|\^/| Maple 2016 (X86 64 LINUX)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2016
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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#BEGIN OUTFILE1
# before write maple top matter
# before write_ats library and user def block
#BEGIN ATS LIBRARY BLOCK
# Begin Function number 2
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s\n",str);
> fi;# end if 1;
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
# End Function number 2
# Begin Function number 3
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s",str);
> fi;# end if 1;
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
# End Function number 3
# Begin Function number 4
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> print(label,str);
> fi;# end if 1;
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
# End Function number 4
# Begin Function number 5
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 5
# Begin Function number 6
> omniout_complex := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> if vallen = 4 then
> printf("%-30s = %-20.4g %-20g %s \n",prelabel,Re(value), Im(value), postlabel);
> else
> printf("%-30s = %-20.12g %-20.12g %s \n",prelabel,Re(value),Im(value), postlabel);
> fi;# end if 0;
> fi;# end if -1;
> end;
omniout_complex := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then printf("%-30s = %-20.4g %-20g %s \n", prelabel,
Re(value), Im(value), postlabel)
else printf("%-30s = %-20.12g %-20.12g %s \n", prelabel, Re(value),
Im(value), postlabel)
end if
end if
end proc
# End Function number 6
# Begin Function number 7
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number -1
> if vallen = 5 then # if number 0
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;# end if 0;
> fi;# end if -1;
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 7
# Begin Function number 8
> logitem_time := proc(fd,secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> fprintf(fd,"
");
> if (secs_in >= 0) then # if number -1
> years_int := int_trunc(secs_in / glob_sec_in_year);
> sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
> days_int := int_trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := sec_temp mod int_trunc(glob_sec_in_day) ;
> hours_int := int_trunc(sec_temp / glob_sec_in_hour);
> sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
> minutes_int := int_trunc(sec_temp / glob_sec_in_minute);
> sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
> if (years_int > 0) then # if number 0
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 1
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 2
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 3
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 3
> else
> fprintf(fd," 0.0 Seconds");
> fi;# end if 2
> fprintf(fd," | \n");
> end;
logitem_time := proc(fd, secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
fprintf(fd, "");
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, " 0.0 Seconds")
end if;
fprintf(fd, " | \n")
end proc
# End Function number 8
# Begin Function number 9
> omniout_timestr := proc(secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> if (secs_in >= 0) then # if number 2
> years_int := int_trunc(secs_in / glob_sec_in_year);
> sec_temp := (int_trunc(secs_in) mod int_trunc(glob_sec_in_year));
> days_int := int_trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_day)) ;
> hours_int := int_trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_hour));
> minutes_int := int_trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod int_trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 3
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 4
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 5
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 6
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 6
> else
> printf(" 0.0 Seconds\n");
> fi;# end if 5
> end;
omniout_timestr := proc(secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" 0.0 Seconds\n")
end if
end proc
# End Function number 9
# Begin Function number 10
> zero_ats_ar := proc(arr_a)
> global ATS_MAX_TERMS;
> local iii;
> iii := 1;
> while (iii <= ATS_MAX_TERMS) do # do number 1
> arr_a [iii] := glob__0;
> iii := iii + 1;
> od;# end do number 1
> end;
zero_ats_ar := proc(arr_a)
local iii;
global ATS_MAX_TERMS;
iii := 1;
while iii <= ATS_MAX_TERMS do arr_a[iii] := glob__0; iii := iii + 1
end do
end proc
# End Function number 10
# Begin Function number 11
> ats := proc(mmm_ats,arr_a,arr_b,jjj_ats)
> global ATS_MAX_TERMS;
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := glob__0;
> if (jjj_ats <= mmm_ats) then # if number 5
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> if ((lll_ats <= ATS_MAX_TERMS and (iii_ats <= ATS_MAX_TERMS) )) then # if number 6
> ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]);
> fi;# end if 6;
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 5;
> ret_ats;
> end;
ats := proc(mmm_ats, arr_a, arr_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
global ATS_MAX_TERMS;
ret_ats := glob__0;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
if lll_ats <= ATS_MAX_TERMS and iii_ats <= ATS_MAX_TERMS then
ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats])
end if;
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
# End Function number 11
# Begin Function number 12
> att := proc(mmm_att,arr_aa,arr_bb,jjj_att)
> global ATS_MAX_TERMS;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := glob__0;
> if (jjj_att < mmm_att) then # if number 5
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while ((iii_att < mmm_att) and (iii_att <= ATS_MAX_TERMS) ) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if ((lll_att <= ATS_MAX_TERMS and (iii_att <= ATS_MAX_TERMS) )) then # if number 6
> ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att);
> fi;# end if 6;
> iii_att := iii_att + 1;
> od;# end do number 1;
> ret_att := ret_att / c(mmm_att) ;
> fi;# end if 5;
> ret_att;
> end;
att := proc(mmm_att, arr_aa, arr_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global ATS_MAX_TERMS;
ret_att := glob__0;
if jjj_att < mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att < mmm_att and iii_att <= ATS_MAX_TERMS do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= ATS_MAX_TERMS and iii_att <= ATS_MAX_TERMS then
ret_att :=
ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])*c(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/c(mmm_att)
end if;
ret_att
end proc
# End Function number 12
# Begin Function number 13
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
# End Function number 13
# Begin Function number 14
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
# End Function number 14
# Begin Function number 15
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
# End Function number 15
# Begin Function number 16
> logitem_good_digits := proc(file,rel_error)
> global glob_small_float,glob_prec;
> local good_digits;
> fprintf(file,"");
> fprintf(file,"%d",glob_min_good_digits);
> fprintf(file," | ");
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float, glob_prec;
fprintf(file, "");
fprintf(file, "%d", glob_min_good_digits);
fprintf(file, " | ")
end proc
# End Function number 16
# Begin Function number 17
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
# End Function number 17
# Begin Function number 18
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
# End Function number 18
# Begin Function number 19
> logitem_complex := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g + %g I",Re(x),Im(x));
> fprintf(file," | ");
> end;
logitem_complex := proc(file, x)
fprintf(file, "");
fprintf(file, "%g + %g I", Re(x), Im(x));
fprintf(file, " | ")
end proc
# End Function number 19
# Begin Function number 20
> logitem_h_reason := proc(file)
> global glob_h_reason;
> fprintf(file,"");
> if (glob_h_reason = 1) then # if number 5
> fprintf(file,"Max H");
> elif
> (glob_h_reason = 2) then # if number 6
> fprintf(file,"Display Interval");
> elif
> (glob_h_reason = 3) then # if number 7
> fprintf(file,"Optimal");
> elif
> (glob_h_reason = 4) then # if number 8
> fprintf(file,"Pole Accuracy");
> elif
> (glob_h_reason = 5) then # if number 9
> fprintf(file,"Min H (Pole)");
> elif
> (glob_h_reason = 6) then # if number 10
> fprintf(file,"Pole");
> elif
> (glob_h_reason = 7) then # if number 11
> fprintf(file,"Opt Iter");
> else
> fprintf(file,"Impossible");
> fi;# end if 11
> fprintf(file," | ");
> end;
logitem_h_reason := proc(file)
global glob_h_reason;
fprintf(file, "");
if glob_h_reason = 1 then fprintf(file, "Max H")
elif glob_h_reason = 2 then fprintf(file, "Display Interval")
elif glob_h_reason = 3 then fprintf(file, "Optimal")
elif glob_h_reason = 4 then fprintf(file, "Pole Accuracy")
elif glob_h_reason = 5 then fprintf(file, "Min H (Pole)")
elif glob_h_reason = 6 then fprintf(file, "Pole")
elif glob_h_reason = 7 then fprintf(file, "Opt Iter")
else fprintf(file, "Impossible")
end if;
fprintf(file, " | ")
end proc
# End Function number 20
# Begin Function number 21
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
# End Function number 21
# Begin Function number 22
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file) fprintf(file, "\n") end proc
# End Function number 22
# Begin Function number 23
> chk_data := proc()
> global glob_max_iter,ALWAYS, ATS_MAX_TERMS;
> local errflag;
> errflag := false;
> if (glob_max_iter < 2) then # if number 11
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 11;
> if (errflag) then # if number 11
> quit;
> fi;# end if 11
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, ATS_MAX_TERMS;
errflag := false;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
# End Function number 23
# Begin Function number 24
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := c(clock_sec2);
> sub1 := c(t_end2-t_start2);
> sub2 := c(t2-t_start2);
> if (sub1 = glob__0) then # if number 11
> sec_left := glob__0;
> else
> if (sub2 > glob__0) then # if number 12
> rrr := (sub1/sub2);
> sec_left := rrr * c(ms2) - c(ms2);
> else
> sec_left := glob__0;
> fi;# end if 12
> fi;# end if 11;
> sec_left;
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := c(clock_sec2);
sub1 := c(t_end2 - t_start2);
sub2 := c(t2 - t_start2);
if sub1 = glob__0 then sec_left := glob__0
else
if glob__0 < sub2 then
rrr := sub1/sub2; sec_left := rrr*c(ms2) - c(ms2)
else sec_left := glob__0
end if
end if;
sec_left
end proc
# End Function number 24
# Begin Function number 25
> comp_percent := proc(t_end2,t_start2, t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub2 > glob_small_float) then # if number 11
> rrr := (glob__100*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 11;
> rrr;
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < sub2 then rrr := glob__100*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
# End Function number 25
# Begin Function number 26
> comp_rad_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 11
> ret := float_abs(term1 * glob_h / term2);
> else
> ret := glob_larger_float;
> fi;# end if 11;
> ret;
> #BOTTOM TWO TERM RADIUS ANALYSIS
> end;
comp_rad_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := float_abs(term1*glob_h/term2)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 26
# Begin Function number 27
> comp_ord_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM ORDER ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 11
> ret := glob__1 + float_abs(term2) * c(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(c(last_no));
> else
> ret := glob_larger_float;
> fi;# end if 11;
> ret;
> #BOTTOM TWO TERM ORDER ANALYSIS
> end;
comp_ord_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := glob__1 + float_abs(term2)*
c(last_no)*ln(float_abs(term1*glob_h/term2))/ln(c(last_no))
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 27
# Begin Function number 28
> c := proc(in_val)
> #To Force Conversion when needed
> local ret;
> ret := evalc(in_val);
> ret;
> #End Conversion
> end;
c := proc(in_val) local ret; ret := evalc(in_val); ret end proc
# End Function number 28
# Begin Function number 29
> comp_rad_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret,temp;
> temp := float_abs(term2*term2*c(last_no)+glob__m2*term2*term2-term1*term3*c(last_no)+term1*term3);
> if (float_abs(temp) > glob__0) then # if number 11
> ret := float_abs((term2*glob_h*term1)/(temp));
> else
> ret := glob_larger_float;
> fi;# end if 11;
> ret;
> #BOTTOM THREE TERM RADIUS ANALYSIS
> end;
comp_rad_from_three_terms := proc(term1, term2, term3, last_no)
local ret, temp;
global glob_h, glob_larger_float;
temp := float_abs(term2*term2*c(last_no) + glob__m2*term2*term2
- term1*term3*c(last_no) + term1*term3);
if glob__0 < float_abs(temp) then
ret := float_abs(term2*glob_h*term1/temp)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 29
# Begin Function number 30
> comp_ord_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM ORDER ANALYSIS
> local ret;
> ret := float_abs((glob__4*term1*term3*c(last_no)-glob__3*term1*term3-glob__4*term2*term2*c(last_no)+glob__4*term2*term2+term2*term2*c(last_no*last_no)-term1*term3*c(last_no*last_no))/(term2*term2*c(last_no)-glob__2*term2*term2-term1*term3*c(last_no)+term1*term3));
> ret;
> #TOP THREE TERM ORDER ANALYSIS
> end;
comp_ord_from_three_terms := proc(term1, term2, term3, last_no)
local ret;
ret := float_abs((glob__4*term1*term3*c(last_no) - glob__3*term1*term3
- glob__4*term2*term2*c(last_no) + glob__4*term2*term2
+ term2*term2*c(last_no*last_no) - term1*term3*c(last_no*last_no))
/(term2*term2*c(last_no) - glob__2*term2*term2
- term1*term3*c(last_no) + term1*term3));
ret
end proc
# End Function number 30
# Begin Function number 31
> comp_rad_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> #TOP SIX TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float,glob_six_term_ord_save;
> local ret,rm0,rm1,rm2,rm3,rm4,nr1,nr2,dr1,dr2,ds2,rad_c,ord_no,ds1,rcs;
> if ((term5 <> glob__0) and (term4 <> glob__0) and (term3 <> glob__0) and (term2 <> glob__0) and (term1 <> glob__0)) then # if number 11
> rm0 := term6/term5;
> rm1 := term5/term4;
> rm2 := term4/term3;
> rm3 := term3/term2;
> rm4 := term2/term1;
> nr1 := c(last_no-1)*rm0 - glob__2*c(last_no-2)*rm1 + c(last_no-3)*rm2;
> nr2 := c(last_no-2)*rm1 - glob__2*c(last_no-3)*rm2 + c(last_no-4)*rm3;
> dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
> dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
> ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
> ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
> if ((float_abs(nr1 * dr2 - nr2 * dr1) = glob__0) or (float_abs(dr1) = glob__0)) then # if number 12
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> else
> if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0) then # if number 13
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) -c(last_no)/glob__2;
> if (float_abs(rcs) <> glob__0) then # if number 14
> if (rcs > glob__0) then # if number 15
> rad_c := float_abs( sqrt(rcs) * float_abs(glob_h));
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 15
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 14
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 13
> fi;# end if 12
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 11;
> glob_six_term_ord_save := ord_no;
> rad_c;
> #BOTTOM SIX TERM RADIUS ANALYSIS
> end;
comp_rad_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
local ret, rm0, rm1, rm2, rm3, rm4, nr1, nr2, dr1, dr2, ds2, rad_c, ord_no,
ds1, rcs;
global glob_h, glob_larger_float, glob_six_term_ord_save;
if term5 <> glob__0 and term4 <> glob__0 and term3 <> glob__0 and
term2 <> glob__0 and term1 <> glob__0 then
rm0 := term6/term5;
rm1 := term5/term4;
rm2 := term4/term3;
rm3 := term3/term2;
rm4 := term2/term1;
nr1 := c(last_no - 1)*rm0 - glob__2*c(last_no - 2)*rm1
+ c(last_no - 3)*rm2;
nr2 := c(last_no - 2)*rm1 - glob__2*c(last_no - 3)*rm2
+ c(last_no - 4)*rm3;
dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
if
float_abs(nr1*dr2 - nr2*dr1) = glob__0 or float_abs(dr1) = glob__0
then rad_c := glob_larger_float; ord_no := glob_larger_float
else
if glob__0 < float_abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no :=
(rcs*nr1 - ds1)/(glob__2*dr1) - c(last_no)/glob__2;
if float_abs(rcs) <> glob__0 then
if glob__0 < rcs then
rad_c := float_abs(sqrt(rcs)*float_abs(glob_h))
else
rad_c := glob_larger_float;
ord_no := glob_larger_float
end if
else
rad_c := glob_larger_float; ord_no := glob_larger_float
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if;
glob_six_term_ord_save := ord_no;
rad_c
end proc
# End Function number 31
# Begin Function number 32
> comp_ord_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> global glob_six_term_ord_save;
> #TOP SIX TERM ORDER ANALYSIS
> #TOP SAVED FROM SIX TERM RADIUS ANALYSIS
> glob_six_term_ord_save;
> #BOTTOM SIX TERM ORDER ANALYSIS
> end;
comp_ord_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
global glob_six_term_ord_save;
glob_six_term_ord_save
end proc
# End Function number 32
# Begin Function number 33
> factorial_2 := proc(nnn)
> ret := nnn!;
> ret;;
> end;
Warning, `ret` is implicitly declared local to procedure `factorial_2`
factorial_2 := proc(nnn) local ret; ret := nnn!; ret end proc
# End Function number 33
# Begin Function number 34
> factorial_1 := proc(nnn)
> global ATS_MAX_TERMS,array_fact_1;
> local ret;
> if (nnn <= ATS_MAX_TERMS) then # if number 11
> if (array_fact_1[nnn] = 0) then # if number 12
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 12;
> else
> ret := factorial_2(nnn);
> fi;# end if 11;
> ret;
> end;
factorial_1 := proc(nnn)
local ret;
global ATS_MAX_TERMS, array_fact_1;
if nnn <= ATS_MAX_TERMS then
if array_fact_1[nnn] = 0 then
ret := factorial_2(nnn); array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := factorial_2(nnn)
end if;
ret
end proc
# End Function number 34
# Begin Function number 35
> factorial_3 := proc(mmm,nnn)
> global ATS_MAX_TERMS,array_fact_2;
> local ret;
> if ((nnn <= ATS_MAX_TERMS) and (mmm <= ATS_MAX_TERMS)) then # if number 11
> if (array_fact_2[mmm,nnn] = 0) then # if number 12
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 12;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 11;
> ret;
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global ATS_MAX_TERMS, array_fact_2;
if nnn <= ATS_MAX_TERMS and mmm <= ATS_MAX_TERMS then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := factorial_2(mmm)/factorial_2(nnn)
end if;
ret
end proc
# End Function number 35
# Begin Function number 36
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
# End Function number 36
# Begin Function number 37
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
# End Function number 37
# Begin Function number 38
> float_abs := proc(x)
> abs(x);
> end;
float_abs := proc(x) abs(x) end proc
# End Function number 38
# Begin Function number 39
> expt := proc(x,y)
> x^y;
> end;
expt := proc(x, y) x^y end proc
# End Function number 39
# Begin Function number 40
> neg := proc(x)
> -x;
> end;
neg := proc(x) -x end proc
# End Function number 40
# Begin Function number 41
> int_trunc := proc(x)
> trunc(x);
> end;
int_trunc := proc(x) trunc(x) end proc
# End Function number 41
# Begin Function number 42
> estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer)
> local desired_abs_gbl_error,range,estimated_steps,step_error;
> global glob_desired_digits_correct,ALWAYS,ATS_MAX_TERMS;
> omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
> desired_abs_gbl_error := expt(glob__10,c( -glob_desired_digits_correct)) * c(float_abs(c(estimated_answer)));
> omniout_float(ALWAYS,"estimated_h",32,estimated_h,32,"");
> omniout_float(ALWAYS,"estimated_answer",32,estimated_answer,32,"");
> omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,"");
> range := (x_end - x_start);
> omniout_float(ALWAYS,"range",32,range,32,"");
> estimated_steps := range / estimated_h;
> omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,"");
> step_error := (c(float_abs(desired_abs_gbl_error) /sqrt(c( estimated_steps))/c(ATS_MAX_TERMS)));
> omniout_float(ALWAYS,"step_error",32,step_error,32,"");
> (step_error);;
> end;
estimated_needed_step_error := proc(
x_start, x_end, estimated_h, estimated_answer)
local desired_abs_gbl_error, range, estimated_steps, step_error;
global glob_desired_digits_correct, ALWAYS, ATS_MAX_TERMS;
omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, "");
desired_abs_gbl_error :=
expt(glob__10, c(-glob_desired_digits_correct))*
c(float_abs(c(estimated_answer)));
omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, "");
omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, "")
;
omniout_float(ALWAYS, "desired_abs_gbl_error", 32,
desired_abs_gbl_error, 32, "");
range := x_end - x_start;
omniout_float(ALWAYS, "range", 32, range, 32, "");
estimated_steps := range/estimated_h;
omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, "");
step_error := c(float_abs(desired_abs_gbl_error)/(
sqrt(c(estimated_steps))*c(ATS_MAX_TERMS)));
omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
step_error
end proc
# End Function number 42
#END ATS LIBRARY BLOCK
#BEGIN USER FUNCTION BLOCK
#BEGIN BLOCK 3
#BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return(c(2.0) - cos(c(x)) - sin(c(x)));
> end;
exact_soln_y := proc(x) return c(2.0) - 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_g,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local min_size;
> min_size := glob_estimated_size_answer;
> if (float_abs(array_y[1]) < min_size) then # if number 3
> min_size := float_abs(array_y[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> if (min_size < glob__1) then # if number 3
> min_size := glob__1;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> min_size;
> end;
est_size_answer := proc()
local min_size;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_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_g,
array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
min_size := glob_estimated_size_answer;
if float_abs(array_y[1]) < min_size then
min_size := float_abs(array_y[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if min_size < glob__1 then
min_size := glob__1;
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
min_size
end proc
# End Function number 4
# Begin Function number 5
> test_suggested_h := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#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_g,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> max_estimated_step_error := glob__small;
> no_terms := ATS_MAX_TERMS;
> hn_div_ho := glob__0_5;
> hn_div_ho_2 := glob__0_25;
> hn_div_ho_3 := glob__0_125;
> omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,"");
> omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,"");
> omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,"");
> est_tmp := float_abs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3);
> if (est_tmp >= max_estimated_step_error) then # if number 3
> max_estimated_step_error := est_tmp;
> fi;# end if 3;
> omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,"");
> max_estimated_step_error;
> end;
test_suggested_h := proc()
local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3,
no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_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_g,
array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
max_estimated_step_error := glob__small;
no_terms := ATS_MAX_TERMS;
hn_div_ho := glob__0_5;
hn_div_ho_2 := glob__0_25;
hn_div_ho_3 := glob__0_125;
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, "");
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, "");
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, "");
est_tmp := float_abs(array_y[no_terms - 3]
+ array_y[no_terms - 2]*hn_div_ho
+ array_y[no_terms - 1]*hn_div_ho_2
+ array_y[no_terms]*hn_div_ho_3);
if max_estimated_step_error <= est_tmp then
max_estimated_step_error := est_tmp
end if;
omniout_float(ALWAYS, "max_estimated_step_error", 32,
max_estimated_step_error, 32, "");
max_estimated_step_error
end proc
# End Function number 5
# Begin Function number 6
> track_estimated_error := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#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_g,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> no_terms := ATS_MAX_TERMS;
> hn_div_ho := glob__0_5;
> hn_div_ho_2 := glob__0_25;
> hn_div_ho_3 := glob__0_125;
> est_tmp := c(float_abs(array_y[no_terms-3])) + c(float_abs(array_y[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y[no_terms])) * c(hn_div_ho_3);
> if (glob_prec * c(float_abs(array_y[1])) > c(est_tmp)) then # if number 3
> est_tmp := c(glob_prec) * c(float_abs(array_y[1]));
> fi;# end if 3;
> if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 3
> array_max_est_error[1] := c(est_tmp);
> fi;# end if 3
> ;
> end;
track_estimated_error := proc()
local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_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_g,
array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
no_terms := ATS_MAX_TERMS;
hn_div_ho := glob__0_5;
hn_div_ho_2 := glob__0_25;
hn_div_ho_3 := glob__0_125;
est_tmp := c(float_abs(array_y[no_terms - 3]))
+ c(float_abs(array_y[no_terms - 2]))*c(hn_div_ho)
+ c(float_abs(array_y[no_terms - 1]))*c(hn_div_ho_2)
+ c(float_abs(array_y[no_terms]))*c(hn_div_ho_3);
if c(est_tmp) < glob_prec*c(float_abs(array_y[1])) then
est_tmp := c(glob_prec)*c(float_abs(array_y[1]))
end if;
if c(array_max_est_error[1]) <= c(est_tmp) then
array_max_est_error[1] := c(est_tmp)
end if
end proc
# End Function number 6
# Begin Function number 7
> reached_interval := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#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_g,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local ret;
> if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 3
> ret := true;
> else
> ret := false;
> fi;# end if 3;
> return(ret);
> end;
reached_interval := proc()
local ret;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_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_g,
array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
if glob_check_sign*glob_next_display - glob_h/glob__10 <=
glob_check_sign*array_x[1] then ret := true
else ret := false
end if;
return ret
end proc
# End Function number 7
# Begin Function number 8
> display_alot := proc(iter)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#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_g,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err;
> #TOP DISPLAY ALOT
> ind_var := array_x[1];
> omniout_complex(ALWAYS,"x[1] ",33,ind_var,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> omniout_complex(ALWAYS,"h ",33,glob_h,20," ");
> omniout_complex(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> closed_form_val_y := evalf(exact_soln_y(ind_var));
> omniout_complex(ALWAYS,"y[1] (closed_form) ",33,closed_form_val_y,20," ");
> abserr := float_abs(numeric_val - closed_form_val_y);
> if (float_abs(closed_form_val_y) > 0.0) then # if number 3
> relerr := abserr/float_abs(closed_form_val_y);
> if (float_abs(c(relerr)) > 0.0) then # if number 4
> glob_good_digits := round(-log10(relerr));
> else
> relerr := 0.0 ;
> glob_good_digits := Digits - 2;
> fi;# end if 4;
> else
> ;
> relerr := glob__m1 ;
> glob_good_digits := -16;
> fi;# end if 3;
> if (glob_good_digits < glob_min_good_digits) then # if number 3
> glob_min_good_digits := glob_good_digits;
> fi;# end if 3;
> omniout_float(ALWAYS,"absolute error ",4,abserr,4," ");
> omniout_float(ALWAYS,"relative error ",4,relerr * glob__100 ,4,"%");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> #BOTTOM DISPLAY ALOT
> end;
display_alot := proc(iter)
local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no,
est_rel_err;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_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_g,
array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
ind_var := array_x[1];
omniout_complex(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
omniout_complex(ALWAYS, "h ", 33, glob_h,
20, " ");
omniout_complex(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
closed_form_val_y := evalf(exact_soln_y(ind_var));
omniout_complex(ALWAYS, "y[1] (closed_form) ", 33,
closed_form_val_y, 20, " ");
abserr := float_abs(numeric_val - closed_form_val_y);
if 0. < float_abs(closed_form_val_y) then
relerr := abserr/float_abs(closed_form_val_y);
if 0. < float_abs(c(relerr)) then
glob_good_digits := round(-log10(relerr))
else relerr := 0.; glob_good_digits := Digits - 2
end if
else relerr := glob__m1; glob_good_digits := -16
end if;
if glob_good_digits < glob_min_good_digits then
glob_min_good_digits := glob_good_digits
end if;
omniout_float(ALWAYS, "absolute error ", 4, abserr, 4,
" ");
omniout_float(ALWAYS, "relative error ", 4,
relerr*glob__100, 4, "%");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ")
end proc
# End Function number 8
# Begin Function number 9
> prog_report := proc(x_start,x_end)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#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_g,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := (clock_sec1) - (glob_orig_start_sec);
> glob_clock_sec := (clock_sec1) - (glob_clock_start_sec);
> left_sec := (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1);
> expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h) ,( clock_sec1) - (glob_orig_start_sec));
> opt_clock_sec := ( clock_sec1) - (glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec));
> glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
> percent_done := comp_percent((x_end),(x_start),(array_x[1]) + (glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr((total_clock_sec));
> if (c(percent_done) < glob__100) then # if number 3
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr((expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr((glob_optimal_expect_sec));
> omniout_str_noeol(INFO,"Expected Total Time ");
> omniout_timestr((glob_total_exp_sec));
> fi;# end if 3;
> #BOTTOM PROGRESS REPORT
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_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_g,
array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec := clock_sec1 - glob_orig_start_sec;
glob_clock_sec := clock_sec1 - glob_clock_start_sec;
left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1;
expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h,
clock_sec1 - glob_orig_start_sec);
opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec;
glob_optimal_expect_sec :=
comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec)
;
glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h);
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(total_clock_sec);
if c(percent_done) < glob__100 then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(expect_sec);
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(glob_optimal_expect_sec);
omniout_str_noeol(INFO, "Expected Total Time ");
omniout_timestr(glob_total_exp_sec)
end if
end proc
# End Function number 9
# Begin Function number 10
> check_for_pole := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#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_g,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad, last_no;
> #TOP CHECK FOR POLE
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,1] := glob_larger_float;
> array_ord_test_poles[1,1] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 3
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 3;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 3
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 4
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 5
> found_sing := 0;
> fi;# end if 5;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 5
> if (rad_c < array_rad_test_poles[1,1]) then # if number 6
> array_rad_test_poles[1,1] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,1] := rad_c;
> array_ord_test_poles[1,1] := tmp_ord;
> fi;# end if 6;
> fi;# end if 5;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,2] := glob_larger_float;
> array_ord_test_poles[1,2] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 5
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 5;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 6
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 7
> found_sing := 0;
> fi;# end if 7;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 7
> if (rad_c < array_rad_test_poles[1,2]) then # if number 8
> array_rad_test_poles[1,2] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,2] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 9
> glob_min_pole_est := rad_c;
> fi;# end if 9;
> array_ord_test_poles[1,2] := tmp_ord;
> fi;# end if 8;
> fi;# end if 7;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,3] := glob_larger_float;
> array_ord_test_poles[1,3] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 7
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 7;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 8
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 9
> found_sing := 0;
> fi;# end if 9;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 9
> if (rad_c < array_rad_test_poles[1,3]) then # if number 10
> array_rad_test_poles[1,3] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,3] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 11
> glob_min_pole_est := rad_c;
> fi;# end if 11;
> array_ord_test_poles[1,3] := tmp_ord;
> fi;# end if 10;
> fi;# end if 9;
> #BOTTOM general radius test1
> ;
> if (true) then # if number 9
> display_poles();
> fi;# end if 9
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2,
term3, part1, part2, part3, part4, part5, part6, part7, part8, part9,
part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4,
found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio,
prev_tmp_rad, last_no;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_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_g,
array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 1] := glob_larger_float;
array_ord_test_poles[1, 1] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do
tmp_rad := comp_rad_from_ratio(array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 1] then
array_rad_test_poles[1, 1] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_ratio(array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
array_rad_test_poles[1, 1] := rad_c;
array_ord_test_poles[1, 1] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 2] := glob_larger_float;
array_ord_test_poles[1, 2] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do
tmp_rad := comp_rad_from_three_terms(
array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 2] then
array_rad_test_poles[1, 2] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_three_terms(
array_y_higher[1, last_no - 2],
array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
last_no);
array_rad_test_poles[1, 2] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 2] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 3] := glob_larger_float;
array_ord_test_poles[1, 3] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do
tmp_rad := comp_rad_from_six_terms(array_y_higher[1, last_no - 5],
array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3],
array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 3] then
array_rad_test_poles[1, 3] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_six_terms(
array_y_higher[1, last_no - 5],
array_y_higher[1, last_no - 4],
array_y_higher[1, last_no - 3],
array_y_higher[1, last_no - 2],
array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
last_no);
array_rad_test_poles[1, 3] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 3] := tmp_ord
end if
end if;
display_poles()
end proc
# End Function number 10
# Begin Function number 11
> atomall := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
#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_g,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> # before write maple main top matter
> # before generate constants assign
> # before generate globals assign
> #END OUTFILE1
> #BEGIN OUTFILE2
> #END OUTFILE2
> #BEGIN ATOMHDR1
> #emit pre sin 1 $eq_no = 1
> array_tmp1[1] := sin(array_x[1]);
> array_tmp1_g[1] := cos(array_x[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
> #emit pre cos 1 $eq_no = 1
> array_tmp3[1] := cos(array_x[1]);
> array_tmp3_g[1] := sin(array_x[1]);
> #emit pre sub FULL FULL $eq_no = 1 i = 1
> array_tmp4[1] := array_tmp2[1] - array_tmp3[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y_set_initial[1,2]) then # if number 1
> if (1 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp4[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
> if (2 <= ATS_MAX_TERMS) then # if number 3
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(1);
> array_y_higher[2,1] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre 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 add CONST FULL $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre cos ID_LINEAR iii = 2 $eq_no = 1
> array_tmp3[2] := neg(array_tmp3_g[1]) * array_x[2] / c(1);
> array_tmp3_g[2] := array_tmp3[1] * array_x[2] / c(1);
> #emit pre sub FULL FULL $eq_no = 1 i = 2
> array_tmp4[2] := array_tmp2[2] - array_tmp3[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y_set_initial[1,3]) then # if number 1
> if (2 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp4[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2));
> if (3 <= ATS_MAX_TERMS) then # if number 3
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y_higher[2,2] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre 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 add CONST FULL $eq_no = 1 i = 3
> array_tmp2[3] := array_tmp1[3];
> #emit pre cos ID_LINEAR iii = 3 $eq_no = 1
> array_tmp3[3] := neg(array_tmp3_g[2]) * array_x[2] / c(2);
> array_tmp3_g[3] := array_tmp3[2] * array_x[2] / c(2);
> #emit pre sub FULL FULL $eq_no = 1 i = 3
> array_tmp4[3] := array_tmp2[3] - array_tmp3[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y_set_initial[1,4]) then # if number 1
> if (3 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp4[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3));
> if (4 <= ATS_MAX_TERMS) then # if number 3
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y_higher[2,3] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre 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 add CONST FULL $eq_no = 1 i = 4
> array_tmp2[4] := array_tmp1[4];
> #emit pre cos ID_LINEAR iii = 4 $eq_no = 1
> array_tmp3[4] := neg(array_tmp3_g[3]) * array_x[2] / c(3);
> array_tmp3_g[4] := array_tmp3[3] * array_x[2] / c(3);
> #emit pre sub FULL FULL $eq_no = 1 i = 4
> array_tmp4[4] := array_tmp2[4] - array_tmp3[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y_set_initial[1,5]) then # if number 1
> if (4 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp4[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4));
> if (5 <= ATS_MAX_TERMS) then # if number 3
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y_higher[2,4] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre 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 add CONST FULL $eq_no = 1 i = 5
> array_tmp2[5] := array_tmp1[5];
> #emit pre cos ID_LINEAR iii = 5 $eq_no = 1
> array_tmp3[5] := neg(array_tmp3_g[4]) * array_x[2] / c(4);
> array_tmp3_g[5] := array_tmp3[4] * array_x[2] / c(4);
> #emit pre sub FULL FULL $eq_no = 1 i = 5
> array_tmp4[5] := array_tmp2[5] - array_tmp3[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y_set_initial[1,6]) then # if number 1
> if (5 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp4[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5));
> if (6 <= ATS_MAX_TERMS) then # if number 3
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y_higher[2,5] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= ATS_MAX_TERMS) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit 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 NOT FULL - FULL add $eq_no = 1
> array_tmp2[kkk] := array_tmp1[kkk];
> #emit cos LINEAR $eq_no = 1
> array_tmp3[kkk] := neg(array_tmp3_g[kkk - 1]) * array_x[2] / c(kkk - 1);
> array_tmp3_g[kkk] := array_tmp3[kkk - 1] * array_x[2] / c(kkk - 1);
> #emit FULL - FULL sub $eq_no = 1
> array_tmp4[kkk] := array_tmp2[kkk] - array_tmp3[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1
> if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2
> temporary := c(array_tmp4[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
> array_y[kkk + order_d] := c(temporary);
> array_y_higher[1,kkk + order_d] := c(temporary);
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := c(temporary) / c(glob_h) * c(adj2);
> else
> temporary := c(temporary);
> fi;# end if 4;
> array_y_higher[adj3,term] := c(temporary);
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 1
> fi;# end if 2
> fi;# end if 1;
> kkk := kkk + 1;
> od;# end do number 1;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_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_g,
array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
array_tmp1[1] := sin(array_x[1]);
array_tmp1_g[1] := cos(array_x[1]);
array_tmp2[1] := array_const_0D0[1] + array_tmp1[1];
array_tmp3[1] := cos(array_x[1]);
array_tmp3_g[1] := sin(array_x[1]);
array_tmp4[1] := array_tmp2[1] - array_tmp3[1];
if not array_y_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
if 2 <= ATS_MAX_TERMS then
array_y[2] := temporary; array_y_higher[1, 2] := temporary
end if;
temporary := c(temporary)*c(1)/c(glob_h);
array_y_higher[2, 1] := c(temporary)
end if
end if;
kkk := 2;
array_tmp1[2] := array_tmp1_g[1]*array_x[2]/c(1);
array_tmp1_g[2] := neg(array_tmp1[1])*array_x[2]/c(1);
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := neg(array_tmp3_g[1])*array_x[2]/c(1);
array_tmp3_g[2] := array_tmp3[1]*array_x[2]/c(1);
array_tmp4[2] := array_tmp2[2] - array_tmp3[2];
if not array_y_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
if 3 <= ATS_MAX_TERMS then
array_y[3] := temporary; array_y_higher[1, 3] := temporary
end if;
temporary := c(temporary)*c(2)/c(glob_h);
array_y_higher[2, 2] := c(temporary)
end if
end if;
kkk := 3;
array_tmp1[3] := array_tmp1_g[2]*array_x[2]/c(2);
array_tmp1_g[3] := neg(array_tmp1[2])*array_x[2]/c(2);
array_tmp2[3] := array_tmp1[3];
array_tmp3[3] := neg(array_tmp3_g[2])*array_x[2]/c(2);
array_tmp3_g[3] := array_tmp3[2]*array_x[2]/c(2);
array_tmp4[3] := array_tmp2[3] - array_tmp3[3];
if not array_y_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[3])*expt(glob_h, c(1))*c(factorial_3(2, 3));
if 4 <= ATS_MAX_TERMS then
array_y[4] := temporary; array_y_higher[1, 4] := temporary
end if;
temporary := c(temporary)*c(3)/c(glob_h);
array_y_higher[2, 3] := c(temporary)
end if
end if;
kkk := 4;
array_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] := array_tmp1[4];
array_tmp3[4] := neg(array_tmp3_g[3])*array_x[2]/c(3);
array_tmp3_g[4] := array_tmp3[3]*array_x[2]/c(3);
array_tmp4[4] := array_tmp2[4] - array_tmp3[4];
if not array_y_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[4])*expt(glob_h, c(1))*c(factorial_3(3, 4));
if 5 <= ATS_MAX_TERMS then
array_y[5] := temporary; array_y_higher[1, 5] := temporary
end if;
temporary := c(temporary)*c(4)/c(glob_h);
array_y_higher[2, 4] := c(temporary)
end if
end if;
kkk := 5;
array_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] := array_tmp1[5];
array_tmp3[5] := neg(array_tmp3_g[4])*array_x[2]/c(4);
array_tmp3_g[5] := array_tmp3[4]*array_x[2]/c(4);
array_tmp4[5] := array_tmp2[5] - array_tmp3[5];
if not array_y_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp4[5])*expt(glob_h, c(1))*c(factorial_3(4, 5));
if 6 <= ATS_MAX_TERMS then
array_y[6] := temporary; array_y_higher[1, 6] := temporary
end if;
temporary := c(temporary)*c(5)/c(glob_h);
array_y_higher[2, 5] := c(temporary)
end if
end if;
kkk := 6;
while kkk <= ATS_MAX_TERMS do
array_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] := array_tmp1[kkk];
array_tmp3[kkk] := neg(array_tmp3_g[kkk - 1])*array_x[2]/c(kkk - 1)
;
array_tmp3_g[kkk] := array_tmp3[kkk - 1]*array_x[2]/c(kkk - 1);
array_tmp4[kkk] := array_tmp2[kkk] - array_tmp3[kkk];
order_d := 1;
if kkk + order_d <= ATS_MAX_TERMS then
if not array_y_set_initial[1, kkk + order_d] then
temporary := c(array_tmp4[kkk])*expt(glob_h, c(order_d))*
c(factorial_3(kkk - 1, kkk + order_d - 1));
array_y[kkk + order_d] := c(temporary);
array_y_higher[1, kkk + order_d] := c(temporary);
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while
1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1
do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := c(temporary)*c(adj2)/c(glob_h)
else temporary := c(temporary)
end if;
array_y_higher[adj3, term] := c(temporary)
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
# End Function number 12
#END OUTFILE5
# Begin Function number 12
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it;
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> #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_g,
> array_tmp3,
> array_tmp4,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> ATS_MAX_TERMS := 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_g:= Array(0..(40),[]);
> array_tmp3:= Array(0..(40),[]);
> array_tmp4:= 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_g[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp3[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp4[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_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_g);
> zero_ats_ar(array_tmp3);
> zero_ats_ar(array_tmp4);
> zero_ats_ar(array_m1);
> zero_ats_ar(array_const_1);
> array_const_1[1] := c(1);
> zero_ats_ar(array_const_0D0);
> array_const_0D0[1] := c(0.0);
> zero_ats_ar(array_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/subpostcpx.cpx#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = 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,"");
> 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(c(2.0) - cos(c(x)) - sin(c(x)));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"next_delta := proc()");
> omniout_str(ALWAYS,"global glob_nxt, x_delta;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"x_delta := [ 0.001 + 0.00004 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.000 + 0.000 * I ];");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_nxt := glob_nxt + 1;");
> omniout_str(ALWAYS,"it := x_delta[glob_nxt];");
> omniout_str(ALWAYS,"return it;");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := glob__0;
> glob_smallish_float := glob__0;
> glob_large_float := c(1.0e100);
> glob_larger_float := c( 1.1e100);
> glob_almost_1 := c( 0.99);
> # before second block
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #BEGIN BLOCK 2
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := 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 ) = 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,"2017-11-26T16:38:20-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"sub")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = 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 diffeq.mxt")
> ;
> logitem_str(html_log_file,"sub 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_g,
array_tmp3, array_tmp4, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
ATS_MAX_TERMS := 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_g := Array(0 .. 40, []);
array_tmp3 := Array(0 .. 40, []);
array_tmp4 := 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_g[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 40 do array_tmp3[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp4[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_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_g);
zero_ats_ar(array_tmp3);
zero_ats_ar(array_tmp4);
zero_ats_ar(array_m1);
zero_ats_ar(array_const_1);
array_const_1[1] := c(1);
zero_ats_ar(array_const_0D0);
array_const_0D0[1] := c(0.);
zero_ats_ar(array_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/subpostcpx.cpx#################");
omniout_str(ALWAYS,
"diff ( y , x , 1 ) = 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, "");
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(c(2.0) - cos(c(x)) - sin(c(x)));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "next_delta := proc()");
omniout_str(ALWAYS, "global glob_nxt, x_delta;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "x_delta := [ 0.001 + 0.00004 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
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omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 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 ) = 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, "2017-11-26T16:38:20-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file, "sub");
logitem_str(html_log_file, "diff ( y , x , 1 ) = si\
n ( 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 diffeq.mxt");
logitem_str(html_log_file,
"sub 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=3.7MB, alloc=40.3MB, time=0.08
##############ECHO OF PROBLEM#################
##############temp/subpostcpx.cpx#################
diff ( y , x , 1 ) = 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(c(2.0) - 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,
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0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 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) = 0.899683666821 -0.0896663446032
y[1] (closed_form) = 0.899683666821 -0.0896663446032
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) = 32.4 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1001 0.105
h = 0.0001 0.003
y[1] (numeric) = 0.89903432985 -0.0941540425845
y[1] (closed_form) = 0.899031573455 -0.0941542184445
absolute error = 2.762e-06
relative error = 0.0003055 %
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) = 32.4 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1002 0.108
h = 0.001 0.001
y[1] (numeric) = 0.898590502028 -0.0968428005977
y[1] (closed_form) = 0.898591059307 -0.0968427969515
absolute error = 5.573e-07
relative error = 6.166e-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) = 32.4 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1012 0.109
h = 0.001 0.003
y[1] (numeric) = 0.897570085248 -0.0976229192738
y[1] (closed_form) = 0.89757229418 -0.0976233795729
absolute error = 2.256e-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 = 1.122
Order of pole (three term test) = 32.4 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1022 0.112
h = 0.0001 0.004
y[1] (numeric) = 0.896310542266 -0.10019863518
y[1] (closed_form) = 0.896309342893 -0.100198288515
absolute error = 1.248e-06
relative error = 0.0001384 %
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) = 32.4 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1023 0.116
h = 0.003 0.006
y[1] (numeric) = 0.89572152274 -0.103778013456
y[1] (closed_form) = 0.895718243986 -0.103779808434
absolute error = 3.738e-06
relative error = 0.0004145 %
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) = 32.4 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1053 0.122
h = 0.0001 0.005
y[1] (numeric) = 0.892246633824 -0.108781700013
y[1] (closed_form) = 0.892240283078 -0.108770734935
absolute error = 1.267e-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 = 0.3759
Order of pole (three term test) = 32.39 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1054 0.127
h = 0.0001 0.003
y[1] (numeric) = 0.89146730597 -0.113241153985
y[1] (closed_form) = 0.891464384323 -0.113238022414
absolute error = 4.283e-06
relative error = 0.0004766 %
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) = 32.39 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) = 0.890949211039 -0.115916846854
y[1] (closed_form) = 0.890949627874 -0.115913479322
absolute error = 3.393e-06
relative error = 0.0003777 %
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 = 0.2385
Order of pole (three term test) = 32.39 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1065 0.131
h = 0.001 0.003
y[1] (numeric) = 0.889907392392 -0.116668586533
y[1] (closed_form) = 0.889909482486 -0.116665659534
absolute error = 3.597e-06
relative error = 0.0004007 %
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 = 1.132
Order of pole (three term test) = 32.39 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1075 0.134
h = 0.0001 0.004
y[1] (numeric) = 0.888576594986 -0.119208885313
y[1] (closed_form) = 0.888575234674 -0.11920520072
absolute error = 3.928e-06
relative error = 0.0004381 %
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) = 32.39 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1076 0.138
h = 0.003 0.006
y[1] (numeric) = 0.887888046827 -0.122772041245
y[1] (closed_form) = 0.887884624434 -0.122770550763
absolute error = 3.733e-06
relative error = 0.0004165 %
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) = 32.39 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1106 0.144
h = 0.0001 0.005
y[1] (numeric) = 0.884273208374 -0.12768067898
y[1] (closed_form) = 0.884266479172 -0.127666367127
absolute error = 1.581e-05
relative error = 0.00177 %
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) = 32.39 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1107 0.149
h = 0.0001 0.003
y[1] (numeric) = 0.883368522882 -0.132121387928
y[1] (closed_form) = 0.883365379428 -0.132114924029
absolute error = 7.188e-06
relative error = 0.0008047 %
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) = 32.39 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1108 0.152
h = 0.001 0.001
y[1] (numeric) = 0.882775300612 -0.134785114734
y[1] (closed_form) = 0.882775522023 -0.134778359091
absolute error = 6.759e-06
relative error = 0.0007569 %
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) = 32.39 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1118 0.153
h = 0.001 0.003
y[1] (numeric) = 0.881711429789 -0.135508575181
y[1] (closed_form) = 0.881713346728 -0.135502237249
absolute error = 6.621e-06
relative error = 0.0007423 %
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) = 32.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1128 0.156
h = 0.0001 0.004
y[1] (numeric) = 0.880308178776 -0.13801430465
y[1] (closed_form) = 0.88030660181 -0.138007257344
absolute error = 7.222e-06
relative error = 0.0008105 %
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) = 32.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1129 0.16
h = 0.003 0.006
y[1] (numeric) = 0.879518957069 -0.141562702179
y[1] (closed_form) = 0.879515333869 -0.141557901972
absolute error = 6.014e-06
relative error = 0.0006751 %
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) = 32.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1159 0.166
h = 0.0001 0.005
y[1] (numeric) = 0.87576137621 -0.146377686008
y[1] (closed_form) = 0.875754212868 -0.146359996498
absolute error = 1.908e-05
relative error = 0.002149 %
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) = 32.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.116 0.171
h = 0.0001 0.003
y[1] (numeric) = 0.874729884961 -0.150801463564
y[1] (closed_form) = 0.87472646382 -0.150791640869
absolute error = 1.040e-05
relative error = 0.001172 %
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) = 32.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1161 0.174
h = 0.001 0.001
y[1] (numeric) = 0.87406064366 -0.153454300411
y[1] (closed_form) = 0.874060615371 -0.153444130839
absolute error = 1.017e-05
relative error = 0.001146 %
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) = 32.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1171 0.175
h = 0.001 0.003
y[1] (numeric) = 0.872974066896 -0.154149563353
y[1] (closed_form) = 0.872975757077 -0.154139789258
absolute error = 9.919e-06
relative error = 0.001119 %
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) = 32.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1181 0.178
h = 0.0001 0.004
y[1] (numeric) = 0.87149713812 -0.156621538667
y[1] (closed_form) = 0.87149528947 -0.156611102279
absolute error = 1.060e-05
relative error = 0.001197 %
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) = 32.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1182 0.182
h = 0.003 0.006
y[1] (numeric) = 0.870606055492 -0.16015661153
y[1] (closed_form) = 0.870602174999 -0.160148475775
absolute error = 9.014e-06
relative error = 0.001018 %
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) = 32.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1212 0.188
h = 0.0001 0.005
y[1] (numeric) = 0.86670289612 -0.164879260378
y[1] (closed_form) = 0.866695243544 -0.164858160688
absolute error = 2.244e-05
relative error = 0.002544 %
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) = 32.37 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1213 0.193
h = 0.0001 0.003
y[1] (numeric) = 0.865543097131 -0.169287882881
y[1] (closed_form) = 0.86553934308 -0.169274673326
absolute error = 1.373e-05
relative error = 0.001557 %
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) = 32.37 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1214 0.196
h = 0.001 0.001
y[1] (numeric) = 0.864796912988 -0.171930883178
y[1] (closed_form) = 0.864796581403 -0.171917272248
absolute error = 1.361e-05
relative error = 0.001544 %
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) = 32.37 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=74.2MB, alloc=44.3MB, time=0.90
x[1] = 0.1224 0.197
h = 0.0001 0.004
y[1] (numeric) = 0.863686972739 -0.172598012194
y[1] (closed_form) = 0.863688383259 -0.172584775086
absolute error = 1.331e-05
relative error = 0.001511 %
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) = 32.37 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1225 0.201
h = 0.003 0.006
y[1] (numeric) = 0.862711657866 -0.176123393596
y[1] (closed_form) = 0.862706482248 -0.176113084273
absolute error = 1.154e-05
relative error = 0.00131 %
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) = 32.37 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1255 0.207
h = 0.0001 0.005
y[1] (numeric) = 0.858679804166 -0.180769342604
y[1] (closed_form) = 0.858670656865 -0.180746002411
absolute error = 2.507e-05
relative error = 0.002857 %
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) = 32.37 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1256 0.212
h = 0.0001 0.003
y[1] (numeric) = 0.857408165048 -0.18516786822
y[1] (closed_form) = 0.85740305113 -0.185152439981
absolute error = 1.625e-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 = 0.3189
Order of pole (three term test) = 32.37 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1257 0.215
h = 0.001 0.001
y[1] (numeric) = 0.856594885779 -0.187804160079
y[1] (closed_form) = 0.856593220503 -0.187788283668
absolute error = 1.596e-05
relative error = 0.00182 %
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) = 32.36 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1267 0.216
h = 0.001 0.003
y[1] (numeric) = 0.855463970924 -0.188447398349
y[1] (closed_form) = 0.855464068414 -0.18843187729
absolute error = 1.552e-05
relative error = 0.001772 %
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) = 32.36 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1277 0.219
h = 0.0001 0.004
y[1] (numeric) = 0.853846217568 -0.190859536403
y[1] (closed_form) = 0.853842689252 -0.190843438241
absolute error = 1.648e-05
relative error = 0.001884 %
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) = 32.36 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1278 0.223
h = 0.003 0.006
y[1] (numeric) = 0.852762166427 -0.194374777995
y[1] (closed_form) = 0.8527566298 -0.194361081505
absolute error = 1.477e-05
relative error = 0.001689 %
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) = 32.36 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1308 0.229
h = 0.0001 0.005
y[1] (numeric) = 0.84857934989 -0.198930678825
y[1] (closed_form) = 0.848569611913 -0.19890386411
absolute error = 2.853e-05
relative error = 0.003273 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4011
Order of pole (three term test) = 32.36 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1309 0.234
h = 0.0001 0.003
y[1] (numeric) = 0.847176481182 -0.203317276495
y[1] (closed_form) = 0.847170932902 -0.203298405478
absolute error = 1.967e-05
relative error = 0.002258 %
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) = 32.36 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.131 0.237
h = 0.001 0.001
y[1] (numeric) = 0.846284464219 -0.205945644386
y[1] (closed_form) = 0.846282397302 -0.205926271808
absolute error = 1.948e-05
relative error = 0.002237 %
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) = 32.36 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.132 0.238
h = 0.001 0.003
y[1] (numeric) = 0.84512895146 -0.206560826242
y[1] (closed_form) = 0.845128672279 -0.206541788424
absolute error = 1.904e-05
relative error = 0.002188 %
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) = 32.36 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.133 0.241
h = 0.0001 0.004
y[1] (numeric) = 0.843433882121 -0.208941378094
y[1] (closed_form) = 0.843429927935 -0.208921807074
absolute error = 1.997e-05
relative error = 0.002298 %
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) = 32.35 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1331 0.245
h = 0.003 0.006
y[1] (numeric) = 0.842244346809 -0.212447248976
y[1] (closed_form) = 0.842238394507 -0.2124301349
absolute error = 1.812e-05
relative error = 0.002086 %
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) = 32.35 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1361 0.251
h = 0.0001 0.005
y[1] (numeric) = 0.837907597876 -0.216914203261
y[1] (closed_form) = 0.8378972157 -0.216883876643
absolute error = 3.205e-05
relative error = 0.003704 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4086
Order of pole (three term test) = 32.35 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1362 0.256
h = 0.0001 0.003
y[1] (numeric) = 0.836371836946 -0.22129054576
y[1] (closed_form) = 0.83636580084 -0.221268199184
absolute error = 2.315e-05
relative error = 0.002676 %
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) = 32.35 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1363 0.259
h = 0.001 0.001
y[1] (numeric) = 0.835400062617 -0.223911979982
y[1] (closed_form) = 0.835397542297 -0.223889079041
absolute error = 2.304e-05
relative error = 0.002664 %
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) = 32.35 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1373 0.26
h = 0.001 0.003
y[1] (numeric) = 0.834219281658 -0.224499116414
y[1] (closed_form) = 0.834218574782 -0.224476530208
absolute error = 2.260e-05
relative error = 0.002616 %
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) = 32.35 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=116.3MB, alloc=44.3MB, time=1.40
x[1] = 0.1383 0.263
h = 0.0001 0.004
y[1] (numeric) = 0.832445568327 -0.226848772091
y[1] (closed_form) = 0.832441135697 -0.226825695484
absolute error = 2.350e-05
relative error = 0.002724 %
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) = 32.35 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1384 0.267
h = 0.003 0.006
y[1] (numeric) = 0.831149188876 -0.23034659325
y[1] (closed_form) = 0.831142766841 -0.230326029512
absolute error = 2.154e-05
relative error = 0.002498 %
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) = 32.34 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1414 0.273
h = 0.0001 0.005
y[1] (numeric) = 0.826655488552 -0.234725626168
y[1] (closed_form) = 0.826644409181 -0.234691748516
absolute error = 3.564e-05
relative error = 0.004148 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.4169
Order of pole (three term test) = 32.34 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1415 0.278
h = 0.0001 0.003
y[1] (numeric) = 0.824985114571 -0.239093350605
y[1] (closed_form) = 0.824978537762 -0.23906749399
absolute error = 2.668e-05
relative error = 0.003106 %
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) = 32.34 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1416 0.281
h = 0.001 0.001
y[1] (numeric) = 0.823932528457 -0.241708819695
y[1] (closed_form) = 0.823929503591 -0.241682356476
absolute error = 2.664e-05
relative error = 0.003102 %
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) = 32.34 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1426 0.282
h = 0.001 0.003
y[1] (numeric) = 0.822725804024 -0.242267903011
y[1] (closed_form) = 0.822724619061 -0.242241735072
absolute error = 2.619e-05
relative error = 0.003054 %
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) = 32.34 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1436 0.285
h = 0.0001 0.004
y[1] (numeric) = 0.820872090043 -0.244587320115
y[1] (closed_form) = 0.820867126993 -0.244560703482
absolute error = 2.708e-05
relative error = 0.003161 %
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) = 32.34 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1437 0.289
h = 0.003 0.006
y[1] (numeric) = 0.819467459651 -0.248078383948
y[1] (closed_form) = 0.819460514413 -0.248054336792
absolute error = 2.503e-05
relative error = 0.002923 %
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) = 32.34 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1467 0.295
h = 0.0001 0.005
y[1] (numeric) = 0.814813737887 -0.25237044399
y[1] (closed_form) = 0.814801908834 -0.25233297439
absolute error = 3.929e-05
relative error = 0.004606 %
Correct 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) = 32.33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1468 0.3
h = 0.0001 0.003
y[1] (numeric) = 0.813006970662 -0.256731152148
y[1] (closed_form) = 0.812999800846 -0.256701749288
absolute error = 3.026e-05
relative error = 0.00355 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.345
Order of pole (three term test) = 32.33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1469 0.303
h = 0.001 0.001
y[1] (numeric) = 0.811872482891 -0.259341603076
y[1] (closed_form) = 0.811868902935 -0.259311541926
absolute error = 3.027e-05
relative error = 0.003552 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2717
Order of pole (three term test) = 32.33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1479 0.304
h = 0.0001 0.004
y[1] (numeric) = 0.810639134422 -0.259872606747
y[1] (closed_form) = 0.8106374216 -0.259842821984
absolute error = 2.983e-05
relative error = 0.003505 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.633
Order of pole (three term test) = 32.33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.148 0.308
h = 0.003 0.006
y[1] (numeric) = 0.809144889927 -0.263359256469
y[1] (closed_form) = 0.809136412858 -0.263333014501
absolute error = 2.758e-05
relative error = 0.003241 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9721
Order of pole (three term test) = 32.33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.151 0.314
h = 0.0001 0.005
y[1] (numeric) = 0.804349906379 -0.267579110838
y[1] (closed_form) = 0.804336349865 -0.267539349883
absolute error = 4.201e-05
relative error = 0.004956 %
Correct 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) = 32.32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1511 0.319
h = 0.0001 0.003
y[1] (numeric) = 0.802424206404 -0.271936690242
y[1] (closed_form) = 0.802415444802 -0.271905037309
absolute error = 3.284e-05
relative error = 0.003877 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.3521
Order of pole (three term test) = 32.32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1512 0.322
h = 0.001 0.001
y[1] (numeric) = 0.801218275255 -0.274544557626
y[1] (closed_form) = 0.801213136977 -0.274512201864
absolute error = 3.276e-05
relative error = 0.003868 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2774
Order of pole (three term test) = 32.32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1522 0.323
h = 0.001 0.003
y[1] (numeric) = 0.7999611252 -0.275051683799
y[1] (closed_form) = 0.799957877908 -0.275019588273
absolute error = 3.226e-05
relative error = 0.003814 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.318
Order of pole (three term test) = 32.32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1532 0.326
h = 0.0001 0.004
y[1] (numeric) = 0.797954493309 -0.277317465557
y[1] (closed_form) = 0.797947366683 -0.277284996731
absolute error = 3.324e-05
relative error = 0.003935 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.748
Order of pole (three term test) = 32.32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1533 0.33
h = 0.003 0.006
y[1] (numeric) = 0.796344479096 -0.280800629799
y[1] (closed_form) = 0.796335380398 -0.280770837648
absolute error = 3.115e-05
relative error = 0.003689 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9959
Order of pole (three term test) = 32.32 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=159.9MB, alloc=52.3MB, time=1.93
x[1] = 0.1563 0.336
h = 0.0001 0.005
y[1] (numeric) = 0.791383629157 -0.284935109176
y[1] (closed_form) = 0.791369226067 -0.284891675908
absolute error = 4.576e-05
relative error = 0.00544 %
Correct 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) = 32.31 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1564 0.341
h = 0.0001 0.003
y[1] (numeric) = 0.789318079446 -0.289288582822
y[1] (closed_form) = 0.789308628499 -0.289253312187
absolute error = 3.651e-05
relative error = 0.004344 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.361
Order of pole (three term test) = 32.31 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1565 0.344
h = 0.001 0.001
y[1] (numeric) = 0.788028132499 -0.291893151343
y[1] (closed_form) = 0.788022346155 -0.291857127159
absolute error = 3.649e-05
relative error = 0.004342 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2845
Order of pole (three term test) = 32.31 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1575 0.345
h = 0.001 0.003
y[1] (numeric) = 0.786743076079 -0.292372106035
y[1] (closed_form) = 0.786739209436 -0.292336324228
absolute error = 3.599e-05
relative error = 0.004288 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.351
Order of pole (three term test) = 32.31 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1585 0.348
h = 0.0001 0.004
y[1] (numeric) = 0.784652403845 -0.294609368522
y[1] (closed_form) = 0.784644600803 -0.294573252052
absolute error = 3.695e-05
relative error = 0.004409 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7672
Order of pole (three term test) = 32.31 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1586 0.352
h = 0.003 0.006
y[1] (numeric) = 0.782929861289 -0.298089335767
y[1] (closed_form) = 0.782920089073 -0.298055954699
absolute error = 3.478e-05
relative error = 0.004152 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.022
Order of pole (three term test) = 32.31 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1616 0.358
h = 0.0001 0.005
y[1] (numeric) = 0.777799918961 -0.302139168197
y[1] (closed_form) = 0.777784618167 -0.302092016426
absolute error = 4.957e-05
relative error = 0.005941 %
Correct 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) = 32.3 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1617 0.363
h = 0.0001 0.003
y[1] (numeric) = 0.775592562476 -0.30649003921
y[1] (closed_form) = 0.775582371412 -0.306451109561
absolute error = 4.024e-05
relative error = 0.004826 %
Correct 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) = 32.3 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1618 0.366
h = 0.001 0.001
y[1] (numeric) = 0.774217404182 -0.309092195511
y[1] (closed_form) = 0.774210920847 -0.309052462104
absolute error = 4.026e-05
relative error = 0.004829 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2921
Order of pole (three term test) = 32.3 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1628 0.367
h = 0.001 0.003
y[1] (numeric) = 0.772903743811 -0.309542897392
y[1] (closed_form) = 0.77289920971 -0.30950338906
absolute error = 3.977e-05
relative error = 0.004777 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.388
Order of pole (three term test) = 32.3 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1638 0.37
h = 0.0001 0.004
y[1] (numeric) = 0.770727556279 -0.311752173044
y[1] (closed_form) = 0.770719026996 -0.311712367617
absolute error = 4.071e-05
relative error = 0.004897 %
Correct 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) = 32.3 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1639 0.374
h = 0.003 0.006
y[1] (numeric) = 0.768890888444 -0.315230128161
y[1] (closed_form) = 0.76888039135 -0.315193117651
absolute error = 3.847e-05
relative error = 0.00463 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.05
Order of pole (three term test) = 32.29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1669 0.38
h = 0.0001 0.005
y[1] (numeric) = 0.763588570375 -0.319195963661
y[1] (closed_form) = 0.76357232121 -0.319145045295
absolute error = 5.345e-05
relative error = 0.006458 %
Correct 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) = 32.29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.167 0.385
h = 0.0001 0.003
y[1] (numeric) = 0.761237386032 -0.323545700908
y[1] (closed_form) = 0.761226404595 -0.323503069091
absolute error = 4.402e-05
relative error = 0.005323 %
Correct 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) = 32.29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1671 0.388
h = 0.001 0.001
y[1] (numeric) = 0.759775782557 -0.326146310661
y[1] (closed_form) = 0.759768553852 -0.326102825376
absolute error = 4.408e-05
relative error = 0.005332 %
Correct 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) = 32.29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1681 0.389
h = 0.001 0.003
y[1] (numeric) = 0.758432814195 -0.326568658845
y[1] (closed_form) = 0.758427565094 -0.326525381892
absolute error = 4.359e-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 = 1.427
Order of pole (three term test) = 32.29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1691 0.392
h = 0.0001 0.004
y[1] (numeric) = 0.75616960395 -0.328750447397
y[1] (closed_form) = 0.756160299132 -0.328706909848
absolute error = 4.452e-05
relative error = 0.0054 %
Correct 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) = 32.28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1692 0.396
h = 0.003 0.006
y[1] (numeric) = 0.754217162336 -0.332227547721
y[1] (closed_form) = 0.75420588952 -0.33218686542
absolute error = 4.222e-05
relative error = 0.005122 %
Correct 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) = 32.28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1722 0.402
h = 0.0001 0.005
y[1] (numeric) = 0.748739126176 -0.336109957812
y[1] (closed_form) = 0.748721878417 -0.336055222818
absolute error = 5.739e-05
relative error = 0.006993 %
Correct 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) = 32.28 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=203.6MB, alloc=52.3MB, time=2.44
x[1] = 0.1723 0.407
h = 0.0001 0.003
y[1] (numeric) = 0.74624202758 -0.340459996099
y[1] (closed_form) = 0.746230206016 -0.34041361709
absolute error = 4.786e-05
relative error = 0.005835 %
Correct 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) = 32.27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1724 0.41
h = 0.001 0.001
y[1] (numeric) = 0.744692706038 -0.343059904108
y[1] (closed_form) = 0.74468468412 -0.343012622407
absolute error = 4.796e-05
relative error = 0.005849 %
Correct 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) = 32.27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1734 0.411
h = 0.0001 0.004
y[1] (numeric) = 0.743319718896 -0.343453777952
y[1] (closed_form) = 0.743313707805 -0.343406688395
absolute error = 4.747e-05
relative error = 0.005798 %
Correct 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) = 32.27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1735 0.415
h = 0.003 0.006
y[1] (numeric) = 0.741271337083 -0.346931203911
y[1] (closed_form) = 0.741258291177 -0.346888273464
absolute error = 4.487e-05
relative error = 0.005482 %
Correct 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) = 32.27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1765 0.421
h = 0.0001 0.005
y[1] (numeric) = 0.735638339947 -0.35074434999
y[1] (closed_form) = 0.73561912585 -0.350687238584
absolute error = 6.026e-05
relative error = 0.007394 %
Correct 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) = 32.27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1766 0.426
h = 0.0001 0.003
y[1] (numeric) = 0.733013947898 -0.355097543661
y[1] (closed_form) = 0.733000297728 -0.355048850172
absolute error = 5.057e-05
relative error = 0.006209 %
Correct 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) = 32.26 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1767 0.429
h = 0.001 0.001
y[1] (numeric) = 0.731388076833 -0.357698574535
y[1] (closed_form) = 0.731378267666 -0.357648935774
absolute error = 5.060e-05
relative error = 0.006215 %
Correct 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) = 32.26 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1777 0.43
h = 0.001 0.003
y[1] (numeric) = 0.729988334461 -0.358068195988
y[1] (closed_form) = 0.729980563512 -0.358018735498
absolute error = 5.007e-05
relative error = 0.006158 %
Correct 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) = 32.26 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1787 0.433
h = 0.0001 0.004
y[1] (numeric) = 0.727558753762 -0.36020113555
y[1] (closed_form) = 0.727546810072 -0.360151480321
absolute error = 5.107e-05
relative error = 0.006291 %
Correct 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) = 32.26 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1788 0.437
h = 0.003 0.006
y[1] (numeric) = 0.725386336829 -0.363681059804
y[1] (closed_form) = 0.725372421364 -0.363634374394
absolute error = 4.872e-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 = 1.142
Order of pole (three term test) = 32.26 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1818 0.443
h = 0.0001 0.005
y[1] (numeric) = 0.719571244128 -0.367411674752
y[1] (closed_form) = 0.719550938482 -0.36735064893
absolute error = 6.432e-05
relative error = 0.007961 %
Correct 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) = 32.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1819 0.448
h = 0.0001 0.003
y[1] (numeric) = 0.716796893427 -0.371767775953
y[1] (closed_form) = 0.716782311259 -0.371715246976
absolute error = 5.452e-05
relative error = 0.006752 %
Correct 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) = 32.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.182 0.451
h = 0.001 0.001
y[1] (numeric) = 0.715080838621 -0.374369638121
y[1] (closed_form) = 0.715070148017 -0.374316115498
absolute error = 5.458e-05
relative error = 0.006762 %
Correct 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) = 32.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.183 0.452
h = 0.001 0.003
y[1] (numeric) = 0.713649733876 -0.374710516048
y[1] (closed_form) = 0.713641114357 -0.374657156533
absolute error = 5.405e-05
relative error = 0.006706 %
Correct 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) = 32.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.184 0.455
h = 0.0001 0.004
y[1] (numeric) = 0.711128636245 -0.376817235656
y[1] (closed_form) = 0.711115778224 -0.376763714882
absolute error = 5.504e-05
relative error = 0.00684 %
Correct 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) = 32.24 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1841 0.459
h = 0.003 0.006
y[1] (numeric) = 0.708835448296 -0.380299486904
y[1] (closed_form) = 0.708820613811 -0.380248998785
absolute error = 5.262e-05
relative error = 0.006542 %
Correct 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) = 32.24 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1871 0.465
h = 0.0001 0.005
y[1] (numeric) = 0.702834738751 -0.383947915412
y[1] (closed_form) = 0.702813292525 -0.383882919398
absolute error = 6.844e-05
relative error = 0.008547 %
Correct 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) = 32.24 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1872 0.47
h = 0.0001 0.003
y[1] (numeric) = 0.69990814859 -0.38830826316
y[1] (closed_form) = 0.69989258602 -0.388251848129
absolute error = 5.852e-05
relative error = 0.007312 %
Correct 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) = 32.23 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1873 0.473
h = 0.001 0.001
y[1] (numeric) = 0.698100520852 -0.390911742656
y[1] (closed_form) = 0.698088902414 -0.390854286059
absolute error = 5.862e-05
relative error = 0.007327 %
Correct digits = 4
memory used=247.3MB, alloc=52.3MB, time=2.95
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) = 32.23 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1883 0.474
h = 0.001 0.003
y[1] (numeric) = 0.696637321763 -0.391223698711
y[1] (closed_form) = 0.696627808182 -0.391166390618
absolute error = 5.809e-05
relative error = 0.007271 %
Correct 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) = 32.23 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1893 0.477
h = 0.0001 0.004
y[1] (numeric) = 0.69402306645 -0.393304570902
y[1] (closed_form) = 0.694009246711 -0.393247133968
absolute error = 5.908e-05
relative error = 0.007406 %
Correct 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) = 32.23 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1894 0.481
h = 0.003 0.006
y[1] (numeric) = 0.691607249845 -0.396790201971
y[1] (closed_form) = 0.691591447345 -0.396735861447
absolute error = 5.659e-05
relative error = 0.007098 %
Correct 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) = 32.23 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1924 0.487
h = 0.0001 0.005
y[1] (numeric) = 0.685417336718 -0.400356707969
y[1] (closed_form) = 0.685394701287 -0.400287683911
absolute error = 7.264e-05
relative error = 0.009152 %
Correct 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) = 32.22 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1925 0.492
h = 0.0001 0.003
y[1] (numeric) = 0.682336155886 -0.404722607713
y[1] (closed_form) = 0.682319564971 -0.40466225406
absolute error = 6.259e-05
relative error = 0.00789 %
Correct 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) = 32.22 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1926 0.495
h = 0.001 0.001
y[1] (numeric) = 0.680435523901 -0.407328469951
y[1] (closed_form) = 0.680422931726 -0.407267027259
absolute error = 6.272e-05
relative error = 0.007909 %
Correct 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) = 32.22 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1936 0.496
h = 0.001 0.003
y[1] (numeric) = 0.678939490608 -0.407611305118
y[1] (closed_form) = 0.678929037989 -0.407549996883
absolute error = 6.219e-05
relative error = 0.007854 %
Correct 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) = 32.21 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1946 0.499
h = 0.0001 0.004
y[1] (numeric) = 0.676230400418 -0.409666668919
y[1] (closed_form) = 0.676215572052 -0.409605263197
absolute error = 6.317e-05
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 = 0.9447
Order of pole (three term test) = 32.21 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1947 0.503
h = 0.003 0.006
y[1] (numeric) = 0.673690040821 -0.413156705576
y[1] (closed_form) = 0.67367322177 -0.41309846097
absolute error = 6.062e-05
relative error = 0.007672 %
Correct 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) = 32.21 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1977 0.509
h = 0.0001 0.005
y[1] (numeric) = 0.667307270216 -0.416641471517
y[1] (closed_form) = 0.667283397353 -0.416568359451
absolute error = 7.691e-05
relative error = 0.009777 %
Correct 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) = 32.2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1978 0.514
h = 0.0001 0.003
y[1] (numeric) = 0.664069075728 -0.421014195185
y[1] (closed_form) = 0.664051408975 -0.420949848308
absolute error = 6.673e-05
relative error = 0.008487 %
Correct 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) = 32.2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1979 0.517
h = 0.001 0.001
y[1] (numeric) = 0.662073965222 -0.423623184977
y[1] (closed_form) = 0.662060353893 -0.423557702023
absolute error = 6.688e-05
relative error = 0.00851 %
Correct 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) = 32.2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1989 0.518
h = 0.0001 0.004
y[1] (numeric) = 0.660544349686 -0.423876679306
y[1] (closed_form) = 0.660532913557 -0.423811317323
absolute error = 6.635e-05
relative error = 0.008455 %
Correct 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) = 32.2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.199 0.522
h = 0.003 0.006
y[1] (numeric) = 0.657900685285 -0.427371260374
y[1] (closed_form) = 0.657881845015 -0.4273106803
absolute error = 6.344e-05
relative error = 0.008087 %
Correct 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) = 32.2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.202 0.528
h = 0.0001 0.005
y[1] (numeric) = 0.65134795866 -0.430788108353
y[1] (closed_form) = 0.651321872325 -0.430712498389
absolute error = 7.998e-05
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 = 0.5825
Order of pole (three term test) = 32.19 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2021 0.533
h = 0.0001 0.003
y[1] (numeric) = 0.647972717235 -0.43516960975
y[1] (closed_form) = 0.647952977949 -0.43510284898
absolute error = 6.962e-05
relative error = 0.00892 %
Correct 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) = 32.19 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2022 0.536
h = 0.001 0.001
y[1] (numeric) = 0.64589511773 -0.437783022464
y[1] (closed_form) = 0.645879483798 -0.437715084762
absolute error = 6.971e-05
relative error = 0.008935 %
Correct 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) = 32.18 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2032 0.537
h = 0.001 0.003
y[1] (numeric) = 0.644335636786 -0.438011481175
y[1] (closed_form) = 0.644322209354 -0.437943652846
absolute error = 6.914e-05
relative error = 0.008875 %
Correct 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) = 32.18 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2042 0.54
h = 0.0001 0.004
y[1] (numeric) = 0.641445192851 -0.440021344963
y[1] (closed_form) = 0.641427255245 -0.43995347554
absolute error = 7.020e-05
relative error = 0.009025 %
Correct digits = 4
memory used=291.1MB, alloc=52.3MB, time=3.46
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) = 32.18 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2043 0.544
h = 0.003 0.006
y[1] (numeric) = 0.638667873949 -0.443523757016
y[1] (closed_form) = 0.638647927321 -0.443459171872
absolute error = 6.760e-05
relative error = 0.008694 %
Correct 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) = 32.18 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2073 0.55
h = 0.0001 0.005
y[1] (numeric) = 0.631915306045 -0.446859030412
y[1] (closed_form) = 0.631887892793 -0.446779215663
absolute error = 8.439e-05
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 = 0.6035
Order of pole (three term test) = 32.17 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2074 0.555
h = 0.0001 0.003
y[1] (numeric) = 0.628378360708 -0.451249664247
y[1] (closed_form) = 0.628357457666 -0.451178803662
absolute error = 7.388e-05
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 = 0.4901
Order of pole (three term test) = 32.17 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2075 0.558
h = 0.001 0.001
y[1] (numeric) = 0.626203430448 -0.453867554376
y[1] (closed_form) = 0.626186693415 -0.453795470586
absolute error = 7.400e-05
relative error = 0.009569 %
Correct 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) = 32.17 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2085 0.559
h = 0.001 0.003
y[1] (numeric) = 0.624608949358 -0.454066215459
y[1] (closed_form) = 0.624594456282 -0.453994228592
absolute error = 7.343e-05
relative error = 0.00951 %
Correct 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) = 32.16 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2095 0.562
h = 0.0001 0.004
y[1] (numeric) = 0.621618666312 -0.456051374971
y[1] (closed_form) = 0.621599587712 -0.455979375335
absolute error = 7.448e-05
relative error = 0.009662 %
Correct 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) = 32.16 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2096 0.566
h = 0.003 0.006
y[1] (numeric) = 0.618711015949 -0.459561002924
y[1] (closed_form) = 0.618689915657 -0.45949235516
absolute error = 7.182e-05
relative error = 0.009319 %
Correct 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) = 32.16 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2126 0.572
h = 0.0001 0.005
y[1] (numeric) = 0.611754750273 -0.462814647544
y[1] (closed_form) = 0.611725962943 -0.462730561777
absolute error = 8.888e-05
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 = 0.6258
Order of pole (three term test) = 32.15 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2127 0.577
h = 0.0001 0.003
y[1] (numeric) = 0.608053464476 -0.467215590728
y[1] (closed_form) = 0.608031351397 -0.467140569695
absolute error = 7.821e-05
relative error = 0.0102 %
Correct 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) = 32.15 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2128 0.58
h = 0.001 0.001
y[1] (numeric) = 0.605779601322 -0.469838644597
y[1] (closed_form) = 0.605761717091 -0.469762354499
absolute error = 7.836e-05
relative error = 0.01022 %
Correct 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) = 32.15 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2138 0.581
h = 0.001 0.003
y[1] (numeric) = 0.604149346794 -0.470007226764
y[1] (closed_form) = 0.604133744979 -0.469931021709
absolute error = 7.779e-05
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 = 1.906
Order of pole (three term test) = 32.14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2148 0.584
h = 0.0001 0.004
y[1] (numeric) = 0.601057398324 -0.471967889693
y[1] (closed_form) = 0.601037133547 -0.471891699117
absolute error = 7.884e-05
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 = 1.084
Order of pole (three term test) = 32.14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2149 0.588
h = 0.003 0.006
y[1] (numeric) = 0.598017272328 -0.475485655548
y[1] (closed_form) = 0.597994971486 -0.475412885495
absolute error = 7.611e-05
relative error = 0.009963 %
Correct 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) = 32.14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2179 0.594
h = 0.0001 0.005
y[1] (numeric) = 0.590853378552 -0.47865753248
y[1] (closed_form) = 0.590823170355 -0.478569107194
absolute error = 9.344e-05
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 = 0.6494
Order of pole (three term test) = 32.13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.218 0.599
h = 0.0001 0.003
y[1] (numeric) = 0.586985038417 -0.483069928298
y[1] (closed_form) = 0.586961669441 -0.482990684006
absolute error = 8.262e-05
relative error = 0.01087 %
Correct 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) = 32.13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2181 0.602
h = 0.001 0.001
y[1] (numeric) = 0.584610593921 -0.48569881151
y[1] (closed_form) = 0.584591518856 -0.485618252701
absolute error = 8.279e-05
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 = 0.4162
Order of pole (three term test) = 32.12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2191 0.603
h = 0.001 0.003
y[1] (numeric) = 0.582943783369 -0.485837011419
y[1] (closed_form) = 0.582927030198 -0.485756526341
absolute error = 8.221e-05
relative error = 0.01083 %
Correct 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) = 32.12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2201 0.606
h = 0.0001 0.004
y[1] (numeric) = 0.579748302524 -0.487773350578
y[1] (closed_form) = 0.579726806824 -0.487692906148
absolute error = 8.327e-05
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 = 1.125
Order of pole (three term test) = 32.12 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=334.7MB, alloc=52.3MB, time=3.97
x[1] = 0.2202 0.61
h = 0.003 0.006
y[1] (numeric) = 0.576573494427 -0.491300149154
y[1] (closed_form) = 0.576549946563 -0.491223194983
absolute error = 8.048e-05
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 = 1.501
Order of pole (three term test) = 32.12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2232 0.616
h = 0.0001 0.005
y[1] (numeric) = 0.569197966631 -0.494390033782
y[1] (closed_form) = 0.56916629114 -0.494297198165
absolute error = 9.809e-05
relative error = 0.01301 %
Correct 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) = 32.11 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2233 0.621
h = 0.0001 0.003
y[1] (numeric) = 0.565159779443 -0.498814991779
y[1] (closed_form) = 0.565135109121 -0.498731459199
absolute error = 8.710e-05
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 = 0.5478
Order of pole (three term test) = 32.1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2234 0.624
h = 0.001 0.001
y[1] (numeric) = 0.562683057941 -0.50145034914
y[1] (closed_form) = 0.562662748855 -0.501365456992
absolute error = 8.729e-05
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 = 0.4323
Order of pole (three term test) = 32.1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2244 0.625
h = 0.0001 0.004
y[1] (numeric) = 0.560978899196 -0.501557841069
y[1] (closed_form) = 0.560960952527 -0.501473011918
absolute error = 8.671e-05
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 = 2.6
Order of pole (three term test) = 32.1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2245 0.629
h = 0.003 0.006
y[1] (numeric) = 0.557692280536 -0.505092887189
y[1] (closed_form) = 0.557666454249 -0.505013473944
absolute error = 8.351e-05
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 = 1.552
Order of pole (three term test) = 32.1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2275 0.635
h = 0.0001 0.005
y[1] (numeric) = 0.550130336428 -0.508114536865
y[1] (closed_form) = 0.550096190068 -0.508019042772
absolute error = 0.0001014
relative error = 0.01354 %
Correct 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) = 32.09 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2276 0.64
h = 0.0001 0.003
y[1] (numeric) = 0.545943819905 -0.512553240576
y[1] (closed_form) = 0.545916823924 -0.512467157276
absolute error = 9.022e-05
relative error = 0.01205 %
Correct 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) = 32.08 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2277 0.643
h = 0.001 0.001
y[1] (numeric) = 0.543377754373 -0.51519591776
y[1] (closed_form) = 0.543355178895 -0.515108435593
absolute error = 9.035e-05
relative error = 0.01207 %
Correct 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) = 32.08 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2287 0.644
h = 0.001 0.003
y[1] (numeric) = 0.541640434182 -0.515277157038
y[1] (closed_form) = 0.541620256731 -0.515189728591
absolute error = 8.973e-05
relative error = 0.012 %
Correct 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) = 32.08 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2297 0.647
h = 0.0001 0.004
y[1] (numeric) = 0.538246905335 -0.517169862058
y[1] (closed_form) = 0.538221831767 -0.517082521062
absolute error = 9.087e-05
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 = 1.208
Order of pole (three term test) = 32.07 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2298 0.651
h = 0.003 0.006
y[1] (numeric) = 0.534815525714 -0.520717425811
y[1] (closed_form) = 0.534788366212 -0.520633708059
absolute error = 8.801e-05
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 = 1.613
Order of pole (three term test) = 32.07 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2328 0.657
h = 0.0001 0.005
y[1] (numeric) = 0.527034281087 -0.523656483459
y[1] (closed_form) = 0.52699858109 -0.523556441521
absolute error = 0.0001062
relative error = 0.0143 %
Correct 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) = 32.06 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2329 0.662
h = 0.0001 0.003
y[1] (numeric) = 0.522672518095 -0.528109759194
y[1] (closed_form) = 0.522644136438 -0.528019261086
absolute error = 9.484e-05
relative error = 0.01277 %
Correct 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) = 32.06 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.233 0.665
h = 0.001 0.001
y[1] (numeric) = 0.520000898563 -0.530760076206
y[1] (closed_form) = 0.519977009065 -0.530668134891
absolute error = 9.499e-05
relative error = 0.01279 %
Correct 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) = 32.06 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.234 0.666
h = 0.001 0.003
y[1] (numeric) = 0.51822472514 -0.530809950423
y[1] (closed_form) = 0.51820327619 -0.530718053162
absolute error = 9.437e-05
relative error = 0.01272 %
Correct 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) = 32.05 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.235 0.669
h = 0.0001 0.004
y[1] (numeric) = 0.514722091196 -0.532678654088
y[1] (closed_form) = 0.51469566022 -0.532586867341
absolute error = 9.552e-05
relative error = 0.0129 %
Correct 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) = 32.05 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2351 0.673
h = 0.003 0.006
y[1] (numeric) = 0.51114937186 -0.536237688119
y[1] (closed_form) = 0.511120833793 -0.536149597631
absolute error = 9.260e-05
relative error = 0.0125 %
Correct 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) = 32.05 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2381 0.679
h = 0.0001 0.005
y[1] (numeric) = 0.503144593627 -0.539093678998
y[1] (closed_form) = 0.503107294556 -0.538989011551
absolute error = 0.0001111
relative error = 0.01507 %
Correct 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) = 32.04 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=378.4MB, alloc=52.3MB, time=4.48
x[1] = 0.2382 0.684
h = 0.0001 0.003
y[1] (numeric) = 0.498604556956 -0.543562539866
y[1] (closed_form) = 0.498574745297 -0.543467555345
absolute error = 9.955e-05
relative error = 0.0135 %
Correct 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) = 32.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2383 0.687
h = 0.001 0.001
y[1] (numeric) = 0.495825547271 -0.546221081978
y[1] (closed_form) = 0.495800301811 -0.546124610297
absolute error = 9.972e-05
relative error = 0.01352 %
Correct 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) = 32.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2393 0.688
h = 0.001 0.003
y[1] (numeric) = 0.494009699186 -0.546239199637
y[1] (closed_form) = 0.493986937898 -0.546142762933
absolute error = 9.909e-05
relative error = 0.01346 %
Correct 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) = 32.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2403 0.691
h = 0.0001 0.004
y[1] (numeric) = 0.490395927401 -0.548083937055
y[1] (closed_form) = 0.49036809588 -0.547987632818
absolute error = 0.0001002
relative error = 0.01363 %
Correct 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) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2404 0.695
h = 0.003 0.006
y[1] (numeric) = 0.486679409436 -0.551655230788
y[1] (closed_form) = 0.486649447846 -0.551562697018
absolute error = 9.726e-05
relative error = 0.01322 %
Correct 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) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2434 0.701
h = 0.0001 0.005
y[1] (numeric) = 0.478446781968 -0.554427590153
y[1] (closed_form) = 0.478407838736 -0.55431821705
absolute error = 0.0001161
relative error = 0.01586 %
Correct 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) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2435 0.706
h = 0.0001 0.003
y[1] (numeric) = 0.473725359494 -0.558913014792
y[1] (closed_form) = 0.473694073902 -0.558813469873
absolute error = 0.0001043
relative error = 0.01424 %
Correct 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) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2436 0.709
h = 0.001 0.001
y[1] (numeric) = 0.470837072624 -0.56158034598
y[1] (closed_form) = 0.470810429699 -0.561479270335
absolute error = 0.0001045
relative error = 0.01427 %
Correct 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) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2446 0.71
h = 0.001 0.003
y[1] (numeric) = 0.468980717765 -0.561566291853
y[1] (closed_form) = 0.468956603761 -0.561465242704
absolute error = 0.0001039
relative error = 0.0142 %
Correct 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) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2456 0.713
h = 0.0001 0.004
y[1] (numeric) = 0.465253730311 -0.563387061287
y[1] (closed_form) = 0.465224455525 -0.563286165434
absolute error = 0.0001051
relative error = 0.01438 %
Correct 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) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2457 0.717
h = 0.003 0.006
y[1] (numeric) = 0.461390886383 -0.566971376197
y[1] (closed_form) = 0.461359456698 -0.566874326243
absolute error = 0.000102
relative error = 0.01396 %
Correct 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) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2487 0.723
h = 0.0001 0.005
y[1] (numeric) = 0.452926009675 -0.569659448036
y[1] (closed_form) = 0.452885377543 -0.569545286602
absolute error = 0.0001212
relative error = 0.01665 %
Correct 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) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2488 0.728
h = 0.0001 0.003
y[1] (numeric) = 0.448020002713 -0.574162380334
y[1] (closed_form) = 0.447987199649 -0.574058198609
absolute error = 0.0001092
relative error = 0.015 %
Correct 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) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2489 0.731
h = 0.001 0.001
y[1] (numeric) = 0.445020499753 -0.576839043095
y[1] (closed_form) = 0.444992418297 -0.576733287462
absolute error = 0.0001094
relative error = 0.01502 %
Correct 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) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2499 0.732
h = 0.0001 0.004
y[1] (numeric) = 0.443122795043 -0.57679237784
y[1] (closed_form) = 0.443097288403 -0.576686640825
absolute error = 0.0001088
relative error = 0.01496 %
Correct 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) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.25 0.736
h = 0.003 0.006
y[1] (numeric) = 0.439138381482 -0.580388121301
y[1] (closed_form) = 0.439104404993 -0.580288449636
absolute error = 0.0001053
relative error = 0.01447 %
Correct 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) = 31.96 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.253 0.742
h = 0.0001 0.005
y[1] (numeric) = 0.430468986787 -0.583005884746
y[1] (closed_form) = 0.430425614222 -0.582888862021
absolute error = 0.0001248
relative error = 0.01722 %
Correct 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) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2531 0.747
h = 0.0001 0.003
y[1] (numeric) = 0.425401690102 -0.587526868387
y[1] (closed_form) = 0.425366297065 -0.587419958837
absolute error = 0.0001126
relative error = 0.01553 %
Correct 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) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2532 0.75
h = 0.001 0.001
y[1] (numeric) = 0.422304982614 -0.590213338541
y[1] (closed_form) = 0.422274380645 -0.59010481724
absolute error = 0.0001128
relative error = 0.01554 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5423
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=422.0MB, alloc=52.3MB, time=4.98
x[1] = 0.2542 0.751
h = 0.001 0.003
y[1] (numeric) = 0.420370605597 -0.590138738629
y[1] (closed_form) = 0.420342618801 -0.590030229086
absolute error = 0.0001121
relative error = 0.01547 %
Correct 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) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2552 0.754
h = 0.0001 0.004
y[1] (numeric) = 0.41642697432 -0.591916185595
y[1] (closed_form) = 0.416393652075 -0.591807866226
absolute error = 0.0001133
relative error = 0.01566 %
Correct 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) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2553 0.758
h = 0.0001 0.004
y[1] (numeric) = 0.41228506062 -0.595528477219
y[1] (closed_form) = 0.412249533183 -0.595424147809
absolute error = 0.0001102
relative error = 0.01522 %
Correct 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) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2554 0.762
h = 0.003 0.006
y[1] (numeric) = 0.408115077224 -0.599153009442
y[1] (closed_form) = 0.408079549787 -0.599048680032
absolute error = 0.0001102
relative error = 0.01521 %
Correct 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) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2584 0.768
h = 0.0001 0.005
y[1] (numeric) = 0.399159727939 -0.601679211293
y[1] (closed_form) = 0.399114533754 -0.601557196942
absolute error = 0.0001301
relative error = 0.01802 %
Correct 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) = 31.91 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2585 0.773
h = 0.0001 0.003
y[1] (numeric) = 0.393869078524 -0.606229976725
y[1] (closed_form) = 0.393832074132 -0.606118261446
absolute error = 0.0001177
relative error = 0.01628 %
Correct 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) = 31.91 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2586 0.776
h = 0.001 0.001
y[1] (numeric) = 0.390637722565 -0.608932902919
y[1] (closed_form) = 0.390605606073 -0.608819522913
absolute error = 0.0001178
relative error = 0.01629 %
Correct 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) = 31.91 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2596 0.777
h = 0.001 0.003
y[1] (numeric) = 0.388651622001 -0.608820595372
y[1] (closed_form) = 0.388622176981 -0.60870721745
absolute error = 0.0001171
relative error = 0.01622 %
Correct 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) = 31.9 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2606 0.78
h = 0.0001 0.004
y[1] (numeric) = 0.384566800769 -0.610574185439
y[1] (closed_form) = 0.38453190629 -0.610461021876
absolute error = 0.0001184
relative error = 0.01641 %
Correct 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) = 31.9 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2607 0.784
h = 0.003 0.006
y[1] (numeric) = 0.380244631803 -0.614210006913
y[1] (closed_form) = 0.380207499398 -0.614100927399
absolute error = 0.0001152
relative error = 0.01595 %
Correct 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) = 31.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2637 0.79
h = 0.0001 0.005
y[1] (numeric) = 0.371043101462 -0.616649589913
y[1] (closed_form) = 0.370996080266 -0.616522522589
absolute error = 0.0001355
relative error = 0.01883 %
Correct 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) = 31.88 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2638 0.795
h = 0.0001 0.003
y[1] (numeric) = 0.365557657097 -0.621220682864
y[1] (closed_form) = 0.365519001344 -0.621104085762
absolute error = 0.0001228
relative error = 0.01704 %
Correct 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) = 31.87 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2639 0.798
h = 0.001 0.001
y[1] (numeric) = 0.362208898105 -0.623934557193
y[1] (closed_form) = 0.362175217003 -0.623816253217
absolute error = 0.000123
relative error = 0.01705 %
Correct 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) = 31.87 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2649 0.799
h = 0.001 0.003
y[1] (numeric) = 0.360178794258 -0.623788197383
y[1] (closed_form) = 0.360147834175 -0.623669889422
absolute error = 0.0001223
relative error = 0.01698 %
Correct 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) = 31.87 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2659 0.802
h = 0.0001 0.004
y[1] (numeric) = 0.355971890424 -0.625517540551
y[1] (closed_form) = 0.355935380349 -0.625399463249
absolute error = 0.0001236
relative error = 0.01718 %
Correct 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) = 31.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.266 0.806
h = 0.003 0.006
y[1] (numeric) = 0.351492510009 -0.629169305562
y[1] (closed_form) = 0.351453729475 -0.629055393061
absolute error = 0.0001203
relative error = 0.0167 %
Correct 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) = 31.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.269 0.812
h = 0.0001 0.005
y[1] (numeric) = 0.342040034471 -0.631521236014
y[1] (closed_form) = 0.34199114279 -0.631389022324
absolute error = 0.000141
relative error = 0.01963 %
Correct 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) = 31.84 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2691 0.817
h = 0.0001 0.003
y[1] (numeric) = 0.336356228157 -0.636113461246
y[1] (closed_form) = 0.33631587894 -0.635991895653
absolute error = 0.0001281
relative error = 0.0178 %
Correct 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) = 31.84 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2692 0.82
h = 0.001 0.001
y[1] (numeric) = 0.332887906433 -0.638838740038
y[1] (closed_form) = 0.332852621285 -0.638715425805
absolute error = 0.0001283
relative error = 0.01781 %
Correct 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) = 31.83 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=465.5MB, alloc=52.3MB, time=5.49
x[1] = 0.2702 0.821
h = 0.001 0.003
y[1] (numeric) = 0.330812907868 -0.638657787779
y[1] (closed_form) = 0.330780394526 -0.638534464127
absolute error = 0.0001275
relative error = 0.01774 %
Correct 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) = 31.83 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2712 0.824
h = 0.0001 0.004
y[1] (numeric) = 0.326481600094 -0.640362691371
y[1] (closed_form) = 0.326443433644 -0.640239613488
absolute error = 0.0001289
relative error = 0.01793 %
Correct 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) = 31.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2713 0.828
h = 0.003 0.006
y[1] (numeric) = 0.321842114323 -0.644031020172
y[1] (closed_form) = 0.321801642874 -0.643912189209
absolute error = 0.0001255
relative error = 0.01744 %
Correct 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) = 31.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2743 0.834
h = 0.0001 0.005
y[1] (numeric) = 0.312133835476 -0.646294165888
y[1] (closed_form) = 0.312083030182 -0.646156709658
absolute error = 0.0001465
relative error = 0.02042 %
Correct 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) = 31.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2744 0.839
h = 0.0001 0.003
y[1] (numeric) = 0.306248004848 -0.650908291538
y[1] (closed_form) = 0.306205920452 -0.650781668126
absolute error = 0.0001334
relative error = 0.01855 %
Correct 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) = 31.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2745 0.842
h = 0.001 0.001
y[1] (numeric) = 0.302657903521 -0.653645408435
y[1] (closed_form) = 0.302620975329 -0.653516995001
absolute error = 0.0001336
relative error = 0.01855 %
Correct 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) = 31.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2755 0.843
h = 0.001 0.003
y[1] (numeric) = 0.3005371064 -0.653429297301
y[1] (closed_form) = 0.300503002066 -0.653300869654
absolute error = 0.0001329
relative error = 0.01848 %
Correct 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) = 31.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2765 0.846
h = 0.0001 0.004
y[1] (numeric) = 0.296079022331 -0.655109528483
y[1] (closed_form) = 0.296039159139 -0.654981360511
absolute error = 0.0001342
relative error = 0.01867 %
Correct 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) = 31.78 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2766 0.85
h = 0.003 0.006
y[1] (numeric) = 0.291276460436 -0.658795011537
y[1] (closed_form) = 0.291234255664 -0.658671174004
absolute error = 0.0001308
relative error = 0.01817 %
Correct 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) = 31.78 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2796 0.856
h = 0.0001 0.005
y[1] (numeric) = 0.28130742425 -0.660968140196
y[1] (closed_form) = 0.281254662567 -0.660825342414
absolute error = 0.0001522
relative error = 0.0212 %
Correct 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) = 31.76 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2797 0.861
h = 0.0001 0.003
y[1] (numeric) = 0.275215809728 -0.665604897269
y[1] (closed_form) = 0.275171948826 -0.665473123998
absolute error = 0.0001389
relative error = 0.01929 %
Correct 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) = 31.75 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2798 0.864
h = 0.001 0.001
y[1] (numeric) = 0.271501653646 -0.668354262909
y[1] (closed_form) = 0.271463043849 -0.668220658622
absolute error = 0.0001391
relative error = 0.01928 %
Correct 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) = 31.75 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2808 0.865
h = 0.0001 0.004
y[1] (numeric) = 0.269334141448 -0.668102399763
y[1] (closed_form) = 0.269298408855 -0.667968777122
absolute error = 0.0001383
relative error = 0.01921 %
Correct 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) = 31.75 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2809 0.869
h = 0.003 0.006
y[1] (numeric) = 0.264395982378 -0.671802590126
y[1] (closed_form) = 0.264350877416 -0.671675871873
absolute error = 0.0001345
relative error = 0.01863 %
Correct 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) = 31.74 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2839 0.875
h = 0.0001 0.005
y[1] (numeric) = 0.25419735907 -0.673900358832
y[1] (closed_form) = 0.254141500705 -0.673754385768
absolute error = 0.0001563
relative error = 0.0217 %
Correct 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) = 31.72 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.284 0.88
h = 0.0001 0.003
y[1] (numeric) = 0.24792580718 -0.678559666979
y[1] (closed_form) = 0.247879008022 -0.678424886945
absolute error = 0.0001427
relative error = 0.01975 %
Correct 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) = 31.72 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2841 0.883
h = 0.001 0.001
y[1] (numeric) = 0.244103153812 -0.681321402665
y[1] (closed_form) = 0.244061689224 -0.681184755464
absolute error = 0.0001428
relative error = 0.01973 %
Correct 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) = 31.71 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2851 0.884
h = 0.001 0.003
y[1] (numeric) = 0.241894251025 -0.681038841225
y[1] (closed_form) = 0.241855710572 -0.68090217198
absolute error = 0.000142
relative error = 0.01965 %
Correct 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) = 31.71 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2861 0.887
h = 0.0001 0.004
y[1] (numeric) = 0.237193470341 -0.682673982135
y[1] (closed_form) = 0.237148967192 -0.682537596498
absolute error = 0.0001435
relative error = 0.01985 %
Correct digits = 4
memory used=509.2MB, alloc=52.3MB, time=6.00
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) = 31.7 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2862 0.891
h = 0.003 0.006
y[1] (numeric) = 0.232079505068 -0.68639488278
y[1] (closed_form) = 0.232032587749 -0.686262987309
absolute error = 0.00014
relative error = 0.01932 %
Correct 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) = 31.7 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2892 0.897
h = 0.0001 0.005
y[1] (numeric) = 0.221610626484 -0.688400130715
y[1] (closed_form) = 0.221552731815 -0.688248624622
absolute error = 0.0001622
relative error = 0.02243 %
Correct 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) = 31.68 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2893 0.902
h = 0.0001 0.003
y[1] (numeric) = 0.215126037412 -0.693083377404
y[1] (closed_form) = 0.215077384717 -0.692943269339
absolute error = 0.0001483
relative error = 0.02044 %
Correct 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) = 31.67 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2894 0.905
h = 0.001 0.001
y[1] (numeric) = 0.211174940969 -0.695858092311
y[1] (closed_form) = 0.211131723042 -0.695716076777
absolute error = 0.0001484
relative error = 0.02042 %
Correct 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) = 31.67 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2904 0.906
h = 0.001 0.003
y[1] (numeric) = 0.208917575131 -0.695538613694
y[1] (closed_form) = 0.208877337162 -0.695396573201
absolute error = 0.0001476
relative error = 0.02033 %
Correct 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) = 31.66 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2914 0.909
h = 0.0001 0.004
y[1] (numeric) = 0.204082935963 -0.697148218724
y[1] (closed_form) = 0.204036621707 -0.697006472221
absolute error = 0.0001491
relative error = 0.02053 %
Correct 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) = 31.65 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2915 0.913
h = 0.003 0.006
y[1] (numeric) = 0.198796963792 -0.700887832979
y[1] (closed_form) = 0.198748192758 -0.700750664352
absolute error = 0.0001456
relative error = 0.01999 %
Correct 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) = 31.65 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2945 0.919
h = 0.0001 0.005
y[1] (numeric) = 0.188052589272 -0.702799032852
y[1] (closed_form) = 0.187992616511 -0.702641886291
absolute error = 0.0001682
relative error = 0.02313 %
Correct 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) = 31.63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2946 0.924
h = 0.0001 0.003
y[1] (numeric) = 0.181350914331 -0.707506840962
y[1] (closed_form) = 0.181300367864 -0.707361304779
absolute error = 0.0001541
relative error = 0.0211 %
Correct 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) = 31.62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2947 0.927
h = 0.001 0.001
y[1] (numeric) = 0.177268926304 -0.71029487868
y[1] (closed_form) = 0.177223917729 -0.710147395124
absolute error = 0.0001542
relative error = 0.02107 %
Correct 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) = 31.62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2957 0.928
h = 0.001 0.003
y[1] (numeric) = 0.174962142739 -0.70993781077
y[1] (closed_form) = 0.174920171307 -0.709790300024
absolute error = 0.0001534
relative error = 0.02098 %
Correct 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) = 31.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2967 0.931
h = 0.0001 0.004
y[1] (numeric) = 0.169991065477 -0.711521486251
y[1] (closed_form) = 0.169942901328 -0.711374278594
absolute error = 0.0001549
relative error = 0.02118 %
Correct 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) = 31.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2968 0.935
h = 0.003 0.006
y[1] (numeric) = 0.164529804267 -0.71528028631
y[1] (closed_form) = 0.164479138546 -0.715137745752
absolute error = 0.0001513
relative error = 0.02062 %
Correct 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) = 31.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2998 0.941
h = 0.0001 0.005
y[1] (numeric) = 0.153504589481 -0.717095803703
y[1] (closed_form) = 0.153442497207 -0.716932906179
absolute error = 0.0001743
relative error = 0.02378 %
Correct 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) = 31.58 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2999 0.946
h = 0.0001 0.003
y[1] (numeric) = 0.146581675279 -0.721828756681
y[1] (closed_form) = 0.146529195211 -0.721677689375
absolute error = 0.0001599
relative error = 0.02172 %
Correct 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) = 31.57 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3 0.949
h = 0.001 0.001
y[1] (numeric) = 0.142366284378 -0.724630436347
y[1] (closed_form) = 0.142319448303 -0.724477382171
absolute error = 0.0001601
relative error = 0.02168 %
Correct 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) = 31.57 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.301 0.95
h = 0.001 0.003
y[1] (numeric) = 0.140009114646 -0.724235078367
y[1] (closed_form) = 0.139965374291 -0.724081995464
absolute error = 0.0001592
relative error = 0.02159 %
Correct 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) = 31.56 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.302 0.953
h = 0.0001 0.004
y[1] (numeric) = 0.13489896352 -0.72579238699
y[1] (closed_form) = 0.134848911125 -0.725639614969
absolute error = 0.0001608
relative error = 0.02178 %
Correct 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) = 31.55 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3021 0.957
h = 0.003 0.006
y[1] (numeric) = 0.12925904674 -0.729570812912
y[1] (closed_form) = 0.129206445749 -0.729422798757
absolute error = 0.0001571
relative error = 0.02121 %
Correct digits = 4
memory used=553.0MB, alloc=52.3MB, time=6.52
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) = 31.55 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3051 0.963
h = 0.0001 0.005
y[1] (numeric) = 0.117947541631 -0.731288904285
y[1] (closed_form) = 0.117883288799 -0.731120142185
absolute error = 0.0001806
relative error = 0.02438 %
Correct 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) = 31.53 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3052 0.968
h = 0.0001 0.003
y[1] (numeric) = 0.110799128045 -0.736047545446
y[1] (closed_form) = 0.110744674954 -0.735890841042
absolute error = 0.0001659
relative error = 0.02229 %
Correct 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) = 31.52 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3053 0.971
h = 0.001 0.001
y[1] (numeric) = 0.106447758975 -0.738863161307
y[1] (closed_form) = 0.106399059015 -0.738704430943
absolute error = 0.000166
relative error = 0.02225 %
Correct 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) = 31.51 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3063 0.972
h = 0.0001 0.004
y[1] (numeric) = 0.104039220593 -0.738428783269
y[1] (closed_form) = 0.103993676348 -0.738270023353
absolute error = 0.0001652
relative error = 0.02215 %
Correct 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) = 31.51 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3064 0.976
h = 0.003 0.006
y[1] (numeric) = 0.0982506699946 -0.742223849535
y[1] (closed_form) = 0.0981948678629 -0.742072692155
absolute error = 0.0001611
relative error = 0.02153 %
Correct 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) = 31.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3094 0.982
h = 0.0001 0.005
y[1] (numeric) = 0.0866870983344 -0.743860099457
y[1] (closed_form) = 0.0866194452075 -0.743687850539
absolute error = 0.0001851
relative error = 0.02472 %
Correct 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) = 31.48 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3095 0.987
h = 0.0001 0.003
y[1] (numeric) = 0.0793414020327 -0.748644013255
y[1] (closed_form) = 0.0792837142306 -0.748484021804
absolute error = 0.0001701
relative error = 0.0226 %
Correct 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) = 31.47 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3096 0.99
h = 0.001 0.001
y[1] (numeric) = 0.074871045784 -0.751473503932
y[1] (closed_form) = 0.0748192070735 -0.751311451858
absolute error = 0.0001701
relative error = 0.02253 %
Correct 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) = 31.46 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3106 0.991
h = 0.001 0.003
y[1] (numeric) = 0.0724170161144 -0.751005559556
y[1] (closed_form) = 0.0723683859202 -0.750843477058
absolute error = 0.0001692
relative error = 0.02243 %
Correct 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) = 31.46 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3116 0.994
h = 0.0001 0.004
y[1] (numeric) = 0.0670405403719 -0.752514222269
y[1] (closed_form) = 0.0669853682617 -0.752352463097
absolute error = 0.0001709
relative error = 0.02263 %
Correct 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) = 31.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3117 0.998
h = 0.003 0.006
y[1] (numeric) = 0.061059175832 -0.756332452929
y[1] (closed_form) = 0.0610013626725 -0.756175625362
absolute error = 0.0001671
relative error = 0.02203 %
Correct 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) = 31.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3147 1.004
h = 0.0001 0.005
y[1] (numeric) = 0.0491988600965 -0.757867802941
y[1] (closed_form) = 0.0491289696166 -0.757689470017
absolute error = 0.0001915
relative error = 0.02523 %
Correct 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) = 31.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3148 1.009
h = 0.0001 0.003
y[1] (numeric) = 0.0416194514365 -0.762678360349
y[1] (closed_form) = 0.0415597170176 -0.76251252695
absolute error = 0.0001763
relative error = 0.02308 %
Correct 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) = 31.41 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3149 1.012
h = 0.001 0.001
y[1] (numeric) = 0.03700815316 -0.765522299409
y[1] (closed_form) = 0.036954382784 -0.765354367045
absolute error = 0.0001763
relative error = 0.02301 %
Correct 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) = 31.4 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3159 1.013
h = 0.001 0.003
y[1] (numeric) = 0.0345008787999 -0.765013909077
y[1] (closed_form) = 0.034450379657 -0.7648459468
absolute error = 0.0001754
relative error = 0.02291 %
Correct 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) = 31.4 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3169 1.016
h = 0.0001 0.004
y[1] (numeric) = 0.0289774618192 -0.766494739206
y[1] (closed_form) = 0.0289202928264 -0.76632710421
absolute error = 0.0001771
relative error = 0.0231 %
Correct 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) = 31.39 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.317 1.02
h = 0.003 0.006
y[1] (numeric) = 0.0228073339225 -0.770333715436
y[1] (closed_form) = 0.0227474702595 -0.770171107429
absolute error = 0.0001733
relative error = 0.02249 %
Correct 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) = 31.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.32 1.026
h = 0.0001 0.005
y[1] (numeric) = 0.0106445086525 -0.771766099503
y[1] (closed_form) = 0.0105723408531 -0.771581559697
absolute error = 0.0001981
relative error = 0.02568 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.458
Order of pole (three term test) = 31.36 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=596.7MB, alloc=52.3MB, time=7.04
x[1] = 0.3201 1.031
h = 0.0001 0.003
y[1] (numeric) = 0.00282681010195 -0.77660372611
y[1] (closed_form) = 0.00276499081491 -0.776431935957
absolute error = 0.0001826
relative error = 0.02351 %
Correct 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) = 31.35 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3202 1.034
h = 0.001 0.001
y[1] (numeric) = -0.0019281958554 -0.779462334734
y[1] (closed_form) = -0.00198393293954 -0.779288407707
absolute error = 0.0001826
relative error = 0.02344 %
Correct 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) = 31.34 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3212 1.035
h = 0.001 0.003
y[1] (numeric) = -0.00448973946378 -0.778912681917
y[1] (closed_form) = -0.00454214109961 -0.778738726239
absolute error = 0.0001817
relative error = 0.02333 %
Correct 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) = 31.33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3222 1.038
h = 0.0001 0.004
y[1] (numeric) = -0.0101629612903 -0.780365066449
y[1] (closed_form) = -0.0102221638272 -0.780191440599
absolute error = 0.0001834
relative error = 0.02351 %
Correct 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) = 31.32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3223 1.042
h = 0.003 0.006
y[1] (numeric) = -0.0165255609631 -0.784225099543
y[1] (closed_form) = -0.0165875141918 -0.784056597728
absolute error = 0.0001795
relative error = 0.02289 %
Correct 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) = 31.31 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3253 1.048
h = 0.0001 0.005
y[1] (numeric) = -0.028996775134 -0.785552334136
y[1] (closed_form) = -0.0290712598102 -0.785361461212
absolute error = 0.0002049
relative error = 0.02607 %
Correct 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) = 31.29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3254 1.053
h = 0.0001 0.003
y[1] (numeric) = -0.0370574560624 -0.7904174123
y[1] (closed_form) = -0.0371213980301 -0.790239547382
absolute error = 0.000189
relative error = 0.02389 %
Correct 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) = 31.28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3255 1.056
h = 0.001 0.001
y[1] (numeric) = -0.0419590042943 -0.793290884841
y[1] (closed_form) = -0.0420167426277 -0.793110845585
absolute error = 0.0001891
relative error = 0.02381 %
Correct 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) = 31.27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3265 1.057
h = 0.001 0.003
y[1] (numeric) = -0.0445758568283 -0.792699121543
y[1] (closed_form) = -0.0446301939709 -0.792519055662
absolute error = 0.0001881
relative error = 0.0237 %
Correct 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) = 31.27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3275 1.06
h = 0.0001 0.004
y[1] (numeric) = -0.0504018087736 -0.794122399556
y[1] (closed_form) = -0.050463081046 -0.793942664615
absolute error = 0.0001899
relative error = 0.02387 %
Correct 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) = 31.26 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3276 1.064
h = 0.003 0.006
y[1] (numeric) = -0.0569606813047 -0.79800376552
y[1] (closed_form) = -0.0570247627398 -0.797829253356
absolute error = 0.0001859
relative error = 0.02324 %
Correct 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) = 31.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3306 1.07
h = 0.0001 0.005
y[1] (numeric) = -0.069746279822 -0.799223547247
y[1] (closed_form) = -0.0698231205115 -0.799026211541
absolute error = 0.0002118
relative error = 0.0264 %
Correct 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) = 31.22 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3307 1.075
h = 0.0001 0.003
y[1] (numeric) = -0.0780547527987 -0.804116415175
y[1] (closed_form) = -0.0781208548107 -0.803932354218
absolute error = 0.0001956
relative error = 0.02421 %
Correct 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) = 31.21 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3308 1.078
h = 0.001 0.001
y[1] (numeric) = -0.0831057481775 -0.807004918586
y[1] (closed_form) = -0.0831655217883 -0.806818646283
absolute error = 0.0001956
relative error = 0.02412 %
Correct 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) = 31.2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3318 1.079
h = 0.0001 0.004
y[1] (numeric) = -0.0857789647102 -0.806370164713
y[1] (closed_form) = -0.0858352698307 -0.806183868591
absolute error = 0.0001946
relative error = 0.02401 %
Correct 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) = 31.19 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3319 1.083
h = 0.003 0.006
y[1] (numeric) = -0.0925012048074 -0.810269471317
y[1] (closed_form) = -0.0925688057413 -0.810091501954
absolute error = 0.0001904
relative error = 0.02335 %
Correct 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) = 31.18 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3349 1.089
h = 0.0001 0.005
y[1] (numeric) = -0.105563625718 -0.811398667712
y[1] (closed_form) = -0.105644187998 -0.811197477385
absolute error = 0.0002167
relative error = 0.02649 %
Correct 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) = 31.16 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.335 1.094
h = 0.0001 0.003
y[1] (numeric) = -0.114088996756 -0.816318724428
y[1] (closed_form) = -0.114158646918 -0.816131042934
absolute error = 0.0002002
relative error = 0.02429 %
Correct 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) = 31.15 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3351 1.097
h = 0.001 0.001
y[1] (numeric) = -0.119270830831 -0.819222106873
y[1] (closed_form) = -0.119334042909 -0.819032181011
absolute error = 0.0002002
relative error = 0.02418 %
Correct 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) = 31.14 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=640.5MB, alloc=52.3MB, time=7.55
x[1] = 0.3361 1.098
h = 0.001 0.003
y[1] (numeric) = -0.121993947426 -0.818550307207
y[1] (closed_form) = -0.122053631768 -0.818360359752
absolute error = 0.0001991
relative error = 0.02406 %
Correct 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) = 31.13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3371 1.101
h = 0.0001 0.004
y[1] (numeric) = -0.128112463951 -0.819919402053
y[1] (closed_form) = -0.128179341889 -0.819729785372
absolute error = 0.0002011
relative error = 0.02423 %
Correct 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) = 31.12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3372 1.105
h = 0.003 0.006
y[1] (numeric) = -0.135046735909 -0.823843523397
y[1] (closed_form) = -0.135116537274 -0.823659318614
absolute error = 0.000197
relative error = 0.0236 %
Correct 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) = 31.11 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3402 1.111
h = 0.0001 0.005
y[1] (numeric) = -0.148435044705 -0.824860728173
y[1] (closed_form) = -0.148518036304 -0.824652824886
absolute error = 0.0002239
relative error = 0.02672 %
Correct 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) = 31.08 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3403 1.116
h = 0.0001 0.003
y[1] (numeric) = -0.157217474427 -0.829809143809
y[1] (closed_form) = -0.157289354463 -0.829615032136
absolute error = 0.000207
relative error = 0.02451 %
Correct 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) = 31.07 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3404 1.119
h = 0.001 0.001
y[1] (numeric) = -0.162554351486 -0.832727829424
y[1] (closed_form) = -0.162619662284 -0.832531437213
absolute error = 0.000207
relative error = 0.0244 %
Correct 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) = 31.06 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3414 1.12
h = 0.001 0.003
y[1] (numeric) = -0.165335848661 -0.832011326883
y[1] (closed_form) = -0.165397561437 -0.831814917366
absolute error = 0.0002059
relative error = 0.02428 %
Correct 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) = 31.05 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3424 1.123
h = 0.0001 0.004
y[1] (numeric) = -0.171615824868 -0.833349188382
y[1] (closed_form) = -0.17168487492 -0.83315310651
absolute error = 0.0002079
relative error = 0.02444 %
Correct 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) = 31.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3425 1.127
h = 0.003 0.006
y[1] (numeric) = -0.178757769828 -0.837295279497
y[1] (closed_form) = -0.178829809043 -0.837104713316
absolute error = 0.0002037
relative error = 0.0238 %
Correct 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) = 31.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3455 1.133
h = 0.0001 0.005
y[1] (numeric) = -0.192478307775 -0.838197834029
y[1] (closed_form) = -0.192563766597 -0.837983077925
absolute error = 0.0002311
relative error = 0.02688 %
Correct 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) = 31 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3456 1.138
h = 0.0001 0.003
y[1] (numeric) = -0.201522954348 -0.843174816463
y[1] (closed_form) = -0.201597100314 -0.842974143632
absolute error = 0.0002139
relative error = 0.02468 %
Correct 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) = 30.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3457 1.141
h = 0.001 0.001
y[1] (numeric) = -0.207017988285 -0.846108891288
y[1] (closed_form) = -0.207085430331 -0.845905902243
absolute error = 0.0002139
relative error = 0.02456 %
Correct 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) = 30.98 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3467 1.142
h = 0.001 0.003
y[1] (numeric) = -0.209858967088 -0.845346710509
y[1] (closed_form) = -0.20992273918 -0.845143709276
absolute error = 0.0002128
relative error = 0.02443 %
Correct 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) = 30.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3477 1.145
h = 0.0001 0.004
y[1] (numeric) = -0.216303578174 -0.846652484021
y[1] (closed_form) = -0.216374834645 -0.84644980574
absolute error = 0.0002148
relative error = 0.02459 %
Correct 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) = 30.96 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3478 1.149
h = 0.003 0.006
y[1] (numeric) = -0.223657372609 -0.850620678391
y[1] (closed_form) = -0.223731686628 -0.850423621414
absolute error = 0.0002106
relative error = 0.02395 %
Correct 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) = 30.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3508 1.155
h = 0.0001 0.005
y[1] (numeric) = -0.237716605705 -0.851405794301
y[1] (closed_form) = -0.237804569181 -0.851184041823
absolute error = 0.0002386
relative error = 0.02699 %
Correct 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) = 30.92 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3509 1.16
h = 0.0001 0.003
y[1] (numeric) = -0.24702875351 -0.856411503281
y[1] (closed_form) = -0.247105200964 -0.856204134795
absolute error = 0.000221
relative error = 0.0248 %
Correct 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) = 30.9 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.351 1.163
h = 0.001 0.001
y[1] (numeric) = -0.252685133914 -0.85936102349
y[1] (closed_form) = -0.252754739169 -0.859151303619
absolute error = 0.000221
relative error = 0.02467 %
Correct 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) = 30.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.352 1.164
h = 0.001 0.003
y[1] (numeric) = -0.255586711858 -0.85855215441
y[1] (closed_form) = -0.255652573553 -0.85834242832
absolute error = 0.0002198
relative error = 0.02454 %
Correct 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) = 30.89 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=684.3MB, alloc=52.3MB, time=8.06
x[1] = 0.353 1.167
h = 0.0001 0.004
y[1] (numeric) = -0.262199200597 -0.859824932268
y[1] (closed_form) = -0.262272697261 -0.859615522841
absolute error = 0.0002219
relative error = 0.02469 %
Correct 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) = 30.87 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3531 1.171
h = 0.003 0.006
y[1] (numeric) = -0.269769122724 -0.863815324049
y[1] (closed_form) = -0.269845748025 -0.863611643388
absolute error = 0.0002176
relative error = 0.02405 %
Correct 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) = 30.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3561 1.177
h = 0.0001 0.005
y[1] (numeric) = -0.284173643995 -0.864480080428
y[1] (closed_form) = -0.284264149069 -0.864251184245
absolute error = 0.0002461
relative error = 0.02705 %
Correct 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) = 30.83 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3562 1.182
h = 0.0001 0.003
y[1] (numeric) = -0.293758706074 -0.869514626412
y[1] (closed_form) = -0.293837490061 -0.869300424184
absolute error = 0.0002282
relative error = 0.02487 %
Correct 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) = 30.81 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3563 1.185
h = 0.001 0.001
y[1] (numeric) = -0.299579699698 -0.872479617589
y[1] (closed_form) = -0.299651499541 -0.87226302933
absolute error = 0.0002282
relative error = 0.02474 %
Correct 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) = 30.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3573 1.186
h = 0.0001 0.004
y[1] (numeric) = -0.302543011035 -0.871623014728
y[1] (closed_form) = -0.302610992002 -0.871406427087
absolute error = 0.000227
relative error = 0.02461 %
Correct 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) = 30.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3574 1.19
h = 0.003 0.006
y[1] (numeric) = -0.310292897902 -0.875631948208
y[1] (closed_form) = -0.310373380192 -0.875424439776
absolute error = 0.0002226
relative error = 0.02396 %
Correct 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) = 30.78 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3604 1.196
h = 0.0001 0.005
y[1] (numeric) = -0.325001493535 -0.876194883171
y[1] (closed_form) = -0.325096060637 -0.875961702564
absolute error = 0.0002516
relative error = 0.02693 %
Correct 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) = 30.75 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3605 1.201
h = 0.0001 0.003
y[1] (numeric) = -0.334825561453 -0.88125764215
y[1] (closed_form) = -0.334908225578 -0.881039427376
absolute error = 0.0002333
relative error = 0.02476 %
Correct 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) = 30.73 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3606 1.204
h = 0.001 0.001
y[1] (numeric) = -0.340790740474 -0.88423796209
y[1] (closed_form) = -0.340866295683 -0.884017330144
absolute error = 0.0002332
relative error = 0.02461 %
Correct 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) = 30.72 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3616 1.205
h = 0.001 0.003
y[1] (numeric) = -0.343808697344 -0.883340160869
y[1] (closed_form) = -0.34388036736 -0.883119535215
absolute error = 0.000232
relative error = 0.02448 %
Correct 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) = 30.71 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3626 1.208
h = 0.0001 0.004
y[1] (numeric) = -0.350742855865 -0.884551033402
y[1] (closed_form) = -0.350822450698 -0.884330710218
absolute error = 0.0002343
relative error = 0.02462 %
Correct 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) = 30.7 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3627 1.212
h = 0.003 0.006
y[1] (numeric) = -0.358726419383 -0.888585540975
y[1] (closed_form) = -0.358809281199 -0.888371152479
absolute error = 0.0002298
relative error = 0.02399 %
Correct 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) = 30.68 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3657 1.218
h = 0.0001 0.005
y[1] (numeric) = -0.373792956013 -0.889022400857
y[1] (closed_form) = -0.373890133952 -0.888781792516
absolute error = 0.0002595
relative error = 0.02691 %
Correct 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) = 30.65 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3658 1.223
h = 0.0001 0.003
y[1] (numeric) = -0.383900361746 -0.894114135219
y[1] (closed_form) = -0.383985427946 -0.893888820358
absolute error = 0.0002408
relative error = 0.02476 %
Correct 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) = 30.63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3659 1.226
h = 0.001 0.001
y[1] (numeric) = -0.39003644376 -0.897109930888
y[1] (closed_form) = -0.390114252071 -0.896882165185
absolute error = 0.0002407
relative error = 0.02461 %
Correct 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) = 30.62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3669 1.227
h = 0.001 0.003
y[1] (numeric) = -0.393118303578 -0.89616236766
y[1] (closed_form) = -0.393192148104 -0.895934616741
absolute error = 0.0002394
relative error = 0.02447 %
Correct 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) = 30.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3679 1.23
h = 0.0001 0.004
y[1] (numeric) = -0.400230014208 -0.897337385903
y[1] (closed_form) = -0.400311944515 -0.897109926421
absolute error = 0.0002418
relative error = 0.02461 %
Correct 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) = 30.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.368 1.234
h = 0.003 0.006
y[1] (numeric) = -0.408442524591 -0.901394189539
y[1] (closed_form) = -0.408527801007 -0.901172777714
absolute error = 0.0002373
relative error = 0.02398 %
Correct 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) = 30.58 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=727.9MB, alloc=52.3MB, time=8.56
x[1] = 0.371 1.24
h = 0.0001 0.005
y[1] (numeric) = -0.423873973278 -0.901701659729
y[1] (closed_form) = -0.423973797542 -0.901453465098
absolute error = 0.0002675
relative error = 0.02685 %
Correct 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) = 30.55 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3711 1.245
h = 0.0001 0.003
y[1] (numeric) = -0.434270512505 -0.906822333686
y[1] (closed_form) = -0.434358014313 -0.906589769978
absolute error = 0.0002485
relative error = 0.02472 %
Correct 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) = 30.53 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3712 1.248
h = 0.001 0.001
y[1] (numeric) = -0.440580993765 -0.909833539892
y[1] (closed_form) = -0.440661084831 -0.909598492247
absolute error = 0.0002483
relative error = 0.02457 %
Correct 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) = 30.52 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3722 1.249
h = 0.001 0.003
y[1] (numeric) = -0.443727940632 -0.908835063898
y[1] (closed_form) = -0.443803987516 -0.90860004046
absolute error = 0.000247
relative error = 0.02443 %
Correct 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) = 30.51 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3732 1.252
h = 0.0001 0.004
y[1] (numeric) = -0.451020719798 -0.909973104991
y[1] (closed_form) = -0.45110501718 -0.909738360205
absolute error = 0.0002494
relative error = 0.02456 %
Correct 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) = 30.49 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3733 1.256
h = 0.003 0.006
y[1] (numeric) = -0.459466867433 -0.914052138977
y[1] (closed_form) = -0.459554592989 -0.913823556792
absolute error = 0.0002448
relative error = 0.02394 %
Correct 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) = 30.48 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3763 1.262
h = 0.0001 0.005
y[1] (numeric) = -0.475270335435 -0.914226760772
y[1] (closed_form) = -0.475372840949 -0.913970817215
absolute error = 0.0002757
relative error = 0.02676 %
Correct 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) = 30.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3764 1.267
h = 0.0001 0.003
y[1] (numeric) = -0.485961942407 -0.919376284298
y[1] (closed_form) = -0.486051912776 -0.919136319109
absolute error = 0.0002563
relative error = 0.02465 %
Correct 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) = 30.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3765 1.27
h = 0.001 0.001
y[1] (numeric) = -0.492450402271 -0.922402802203
y[1] (closed_form) = -0.492532805086 -0.922160320577
absolute error = 0.0002561
relative error = 0.0245 %
Correct 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) = 30.41 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3775 1.271
h = 0.001 0.003
y[1] (numeric) = -0.495663638091 -0.92135222429
y[1] (closed_form) = -0.495741914489 -0.921109777249
absolute error = 0.0002548
relative error = 0.02436 %
Correct 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) = 30.4 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3785 1.274
h = 0.0001 0.004
y[1] (numeric) = -0.503141076147 -0.922452106287
y[1] (closed_form) = -0.503227771589 -0.922209923315
absolute error = 0.0002572
relative error = 0.02448 %
Correct 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) = 30.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3786 1.278
h = 0.003 0.006
y[1] (numeric) = -0.511825663129 -0.926553260556
y[1] (closed_form) = -0.511915871809 -0.926317357141
absolute error = 0.0002526
relative error = 0.02386 %
Correct 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) = 30.36 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3816 1.284
h = 0.0001 0.005
y[1] (numeric) = -0.528008396332 -0.926591427921
y[1] (closed_form) = -0.528113617436 -0.926327568646
absolute error = 0.0002841
relative error = 0.02664 %
Correct 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) = 30.32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3817 1.289
h = 0.0001 0.003
y[1] (numeric) = -0.539001146556 -0.931769655329
y[1] (closed_form) = -0.539093617838 -0.931522132076
absolute error = 0.0002642
relative error = 0.02455 %
Correct 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) = 30.3 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3818 1.292
h = 0.001 0.001
y[1] (numeric) = -0.545671249099 -0.934811351567
y[1] (closed_form) = -0.545755991978 -0.934561279995
absolute error = 0.000264
relative error = 0.0244 %
Correct 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) = 30.29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3828 1.293
h = 0.0001 0.004
y[1] (numeric) = -0.548951993845 -0.93370744337
y[1] (closed_form) = -0.5490325262 -0.933457417738
absolute error = 0.0002627
relative error = 0.02426 %
Correct 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) = 30.28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3829 1.297
h = 0.003 0.006
y[1] (numeric) = -0.557835188802 -0.937826956924
y[1] (closed_form) = -0.557929612713 -0.937586792717
absolute error = 0.0002581
relative error = 0.02365 %
Correct 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) = 30.26 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3859 1.303
h = 0.0001 0.005
y[1] (numeric) = -0.574351977518 -0.937749304185
y[1] (closed_form) = -0.574461621561 -0.937480662181
absolute error = 0.0002902
relative error = 0.02639 %
Correct 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) = 30.22 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.386 1.308
h = 0.0001 0.003
y[1] (numeric) = -0.58560857829 -0.942955767062
y[1] (closed_form) = -0.58570528169 -0.942703774681
absolute error = 0.0002699
relative error = 0.02432 %
Correct 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) = 30.2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=771.6MB, alloc=52.3MB, time=9.07
x[1] = 0.3861 1.311
h = 0.001 0.001
y[1] (numeric) = -0.592437854795 -0.946012619198
y[1] (closed_form) = -0.592526688414 -0.945758049586
absolute error = 0.0002696
relative error = 0.02416 %
Correct 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) = 30.19 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3871 1.312
h = 0.001 0.003
y[1] (numeric) = -0.59577835582 -0.944862616147
y[1] (closed_form) = -0.595862904839 -0.944608102019
absolute error = 0.0002682
relative error = 0.02401 %
Correct 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) = 30.18 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3881 1.315
h = 0.0001 0.004
y[1] (numeric) = -0.603609706393 -0.945890443201
y[1] (closed_form) = -0.603702998741 -0.945636163183
absolute error = 0.0002709
relative error = 0.02414 %
Correct 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) = 30.16 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3882 1.319
h = 0.003 0.006
y[1] (numeric) = -0.612750887708 -0.950035289084
y[1] (closed_form) = -0.612847858339 -0.949787512815
absolute error = 0.0002661
relative error = 0.02354 %
Correct 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) = 30.14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3912 1.325
h = 0.0001 0.005
y[1] (numeric) = -0.629660849208 -0.949814158634
y[1] (closed_form) = -0.629773273213 -0.949537279586
absolute error = 0.0002988
relative error = 0.02623 %
Correct 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) = 30.1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3913 1.33
h = 0.0001 0.003
y[1] (numeric) = -0.641230287074 -0.955048977506
y[1] (closed_form) = -0.641329551892 -0.954789125276
absolute error = 0.0002782
relative error = 0.02418 %
Correct 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) = 30.07 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3914 1.333
h = 0.001 0.001
y[1] (numeric) = -0.64824825796 -0.958120710863
y[1] (closed_form) = -0.648339484412 -0.957858250681
absolute error = 0.0002779
relative error = 0.02402 %
Correct 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) = 30.06 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3924 1.334
h = 0.001 0.003
y[1] (numeric) = -0.651658602794 -0.956914999599
y[1] (closed_form) = -0.651745456945 -0.95665260812
absolute error = 0.0002764
relative error = 0.02388 %
Correct 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) = 30.05 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3934 1.337
h = 0.0001 0.004
y[1] (numeric) = -0.659685320521 -0.957900993331
y[1] (closed_form) = -0.659781097925 -0.957638816028
absolute error = 0.0002791
relative error = 0.024 %
Correct 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) = 30.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3935 1.341
h = 0.003 0.006
y[1] (numeric) = -0.669079318447 -0.962067450889
y[1] (closed_form) = -0.669178868128 -0.961811900264
absolute error = 0.0002743
relative error = 0.02341 %
Correct 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) = 30.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3965 1.347
h = 0.0001 0.005
y[1] (numeric) = -0.686390110795 -0.961698798207
y[1] (closed_form) = -0.68650534735 -0.961413502948
absolute error = 0.0003077
relative error = 0.02605 %
Correct 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) = 29.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3966 1.352
h = 0.0001 0.003
y[1] (numeric) = -0.698278881379 -0.966961661549
y[1] (closed_form) = -0.698380738174 -0.966693781136
absolute error = 0.0002866
relative error = 0.02403 %
Correct 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) = 29.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3967 1.355
h = 0.001 0.001
y[1] (numeric) = -0.705489462681 -0.970048039885
y[1] (closed_form) = -0.705583108252 -0.969777521485
absolute error = 0.0002863
relative error = 0.02387 %
Correct 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) = 29.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3977 1.356
h = 0.001 0.003
y[1] (numeric) = -0.708970924985 -0.968785275344
y[1] (closed_form) = -0.709060108577 -0.968514839917
absolute error = 0.0002848
relative error = 0.02372 %
Correct 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) = 29.91 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3987 1.359
h = 0.0001 0.004
y[1] (numeric) = -0.717196899381 -0.96972801332
y[1] (closed_form) = -0.717295190268 -0.96945777015
absolute error = 0.0002876
relative error = 0.02384 %
Correct 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) = 29.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3988 1.363
h = 0.003 0.006
y[1] (numeric) = -0.726848968547 -0.973915791288
y[1] (closed_form) = -0.726951128969 -0.973652299868
absolute error = 0.0002826
relative error = 0.02326 %
Correct 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) = 29.87 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4018 1.369
h = 0.0001 0.005
y[1] (numeric) = -0.744568398152 -0.973395411113
y[1] (closed_form) = -0.744686479164 -0.973101515985
absolute error = 0.0003167
relative error = 0.02585 %
Correct 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) = 29.83 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4019 1.374
h = 0.0001 0.003
y[1] (numeric) = -0.756783149207 -0.978685945712
y[1] (closed_form) = -0.756887627849 -0.978409864517
absolute error = 0.0002952
relative error = 0.02386 %
Correct 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) = 29.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.402 1.377
h = 0.001 0.001
y[1] (numeric) = -0.764190348192 -0.981786694542
y[1] (closed_form) = -0.764286438393 -0.981507946038
absolute error = 0.0002948
relative error = 0.0237 %
Correct 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) = 29.78 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=815.3MB, alloc=52.3MB, time=9.59
x[1] = 0.403 1.378
h = 0.001 0.003
y[1] (numeric) = -0.767744220745 -0.980465489063
y[1] (closed_form) = -0.767835757273 -0.980186838879
absolute error = 0.0002933
relative error = 0.02356 %
Correct 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) = 29.77 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.404 1.381
h = 0.0001 0.004
y[1] (numeric) = -0.776173422081 -0.981363482654
y[1] (closed_form) = -0.776274254145 -0.981085000773
absolute error = 0.0002962
relative error = 0.02367 %
Correct 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) = 29.75 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4041 1.385
h = 0.003 0.006
y[1] (numeric) = -0.78608893975 -0.985572239303
y[1] (closed_form) = -0.786193741945 -0.985300636419
absolute error = 0.0002911
relative error = 0.0231 %
Correct 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) = 29.73 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4071 1.391
h = 0.0001 0.005
y[1] (numeric) = -0.804224963943 -0.984895761897
y[1] (closed_form) = -0.804345920611 -0.984593078656
absolute error = 0.000326
relative error = 0.02564 %
Correct 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) = 29.68 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4072 1.396
h = 0.0001 0.003
y[1] (numeric) = -0.816772498299 -0.990213531132
y[1] (closed_form) = -0.816879627939 -0.989929072206
absolute error = 0.000304
relative error = 0.02368 %
Correct 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) = 29.65 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4073 1.399
h = 0.001 0.001
y[1] (numeric) = -0.824380415227 -0.993328336669
y[1] (closed_form) = -0.824478974762 -0.99304118185
absolute error = 0.0003036
relative error = 0.02352 %
Correct 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) = 29.64 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4083 1.4
h = 0.003 0.006
y[1] (numeric) = -0.828008010193 -0.991947259057
y[1] (closed_form) = -0.828101922307 -0.991660219014
absolute error = 0.000302
relative error = 0.02338 %
Correct 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) = 29.63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4113 1.406
h = 0.0001 0.005
y[1] (numeric) = -0.846400127644 -0.991144869673
y[1] (closed_form) = -0.846541442652 -0.990831442192
absolute error = 0.0003438
relative error = 0.02638 %
Correct 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) = 29.57 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4114 1.411
h = 0.0001 0.003
y[1] (numeric) = -0.859181279357 -0.996472494437
y[1] (closed_form) = -0.85930862229 -0.996177585965
absolute error = 0.0003212
relative error = 0.02442 %
Correct 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) = 29.55 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4115 1.414
h = 0.001 0.001
y[1] (numeric) = -0.866930039192 -0.99959158442
y[1] (closed_form) = -0.867048683732 -0.999293965552
absolute error = 0.0003204
relative error = 0.02422 %
Correct 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) = 29.53 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4125 1.415
h = 0.001 0.003
y[1] (numeric) = -0.870607565911 -0.998166571047
y[1] (closed_form) = -0.870721497782 -0.997869081356
absolute error = 0.0003186
relative error = 0.02405 %
Correct 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) = 29.52 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4135 1.418
h = 0.0001 0.004
y[1] (numeric) = -0.879387811124 -0.998980129554
y[1] (closed_form) = -0.879511365282 -0.99868275798
absolute error = 0.000322
relative error = 0.0242 %
Correct 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) = 29.49 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4136 1.422
h = 0.003 0.006
y[1] (numeric) = -0.889761050995 -1.00321643165
y[1] (closed_form) = -0.889888756194 -1.00292615616
absolute error = 0.0003171
relative error = 0.02365 %
Correct 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) = 29.47 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4166 1.428
h = 0.0001 0.005
y[1] (numeric) = -0.908614529267 -1.00225515124
y[1] (closed_form) = -0.908758765898 -1.00193260651
absolute error = 0.0003533
relative error = 0.02612 %
Correct 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) = 29.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4167 1.433
h = 0.0001 0.003
y[1] (numeric) = -0.921740292156 -1.00760894467
y[1] (closed_form) = -0.921870328881 -1.00730534899
absolute error = 0.0003303
relative error = 0.02419 %
Correct 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) = 29.39 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4168 1.436
h = 0.001 0.001
y[1] (numeric) = -0.929696896485 -1.01074136092
y[1] (closed_form) = -0.929818045466 -1.0104350277
absolute error = 0.0003294
relative error = 0.02399 %
Correct 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) = 29.37 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4178 1.437
h = 0.001 0.003
y[1] (numeric) = -0.933450366565 -1.00925392416
y[1] (closed_form) = -0.933566705604 -1.00894773855
absolute error = 0.0003275
relative error = 0.02383 %
Correct 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) = 29.36 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4188 1.44
h = 0.0001 0.004
y[1] (numeric) = -0.942444878906 -1.01001828964
y[1] (closed_form) = -0.9425710401 -1.00971219233
absolute error = 0.0003311
relative error = 0.02397 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.633
Order of pole (three term test) = 29.33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4189 1.444
h = 0.003 0.006
y[1] (numeric) = -0.953096634131 -1.01427424497
y[1] (closed_form) = -0.953227056376 -1.01397537693
absolute error = 0.0003261
relative error = 0.02343 %
Correct 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) = 29.31 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=859.0MB, alloc=52.3MB, time=10.09
x[1] = 0.4219 1.45
h = 0.0001 0.005
y[1] (numeric) = -0.97238873972 -1.01314406364
y[1] (closed_form) = -0.972535926991 -1.01281220065
absolute error = 0.000363
relative error = 0.02585 %
Correct 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) = 29.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.422 1.455
h = 0.0001 0.003
y[1] (numeric) = -0.985866346717 -1.01852340549
y[1] (closed_form) = -0.985999104199 -1.01821093354
absolute error = 0.0003395
relative error = 0.02395 %
Correct 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) = 29.22 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4221 1.458
h = 0.001 0.001
y[1] (numeric) = -0.994035153674 -1.02166872053
y[1] (closed_form) = -0.994158829368 -1.02135348471
absolute error = 0.0003386
relative error = 0.02376 %
Correct 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) = 29.2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4231 1.459
h = 0.001 0.003
y[1] (numeric) = -0.997865931509 -1.02011730684
y[1] (closed_form) = -0.997984697832 -1.01980223828
absolute error = 0.0003367
relative error = 0.0236 %
Correct 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) = 29.19 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4241 1.462
h = 0.0001 0.004
y[1] (numeric) = -1.00707899005 -1.02083073011
y[1] (closed_form) = -1.00720778289 -1.02051571778
absolute error = 0.0003403
relative error = 0.02374 %
Correct 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) = 29.16 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4242 1.466
h = 0.003 0.006
y[1] (numeric) = -1.01801510957 -1.02510579489
y[1] (closed_form) = -1.0181482771 -1.0247981473
absolute error = 0.0003352
relative error = 0.02321 %
Correct 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) = 29.14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4272 1.472
h = 0.0001 0.005
y[1] (numeric) = -1.0377543746 -1.0238016981
y[1] (closed_form) = -1.03790454071 -1.0234603109
absolute error = 0.000373
relative error = 0.02559 %
Correct 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) = 29.08 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4273 1.477
h = 0.0001 0.003
y[1] (numeric) = -1.05159122502 -1.02920589772
y[1] (closed_form) = -1.05172672939 -1.02888435576
absolute error = 0.0003489
relative error = 0.02372 %
Correct 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) = 29.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4274 1.48
h = 0.001 0.001
y[1] (numeric) = -1.05997669249 -1.03236364045
y[1] (closed_form) = -1.06010291625 -1.03203930916
absolute error = 0.000348
relative error = 0.02352 %
Correct 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) = 29.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4284 1.481
h = 0.0001 0.004
y[1] (numeric) = -1.0638861628 -1.03074664911
y[1] (closed_form) = -1.06400737556 -1.03042250593
absolute error = 0.0003461
relative error = 0.02336 %
Correct 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) = 29.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4285 1.485
h = 0.003 0.006
y[1] (numeric) = -1.07505924505 -1.03503735437
y[1] (closed_form) = -1.07519730846 -1.03472450939
absolute error = 0.000342
relative error = 0.02292 %
Correct 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) = 28.98 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4315 1.491
h = 0.0001 0.005
y[1] (numeric) = -1.09519252333 -1.03358486929
y[1] (closed_form) = -1.09534779544 -1.03323763103
absolute error = 0.0003804
relative error = 0.02526 %
Correct 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) = 28.92 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4316 1.496
h = 0.0001 0.003
y[1] (numeric) = -1.1093443695 -1.03901425973
y[1] (closed_form) = -1.10948477297 -1.03868726485
absolute error = 0.0003559
relative error = 0.02341 %
Correct 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) = 28.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4317 1.499
h = 0.001 0.001
y[1] (numeric) = -1.11791983889 -1.04218494337
y[1] (closed_form) = -1.11805078699 -1.0418551355
absolute error = 0.0003549
relative error = 0.02322 %
Correct 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) = 28.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4327 1.5
h = 0.001 0.003
y[1] (numeric) = -1.12189897763 -1.04051114656
y[1] (closed_form) = -1.12202482518 -1.0401815445
absolute error = 0.0003528
relative error = 0.02306 %
Correct 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) = 28.85 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4337 1.503
h = 0.0001 0.004
y[1] (numeric) = -1.1315310498 -1.04112759501
y[1] (closed_form) = -1.13166731686 -1.04079798587
absolute error = 0.0003567
relative error = 0.0232 %
Correct 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) = 28.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4338 1.507
h = 0.003 0.006
y[1] (numeric) = -1.14301212372 -1.0454401303
y[1] (closed_form) = -1.1431529852 -1.04511814571
absolute error = 0.0003514
relative error = 0.02269 %
Correct 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) = 28.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4368 1.513
h = 0.0001 0.005
y[1] (numeric) = -1.16360893949 -1.04380401322
y[1] (closed_form) = -1.16376724316 -1.04344685435
absolute error = 0.0003907
relative error = 0.02499 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.84
Order of pole (three term test) = 28.73 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4369 1.518
h = 0.0001 0.003
y[1] (numeric) = -1.17813426161 -1.04925687481
y[1] (closed_form) = -1.17827746073 -1.04892043691
absolute error = 0.0003656
relative error = 0.02318 %
Correct digits = 4
memory used=902.9MB, alloc=52.3MB, time=10.60
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) = 28.69 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.437 1.521
h = 0.001 0.001
y[1] (numeric) = -1.18693496563 -1.05243904517
y[1] (closed_form) = -1.18706850136 -1.05209977044
absolute error = 0.0003646
relative error = 0.02299 %
Correct 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) = 28.67 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.438 1.522
h = 0.001 0.003
y[1] (numeric) = -1.19099544891 -1.05069657995
y[1] (closed_form) = -1.19112377826 -1.05035753422
absolute error = 0.0003625
relative error = 0.02283 %
Correct 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) = 28.66 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.439 1.525
h = 0.0001 0.004
y[1] (numeric) = -1.2008588226 -1.05125672063
y[1] (closed_form) = -1.2009977892 -1.05091762902
absolute error = 0.0003665
relative error = 0.02296 %
Correct 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) = 28.63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4391 1.529
h = 0.003 0.006
y[1] (numeric) = -1.21264175161 -1.05558656099
y[1] (closed_form) = -1.21278543707 -1.05525523624
absolute error = 0.0003611
relative error = 0.02246 %
Correct 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) = 28.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4421 1.535
h = 0.0001 0.005
y[1] (numeric) = -1.23371111385 -1.0537612624
y[1] (closed_form) = -1.23387247477 -1.05339396228
absolute error = 0.0004012
relative error = 0.02473 %
Correct 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) = 28.53 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4422 1.54
h = 0.0001 0.003
y[1] (numeric) = -1.24861780606 -1.05923669368
y[1] (closed_form) = -1.24876382445 -1.05889060508
absolute error = 0.0003756
relative error = 0.02294 %
Correct 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) = 28.49 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4423 1.543
h = 0.001 0.001
y[1] (numeric) = -1.25764849927 -1.06242974909
y[1] (closed_form) = -1.25778464121 -1.06208080079
absolute error = 0.0003746
relative error = 0.02275 %
Correct 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) = 28.47 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4433 1.544
h = 0.001 0.003
y[1] (numeric) = -1.261791772 -1.06061687406
y[1] (closed_form) = -1.26192259938 -1.06026817927
absolute error = 0.0003724
relative error = 0.0226 %
Correct 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) = 28.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4443 1.547
h = 0.0001 0.004
y[1] (numeric) = -1.27189107476 -1.06111866203
y[1] (closed_form) = -1.27203276199 -1.06076988006
absolute error = 0.0003765
relative error = 0.02273 %
Correct 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) = 28.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4444 1.551
h = 0.003 0.006
y[1] (numeric) = -1.28398224076 -1.06546503355
y[1] (closed_form) = -1.28412877527 -1.06512416318
absolute error = 0.000371
relative error = 0.02224 %
Correct 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) = 28.39 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4474 1.557
h = 0.0001 0.005
y[1] (numeric) = -1.30553332979 -1.06344480752
y[1] (closed_form) = -1.30569777268 -1.06306714017
absolute error = 0.0004119
relative error = 0.02446 %
Correct 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) = 28.32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4475 1.562
h = 0.0001 0.003
y[1] (numeric) = -1.32082946535 -1.06894182834
y[1] (closed_form) = -1.32097832568 -1.06858587632
absolute error = 0.0003858
relative error = 0.02271 %
Correct 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) = 28.28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4476 1.565
h = 0.001 0.001
y[1] (numeric) = -1.33009500974 -1.07214511848
y[1] (closed_form) = -1.33023377538 -1.07178628488
absolute error = 0.0003847
relative error = 0.02252 %
Correct 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) = 28.26 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4486 1.566
h = 0.001 0.003
y[1] (numeric) = -1.33432253812 -1.07026004082
y[1] (closed_form) = -1.33445587868 -1.0699014866
absolute error = 0.0003825
relative error = 0.02237 %
Correct 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) = 28.24 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4496 1.569
h = 0.0001 0.004
y[1] (numeric) = -1.34466249151 -1.07070134952
y[1] (closed_form) = -1.34480691942 -1.07034266424
absolute error = 0.0003867
relative error = 0.0225 %
Correct 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) = 28.21 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4497 1.573
h = 0.003 0.006
y[1] (numeric) = -1.35706842078 -1.07506341393
y[1] (closed_form) = -1.35721782845 -1.07471278748
absolute error = 0.0003811
relative error = 0.02202 %
Correct 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) = 28.17 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4527 1.579
h = 0.0001 0.005
y[1] (numeric) = -1.37911059108 -1.0728423133
y[1] (closed_form) = -1.37927813963 -1.07245404729
absolute error = 0.0004229
relative error = 0.0242 %
Correct 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) = 28.1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4528 1.584
h = 0.0001 0.003
y[1] (numeric) = -1.39480442584 -1.07835986256
y[1] (closed_form) = -1.39495614978 -1.07799382922
absolute error = 0.0003962
relative error = 0.02248 %
Correct 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) = 28.06 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4529 1.587
h = 0.001 0.001
y[1] (numeric) = -1.40430979285 -1.08157268699
y[1] (closed_form) = -1.40445119858 -1.08120375124
absolute error = 0.0003951
relative error = 0.02229 %
Correct digits = 4
memory used=946.7MB, alloc=52.3MB, time=11.11
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) = 28.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4539 1.588
h = 0.0001 0.004
y[1] (numeric) = -1.40862306468 -1.07961356132
y[1] (closed_form) = -1.40875893239 -1.0792449322
absolute error = 0.0003929
relative error = 0.02214 %
Correct 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) = 28.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.454 1.592
h = 0.003 0.006
y[1] (numeric) = -1.42129133517 -1.08398829634
y[1] (closed_form) = -1.42144606096 -1.08363182992
absolute error = 0.0003886
relative error = 0.02174 %
Correct 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) = 27.98 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.457 1.598
h = 0.0001 0.005
y[1] (numeric) = -1.44376633082 -1.08159537465
y[1] (closed_form) = -1.44393940761 -1.08120052907
absolute error = 0.0004311
relative error = 0.0239 %
Correct 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) = 27.9 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4571 1.603
h = 0.0001 0.003
y[1] (numeric) = -1.4598090191 -1.08713455547
y[1] (closed_form) = -1.45996605491 -1.08676239602
absolute error = 0.0004039
relative error = 0.02219 %
Correct 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) = 27.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4572 1.606
h = 0.001 0.001
y[1] (numeric) = -1.46952478227 -1.09035792589
y[1] (closed_form) = -1.46967130341 -1.0899828442
absolute error = 0.0004027
relative error = 0.02201 %
Correct 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) = 27.83 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4582 1.607
h = 0.001 0.003
y[1] (numeric) = -1.47391398023 -1.08833458931
y[1] (closed_form) = -1.47405486381 -1.08795983747
absolute error = 0.0004004
relative error = 0.02185 %
Correct 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) = 27.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4592 1.61
h = 0.0001 0.004
y[1] (numeric) = -1.48471540769 -1.08866041594
y[1] (closed_form) = -1.48486781602 -1.08828544717
absolute error = 0.0004048
relative error = 0.02199 %
Correct 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) = 27.78 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4593 1.614
h = 0.003 0.006
y[1] (numeric) = -1.49772475386 -1.09305316163
y[1] (closed_form) = -1.49788239775 -1.09268653404
absolute error = 0.0003991
relative error = 0.02152 %
Correct 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) = 27.74 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4623 1.62
h = 0.0001 0.005
y[1] (numeric) = -1.52070878746 -1.09044786311
y[1] (closed_form) = -1.52088501409 -1.09004197362
absolute error = 0.0004425
relative error = 0.02365 %
Correct 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) = 27.66 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4624 1.625
h = 0.0001 0.003
y[1] (numeric) = -1.53716505028 -1.09600547768
y[1] (closed_form) = -1.53732498993 -1.0956228176
absolute error = 0.0004147
relative error = 0.02197 %
Correct 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) = 27.62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4625 1.628
h = 0.001 0.001
y[1] (numeric) = -1.54713019514 -1.09923700297
y[1] (closed_form) = -1.54727938649 -1.09885140181
absolute error = 0.0004135
relative error = 0.02179 %
Correct 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) = 27.59 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4635 1.629
h = 0.001 0.003
y[1] (numeric) = -1.55160798676 -1.09713605889
y[1] (closed_form) = -1.551751423 -1.0967508175
absolute error = 0.0004111
relative error = 0.02163 %
Correct 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) = 27.57 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4645 1.632
h = 0.0001 0.004
y[1] (numeric) = -1.56266413459 -1.09739491326
y[1] (closed_form) = -1.56281933775 -1.09700940335
absolute error = 0.0004156
relative error = 0.02176 %
Correct 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) = 27.53 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4646 1.636
h = 0.003 0.006
y[1] (numeric) = -1.57600774941 -1.10180066487
y[1] (closed_form) = -1.57616833271 -1.1014236507
absolute error = 0.0004098
relative error = 0.02131 %
Correct 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) = 27.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4676 1.642
h = 0.0001 0.005
y[1] (numeric) = -1.59951069229 -1.09897644141
y[1] (closed_form) = -1.59969008939 -1.09855926037
absolute error = 0.0004541
relative error = 0.0234 %
Correct 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) = 27.41 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4677 1.647
h = 0.0001 0.003
y[1] (numeric) = -1.61638932856 -1.10455118567
y[1] (closed_form) = -1.61655219068 -1.10415779172
absolute error = 0.0004258
relative error = 0.02175 %
Correct 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) = 27.36 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4678 1.65
h = 0.001 0.001
y[1] (numeric) = -1.6266091521 -1.10779001513
y[1] (closed_form) = -1.6267610267 -1.10739366241
absolute error = 0.0004245
relative error = 0.02157 %
Correct 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) = 27.33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4688 1.651
h = 0.001 0.003
y[1] (numeric) = -1.63117708894 -1.10560946137
y[1] (closed_form) = -1.63132308833 -1.10521349985
absolute error = 0.000422
relative error = 0.02142 %
Correct 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) = 27.31 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4698 1.654
h = 0.0001 0.004
y[1] (numeric) = -1.64249305826 -1.10579888301
memory used=990.5MB, alloc=52.3MB, time=11.62
y[1] (closed_form) = -1.64265107205 -1.10540259851
absolute error = 0.0004266
relative error = 0.02155 %
Correct 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) = 27.28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4699 1.658
h = 0.003 0.006
y[1] (numeric) = -1.65617805287 -1.11021653724
y[1] (closed_form) = -1.65634159581 -1.10982890568
absolute error = 0.0004207
relative error = 0.0211 %
Correct 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) = 27.24 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4729 1.664
h = 0.0001 0.005
y[1] (numeric) = -1.68020996191 -1.10716661992
y[1] (closed_form) = -1.68039254893 -1.1067378938
absolute error = 0.000466
relative error = 0.02316 %
Correct 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) = 27.15 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.473 1.669
h = 0.0001 0.003
y[1] (numeric) = -1.69751996713 -1.11275709914
y[1] (closed_form) = -1.69768576916 -1.11235273249
absolute error = 0.000437
relative error = 0.02153 %
Correct 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) = 27.1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4731 1.672
h = 0.001 0.001
y[1] (numeric) = -1.70799988413 -1.11600232597
y[1] (closed_form) = -1.70815445374 -1.11559498407
absolute error = 0.0004357
relative error = 0.02136 %
Correct 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) = 27.07 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4741 1.673
h = 0.001 0.003
y[1] (numeric) = -1.71265954029 -1.11374010304
y[1] (closed_form) = -1.71280811199 -1.11333318532
absolute error = 0.0004332
relative error = 0.02121 %
Correct 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) = 27.05 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4751 1.676
h = 0.0001 0.004
y[1] (numeric) = -1.72424053448 -1.11385753923
y[1] (closed_form) = -1.72440137347 -1.11345024114
absolute error = 0.0004379
relative error = 0.02133 %
Correct 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) = 27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4752 1.68
h = 0.003 0.006
y[1] (numeric) = -1.73827417846 -1.11828591862
y[1] (closed_form) = -1.73844070015 -1.11788743329
absolute error = 0.0004319
relative error = 0.0209 %
Correct 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) = 26.96 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4782 1.686
h = 0.0001 0.005
y[1] (numeric) = -1.76284529906 -1.11500331223
y[1] (closed_form) = -1.76303109419 -1.1145627815
absolute error = 0.0004781
relative error = 0.02292 %
Correct 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) = 26.87 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4783 1.691
h = 0.0001 0.003
y[1] (numeric) = -1.78059586903 -1.12060803824
y[1] (closed_form) = -1.78076462722 -1.12019245437
absolute error = 0.0004485
relative error = 0.02132 %
Correct 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) = 26.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4784 1.694
h = 0.001 0.001
y[1] (numeric) = -1.79134141439 -1.1238586979
y[1] (closed_form) = -1.79149868942 -1.12344012359
absolute error = 0.0004471
relative error = 0.02115 %
Correct 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) = 26.78 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4794 1.695
h = 0.0001 0.004
y[1] (numeric) = -1.79609438671 -1.12151268771
y[1] (closed_form) = -1.79624553851 -1.12109457213
absolute error = 0.0004446
relative error = 0.021 %
Correct 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) = 26.76 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4795 1.699
h = 0.003 0.006
y[1] (numeric) = -1.81041865451 -1.1259494706
y[1] (closed_form) = -1.81059094211 -1.12554441055
absolute error = 0.0004402
relative error = 0.02065 %
Correct 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) = 26.72 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4825 1.705
h = 0.0001 0.005
y[1] (numeric) = -1.83546515036 -1.12246738752
y[1] (closed_form) = -1.83565691974 -1.12201944739
absolute error = 0.0004873
relative error = 0.02265 %
Correct 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) = 26.62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4826 1.71
h = 0.0001 0.003
y[1] (numeric) = -1.85360231958 -1.12808851244
y[1] (closed_form) = -1.85377682631 -1.12766603403
absolute error = 0.0004571
relative error = 0.02107 %
Correct 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) = 26.57 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4827 1.713
h = 0.001 0.001
y[1] (numeric) = -1.86458098655 -1.13134628694
y[1] (closed_form) = -1.86474378972 -1.13092080296
absolute error = 0.0004556
relative error = 0.02089 %
Correct 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) = 26.53 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4837 1.714
h = 0.001 0.003
y[1] (numeric) = -1.8694166121 -1.12892755147
y[1] (closed_form) = -1.86957318158 -1.12850255576
absolute error = 0.0004529
relative error = 0.02074 %
Correct 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) = 26.51 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4847 1.717
h = 0.0001 0.004
y[1] (numeric) = -1.88150589618 -1.12890722764
y[1] (closed_form) = -1.881675219 -1.12848173977
absolute error = 0.0004579
relative error = 0.02087 %
Correct 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) = 26.47 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4848 1.721
h = 0.003 0.006
y[1] (numeric) = -1.8962081078 -1.13335653184
y[1] (closed_form) = -1.89638340952 -1.13294016332
absolute error = 0.0004518
relative error = 0.02045 %
Correct 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) = 26.42 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1034.3MB, alloc=52.3MB, time=12.14
x[1] = 0.4878 1.727
h = 0.0001 0.005
y[1] (numeric) = -1.92181348169 -1.12962824934
y[1] (closed_form) = -1.92200849285 -1.12916800543
absolute error = 0.0004999
relative error = 0.02242 %
Correct 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) = 26.32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4879 1.732
h = 0.0001 0.003
y[1] (numeric) = -1.94040889387 -1.13526070886
y[1] (closed_form) = -1.94058638663 -1.13482654287
absolute error = 0.000469
relative error = 0.02086 %
Correct 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) = 26.26 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.488 1.735
h = 0.001 0.001
y[1] (numeric) = -1.95166382899 -1.1385220312
y[1] (closed_form) = -1.95182935631 -1.13808484685
absolute error = 0.0004675
relative error = 0.02069 %
Correct 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) = 26.23 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.489 1.736
h = 0.001 0.003
y[1] (numeric) = -1.95659583042 -1.13601542617
y[1] (closed_form) = -1.95675499366 -1.1355787677
absolute error = 0.0004648
relative error = 0.02054 %
Correct 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) = 26.2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.49 1.739
h = 0.0001 0.004
y[1] (numeric) = -1.9689656401 -1.13591534937
y[1] (closed_form) = -1.96913782562 -1.13547813251
absolute error = 0.0004699
relative error = 0.02067 %
Correct 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) = 26.16 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4901 1.743
h = 0.003 0.006
y[1] (numeric) = -1.98403821712 -1.14037167348
y[1] (closed_form) = -1.98421654864 -1.13994374366
absolute error = 0.0004636
relative error = 0.02026 %
Correct 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) = 26.11 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4931 1.749
h = 0.0001 0.005
y[1] (numeric) = -2.0102132736 -1.13638952013
y[1] (closed_form) = -2.01041154099 -1.13591669502
absolute error = 0.0005127
relative error = 0.0222 %
Correct 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) = 26.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4932 1.754
h = 0.0001 0.003
y[1] (numeric) = -2.02927672043 -1.14203154542
y[1] (closed_form) = -2.02945721174 -1.14158543041
absolute error = 0.0004812
relative error = 0.02067 %
Correct 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) = 25.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4933 1.757
h = 0.001 0.001
y[1] (numeric) = -2.04081381568 -1.14529527767
y[1] (closed_form) = -2.04098207351 -1.14484613292
absolute error = 0.0004796
relative error = 0.0205 %
Correct 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) = 25.91 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4943 1.758
h = 0.001 0.003
y[1] (numeric) = -2.045843857 -1.14269851003
y[1] (closed_form) = -2.04600561761 -1.14224993051
absolute error = 0.0004769
relative error = 0.02035 %
Correct 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) = 25.88 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4953 1.761
h = 0.0001 0.004
y[1] (numeric) = -2.05849980863 -1.1425157498
y[1] (closed_form) = -2.05867486626 -1.14206654233
absolute error = 0.0004821
relative error = 0.02048 %
Correct 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) = 25.83 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4954 1.765
h = 0.003 0.006
y[1] (numeric) = -2.07395066227 -1.14697761036
y[1] (closed_form) = -2.07413203797 -1.14653786044
absolute error = 0.0004757
relative error = 0.02007 %
Correct 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) = 25.78 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4984 1.771
h = 0.0001 0.005
y[1] (numeric) = -2.10070640645 -1.14273366611
y[1] (closed_form) = -2.10090794305 -1.14224797588
absolute error = 0.0005258
relative error = 0.02199 %
Correct 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) = 25.67 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4985 1.776
h = 0.0001 0.003
y[1] (numeric) = -2.12024789519 -1.14838338358
y[1] (closed_form) = -2.12043139617 -1.14792505194
absolute error = 0.0004937
relative error = 0.02048 %
Correct 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) = 25.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4986 1.779
h = 0.001 0.001
y[1] (numeric) = -2.13207317175 -1.15164832308
y[1] (closed_form) = -2.13224416493 -1.1511869518
absolute error = 0.000492
relative error = 0.02031 %
Correct 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) = 25.57 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4996 1.78
h = 0.001 0.003
y[1] (numeric) = -2.13720294068 -1.14895903582
y[1] (closed_form) = -2.13736730064 -1.14849827088
absolute error = 0.0004892
relative error = 0.02016 %
Correct 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) = 25.55 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5006 1.783
h = 0.0001 0.004
y[1] (numeric) = -2.15015076175 -1.14869055722
y[1] (closed_form) = -2.15032869941 -1.14822909142
absolute error = 0.0004946
relative error = 0.02029 %
Correct 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) = 25.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5007 1.787
h = 0.003 0.006
y[1] (numeric) = -2.16598797699 -1.1531563851
y[1] (closed_form) = -2.16617240988 -1.15270455018
absolute error = 0.000488
relative error = 0.01989 %
Correct 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) = 25.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5037 1.793
h = 0.0001 0.005
y[1] (numeric) = -2.19333561766 -1.14864247512
y[1] (closed_form) = -2.19354043497 -1.14814362923
absolute error = 0.0005393
relative error = 0.02178 %
Correct 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) = 25.33 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1078.0MB, alloc=52.3MB, time=12.65
x[1] = 0.5038 1.798
h = 0.0001 0.003
y[1] (numeric) = -2.21336537534 -1.15429790318
y[1] (closed_form) = -2.21355189564 -1.15382708105
absolute error = 0.0005064
relative error = 0.02029 %
Correct 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) = 25.26 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5039 1.801
h = 0.001 0.001
y[1] (numeric) = -2.22548498607 -1.15756278063
y[1] (closed_form) = -2.22565871783 -1.15708891049
absolute error = 0.0005047
relative error = 0.02012 %
Correct 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) = 25.22 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5049 1.802
h = 0.0001 0.004
y[1] (numeric) = -2.23071619419 -1.15477855128
y[1] (closed_form) = -2.23088315387 -1.15430533042
absolute error = 0.0005018
relative error = 0.01998 %
Correct 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) = 25.19 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.505 1.806
h = 0.003 0.006
y[1] (numeric) = -2.24687550229 -1.15924701757
y[1] (closed_form) = -2.24706617524 -1.15878777061
absolute error = 0.0004973
relative error = 0.01967 %
Correct 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) = 25.14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.508 1.812
h = 0.0001 0.005
y[1] (numeric) = -2.27474511451 -1.15450122092
y[1] (closed_form) = -2.27495637612 -1.15399402309
absolute error = 0.0005494
relative error = 0.02154 %
Correct 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) = 25.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5081 1.817
h = 0.0001 0.003
y[1] (numeric) = -2.29520348438 -1.160165879
y[1] (closed_form) = -2.29539621434 -1.15968728798
absolute error = 0.0005159
relative error = 0.02006 %
Correct 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) = 24.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5082 1.82
h = 0.001 0.001
y[1] (numeric) = -2.30758150017 -1.16343324258
y[1] (closed_form) = -2.30776119478 -1.16295159416
absolute error = 0.0005141
relative error = 0.01989 %
Correct 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) = 24.91 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5092 1.821
h = 0.001 0.003
y[1] (numeric) = -2.31290258422 -1.16056653587
y[1] (closed_form) = -2.31307538432 -1.16008557349
absolute error = 0.0005111
relative error = 0.01975 %
Correct 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) = 24.88 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5102 1.824
h = 0.0001 0.004
y[1] (numeric) = -2.32641025046 -1.16013375193
y[1] (closed_form) = -2.3265971676 -1.15965194715
absolute error = 0.0005168
relative error = 0.01988 %
Correct 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) = 24.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5103 1.828
h = 0.003 0.006
y[1] (numeric) = -2.34298852301 -1.16460731933
y[1] (closed_form) = -2.34318227685 -1.1641354779
absolute error = 0.0005101
relative error = 0.0195 %
Correct 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) = 24.77 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5133 1.834
h = 0.0001 0.005
y[1] (numeric) = -2.37147154664 -1.15957578495
y[1] (closed_form) = -2.37168610974 -1.1590548728
absolute error = 0.0005634
relative error = 0.02134 %
Correct 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) = 24.64 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5134 1.839
h = 0.0001 0.003
y[1] (numeric) = -2.39243784166 -1.16524229581
y[1] (closed_form) = -2.39263360819 -1.16475068764
absolute error = 0.0005292
relative error = 0.01988 %
Correct 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) = 24.57 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5135 1.842
h = 0.001 0.001
y[1] (numeric) = -2.40512201681 -1.16850712823
y[1] (closed_form) = -2.40530445495 -1.16801245722
absolute error = 0.0005272
relative error = 0.01972 %
Correct 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) = 24.52 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5145 1.843
h = 0.001 0.003
y[1] (numeric) = -2.41054782 -1.16554081352
y[1] (closed_form) = -2.41072321923 -1.16504687498
absolute error = 0.0005242
relative error = 0.01958 %
Correct 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) = 24.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5155 1.846
h = 0.0001 0.004
y[1] (numeric) = -2.42436441244 -1.16501310053
y[1] (closed_form) = -2.42455422696 -1.16451823649
absolute error = 0.00053
relative error = 0.01971 %
Correct 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) = 24.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5156 1.85
h = 0.003 0.006
y[1] (numeric) = -2.44135318768 -1.16948575297
y[1] (closed_form) = -2.44155003125 -1.16900103402
absolute error = 0.0005232
relative error = 0.01933 %
Correct 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) = 24.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5186 1.856
h = 0.0001 0.005
y[1] (numeric) = -2.47046143534 -1.16415954412
y[1] (closed_form) = -2.47067930683 -1.16362460737
absolute error = 0.0005776
relative error = 0.02115 %
Correct 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) = 24.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5187 1.861
h = 0.0001 0.003
y[1] (numeric) = -2.49194653605 -1.16982560155
y[1] (closed_form) = -2.4921453443 -1.16932068369
absolute error = 0.0005426
relative error = 0.01971 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.203
Order of pole (three term test) = 24.17 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5188 1.864
h = 0.001 0.001
y[1] (numeric) = -2.50494341497 -1.17308643314
y[1] (closed_form) = -2.50512859502 -1.17257844871
absolute error = 0.0005407
relative error = 0.01955 %
Correct 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) = 24.12 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1121.9MB, alloc=52.3MB, time=13.16
x[1] = 0.5198 1.865
h = 0.001 0.003
y[1] (numeric) = -2.51047571927 -1.17001789263
y[1] (closed_form) = -2.51065371296 -1.16951068908
absolute error = 0.0005375
relative error = 0.01941 %
Correct 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) = 24.1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5208 1.868
h = 0.0001 0.004
y[1] (numeric) = -2.52460741412 -1.16939178771
y[1] (closed_form) = -2.52480012772 -1.16888357179
absolute error = 0.0005435
relative error = 0.01954 %
Correct 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) = 24.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5209 1.872
h = 0.003 0.006
y[1] (numeric) = -2.54201548073 -1.17386160229
y[1] (closed_form) = -2.5422154213 -1.17336371618
absolute error = 0.0005365
relative error = 0.01916 %
Correct 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) = 23.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5239 1.878
h = 0.0001 0.005
y[1] (numeric) = -2.57176098137 -1.16823150209
y[1] (closed_form) = -2.57198216638 -1.16768222328
absolute error = 0.0005921
relative error = 0.02096 %
Correct 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) = 23.84 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.524 1.883
h = 0.0001 0.003
y[1] (numeric) = -2.59377600473 -1.17389467866
y[1] (closed_form) = -2.59397785815 -1.17337615179
absolute error = 0.0005564
relative error = 0.01954 %
Correct 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) = 23.76 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5241 1.886
h = 0.001 0.001
y[1] (numeric) = -2.60709227349 -1.17714996501
y[1] (closed_form) = -2.60728019195 -1.17662836962
absolute error = 0.0005544
relative error = 0.01938 %
Correct 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) = 23.71 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5251 1.887
h = 0.001 0.003
y[1] (numeric) = -2.61273288555 -1.17397650944
y[1] (closed_form) = -2.61291346712 -1.17345574538
absolute error = 0.0005512
relative error = 0.01924 %
Correct 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) = 23.68 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5261 1.89
h = 0.0001 0.004
y[1] (numeric) = -2.62718597977 -1.17324843139
y[1] (closed_form) = -2.62738159233 -1.17272656418
absolute error = 0.0005573
relative error = 0.01937 %
Correct 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) = 23.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5262 1.894
h = 0.003 0.006
y[1] (numeric) = -2.64502231692 -1.17771338613
y[1] (closed_form) = -2.64522536007 -1.17720203647
absolute error = 0.0005502
relative error = 0.019 %
Correct 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) = 23.55 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5292 1.9
h = 0.0001 0.005
y[1] (numeric) = -2.67541731914 -1.1717698905
y[1] (closed_form) = -2.67564182097 -1.17120594488
absolute error = 0.000607
relative error = 0.02078 %
Correct 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) = 23.4 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5293 1.905
h = 0.0001 0.003
y[1] (numeric) = -2.69797362307 -1.17742763389
y[1] (closed_form) = -2.69817852332 -1.17689519178
absolute error = 0.0005705
relative error = 0.01938 %
Correct 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) = 23.32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5294 1.908
h = 0.001 0.001
y[1] (numeric) = -2.71161611205 -1.18067575356
y[1] (closed_form) = -2.71180676351 -1.18014024284
absolute error = 0.0005684
relative error = 0.01922 %
Correct 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) = 23.27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5304 1.909
h = 0.0001 0.004
y[1] (numeric) = -2.71736686344 -1.1773946206
y[1] (closed_form) = -2.71755002433 -1.17685999374
absolute error = 0.0005651
relative error = 0.01908 %
Correct 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) = 23.24 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5305 1.913
h = 0.003 0.006
y[1] (numeric) = -2.73556025743 -1.18185471635
y[1] (closed_form) = -2.73577004171 -1.18133500312
absolute error = 0.0005605
relative error = 0.01881 %
Correct 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) = 23.17 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5335 1.919
h = 0.0001 0.005
y[1] (numeric) = -2.76652820024 -1.17564156477
y[1] (closed_form) = -2.7667596404 -1.17506819917
absolute error = 0.0006183
relative error = 0.02057 %
Correct 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) = 23.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5336 1.924
h = 0.0001 0.003
y[1] (numeric) = -2.78955981135 -1.18129912587
y[1] (closed_form) = -2.789771407 -1.18075792261
absolute error = 0.0005811
relative error = 0.01918 %
Correct 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) = 22.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5337 1.927
h = 0.001 0.001
y[1] (numeric) = -2.80348879474 -1.18454371717
y[1] (closed_form) = -2.80368586568 -1.1839994429
absolute error = 0.0005789
relative error = 0.01902 %
Correct 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) = 22.88 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5347 1.928
h = 0.001 0.003
y[1] (numeric) = -2.80933716507 -1.18116897218
y[1] (closed_form) = -2.80952660992 -1.18062562683
absolute error = 0.0005754
relative error = 0.01888 %
Correct 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) = 22.85 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5357 1.931
h = 0.0001 0.004
y[1] (numeric) = -2.82440681117 -1.18024520741
y[1] (closed_form) = -2.82461188471 -1.17970058313
absolute error = 0.000582
relative error = 0.01901 %
Correct 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) = 22.78 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1165.8MB, alloc=52.3MB, time=13.67
x[1] = 0.5358 1.935
h = 0.003 0.006
y[1] (numeric) = -2.84306474548 -1.18470074878
y[1] (closed_form) = -2.84327764185 -1.18416700216
absolute error = 0.0005746
relative error = 0.01866 %
Correct 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) = 22.71 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5388 1.941
h = 0.0001 0.005
y[1] (numeric) = -2.87470569951 -1.17815588008
y[1] (closed_form) = -2.87494046158 -1.17756722337
absolute error = 0.0006337
relative error = 0.0204 %
Correct 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) = 22.55 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5389 1.946
h = 0.0001 0.003
y[1] (numeric) = -2.89830041671 -1.18380305544
y[1] (closed_form) = -2.89851506112 -1.1832473482
absolute error = 0.0005957
relative error = 0.01903 %
Correct 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) = 22.46 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.539 1.949
h = 0.001 0.001
y[1] (numeric) = -2.91256874518 -1.18703733549
y[1] (closed_form) = -2.91276853749 -1.18647856069
absolute error = 0.0005934
relative error = 0.01887 %
Correct 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) = 22.41 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.54 1.95
h = 0.001 0.003
y[1] (numeric) = -2.91853076498 -1.18354959521
y[1] (closed_form) = -2.91872277147 -1.18299180587
absolute error = 0.0005899
relative error = 0.01873 %
Correct 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) = 22.37 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.541 1.953
h = 0.0001 0.004
y[1] (numeric) = -2.93394055716 -1.18251301065
y[1] (closed_form) = -2.93414852268 -1.18195383991
absolute error = 0.0005966
relative error = 0.01886 %
Correct 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) = 22.3 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5411 1.957
h = 0.003 0.006
y[1] (numeric) = -2.95305356234 -1.18695744816
y[1] (closed_form) = -2.95326957136 -1.18640935176
absolute error = 0.0005891
relative error = 0.01851 %
Correct 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) = 22.23 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5441 1.963
h = 0.0001 0.005
y[1] (numeric) = -2.98538042706 -1.18007049915
y[1] (closed_form) = -2.98561850876 -1.17946620481
absolute error = 0.0006495
relative error = 0.02023 %
Correct 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) = 22.07 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5442 1.968
h = 0.0001 0.003
y[1] (numeric) = -3.00955032472 -1.18570436074
y[1] (closed_form) = -3.00976801413 -1.18513382269
absolute error = 0.0006107
relative error = 0.01888 %
Correct 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) = 21.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5443 1.971
h = 0.001 0.001
y[1] (numeric) = -3.02416525782 -1.1889264765
y[1] (closed_form) = -3.02436776027 -1.18835287641
absolute error = 0.0006083
relative error = 0.01872 %
Correct 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) = 21.91 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5453 1.972
h = 0.001 0.003
y[1] (numeric) = -3.03024283191 -1.18532276035
y[1] (closed_form) = -3.03043738549 -1.18475020454
absolute error = 0.0006047
relative error = 0.01858 %
Correct 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) = 21.88 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5463 1.975
h = 0.0001 0.004
y[1] (numeric) = -3.0459995541 -1.18416928956
y[1] (closed_form) = -3.04621040399 -1.18359524552
absolute error = 0.0006115
relative error = 0.01871 %
Correct 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) = 21.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5464 1.979
h = 0.003 0.006
y[1] (numeric) = -3.06557738073 -1.18860019203
y[1] (closed_form) = -3.06579650105 -1.18803742218
absolute error = 0.0006039
relative error = 0.01837 %
Correct 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) = 21.72 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5494 1.985
h = 0.0001 0.005
y[1] (numeric) = -3.09860328853 -1.18136048361
y[1] (closed_form) = -3.09884468545 -1.18074019718
absolute error = 0.0006656
relative error = 0.02007 %
Correct 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) = 21.56 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5495 1.99
h = 0.0001 0.003
y[1] (numeric) = -3.12336070018 -1.18697796318
y[1] (closed_form) = -3.12358142876 -1.18639226004
absolute error = 0.0006259
relative error = 0.01873 %
Correct 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) = 21.46 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5496 1.993
h = 0.001 0.001
y[1] (numeric) = -3.13832965265 -1.19018597522
y[1] (closed_form) = -3.13853485176 -1.1895972177
absolute error = 0.0006235
relative error = 0.01858 %
Correct 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) = 21.4 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5506 1.994
h = 0.001 0.003
y[1] (numeric) = -3.14452471148 -1.18646322278
y[1] (closed_form) = -3.14472179529 -1.18587557068
absolute error = 0.0006198
relative error = 0.01844 %
Correct 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) = 21.36 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5516 1.997
h = 0.0001 0.004
y[1] (numeric) = -3.16063527852 -1.18518866513
y[1] (closed_form) = -3.16084900301 -1.18459941348
absolute error = 0.0006268
relative error = 0.01857 %
Correct 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) = 21.28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5517 2.001
h = 0.003 0.006
y[1] (numeric) = -3.18068788594 -1.18960348682
y[1] (closed_form) = -3.18091011418 -1.18902571243
absolute error = 0.000619
relative error = 0.01823 %
Correct 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) = 21.2 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1209.5MB, alloc=52.3MB, time=14.18
x[1] = 0.5547 2.007
h = 0.0001 0.005
y[1] (numeric) = -3.21442620566 -1.182000016
y[1] (closed_form) = -3.21467091117 -1.18136337499
absolute error = 0.0006821
relative error = 0.01991 %
Correct 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) = 21.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5548 2.012
h = 0.0001 0.003
y[1] (numeric) = -3.23978372886 -1.18759790083
y[1] (closed_form) = -3.24000748863 -1.18699669067
absolute error = 0.0006415
relative error = 0.01859 %
Correct 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) = 20.92 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5549 2.015
h = 0.001 0.001
y[1] (numeric) = -3.25511427355 -1.19078978073
y[1] (closed_form) = -3.25532215354 -1.19018552609
absolute error = 0.000639
relative error = 0.01844 %
Correct 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) = 20.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5559 2.016
h = 0.0001 0.004
y[1] (numeric) = -3.26142877338 -1.18694484992
y[1] (closed_form) = -3.2616283682 -1.18634176423
absolute error = 0.0006353
relative error = 0.0183 %
Correct 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) = 20.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.556 2.02
h = 0.003 0.006
y[1] (numeric) = -3.28187723341 -1.19134531074
y[1] (closed_form) = -3.28210673095 -1.19075809402
absolute error = 0.0006305
relative error = 0.01806 %
Correct 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) = 20.74 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.559 2.026
h = 0.0001 0.005
y[1] (numeric) = -3.31624417976 -1.18342836864
y[1] (closed_form) = -3.31649634113 -1.18278109989
absolute error = 0.0006947
relative error = 0.01973 %
Correct 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) = 20.55 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5591 2.031
h = 0.0001 0.003
y[1] (numeric) = -3.34212884032 -1.18901405847
y[1] (closed_form) = -3.34235980568 -1.18840296364
absolute error = 0.0006533
relative error = 0.01842 %
Correct 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) = 20.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5592 2.034
h = 0.001 0.001
y[1] (numeric) = -3.35777704534 -1.19219479116
y[1] (closed_form) = -3.35799182289 -1.19158065792
absolute error = 0.0006506
relative error = 0.01826 %
Correct 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) = 20.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5602 2.035
h = 0.001 0.003
y[1] (numeric) = -3.36419745021 -1.18824356841
y[1] (closed_form) = -3.36440379277 -1.1876306587
absolute error = 0.0006467
relative error = 0.01813 %
Correct 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) = 20.34 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5612 2.038
h = 0.0001 0.004
y[1] (numeric) = -3.38098686853 -1.18673645749
y[1] (closed_form) = -3.38121051331 -1.18612173306
absolute error = 0.0006541
relative error = 0.01826 %
Correct 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) = 20.26 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5613 2.042
h = 0.003 0.006
y[1] (numeric) = -3.40195043964 -1.19112011967
y[1] (closed_form) = -3.4021830374 -1.19051726198
absolute error = 0.0006462
relative error = 0.01793 %
Correct 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) = 20.17 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5643 2.048
h = 0.0001 0.005
y[1] (numeric) = -3.43705545616 -1.18281821729
y[1] (closed_form) = -3.43731091214 -1.18215389725
absolute error = 0.0007117
relative error = 0.01958 %
Correct 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) = 19.98 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5644 2.053
h = 0.0001 0.003
y[1] (numeric) = -3.46356443186 -1.18837809222
y[1] (closed_form) = -3.46379841184 -1.18775083317
absolute error = 0.0006695
relative error = 0.01828 %
Correct 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) = 19.87 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5645 2.056
h = 0.001 0.001
y[1] (numeric) = -3.47958877828 -1.19153876702
y[1] (closed_form) = -3.47980620519 -1.19090848374
absolute error = 0.0006667
relative error = 0.01813 %
Correct 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) = 19.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5655 2.057
h = 0.001 0.003
y[1] (numeric) = -3.48613237332 -1.18745931937
y[1] (closed_form) = -3.48634118876 -1.18683032775
absolute error = 0.0006627
relative error = 0.018 %
Correct 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) = 19.76 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5665 2.06
h = 0.0001 0.004
y[1] (numeric) = -3.50329621644 -1.18581841927
y[1] (closed_form) = -3.50352269954 -1.18518748817
absolute error = 0.0006703
relative error = 0.01812 %
Correct 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) = 19.67 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5666 2.064
h = 0.003 0.006
y[1] (numeric) = -3.5247642834 -1.1901781809
y[1] (closed_form) = -3.52499997192 -1.18955932909
absolute error = 0.0006622
relative error = 0.0178 %
Correct 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) = 19.58 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5696 2.07
h = 0.0001 0.005
y[1] (numeric) = -3.56062143911 -1.1814793461
y[1] (closed_form) = -3.56088017635 -1.18079758826
absolute error = 0.0007292
relative error = 0.01944 %
Correct 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) = 19.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5697 2.075
h = 0.0001 0.003
y[1] (numeric) = -3.58776811267 -1.18700975864
y[1] (closed_form) = -3.58800509275 -1.18636597076
absolute error = 0.000686
relative error = 0.01815 %
Correct 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) = 19.27 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1253.2MB, alloc=52.3MB, time=14.69
x[1] = 0.5698 2.078
h = 0.001 0.001
y[1] (numeric) = -3.60417664347 -1.19014807941
y[1] (closed_form) = -3.60439669698 -1.18950128396
absolute error = 0.0006832
relative error = 0.018 %
Correct 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) = 19.2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5708 2.079
h = 0.001 0.003
y[1] (numeric) = -3.61084546065 -1.18593702087
y[1] (closed_form) = -3.61105672259 -1.18529158782
absolute error = 0.0006791
relative error = 0.01787 %
Correct 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) = 19.15 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5718 2.082
h = 0.0001 0.004
y[1] (numeric) = -3.62839117129 -1.18415758056
y[1] (closed_form) = -3.62862047391 -1.18351007824
absolute error = 0.0006869
relative error = 0.018 %
Correct 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) = 19.06 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5719 2.086
h = 0.003 0.006
y[1] (numeric) = -3.65037453865 -1.18849042262
y[1] (closed_form) = -3.65061330616 -1.1878552155
absolute error = 0.0006786
relative error = 0.01768 %
Correct 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) = 18.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5749 2.092
h = 0.0001 0.005
y[1] (numeric) = -3.68699815292 -1.17938232688
y[1] (closed_form) = -3.68726015548 -1.17868273599
absolute error = 0.000747
relative error = 0.0193 %
Correct 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) = 18.76 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.575 2.097
h = 0.0001 0.003
y[1] (numeric) = -3.71479619091 -1.18487946739
y[1] (closed_form) = -3.7150361541 -1.18421877783
absolute error = 0.0007029
relative error = 0.01803 %
Correct 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) = 18.64 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5751 2.1
h = 0.001 0.001
y[1] (numeric) = -3.73159711904 -1.1879930382
y[1] (closed_form) = -3.73181977373 -1.1873293603
absolute error = 0.0007
relative error = 0.01788 %
Correct 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) = 18.57 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5761 2.101
h = 0.001 0.003
y[1] (numeric) = -3.73839321673 -1.18364689357
y[1] (closed_form) = -3.73860689606 -1.18298465147
absolute error = 0.0006959
relative error = 0.01775 %
Correct 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) = 18.52 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5771 2.104
h = 0.0001 0.004
y[1] (numeric) = -3.75632837937 -1.18172400978
y[1] (closed_form) = -3.75656048015 -1.18105956351
absolute error = 0.0007038
relative error = 0.01787 %
Correct 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) = 18.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5772 2.108
h = 0.003 0.006
y[1] (numeric) = -3.77883808034 -1.1860267808
y[1] (closed_form) = -3.77907991266 -1.18537484902
absolute error = 0.0006953
relative error = 0.01756 %
Correct 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) = 18.33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5802 2.114
h = 0.0001 0.005
y[1] (numeric) = -3.81624272655 -1.17649673026
y[1] (closed_form) = -3.81650797582 -1.17577890221
absolute error = 0.0007653
relative error = 0.01916 %
Correct 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) = 18.12 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5803 2.119
h = 0.0001 0.003
y[1] (numeric) = -3.84470608475 -1.18195662202
y[1] (closed_form) = -3.84494901147 -1.18127864952
absolute error = 0.0007202
relative error = 0.0179 %
Correct 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) = 17.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5804 2.122
h = 0.001 0.001
y[1] (numeric) = -3.86190779627 -1.18504294414
y[1] (closed_form) = -3.86213302398 -1.18436200522
absolute error = 0.0007172
relative error = 0.01775 %
Correct 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) = 17.92 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5814 2.123
h = 0.0001 0.004
y[1] (numeric) = -3.86883325937 -1.18055814694
y[1] (closed_form) = -3.86904932418 -1.17987871997
absolute error = 0.000713
relative error = 0.01763 %
Correct 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) = 17.87 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5815 2.127
h = 0.003 0.006
y[1] (numeric) = -3.8917818078 -1.18483473597
y[1] (closed_form) = -3.89203146454 -1.18417214132
absolute error = 0.0007081
relative error = 0.0174 %
Correct 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) = 17.77 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5845 2.133
h = 0.0001 0.005
y[1] (numeric) = -3.92987584593 -1.17494057484
y[1] (closed_form) = -3.93014909104 -1.1742107557
absolute error = 0.0007793
relative error = 0.019 %
Correct 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) = 17.55 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5846 2.138
h = 0.0001 0.003
y[1] (numeric) = -3.95892380122 -1.18037324536
y[1] (closed_form) = -3.95917446755 -1.17968411846
absolute error = 0.0007333
relative error = 0.01775 %
Correct 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) = 17.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5847 2.141
h = 0.001 0.001
y[1] (numeric) = -3.97647771069 -1.18343894438
y[1] (closed_form) = -3.97671033457 -1.18274686735
absolute error = 0.0007301
relative error = 0.0176 %
Correct 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) = 17.34 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5857 2.142
h = 0.001 0.003
y[1] (numeric) = -3.98351792827 -1.17883344778
y[1] (closed_form) = -3.98374122379 -1.17814294821
absolute error = 0.0007257
relative error = 0.01747 %
Correct 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) = 17.29 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1297.1MB, alloc=52.3MB, time=15.20
x[1] = 0.5867 2.145
h = 0.0001 0.004
y[1] (numeric) = -4.00220030591 -1.17663492004
y[1] (closed_form) = -4.00244275425 -1.17594195577
absolute error = 0.0007342
relative error = 0.0176 %
Correct 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) = 17.19 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5868 2.149
h = 0.003 0.006
y[1] (numeric) = -4.02572001064 -1.18087946862
y[1] (closed_form) = -4.02597270371 -1.18019943947
absolute error = 0.0007255
relative error = 0.01729 %
Correct 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) = 17.09 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5898 2.155
h = 0.0001 0.005
y[1] (numeric) = -4.06462304893 -1.17053890927
y[1] (closed_form) = -4.06489950376 -1.16979007639
absolute error = 0.0007982
relative error = 0.01887 %
Correct 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) = 16.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5899 2.16
h = 0.0001 0.003
y[1] (numeric) = -4.09436313366 -1.17592664376
y[1] (closed_form) = -4.09461672467 -1.17521950126
absolute error = 0.0007512
relative error = 0.01763 %
Correct 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) = 16.73 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.59 2.163
h = 0.001 0.001
y[1] (numeric) = -4.11233393576 -1.17896026519
y[1] (closed_form) = -4.11256907733 -1.17825019961
absolute error = 0.000748
relative error = 0.01748 %
Correct 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) = 16.65 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.591 2.164
h = 0.001 0.003
y[1] (numeric) = -4.11950751441 -1.17420925503
y[1] (closed_form) = -4.11973313286 -1.17350084833
absolute error = 0.0007435
relative error = 0.01736 %
Correct 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) = 16.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.592 2.167
h = 0.0001 0.004
y[1] (numeric) = -4.13860191023 -1.17185247608
y[1] (closed_form) = -4.13884708528 -1.17114145429
absolute error = 0.0007521
relative error = 0.01749 %
Correct 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) = 16.49 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5921 2.171
h = 0.003 0.006
y[1] (numeric) = -4.16268085668 -1.17605731117
y[1] (closed_form) = -4.16293656458 -1.17535945381
absolute error = 0.0007432
relative error = 0.01718 %
Correct 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) = 16.39 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5951 2.177
h = 0.0001 0.005
y[1] (numeric) = -4.20240822032 -1.16525656623
y[1] (closed_form) = -4.20268785815 -1.164488289
absolute error = 0.0008176
relative error = 0.01875 %
Correct 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) = 16.15 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5952 2.182
h = 0.0001 0.003
y[1] (numeric) = -4.23285525017 -1.17059488516
y[1] (closed_form) = -4.23311173845 -1.16986932079
absolute error = 0.0007696
relative error = 0.01752 %
Correct 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) = 16.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5953 2.185
h = 0.001 0.001
y[1] (numeric) = -4.25125184571 -1.17359362099
y[1] (closed_form) = -4.25148946846 -1.17286516356
absolute error = 0.0007662
relative error = 0.01737 %
Correct 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) = 15.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5963 2.186
h = 0.001 0.003
y[1] (numeric) = -4.258560948 -1.16869325817
y[1] (closed_form) = -4.25878884893 -1.16796654403
absolute error = 0.0007616
relative error = 0.01725 %
Correct 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) = 15.88 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5973 2.189
h = 0.0001 0.004
y[1] (numeric) = -4.27807551792 -1.16617270035
y[1] (closed_form) = -4.27832338753 -1.16544321496
absolute error = 0.0007704
relative error = 0.01738 %
Correct 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) = 15.77 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5974 2.193
h = 0.003 0.006
y[1] (numeric) = -4.30272566488 -1.17033412339
y[1] (closed_form) = -4.30298436334 -1.16961803531
absolute error = 0.0007614
relative error = 0.01707 %
Correct 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) = 15.66 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6004 2.199
h = 0.0001 0.005
y[1] (numeric) = -4.34329294755 -1.15905900343
y[1] (closed_form) = -4.34357573859 -1.15827084164
absolute error = 0.0008374
relative error = 0.01863 %
Correct 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) = 15.41 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6005 2.204
h = 0.0001 0.003
y[1] (numeric) = -4.37446204902 -1.16434323987
y[1] (closed_form) = -4.37472140418 -1.1635988383
absolute error = 0.0007883
relative error = 0.01741 %
Correct 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) = 15.28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6006 2.207
h = 0.001 0.001
y[1] (numeric) = -4.39329352477 -1.16730416689
y[1] (closed_form) = -4.39353358904 -1.16655690536
absolute error = 0.0007849
relative error = 0.01727 %
Correct 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) = 15.2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6016 2.208
h = 0.001 0.003
y[1] (numeric) = -4.40074034025 -1.1622505126
y[1] (closed_form) = -4.40097047996 -1.16150508183
absolute error = 0.0007801
relative error = 0.01714 %
Correct 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) = 15.14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6026 2.211
h = 0.0001 0.004
y[1] (numeric) = -4.42068339356 -1.1595604756
y[1] (closed_form) = -4.4209339225 -1.15881211149
absolute error = 0.0007892
relative error = 0.01727 %
Correct digits = 4
memory used=1340.9MB, alloc=52.3MB, time=15.71
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) = 15.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6027 2.215
h = 0.003 0.006
y[1] (numeric) = -4.44591695011 -1.16367463502
y[1] (closed_form) = -4.44617861196 -1.16293990467
absolute error = 0.0007799
relative error = 0.01697 %
Correct 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) = 14.92 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6057 2.221
h = 0.0001 0.005
y[1] (numeric) = -4.4873400178 -1.15191053844
y[1] (closed_form) = -4.48762592907 -1.15110204208
absolute error = 0.0008576
relative error = 0.01851 %
Correct 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) = 14.66 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6058 2.226
h = 0.0001 0.003
y[1] (numeric) = -4.51924663397 -1.15713583242
y[1] (closed_form) = -4.51950882254 -1.15637216904
absolute error = 0.0008074
relative error = 0.01731 %
Correct 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) = 14.53 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6059 2.229
h = 0.001 0.001
y[1] (numeric) = -4.53852226617 -1.16005590874
y[1] (closed_form) = -4.53876472904 -1.1592894217
absolute error = 0.0008039
relative error = 0.01716 %
Correct 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) = 14.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6069 2.23
h = 0.0001 0.004
y[1] (numeric) = -4.5461090114 -1.15484492219
y[1] (closed_form) = -4.54634134287 -1.15408035653
absolute error = 0.0007991
relative error = 0.01704 %
Correct 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) = 14.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.607 2.234
h = 0.003 0.006
y[1] (numeric) = -4.57182900931 -1.15891839647
y[1] (closed_form) = -4.57209907694 -1.15817162473
absolute error = 0.0007941
relative error = 0.01684 %
Correct 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) = 14.27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.61 2.24
h = 0.0001 0.005
y[1] (numeric) = -4.61400769323 -1.14673184665
y[1] (closed_form) = -4.61430216117 -1.14590982256
absolute error = 0.0008732
relative error = 0.01837 %
Correct 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) = 14.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6101 2.245
h = 0.0001 0.003
y[1] (numeric) = -4.64656253456 -1.15191140309
y[1] (closed_form) = -4.64683301942 -1.15113515273
absolute error = 0.000822
relative error = 0.01717 %
Correct 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) = 13.87 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6102 2.248
h = 0.001 0.001
y[1] (numeric) = -4.66622859544 -1.15479923217
y[1] (closed_form) = -4.6664789721 -1.1540201867
absolute error = 0.0008183
relative error = 0.01702 %
Correct 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) = 13.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6112 2.249
h = 0.001 0.003
y[1] (numeric) = -4.67393952477 -1.14945120713
y[1] (closed_form) = -4.67417958755 -1.1486741611
absolute error = 0.0008133
relative error = 0.0169 %
Correct 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) = 13.73 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6122 2.252
h = 0.0001 0.004
y[1] (numeric) = -4.69470472431 -1.146435372
y[1] (closed_form) = -4.69496598398 -1.14565507995
absolute error = 0.0008229
relative error = 0.01703 %
Correct 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) = 13.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6123 2.256
h = 0.003 0.006
y[1] (numeric) = -4.72105792048 -1.15045809538
y[1] (closed_form) = -4.72133089805 -1.14969189059
absolute error = 0.0008134
relative error = 0.01674 %
Correct 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) = 13.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6153 2.262
h = 0.0001 0.005
y[1] (numeric) = -4.76412283623 -1.13775446297
y[1] (closed_form) = -4.76442035972 -1.13691123968
absolute error = 0.0008942
relative error = 0.01826 %
Correct 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) = 13.23 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6154 2.267
h = 0.0001 0.003
y[1] (numeric) = -4.79744485476 -1.14286569291
y[1] (closed_form) = -4.79771810747 -1.1420693649
absolute error = 0.0008419
relative error = 0.01707 %
Correct 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) = 13.1 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6155 2.27
h = 0.001 0.001
y[1] (numeric) = -4.81757288909 -1.14570679901
y[1] (closed_form) = -4.81782558063 -1.14490771833
absolute error = 0.0008381
relative error = 0.01692 %
Correct 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) = 13.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6165 2.271
h = 0.001 0.003
y[1] (numeric) = -4.825427996 -1.14019367026
y[1] (closed_form) = -4.82567015895 -1.13939668569
absolute error = 0.000833
relative error = 0.0168 %
Correct 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) = 12.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6175 2.274
h = 0.0001 0.004
y[1] (numeric) = -4.84664639419 -1.1369911594
y[1] (closed_form) = -4.84691019972 -1.13619074894
absolute error = 0.0008428
relative error = 0.01693 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.87
Order of pole (three term test) = 12.83 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6176 2.278
h = 0.003 0.006
y[1] (numeric) = -4.87361940403 -1.14095486992
y[1] (closed_form) = -4.87389525562 -1.14016879372
absolute error = 0.0008331
relative error = 0.01664 %
Correct 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) = 12.72 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6206 2.284
h = 0.0001 0.005
y[1] (numeric) = -4.91758722317 -1.12771831954
y[1] (closed_form) = -4.91788775951 -1.12685341785
absolute error = 0.0009156
relative error = 0.01815 %
Correct digits = 4
memory used=1384.8MB, alloc=52.3MB, time=16.22
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) = 12.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6207 2.289
h = 0.0001 0.003
y[1] (numeric) = -4.9516928032 -1.13275578203
y[1] (closed_form) = -4.95196878094 -1.1319389242
absolute error = 0.0008622
relative error = 0.01697 %
Correct 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) = 12.32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6208 2.292
h = 0.001 0.001
y[1] (numeric) = -4.9722926504 -1.13554676625
y[1] (closed_form) = -4.97254760398 -1.13472720174
absolute error = 0.0008583
relative error = 0.01683 %
Correct 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) = 12.24 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6218 2.293
h = 0.001 0.003
y[1] (numeric) = -4.98029423044 -1.12986418827
y[1] (closed_form) = -4.98053843642 -1.12904681995
absolute error = 0.0008531
relative error = 0.0167 %
Correct 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) = 12.17 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6228 2.296
h = 0.0001 0.004
y[1] (numeric) = -5.00197475438 -1.12646859309
y[1] (closed_form) = -5.00224105767 -1.12564761239
absolute error = 0.0008631
relative error = 0.01683 %
Correct 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) = 12.05 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6229 2.3
h = 0.003 0.006
y[1] (numeric) = -5.02958079989 -1.13036880731
y[1] (closed_form) = -5.02985948625 -1.12956241161
absolute error = 0.0008532
relative error = 0.01655 %
Correct 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) = 11.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6259 2.306
h = 0.0001 0.005
y[1] (numeric) = -5.07446848135 -1.11658305004
y[1] (closed_form) = -5.07477198418 -1.11569598016
absolute error = 0.0009376
relative error = 0.01804 %
Correct 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) = 11.67 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.626 2.311
h = 0.0001 0.003
y[1] (numeric) = -5.10937434722 -1.12154108774
y[1] (closed_form) = -5.10965300362 -1.12070323795
absolute error = 0.000883
relative error = 0.01688 %
Correct 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) = 11.54 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6261 2.314
h = 0.001 0.001
y[1] (numeric) = -5.13045605015 -1.1242784183
y[1] (closed_form) = -5.13071320917 -1.12343791148
absolute error = 0.000879
relative error = 0.01673 %
Correct 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) = 11.47 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6271 2.315
h = 0.001 0.003
y[1] (numeric) = -5.13860642615 -1.11842193418
y[1] (closed_form) = -5.13885261418 -1.11758372714
absolute error = 0.0008736
relative error = 0.01661 %
Correct 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) = 11.4 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6281 2.318
h = 0.0001 0.004
y[1] (numeric) = -5.16075816855 -1.11482665026
y[1] (closed_form) = -5.16102691787 -1.11398463755
absolute error = 0.0008839
relative error = 0.01674 %
Correct 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) = 11.28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6282 2.322
h = 0.003 0.006
y[1] (numeric) = -5.18901074556 -1.11865870816
y[1] (closed_form) = -5.189292224 -1.11783153494
absolute error = 0.0008738
relative error = 0.01646 %
Correct 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) = 11.19 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6312 2.328
h = 0.0001 0.005
y[1] (numeric) = -5.23483553958 -1.10430699015
y[1] (closed_form) = -5.23514195869 -1.1033972515
absolute error = 0.00096
relative error = 0.01794 %
Correct 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) = 10.91 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6313 2.333
h = 0.0001 0.003
y[1] (numeric) = -5.27055876197 -1.10917972288
y[1] (closed_form) = -5.27084004698 -1.10832040878
absolute error = 0.0009042
relative error = 0.01679 %
Correct 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) = 10.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6314 2.336
h = 0.001 0.001
y[1] (numeric) = -5.29213257064 -1.11185973118
y[1] (closed_form) = -5.29239187465 -1.1109978135
absolute error = 0.0009001
relative error = 0.01664 %
Correct 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) = 10.73 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6324 2.337
h = 0.0001 0.004
y[1] (numeric) = -5.30043409271 -1.10582477
y[1] (closed_form) = -5.30068219786 -1.10496525928
absolute error = 0.0008946
relative error = 0.01652 %
Correct 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) = 10.65 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6325 2.341
h = 0.003 0.006
y[1] (numeric) = -5.32922573903 -1.10959854068
y[1] (closed_form) = -5.32951622962 -1.10875777146
absolute error = 0.0008895
relative error = 0.01634 %
Correct 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) = 10.57 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6355 2.347
h = 0.0001 0.005
y[1] (numeric) = -5.37587822932 -1.09475733093
y[1] (closed_form) = -5.37619378443 -1.09383233494
absolute error = 0.0009773
relative error = 0.01781 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 20.37
Order of pole (three term test) = 10.29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6356 2.352
h = 0.0001 0.003
y[1] (numeric) = -5.4123200596 -1.09956177185
y[1] (closed_form) = -5.41261021842 -1.09868825682
absolute error = 0.0009204
relative error = 0.01667 %
Correct 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) = 10.19 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1428.5MB, alloc=52.3MB, time=16.73
x[1] = 0.6357 2.355
h = 0.001 0.001
y[1] (numeric) = -5.43432657034 -1.10219542589
y[1] (closed_form) = -5.43459432266 -1.10131935051
absolute error = 0.0009161
relative error = 0.01652 %
Correct 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) = 10.13 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6367 2.356
h = 0.001 0.003
y[1] (numeric) = -5.44276229892 -1.09600492741
y[1] (closed_form) = -5.44301865127 -1.09513135144
absolute error = 0.0009104
relative error = 0.0164 %
Correct 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) = 10.06 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6377 2.359
h = 0.0001 0.004
y[1] (numeric) = -5.46581822177 -1.09202567609
y[1] (closed_form) = -5.46609802641 -1.09114792181
absolute error = 0.0009213
relative error = 0.01653 %
Correct 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) = 9.956 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6378 2.363
h = 0.003 0.006
y[1] (numeric) = -5.49531167321 -1.09572597541
y[1] (closed_form) = -5.49560487257 -1.09486354871
absolute error = 0.0009109
relative error = 0.01626 %
Correct 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) = 9.883 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6408 2.369
h = 0.0001 0.005
y[1] (numeric) = -5.54293437679 -1.08028656624
y[1] (closed_form) = -5.54325275042 -1.0793379398
absolute error = 0.001001
relative error = 0.01772 %
Correct 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) = 9.624 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6409 2.374
h = 0.0001 0.003
y[1] (numeric) = -5.58022634862 -1.08499435783
y[1] (closed_form) = -5.58051903862 -1.08409847101
absolute error = 0.0009425
relative error = 0.01658 %
Correct 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) = 9.545 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.641 2.377
h = 0.001 0.001
y[1] (numeric) = -5.60274465028 -1.08756361307
y[1] (closed_form) = -5.60301443015 -1.08666522666
absolute error = 0.000938
relative error = 0.01644 %
Correct 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) = 9.499 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.642 2.378
h = 0.001 0.003
y[1] (numeric) = -5.61133602832 -1.08118584843
y[1] (closed_form) = -5.6115941718 -1.08029007556
absolute error = 0.0009322
relative error = 0.01631 %
Correct 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) = 9.429 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.643 2.381
h = 0.0001 0.004
y[1] (numeric) = -5.63489020706 -1.07698700208
y[1] (closed_form) = -5.63517229424 -1.07608683719
absolute error = 0.0009433
relative error = 0.01644 %
Correct 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) = 9.335 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6431 2.385
h = 0.003 0.006
y[1] (numeric) = -5.66507041919 -1.08060496308
y[1] (closed_form) = -5.66536627417 -1.07972039131
absolute error = 0.0009327
relative error = 0.01617 %
Correct 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) = 9.283 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6461 2.391
h = 0.0001 0.005
y[1] (numeric) = -5.71368144759 -1.06454920883
y[1] (closed_form) = -5.71400257798 -1.06357641922
absolute error = 0.001024
relative error = 0.01763 %
Correct 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) = 9.047 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6462 2.396
h = 0.0001 0.003
y[1] (numeric) = -5.75184166118 -1.06915380035
y[1] (closed_form) = -5.75213682118 -1.06823503904
absolute error = 0.000965
relative error = 0.01649 %
Correct 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) = 8.999 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6463 2.399
h = 0.001 0.001
y[1] (numeric) = -5.77488261956 -1.0716545765
y[1] (closed_form) = -5.77515435478 -1.07073338057
absolute error = 0.0009604
relative error = 0.01635 %
Correct 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) = 8.973 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6473 2.4
h = 0.001 0.003
y[1] (numeric) = -5.78363207666 -1.06508463427
y[1] (closed_form) = -5.78389193436 -1.06416616991
absolute error = 0.0009545
relative error = 0.01623 %
Correct 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) = 8.906 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6483 2.403
h = 0.0001 0.004
y[1] (numeric) = -5.80769427093 -1.0606587853
y[1] (closed_form) = -5.80797857362 -1.0597357076
absolute error = 0.0009659
relative error = 0.01636 %
Correct 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) = 8.829 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6484 2.407
h = 0.003 0.006
y[1] (numeric) = -5.83857584736 -1.06418901892
y[1] (closed_form) = -5.83887430088 -1.06328180381
absolute error = 0.000955
relative error = 0.01609 %
Correct 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) = 8.806 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6514 2.413
h = 0.0001 0.005
y[1] (numeric) = -5.88819361898 -1.04749826246
y[1] (closed_form) = -5.88851743997 -1.04650076527
absolute error = 0.001049
relative error = 0.01754 %
Correct 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) = 8.606 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6515 2.418
h = 0.0001 0.003
y[1] (numeric) = -5.92724054631 -1.0519928536
y[1] (closed_form) = -5.92753811092 -1.05105070409
absolute error = 0.000988
relative error = 0.01641 %
Correct 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) = 8.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6516 2.421
h = 0.001 0.001
y[1] (numeric) = -5.95081524953 -1.05442091726
y[1] (closed_form) = -5.95108886346 -1.05347640245
absolute error = 0.0009833
relative error = 0.01627 %
Correct 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) = 8.599 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1472.2MB, alloc=52.3MB, time=17.24
x[1] = 0.6526 2.422
h = 0.001 0.003
y[1] (numeric) = -5.95972524254 -1.04765376153
y[1] (closed_form) = -5.95998673305 -1.04671210033
absolute error = 0.0009773
relative error = 0.01615 %
Correct 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) = 8.538 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6536 2.425
h = 0.0001 0.004
y[1] (numeric) = -5.98430539066 -1.04299328036
y[1] (closed_form) = -5.98459183753 -1.04204677671
absolute error = 0.0009889
relative error = 0.01628 %
Correct 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) = 8.485 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6537 2.429
h = 0.003 0.006
y[1] (numeric) = -6.01590323432 -1.04643019398
y[1] (closed_form) = -6.01620422518 -1.04549982632
absolute error = 0.0009778
relative error = 0.01601 %
Correct 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) = 8.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6567 2.435
h = 0.0001 0.005
y[1] (numeric) = -6.06654647845 -1.02908525388
y[1] (closed_form) = -6.06687291937 -1.02806249282
absolute error = 0.001074
relative error = 0.01745 %
Correct 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) = 8.352 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6568 2.44
h = 0.0001 0.003
y[1] (numeric) = -6.10649897012 -1.03346278739
y[1] (closed_form) = -6.1067988696 -1.03249672474
absolute error = 0.001012
relative error = 0.01633 %
Correct 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) = 8.397 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6569 2.443
h = 0.001 0.001
y[1] (numeric) = -6.13061873269 -1.03581374754
y[1] (closed_form) = -6.13089414412 -1.03484539342
absolute error = 0.001007
relative error = 0.01619 %
Correct 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) = 8.428 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6579 2.444
h = 0.0001 0.004
y[1] (numeric) = -6.13969174565 -1.02884421503
y[1] (closed_form) = -6.13995478291 -1.0278788407
absolute error = 0.001001
relative error = 0.01607 %
Correct 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) = 8.376 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.658 2.448
h = 0.003 0.006
y[1] (numeric) = -6.1718867931 -1.0322016625
y[1] (closed_form) = -6.17219742555 -1.03125594805
absolute error = 0.0009954
relative error = 0.01591 %
Correct 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) = 8.429 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.661 2.454
h = 0.0001 0.005
y[1] (numeric) = -6.22343608163 -1.01429037785
y[1] (closed_form) = -6.22377225321 -1.01325041502
absolute error = 0.001093
relative error = 0.01733 %
Correct 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) = 8.338 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6611 2.459
h = 0.0001 0.003
y[1] (numeric) = -6.26418495585 -1.01857239881
y[1] (closed_form) = -6.26449432492 -1.01759031932
absolute error = 0.00103
relative error = 0.01622 %
Correct 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) = 8.434 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6612 2.462
h = 0.001 0.001
y[1] (numeric) = -6.28878411626 -1.02086003127
y[1] (closed_form) = -6.2890685244 -1.019875721
absolute error = 0.001025
relative error = 0.01608 %
Correct 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) = 8.495 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6622 2.463
h = 0.001 0.003
y[1] (numeric) = -6.29800195807 -1.01371404825
y[1] (closed_form) = -6.29827377066 -1.0127328267
absolute error = 0.001018
relative error = 0.01596 %
Correct 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) = 8.454 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6632 2.466
h = 0.0001 0.004
y[1] (numeric) = -6.32357599237 -1.00860233825
y[1] (closed_form) = -6.32387374322 -1.00761583276
absolute error = 0.00103
relative error = 0.01609 %
Correct 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) = 8.464 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6633 2.47
h = 0.003 0.006
y[1] (numeric) = -6.35654863382 -1.01185896334
y[1] (closed_form) = -6.35686168473 -1.01088911812
absolute error = 0.001019
relative error = 0.01583 %
Correct 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) = 8.564 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6663 2.476
h = 0.0001 0.005
y[1] (numeric) = -6.40915933098 -0.993256594293
y[1] (closed_form) = -6.40949798531 -0.992190299027
absolute error = 0.001119
relative error = 0.01725 %
Correct 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) = 8.55 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6664 2.481
h = 0.0001 0.003
y[1] (numeric) = -6.45084996936 -0.997407951146
y[1] (closed_form) = -6.45116153798 -0.996400950141
absolute error = 0.001054
relative error = 0.01615 %
Correct 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) = 8.707 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6665 2.484
h = 0.001 0.001
y[1] (numeric) = -6.4760159165 -0.999610015225
y[1] (closed_form) = -6.4763019648 -0.998600865942
absolute error = 0.001049
relative error = 0.01601 %
Correct 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) = 8.805 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6675 2.485
h = 0.001 0.003
y[1] (numeric) = -6.48540153785 -0.992251729084
y[1] (closed_form) = -6.48567473052 -0.991245802626
absolute error = 0.001042
relative error = 0.01589 %
Correct 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) = 8.778 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6685 2.488
h = 0.0001 0.004
y[1] (numeric) = -6.51152306893 -0.986882407957
y[1] (closed_form) = -6.51182274112 -0.985870944985
absolute error = 0.001055
relative error = 0.01602 %
Correct 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) = 8.827 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1516.1MB, alloc=52.3MB, time=17.76
x[1] = 0.6686 2.492
h = 0.003 0.006
y[1] (numeric) = -6.54525638908 -0.990028725093
y[1] (closed_form) = -6.54557178486 -0.98903420735
absolute error = 0.001043
relative error = 0.01576 %
Correct 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) = 8.977 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6716 2.498
h = 0.0001 0.005
y[1] (numeric) = -6.59894814288 -0.970714520659
y[1] (closed_form) = -6.59928919555 -0.969621301255
absolute error = 0.001145
relative error = 0.01717 %
Correct 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) = 9.044 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6717 2.503
h = 0.0001 0.003
y[1] (numeric) = -6.6416005213 -0.974727383102
y[1] (closed_form) = -6.64191420653 -0.973694902236
absolute error = 0.001079
relative error = 0.01607 %
Correct 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) = 9.261 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6718 2.506
h = 0.001 0.001
y[1] (numeric) = -6.66734524246 -0.976839013624
y[1] (closed_form) = -6.66763283585 -0.975804471953
absolute error = 0.001074
relative error = 0.01593 %
Correct 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) = 9.394 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6728 2.507
h = 0.001 0.003
y[1] (numeric) = -6.6769012064 -0.969262880666
y[1] (closed_form) = -6.67717567895 -0.968231700394
absolute error = 0.001067
relative error = 0.01582 %
Correct 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) = 9.383 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6738 2.51
h = 0.0001 0.004
y[1] (numeric) = -6.70358089143 -0.963627408404
y[1] (closed_form) = -6.70388239557 -0.962590430347
absolute error = 0.00108
relative error = 0.01595 %
Correct 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) = 9.471 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6739 2.514
h = 0.003 0.006
y[1] (numeric) = -6.73809100385 -0.966656984858
y[1] (closed_form) = -6.73840866622 -0.965637241043
absolute error = 0.001068
relative error = 0.01569 %
Correct 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) = 9.665 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6769 2.52
h = 0.0001 0.005
y[1] (numeric) = -6.79288378917 -0.946609617385
y[1] (closed_form) = -6.79322715058 -0.945488869311
absolute error = 0.001172
relative error = 0.01709 %
Correct 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) = 9.813 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.677 2.525
h = 0.0001 0.003
y[1] (numeric) = -6.83651828969 -0.950475867682
y[1] (closed_form) = -6.83683400362 -0.949417336499
absolute error = 0.001105
relative error = 0.016 %
Correct 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) = 10.08 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6771 2.528
h = 0.001 0.001
y[1] (numeric) = -6.86285401495 -0.952492023263
y[1] (closed_form) = -6.86314305314 -0.951431523892
absolute error = 0.001099
relative error = 0.01586 %
Correct 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) = 10.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6781 2.529
h = 0.001 0.003
y[1] (numeric) = -6.87258291135 -0.944692360737
y[1] (closed_form) = -6.87285855832 -0.94363536593
absolute error = 0.001092
relative error = 0.01575 %
Correct 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) = 10.25 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6791 2.532
h = 0.0001 0.004
y[1] (numeric) = -6.89983159993 -0.938781945824
y[1] (closed_form) = -6.90013484151 -0.937718883015
absolute error = 0.001105
relative error = 0.01588 %
Correct 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) = 10.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6792 2.536
h = 0.003 0.006
y[1] (numeric) = -6.93513494512 -0.941688114479
y[1] (closed_form) = -6.93545479094 -0.940642579015
absolute error = 0.001093
relative error = 0.01562 %
Correct 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) = 10.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6822 2.542
h = 0.0001 0.005
y[1] (numeric) = -6.99104906783 -0.920885665267
y[1] (closed_form) = -6.99139464301 -0.919736770901
absolute error = 0.0012
relative error = 0.01701 %
Correct 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) = 10.83 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6823 2.547
h = 0.0001 0.003
y[1] (numeric) = -7.03568648609 -0.924596889792
y[1] (closed_form) = -7.03600413567 -0.923511725483
absolute error = 0.001131
relative error = 0.01593 %
Correct 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) = 11.15 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6824 2.55
h = 0.001 0.001
y[1] (numeric) = -7.06262569271 -0.926512347684
y[1] (closed_form) = -7.06291607002 -0.92542531313
absolute error = 0.001125
relative error = 0.0158 %
Correct 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) = 11.35 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6834 2.551
h = 0.0001 0.004
y[1] (numeric) = -7.0725301382 -0.918483330594
y[1] (closed_form) = -7.0728068486 -0.917399948491
absolute error = 0.001118
relative error = 0.01568 %
Correct 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) = 11.36 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6835 2.555
h = 0.003 0.006
y[1] (numeric) = -7.10849484061 -0.921284730653
y[1] (closed_form) = -7.10882497774 -0.920221879066
absolute error = 0.001113
relative error = 0.01553 %
Correct 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) = 11.63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6865 2.561
h = 0.0001 0.005
y[1] (numeric) = -7.16540005044 -0.89982801097
y[1] (closed_form) = -7.16575596205 -0.898659731344
absolute error = 0.001221
relative error = 0.01691 %
Correct 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) = 11.91 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1559.9MB, alloc=52.3MB, time=18.28
x[1] = 0.6866 2.566
h = 0.0001 0.003
y[1] (numeric) = -7.21091970949 -0.90341111643
y[1] (closed_form) = -7.21124743918 -0.902307894519
absolute error = 0.001151
relative error = 0.01584 %
Correct 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) = 12.26 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6867 2.569
h = 0.001 0.001
y[1] (numeric) = -7.23838984386 -0.905242968104
y[1] (closed_form) = -7.23868977627 -0.904137957342
absolute error = 0.001145
relative error = 0.0157 %
Correct 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) = 12.48 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6877 2.57
h = 0.001 0.003
y[1] (numeric) = -7.24845034092 -0.897013888788
y[1] (closed_form) = -7.24873636298 -0.895912658282
absolute error = 0.001138
relative error = 0.01558 %
Correct 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) = 12.51 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6887 2.573
h = 0.0001 0.004
y[1] (numeric) = -7.27679089452 -0.890574674255
y[1] (closed_form) = -7.27710559221 -0.889466855268
absolute error = 0.001152
relative error = 0.01571 %
Correct 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) = 12.69 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6888 2.577
h = 0.003 0.006
y[1] (numeric) = -7.31361683132 -0.893242560446
y[1] (closed_form) = -7.31394899083 -0.892152830831
absolute error = 0.001139
relative error = 0.01546 %
Correct 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) = 12.98 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6918 2.583
h = 0.0001 0.005
y[1] (numeric) = -7.37168233664 -0.870988601024
y[1] (closed_form) = -7.37204027812 -0.869790988835
absolute error = 0.00125
relative error = 0.01684 %
Correct 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) = 13.32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6919 2.588
h = 0.0001 0.003
y[1] (numeric) = -7.41824484482 -0.874400467163
y[1] (closed_form) = -7.41857432996 -0.873269492686
absolute error = 0.001178
relative error = 0.01577 %
Correct 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) = 13.71 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.692 2.591
h = 0.001 0.001
y[1] (numeric) = -7.44634241864 -0.876121557696
y[1] (closed_form) = -7.44664348576 -0.874988902554
absolute error = 0.001172
relative error = 0.01563 %
Correct 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) = 13.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.693 2.592
h = 0.001 0.003
y[1] (numeric) = -7.45658347774 -0.867651926948
y[1] (closed_form) = -7.45687034867 -0.86652320902
absolute error = 0.001165
relative error = 0.01551 %
Correct 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) = 13.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.694 2.595
h = 0.0001 0.004
y[1] (numeric) = -7.48552527692 -0.860911308353
y[1] (closed_form) = -7.4858414191 -0.859775704839
absolute error = 0.001179
relative error = 0.01564 %
Correct 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) = 14.2 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6941 2.599
h = 0.003 0.006
y[1] (numeric) = -7.5231934273 -0.863435566488
y[1] (closed_form) = -7.52352751137 -0.862318357453
absolute error = 0.001166
relative error = 0.0154 %
Correct 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) = 14.52 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6971 2.605
h = 0.0001 0.005
y[1] (numeric) = -7.58244051147 -0.840360679333
y[1] (closed_form) = -7.5828003716 -0.839133077994
absolute error = 0.001279
relative error = 0.01677 %
Correct 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) = 14.92 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6972 2.61
h = 0.0001 0.003
y[1] (numeric) = -7.6300678934 -0.843592002497
y[1] (closed_form) = -7.63039902534 -0.842432655886
absolute error = 0.001206
relative error = 0.01571 %
Correct 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) = 15.34 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6973 2.613
h = 0.001 0.001
y[1] (numeric) = -7.65880611838 -0.845196563723
y[1] (closed_form) = -7.65910819822 -0.844035650491
absolute error = 0.0012
relative error = 0.01557 %
Correct 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) = 15.59 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6983 2.614
h = 0.001 0.003
y[1] (numeric) = -7.66923043337 -0.836480131647
y[1] (closed_form) = -7.66951802564 -0.835323317695
absolute error = 0.001192
relative error = 0.01545 %
Correct 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) = 15.65 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6993 2.617
h = 0.0001 0.004
y[1] (numeric) = -7.69878510134 -0.829428286049
y[1] (closed_form) = -7.69910257221 -0.82826427944
absolute error = 0.001207
relative error = 0.01558 %
Correct 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) = 15.88 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6994 2.621
h = 0.003 0.006
y[1] (numeric) = -7.73731322776 -0.831801282113
y[1] (closed_form) = -7.73764913306 -0.830655979294
absolute error = 0.001194
relative error = 0.01534 %
Correct 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) = 16.23 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7024 2.627
h = 0.0001 0.005
y[1] (numeric) = -7.79776352141 -0.807881129389
y[1] (closed_form) = -7.79812518286 -0.806622868192
absolute error = 0.001309
relative error = 0.0167 %
Correct 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) = 16.67 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7025 2.632
h = 0.0001 0.003
y[1] (numeric) = -7.8464782451 -0.810922275263
y[1] (closed_form) = -7.84681090934 -0.809733923627
absolute error = 0.001234
relative error = 0.01564 %
Correct 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) = 17.12 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1603.7MB, alloc=52.3MB, time=18.80
x[1] = 0.7026 2.635
h = 0.001 0.001
y[1] (numeric) = -7.87587059787 -0.812404336473
y[1] (closed_form) = -7.8761735623 -0.811214538325
absolute error = 0.001228
relative error = 0.01551 %
Correct 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) = 17.4 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7036 2.636
h = 0.001 0.003
y[1] (numeric) = -7.88648088861 -0.803434697915
y[1] (closed_form) = -7.88676906845 -0.802249166358
absolute error = 0.00122
relative error = 0.01539 %
Correct 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) = 17.46 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7046 2.639
h = 0.0001 0.004
y[1] (numeric) = -7.91666025539 -0.796061517545
y[1] (closed_form) = -7.91697893313 -0.794868476012
absolute error = 0.001235
relative error = 0.01552 %
Correct 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) = 17.71 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7047 2.643
h = 0.003 0.006
y[1] (numeric) = -7.95606647713 -0.798275348
y[1] (closed_form) = -7.9564040946 -0.797101323795
absolute error = 0.001222
relative error = 0.01528 %
Correct 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) = 18.08 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7077 2.649
h = 0.0001 0.005
y[1] (numeric) = -8.01774196232 -0.773484925884
y[1] (closed_form) = -8.01810530144 -0.772195319722
absolute error = 0.00134
relative error = 0.01663 %
Correct 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) = 18.57 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7078 2.654
h = 0.0001 0.003
y[1] (numeric) = -8.06756694716 -0.776325919859
y[1] (closed_form) = -8.06790102313 -0.775107916727
absolute error = 0.001263
relative error = 0.01558 %
Correct 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) = 19.05 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7079 2.657
h = 0.001 0.001
y[1] (numeric) = -8.09762717401 -0.777679301942
y[1] (closed_form) = -8.09793088859 -0.776459978672
absolute error = 0.001257
relative error = 0.01545 %
Correct 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) = 19.34 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7089 2.658
h = 0.0001 0.004
y[1] (numeric) = -8.10842618609 -0.76844989293
y[1] (closed_form) = -8.1087148133 -0.767235008958
absolute error = 0.001249
relative error = 0.01533 %
Correct 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) = 19.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.709 2.662
h = 0.003 0.006
y[1] (numeric) = -8.14856449234 -0.770528904687
y[1] (closed_form) = -8.1489130674 -0.769335351646
absolute error = 0.001243
relative error = 0.01519 %
Correct 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) = 19.81 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.712 2.668
h = 0.0001 0.005
y[1] (numeric) = -8.21132324028 -0.744983798046
y[1] (closed_form) = -8.21169752731 -0.743672357142
absolute error = 0.001364
relative error = 0.01654 %
Correct 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) = 20.33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7121 2.673
h = 0.0001 0.003
y[1] (numeric) = -8.2621251572 -0.747657858921
y[1] (closed_form) = -8.26246993403 -0.746419507191
absolute error = 0.001285
relative error = 0.01549 %
Correct 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) = 20.84 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7122 2.676
h = 0.001 0.001
y[1] (numeric) = -8.29277312186 -0.748903550317
y[1] (closed_form) = -8.29308695491 -0.747663984298
absolute error = 0.001279
relative error = 0.01536 %
Correct 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) = 21.14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7132 2.677
h = 0.001 0.003
y[1] (numeric) = -8.30374000084 -0.7394474524
y[1] (closed_form) = -8.30403847907 -0.738212475068
absolute error = 0.001271
relative error = 0.01524 %
Correct 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) = 21.22 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7142 2.68
h = 0.0001 0.004
y[1] (numeric) = -8.33511811932 -0.731456218373
y[1] (closed_form) = -8.33544828441 -0.730213120062
absolute error = 0.001286
relative error = 0.01537 %
Correct 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) = 21.51 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7143 2.684
h = 0.003 0.006
y[1] (numeric) = -8.37620987694 -0.733362873811
y[1] (closed_form) = -8.37655995319 -0.732139393982
absolute error = 0.001273
relative error = 0.01513 %
Correct 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) = 21.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7173 2.69
h = 0.0001 0.005
y[1] (numeric) = -8.44023598699 -0.706899413986
y[1] (closed_form) = -8.44061171258 -0.705555312335
absolute error = 0.001396
relative error = 0.01648 %
Correct 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) = 22.49 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7174 2.695
h = 0.0001 0.003
y[1] (numeric) = -8.4921921709 -0.709354108848
y[1] (closed_form) = -8.49253812633 -0.708084864011
absolute error = 0.001316
relative error = 0.01544 %
Correct 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) = 23.03 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7175 2.698
h = 0.001 0.001
y[1] (numeric) = -8.52353440232 -0.710459219361
y[1] (closed_form) = -8.52384872576 -0.709188898666
absolute error = 0.001309
relative error = 0.0153 %
Correct 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) = 23.35 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7185 2.699
h = 0.001 0.003
y[1] (numeric) = -8.53469526191 -0.700730735194
y[1] (closed_form) = -8.53499391674 -0.699465186257
absolute error = 0.0013
relative error = 0.01518 %
Correct 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) = 23.44 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1647.5MB, alloc=52.3MB, time=19.31
x[1] = 0.7195 2.702
h = 0.0001 0.004
y[1] (numeric) = -8.56673322412 -0.692387760306
y[1] (closed_form) = -8.56706422056 -0.691113742284
absolute error = 0.001316
relative error = 0.01532 %
Correct 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) = 23.74 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7196 2.706
h = 0.003 0.006
y[1] (numeric) = -8.60875704595 -0.694111311304
y[1] (closed_form) = -8.60910849703 -0.692857237697
absolute error = 0.001302
relative error = 0.01508 %
Correct 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) = 24.18 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7226 2.712
h = 0.0001 0.005
y[1] (numeric) = -8.67407353732 -0.666702500979
y[1] (closed_form) = -8.67445055866 -0.665325010614
absolute error = 0.001428
relative error = 0.01642 %
Correct 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) = 24.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7227 2.717
h = 0.0001 0.003
y[1] (numeric) = -8.7272082487 -0.668926831876
y[1] (closed_form) = -8.72755524382 -0.667626007038
absolute error = 0.001346
relative error = 0.01538 %
Correct 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) = 25.35 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7228 2.72
h = 0.001 0.001
y[1] (numeric) = -8.75925929425 -0.669884555788
y[1] (closed_form) = -8.75957395449 -0.668582800409
absolute error = 0.001339
relative error = 0.01524 %
Correct 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) = 25.69 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7238 2.721
h = 0.001 0.003
y[1] (numeric) = -8.77061695409 -0.659876647022
y[1] (closed_form) = -8.77091562589 -0.658579852302
absolute error = 0.001331
relative error = 0.01513 %
Correct 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) = 25.78 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7248 2.724
h = 0.0001 0.004
y[1] (numeric) = -8.80332742114 -0.651170655701
y[1] (closed_form) = -8.80365910209 -0.649865032385
absolute error = 0.001347
relative error = 0.01526 %
Correct 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) = 26.11 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7249 2.728
h = 0.003 0.006
y[1] (numeric) = -8.84630286874 -0.652702087364
y[1] (closed_form) = -8.84665556179 -0.651416738721
absolute error = 0.001333
relative error = 0.01503 %
Correct 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) = 26.57 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7279 2.734
h = 0.0001 0.005
y[1] (numeric) = -8.9129331285 -0.624320197274
y[1] (closed_form) = -8.9133112956 -0.622908574705
absolute error = 0.001461
relative error = 0.01636 %
Correct 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) = 27.22 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.728 2.739
h = 0.0001 0.003
y[1] (numeric) = -8.96727111143 -0.626302786374
y[1] (closed_form) = -8.96761900043 -0.62496968
absolute error = 0.001378
relative error = 0.01533 %
Correct 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) = 27.81 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7281 2.742
h = 0.001 0.001
y[1] (numeric) = -9.00004580726 -0.62710608546
y[1] (closed_form) = -9.00036064354 -0.625772200981
absolute error = 0.001371
relative error = 0.01519 %
Correct 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) = 28.16 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7291 2.743
h = 0.001 0.003
y[1] (numeric) = -9.01160311154 -0.616811540455
y[1] (closed_form) = -9.01190163342 -0.615482811526
absolute error = 0.001362
relative error = 0.01508 %
Correct 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) = 28.27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7301 2.746
h = 0.0001 0.004
y[1] (numeric) = -9.04499896649 -0.60773093478
y[1] (closed_form) = -9.04533117805 -0.606393006021
absolute error = 0.001379
relative error = 0.01521 %
Correct 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) = 28.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7302 2.75
h = 0.003 0.006
y[1] (numeric) = -9.08894599052 -0.609060922688
y[1] (closed_form) = -9.08929978594 -0.607743603202
absolute error = 0.001364
relative error = 0.01497 %
Correct 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) = 29.09 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7332 2.756
h = 0.0001 0.005
y[1] (numeric) = -9.15691377775 -0.579677473524
y[1] (closed_form) = -9.15729293318 -0.578230959433
absolute error = 0.001495
relative error = 0.0163 %
Correct 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) = 29.78 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7333 2.761
h = 0.0001 0.003
y[1] (numeric) = -9.21248026853 -0.581406552154
y[1] (closed_form) = -9.2128288985 -0.580040447784
absolute error = 0.00141
relative error = 0.01527 %
Correct 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) = 30.4 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7334 2.764
h = 0.001 0.001
y[1] (numeric) = -9.24599374473 -0.582048149017
y[1] (closed_form) = -9.24630858888 -0.580681426331
absolute error = 0.001403
relative error = 0.01514 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 29.64
Order of pole (three term test) = 30.77 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7344 2.765
h = 0.0001 0.004
y[1] (numeric) = -9.25775356182 -0.571459578888
y[1] (closed_form) = -9.25805175937 -0.570098212797
absolute error = 0.001394
relative error = 0.01502 %
Correct 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) = 30.88 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7345 2.769
h = 0.003 0.006
y[1] (numeric) = -9.30251057152 -0.572619238968
y[1] (closed_form) = -9.30287600244 -0.571279907
absolute error = 0.001388
relative error = 0.0149 %
Correct 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) = 31.39 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1691.4MB, alloc=52.3MB, time=19.82
x[1] = 0.7375 2.775
h = 0.0001 0.005
y[1] (numeric) = -9.37166137711 -0.542366614103
y[1] (closed_form) = -9.37205209088 -0.540895519991
absolute error = 0.001522
relative error = 0.01621 %
Correct 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) = 32.11 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7376 2.78
h = 0.0001 0.003
y[1] (numeric) = -9.42830913539 -0.543882801003
y[1] (closed_form) = -9.42866909135 -0.542493778653
absolute error = 0.001435
relative error = 0.01519 %
Correct 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) = 32.75 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7377 2.783
h = 0.001 0.001
y[1] (numeric) = -9.46247292183 -0.544388245948
y[1] (closed_form) = -9.46279844649 -0.542998739911
absolute error = 0.001427
relative error = 0.01506 %
Correct 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) = 33.14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7387 2.784
h = 0.001 0.003
y[1] (numeric) = -9.47441299583 -0.533542992935
y[1] (closed_form) = -9.47472158038 -0.532159017545
absolute error = 0.001418
relative error = 0.01494 %
Correct 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) = 33.26 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7397 2.787
h = 0.0001 0.004
y[1] (numeric) = -9.50912406405 -0.52374184752
y[1] (closed_form) = -9.50946764468 -0.522347957671
absolute error = 0.001436
relative error = 0.01507 %
Correct 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) = 33.64 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7398 2.791
h = 0.003 0.006
y[1] (numeric) = -9.55493610284 -0.524683233996
y[1] (closed_form) = -9.55530236639 -0.523310594886
absolute error = 0.001421
relative error = 0.01485 %
Correct 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) = 34.16 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7428 2.797
h = 0.0001 0.005
y[1] (numeric) = -9.62547001179 -0.493374290344
y[1] (closed_form) = -9.6258614098 -0.491866846503
absolute error = 0.001557
relative error = 0.01616 %
Correct 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) = 34.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7429 2.802
h = 0.0001 0.003
y[1] (numeric) = -9.68339472866 -0.494614303895
y[1] (closed_form) = -9.68375513023 -0.493190907622
absolute error = 0.001468
relative error = 0.01514 %
Correct 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) = 35.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.743 2.805
h = 0.001 0.001
y[1] (numeric) = -9.71832634288 -0.494944033663
y[1] (closed_form) = -9.71865155078 -0.493520327639
absolute error = 0.00146
relative error = 0.01501 %
Correct 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) = 36.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.744 2.806
h = 0.001 0.003
y[1] (numeric) = -9.73047442313 -0.483790555722
y[1] (closed_form) = -9.73078234676 -0.482372593222
absolute error = 0.001451
relative error = 0.01489 %
Correct 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) = 36.14 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.745 2.809
h = 0.0001 0.004
y[1] (numeric) = -9.76590914058 -0.473579924488
y[1] (closed_form) = -9.76625277939 -0.47215164108
absolute error = 0.001469
relative error = 0.01502 %
Correct 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) = 36.54 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7451 2.813
h = 0.003 0.006
y[1] (numeric) = -9.81275216507 -0.474291656083
y[1] (closed_form) = -9.81311910134 -0.472884970725
absolute error = 0.001454
relative error = 0.0148 %
Correct 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) = 37.09 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7481 2.819
h = 0.0001 0.005
y[1] (numeric) = -9.8846940336 -0.441895669426
y[1] (closed_form) = -9.88508593594 -0.440351069427
absolute error = 0.001594
relative error = 0.0161 %
Correct 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) = 37.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7482 2.824
h = 0.0001 0.003
y[1] (numeric) = -9.94392240746 -0.442846565908
y[1] (closed_form) = -9.94428308019 -0.441388034831
absolute error = 0.001502
relative error = 0.01509 %
Correct 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) = 38.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7483 2.827
h = 0.001 0.001
y[1] (numeric) = -9.97963785247 -0.442992584159
y[1] (closed_form) = -9.97996255305 -0.441533925335
absolute error = 0.001494
relative error = 0.01496 %
Correct 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) = 39.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7493 2.828
h = 0.001 0.003
y[1] (numeric) = -9.99199687638 -0.431522963019
y[1] (closed_form) = -9.992303942 -0.430070267243
absolute error = 0.001485
relative error = 0.01485 %
Correct 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) = 39.16 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7503 2.831
h = 0.0001 0.004
y[1] (numeric) = -10.0281690173 -0.420889926703
y[1] (closed_form) = -10.028512531 -0.419426490536
absolute error = 0.001503
relative error = 0.01498 %
Correct 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) = 39.58 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7504 2.835
h = 0.003 0.006
y[1] (numeric) = -10.0760645502 -0.421361403288
y[1] (closed_form) = -10.0764319917 -0.419919916895
absolute error = 0.001488
relative error = 0.01475 %
Correct 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) = 40.15 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7534 2.841
h = 0.0001 0.005
y[1] (numeric) = -10.149439623 -0.387846825438
y[1] (closed_form) = -10.1498318413 -0.386264245794
absolute error = 0.00163
relative error = 0.01605 %
Correct digits = 4
memory used=1735.1MB, alloc=52.3MB, time=20.33
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) = 41 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7535 2.846
h = 0.0001 0.003
y[1] (numeric) = -10.2099988791 -0.388495225281
y[1] (closed_form) = -10.2103596405 -0.387000782437
absolute error = 0.001537
relative error = 0.01505 %
Correct 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) = 41.74 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7536 2.849
h = 0.001 0.001
y[1] (numeric) = -10.2465144725 -0.388449269114
y[1] (closed_form) = -10.2468384668 -0.386954888856
absolute error = 0.001529
relative error = 0.01491 %
Correct 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) = 42.18 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7546 2.85
h = 0.001 0.003
y[1] (numeric) = -10.2590873999 -0.376655393168
y[1] (closed_form) = -10.2593934019 -0.375167202316
absolute error = 0.001519
relative error = 0.0148 %
Correct 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) = 42.33 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7556 2.853
h = 0.0001 0.004
y[1] (numeric) = -10.2960109761 -0.365586667942
y[1] (closed_form) = -10.2963541733 -0.364087303818
absolute error = 0.001538
relative error = 0.01493 %
Correct 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) = 42.77 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7557 2.857
h = 0.003 0.006
y[1] (numeric) = -10.3449809642 -0.365806934388
y[1] (closed_form) = -10.3453487353 -0.364329876189
absolute error = 0.001522
relative error = 0.0147 %
Correct 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) = 43.37 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7587 2.863
h = 0.0001 0.005
y[1] (numeric) = -10.4198148783 -0.331141372919
y[1] (closed_form) = -10.4202072155 -0.329519972753
absolute error = 0.001668
relative error = 0.016 %
Correct 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) = 44.27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7588 2.868
h = 0.0001 0.003
y[1] (numeric) = -10.4817327783 -0.33147344825
y[1] (closed_form) = -10.4820934375 -0.329942300282
absolute error = 0.001573
relative error = 0.015 %
Correct 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) = 45.04 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7589 2.871
h = 0.001 0.001
y[1] (numeric) = -10.5190651576 -0.331226980628
y[1] (closed_form) = -10.519388238 -0.329696094184
absolute error = 0.001565
relative error = 0.01487 %
Correct 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) = 45.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7599 2.872
h = 0.001 0.003
y[1] (numeric) = -10.5318549702 -0.319100540551
y[1] (closed_form) = -10.5321596943 -0.317576076888
absolute error = 0.001555
relative error = 0.01475 %
Correct 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) = 45.65 0
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff ( y , x , 1 ) = 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=1758.5MB, alloc=52.3MB, time=20.59