0.0001 0.005
y[1] (numeric) = 1.21116031539 -5.64898723046
y[1] (closed_form) = 1.21057558857 -5.64931874314
absolute error = 0.0006722
relative error = 0.01163 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.78
Order of pole (three term test) = 48.71 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5803 2.119
h = 0.0001 0.003
y[1] (numeric) = 1.21643131976 -5.67828084642
y[1] (closed_form) = 1.21588515098 -5.67859017708
absolute error = 0.0006277
relative error = 0.01081 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.39
Order of pole (three term test) = 48.87 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5804 2.122
h = 0.001 0.001
y[1] (numeric) = 1.21939751183 -5.69597694281
y[1] (closed_form) = 1.21884825652 -5.69626906878
absolute error = 0.0006221
relative error = 0.01068 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.207
Order of pole (three term test) = 48.98 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5814 2.123
h = 0.0001 0.004
y[1] (numeric) = 1.2147126712 -5.70303359674
y[1] (closed_form) = 1.21416478689 -5.70331678109
absolute error = 0.0006167
relative error = 0.01058 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49.38
Order of pole (three term test) = 49.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5815 2.127
h = 0.003 0.006
y[1] (numeric) = 1.2188359491 -5.72664139379
y[1] (closed_form) = 1.21830483063 -5.72695711344
absolute error = 0.0006179
relative error = 0.01055 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.5
Order of pole (three term test) = 49.15 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5845 2.133
h = 0.0001 0.005
y[1] (numeric) = 1.20824321125 -5.76562174114
y[1] (closed_form) = 1.20764684948 -5.76596117366
absolute error = 0.0006862
relative error = 0.01165 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.27
Order of pole (three term test) = 49.39 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5846 2.138
h = 0.0001 0.003
y[1] (numeric) = 1.21349405397 -5.7954851176
y[1] (closed_form) = 1.21293711196 -5.79580211472
absolute error = 0.0006408
relative error = 0.01082 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.8
Order of pole (three term test) = 49.56 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1298.0MB, alloc=52.3MB, time=15.32
x[1] = 0.5847 2.141
h = 0.001 0.001
y[1] (numeric) = 1.21644397079 -5.81352460966
y[1] (closed_form) = 1.21588396289 -5.81382404982
absolute error = 0.000635
relative error = 0.01069 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.525
Order of pole (three term test) = 49.67 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5857 2.142
h = 0.001 0.003
y[1] (numeric) = 1.21164275102 -5.82069439178
y[1] (closed_form) = 1.21108418321 -5.82098472131
absolute error = 0.0006295
relative error = 0.01059 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 40.54
Order of pole (three term test) = 49.71 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5867 2.145
h = 0.0001 0.004
y[1] (numeric) = 1.20918300138 -5.83983200073
y[1] (closed_form) = 1.2086222298 -5.84014102819
absolute error = 0.0006403
relative error = 0.01074 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.08
Order of pole (three term test) = 49.83 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5868 2.149
h = 0.003 0.006
y[1] (numeric) = 1.21328114125 -5.86399674962
y[1] (closed_form) = 1.21273308795 -5.86431563369
absolute error = 0.0006341
relative error = 0.01059 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.82
Order of pole (three term test) = 49.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5898 2.155
h = 0.0001 0.005
y[1] (numeric) = 1.20226181084 -5.90377042094
y[1] (closed_form) = 1.20164689252 -5.9041131783
absolute error = 0.000704
relative error = 0.01168 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.87
Order of pole (three term test) = 50.21 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5899 2.16
h = 0.0001 0.003
y[1] (numeric) = 1.20747590423 -5.93430911497
y[1] (closed_form) = 1.20690143226 -5.93462915536
absolute error = 0.0006576
relative error = 0.01086 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.28
Order of pole (three term test) = 50.39 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.59 2.163
h = 0.001 0.001
y[1] (numeric) = 1.21039878203 -5.95275552712
y[1] (closed_form) = 1.20982127625 -5.9530575936
absolute error = 0.0006517
relative error = 0.01073 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.908
Order of pole (three term test) = 50.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.591 2.164
h = 0.001 0.003
y[1] (numeric) = 1.20545698202 -5.960056864
y[1] (closed_form) = 1.20488100188 -5.96034962105
absolute error = 0.0006461
relative error = 0.01063 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 42.36
Order of pole (three term test) = 50.55 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.592 2.167
h = 0.0001 0.004
y[1] (numeric) = 1.2028470291 -5.97959793349
y[1] (closed_form) = 1.20226868675 -5.97990980079
absolute error = 0.0006571
relative error = 0.01077 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.12
Order of pole (three term test) = 50.67 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5921 2.171
h = 0.003 0.006
y[1] (numeric) = 1.20691198764 -6.0043086383
y[1] (closed_form) = 1.2063465956 -6.00463065993
absolute error = 0.0006507
relative error = 0.01062 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 32.21
Order of pole (three term test) = 50.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5951 2.177
h = 0.0001 0.005
y[1] (numeric) = 1.19545176478 -6.04489119743
y[1] (closed_form) = 1.19481784995 -6.04523724803
absolute error = 0.0007222
relative error = 0.01172 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 14.5
Order of pole (three term test) = 51.07 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5952 2.182
h = 0.0001 0.003
y[1] (numeric) = 1.2006243639 -6.07612034833
y[1] (closed_form) = 1.20003194574 -6.07644339948
absolute error = 0.0006748
relative error = 0.01089 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.79
Order of pole (three term test) = 51.26 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5953 2.185
h = 0.001 0.001
y[1] (numeric) = 1.20351723325 -6.09498277239
y[1] (closed_form) = 1.20292181618 -6.09528742375
absolute error = 0.0006688
relative error = 0.01077 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.309
Order of pole (three term test) = 51.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5963 2.186
h = 0.001 0.003
y[1] (numeric) = 1.19843089713 -6.10241784034
y[1] (closed_form) = 1.19783709412 -6.10271297961
absolute error = 0.0006631
relative error = 0.01066 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 44.27
Order of pole (three term test) = 51.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5973 2.189
h = 0.0001 0.004
y[1] (numeric) = 1.19566499367 -6.12237067089
y[1] (closed_form) = 1.19506866447 -6.12268534092
absolute error = 0.0006743
relative error = 0.01081 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.2
Order of pole (three term test) = 51.55 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5974 2.193
h = 0.003 0.006
y[1] (numeric) = 1.1996928612 -6.14763954584
y[1] (closed_form) = 1.19910971788 -6.14796467553
absolute error = 0.0006677
relative error = 0.01066 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 33.66
Order of pole (three term test) = 51.71 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6004 2.199
h = 0.0001 0.005
y[1] (numeric) = 1.18777705636 -6.18904682255
y[1] (closed_form) = 1.18712369562 -6.18939613189
absolute error = 0.0007409
relative error = 0.01176 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 15.15
Order of pole (three term test) = 51.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6005 2.204
h = 0.0001 0.003
y[1] (numeric) = 1.19290323632 -6.22098187476
y[1] (closed_form) = 1.19229244686 -6.22130790134
absolute error = 0.0006924
relative error = 0.01093 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.32
Order of pole (three term test) = 52.17 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6006 2.207
h = 0.001 0.001
y[1] (numeric) = 1.19576301709 -6.24026958518
y[1] (closed_form) = 1.19514926655 -6.24057677704
absolute error = 0.0006863
relative error = 0.0108 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.728
Order of pole (three term test) = 52.29 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1341.7MB, alloc=52.3MB, time=15.83
x[1] = 0.6016 2.208
h = 0.001 0.003
y[1] (numeric) = 1.19052809189 -6.24784058781
y[1] (closed_form) = 1.18991604677 -6.24813806094
absolute error = 0.0006805
relative error = 0.0107 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 46.26
Order of pole (three term test) = 52.34 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6026 2.211
h = 0.0001 0.004
y[1] (numeric) = 1.1876003235 -6.26821363133
y[1] (closed_form) = 1.18698558251 -6.26853106401
absolute error = 0.0006919
relative error = 0.01084 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.34
Order of pole (three term test) = 52.47 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6027 2.215
h = 0.003 0.006
y[1] (numeric) = 1.19158704328 -6.29405313642
y[1] (closed_form) = 1.19098572731 -6.29438134197
absolute error = 0.0006851
relative error = 0.01069 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 35.17
Order of pole (three term test) = 52.64 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6057 2.221
h = 0.0001 0.005
y[1] (numeric) = 1.17920056685 -6.33630123027
y[1] (closed_form) = 1.17852730118 -6.33665376077
absolute error = 0.00076
relative error = 0.01179 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 15.83
Order of pole (three term test) = 52.91 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6058 2.226
h = 0.0001 0.003
y[1] (numeric) = 1.18427521697 -6.36895793921
y[1] (closed_form) = 1.18364562203 -6.36928690298
absolute error = 0.0007104
relative error = 0.01097 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.87
Order of pole (three term test) = 53.12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6059 2.229
h = 0.001 0.001
y[1] (numeric) = 1.18709871477 -6.38868039667
y[1] (closed_form) = 1.18646619961 -6.38899008148
absolute error = 0.0007043
relative error = 0.01084 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.17
Order of pole (three term test) = 53.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6069 2.23
h = 0.0001 0.004
y[1] (numeric) = 1.18171104807 -6.39638956488
y[1] (closed_form) = 1.18108033275 -6.3966893203
absolute error = 0.0006983
relative error = 0.01074 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 61.17
Order of pole (three term test) = 53.3 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.607 2.234
h = 0.003 0.006
y[1] (numeric) = 1.18566191649 -6.42270523437
y[1] (closed_form) = 1.18504891116 -6.42304177836
absolute error = 0.0006993
relative error = 0.01071 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 36.54
Order of pole (three term test) = 53.47 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.61 2.24
h = 0.0001 0.005
y[1] (numeric) = 1.17286818688 -6.46569603531
y[1] (closed_form) = 1.17218171164 -6.46605704607
absolute error = 0.0007756
relative error = 0.0118 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.44
Order of pole (three term test) = 53.75 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6101 2.245
h = 0.0001 0.003
y[1] (numeric) = 1.17790310073 -6.49898748095
y[1] (closed_form) = 1.17726125952 -6.49932466656
absolute error = 0.000725
relative error = 0.01098 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.37
Order of pole (three term test) = 53.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6102 2.248
h = 0.001 0.001
y[1] (numeric) = 1.18069805501 -6.51909236096
y[1] (closed_form) = 1.18005332584 -6.51940987713
absolute error = 0.0007187
relative error = 0.01085 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.56
Order of pole (three term test) = 54.1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6112 2.249
h = 0.001 0.003
y[1] (numeric) = 1.17517719317 -6.52692415352
y[1] (closed_form) = 1.17453434504 -6.5272315545
absolute error = 0.0007126
relative error = 0.01074 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.22
Order of pole (three term test) = 54.16 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6122 2.252
h = 0.0001 0.004
y[1] (numeric) = 1.17193714908 -6.54810424167
y[1] (closed_form) = 1.17129127887 -6.54843242497
absolute error = 0.0007245
relative error = 0.01089 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.59
Order of pole (three term test) = 54.3 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6123 2.256
h = 0.003 0.006
y[1] (numeric) = 1.17584314115 -6.57504019236
y[1] (closed_form) = 1.17521115454 -6.57537974991
absolute error = 0.0007174
relative error = 0.01074 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.18
Order of pole (three term test) = 54.48 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6153 2.262
h = 0.0001 0.005
y[1] (numeric) = 1.16254975993 -6.61890269051
y[1] (closed_form) = 1.16184249879 -6.61926684974
absolute error = 0.0007955
relative error = 0.01184 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.18
Order of pole (three term test) = 54.77 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6154 2.267
h = 0.0001 0.003
y[1] (numeric) = 1.16752331569 -6.65294602481
y[1] (closed_form) = 1.16686183576 -6.65328607368
absolute error = 0.0007438
relative error = 0.01101 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.97
Order of pole (three term test) = 55 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6155 2.27
h = 0.001 0.001
y[1] (numeric) = 1.17027584432 -6.67350380517
y[1] (closed_form) = 1.16961152317 -6.67382372254
absolute error = 0.0007373
relative error = 0.01088 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.03
Order of pole (three term test) = 55.14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6165 2.271
h = 0.001 0.003
y[1] (numeric) = 1.16459426867 -6.68147803978
y[1] (closed_form) = 1.16393192883 -6.68178762356
absolute error = 0.0007311
relative error = 0.01078 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 52.47
Order of pole (three term test) = 55.2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6175 2.274
h = 0.0001 0.004
y[1] (numeric) = 1.16117458171 -6.70310345546
y[1] (closed_form) = 1.1605090329 -6.70343427509
absolute error = 0.0007432
relative error = 0.01092 %
Correct digits = 4
memory used=1385.6MB, alloc=52.3MB, time=16.34
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.87
Order of pole (three term test) = 55.34 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6176 2.278
h = 0.003 0.006
y[1] (numeric) = 1.16502712395 -6.73064713641
y[1] (closed_form) = 1.1643757084 -6.73098966701
absolute error = 0.000736
relative error = 0.01077 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 39.9
Order of pole (three term test) = 55.53 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6206 2.284
h = 0.0001 0.005
y[1] (numeric) = 1.15121780084 -6.77539822943
y[1] (closed_form) = 1.15048926609 -6.77576549028
absolute error = 0.0008159
relative error = 0.01187 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.96
Order of pole (three term test) = 55.84 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6207 2.289
h = 0.0001 0.003
y[1] (numeric) = 1.15612432657 -6.81021013346
y[1] (closed_form) = 1.1554427467 -6.81055299839
absolute error = 0.000763
relative error = 0.01104 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 14.6
Order of pole (three term test) = 56.08 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6208 2.292
h = 0.001 0.001
y[1] (numeric) = 1.15883089005 -6.83123082886
y[1] (closed_form) = 1.15814651909 -6.83155309041
absolute error = 0.0007564
relative error = 0.01092 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.53
Order of pole (three term test) = 56.22 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6218 2.293
h = 0.001 0.003
y[1] (numeric) = 1.15298415048 -6.83934981612
y[1] (closed_form) = 1.15230186443 -6.83966152141
absolute error = 0.0007501
relative error = 0.01081 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 54.84
Order of pole (three term test) = 56.28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6228 2.296
h = 0.0001 0.004
y[1] (numeric) = 1.14937821813 -6.86142962131
y[1] (closed_form) = 1.14869252979 -6.86176302494
absolute error = 0.0007624
relative error = 0.01096 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.22
Order of pole (three term test) = 56.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6229 2.3
h = 0.003 0.006
y[1] (numeric) = 1.15317264332 -6.8895944888
y[1] (closed_form) = 1.15250134162 -6.88993994873
absolute error = 0.000755
relative error = 0.01081 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 41.69
Order of pole (three term test) = 56.63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6259 2.306
h = 0.0001 0.005
y[1] (numeric) = 1.13883064559 -6.93525135915
y[1] (closed_form) = 1.13808033908 -6.93562167121
absolute error = 0.0008367
relative error = 0.0119 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 18.76
Order of pole (three term test) = 56.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.626 2.311
h = 0.0001 0.003
y[1] (numeric) = 1.14366425952 -6.97084884873
y[1] (closed_form) = 1.14296210867 -6.97119447915
absolute error = 0.0007826
relative error = 0.01108 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 15.26
Order of pole (three term test) = 57.2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6261 2.314
h = 0.001 0.001
y[1] (numeric) = 1.14632118944 -6.9923426742
y[1] (closed_form) = 1.14561630117 -6.99266721931
absolute error = 0.000776
relative error = 0.01095 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.05
Order of pole (three term test) = 57.35 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6271 2.315
h = 0.001 0.003
y[1] (numeric) = 1.14030472681 -7.00060875217
y[1] (closed_form) = 1.13960203045 -7.00092251404
absolute error = 0.0007696
relative error = 0.01085 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 57.3
Order of pole (three term test) = 57.41 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6281 2.318
h = 0.0001 0.004
y[1] (numeric) = 1.13650575563 -7.0231521726
y[1] (closed_form) = 1.13579945705 -7.02348810438
absolute error = 0.0007821
relative error = 0.01099 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 32.62
Order of pole (three term test) = 57.57 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6282 2.322
h = 0.003 0.006
y[1] (numeric) = 1.14023722519 -7.05195195257
y[1] (closed_form) = 1.13954557037 -7.05230029483
absolute error = 0.0007744
relative error = 0.01084 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 43.57
Order of pole (three term test) = 57.78 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6312 2.328
h = 0.0001 0.005
y[1] (numeric) = 1.12534536601 -7.09853207144
y[1] (closed_form) = 1.12457277896 -7.09890538062
absolute error = 0.0008581
relative error = 0.01194 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 19.61
Order of pole (three term test) = 58.12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6313 2.333
h = 0.0001 0.003
y[1] (numeric) = 1.13009996993 -7.13493250356
y[1] (closed_form) = 1.12937676704 -7.13528084536
absolute error = 0.0008027
relative error = 0.01111 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 15.95
Order of pole (three term test) = 58.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6314 2.336
h = 0.001 0.001
y[1] (numeric) = 1.1327034649 -7.15690987828
y[1] (closed_form) = 1.13197758192 -7.15723664258
absolute error = 0.000796
relative error = 0.01099 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.59
Order of pole (three term test) = 58.54 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6324 2.337
h = 0.0001 0.004
y[1] (numeric) = 1.12651260838 -7.16532541251
y[1] (closed_form) = 1.12578902782 -7.16564116218
absolute error = 0.0007895
relative error = 0.01088 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 75.77
Order of pole (three term test) = 58.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6325 2.341
h = 0.003 0.006
y[1] (numeric) = 1.13018989714 -7.19465491992
y[1] (closed_form) = 1.129484961 -7.1950122058
absolute error = 0.0007903
relative error = 0.01085 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 45.26
Order of pole (three term test) = 58.81 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6355 2.347
h = 0.0001 0.005
y[1] (numeric) = 1.11482190368 -7.24205079141
y[1] (closed_form) = 1.11403434332 -7.24243316066
absolute error = 0.0008755
relative error = 0.01195 %
Correct digits = 4
memory used=1429.4MB, alloc=52.3MB, time=16.86
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 20.37
Order of pole (three term test) = 59.16 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6356 2.352
h = 0.0001 0.003
y[1] (numeric) = 1.11951329732 -7.27915757815
y[1] (closed_form) = 1.11877619782 -7.27951471908
absolute error = 0.0008191
relative error = 0.01112 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.56
Order of pole (three term test) = 59.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6357 2.355
h = 0.001 0.001
y[1] (numeric) = 1.12207358141 -7.30156037872
y[1] (closed_form) = 1.1213338482 -7.30189550938
absolute error = 0.0008121
relative error = 0.01099 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.08
Order of pole (three term test) = 59.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6367 2.356
h = 0.001 0.003
y[1] (numeric) = 1.11573060408 -7.31010863038
y[1] (closed_form) = 1.11499326849 -7.31043254227
absolute error = 0.0008053
relative error = 0.01089 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 62.2
Order of pole (three term test) = 59.66 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6377 2.359
h = 0.0001 0.004
y[1] (numeric) = 1.1115594658 -7.33354235671
y[1] (closed_form) = 1.11081814357 -7.33388934337
absolute error = 0.0008185
relative error = 0.01103 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 35.41
Order of pole (three term test) = 59.83 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6378 2.363
h = 0.003 0.006
y[1] (numeric) = 1.11516826402 -7.36356193212
y[1] (closed_form) = 1.11444207854 -7.36392200948
absolute error = 0.0008106
relative error = 0.01088 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 47.29
Order of pole (three term test) = 60.06 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6408 2.369
h = 0.0001 0.005
y[1] (numeric) = 1.09921739521 -7.41191456207
y[1] (closed_form) = 1.09840657779 -7.41229982384
absolute error = 0.0008977
relative error = 0.01198 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 21.28
Order of pole (three term test) = 60.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6409 2.374
h = 0.0001 0.003
y[1] (numeric) = 1.10381804853 -7.44985759805
y[1] (closed_form) = 1.1030589737 -7.45021734578
absolute error = 0.00084
relative error = 0.01115 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.31
Order of pole (three term test) = 60.7 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.641 2.377
h = 0.001 0.001
y[1] (numeric) = 1.10631758597 -7.47276394132
y[1] (closed_form) = 1.10555594184 -7.4731011669
absolute error = 0.000833
relative error = 0.01103 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 13.67
Order of pole (three term test) = 60.88 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.642 2.378
h = 0.001 0.003
y[1] (numeric) = 1.09979124587 -7.48146618296
y[1] (closed_form) = 1.09903211664 -7.48179194994
absolute error = 0.0008261
relative error = 0.01092 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 65
Order of pole (three term test) = 60.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.643 2.381
h = 0.0001 0.004
y[1] (numeric) = 1.0954066494 -7.50539093395
y[1] (closed_form) = 1.09464331368 -7.50574027433
absolute error = 0.0008395
relative error = 0.01107 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37
Order of pole (three term test) = 61.12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6431 2.385
h = 0.003 0.006
y[1] (numeric) = 1.09893782935 -7.53608628888
y[1] (closed_form) = 1.09818989853 -7.53644910067
absolute error = 0.0008313
relative error = 0.01091 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 49.42
Order of pole (three term test) = 61.36 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6461 2.391
h = 0.0001 0.005
y[1] (numeric) = 1.08238553616 -7.58541400234
y[1] (closed_form) = 1.08155092118 -7.58580209132
absolute error = 0.0009204
relative error = 0.01201 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.24
Order of pole (three term test) = 61.73 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6462 2.396
h = 0.0001 0.003
y[1] (numeric) = 1.08688869771 -7.62421165959
y[1] (closed_form) = 1.0861071366 -7.62457394926
absolute error = 0.0008614
relative error = 0.01119 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 18.09
Order of pole (three term test) = 62.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6463 2.399
h = 0.001 0.001
y[1] (numeric) = 1.08932328592 -7.64763257202
y[1] (closed_form) = 1.08853922401 -7.6479718168
absolute error = 0.0008543
relative error = 0.01106 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 14.28
Order of pole (three term test) = 62.21 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6473 2.4
h = 0.001 0.003
y[1] (numeric) = 1.08260857804 -7.65649124914
y[1] (closed_form) = 1.08182715212 -7.65681879084
absolute error = 0.0008473
relative error = 0.01096 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 67.92
Order of pole (three term test) = 62.28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6483 2.403
h = 0.0001 0.004
y[1] (numeric) = 1.07800294466 -7.68091691006
y[1] (closed_form) = 1.07721708498 -7.68126853354
absolute error = 0.0008609
relative error = 0.0111 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.67
Order of pole (three term test) = 62.47 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6484 2.407
h = 0.003 0.006
y[1] (numeric) = 1.08145095759 -7.71230286276
y[1] (closed_form) = 1.08068077484 -7.7126683481
absolute error = 0.0008525
relative error = 0.01095 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 51.64
Order of pole (three term test) = 62.72 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6514 2.413
h = 0.0001 0.005
y[1] (numeric) = 1.06427818935 -7.76262428907
y[1] (closed_form) = 1.06341922481 -7.76301513568
absolute error = 0.0009437
relative error = 0.01204 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.24
Order of pole (three term test) = 63.11 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1473.2MB, alloc=52.3MB, time=17.37
x[1] = 0.6515 2.418
h = 0.0001 0.003
y[1] (numeric) = 1.06867686393 -7.80229530656
y[1] (closed_form) = 1.06787229474 -7.8026600692
absolute error = 0.0008834
relative error = 0.01122 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 18.9
Order of pole (three term test) = 63.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6516 2.421
h = 0.001 0.001
y[1] (numeric) = 1.07104215072 -7.82624203406
y[1] (closed_form) = 1.07023515347 -7.82658321797
absolute error = 0.0008762
relative error = 0.01109 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 14.93
Order of pole (three term test) = 63.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6526 2.422
h = 0.001 0.003
y[1] (numeric) = 1.06413394766 -7.83525961954
y[1] (closed_form) = 1.06332971143 -7.83558885117
absolute error = 0.000869
relative error = 0.01099 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 70.98
Order of pole (three term test) = 63.68 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6536 2.425
h = 0.0001 0.004
y[1] (numeric) = 1.05929948106 -7.86019625248
y[1] (closed_form) = 1.05849057617 -7.86055008425
absolute error = 0.0008829
relative error = 0.01113 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 40.41
Order of pole (three term test) = 63.88 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6537 2.429
h = 0.003 0.006
y[1] (numeric) = 1.06265857924 -7.89228791666
y[1] (closed_form) = 1.06186562721 -7.8926560107
absolute error = 0.0008742
relative error = 0.01098 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 53.97
Order of pole (three term test) = 64.13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6567 2.435
h = 0.0001 0.005
y[1] (numeric) = 1.04484577064 -7.94362199351
y[1] (closed_form) = 1.04396189281 -7.94401552376
absolute error = 0.0009675
relative error = 0.01208 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.29
Order of pole (three term test) = 64.54 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6568 2.44
h = 0.0001 0.003
y[1] (numeric) = 1.04913271172 -7.98418548401
y[1] (closed_form) = 1.0483046016 -7.98455264641
absolute error = 0.0009059
relative error = 0.01125 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 19.75
Order of pole (three term test) = 64.87 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6569 2.443
h = 0.001 0.001
y[1] (numeric) = 1.05142419069 -8.00866949606
y[1] (closed_form) = 1.05059372964 -8.0090125346
absolute error = 0.0008985
relative error = 0.01112 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 15.6
Order of pole (three term test) = 65.07 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6579 2.444
h = 0.0001 0.004
y[1] (numeric) = 1.04431723977 -8.01784849012
y[1] (closed_form) = 1.04348966882 -8.01817932236
absolute error = 0.0008912
relative error = 0.01102 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 93.85
Order of pole (three term test) = 65.14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.658 2.448
h = 0.003 0.006
y[1] (numeric) = 1.0476003463 -8.05052887284
y[1] (closed_form) = 1.04679232857 -8.05090653969
absolute error = 0.0008919
relative error = 0.01099 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 56.06
Order of pole (three term test) = 65.41 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.661 2.454
h = 0.0001 0.005
y[1] (numeric) = 1.02923291764 -8.10275795988
y[1] (closed_form) = 1.02833209144 -8.10316114608
absolute error = 0.0009869
relative error = 0.01208 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.23
Order of pole (three term test) = 65.83 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6611 2.459
h = 0.0001 0.003
y[1] (numeric) = 1.03342862984 -8.14410671022
y[1] (closed_form) = 1.03258477453 -8.14448326815
absolute error = 0.0009241
relative error = 0.01126 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 20.52
Order of pole (three term test) = 66.17 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6612 2.462
h = 0.001 0.001
y[1] (numeric) = 1.03565943793 -8.16906351235
y[1] (closed_form) = 1.03481329503 -8.16941546694
absolute error = 0.0009164
relative error = 0.01113 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.2
Order of pole (three term test) = 66.37 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6622 2.463
h = 0.001 0.003
y[1] (numeric) = 1.02837907118 -8.17838591944
y[1] (closed_form) = 1.0275359297 -8.17872544358
absolute error = 0.0009089
relative error = 0.01103 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 77.04
Order of pole (three term test) = 66.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6632 2.466
h = 0.0001 0.004
y[1] (numeric) = 1.02310365733 -8.20430370562
y[1] (closed_form) = 1.02225539543 -8.20466882452
absolute error = 0.0009235
relative error = 0.01117 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 43.86
Order of pole (three term test) = 66.67 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6633 2.47
h = 0.003 0.006
y[1] (numeric) = 1.02629014651 -8.23775102556
y[1] (closed_form) = 1.02545836652 -8.23813117582
absolute error = 0.0009145
relative error = 0.01102 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 58.58
Order of pole (three term test) = 66.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6663 2.476
h = 0.0001 0.005
y[1] (numeric) = 1.00724508982 -8.29102908457
y[1] (closed_form) = 1.00631826824 -8.29143481144
absolute error = 0.001012
relative error = 0.01211 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.36
Order of pole (three term test) = 67.39 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6664 2.481
h = 0.0001 0.003
y[1] (numeric) = 1.0113151273 -8.33330698514
y[1] (closed_form) = 1.01044670831 -8.33368580148
absolute error = 0.0009474
relative error = 0.01129 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 21.44
Order of pole (three term test) = 67.74 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6665 2.484
h = 0.001 0.001
y[1] (numeric) = 1.01346345852 -8.35882308151
y[1] (closed_form) = 1.01259283753 -8.35917672762
absolute error = 0.0009397
relative error = 0.01116 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 16.93
Order of pole (three term test) = 67.95 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1517.0MB, alloc=52.3MB, time=17.88
x[1] = 0.6675 2.485
h = 0.001 0.003
y[1] (numeric) = 1.00597425679 -8.36831168812
y[1] (closed_form) = 1.0051067741 -8.36865264055
absolute error = 0.0009321
relative error = 0.01106 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 80.51
Order of pole (three term test) = 68.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6685 2.488
h = 0.0001 0.004
y[1] (numeric) = 1.00044657845 -8.39477033514
y[1] (closed_form) = 0.999573717413 -8.39513743025
absolute error = 0.0009469
relative error = 0.0112 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 45.83
Order of pole (three term test) = 68.26 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6686 2.492
h = 0.003 0.006
y[1] (numeric) = 1.00352674782 -8.428968362
y[1] (closed_form) = 1.00267065615 -8.42935091876
absolute error = 0.0009377
relative error = 0.01105 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 61.21
Order of pole (three term test) = 68.55 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6716 2.498
h = 0.0001 0.005
y[1] (numeric) = 0.983782954644 -8.48331524203
y[1] (closed_form) = 0.98282953896 -8.48372342215
absolute error = 0.001037
relative error = 0.01214 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.55
Order of pole (three term test) = 69.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6717 2.503
h = 0.0001 0.003
y[1] (numeric) = 0.987719313076 -8.5265425175
y[1] (closed_form) = 0.986825764577 -8.52692350617
absolute error = 0.0009714
relative error = 0.01132 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.4
Order of pole (three term test) = 69.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6718 2.506
h = 0.001 0.001
y[1] (numeric) = 0.989780196084 -8.55263004249
y[1] (closed_form) = 0.988884536047 -8.55298528207
absolute error = 0.0009635
relative error = 0.01119 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 17.69
Order of pole (three term test) = 69.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6728 2.507
h = 0.001 0.003
y[1] (numeric) = 0.982076531977 -8.56228742809
y[1] (closed_form) = 0.981184151483 -8.5626297057
absolute error = 0.0009558
relative error = 0.01109 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 84.13
Order of pole (three term test) = 69.69 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6738 2.51
h = 0.0001 0.004
y[1] (numeric) = 0.976287898322 -8.5892977099
y[1] (closed_form) = 0.975389873023 -8.58966668875
absolute error = 0.0009709
relative error = 0.01123 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 47.89
Order of pole (three term test) = 69.92 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6739 2.514
h = 0.003 0.006
y[1] (numeric) = 0.979255176617 -8.62426275369
y[1] (closed_form) = 0.978374212168 -8.62464763544
absolute error = 0.0009614
relative error = 0.01108 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 63.97
Order of pole (three term test) = 70.22 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6769 2.52
h = 0.0001 0.005
y[1] (numeric) = 0.958790970654 -8.6796986281
y[1] (closed_form) = 0.957810349427 -8.68010916896
absolute error = 0.001063
relative error = 0.01217 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.79
Order of pole (three term test) = 70.7 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.677 2.525
h = 0.0001 0.003
y[1] (numeric) = 0.96258536334 -8.72389590479
y[1] (closed_form) = 0.961666107535 -8.72427897485
absolute error = 0.0009959
relative error = 0.01135 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.41
Order of pole (three term test) = 71.09 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6771 2.528
h = 0.001 0.001
y[1] (numeric) = 0.964553653676 -8.75056723295
y[1] (closed_form) = 0.963632381832 -8.75092396282
absolute error = 0.0009879
relative error = 0.01122 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 18.49
Order of pole (three term test) = 71.33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6781 2.529
h = 0.001 0.003
y[1] (numeric) = 0.956629762636 -8.76039600392
y[1] (closed_form) = 0.955711916107 -8.76073949839
absolute error = 0.00098
relative error = 0.01112 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 87.92
Order of pole (three term test) = 71.41 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6791 2.532
h = 0.0001 0.004
y[1] (numeric) = 0.950571235219 -8.78796888511
y[1] (closed_form) = 0.949647468624 -8.78833965025
absolute error = 0.0009954
relative error = 0.01126 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.05
Order of pole (three term test) = 71.65 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6792 2.536
h = 0.003 0.006
y[1] (numeric) = 0.953418820823 -8.82371757921
y[1] (closed_form) = 0.952512410633 -8.82410469974
absolute error = 0.0009856
relative error = 0.01111 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 66.85
Order of pole (three term test) = 71.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6822 2.542
h = 0.0001 0.005
y[1] (numeric) = 0.932211943348 -8.88026294988
y[1] (closed_form) = 0.93120349219 -8.88067575371
absolute error = 0.00109
relative error = 0.0122 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.08
Order of pole (three term test) = 72.47 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6823 2.547
h = 0.0001 0.003
y[1] (numeric) = 0.93585579265 -8.92545126326
y[1] (closed_form) = 0.934910239536 -8.92583631872
absolute error = 0.001021
relative error = 0.01138 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.46
Order of pole (three term test) = 72.88 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6824 2.55
h = 0.001 0.001
y[1] (numeric) = 0.937726167475 -8.95271901369
y[1] (closed_form) = 0.936778699046 -8.95307712538
absolute error = 0.001013
relative error = 0.01125 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 19.32
Order of pole (three term test) = 73.12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6834 2.551
h = 0.0001 0.004
y[1] (numeric) = 0.929576144576 -8.9627218032
y[1] (closed_form) = 0.928632251882 -8.96306640083
absolute error = 0.001005
relative error = 0.01115 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 116.2
Order of pole (three term test) = 73.21 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1560.9MB, alloc=52.3MB, time=18.39
x[1] = 0.6835 2.555
h = 0.003 0.006
y[1] (numeric) = 0.932321888101 -8.99912415319
y[1] (closed_form) = 0.931398412691 -8.99952149681
absolute error = 0.001005
relative error = 0.01111 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 69.44
Order of pole (three term test) = 73.54 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6865 2.561
h = 0.0001 0.005
y[1] (numeric) = 0.910471018693 -9.05665043108
y[1] (closed_form) = 0.909443408167 -9.05707349842
absolute error = 0.001111
relative error = 0.01221 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.25
Order of pole (three term test) = 74.06 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6866 2.566
h = 0.0001 0.003
y[1] (numeric) = 0.913990341845 -9.1027108963
y[1] (closed_form) = 0.913026973435 -9.10310595914
absolute error = 0.001041
relative error = 0.01138 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.41
Order of pole (three term test) = 74.48 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6867 2.569
h = 0.001 0.001
y[1] (numeric) = 0.915779345497 -9.13050357831
y[1] (closed_form) = 0.914814145401 -9.13087116637
absolute error = 0.001033
relative error = 0.01126 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 20.07
Order of pole (three term test) = 74.74 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6877 2.57
h = 0.001 0.003
y[1] (numeric) = 0.907431953796 -9.14066107814
y[1] (closed_form) = 0.90647045933 -9.14101490614
absolute error = 0.001025
relative error = 0.01115 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 95.43
Order of pole (three term test) = 74.83 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6887 2.573
h = 0.0001 0.004
y[1] (numeric) = 0.900853570299 -9.16931415166
y[1] (closed_form) = 0.899885626353 -9.169696343
absolute error = 0.001041
relative error = 0.01129 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 54.33
Order of pole (three term test) = 75.09 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6888 2.577
h = 0.003 0.006
y[1] (numeric) = 0.903469332905 -9.20656806742
y[1] (closed_form) = 0.902519311972 -9.20696748331
absolute error = 0.001031
relative error = 0.01114 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 72.56
Order of pole (three term test) = 75.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6918 2.583
h = 0.0001 0.005
y[1] (numeric) = 0.880833025798 -9.26524316149
y[1] (closed_form) = 0.879776386801 -9.265668303
absolute error = 0.001139
relative error = 0.01224 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 32.65
Order of pole (three term test) = 75.98 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6919 2.588
h = 0.0001 0.003
y[1] (numeric) = 0.884185302283 -9.31233503129
y[1] (closed_form) = 0.883194504078 -9.31273189425
absolute error = 0.001067
relative error = 0.01141 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 26.55
Order of pole (three term test) = 76.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.692 2.591
h = 0.001 0.001
y[1] (numeric) = 0.885866150043 -9.34074835191
y[1] (closed_form) = 0.884873630942 -9.34111711254
absolute error = 0.001059
relative error = 0.01128 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 20.97
Order of pole (three term test) = 76.68 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.693 2.592
h = 0.001 0.003
y[1] (numeric) = 0.877281285909 -9.35108491509
y[1] (closed_form) = 0.876292631801 -9.35143962695
absolute error = 0.00105
relative error = 0.01118 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 99.72
Order of pole (three term test) = 76.78 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.694 2.595
h = 0.0001 0.004
y[1] (numeric) = 0.870406148854 -9.38033315108
y[1] (closed_form) = 0.869410743514 -9.38071682798
absolute error = 0.001067
relative error = 0.01132 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 56.77
Order of pole (three term test) = 77.05 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6941 2.599
h = 0.003 0.006
y[1] (numeric) = 0.872881637236 -9.41842023205
y[1] (closed_form) = 0.871904462409 -9.4188216196
absolute error = 0.001056
relative error = 0.01117 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 75.82
Order of pole (three term test) = 77.41 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6971 2.605
h = 0.0001 0.005
y[1] (numeric) = 0.84943588795 -9.47826561444
y[1] (closed_form) = 0.848349557503 -9.47869271636
absolute error = 0.001167
relative error = 0.01227 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 34.12
Order of pole (three term test) = 77.98 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6972 2.61
h = 0.0001 0.003
y[1] (numeric) = 0.85261166349 -9.52641114088
y[1] (closed_form) = 0.851592809124 -9.52680969266
absolute error = 0.001094
relative error = 0.01144 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.75
Order of pole (three term test) = 78.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6973 2.613
h = 0.001 0.001
y[1] (numeric) = 0.854178495205 -9.55545844639
y[1] (closed_form) = 0.8531580365 -9.55582825509
absolute error = 0.001085
relative error = 0.01131 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 21.91
Order of pole (three term test) = 78.72 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6983 2.614
h = 0.001 0.003
y[1] (numeric) = 0.845349833933 -9.56597678345
y[1] (closed_form) = 0.844333404623 -9.56633224916
absolute error = 0.001077
relative error = 0.01121 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 104.2
Order of pole (three term test) = 78.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6993 2.617
h = 0.0001 0.004
y[1] (numeric) = 0.838167987579 -9.59583191345
y[1] (closed_form) = 0.837144495455 -9.59621695753
absolute error = 0.001094
relative error = 0.01135 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 59.32
Order of pole (three term test) = 79.1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6994 2.621
h = 0.003 0.006
y[1] (numeric) = 0.840495447788 -9.63477010173
y[1] (closed_form) = 0.839490497858 -9.63517335489
absolute error = 0.001083
relative error = 0.0112 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 79.23
Order of pole (three term test) = 79.48 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1604.7MB, alloc=52.3MB, time=18.90
x[1] = 0.7024 2.627
h = 0.0001 0.005
y[1] (numeric) = 0.816215609867 -9.69580758934
y[1] (closed_form) = 0.815098910997 -9.69623653189
absolute error = 0.001196
relative error = 0.01229 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 35.66
Order of pole (three term test) = 80.07 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7025 2.632
h = 0.0001 0.003
y[1] (numeric) = 0.819205103981 -9.74502946371
y[1] (closed_form) = 0.818157553902 -9.74542958726
absolute error = 0.001121
relative error = 0.01147 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29
Order of pole (three term test) = 80.55 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7026 2.635
h = 0.001 0.001
y[1] (numeric) = 0.820651859658 -9.77472436285
y[1] (closed_form) = 0.819602827772 -9.77509508909
absolute error = 0.001113
relative error = 0.01134 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 22.9
Order of pole (three term test) = 80.84 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7036 2.636
h = 0.001 0.003
y[1] (numeric) = 0.811572922998 -9.78542721034
y[1] (closed_form) = 0.81052809009 -9.78578329377
absolute error = 0.001104
relative error = 0.01124 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 108.9
Order of pole (three term test) = 80.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7046 2.639
h = 0.0001 0.004
y[1] (numeric) = 0.804074130234 -9.81590117106
y[1] (closed_form) = 0.803021912809 -9.81628745801
absolute error = 0.001121
relative error = 0.01138 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 61.99
Order of pole (three term test) = 81.24 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7047 2.643
h = 0.003 0.006
y[1] (numeric) = 0.806245542336 -9.85570876226
y[1] (closed_form) = 0.805212182994 -9.85611376934
absolute error = 0.00111
relative error = 0.01122 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 82.8
Order of pole (three term test) = 81.63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7077 2.649
h = 0.0001 0.005
y[1] (numeric) = 0.781106311025 -9.91796052098
y[1] (closed_form) = 0.779958552483 -9.91839117813
absolute error = 0.001226
relative error = 0.01232 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.26
Order of pole (three term test) = 82.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7078 2.654
h = 0.0001 0.003
y[1] (numeric) = 0.783899407277 -9.96828188186
y[1] (closed_form) = 0.782822508485 -9.96868345413
absolute error = 0.001149
relative error = 0.01149 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.3
Order of pole (three term test) = 82.75 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7079 2.657
h = 0.001 0.001
y[1] (numeric) = 0.785219821149 -9.99863825063
y[1] (closed_form) = 0.78414156926 -9.99900975761
absolute error = 0.00114
relative error = 0.01137 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 23.93
Order of pole (three term test) = 83.05 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7089 2.658
h = 0.0001 0.004
y[1] (numeric) = 0.775883973713 -10.0095283709
y[1] (closed_form) = 0.774810095716 -10.0098849295
absolute error = 0.001132
relative error = 0.01127 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 144
Order of pole (three term test) = 83.16 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.709 2.662
h = 0.003 0.006
y[1] (numeric) = 0.777923019376 -10.0500610619
y[1] (closed_form) = 0.776870355004 -10.0504769596
absolute error = 0.001132
relative error = 0.01123 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 86.01
Order of pole (three term test) = 83.57 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.712 2.668
h = 0.0001 0.005
y[1] (numeric) = 0.752038102847 -10.113386704
y[1] (closed_form) = 0.750868710795 -10.1138282384
absolute error = 0.00125
relative error = 0.01233 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.71
Order of pole (three term test) = 84.21 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7121 2.673
h = 0.0001 0.003
y[1] (numeric) = 0.754667262138 -10.1646758524
y[1] (closed_form) = 0.753570230729 -10.1650880546
absolute error = 0.001172
relative error = 0.0115 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 31.48
Order of pole (three term test) = 84.73 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7122 2.676
h = 0.001 0.001
y[1] (numeric) = 0.755881855546 -10.1956145218
y[1] (closed_form) = 0.754783578758 -10.1959960709
absolute error = 0.001163
relative error = 0.01137 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 24.86
Order of pole (three term test) = 85.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7132 2.677
h = 0.001 0.003
y[1] (numeric) = 0.746321707799 -10.2066712425
y[1] (closed_form) = 0.745227956111 -10.2070375735
absolute error = 0.001153
relative error = 0.01127 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 118.2
Order of pole (three term test) = 85.15 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7142 2.68
h = 0.0001 0.004
y[1] (numeric) = 0.738212627346 -10.2383332652
y[1] (closed_form) = 0.73711087238 -10.2387309994
absolute error = 0.001171
relative error = 0.01141 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 67.29
Order of pole (three term test) = 85.48 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7143 2.684
h = 0.003 0.006
y[1] (numeric) = 0.740082268595 -10.279810642
y[1] (closed_form) = 0.738999977246 -10.280228078
absolute error = 0.00116
relative error = 0.01125 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 89.87
Order of pole (three term test) = 85.91 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7173 2.69
h = 0.0001 0.005
y[1] (numeric) = 0.713289336881 -10.3443930647
y[1] (closed_form) = 0.712087558243 -10.3448360705
absolute error = 0.001281
relative error = 0.01235 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 40.45
Order of pole (three term test) = 86.57 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7174 2.695
h = 0.0001 0.003
y[1] (numeric) = 0.715702633949 -10.3968261041
y[1] (closed_form) = 0.714575000378 -10.3972395177
absolute error = 0.001201
relative error = 0.01152 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 32.89
Order of pole (three term test) = 87.11 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1648.6MB, alloc=52.3MB, time=19.42
x[1] = 0.7175 2.698
h = 0.001 0.001
y[1] (numeric) = 0.716778830787 -10.4284528719
y[1] (closed_form) = 0.715650092454 -10.428834938
absolute error = 0.001192
relative error = 0.0114 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 25.97
Order of pole (three term test) = 87.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7185 2.699
h = 0.001 0.003
y[1] (numeric) = 0.706949028118 -10.4397021564
y[1] (closed_form) = 0.705825000048 -10.440068688
absolute error = 0.001182
relative error = 0.0113 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 123.5
Order of pole (three term test) = 87.56 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7195 2.702
h = 0.0001 0.004
y[1] (numeric) = 0.698492244677 -10.4720184523
y[1] (closed_form) = 0.697359861189 -10.4724170473
absolute error = 0.0012
relative error = 0.01144 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 70.32
Order of pole (three term test) = 87.9 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7196 2.706
h = 0.003 0.006
y[1] (numeric) = 0.700181586714 -10.5144196889
y[1] (closed_form) = 0.699068995064 -10.5148385347
absolute error = 0.001189
relative error = 0.01128 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 93.92
Order of pole (three term test) = 88.34 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7226 2.712
h = 0.0001 0.005
y[1] (numeric) = 0.672453362543 -10.5802820883
y[1] (closed_form) = 0.671218463553 -10.5807264205
absolute error = 0.001312
relative error = 0.01238 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 42.27
Order of pole (three term test) = 89.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7227 2.717
h = 0.0001 0.003
y[1] (numeric) = 0.674639669351 -10.633883487
y[1] (closed_form) = 0.67348074056 -10.6342979708
absolute error = 0.001231
relative error = 0.01155 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 34.37
Order of pole (three term test) = 89.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7228 2.72
h = 0.001 0.001
y[1] (numeric) = 0.67557058436 -10.6662130235
y[1] (closed_form) = 0.674410698229 -10.6665954508
absolute error = 0.001221
relative error = 0.01143 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 27.14
Order of pole (three term test) = 89.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7238 2.721
h = 0.001 0.003
y[1] (numeric) = 0.665464021604 -10.6776577082
y[1] (closed_form) = 0.66430903667 -10.6780242786
absolute error = 0.001212
relative error = 0.01133 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 129.1
Order of pole (three term test) = 90.07 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7248 2.724
h = 0.0001 0.004
y[1] (numeric) = 0.656648142803 -10.7106410387
y[1] (closed_form) = 0.655484439024 -10.7110403455
absolute error = 0.00123
relative error = 0.01146 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 73.48
Order of pole (three term test) = 90.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7249 2.728
h = 0.003 0.006
y[1] (numeric) = 0.658148067118 -10.7539858608
y[1] (closed_form) = 0.657004487699 -10.7544059811
absolute error = 0.001218
relative error = 0.01131 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 98.14
Order of pole (three term test) = 90.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7279 2.734
h = 0.0001 0.005
y[1] (numeric) = 0.629456548281 -10.8211517983
y[1] (closed_form) = 0.628187779765 -10.8215973049
absolute error = 0.001345
relative error = 0.01241 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 44.17
Order of pole (three term test) = 91.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.728 2.739
h = 0.0001 0.003
y[1] (numeric) = 0.63140436082 -10.8759465043
y[1] (closed_form) = 0.630213429232 -10.8763619103
absolute error = 0.001261
relative error = 0.01158 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 35.92
Order of pole (three term test) = 92.2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7281 2.742
h = 0.001 0.001
y[1] (numeric) = 0.632182878605 -10.9089937663
y[1] (closed_form) = 0.630991144139 -10.9093763921
absolute error = 0.001252
relative error = 0.01145 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 28.36
Order of pole (three term test) = 92.56 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7291 2.743
h = 0.001 0.003
y[1] (numeric) = 0.621792278846 -10.9206367121
y[1] (closed_form) = 0.620605642445 -10.9210031525
absolute error = 0.001242
relative error = 0.01135 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 134.9
Order of pole (three term test) = 92.69 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7301 2.746
h = 0.0001 0.004
y[1] (numeric) = 0.612605593028 -10.954300059
y[1] (closed_form) = 0.611409862744 -10.9546999217
absolute error = 0.001261
relative error = 0.01149 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 76.78
Order of pole (three term test) = 93.06 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7302 2.75
h = 0.003 0.006
y[1] (numeric) = 0.613906674691 -10.9986085784
y[1] (closed_form) = 0.612731405609 -10.9990298313
absolute error = 0.001248
relative error = 0.01133 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 102.6
Order of pole (three term test) = 93.54 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7332 2.756
h = 0.0001 0.005
y[1] (numeric) = 0.584223115784 -11.067101985
y[1] (closed_form) = 0.58291971285 -11.0675485066
absolute error = 0.001378
relative error = 0.01243 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 46.15
Order of pole (three term test) = 94.3 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7333 2.761
h = 0.0001 0.003
y[1] (numeric) = 0.585920543008 -11.1231154347
y[1] (closed_form) = 0.584696886241 -11.123531608
absolute error = 0.001292
relative error = 0.0116 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 37.53
Order of pole (three term test) = 94.92 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7334 2.764
h = 0.001 0.001
y[1] (numeric) = 0.586539311307 -11.1568956708
y[1] (closed_form) = 0.585315013402 -11.157278325
absolute error = 0.001283
relative error = 0.01148 %
Correct digits = 4
memory used=1692.4MB, alloc=52.3MB, time=19.93
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.64
Order of pole (three term test) = 95.3 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7344 2.765
h = 0.0001 0.004
y[1] (numeric) = 0.575857221893 -11.1687397628
y[1] (closed_form) = 0.574638225019 -11.1691058968
absolute error = 0.001273
relative error = 0.01138 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 178.3
Order of pole (three term test) = 95.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7345 2.769
h = 0.003 0.006
y[1] (numeric) = 0.576990018412 -11.2138519378
y[1] (closed_form) = 0.575792936344 -11.214284761
absolute error = 0.001273
relative error = 0.01134 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 106.5
Order of pole (three term test) = 95.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7375 2.775
h = 0.0001 0.005
y[1] (numeric) = 0.546445152402 -11.2835197317
y[1] (closed_form) = 0.545117348583 -11.2839777436
absolute error = 0.001405
relative error = 0.01243 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 47.94
Order of pole (three term test) = 96.71 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7376 2.78
h = 0.0001 0.003
y[1] (numeric) = 0.54793216963 -11.3406061664
y[1] (closed_form) = 0.546685787259 -11.3410335971
absolute error = 0.001318
relative error = 0.0116 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 38.99
Order of pole (three term test) = 97.36 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7377 2.783
h = 0.001 0.001
y[1] (numeric) = 0.54841634134 -11.3750317861
y[1] (closed_form) = 0.547169454017 -11.3754250472
absolute error = 0.001307
relative error = 0.01148 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 30.79
Order of pole (three term test) = 97.75 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7387 2.784
h = 0.001 0.003
y[1] (numeric) = 0.537479685545 -11.3870549426
y[1] (closed_form) = 0.536238274884 -11.3874313879
absolute error = 0.001297
relative error = 0.01138 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 146.4
Order of pole (three term test) = 97.88 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7397 2.787
h = 0.0001 0.004
y[1] (numeric) = 0.527579190739 -11.422023723
y[1] (closed_form) = 0.526327964843 -11.4224349069
absolute error = 0.001317
relative error = 0.01152 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 83.35
Order of pole (three term test) = 98.28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7398 2.791
h = 0.003 0.006
y[1] (numeric) = 0.528496164333 -11.4681829859
y[1] (closed_form) = 0.527266045276 -11.4686166682
absolute error = 0.001304
relative error = 0.01136 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 111.3
Order of pole (three term test) = 98.81 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7428 2.797
h = 0.0001 0.005
y[1] (numeric) = 0.496904023053 -11.5392241417
y[1] (closed_form) = 0.495540116518 -11.539682861
absolute error = 0.001439
relative error = 0.01246 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 50.1
Order of pole (three term test) = 99.62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7429 2.802
h = 0.0001 0.003
y[1] (numeric) = 0.498117776441 -11.5975781347
y[1] (closed_form) = 0.496837282235 -11.5980060337
absolute error = 0.00135
relative error = 0.01163 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 40.74
Order of pole (three term test) = 100.3 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.743 2.805
h = 0.001 0.001
y[1] (numeric) = 0.498428053681 -11.6327659914
y[1] (closed_form) = 0.497147230279 -11.6331589529
absolute error = 0.00134
relative error = 0.01151 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 32.17
Order of pole (three term test) = 100.7 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.744 2.806
h = 0.001 0.003
y[1] (numeric) = 0.487185593871 -11.6449958191
y[1] (closed_form) = 0.485910461826 -11.6453716182
absolute error = 0.001329
relative error = 0.01141 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 153
Order of pole (three term test) = 100.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.745 2.809
h = 0.0001 0.004
y[1] (numeric) = 0.476879112577 -11.6806831525
y[1] (closed_form) = 0.475593755354 -11.6810944143
absolute error = 0.00135
relative error = 0.01154 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 87.1
Order of pole (three term test) = 101.3 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7451 2.813
h = 0.003 0.006
y[1] (numeric) = 0.47756876308 -11.7278659674
y[1] (closed_form) = 0.476304862183 -11.728300347
absolute error = 0.001336
relative error = 0.01139 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 116.3
Order of pole (three term test) = 101.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7481 2.819
h = 0.0001 0.005
y[1] (numeric) = 0.444898374897 -11.8003055065
y[1] (closed_form) = 0.443497553957 -11.8007647515
absolute error = 0.001474
relative error = 0.01248 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 52.35
Order of pole (three term test) = 102.7 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7482 2.824
h = 0.0001 0.003
y[1] (numeric) = 0.445825808637 -11.8599539457
y[1] (closed_form) = 0.444510436126 -11.8603821368
absolute error = 0.001383
relative error = 0.01166 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 42.57
Order of pole (three term test) = 103.4 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7483 2.827
h = 0.001 0.001
y[1] (numeric) = 0.445954126437 -11.8959201548
y[1] (closed_form) = 0.444638608485 -11.8963126244
absolute error = 0.001373
relative error = 0.01153 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 33.62
Order of pole (three term test) = 103.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7493 2.828
h = 0.001 0.003
y[1] (numeric) = 0.434397884706 -11.9083596076
y[1] (closed_form) = 0.433088279404 -11.9087345617
absolute error = 0.001362
relative error = 0.01143 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 159.9
Order of pole (three term test) = 103.9 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1736.1MB, alloc=52.3MB, time=20.44
x[1] = 0.7503 2.831
h = 0.0001 0.004
y[1] (numeric) = 0.423672395047 -11.944779361
y[1] (closed_form) = 0.422352141689 -11.9451905158
absolute error = 0.001383
relative error = 0.01157 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 91.01
Order of pole (three term test) = 104.4 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7504 2.835
h = 0.003 0.006
y[1] (numeric) = 0.424124033017 -11.9930074004
y[1] (closed_form) = 0.422825589864 -11.9934423079
absolute error = 0.001369
relative error = 0.01141 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 121.6
Order of pole (three term test) = 105 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7534 2.841
h = 0.0001 0.005
y[1] (numeric) = 0.390343608571 -12.0668707304
y[1] (closed_form) = 0.388905044588 -12.0673303111
absolute error = 0.00151
relative error = 0.01251 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 54.71
Order of pole (three term test) = 105.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7535 2.846
h = 0.0001 0.003
y[1] (numeric) = 0.39097123443 -12.1278410273
y[1] (closed_form) = 0.389620201173 -12.1282693261
absolute error = 0.001417
relative error = 0.01168 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 44.49
Order of pole (three term test) = 106.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7536 2.849
h = 0.001 0.001
y[1] (numeric) = 0.390909263335 -12.1646020165
y[1] (closed_form) = 0.389558276657 -12.1649937935
absolute error = 0.001407
relative error = 0.01156 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 35.13
Order of pole (three term test) = 107 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7546 2.85
h = 0.001 0.003
y[1] (numeric) = 0.379031069828 -12.1772540706
y[1] (closed_form) = 0.377686223874 -12.1776279725
absolute error = 0.001396
relative error = 0.01146 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 167.1
Order of pole (three term test) = 107.2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7556 2.853
h = 0.0001 0.004
y[1] (numeric) = 0.367873188077 -12.2144203473
y[1] (closed_form) = 0.366517257894 -12.2148312019
absolute error = 0.001417
relative error = 0.01159 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 95.11
Order of pole (three term test) = 107.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7557 2.857
h = 0.003 0.006
y[1] (numeric) = 0.368075771793 -12.2637157049
y[1] (closed_form) = 0.366742010097 -12.2641509628
absolute error = 0.001403
relative error = 0.01143 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 127
Order of pole (three term test) = 108.2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7587 2.863
h = 0.0001 0.005
y[1] (numeric) = 0.333152683582 -12.3390286235
y[1] (closed_form) = 0.331675530629 -12.3394883412
absolute error = 0.001547
relative error = 0.01253 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 57.17
Order of pole (three term test) = 109.2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7588 2.868
h = 0.0001 0.003
y[1] (numeric) = 0.333466568354 -12.4013487222
y[1] (closed_form) = 0.332079075629 -12.4017769362
absolute error = 0.001452
relative error = 0.0117 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 46.49
Order of pole (three term test) = 109.9 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7589 2.871
h = 0.001 0.001
y[1] (numeric) = 0.333205706797 -12.4389212371
y[1] (closed_form) = 0.331818461209 -12.4393121125
absolute error = 0.001441
relative error = 0.01158 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 36.71
Order of pole (three term test) = 110.4 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7599 2.872
h = 0.001 0.003
y[1] (numeric) = 0.320997195292 -12.4517888908
y[1] (closed_form) = 0.31961632547 -12.4521615246
absolute error = 0.00143
relative error = 0.01148 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 174.6
Order of pole (three term test) = 110.5 0
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff ( y , x , 1 ) = neg ( sin ( x ) ) - cos ( x ) ;
Iterations = 754
Total Elapsed Time = 20 Seconds
Expected Time Remaining = 0 Seconds
Optimized Time Remaining = 0 Seconds
Expected Total Time = 20 Seconds
> quit
memory used=1765.0MB, alloc=52.3MB, time=20.76