|\^/| 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(0.05) * c(x) * c(x) + c(0.2) * c(x) - cos(c(0.3) * c( x) + c(0.1)) /c( 0.3));
> end;
exact_soln_y := proc(x)
return
c(0.05)*c(x)*c(x) + c(0.2)*c(x) - cos(c(0.3)*c(x) + c(0.1))/c(0.3)
end proc
> next_delta := proc()
> global glob_nxt, x_delta;
> x_delta := [ 0.001 + 0.00004 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.000 + 0.000 * I ];
> glob_nxt := glob_nxt + 1;
> it := x_delta[glob_nxt];
> return it;
> end;
Warning, `it` is implicitly declared local to procedure `next_delta`
next_delta := proc()
local it;
global glob_nxt, x_delta;
x_delta := [0.001 + 0.00004*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0. + 0.*I];
glob_nxt := glob_nxt + 1;
it := x_delta[glob_nxt];
return it
end proc
#END USER DEF BLOCK
#END BLOCK 3
#END USER FUNCTION BLOCK
# before write_aux functions
# Begin Function number 2
> display_poles := proc()
> local rad_given;
> global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ;
> if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1
> rad_given := float_abs(array_x[1] - (array_given_rad_poles[1,1] + array_given_rad_poles[1,2] * I ));
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," ");
> omniout_complex(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," ");
> if ((float_abs(rad_given) < float_abs(glob_least_given_sing)) and
> (float_abs(rad_given) > 0.0)) then # if number 2
> glob_least_given_sing := rad_given;
> fi;# end if 2;
> elif
> (glob_type_given_pole = 3) then # if number 2
> omniout_str(ALWAYS,"NO POLE (given) for Equation 1");
> elif
> (glob_type_given_pole = 5) then # if number 3
> omniout_str(ALWAYS,"SOME POLE (given) for Equation 1");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 1");
> fi;# end if 3;
> if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," ");
> if ((float_abs(array_rad_test_poles[1,1]) < glob_least_ratio_sing)) then # if number 4
> glob_least_ratio_sing := array_rad_test_poles[1,1];
> fi;# end if 4;
> omniout_complex(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," ");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," ");
> if ((float_abs(array_rad_test_poles[1,2]) < glob_least_3_sing)) then # if number 4
> glob_least_3_sing := array_rad_test_poles[1,2];
> fi;# end if 4;
> omniout_complex(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," ");
> if ((float_abs(array_rad_test_poles[1,3]) < glob_least_6_sing)) then # if number 4
> glob_least_6_sing := array_rad_test_poles[1,3];
> fi;# end if 4;
> omniout_complex(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1");
> fi;# end if 3
> ;
> end;
display_poles := proc()
local rad_given;
global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float,
glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord,
glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
glob_least_3_sing, glob_least_6_sing, glob_least_given_sing,
glob_least_ratio_sing, array_x;
if glob_type_given_pole = 1 or glob_type_given_pole = 2 then
rad_given := float_abs(array_x[1] - array_given_rad_poles[1, 1]
- array_given_rad_poles[1, 2]*I);
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 1 ", 4,
rad_given, 4, " ");
omniout_complex(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles[1, 1], 4, " ");
if float_abs(rad_given) < float_abs(glob_least_given_sing) and
0. < float_abs(rad_given) then glob_least_given_sing := rad_given
end if
elif glob_type_given_pole = 3 then
omniout_str(ALWAYS, "NO POLE (given) for Equation 1")
elif glob_type_given_pole = 5 then
omniout_str(ALWAYS, "SOME POLE (given) for Equation 1")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 1")
end if;
if array_rad_test_poles[1, 1] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (ratio test) for eq 1 ", 4,
array_rad_test_poles[1, 1], 4, " ");
if float_abs(array_rad_test_poles[1, 1]) < glob_least_ratio_sing
then glob_least_ratio_sing := array_rad_test_poles[1, 1]
end if;
omniout_complex(ALWAYS,
"Order of pole (ratio test) ", 4,
array_ord_test_poles[1, 1], 4, " ")
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 2] and
array_rad_test_poles[1, 2] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 1 ", 4,
array_rad_test_poles[1, 2], 4, " ");
if float_abs(array_rad_test_poles[1, 2]) < glob_least_3_sing then
glob_least_3_sing := array_rad_test_poles[1, 2]
end if;
omniout_complex(ALWAYS,
"Order of pole (three term test) ", 4,
array_ord_test_poles[1, 2], 4, " ")
else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 3] and
array_rad_test_poles[1, 3] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 1 ", 4,
array_rad_test_poles[1, 3], 4, " ");
if float_abs(array_rad_test_poles[1, 3]) < glob_least_6_sing then
glob_least_6_sing := array_rad_test_poles[1, 3]
end if;
omniout_complex(ALWAYS,
"Order of pole (six term test) ", 4,
array_ord_test_poles[1, 3], 4, " ")
else omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 1")
end if
end proc
# End Function number 2
# Begin Function number 3
> my_check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 3
> ret := glob__1;
> else
> ret := glob__m1;
> fi;# end if 3;
> ret;;
> end;
my_check_sign := proc(x0, xf)
local ret;
if x0 < xf then ret := glob__1 else ret := glob__m1 end if; ret
end proc
# End Function number 3
# Begin Function number 4
> est_size_answer := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6_g,
> array_tmp6,
> array_tmp7,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local min_size;
> min_size := glob_estimated_size_answer;
> if (float_abs(array_y[1]) < min_size) then # if number 3
> min_size := float_abs(array_y[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> if (min_size < glob__1) then # if number 3
> min_size := glob__1;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> min_size;
> end;
est_size_answer := proc()
local min_size;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6_g,
array_tmp6, array_tmp7, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
min_size := glob_estimated_size_answer;
if float_abs(array_y[1]) < min_size then
min_size := float_abs(array_y[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if min_size < glob__1 then
min_size := glob__1;
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
min_size
end proc
# End Function number 4
# Begin Function number 5
> test_suggested_h := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6_g,
> array_tmp6,
> array_tmp7,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> max_estimated_step_error := glob__small;
> no_terms := ATS_MAX_TERMS;
> hn_div_ho := glob__0_5;
> hn_div_ho_2 := glob__0_25;
> hn_div_ho_3 := glob__0_125;
> omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,"");
> omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,"");
> omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,"");
> est_tmp := float_abs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3);
> if (est_tmp >= max_estimated_step_error) then # if number 3
> max_estimated_step_error := est_tmp;
> fi;# end if 3;
> omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,"");
> max_estimated_step_error;
> end;
test_suggested_h := proc()
local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3,
no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6_g,
array_tmp6, array_tmp7, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
max_estimated_step_error := glob__small;
no_terms := ATS_MAX_TERMS;
hn_div_ho := glob__0_5;
hn_div_ho_2 := glob__0_25;
hn_div_ho_3 := glob__0_125;
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, "");
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, "");
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, "");
est_tmp := float_abs(array_y[no_terms - 3]
+ array_y[no_terms - 2]*hn_div_ho
+ array_y[no_terms - 1]*hn_div_ho_2
+ array_y[no_terms]*hn_div_ho_3);
if max_estimated_step_error <= est_tmp then
max_estimated_step_error := est_tmp
end if;
omniout_float(ALWAYS, "max_estimated_step_error", 32,
max_estimated_step_error, 32, "");
max_estimated_step_error
end proc
# End Function number 5
# Begin Function number 6
> track_estimated_error := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6_g,
> array_tmp6,
> array_tmp7,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> no_terms := ATS_MAX_TERMS;
> hn_div_ho := glob__0_5;
> hn_div_ho_2 := glob__0_25;
> hn_div_ho_3 := glob__0_125;
> est_tmp := c(float_abs(array_y[no_terms-3])) + c(float_abs(array_y[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y[no_terms])) * c(hn_div_ho_3);
> if (glob_prec * c(float_abs(array_y[1])) > c(est_tmp)) then # if number 3
> est_tmp := c(glob_prec) * c(float_abs(array_y[1]));
> fi;# end if 3;
> if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 3
> array_max_est_error[1] := c(est_tmp);
> fi;# end if 3
> ;
> end;
track_estimated_error := proc()
local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6_g,
array_tmp6, array_tmp7, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
no_terms := ATS_MAX_TERMS;
hn_div_ho := glob__0_5;
hn_div_ho_2 := glob__0_25;
hn_div_ho_3 := glob__0_125;
est_tmp := c(float_abs(array_y[no_terms - 3]))
+ c(float_abs(array_y[no_terms - 2]))*c(hn_div_ho)
+ c(float_abs(array_y[no_terms - 1]))*c(hn_div_ho_2)
+ c(float_abs(array_y[no_terms]))*c(hn_div_ho_3);
if c(est_tmp) < glob_prec*c(float_abs(array_y[1])) then
est_tmp := c(glob_prec)*c(float_abs(array_y[1]))
end if;
if c(array_max_est_error[1]) <= c(est_tmp) then
array_max_est_error[1] := c(est_tmp)
end if
end proc
# End Function number 6
# Begin Function number 7
> reached_interval := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6_g,
> array_tmp6,
> array_tmp7,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local ret;
> if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 3
> ret := true;
> else
> ret := false;
> fi;# end if 3;
> return(ret);
> end;
reached_interval := proc()
local ret;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6_g,
array_tmp6, array_tmp7, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
if glob_check_sign*glob_next_display - glob_h/glob__10 <=
glob_check_sign*array_x[1] then ret := true
else ret := false
end if;
return ret
end proc
# End Function number 7
# Begin Function number 8
> display_alot := proc(iter)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6_g,
> array_tmp6,
> array_tmp7,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err;
> #TOP DISPLAY ALOT
> ind_var := array_x[1];
> omniout_complex(ALWAYS,"x[1] ",33,ind_var,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> omniout_complex(ALWAYS,"h ",33,glob_h,20," ");
> omniout_complex(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> closed_form_val_y := evalf(exact_soln_y(ind_var));
> omniout_complex(ALWAYS,"y[1] (closed_form) ",33,closed_form_val_y,20," ");
> abserr := float_abs(numeric_val - closed_form_val_y);
> if (float_abs(closed_form_val_y) > 0.0) then # if number 3
> relerr := abserr/float_abs(closed_form_val_y);
> if (float_abs(c(relerr)) > 0.0) then # if number 4
> glob_good_digits := round(-log10(relerr));
> else
> relerr := 0.0 ;
> glob_good_digits := Digits - 2;
> fi;# end if 4;
> else
> ;
> relerr := glob__m1 ;
> glob_good_digits := -16;
> fi;# end if 3;
> if (glob_good_digits < glob_min_good_digits) then # if number 3
> glob_min_good_digits := glob_good_digits;
> fi;# end if 3;
> omniout_float(ALWAYS,"absolute error ",4,abserr,4," ");
> omniout_float(ALWAYS,"relative error ",4,relerr * glob__100 ,4,"%");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> #BOTTOM DISPLAY ALOT
> end;
display_alot := proc(iter)
local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no,
est_rel_err;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6_g,
array_tmp6, array_tmp7, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
ind_var := array_x[1];
omniout_complex(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
omniout_complex(ALWAYS, "h ", 33, glob_h,
20, " ");
omniout_complex(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
closed_form_val_y := evalf(exact_soln_y(ind_var));
omniout_complex(ALWAYS, "y[1] (closed_form) ", 33,
closed_form_val_y, 20, " ");
abserr := float_abs(numeric_val - closed_form_val_y);
if 0. < float_abs(closed_form_val_y) then
relerr := abserr/float_abs(closed_form_val_y);
if 0. < float_abs(c(relerr)) then
glob_good_digits := round(-log10(relerr))
else relerr := 0.; glob_good_digits := Digits - 2
end if
else relerr := glob__m1; glob_good_digits := -16
end if;
if glob_good_digits < glob_min_good_digits then
glob_min_good_digits := glob_good_digits
end if;
omniout_float(ALWAYS, "absolute error ", 4, abserr, 4,
" ");
omniout_float(ALWAYS, "relative error ", 4,
relerr*glob__100, 4, "%");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ")
end proc
# End Function number 8
# Begin Function number 9
> prog_report := proc(x_start,x_end)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6_g,
> array_tmp6,
> array_tmp7,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := (clock_sec1) - (glob_orig_start_sec);
> glob_clock_sec := (clock_sec1) - (glob_clock_start_sec);
> left_sec := (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1);
> expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h) ,( clock_sec1) - (glob_orig_start_sec));
> opt_clock_sec := ( clock_sec1) - (glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec));
> glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
> percent_done := comp_percent((x_end),(x_start),(array_x[1]) + (glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr((total_clock_sec));
> if (c(percent_done) < glob__100) then # if number 3
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr((expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr((glob_optimal_expect_sec));
> omniout_str_noeol(INFO,"Expected Total Time ");
> omniout_timestr((glob_total_exp_sec));
> fi;# end if 3;
> #BOTTOM PROGRESS REPORT
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6_g,
array_tmp6, array_tmp7, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec := clock_sec1 - glob_orig_start_sec;
glob_clock_sec := clock_sec1 - glob_clock_start_sec;
left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1;
expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h,
clock_sec1 - glob_orig_start_sec);
opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec;
glob_optimal_expect_sec :=
comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec)
;
glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h);
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(total_clock_sec);
if c(percent_done) < glob__100 then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(expect_sec);
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(glob_optimal_expect_sec);
omniout_str_noeol(INFO, "Expected Total Time ");
omniout_timestr(glob_total_exp_sec)
end if
end proc
# End Function number 9
# Begin Function number 10
> check_for_pole := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6_g,
> array_tmp6,
> array_tmp7,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad, last_no;
> #TOP CHECK FOR POLE
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,1] := glob_larger_float;
> array_ord_test_poles[1,1] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 3
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 3;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 3
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 4
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 5
> found_sing := 0;
> fi;# end if 5;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 5
> if (rad_c < array_rad_test_poles[1,1]) then # if number 6
> array_rad_test_poles[1,1] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,1] := rad_c;
> array_ord_test_poles[1,1] := tmp_ord;
> fi;# end if 6;
> fi;# end if 5;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,2] := glob_larger_float;
> array_ord_test_poles[1,2] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 5
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 5;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 6
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 7
> found_sing := 0;
> fi;# end if 7;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 7
> if (rad_c < array_rad_test_poles[1,2]) then # if number 8
> array_rad_test_poles[1,2] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,2] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 9
> glob_min_pole_est := rad_c;
> fi;# end if 9;
> array_ord_test_poles[1,2] := tmp_ord;
> fi;# end if 8;
> fi;# end if 7;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,3] := glob_larger_float;
> array_ord_test_poles[1,3] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 7
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 7;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 8
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 9
> found_sing := 0;
> fi;# end if 9;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 9
> if (rad_c < array_rad_test_poles[1,3]) then # if number 10
> array_rad_test_poles[1,3] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,3] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 11
> glob_min_pole_est := rad_c;
> fi;# end if 11;
> array_ord_test_poles[1,3] := tmp_ord;
> fi;# end if 10;
> fi;# end if 9;
> #BOTTOM general radius test1
> ;
> if (true) then # if number 9
> display_poles();
> fi;# end if 9
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2,
term3, part1, part2, part3, part4, part5, part6, part7, part8, part9,
part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4,
found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio,
prev_tmp_rad, last_no;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6_g,
array_tmp6, array_tmp7, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 1] := glob_larger_float;
array_ord_test_poles[1, 1] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do
tmp_rad := comp_rad_from_ratio(array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 1] then
array_rad_test_poles[1, 1] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_ratio(array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
array_rad_test_poles[1, 1] := rad_c;
array_ord_test_poles[1, 1] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 2] := glob_larger_float;
array_ord_test_poles[1, 2] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do
tmp_rad := comp_rad_from_three_terms(
array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 2] then
array_rad_test_poles[1, 2] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_three_terms(
array_y_higher[1, last_no - 2],
array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
last_no);
array_rad_test_poles[1, 2] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 2] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 3] := glob_larger_float;
array_ord_test_poles[1, 3] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do
tmp_rad := comp_rad_from_six_terms(array_y_higher[1, last_no - 5],
array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3],
array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 3] then
array_rad_test_poles[1, 3] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_six_terms(
array_y_higher[1, last_no - 5],
array_y_higher[1, last_no - 4],
array_y_higher[1, last_no - 3],
array_y_higher[1, last_no - 2],
array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
last_no);
array_rad_test_poles[1, 3] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 3] := tmp_ord
end if
end if;
display_poles()
end proc
# End Function number 10
# Begin Function number 11
> atomall := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6_g,
> array_tmp6,
> array_tmp7,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> # before write maple main top matter
> # before generate constants assign
> # before generate globals assign
> #END OUTFILE1
> #BEGIN OUTFILE2
> #END OUTFILE2
> #BEGIN ATOMHDR1
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 1
> array_tmp1[1] := array_const_0D1[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp2[1] := array_tmp1[1] + array_const_0D2[1];
> #emit pre add CONST - LINEAR $eq_no = 1 i = 1
> array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 1
> array_tmp4[1] := array_const_0D3[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp5[1] := array_tmp4[1] + array_const_0D1[1];
> #emit pre sin 1 $eq_no = 1
> array_tmp6[1] := sin(array_tmp5[1]);
> array_tmp6_g[1] := cos(array_tmp5[1]);
> #emit pre add LINEAR - FULL $eq_no = 1 i = 1
> array_tmp7[1] := array_tmp3[1] + array_tmp6[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_tmp7[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
> if (2 <= ATS_MAX_TERMS) then # if number 3
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(1);
> array_y_higher[2,1] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
> array_tmp1[2] := array_const_0D1[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre add CONST - LINEAR $eq_no = 1 i = 2
> array_tmp3[2] := array_tmp2[2];
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
> array_tmp4[2] := array_const_0D3[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp5[2] := array_tmp4[2];
> #emit pre sin ID_LINEAR iii = 2 $eq_no = 1
> array_tmp6[2] := array_tmp6_g[1] * array_tmp5[2] / c(1);
> array_tmp6_g[2] := neg(array_tmp6[1]) * array_tmp5[2] / c(1);
> #emit pre add LINEAR - FULL $eq_no = 1 i = 2
> array_tmp7[2] := array_tmp3[2] + array_tmp6[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_tmp7[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_tmp6[3] := array_tmp6_g[2] * array_tmp5[2] / c(2);
> array_tmp6_g[3] := neg(array_tmp6[2]) * array_tmp5[2] / c(2);
> #emit pre add LINEAR FULL $eq_no = 1 i = 3
> array_tmp7[3] := array_tmp6[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_tmp7[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_tmp6[4] := array_tmp6_g[3] * array_tmp5[2] / c(3);
> array_tmp6_g[4] := neg(array_tmp6[3]) * array_tmp5[2] / c(3);
> #emit pre add LINEAR FULL $eq_no = 1 i = 4
> array_tmp7[4] := array_tmp6[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_tmp7[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_tmp6[5] := array_tmp6_g[4] * array_tmp5[2] / c(4);
> array_tmp6_g[5] := neg(array_tmp6[4]) * array_tmp5[2] / c(4);
> #emit pre add LINEAR FULL $eq_no = 1 i = 5
> array_tmp7[5] := array_tmp6[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_tmp7[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_tmp6[kkk] := array_tmp6_g[kkk - 1] * array_tmp5[2] / c(kkk - 1);
> array_tmp6_g[kkk] := neg(array_tmp6[kkk - 1]) * array_tmp5[2] / c(kkk - 1);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp7[kkk] := array_tmp6[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_tmp7[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
> array_y[kkk + order_d] := c(temporary);
> array_y_higher[1,kkk + order_d] := c(temporary);
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := c(temporary) / c(glob_h) * c(adj2);
> else
> temporary := c(temporary);
> fi;# end if 4;
> array_y_higher[adj3,term] := c(temporary);
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 1
> fi;# end if 2
> fi;# end if 1;
> kkk := kkk + 1;
> od;# end do number 1;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6_g,
array_tmp6, array_tmp7, array_m1, array_y_higher, array_y_higher_work,
array_y_higher_work2, array_y_set_initial, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
array_fact_2, ATS_MAX_TERMS, glob_last;
array_tmp1[1] := array_const_0D1[1]*array_x[1];
array_tmp2[1] := array_tmp1[1] + array_const_0D2[1];
array_tmp3[1] := array_const_0D0[1] + array_tmp2[1];
array_tmp4[1] := array_const_0D3[1]*array_x[1];
array_tmp5[1] := array_tmp4[1] + array_const_0D1[1];
array_tmp6[1] := sin(array_tmp5[1]);
array_tmp6_g[1] := cos(array_tmp5[1]);
array_tmp7[1] := array_tmp3[1] + array_tmp6[1];
if not array_y_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp7[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
if 2 <= ATS_MAX_TERMS then
array_y[2] := temporary; array_y_higher[1, 2] := temporary
end if;
temporary := c(temporary)*c(1)/c(glob_h);
array_y_higher[2, 1] := c(temporary)
end if
end if;
kkk := 2;
array_tmp1[2] := array_const_0D1[1]*array_x[2];
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := array_tmp2[2];
array_tmp4[2] := array_const_0D3[1]*array_x[2];
array_tmp5[2] := array_tmp4[2];
array_tmp6[2] := array_tmp6_g[1]*array_tmp5[2]/c(1);
array_tmp6_g[2] := neg(array_tmp6[1])*array_tmp5[2]/c(1);
array_tmp7[2] := array_tmp3[2] + array_tmp6[2];
if not array_y_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp7[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_tmp6[3] := array_tmp6_g[2]*array_tmp5[2]/c(2);
array_tmp6_g[3] := neg(array_tmp6[2])*array_tmp5[2]/c(2);
array_tmp7[3] := array_tmp6[3];
if not array_y_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp7[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_tmp6[4] := array_tmp6_g[3]*array_tmp5[2]/c(3);
array_tmp6_g[4] := neg(array_tmp6[3])*array_tmp5[2]/c(3);
array_tmp7[4] := array_tmp6[4];
if not array_y_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp7[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_tmp6[5] := array_tmp6_g[4]*array_tmp5[2]/c(4);
array_tmp6_g[5] := neg(array_tmp6[4])*array_tmp5[2]/c(4);
array_tmp7[5] := array_tmp6[5];
if not array_y_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp7[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_tmp6[kkk] := array_tmp6_g[kkk - 1]*array_tmp5[2]/c(kkk - 1);
array_tmp6_g[kkk] :=
neg(array_tmp6[kkk - 1])*array_tmp5[2]/c(kkk - 1);
array_tmp7[kkk] := array_tmp6[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_tmp7[kkk])*expt(glob_h, c(order_d))*
c(factorial_3(kkk - 1, kkk + order_d - 1));
array_y[kkk + order_d] := c(temporary);
array_y_higher[1, kkk + order_d] := c(temporary);
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while
1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1
do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := c(temporary)*c(adj2)/c(glob_h)
else temporary := c(temporary)
end if;
array_y_higher[adj3, term] := c(temporary)
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
# End Function number 12
#END OUTFILE5
# Begin Function number 12
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it;
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6_g,
> array_tmp6,
> array_tmp7,
> 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:= Array(0..(40),[]);
> array_tmp2:= Array(0..(40),[]);
> array_tmp3:= Array(0..(40),[]);
> array_tmp4:= Array(0..(40),[]);
> array_tmp5:= Array(0..(40),[]);
> array_tmp6_g:= Array(0..(40),[]);
> array_tmp6:= Array(0..(40),[]);
> array_tmp7:= 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[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp3[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp4[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp5[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp6_g[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp6[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp7[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);
> zero_ats_ar(array_tmp2);
> zero_ats_ar(array_tmp3);
> zero_ats_ar(array_tmp4);
> zero_ats_ar(array_tmp5);
> zero_ats_ar(array_tmp6_g);
> zero_ats_ar(array_tmp6);
> zero_ats_ar(array_tmp7);
> zero_ats_ar(array_m1);
> zero_ats_ar(array_const_1);
> array_const_1[1] := c(1);
> zero_ats_ar(array_const_0D0);
> array_const_0D0[1] := c(0.0);
> zero_ats_ar(array_const_0D1);
> array_const_0D1[1] := c(0.1);
> zero_ats_ar(array_const_0D2);
> array_const_0D2[1] := c(0.2);
> zero_ats_ar(array_const_0D3);
> array_const_0D3[1] := c(0.3);
> 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/add_lin_fullpostcpx.cpx#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) + sin ( 0.3 * x + 0.1 ) ; ");
> 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 := false;");
> 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,"#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,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"return(c(0.05) * c(x) * c(x) + c(0.2) * c(x) - cos(c(0.3) * c( x) + c(0.1)) /c( 0.3));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"next_delta := proc()");
> omniout_str(ALWAYS,"global glob_nxt, x_delta;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"x_delta := [ 0.001 + 0.00004 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.000 + 0.000 * I ];");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_nxt := glob_nxt + 1;");
> omniout_str(ALWAYS,"it := x_delta[glob_nxt];");
> omniout_str(ALWAYS,"return it;");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := glob__0;
> glob_smallish_float := glob__0;
> glob_large_float := c(1.0e100);
> glob_larger_float := c( 1.1e100);
> glob_almost_1 := c( 0.99);
> # before second block
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #BEGIN BLOCK 2
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := 0.1 + 0.1 * I;
> x_end := 99.0 + 99.0 * I;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := false;
> 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 ) = ( 0.1 * x + 0.2 ) + sin ( 0.3 * x + 0.1 ) ; ");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 10
> logstart(html_log_file);
> logitem_str(html_log_file,"2017-11-26T14:31:46-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"add_lin_full")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) + sin ( 0.3 * x + 0.1 ) ; ")
> ;
> 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,"add_lin_full diffeq.mxt")
> ;
> logitem_str(html_log_file,"add_lin_full maple results")
> ;
> logitem_str(html_log_file,"OK")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 15;
> if (glob_html_log) then # if number 15
> fclose(html_log_file);
> fi;# end if 15
> ;
> ;;
> end;
> # End Function number 12
> #END OUTFILEMAIN
> end;
Warning, `h_new` is implicitly declared local to procedure `main`
Warning, `ratio` is implicitly declared local to procedure `main`
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max,
term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order,
sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it,
last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err,
estimated_step_error, min_value, est_answer, found_h, repeat_it, h_new,
ratio;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6_g,
array_tmp6, array_tmp7, 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 := Array(0 .. 40, []);
array_tmp2 := Array(0 .. 40, []);
array_tmp3 := Array(0 .. 40, []);
array_tmp4 := Array(0 .. 40, []);
array_tmp5 := Array(0 .. 40, []);
array_tmp6_g := Array(0 .. 40, []);
array_tmp6 := Array(0 .. 40, []);
array_tmp7 := 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[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp3[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp4[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp5[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp6_g[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 40 do array_tmp6[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp7[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);
zero_ats_ar(array_tmp2);
zero_ats_ar(array_tmp3);
zero_ats_ar(array_tmp4);
zero_ats_ar(array_tmp5);
zero_ats_ar(array_tmp6_g);
zero_ats_ar(array_tmp6);
zero_ats_ar(array_tmp7);
zero_ats_ar(array_m1);
zero_ats_ar(array_const_1);
array_const_1[1] := c(1);
zero_ats_ar(array_const_0D0);
array_const_0D0[1] := c(0.);
zero_ats_ar(array_const_0D1);
array_const_0D1[1] := c(0.1);
zero_ats_ar(array_const_0D2);
array_const_0D2[1] := c(0.2);
zero_ats_ar(array_const_0D3);
array_const_0D3[1] := c(0.3);
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/add_lin_fullpostcpx.cpx#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = ( 0.1 * x + \
0.2 ) + sin ( 0.3 * x + 0.1 ) ; ");
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 := false;");
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, "#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, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "return(c(0.05) * c(x) * c(x) + c(0.2) * c(x) - c\
os(c(0.3) * c( x) + c(0.1)) /c( 0.3));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "next_delta := proc()");
omniout_str(ALWAYS, "global glob_nxt, x_delta;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "x_delta := [ 0.001 + 0.00004 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
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omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.000 + 0.000 * I ];");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_nxt := glob_nxt + 1;");
omniout_str(ALWAYS, "it := x_delta[glob_nxt];");
omniout_str(ALWAYS, "return it;");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := glob__0;
glob_smallish_float := glob__0;
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob_almost_1 := c(0.99);
x_start := 0.1 + 0.1*I;
x_end := 99.0 + 99.0*I;
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := false;
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 ) = ( 0.1 * x +\
0.2 ) + sin ( 0.3 * x + 0.1 ) ; ");
omniout_int(INFO, "Iterations ", 32, glob_iter,
4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2017-11-26T14:31:46-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"add_lin_full");
logitem_str(html_log_file, "diff ( y , x , 1 ) = (\
0.1 * x + 0.2 ) + sin ( 0.3 * x + 0.1 ) ; \
");
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, "add_lin_full diffeq.mxt");
logitem_str(html_log_file, "add_lin_full 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=3.6MB, alloc=40.3MB, time=0.08
##############ECHO OF PROBLEM#################
##############temp/add_lin_fullpostcpx.cpx#################
diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) + sin ( 0.3 * x + 0.1 ) ;
!
#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 := false;
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(0.05) * c(x) * c(x) + c(0.2) * c(x) - cos(c(0.3) * c( x) + c(0.1)) /c( 0.3));
end;
next_delta := proc()
global glob_nxt, x_delta;
x_delta := [ 0.001 + 0.00004 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.000 + 0.000 * I ];
glob_nxt := glob_nxt + 1;
it := x_delta[glob_nxt];
return it;
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = 0.1 0.1
h = 0.0001 0.005
y[1] (numeric) = -3.28669376678 0.0339653588616
y[1] (closed_form) = -3.28669376678 0.0339653588616
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 = 0.5499
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1001 0.105
h = 0.0001 0.003
y[1] (numeric) = -3.28686252766 0.0356679871473
y[1] (closed_form) = -3.28686352163 0.035668010033
absolute error = 9.942e-07
relative error = 3.025e-05 %
Correct digits = 7
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2648
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1002 0.108
h = 0.001 0.001
y[1] (numeric) = -3.28695675123 0.0366915441239
y[1] (closed_form) = -3.28695655245 0.0366915234769
absolute error = 1.998e-07
relative error = 6.080e-06 %
Correct digits = 7
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2083
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1012 0.109
h = 0.001 0.003
y[1] (numeric) = -3.28666047607 0.0370748759779
y[1] (closed_form) = -3.28665970144 0.0370746347864
absolute error = 8.113e-07
relative error = 2.468e-05 %
Correct digits = 7
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9912
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1022 0.112
h = 0.0001 0.004
y[1] (numeric) = -3.28645067549 0.0381395426091
y[1] (closed_form) = -3.2864510924 0.0381397029064
absolute error = 4.467e-07
relative error = 1.359e-05 %
Correct digits = 7
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.563
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1023 0.116
h = 0.003 0.006
y[1] (numeric) = -3.28659705967 0.039507185738
y[1] (closed_form) = -3.28659829205 0.0395066529561
absolute error = 1.343e-06
relative error = 4.085e-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 = 0.7478
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1053 0.122
h = 0.0001 0.005
y[1] (numeric) = -3.28585654242 0.0416918009299
y[1] (closed_form) = -3.28585841446 0.0416959226192
absolute error = 4.527e-06
relative error = 0.0001378 %
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 = 0.3358
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1054 0.127
h = 0.0001 0.003
y[1] (numeric) = -3.28607071088 0.0434089154476
y[1] (closed_form) = -3.28607165741 0.0434101311128
absolute error = 1.541e-06
relative error = 4.688e-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 = 0.2713
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1055 0.13
h = 0.001 0.001
y[1] (numeric) = -3.28619094171 0.0444397605575
y[1] (closed_form) = -3.28619069551 0.0444409318631
absolute error = 1.197e-06
relative error = 3.642e-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 = 0.2134
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=30.1MB, alloc=40.3MB, time=0.37
x[1] = 0.1065 0.131
h = 0.001 0.003
y[1] (numeric) = -3.28590126831 0.044833971341
y[1] (closed_form) = -3.2859004464 0.0448349216976
absolute error = 1.256e-06
relative error = 3.823e-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 = 1.015
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1075 0.134
h = 0.0001 0.004
y[1] (numeric) = -3.28571554897 0.0459137937069
y[1] (closed_form) = -3.28571591835 0.0459151463914
absolute error = 1.402e-06
relative error = 4.267e-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 = 0.5768
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1076 0.138
h = 0.003 0.006
y[1] (numeric) = -3.28589667801 0.0472908696652
y[1] (closed_form) = -3.28589786336 0.0472915298188
absolute error = 1.357e-06
relative error = 4.129e-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 = 0.7665
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1106 0.144
h = 0.0001 0.005
y[1] (numeric) = -3.28520217702 0.0495145501966
y[1] (closed_form) = -3.28520399879 0.0495198654459
absolute error = 5.619e-06
relative error = 0.000171 %
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 = 0.3443
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1107 0.149
h = 0.0001 0.003
y[1] (numeric) = -3.28545982477 0.05124325353
y[1] (closed_form) = -3.28546072305 0.0512456619655
absolute error = 2.571e-06
relative error = 7.823e-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 = 0.2782
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1108 0.152
h = 0.001 0.001
y[1] (numeric) = -3.28560605872 0.0522814052504
y[1] (closed_form) = -3.28560576424 0.0522837684794
absolute error = 2.382e-06
relative error = 7.247e-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 = 0.2189
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1118 0.153
h = 0.001 0.003
y[1] (numeric) = -3.28532297972 0.0526865000231
y[1] (closed_form) = -3.28532210966 0.0526886418825
absolute error = 2.312e-06
relative error = 7.036e-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 = 1.042
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1128 0.156
h = 0.0001 0.004
y[1] (numeric) = -3.2851613319 0.0537814956513
y[1] (closed_form) = -3.2851616529 0.0537840407089
absolute error = 2.565e-06
relative error = 7.807e-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 = 0.5918
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1129 0.16
h = 0.003 0.006
y[1] (numeric) = -3.28537720069 0.055168029396
y[1] (closed_form) = -3.28537833821 0.0551698824626
absolute error = 2.174e-06
relative error = 6.617e-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 = 0.7865
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1159 0.166
h = 0.0001 0.005
y[1] (numeric) = -3.28472869073 0.0574308098284
y[1] (closed_form) = -3.28473046137 0.0574373187679
absolute error = 6.745e-06
relative error = 0.0002053 %
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 = 0.3533
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.116 0.171
h = 0.0001 0.003
y[1] (numeric) = -3.2850298121 0.0591711338256
y[1] (closed_form) = -3.28503066129 0.059174735058
absolute error = 3.700e-06
relative error = 0.0001126 %
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 = 0.2856
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1161 0.174
h = 0.001 0.001
y[1] (numeric) = -3.2852020457 0.0602166112675
y[1] (closed_form) = -3.28520170206 0.0602201664263
absolute error = 3.572e-06
relative error = 0.0001087 %
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 = 0.2247
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1171 0.175
h = 0.001 0.003
y[1] (numeric) = -3.28492555377 0.060632595527
y[1] (closed_form) = -3.28492463465 0.0606359288799
absolute error = 3.458e-06
relative error = 0.0001052 %
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 = 1.069
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1181 0.178
h = 0.0001 0.004
y[1] (numeric) = -3.28478796826 0.0617427827902
y[1] (closed_form) = -3.28478824002 0.0617465202427
absolute error = 3.747e-06
relative error = 0.0001141 %
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 = 0.6077
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1182 0.182
h = 0.003 0.006
y[1] (numeric) = -3.28503857261 0.0631388001155
y[1] (closed_form) = -3.28503966147 0.0631418461087
absolute error = 3.235e-06
relative error = 9.845e-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 = 0.8079
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1212 0.188
h = 0.0001 0.005
y[1] (numeric) = -3.28443602921 0.065440716935
y[1] (closed_form) = -3.28443774785 0.0654484197311
absolute error = 7.892e-06
relative error = 0.0002402 %
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 = 0.3629
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1213 0.193
h = 0.0001 0.003
y[1] (numeric) = -3.2847806197 0.0671926944861
y[1] (closed_form) = -3.28478141893 0.067197488578
absolute error = 4.860e-06
relative error = 0.0001479 %
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 = 0.2934
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1214 0.196
h = 0.001 0.001
y[1] (numeric) = -3.28497885017 0.0682455173951
y[1] (closed_form) = -3.28497845647 0.0682502645262
absolute error = 4.763e-06
relative error = 0.000145 %
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 = 0.231
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1224 0.197
h = 0.0001 0.004
y[1] (numeric) = -3.284708938 0.068672397077
y[1] (closed_form) = -3.28470796892 0.0686769219499
absolute error = 4.627e-06
relative error = 0.0001408 %
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 = 1.391
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1225 0.201
h = 0.003 0.006
y[1] (numeric) = -3.28498796168 0.0700761356069
y[1] (closed_form) = -3.28498940087 0.0700800189869
absolute error = 4.141e-06
relative error = 0.000126 %
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 = 0.8269
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1255 0.207
h = 0.0001 0.005
y[1] (numeric) = -3.28442543261 0.0724112232403
y[1] (closed_form) = -3.28442749866 0.0724197643871
absolute error = 8.787e-06
relative error = 0.0002675 %
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 = 0.3715
Order of pole (three term test) = 32.02 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=73.9MB, alloc=52.3MB, time=0.91
x[1] = 0.1256 0.212
h = 0.0001 0.003
y[1] (numeric) = -3.2848075765 0.0741727411646
y[1] (closed_form) = -3.28480872491 0.0741783726411
absolute error = 5.747e-06
relative error = 0.0001749 %
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 = 0.3004
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1257 0.215
h = 0.001 0.001
y[1] (numeric) = -3.28502827034 0.0752315934623
y[1] (closed_form) = -3.28502822569 0.0752371771997
absolute error = 5.584e-06
relative error = 0.0001699 %
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) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1267 0.216
h = 0.001 0.003
y[1] (numeric) = -3.28476414586 0.0756677783879
y[1] (closed_form) = -3.2847635259 0.0756731394644
absolute error = 5.397e-06
relative error = 0.0001643 %
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 = 1.125
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1277 0.219
h = 0.0001 0.004
y[1] (numeric) = -3.2846714934 0.0768059991409
y[1] (closed_form) = -3.28467206405 0.0768117660785
absolute error = 5.795e-06
relative error = 0.0001764 %
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 = 0.6395
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1278 0.223
h = 0.003 0.006
y[1] (numeric) = -3.28498683825 0.0782193210289
y[1] (closed_form) = -3.28498822719 0.0782243974661
absolute error = 5.263e-06
relative error = 0.0001602 %
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 = 0.8504
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1308 0.229
h = 0.0001 0.005
y[1] (numeric) = -3.28447023285 0.0805936183365
y[1] (closed_form) = -3.28447224521 0.0806033537556
absolute error = 9.941e-06
relative error = 0.0003026 %
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 = 0.3821
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1309 0.234
h = 0.0001 0.003
y[1] (numeric) = -3.28489584094 0.0823668538135
y[1] (closed_form) = -3.28489693773 0.082373678372
absolute error = 6.912e-06
relative error = 0.0002104 %
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 = 0.309
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.131 0.237
h = 0.001 0.001
y[1] (numeric) = -3.28514252854 0.0834330900261
y[1] (closed_form) = -3.2851424321 0.0834398659208
absolute error = 6.777e-06
relative error = 0.0002062 %
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 = 0.2433
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.132 0.238
h = 0.001 0.003
y[1] (numeric) = -3.2848849704 0.0838801826711
y[1] (closed_form) = -3.28488429872 0.0838867354231
absolute error = 6.587e-06
relative error = 0.0002005 %
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 = 1.158
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.133 0.241
h = 0.0001 0.004
y[1] (numeric) = -3.28481635688 0.0850336523795
y[1] (closed_form) = -3.28481687572 0.085040611983
absolute error = 6.979e-06
relative error = 0.0002124 %
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 = 0.6579
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1331 0.245
h = 0.003 0.006
y[1] (numeric) = -3.28516643073 0.0864565362876
y[1] (closed_form) = -3.28516776853 0.0864628058982
absolute error = 6.411e-06
relative error = 0.0001951 %
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 = 0.875
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1361 0.251
h = 0.0001 0.005
y[1] (numeric) = -3.28469572683 0.0888700852579
y[1] (closed_form) = -3.28469768455 0.0888810152182
absolute error = 1.110e-05
relative error = 0.0003379 %
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 = 0.3931
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1362 0.256
h = 0.0001 0.003
y[1] (numeric) = -3.28516479789 0.0906550741512
y[1] (closed_form) = -3.28516584216 0.0906630919567
absolute error = 8.086e-06
relative error = 0.000246 %
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 = 0.318
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1363 0.259
h = 0.001 0.001
y[1] (numeric) = -3.28543747843 0.0917287158358
y[1] (closed_form) = -3.28543732925 0.0917366840327
absolute error = 7.970e-06
relative error = 0.0002425 %
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 = 0.2504
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1373 0.26
h = 0.001 0.003
y[1] (numeric) = -3.28518647941 0.092186723389
y[1] (closed_form) = -3.28518575505 0.0921944679456
absolute error = 7.778e-06
relative error = 0.0002367 %
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 = 1.191
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1383 0.263
h = 0.0001 0.004
y[1] (numeric) = -3.28514189756 0.0933554636871
y[1] (closed_form) = -3.28514236364 0.0933636161168
absolute error = 8.166e-06
relative error = 0.0002485 %
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 = 0.677
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1384 0.267
h = 0.003 0.006
y[1] (numeric) = -3.28552669975 0.0947879386423
y[1] (closed_form) = -3.28552798552 0.0947954015782
absolute error = 7.573e-06
relative error = 0.0002304 %
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 = 0.9006
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1414 0.273
h = 0.0001 0.005
y[1] (numeric) = -3.28510187598 0.0972407831927
y[1] (closed_form) = -3.28510377811 0.0972529079989
absolute error = 1.227e-05
relative error = 0.0003734 %
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 = 0.4046
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1415 0.278
h = 0.0001 0.003
y[1] (numeric) = -3.28561440997 0.0990375624128
y[1] (closed_form) = -3.28561540076 0.0990467736663
absolute error = 9.264e-06
relative error = 0.0002818 %
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 = 0.3273
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1416 0.281
h = 0.001 0.001
y[1] (numeric) = -3.28591308329 0.100118631765
y[1] (closed_form) = -3.2859128804 0.100127792444
absolute error = 9.163e-06
relative error = 0.0002787 %
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 = 0.2577
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1426 0.282
h = 0.001 0.003
y[1] (numeric) = -3.28566863621 0.100587561853
y[1] (closed_form) = -3.28566785817 0.100596498379
absolute error = 8.970e-06
relative error = 0.0002729 %
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 = 1.226
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=117.7MB, alloc=52.3MB, time=1.42
x[1] = 0.1436 0.285
h = 0.0001 0.004
y[1] (numeric) = -3.28564807925 0.101771595223
y[1] (closed_form) = -3.28564849161 0.101780940675
absolute error = 9.355e-06
relative error = 0.0002846 %
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 = 0.6969
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1437 0.289
h = 0.003 0.006
y[1] (numeric) = -3.28606761005 0.103213691095
y[1] (closed_form) = -3.28606884286 0.103222347544
absolute error = 8.744e-06
relative error = 0.000266 %
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 = 0.9271
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1467 0.295
h = 0.0001 0.005
y[1] (numeric) = -3.28568864582 0.105705877074
y[1] (closed_form) = -3.28569049138 0.105719197066
absolute error = 1.345e-05
relative error = 0.0004091 %
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 = 0.4165
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1468 0.3
h = 0.0001 0.003
y[1] (numeric) = -3.28624464381 0.107514484579
y[1] (closed_form) = -3.28624558016 0.107524889518
absolute error = 1.045e-05
relative error = 0.0003177 %
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 = 0.337
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1469 0.303
h = 0.001 0.001
y[1] (numeric) = -3.28656931046 0.108603004432
y[1] (closed_form) = -3.28656905285 0.108613357811
absolute error = 1.036e-05
relative error = 0.0003149 %
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 = 0.2653
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1479 0.304
h = 0.0001 0.004
y[1] (numeric) = -3.28633140815 0.109082865122
y[1] (closed_form) = -3.28633057543 0.109092993817
absolute error = 1.016e-05
relative error = 0.0003091 %
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 = 1.597
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.148 0.308
h = 0.003 0.006
y[1] (numeric) = -3.28677935614 0.110532797544
y[1] (closed_form) = -3.28678093662 0.110542293313
absolute error = 9.626e-06
relative error = 0.0002927 %
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 = 0.9503
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.151 0.314
h = 0.0001 0.005
y[1] (numeric) = -3.2864403198 0.113058339542
y[1] (closed_form) = -3.2864425099 0.113072500461
absolute error = 1.433e-05
relative error = 0.0004358 %
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 = 0.4268
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1511 0.319
h = 0.0001 0.003
y[1] (numeric) = -3.28703387343 0.11487664186
y[1] (closed_form) = -3.28703515615 0.114887886323
absolute error = 1.132e-05
relative error = 0.0003441 %
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 = 0.3454
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1512 0.322
h = 0.001 0.001
y[1] (numeric) = -3.28738100434 0.115971283975
y[1] (closed_form) = -3.28738109282 0.115982476017
absolute error = 1.119e-05
relative error = 0.0003403 %
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 = 0.272
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1522 0.323
h = 0.001 0.003
y[1] (numeric) = -3.2871488602 0.11646048231
y[1] (closed_form) = -3.28714837357 0.116471449201
absolute error = 1.098e-05
relative error = 0.0003337 %
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 = 1.294
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1532 0.326
h = 0.0001 0.004
y[1] (numeric) = -3.28717317441 0.117672749248
y[1] (closed_form) = -3.2871738782 0.117684127107
absolute error = 1.140e-05
relative error = 0.0003466 %
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 = 0.7353
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1533 0.33
h = 0.003 0.006
y[1] (numeric) = -3.28765744641 0.119132416057
y[1] (closed_form) = -3.28765897215 0.119143105794
absolute error = 1.080e-05
relative error = 0.0003282 %
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 = 0.9783
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1563 0.336
h = 0.0001 0.005
y[1] (numeric) = -3.28736423398 0.12169739016
y[1] (closed_form) = -3.28736636563 0.121712747007
absolute error = 1.550e-05
relative error = 0.0004713 %
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 = 0.4394
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1564 0.341
h = 0.0001 0.003
y[1] (numeric) = -3.28800125716 0.123527594147
y[1] (closed_form) = -3.2880024836 0.123540032843
absolute error = 1.250e-05
relative error = 0.0003799 %
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 = 0.3556
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1565 0.344
h = 0.001 0.001
y[1] (numeric) = -3.28837438448 0.124629730929
y[1] (closed_form) = -3.28837441635 0.12464211618
absolute error = 1.239e-05
relative error = 0.0003764 %
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 = 0.28
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1575 0.345
h = 0.001 0.003
y[1] (numeric) = -3.28814877199 0.125129876127
y[1] (closed_form) = -3.28814822875 0.125142035667
absolute error = 1.217e-05
relative error = 0.0003699 %
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 = 1.332
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1585 0.348
h = 0.0001 0.004
y[1] (numeric) = -3.28819709471 0.126357505205
y[1] (closed_form) = -3.28819774192 0.126370076856
absolute error = 1.259e-05
relative error = 0.0003826 %
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 = 0.7569
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1586 0.352
h = 0.003 0.006
y[1] (numeric) = -3.28871610153 0.127826883006
y[1] (closed_form) = -3.28871757155 0.127838767004
absolute error = 1.197e-05
relative error = 0.0003638 %
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 = 1.007
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1616 0.358
h = 0.0001 0.005
y[1] (numeric) = -3.2884686947 0.130431340585
y[1] (closed_form) = -3.28847076687 0.130447893802
absolute error = 1.668e-05
relative error = 0.0005069 %
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 = 0.4522
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1617 0.363
h = 0.0001 0.003
y[1] (numeric) = -3.28914919179 0.132273487195
y[1] (closed_form) = -3.28915036094 0.132287120463
absolute error = 1.368e-05
relative error = 0.0004157 %
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 = 0.366
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1618 0.366
h = 0.001 0.001
y[1] (numeric) = -3.28954831802 0.133383143301
y[1] (closed_form) = -3.2895482922 0.13339672208
absolute error = 1.358e-05
relative error = 0.0004124 %
Correct digits = 5
memory used=161.6MB, alloc=52.3MB, time=1.93
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.2882
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1628 0.367
h = 0.001 0.003
y[1] (numeric) = -3.2893292301 0.133894244683
y[1] (closed_form) = -3.28932862916 0.133907597176
absolute error = 1.337e-05
relative error = 0.000406 %
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 = 1.371
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1638 0.37
h = 0.0001 0.004
y[1] (numeric) = -3.28940155645 0.13513726166
y[1] (closed_form) = -3.28940214605 0.135151027438
absolute error = 1.378e-05
relative error = 0.0004185 %
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 = 0.779
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1639 0.374
h = 0.003 0.006
y[1] (numeric) = -3.2899553019 0.136616383579
y[1] (closed_form) = -3.2899567152 0.136629462162
absolute error = 1.315e-05
relative error = 0.0003995 %
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 = 1.037
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1669 0.38
h = 0.0001 0.005
y[1] (numeric) = -3.28975368312 0.139260377938
y[1] (closed_form) = -3.28975569474 0.139278128005
absolute error = 1.786e-05
relative error = 0.0005425 %
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 = 0.4654
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.167 0.385
h = 0.0001 0.003
y[1] (numeric) = -3.29047765964 0.14111450918
y[1] (closed_form) = -3.29047877045 0.141129337394
absolute error = 1.487e-05
relative error = 0.0004515 %
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 = 0.3766
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1671 0.388
h = 0.001 0.001
y[1] (numeric) = -3.29090278794 0.142231709911
y[1] (closed_form) = -3.29090270337 0.142246482572
absolute error = 1.477e-05
relative error = 0.0004485 %
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 = 0.2966
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1681 0.389
h = 0.001 0.003
y[1] (numeric) = -3.29069021755 0.142753777237
y[1] (closed_form) = -3.29068955783 0.142768323021
absolute error = 1.456e-05
relative error = 0.0004421 %
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 = 1.411
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1691 0.392
h = 0.0001 0.004
y[1] (numeric) = -3.29078654316 0.144012208724
y[1] (closed_form) = -3.29078707408 0.144027168998
absolute error = 1.497e-05
relative error = 0.0004545 %
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 = 0.8017
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1692 0.396
h = 0.003 0.006
y[1] (numeric) = -3.29137503195 0.145501108734
y[1] (closed_form) = -3.29137638751 0.145515382265
absolute error = 1.434e-05
relative error = 0.0004352 %
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 = 1.067
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1722 0.402
h = 0.0001 0.005
y[1] (numeric) = -3.29121918446 0.148184695118
y[1] (closed_form) = -3.29122113446 0.148203642549
absolute error = 1.905e-05
relative error = 0.0005782 %
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 = 0.4789
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1723 0.407
h = 0.0001 0.003
y[1] (numeric) = -3.29198664707 0.150050854058
y[1] (closed_form) = -3.29198769848 0.150066877629
absolute error = 1.606e-05
relative error = 0.0004873 %
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 = 0.3875
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1724 0.41
h = 0.001 0.001
y[1] (numeric) = -3.29243778127 0.151175625357
y[1] (closed_form) = -3.29243763685 0.15119159229
absolute error = 1.597e-05
relative error = 0.0004845 %
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 = 0.3052
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1734 0.411
h = 0.0001 0.004
y[1] (numeric) = -3.29223172139 0.151708668829
y[1] (closed_form) = -3.29223100178 0.151724408278
absolute error = 1.576e-05
relative error = 0.0004781 %
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 = 1.837
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1735 0.415
h = 0.003 0.006
y[1] (numeric) = -3.29284864297 0.153205536949
y[1] (closed_form) = -3.29285034348 0.153220652471
absolute error = 1.521e-05
relative error = 0.0004614 %
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 = 1.093
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1765 0.421
h = 0.0001 0.005
y[1] (numeric) = -3.29273265358 0.155922703578
y[1] (closed_form) = -3.29273494519 0.15594249525
absolute error = 1.992e-05
relative error = 0.0006044 %
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 = 0.4905
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1766 0.426
h = 0.0001 0.003
y[1] (numeric) = -3.29353769777 0.157798732718
y[1] (closed_form) = -3.29353909269 0.157815598693
absolute error = 1.692e-05
relative error = 0.0005133 %
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 = 0.397
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1767 0.429
h = 0.001 0.001
y[1] (numeric) = -3.29401131119 0.158929731922
y[1] (closed_form) = -3.29401150985 0.158946540314
absolute error = 1.681e-05
relative error = 0.0005097 %
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 = 0.3126
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1777 0.43
h = 0.001 0.003
y[1] (numeric) = -3.29381098066 0.159472154359
y[1] (closed_form) = -3.29381060408 0.159488734731
absolute error = 1.658e-05
relative error = 0.0005029 %
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) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1787 0.433
h = 0.0001 0.004
y[1] (numeric) = -3.29395213774 0.16075905662
y[1] (closed_form) = -3.29395295208 0.160776053807
absolute error = 1.702e-05
relative error = 0.000516 %
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 = 0.8448
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1788 0.437
h = 0.003 0.006
y[1] (numeric) = -3.29460540893 0.16226583068
y[1] (closed_form) = -3.29460704974 0.16228214193
absolute error = 1.639e-05
relative error = 0.000497 %
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 = 1.124
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1818 0.443
h = 0.0001 0.005
y[1] (numeric) = -3.29453516241 0.165022697473
y[1] (closed_form) = -3.29453739033 0.165043687574
absolute error = 2.111e-05
relative error = 0.0006399 %
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 = 0.5045
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=205.5MB, alloc=52.3MB, time=2.44
x[1] = 0.1819 0.448
h = 0.0001 0.003
y[1] (numeric) = -3.29538370866 0.166910837153
y[1] (closed_form) = -3.29538504216 0.166928899358
absolute error = 1.811e-05
relative error = 0.0005489 %
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 = 0.4083
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.182 0.451
h = 0.001 0.001
y[1] (numeric) = -3.29588333727 0.168049456854
y[1] (closed_form) = -3.29588347398 0.168067460352
absolute error = 1.800e-05
relative error = 0.0005455 %
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 = 0.3215
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.183 0.452
h = 0.001 0.003
y[1] (numeric) = -3.29568950439 0.16860287567
y[1] (closed_form) = -3.2956890658 0.168620650512
absolute error = 1.778e-05
relative error = 0.0005388 %
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 = 1.529
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.184 0.455
h = 0.0001 0.004
y[1] (numeric) = -3.29585465127 0.169905273316
y[1] (closed_form) = -3.29585540379 0.169923466268
absolute error = 1.821e-05
relative error = 0.0005517 %
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 = 0.8687
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1841 0.459
h = 0.003 0.006
y[1] (numeric) = -3.29654268477 0.171421927271
y[1] (closed_form) = -3.29654426479 0.171439434714
absolute error = 1.758e-05
relative error = 0.0005325 %
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 = 1.156
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1871 0.465
h = 0.0001 0.005
y[1] (numeric) = -3.29651816657 0.174218555019
y[1] (closed_form) = -3.29652032967 0.174240744167
absolute error = 2.229e-05
relative error = 0.0006754 %
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 = 0.5187
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1872 0.47
h = 0.0001 0.003
y[1] (numeric) = -3.29741022484 0.176118851325
y[1] (closed_form) = -3.29741149579 0.176138110272
absolute error = 1.930e-05
relative error = 0.0005845 %
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 = 0.4198
Order of pole (three term test) = 32.01 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1873 0.473
h = 0.001 0.001
y[1] (numeric) = -3.29793587441 0.177265119306
y[1] (closed_form) = -3.29793594802 0.177284318403
absolute error = 1.920e-05
relative error = 0.0005813 %
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 = 0.3305
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1883 0.474
h = 0.001 0.003
y[1] (numeric) = -3.29774853224 0.177829545962
y[1] (closed_form) = -3.29774803047 0.177848515749
absolute error = 1.898e-05
relative error = 0.0005746 %
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 = 1.572
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1893 0.477
h = 0.0001 0.004
y[1] (numeric) = -3.29793766645 0.179147468897
y[1] (closed_form) = -3.29793835601 0.179166858122
absolute error = 1.940e-05
relative error = 0.0005874 %
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 = 0.893
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1894 0.481
h = 0.003 0.006
y[1] (numeric) = -3.29866047049 0.180674040004
y[1] (closed_form) = -3.29866198863 0.18069274414
absolute error = 1.877e-05
relative error = 0.000568 %
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 = 1.188
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1924 0.487
h = 0.0001 0.005
y[1] (numeric) = -3.29868166687 0.183510491443
y[1] (closed_form) = -3.29868376399 0.183533880292
absolute error = 2.348e-05
relative error = 0.0007108 %
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 = 0.5331
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1925 0.492
h = 0.0001 0.003
y[1] (numeric) = -3.29961724822 0.185422991526
y[1] (closed_form) = -3.29961845549 0.185443447765
absolute error = 2.049e-05
relative error = 0.0006201 %
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 = 0.4314
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1926 0.495
h = 0.001 0.001
y[1] (numeric) = -3.30016892522 0.18657693622
y[1] (closed_form) = -3.30016893457 0.186597331443
absolute error = 2.040e-05
relative error = 0.000617 %
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 = 0.3397
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1936 0.496
h = 0.001 0.003
y[1] (numeric) = -3.29998806684 0.187152382616
y[1] (closed_form) = -3.2999875007 0.18717254786
absolute error = 2.017e-05
relative error = 0.0006103 %
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 = 1.615
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1946 0.499
h = 0.0001 0.004
y[1] (numeric) = -3.30020118641 0.188485861602
y[1] (closed_form) = -3.30020181185 0.188506447644
absolute error = 2.060e-05
relative error = 0.0006231 %
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 = 0.9177
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1947 0.503
h = 0.003 0.006
y[1] (numeric) = -3.30095877014 0.190022387976
y[1] (closed_form) = -3.30096022526 0.190042289341
absolute error = 1.995e-05
relative error = 0.0006035 %
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 = 1.221
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1977 0.509
h = 0.0001 0.005
y[1] (numeric) = -3.3010256681 0.192898727792
y[1] (closed_form) = -3.30102769805 0.19292331703
absolute error = 2.467e-05
relative error = 0.0007462 %
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 = 0.5477
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1978 0.514
h = 0.0001 0.003
y[1] (numeric) = -3.30200478476 0.194823479868
y[1] (closed_form) = -3.30200592718 0.194845133983
absolute error = 2.168e-05
relative error = 0.0006556 %
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 = 0.4432
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1979 0.517
h = 0.001 0.001
y[1] (numeric) = -3.30258249634 0.195985130356
y[1] (closed_form) = -3.3025824402 0.19600672227
absolute error = 2.159e-05
relative error = 0.0006526 %
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 = 0.349
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1989 0.518
h = 0.0001 0.004
y[1] (numeric) = -3.30240811485 0.196571608834
y[1] (closed_form) = -3.30240748312 0.196592970083
absolute error = 2.137e-05
relative error = 0.000646 %
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 = 2.1
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=249.4MB, alloc=52.3MB, time=2.96
x[1] = 0.199 0.522
h = 0.003 0.006
y[1] (numeric) = -3.30319416466 0.198116251225
y[1] (closed_form) = -3.30319596196 0.198136997993
absolute error = 2.082e-05
relative error = 0.0006293 %
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 = 1.249
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.202 0.528
h = 0.0001 0.005
y[1] (numeric) = -3.30330086743 0.201026434715
y[1] (closed_form) = -3.30330323599 0.201051872249
absolute error = 2.555e-05
relative error = 0.000772 %
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 = 0.5604
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2021 0.533
h = 0.0001 0.003
y[1] (numeric) = -3.30431761525 0.202961253514
y[1] (closed_form) = -3.30431909825 0.202983753652
absolute error = 2.255e-05
relative error = 0.0006811 %
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 = 0.4535
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2022 0.536
h = 0.001 0.001
y[1] (numeric) = -3.30491783502 0.204129250427
y[1] (closed_form) = -3.30491811889 0.204151687333
absolute error = 2.244e-05
relative error = 0.0006777 %
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 = 0.3571
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2032 0.537
h = 0.001 0.003
y[1] (numeric) = -3.30474915475 0.204725158132
y[1] (closed_form) = -3.30474886291 0.204747363771
absolute error = 2.221e-05
relative error = 0.0006707 %
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 = 1.698
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2042 0.54
h = 0.0001 0.004
y[1] (numeric) = -3.30500708806 0.206087382439
y[1] (closed_form) = -3.30500798836 0.206110011486
absolute error = 2.265e-05
relative error = 0.0006839 %
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 = 0.9645
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2043 0.544
h = 0.003 0.006
y[1] (numeric) = -3.30582953583 0.20764212303
y[1] (closed_form) = -3.30583126797 0.207664068133
absolute error = 2.201e-05
relative error = 0.0006646 %
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 = 1.283
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2073 0.55
h = 0.0001 0.005
y[1] (numeric) = -3.30598191888 0.21059232059
y[1] (closed_form) = -3.30598421803 0.210618959903
absolute error = 2.674e-05
relative error = 0.0008071 %
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 = 0.5754
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2074 0.555
h = 0.0001 0.003
y[1] (numeric) = -3.30704222839 0.212539483772
y[1] (closed_form) = -3.30704364433 0.212563182983
absolute error = 2.374e-05
relative error = 0.0007164 %
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 = 0.4656
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2075 0.558
h = 0.001 0.001
y[1] (numeric) = -3.30766849818 0.213715242222
y[1] (closed_form) = -3.30766871429 0.213738876977
absolute error = 2.364e-05
relative error = 0.0007131 %
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 = 0.3666
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2085 0.559
h = 0.001 0.003
y[1] (numeric) = -3.30750628219 0.214322206231
y[1] (closed_form) = -3.30750592246 0.214345609003
absolute error = 2.341e-05
relative error = 0.0007062 %
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 = 1.743
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2095 0.562
h = 0.0001 0.004
y[1] (numeric) = -3.30778819827 0.215700079345
y[1] (closed_form) = -3.30778903102 0.215723906975
absolute error = 2.384e-05
relative error = 0.0007193 %
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 = 0.9902
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2096 0.566
h = 0.003 0.006
y[1] (numeric) = -3.3086454574 0.217264888842
y[1] (closed_form) = -3.30864712321 0.217288032917
absolute error = 2.320e-05
relative error = 0.0006998 %
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 = 1.317
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2126 0.572
h = 0.0001 0.005
y[1] (numeric) = -3.30884350996 0.220255170735
y[1] (closed_form) = -3.30884573846 0.22028301262
absolute error = 2.793e-05
relative error = 0.0008423 %
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 = 0.5907
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2127 0.577
h = 0.0001 0.003
y[1] (numeric) = -3.30994739666 0.222214729568
y[1] (closed_form) = -3.30994874432 0.222239628539
absolute error = 2.494e-05
relative error = 0.0007517 %
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 = 0.4779
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2128 0.58
h = 0.001 0.001
y[1] (numeric) = -3.31059972554 0.223398280495
y[1] (closed_form) = -3.31059987265 0.223423113764
absolute error = 2.483e-05
relative error = 0.0007484 %
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 = 0.3763
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2138 0.581
h = 0.001 0.003
y[1] (numeric) = -3.31044396701 0.224016314413
y[1] (closed_form) = -3.31044353813 0.224040914968
absolute error = 2.460e-05
relative error = 0.0007415 %
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 = 1.789
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2148 0.584
h = 0.0001 0.004
y[1] (numeric) = -3.31074986578 0.225409870414
y[1] (closed_form) = -3.31075062973 0.225434897309
absolute error = 2.504e-05
relative error = 0.0007545 %
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 = 1.016
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2149 0.588
h = 0.003 0.006
y[1] (numeric) = -3.31164194894 0.226984790245
y[1] (closed_form) = -3.31164354719 0.227009133967
absolute error = 2.440e-05
relative error = 0.000735 %
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 = 1.352
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2179 0.594
h = 0.0001 0.005
y[1] (numeric) = -3.31188566098 0.230015228694
y[1] (closed_form) = -3.31188781756 0.230044273977
absolute error = 2.913e-05
relative error = 0.0008773 %
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 = 0.6061
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.218 0.599
h = 0.0001 0.003
y[1] (numeric) = -3.3130331415 0.231987235521
y[1] (closed_form) = -3.31303441963 0.232013334976
absolute error = 2.613e-05
relative error = 0.0007868 %
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 = 0.4904
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=293.3MB, alloc=52.3MB, time=3.47
x[1] = 0.2181 0.602
h = 0.001 0.001
y[1] (numeric) = -3.31371153924 0.23317861052
y[1] (closed_form) = -3.31371161605 0.233204643005
absolute error = 2.603e-05
relative error = 0.0007837 %
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 = 0.3861
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2191 0.603
h = 0.001 0.003
y[1] (numeric) = -3.31356223136 0.233807728395
y[1] (closed_form) = -3.31356173202 0.233833527418
absolute error = 2.580e-05
relative error = 0.0007768 %
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 = 1.836
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2201 0.606
h = 0.0001 0.004
y[1] (numeric) = -3.31389211321 0.235217002227
y[1] (closed_form) = -3.3138928071 0.235243229103
absolute error = 2.624e-05
relative error = 0.0007897 %
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 = 1.043
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2202 0.61
h = 0.003 0.006
y[1] (numeric) = -3.31481903395 0.236802074687
y[1] (closed_form) = -3.31482056344 0.236827618765
absolute error = 2.559e-05
relative error = 0.00077 %
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 = 1.387
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2232 0.616
h = 0.0001 0.005
y[1] (numeric) = -3.31510839622 0.239872743875
y[1] (closed_form) = -3.3151104796 0.23990299342
absolute error = 3.032e-05
relative error = 0.0009123 %
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 = 0.6217
Order of pole (three term test) = 32 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2233 0.621
h = 0.0001 0.003
y[1] (numeric) = -3.31629948834 0.241857252118
y[1] (closed_form) = -3.31630069568 0.241884552814
absolute error = 2.733e-05
relative error = 0.0008218 %
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 = 0.503
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2234 0.624
h = 0.001 0.001
y[1] (numeric) = -3.31700396536 0.24305648344
y[1] (closed_form) = -3.31700397058 0.243083715878
absolute error = 2.723e-05
relative error = 0.0008188 %
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 = 0.396
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2244 0.625
h = 0.0001 0.004
y[1] (numeric) = -3.31686110136 0.243696699764
y[1] (closed_form) = -3.31686053025 0.243723697975
absolute error = 2.700e-05
relative error = 0.000812 %
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 = 2.382
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2245 0.629
h = 0.003 0.006
y[1] (numeric) = -3.31781653914 0.245290052658
y[1] (closed_form) = -3.31781840796 0.245316446293
absolute error = 2.646e-05
relative error = 0.0007953 %
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 = 1.417
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2275 0.635
h = 0.0001 0.005
y[1] (numeric) = -3.31814566924 0.248394868381
y[1] (closed_form) = -3.31814808815 0.24842597102
absolute error = 3.120e-05
relative error = 0.0009376 %
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 = 0.6352
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2276 0.64
h = 0.0001 0.003
y[1] (numeric) = -3.31937446567 0.25038966122
y[1] (closed_form) = -3.31937601059 0.250417812298
absolute error = 2.819e-05
relative error = 0.000847 %
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 = 0.5139
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2277 0.643
h = 0.001 0.001
y[1] (numeric) = -3.32010149385 0.251595370493
y[1] (closed_form) = -3.32010183592 0.251623452198
absolute error = 2.808e-05
relative error = 0.0008435 %
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 = 0.4046
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2287 0.644
h = 0.001 0.003
y[1] (numeric) = -3.31996430355 0.252245075286
y[1] (closed_form) = -3.31996406912 0.252272922093
absolute error = 2.785e-05
relative error = 0.0008364 %
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 = 1.923
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2297 0.647
h = 0.0001 0.004
y[1] (numeric) = -3.32033900326 0.253683406581
y[1] (closed_form) = -3.3203399629 0.253711684141
absolute error = 2.829e-05
relative error = 0.0008497 %
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 = 1.092
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2298 0.651
h = 0.003 0.006
y[1] (numeric) = -3.32133091003 0.255287070853
y[1] (closed_form) = -3.32133270775 0.255314666275
absolute error = 2.765e-05
relative error = 0.0008302 %
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 = 1.453
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2328 0.657
h = 0.0001 0.005
y[1] (numeric) = -3.32170567609 0.258432260672
y[1] (closed_form) = -3.32170801936 0.258464569288
absolute error = 3.239e-05
relative error = 0.0009723 %
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 = 0.6511
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2329 0.662
h = 0.0001 0.003
y[1] (numeric) = -3.32297812088 0.260439656966
y[1] (closed_form) = -3.32297959262 0.260469010808
absolute error = 2.939e-05
relative error = 0.0008818 %
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 = 0.5268
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.233 0.665
h = 0.001 0.001
y[1] (numeric) = -3.32373124994 0.261653284183
y[1] (closed_form) = -3.32373151796 0.261682567323
absolute error = 2.928e-05
relative error = 0.0008784 %
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 = 0.4147
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.234 0.666
h = 0.001 0.003
y[1] (numeric) = -3.32360049114 0.26231411565
y[1] (closed_form) = -3.32360018245 0.262343163099
absolute error = 2.905e-05
relative error = 0.0008713 %
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 = 1.971
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.235 0.669
h = 0.0001 0.004
y[1] (numeric) = -3.32399917818 0.263768269501
y[1] (closed_form) = -3.32400006403 0.263797749308
absolute error = 2.949e-05
relative error = 0.0008845 %
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 = 1.119
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2351 0.673
h = 0.003 0.006
y[1] (numeric) = -3.3250259669 0.265382212003
y[1] (closed_form) = -3.32502769223 0.265411010024
absolute error = 2.885e-05
relative error = 0.0008649 %
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 = 1.489
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2381 0.679
h = 0.0001 0.005
y[1] (numeric) = -3.32544636185 0.268567855719
y[1] (closed_form) = -3.32544862814 0.268601371279
absolute error = 3.359e-05
relative error = 0.001007 %
Correct digits = 5
memory used=337.2MB, alloc=52.3MB, time=3.98
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6672
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2382 0.684
h = 0.0001 0.003
y[1] (numeric) = -3.32676247605 0.270587911976
y[1] (closed_form) = -3.32676387327 0.270618469442
absolute error = 3.059e-05
relative error = 0.0009165 %
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 = 0.5398
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2383 0.687
h = 0.001 0.001
y[1] (numeric) = -3.32754171836 0.271809491265
y[1] (closed_form) = -3.32754191096 0.271839976681
absolute error = 3.049e-05
relative error = 0.0009131 %
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 = 0.4249
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2393 0.688
h = 0.001 0.003
y[1] (numeric) = -3.32741738432 0.272481465168
y[1] (closed_form) = -3.327417 0.272511714081
absolute error = 3.025e-05
relative error = 0.0009061 %
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 = 2.02
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2403 0.691
h = 0.0001 0.004
y[1] (numeric) = -3.32784006096 0.273951479862
y[1] (closed_form) = -3.32784087169 0.273982162772
absolute error = 3.069e-05
relative error = 0.0009192 %
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 = 1.147
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2404 0.695
h = 0.003 0.006
y[1] (numeric) = -3.32890174872 0.275575746241
y[1] (closed_form) = -3.32890340035 0.27560574771
absolute error = 3.005e-05
relative error = 0.0008995 %
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 = 1.526
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2434 0.701
h = 0.0001 0.005
y[1] (numeric) = -3.32936776624 0.278801925628
y[1] (closed_form) = -3.32936995418 0.278836649133
absolute error = 3.479e-05
relative error = 0.001041 %
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 = 0.6835
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2435 0.706
h = 0.0001 0.003
y[1] (numeric) = -3.33072757202 0.280834699442
y[1] (closed_form) = -3.33072889338 0.28086646143
absolute error = 3.179e-05
relative error = 0.0009511 %
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 = 0.5529
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2436 0.709
h = 0.001 0.001
y[1] (numeric) = -3.33153294063 0.282064265597
y[1] (closed_form) = -3.33153305642 0.282095954163
absolute error = 3.169e-05
relative error = 0.0009478 %
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 = 0.4353
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2446 0.71
h = 0.001 0.003
y[1] (numeric) = -3.33141502466 0.282747398143
y[1] (closed_form) = -3.33141456329 0.282778849378
absolute error = 3.145e-05
relative error = 0.0009408 %
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 = 2.069
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2456 0.713
h = 0.0001 0.004
y[1] (numeric) = -3.33186169365 0.284233312838
y[1] (closed_form) = -3.33186242788 0.284265199741
absolute error = 3.190e-05
relative error = 0.0009538 %
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 = 1.175
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) = -3.33295829842 0.28586794962
y[1] (closed_form) = -3.33295987502 0.28589915542
absolute error = 3.125e-05
relative error = 0.000934 %
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 = 1.563
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) = -3.33346993295 0.289134748425
y[1] (closed_form) = -3.33347204114 0.289170680912
absolute error = 3.599e-05
relative error = 0.001076 %
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 = 0.7
Order of pole (three term test) = 31.99 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2488 0.728
h = 0.0001 0.003
y[1] (numeric) = -3.33487345363 0.291180298484
y[1] (closed_form) = -3.33487469775 0.291213265925
absolute error = 3.299e-05
relative error = 0.0009855 %
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 = 0.5662
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2489 0.731
h = 0.001 0.001
y[1] (numeric) = -3.33570496224 0.292417886961
y[1] (closed_form) = -3.33570499982 0.292450779589
absolute error = 3.289e-05
relative error = 0.0009823 %
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 = 0.4457
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2499 0.732
h = 0.0001 0.004
y[1] (numeric) = -3.33559345765 0.293112194801
y[1] (closed_form) = -3.33559291783 0.293144849253
absolute error = 3.266e-05
relative error = 0.0009753 %
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 = 2.681
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.25 0.736
h = 0.003 0.006
y[1] (numeric) = -3.33671864803 0.294755293128
y[1] (closed_form) = -3.33672056106 0.294787353382
absolute error = 3.212e-05
relative error = 0.0009588 %
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 = 1.594
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.253 0.742
h = 0.0001 0.005
y[1] (numeric) = -3.33727002952 0.298056581038
y[1] (closed_form) = -3.3372724701 0.298093372163
absolute error = 3.687e-05
relative error = 0.0011 %
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 = 0.7142
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2531 0.747
h = 0.0001 0.003
y[1] (numeric) = -3.33871135123 0.300112655163
y[1] (closed_form) = -3.33871292987 0.30014647809
absolute error = 3.386e-05
relative error = 0.00101 %
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 = 0.5777
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2532 0.75
h = 0.001 0.001
y[1] (numeric) = -3.33956546793 0.301356866275
y[1] (closed_form) = -3.33956583915 0.301390613185
absolute error = 3.375e-05
relative error = 0.001006 %
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 = 0.4547
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2542 0.751
h = 0.001 0.003
y[1] (numeric) = -3.3394596101 0.302060730846
y[1] (closed_form) = -3.33945940368 0.302094238843
absolute error = 3.351e-05
relative error = 0.0009993 %
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 = 2.161
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2552 0.754
h = 0.0001 0.004
y[1] (numeric) = -3.33995112277 0.303576053051
y[1] (closed_form) = -3.33995211306 0.303609999906
absolute error = 3.396e-05
relative error = 0.001013 %
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 = 1.227
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=381.0MB, alloc=52.3MB, time=4.49
x[1] = 0.2553 0.758
h = 0.0001 0.004
y[1] (numeric) = -3.34111287582 0.305229697091
y[1] (closed_form) = -3.34111471129 0.305262963432
absolute error = 3.332e-05
relative error = 0.000993 %
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 = 0.9735
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2554 0.762
h = 0.003 0.006
y[1] (numeric) = -3.34228190841 0.306883176308
y[1] (closed_form) = -3.34228374387 0.306916442649
absolute error = 3.332e-05
relative error = 0.0009927 %
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 = 1.638
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2584 0.768
h = 0.0001 0.005
y[1] (numeric) = -3.3428882995 0.310230611715
y[1] (closed_form) = -3.34289065705 0.310268614913
absolute error = 3.808e-05
relative error = 0.001134 %
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 = 0.7337
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2585 0.773
h = 0.0001 0.003
y[1] (numeric) = -3.34438143118 0.312300183814
y[1] (closed_form) = -3.34438292964 0.312335214342
absolute error = 3.506e-05
relative error = 0.001044 %
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 = 0.5934
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2586 0.776
h = 0.001 0.001
y[1] (numeric) = -3.34526654216 0.313552915852
y[1] (closed_form) = -3.34526683192 0.31358786872
absolute error = 3.495e-05
relative error = 0.00104 %
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 = 0.4671
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2596 0.777
h = 0.001 0.003
y[1] (numeric) = -3.34516860542 0.314269690058
y[1] (closed_form) = -3.3451683172 0.314304402995
absolute error = 3.471e-05
relative error = 0.001033 %
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 = 2.22
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2606 0.78
h = 0.0001 0.004
y[1] (numeric) = -3.34568886697 0.315802911595
y[1] (closed_form) = -3.34568977625 0.315838065438
absolute error = 3.517e-05
relative error = 0.001046 %
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 = 1.26
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2607 0.784
h = 0.003 0.006
y[1] (numeric) = -3.34689203363 0.317467587215
y[1] (closed_form) = -3.34689378995 0.317502060856
absolute error = 3.452e-05
relative error = 0.001027 %
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 = 1.676
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2637 0.79
h = 0.0001 0.005
y[1] (numeric) = -3.34754403386 0.320855908371
y[1] (closed_form) = -3.34754630737 0.32089512399
absolute error = 3.928e-05
relative error = 0.001168 %
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 = 0.7506
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2638 0.795
h = 0.0001 0.003
y[1] (numeric) = -3.34908096119 0.322938440116
y[1] (closed_form) = -3.34908237818 0.322974679215
absolute error = 3.627e-05
relative error = 0.001078 %
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 = 0.6071
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2639 0.798
h = 0.001 0.001
y[1] (numeric) = -3.34999225975 0.324199305333
y[1] (closed_form) = -3.34999246695 0.324235465316
absolute error = 3.616e-05
relative error = 0.001074 %
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 = 0.4778
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2649 0.799
h = 0.001 0.003
y[1] (numeric) = -3.34990071511 0.324927308404
y[1] (closed_form) = -3.34990034404 0.324963227562
absolute error = 3.592e-05
relative error = 0.001067 %
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 = 2.271
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2659 0.802
h = 0.0001 0.004
y[1] (numeric) = -3.3504449871 0.326476596532
y[1] (closed_form) = -3.3504458142 0.326512958398
absolute error = 3.637e-05
relative error = 0.00108 %
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 = 1.289
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.266 0.806
h = 0.003 0.006
y[1] (numeric) = -3.35168315499 0.32815183808
y[1] (closed_form) = -3.35168483074 0.328187520049
absolute error = 3.572e-05
relative error = 0.001061 %
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 = 1.715
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.269 0.812
h = 0.0001 0.005
y[1] (numeric) = -3.35238076188 0.331581136703
y[1] (closed_form) = -3.35238294988 0.331621565925
absolute error = 4.049e-05
relative error = 0.001202 %
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 = 0.7677
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2691 0.817
h = 0.0001 0.003
y[1] (numeric) = -3.35396151281 0.333676691156
y[1] (closed_form) = -3.35396284687 0.333714139905
absolute error = 3.747e-05
relative error = 0.001112 %
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 = 0.6209
Order of pole (three term test) = 31.98 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2692 0.82
h = 0.001 0.001
y[1] (numeric) = -3.35489901541 0.334945727673
y[1] (closed_form) = -3.35489913857 0.334983095827
absolute error = 3.737e-05
relative error = 0.001108 %
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 = 0.4887
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2702 0.821
h = 0.001 0.003
y[1] (numeric) = -3.35481385627 0.335684978063
y[1] (closed_form) = -3.35481340086 0.335722104481
absolute error = 3.713e-05
relative error = 0.001101 %
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 = 2.323
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2712 0.824
h = 0.0001 0.004
y[1] (numeric) = -3.35538214393 0.337250376331
y[1] (closed_form) = -3.35538288737 0.337287947291
absolute error = 3.758e-05
relative error = 0.001114 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.318
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2713 0.828
h = 0.003 0.006
y[1] (numeric) = -3.35665533562 0.338936234733
y[1] (closed_form) = -3.35665692936 0.338973126096
absolute error = 3.693e-05
relative error = 0.001095 %
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 = 1.753
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2743 0.834
h = 0.0001 0.005
y[1] (numeric) = -3.35739854745 0.342406604534
y[1] (closed_form) = -3.35740064843 0.342448248578
absolute error = 4.170e-05
relative error = 0.001236 %
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 = 0.785
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=424.8MB, alloc=52.3MB, time=5.00
x[1] = 0.2744 0.839
h = 0.0001 0.003
y[1] (numeric) = -3.35902315106 0.344515245865
y[1] (closed_form) = -3.35902440073 0.344553905377
absolute error = 3.868e-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 = 0.6348
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2745 0.842
h = 0.001 0.001
y[1] (numeric) = -3.35998687485 0.345792492478
y[1] (closed_form) = -3.35998691245 0.345831069895
absolute error = 3.858e-05
relative error = 0.001142 %
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 = 0.4997
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2755 0.843
h = 0.001 0.003
y[1] (numeric) = -3.35990809463 0.34654300909
y[1] (closed_form) = -3.35990755334 0.346581343842
absolute error = 3.834e-05
relative error = 0.001135 %
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 = 2.375
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2765 0.846
h = 0.0001 0.004
y[1] (numeric) = -3.36050040363 0.348124561926
y[1] (closed_form) = -3.36050106192 0.348163343088
absolute error = 3.879e-05
relative error = 0.001148 %
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 = 1.348
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2766 0.85
h = 0.003 0.006
y[1] (numeric) = -3.36180864262 0.349821089002
y[1] (closed_form) = -3.36181015289 0.349859190859
absolute error = 3.813e-05
relative error = 0.001128 %
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 = 1.792
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2796 0.856
h = 0.0001 0.005
y[1] (numeric) = -3.3625974584 0.353332625689
y[1] (closed_form) = -3.36259947084 0.353375485809
absolute error = 4.291e-05
relative error = 0.001269 %
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 = 0.8024
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2797 0.861
h = 0.0001 0.003
y[1] (numeric) = -3.36426594493 0.355454419178
y[1] (closed_form) = -3.36426710869 0.355494290603
absolute error = 3.989e-05
relative error = 0.001179 %
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 = 0.6489
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2798 0.864
h = 0.001 0.001
y[1] (numeric) = -3.3652559077 0.356739915356
y[1] (closed_form) = -3.36525585821 0.356779703164
absolute error = 3.979e-05
relative error = 0.001176 %
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 = 0.5107
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2808 0.865
h = 0.0001 0.004
y[1] (numeric) = -3.36518349983 0.357501717541
y[1] (closed_form) = -3.36518287112 0.357541261739
absolute error = 3.955e-05
relative error = 0.001169 %
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 = 3.071
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2809 0.869
h = 0.003 0.006
y[1] (numeric) = -3.36652043553 0.359206953817
y[1] (closed_form) = -3.36652227855 0.35924591727
absolute error = 3.901e-05
relative error = 0.001152 %
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 = 1.826
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2839 0.875
h = 0.0001 0.005
y[1] (numeric) = -3.36734899741 0.362753460526
y[1] (closed_form) = -3.36735133826 0.362797187232
absolute error = 4.379e-05
relative error = 0.001293 %
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 = 0.8175
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.284 0.88
h = 0.0001 0.003
y[1] (numeric) = -3.3690554397 0.364886104834
y[1] (closed_form) = -3.3690569341 0.364926839145
absolute error = 4.076e-05
relative error = 0.001203 %
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 = 0.6611
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2841 0.883
h = 0.001 0.001
y[1] (numeric) = -3.37006810181 0.36617842123
y[1] (closed_form) = -3.3700683819 0.366219070609
absolute error = 4.065e-05
relative error = 0.001199 %
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 = 0.5203
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2851 0.884
h = 0.001 0.003
y[1] (numeric) = -3.37000130855 0.366949877697
y[1] (closed_form) = -3.37000100911 0.366990282645
absolute error = 4.041e-05
relative error = 0.001192 %
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 = 2.473
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2861 0.887
h = 0.0001 0.004
y[1] (numeric) = -3.37063852619 0.368561325374
y[1] (closed_form) = -3.37063942776 0.368602180285
absolute error = 4.086e-05
relative error = 0.001205 %
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 = 1.403
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2862 0.891
h = 0.003 0.006
y[1] (numeric) = -3.3720121742 0.370277427159
y[1] (closed_form) = -3.37201393099 0.370317603268
absolute error = 4.021e-05
relative error = 0.001185 %
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 = 1.866
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2892 0.897
h = 0.0001 0.005
y[1] (numeric) = -3.37288634135 0.373865284166
y[1] (closed_form) = -3.37288859079 0.373910229398
absolute error = 4.500e-05
relative error = 0.001326 %
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 = 0.8352
Order of pole (three term test) = 31.97 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2893 0.902
h = 0.0001 0.003
y[1] (numeric) = -3.37463672663 0.376011204675
y[1] (closed_form) = -3.37463813229 0.376053153151
absolute error = 4.197e-05
relative error = 0.001236 %
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 = 0.6754
Order of pole (three term test) = 31.96 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2894 0.905
h = 0.001 0.001
y[1] (numeric) = -3.37567566315 0.377311845656
y[1] (closed_form) = -3.37567585323 0.377353707637
absolute error = 4.186e-05
relative error = 0.001232 %
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 = 0.5315
Order of pole (three term test) = 31.96 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2904 0.906
h = 0.001 0.003
y[1] (numeric) = -3.37561523029 0.378094624981
y[1] (closed_form) = -3.3756148405 0.378136241553
absolute error = 4.162e-05
relative error = 0.001225 %
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 = 2.526
Order of pole (three term test) = 31.96 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2914 0.909
h = 0.0001 0.004
y[1] (numeric) = -3.37627648875 0.379722359132
y[1] (closed_form) = -3.37627730078 0.379764427631
absolute error = 4.208e-05
relative error = 0.001238 %
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 = 1.434
Order of pole (three term test) = 31.96 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=468.8MB, alloc=52.3MB, time=5.52
x[1] = 0.2915 0.913
h = 0.003 0.006
y[1] (numeric) = -3.37768525689 0.381449282461
y[1] (closed_form) = -3.37768692593 0.381490672428
absolute error = 4.142e-05
relative error = 0.001219 %
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 = 1.906
Order of pole (three term test) = 31.96 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2945 0.919
h = 0.0001 0.005
y[1] (numeric) = -3.37860503045 0.385078591201
y[1] (closed_form) = -3.3786071869 0.385124756318
absolute error = 4.622e-05
relative error = 0.001359 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8531
Order of pole (three term test) = 31.96 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2946 0.924
h = 0.0001 0.003
y[1] (numeric) = -3.3803993922 0.387237856371
y[1] (closed_form) = -3.38040070756 0.387281020264
absolute error = 4.318e-05
relative error = 0.001269 %
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 = 0.6898
Order of pole (three term test) = 31.96 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2947 0.927
h = 0.001 0.001
y[1] (numeric) = -3.38146462286 0.388546863345
y[1] (closed_form) = -3.38146472136 0.388589939158
absolute error = 4.308e-05
relative error = 0.001266 %
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 = 0.5429
Order of pole (three term test) = 31.96 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2957 0.928
h = 0.001 0.003
y[1] (numeric) = -3.38141054389 0.389340986165
y[1] (closed_form) = -3.38141006213 0.389383815577
absolute error = 4.283e-05
relative error = 0.001258 %
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 = 2.58
Order of pole (three term test) = 31.96 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2967 0.931
h = 0.0001 0.004
y[1] (numeric) = -3.38209585071 0.390985054639
y[1] (closed_form) = -3.38209657161 0.391028337973
absolute error = 4.329e-05
relative error = 0.001271 %
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 = 1.464
Order of pole (three term test) = 31.96 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2968 0.935
h = 0.003 0.006
y[1] (numeric) = -3.38353976597 0.392722854786
y[1] (closed_form) = -3.3835413457 0.392765459852
absolute error = 4.263e-05
relative error = 0.001252 %
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 = 1.947
Order of pole (three term test) = 31.96 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2998 0.941
h = 0.0001 0.005
y[1] (numeric) = -3.3845051478 0.396393718709
y[1] (closed_form) = -3.38450720964 0.396441105104
absolute error = 4.743e-05
relative error = 0.001392 %
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 = 0.8712
Order of pole (three term test) = 31.96 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2999 0.946
h = 0.0001 0.003
y[1] (numeric) = -3.38634352064 0.398566398122
y[1] (closed_form) = -3.38634474412 0.398610778721
absolute error = 4.440e-05
relative error = 0.001302 %
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 = 0.7044
Order of pole (three term test) = 31.96 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3 0.949
h = 0.001 0.001
y[1] (numeric) = -3.38743506587 0.399883813178
y[1] (closed_form) = -3.38743507114 0.399928104089
absolute error = 4.429e-05
relative error = 0.001298 %
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 = 0.5544
Order of pole (three term test) = 31.96 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.301 0.95
h = 0.001 0.003
y[1] (numeric) = -3.38738733426 0.400689300586
y[1] (closed_form) = -3.3873867589 0.400733344085
absolute error = 4.405e-05
relative error = 0.001291 %
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 = 2.634
Order of pole (three term test) = 31.96 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.302 0.953
h = 0.0001 0.004
y[1] (numeric) = -3.38809669745 0.402349752124
y[1] (closed_form) = -3.38809732562 0.402394251574
absolute error = 4.450e-05
relative error = 0.001304 %
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 = 1.495
Order of pole (three term test) = 31.96 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3021 0.957
h = 0.003 0.006
y[1] (numeric) = -3.38957578772 0.404098485267
y[1] (closed_form) = -3.38957727659 0.404142306707
absolute error = 4.385e-05
relative error = 0.001284 %
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 = 1.988
Order of pole (three term test) = 31.96 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3051 0.963
h = 0.0001 0.005
y[1] (numeric) = -3.39058678043 0.407811009839
y[1] (closed_form) = -3.39058874603 0.407859618942
absolute error = 4.865e-05
relative error = 0.001425 %
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 = 0.8894
Order of pole (three term test) = 31.96 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3052 0.968
h = 0.0001 0.003
y[1] (numeric) = -3.39246920011 0.409997174204
y[1] (closed_form) = -3.3924703301 0.410042772833
absolute error = 4.561e-05
relative error = 0.001335 %
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 = 0.7191
Order of pole (three term test) = 31.96 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3053 0.971
h = 0.001 0.001
y[1] (numeric) = -3.39358708099 0.411323040118
y[1] (closed_form) = -3.39358699141 0.411368547427
absolute error = 4.551e-05
relative error = 0.001331 %
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 = 0.5659
Order of pole (three term test) = 31.96 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3063 0.972
h = 0.0001 0.004
y[1] (numeric) = -3.39354569024 0.412139913656
y[1] (closed_form) = -3.39354501963 0.412185172528
absolute error = 4.526e-05
relative error = 0.001324 %
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 = 3.403
Order of pole (three term test) = 31.96 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3064 0.976
h = 0.003 0.006
y[1] (numeric) = -3.39505358536 0.413897575201
y[1] (closed_form) = -3.39505540389 0.413942264818
absolute error = 4.473e-05
relative error = 0.001308 %
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 = 2.023
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3094 0.982
h = 0.0001 0.005
y[1] (numeric) = -3.39610433902 0.417645502498
y[1] (closed_form) = -3.3961066297 0.41769498542
absolute error = 4.954e-05
relative error = 0.001448 %
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 = 0.9052
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3095 0.987
h = 0.0001 0.003
y[1] (numeric) = -3.39802486406 0.41984280646
y[1] (closed_form) = -3.39802632145 0.419889274762
absolute error = 4.649e-05
relative error = 0.001358 %
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 = 0.7318
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3096 0.99
h = 0.001 0.001
y[1] (numeric) = -3.39916553256 0.421175667306
y[1] (closed_form) = -3.39916576915 0.421222042883
absolute error = 4.638e-05
relative error = 0.001354 %
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 = 0.5759
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3106 0.991
h = 0.001 0.003
y[1] (numeric) = -3.3991297306 0.422002283817
y[1] (closed_form) = -3.39912938579 0.422048410063
absolute error = 4.613e-05
relative error = 0.001347 %
Correct digits = 5
memory used=512.7MB, alloc=52.3MB, time=6.04
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.737
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3116 0.994
h = 0.0001 0.004
y[1] (numeric) = -3.39988407661 0.423693066397
y[1] (closed_form) = -3.39988493704 0.423739652448
absolute error = 4.659e-05
relative error = 0.00136 %
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 = 1.553
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3117 0.998
h = 0.003 0.006
y[1] (numeric) = -3.40142882855 0.425461876093
y[1] (closed_form) = -3.40143055326 0.425507784572
absolute error = 4.594e-05
relative error = 0.00134 %
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 = 2.065
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3147 1.004
h = 0.0001 0.005
y[1] (numeric) = -3.40252520116 0.42925166562
y[1] (closed_form) = -3.40252739253 0.429302374027
absolute error = 5.076e-05
relative error = 0.00148 %
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 = 0.9237
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3148 1.009
h = 0.0001 0.003
y[1] (numeric) = -3.40448984348 0.431462588661
y[1] (closed_form) = -3.40449120434 0.431510277572
absolute error = 4.771e-05
relative error = 0.00139 %
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 = 0.7468
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3149 1.012
h = 0.001 0.001
y[1] (numeric) = -3.40565688919 0.432803981522
y[1] (closed_form) = -3.40565702782 0.432851576036
absolute error = 4.759e-05
relative error = 0.001386 %
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 = 0.5877
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3159 1.013
h = 0.001 0.003
y[1] (numeric) = -3.40562741627 0.433642025536
y[1] (closed_form) = -3.40562697309 0.433689369661
absolute error = 4.735e-05
relative error = 0.001379 %
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 = 2.792
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3169 1.016
h = 0.0001 0.004
y[1] (numeric) = -3.40640584482 0.435349335447
y[1] (closed_form) = -3.40640660781 0.435397141501
absolute error = 4.781e-05
relative error = 0.001392 %
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 = 1.585
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.317 1.02
h = 0.003 0.006
y[1] (numeric) = -3.40798585726 0.437129243503
y[1] (closed_form) = -3.4079874865 0.437176372222
absolute error = 4.716e-05
relative error = 0.001372 %
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 = 2.107
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.32 1.026
h = 0.0001 0.005
y[1] (numeric) = -3.4091278535 0.440961006513
y[1] (closed_form) = -3.40912994386 0.44101294194
absolute error = 5.198e-05
relative error = 0.001512 %
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 = 0.9424
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3201 1.031
h = 0.0001 0.003
y[1] (numeric) = -3.41113665212 0.443185622572
y[1] (closed_form) = -3.41113791478 0.44323453352
absolute error = 4.893e-05
relative error = 0.001422 %
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 = 0.7619
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3202 1.034
h = 0.001 0.001
y[1] (numeric) = -3.41233009805 0.44453559219
y[1] (closed_form) = -3.41233013701 0.444584407045
absolute error = 4.881e-05
relative error = 0.001419 %
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 = 0.5995
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3212 1.035
h = 0.001 0.003
y[1] (numeric) = -3.41230694772 0.44538508655
y[1] (closed_form) = -3.41230640442 0.445433649939
absolute error = 4.857e-05
relative error = 0.001411 %
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 = 2.849
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3222 1.038
h = 0.0001 0.004
y[1] (numeric) = -3.41310946864 0.447108975991
y[1] (closed_form) = -3.4131101325 0.447158003469
absolute error = 4.903e-05
relative error = 0.001424 %
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 = 1.617
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3223 1.042
h = 0.003 0.006
y[1] (numeric) = -3.41472477297 0.448900042093
y[1] (closed_form) = -3.41472630509 0.448948392466
absolute error = 4.837e-05
relative error = 0.001405 %
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 = 2.149
Order of pole (three term test) = 31.95 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3253 1.048
h = 0.0001 0.005
y[1] (numeric) = -3.41591239827 0.452773891875
y[1] (closed_form) = -3.41591438589 0.452827055891
absolute error = 5.320e-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 = 0.9613
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3254 1.053
h = 0.0001 0.003
y[1] (numeric) = -3.41796539334 0.455012276032
y[1] (closed_form) = -3.4179665561 0.455062410479
absolute error = 5.015e-05
relative error = 0.001454 %
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 = 0.7771
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3255 1.056
h = 0.001 0.001
y[1] (numeric) = -3.41918526318 0.456370867842
y[1] (closed_form) = -3.41918520074 0.456420904478
absolute error = 5.004e-05
relative error = 0.001451 %
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 = 0.6115
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3265 1.057
h = 0.001 0.003
y[1] (numeric) = -3.41916842896 0.457231835845
y[1] (closed_form) = -3.41916778381 0.457281619922
absolute error = 4.979e-05
relative error = 0.001443 %
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 = 2.906
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3275 1.06
h = 0.0001 0.004
y[1] (numeric) = -3.41999505258 0.45897235792
y[1] (closed_form) = -3.4199956156 0.459022608279
absolute error = 5.025e-05
relative error = 0.001456 %
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 = 1.649
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3276 1.064
h = 0.003 0.006
y[1] (numeric) = -3.4216456811 0.460774642673
y[1] (closed_form) = -3.42164711443 0.460824216151
absolute error = 4.959e-05
relative error = 0.001436 %
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 = 2.192
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3306 1.07
h = 0.0001 0.005
y[1] (numeric) = -3.42287894158 0.464690694554
y[1] (closed_form) = -3.42288082473 0.464745088765
absolute error = 5.443e-05
relative error = 0.001576 %
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 = 0.9803
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=556.5MB, alloc=52.3MB, time=6.57
x[1] = 0.3307 1.075
h = 0.0001 0.003
y[1] (numeric) = -3.42497617439 0.466942923034
y[1] (closed_form) = -3.42497723553 0.46699428248
absolute error = 5.137e-05
relative error = 0.001486 %
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 = 0.7924
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3308 1.078
h = 0.001 0.001
y[1] (numeric) = -3.42622249252 0.46831018317
y[1] (closed_form) = -3.42622232691 0.468361443063
absolute error = 5.126e-05
relative error = 0.001482 %
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 = 0.6236
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3318 1.079
h = 0.0001 0.004
y[1] (numeric) = -3.42621196795 0.469182648569
y[1] (closed_form) = -3.42621121918 0.469233654794
absolute error = 5.101e-05
relative error = 0.001475 %
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 = 3.749
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3319 1.083
h = 0.003 0.006
y[1] (numeric) = -3.42789152707 0.470994098391
y[1] (closed_form) = -3.42789328689 0.471044547384
absolute error = 5.048e-05
relative error = 0.001459 %
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 = 2.229
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3349 1.089
h = 0.0001 0.005
y[1] (numeric) = -3.42916457885 0.474946026626
y[1] (closed_form) = -3.42916678364 0.475001302649
absolute error = 5.532e-05
relative error = 0.001598 %
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 = 0.9968
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.335 1.094
h = 0.0001 0.003
y[1] (numeric) = -3.43130009014 0.477209706105
y[1] (closed_form) = -3.43130147534 0.47726194277
absolute error = 5.226e-05
relative error = 0.001508 %
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 = 0.8058
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3351 1.097
h = 0.001 0.001
y[1] (numeric) = -3.4325692981 0.478584149662
y[1] (closed_form) = -3.43256945518 0.478636285276
absolute error = 5.214e-05
relative error = 0.001504 %
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 = 0.634
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3361 1.098
h = 0.001 0.003
y[1] (numeric) = -3.43256433687 0.479466455952
y[1] (closed_form) = -3.43256391035 0.479518336933
absolute error = 5.188e-05
relative error = 0.001497 %
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 = 3.012
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3371 1.101
h = 0.0001 0.004
y[1] (numeric) = -3.43343603871 0.481237784492
y[1] (closed_form) = -3.43343682235 0.481290135913
absolute error = 5.236e-05
relative error = 0.00151 %
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 = 1.709
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3372 1.105
h = 0.003 0.006
y[1] (numeric) = -3.43515262176 0.483060687272
y[1] (closed_form) = -3.43515427962 0.483112362185
absolute error = 5.170e-05
relative error = 0.00149 %
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 = 2.272
Order of pole (three term test) = 31.94 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3402 1.111
h = 0.0001 0.005
y[1] (numeric) = -3.43647132346 0.487055037557
y[1] (closed_form) = -3.4364734205 0.487111546881
absolute error = 5.655e-05
relative error = 0.001629 %
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 = 1.016
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3403 1.116
h = 0.0001 0.003
y[1] (numeric) = -3.43865115328 0.489332705734
y[1] (closed_form) = -3.43865243363 0.489386170305
absolute error = 5.348e-05
relative error = 0.00154 %
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 = 0.8214
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3404 1.119
h = 0.001 0.001
y[1] (numeric) = -3.43994685723 0.49071590501
y[1] (closed_form) = -3.43994690783 0.490769266746
absolute error = 5.336e-05
relative error = 0.001536 %
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 = 0.6463
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3414 1.12
h = 0.001 0.003
y[1] (numeric) = -3.43994819394 0.491609754191
y[1] (closed_form) = -3.43994766047 0.491662860152
absolute error = 5.311e-05
relative error = 0.001528 %
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 = 3.071
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3424 1.123
h = 0.0001 0.004
y[1] (numeric) = -3.44084403127 0.493397872147
y[1] (closed_form) = -3.44084470904 0.493451450837
absolute error = 5.358e-05
relative error = 0.001541 %
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 = 1.742
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3425 1.127
h = 0.003 0.006
y[1] (numeric) = -3.44259603666 0.495232171638
y[1] (closed_form) = -3.44259759081 0.495285074026
absolute error = 5.293e-05
relative error = 0.001522 %
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 = 2.316
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3455 1.133
h = 0.0001 0.005
y[1] (numeric) = -3.44396039647 0.499269065154
y[1] (closed_form) = -3.44396238394 0.49932680949
absolute error = 5.778e-05
relative error = 0.00166 %
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 = 1.036
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3456 1.138
h = 0.0001 0.003
y[1] (numeric) = -3.44618458938 0.501560801538
y[1] (closed_form) = -3.44618576308 0.501615495618
absolute error = 5.471e-05
relative error = 0.001571 %
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 = 0.8371
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3457 1.141
h = 0.001 0.001
y[1] (numeric) = -3.4475068156 0.502952804665
y[1] (closed_form) = -3.44750675792 0.503007394102
absolute error = 5.459e-05
relative error = 0.001567 %
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 = 0.6587
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3467 1.142
h = 0.001 0.003
y[1] (numeric) = -3.44751444383 0.503858221802
y[1] (closed_form) = -3.44751380157 0.503912554304
absolute error = 5.434e-05
relative error = 0.00156 %
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 = 3.13
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3477 1.145
h = 0.0001 0.004
y[1] (numeric) = -3.44843442878 0.505663185779
y[1] (closed_form) = -3.44843499888 0.505717993335
absolute error = 5.481e-05
relative error = 0.001573 %
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 = 1.776
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=600.3MB, alloc=52.3MB, time=7.09
x[1] = 0.3478 1.149
h = 0.003 0.006
y[1] (numeric) = -3.45022189231 0.507508946154
y[1] (closed_form) = -3.45022334099 0.507563077606
absolute error = 5.415e-05
relative error = 0.001553 %
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 = 2.36
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3508 1.155
h = 0.0001 0.005
y[1] (numeric) = -3.45163191914 0.511588506142
y[1] (closed_form) = -3.4516337952 0.511647487235
absolute error = 5.901e-05
relative error = 0.001691 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.055
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3509 1.16
h = 0.0001 0.003
y[1] (numeric) = -3.45390052082 0.513894391404
y[1] (closed_form) = -3.45390158608 0.51395031663
absolute error = 5.594e-05
relative error = 0.001602 %
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 = 0.853
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.351 1.163
h = 0.001 0.001
y[1] (numeric) = -3.45524929629 0.515295247218
y[1] (closed_form) = -3.45524912847 0.515351065971
absolute error = 5.582e-05
relative error = 0.001598 %
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 = 0.6712
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.352 1.164
h = 0.001 0.003
y[1] (numeric) = -3.45526320961 0.516212257833
y[1] (closed_form) = -3.45526245669 0.516267818474
absolute error = 5.557e-05
relative error = 0.00159 %
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 = 3.189
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.353 1.167
h = 0.0001 0.004
y[1] (numeric) = -3.45620735478 0.518034125354
y[1] (closed_form) = -3.45620781539 0.518090163409
absolute error = 5.604e-05
relative error = 0.001604 %
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 = 1.809
Order of pole (three term test) = 31.93 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3531 1.171
h = 0.003 0.006
y[1] (numeric) = -3.45803031316 0.519891411721
y[1] (closed_form) = -3.45803165458 0.519946773863
absolute error = 5.538e-05
relative error = 0.001584 %
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 = 2.405
Order of pole (three term test) = 31.92 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3561 1.177
h = 0.0001 0.005
y[1] (numeric) = -3.45948601662 0.524013763485
y[1] (closed_form) = -3.45948777943 0.524073983117
absolute error = 6.025e-05
relative error = 0.001722 %
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 = 1.075
Order of pole (three term test) = 31.92 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3562 1.182
h = 0.0001 0.003
y[1] (numeric) = -3.4617990739 0.52633387946
y[1] (closed_form) = -3.46180002888 0.526391037509
absolute error = 5.717e-05
relative error = 0.001633 %
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 = 0.8691
Order of pole (three term test) = 31.92 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3563 1.185
h = 0.001 0.001
y[1] (numeric) = -3.46317442626 0.527743637506
y[1] (closed_form) = -3.46317414644 0.527800687228
absolute error = 5.705e-05
relative error = 0.001629 %
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 = 0.6838
Order of pole (three term test) = 31.92 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3573 1.186
h = 0.0001 0.004
y[1] (numeric) = -3.46319461823 0.528672267586
y[1] (closed_form) = -3.46319375279 0.528729058
absolute error = 5.680e-05
relative error = 0.001621 %
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 = 4.111
Order of pole (three term test) = 31.92 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3574 1.19
h = 0.003 0.006
y[1] (numeric) = -3.46504665052 0.530538973444
y[1] (closed_form) = -3.46504831516 0.530595219203
absolute error = 5.627e-05
relative error = 0.001605 %
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 = 2.443
Order of pole (three term test) = 31.92 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3604 1.196
h = 0.0001 0.005
y[1] (numeric) = -3.46654219093 0.534697716595
y[1] (closed_form) = -3.46654427185 0.5347588268
absolute error = 6.115e-05
relative error = 0.001743 %
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 = 1.093
Order of pole (three term test) = 31.92 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3605 1.201
h = 0.0001 0.003
y[1] (numeric) = -3.46889372334 0.537029617984
y[1] (closed_form) = -3.46889499894 0.537087661561
absolute error = 5.806e-05
relative error = 0.001654 %
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 = 0.883
Order of pole (three term test) = 31.92 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3606 1.204
h = 0.001 0.001
y[1] (numeric) = -3.4702920817 0.53844676195
y[1] (closed_form) = -3.47029212098 0.538504695606
absolute error = 5.793e-05
relative error = 0.00165 %
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 = 0.6947
Order of pole (three term test) = 31.92 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3616 1.205
h = 0.001 0.003
y[1] (numeric) = -3.47031781184 0.539385340148
y[1] (closed_form) = -3.470317265 0.539443013461
absolute error = 5.768e-05
relative error = 0.001642 %
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 = 3.301
Order of pole (three term test) = 31.92 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3626 1.208
h = 0.0001 0.004
y[1] (numeric) = -3.47130715175 0.541238529288
y[1] (closed_form) = -3.47130782069 0.541296684482
absolute error = 5.816e-05
relative error = 0.001655 %
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 = 1.873
Order of pole (three term test) = 31.92 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3627 1.212
h = 0.003 0.006
y[1] (numeric) = -3.47319639771 0.543117015451
y[1] (closed_form) = -3.47319795172 0.543174495044
absolute error = 5.750e-05
relative error = 0.001636 %
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 = 2.489
Order of pole (three term test) = 31.92 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3657 1.218
h = 0.0001 0.005
y[1] (numeric) = -3.47473763606 0.547318788918
y[1] (closed_form) = -3.47473960023 0.547381141099
absolute error = 6.238e-05
relative error = 0.001773 %
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 = 1.113
Order of pole (three term test) = 31.92 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3658 1.223
h = 0.0001 0.003
y[1] (numeric) = -3.47713371524 0.549665075823
y[1] (closed_form) = -3.47713487711 0.549724355458
absolute error = 5.929e-05
relative error = 0.001684 %
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 = 0.8993
Order of pole (three term test) = 31.92 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3659 1.226
h = 0.001 0.001
y[1] (numeric) = -3.47855870433 0.551091215762
y[1] (closed_form) = -3.47855862809 0.551150383578
absolute error = 5.917e-05
relative error = 0.00168 %
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 = 0.7076
Order of pole (three term test) = 31.91 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=644.2MB, alloc=52.3MB, time=7.61
x[1] = 0.3669 1.227
h = 0.001 0.003
y[1] (numeric) = -3.47859070148 0.55204146308
y[1] (closed_form) = -3.47859003857 0.552100369325
absolute error = 5.891e-05
relative error = 0.001673 %
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 = 3.362
Order of pole (three term test) = 31.91 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3679 1.23
h = 0.0001 0.004
y[1] (numeric) = -3.479604241 0.553911725228
y[1] (closed_form) = -3.4796047951 0.553971115812
absolute error = 5.939e-05
relative error = 0.001686 %
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 = 1.907
Order of pole (three term test) = 31.91 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.368 1.234
h = 0.003 0.006
y[1] (numeric) = -3.48152909263 0.55580192836
y[1] (closed_form) = -3.48153053414 0.555860643517
absolute error = 5.873e-05
relative error = 0.001666 %
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 = 2.535
Order of pole (three term test) = 31.91 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.371 1.24
h = 0.0001 0.005
y[1] (numeric) = -3.48311604056 0.560046863374
y[1] (closed_form) = -3.48311788605 0.560110459419
absolute error = 6.362e-05
relative error = 0.001803 %
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 = 1.133
Order of pole (three term test) = 31.91 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3711 1.245
h = 0.0001 0.003
y[1] (numeric) = -3.48555671659 0.562407620974
y[1] (closed_form) = -3.48555776283 0.562468138447
absolute error = 6.053e-05
relative error = 0.001714 %
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 = 0.9158
Order of pole (three term test) = 31.91 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3712 1.248
h = 0.001 0.001
y[1] (numeric) = -3.48700836598 0.563842808467
y[1] (closed_form) = -3.48700817229 0.563903212199
absolute error = 6.040e-05
relative error = 0.00171 %
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 = 0.7205
Order of pole (three term test) = 31.91 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3722 1.249
h = 0.001 0.003
y[1] (numeric) = -3.48704662375 0.564804752211
y[1] (closed_form) = -3.48704584281 0.564864893126
absolute error = 6.015e-05
relative error = 0.001703 %
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 = 3.423
Order of pole (three term test) = 31.91 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3732 1.252
h = 0.0001 0.004
y[1] (numeric) = -3.48808437729 0.566692148441
y[1] (closed_form) = -3.48808481464 0.566752776189
absolute error = 6.063e-05
relative error = 0.001716 %
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 = 1.942
Order of pole (three term test) = 31.91 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3733 1.256
h = 0.003 0.006
y[1] (numeric) = -3.49004487479 0.568594137281
y[1] (closed_form) = -3.49004620193 0.568654089769
absolute error = 5.997e-05
relative error = 0.001696 %
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 = 2.581
Order of pole (three term test) = 31.91 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3763 1.262
h = 0.0001 0.005
y[1] (numeric) = -3.49167754465 0.57288236716
y[1] (closed_form) = -3.49167926951 0.572947208992
absolute error = 6.486e-05
relative error = 0.001833 %
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 = 1.154
Order of pole (three term test) = 31.91 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3764 1.267
h = 0.0001 0.003
y[1] (numeric) = -3.49416286877 0.575257681817
y[1] (closed_form) = -3.49416379745 0.575319438942
absolute error = 6.176e-05
relative error = 0.001744 %
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 = 0.9324
Order of pole (three term test) = 31.91 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3765 1.27
h = 0.001 0.001
y[1] (numeric) = -3.49564120871 0.576701969162
y[1] (closed_form) = -3.49564089561 0.5767636106
absolute error = 6.164e-05
relative error = 0.00174 %
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 = 0.7336
Order of pole (three term test) = 31.91 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3775 1.271
h = 0.001 0.003
y[1] (numeric) = -3.49568572066 0.577675637103
y[1] (closed_form) = -3.49568481973 0.57773701446
absolute error = 6.138e-05
relative error = 0.001732 %
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 = 3.485
Order of pole (three term test) = 31.91 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3785 1.274
h = 0.0001 0.004
y[1] (numeric) = -3.49674770312 0.579580229418
y[1] (closed_form) = -3.49674802177 0.579642096137
absolute error = 6.187e-05
relative error = 0.001745 %
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 = 1.977
Order of pole (three term test) = 31.91 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3786 1.278
h = 0.003 0.006
y[1] (numeric) = -3.4987438876 0.581494073657
y[1] (closed_form) = -3.49874509846 0.581555265277
absolute error = 6.120e-05
relative error = 0.001726 %
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 = 2.628
Order of pole (three term test) = 31.9 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3816 1.284
h = 0.0001 0.005
y[1] (numeric) = -3.50042229244 0.585825733807
y[1] (closed_form) = -3.5004238947 0.585891823386
absolute error = 6.611e-05
relative error = 0.001863 %
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 = 1.175
Order of pole (three term test) = 31.9 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3817 1.289
h = 0.0001 0.003
y[1] (numeric) = -3.50295231701 0.588215693069
y[1] (closed_form) = -3.50295312619 0.588278691698
absolute error = 6.300e-05
relative error = 0.001774 %
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 = 0.9492
Order of pole (three term test) = 31.9 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3818 1.292
h = 0.001 0.001
y[1] (numeric) = -3.50445737843 0.589669133288
y[1] (closed_form) = -3.50445694392 0.58973201426
absolute error = 6.288e-05
relative error = 0.001769 %
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 = 0.7468
Order of pole (three term test) = 31.9 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3828 1.293
h = 0.0001 0.004
y[1] (numeric) = -3.50450813815 0.590654553662
y[1] (closed_form) = -3.50450711522 0.590717169273
absolute error = 6.262e-05
relative error = 0.001762 %
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 = 4.489
Order of pole (three term test) = 31.9 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3829 1.297
h = 0.003 0.006
y[1] (numeric) = -3.50653355747 0.592578089891
y[1] (closed_form) = -3.50653508818 0.592640174
absolute error = 6.210e-05
relative error = 0.001746 %
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 = 2.668
Order of pole (three term test) = 31.9 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3859 1.303
h = 0.0001 0.005
y[1] (numeric) = -3.50825186 0.596946698385
y[1] (closed_form) = -3.50825377672 0.597013688071
absolute error = 6.702e-05
relative error = 0.001883 %
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 = 1.193
Order of pole (three term test) = 31.9 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.386 1.308
h = 0.0001 0.003
y[1] (numeric) = -3.51082057991 0.59934880091
y[1] (closed_form) = -3.51082170616 0.599412694148
absolute error = 6.390e-05
relative error = 0.001794 %
Correct digits = 5
memory used=688.2MB, alloc=52.3MB, time=8.13
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9638
Order of pole (three term test) = 31.9 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3861 1.311
h = 0.001 0.001
y[1] (numeric) = -3.51234877746 0.600809843809
y[1] (closed_form) = -3.51234865835 0.600873617697
absolute error = 6.377e-05
relative error = 0.00179 %
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 = 0.7582
Order of pole (three term test) = 31.9 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3871 1.312
h = 0.001 0.003
y[1] (numeric) = -3.51240505038 0.601805328934
y[1] (closed_form) = -3.51240434229 0.601868836351
absolute error = 6.351e-05
relative error = 0.001782 %
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 = 3.602
Order of pole (three term test) = 31.9 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3881 1.315
h = 0.0001 0.004
y[1] (numeric) = -3.51351236502 0.603741798311
y[1] (closed_form) = -3.51351287904 0.603805799872
absolute error = 6.400e-05
relative error = 0.001795 %
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 = 2.043
Order of pole (three term test) = 31.9 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3882 1.319
h = 0.003 0.006
y[1] (numeric) = -3.51557521041 0.605677465142
y[1] (closed_form) = -3.51557662126 0.605740791858
absolute error = 6.334e-05
relative error = 0.001776 %
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 = 2.716
Order of pole (three term test) = 31.9 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3912 1.325
h = 0.0001 0.005
y[1] (numeric) = -3.5173392757 0.610089761281
y[1] (closed_form) = -3.5173410661 0.610158002482
absolute error = 6.826e-05
relative error = 0.001912 %
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 = 1.214
Order of pole (three term test) = 31.9 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3913 1.33
h = 0.0001 0.003
y[1] (numeric) = -3.5199527976 0.612506673838
y[1] (closed_form) = -3.51995380069 0.612571812145
absolute error = 6.515e-05
relative error = 0.001823 %
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 = 0.9809
Order of pole (three term test) = 31.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3914 1.333
h = 0.001 0.001
y[1] (numeric) = -3.52150777662 0.613976969813
y[1] (closed_form) = -3.52150753238 0.614041986757
absolute error = 6.502e-05
relative error = 0.001819 %
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 = 0.7717
Order of pole (three term test) = 31.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3924 1.334
h = 0.001 0.003
y[1] (numeric) = -3.52157028571 0.614984261232
y[1] (closed_form) = -3.52156945187 0.61504901039
absolute error = 6.475e-05
relative error = 0.001811 %
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 = 3.666
Order of pole (three term test) = 31.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3934 1.337
h = 0.0001 0.004
y[1] (numeric) = -3.52270187518 0.616938109025
y[1] (closed_form) = -3.52270226483 0.617003354957
absolute error = 6.525e-05
relative error = 0.001824 %
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 = 2.079
Order of pole (three term test) = 31.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3935 1.341
h = 0.003 0.006
y[1] (numeric) = -3.52480053105 0.618885835391
y[1] (closed_form) = -3.52480182006 0.61895040662
absolute error = 6.458e-05
relative error = 0.001805 %
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 = 2.764
Order of pole (three term test) = 31.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3965 1.347
h = 0.0001 0.005
y[1] (numeric) = -3.52661037414 0.623341960589
y[1] (closed_form) = -3.52661203619 0.62341145537
absolute error = 6.951e-05
relative error = 0.001941 %
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 = 1.235
Order of pole (three term test) = 31.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3966 1.352
h = 0.0001 0.003
y[1] (numeric) = -3.52926875367 0.625773774133
y[1] (closed_form) = -3.52926963158 0.625840159466
absolute error = 6.639e-05
relative error = 0.001852 %
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 = 0.9981
Order of pole (three term test) = 31.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3967 1.355
h = 0.001 0.001
y[1] (numeric) = -3.53085054702 0.627253378279
y[1] (closed_form) = -3.5308501756 0.627319640209
absolute error = 6.626e-05
relative error = 0.001848 %
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 = 0.7852
Order of pole (three term test) = 31.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3977 1.356
h = 0.001 0.003
y[1] (numeric) = -3.53091928586 0.628272505564
y[1] (closed_form) = -3.5309183242 0.628338498376
absolute error = 6.600e-05
relative error = 0.00184 %
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 = 3.73
Order of pole (three term test) = 31.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3987 1.359
h = 0.0001 0.004
y[1] (numeric) = -3.53207516685 0.630243797383
y[1] (closed_form) = -3.53207543009 0.630310289634
absolute error = 6.649e-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 = 2.116
Order of pole (three term test) = 31.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3988 1.363
h = 0.003 0.006
y[1] (numeric) = -3.53420967782 0.632203656674
y[1] (closed_form) = -3.53421084298 0.63226947436
absolute error = 6.583e-05
relative error = 0.001833 %
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 = 2.812
Order of pole (three term test) = 31.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4018 1.369
h = 0.0001 0.005
y[1] (numeric) = -3.53606531444 0.63670375446
y[1] (closed_form) = -3.53606684606 0.636774504923
absolute error = 7.077e-05
relative error = 0.00197 %
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 = 1.257
Order of pole (three term test) = 31.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4019 1.374
h = 0.0001 0.003
y[1] (numeric) = -3.53876860838 0.639150561152
y[1] (closed_form) = -3.53876935907 0.639218195504
absolute error = 6.764e-05
relative error = 0.001881 %
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 = 1.016
Order of pole (three term test) = 31.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.402 1.377
h = 0.001 0.001
y[1] (numeric) = -3.54037724959 0.640639529297
y[1] (closed_form) = -3.54037674891 0.640707038181
absolute error = 6.751e-05
relative error = 0.001876 %
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 = 0.7989
Order of pole (three term test) = 31.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.403 1.378
h = 0.001 0.003
y[1] (numeric) = -3.54045221176 0.64167052249
y[1] (closed_form) = -3.54045112019 0.641737760906
absolute error = 6.725e-05
relative error = 0.001869 %
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 = 3.795
Order of pole (three term test) = 31.89 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.404 1.381
h = 0.0001 0.004
y[1] (numeric) = -3.5416324014 0.643659324885
y[1] (closed_form) = -3.54163253617 0.643727065441
absolute error = 6.774e-05
relative error = 0.001882 %
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 = 2.153
Order of pole (three term test) = 31.88 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=732.0MB, alloc=52.3MB, time=8.65
x[1] = 0.4041 1.385
h = 0.003 0.006
y[1] (numeric) = -3.54380281301 0.645631391465
y[1] (closed_form) = -3.54380385231 0.645698457587
absolute error = 6.707e-05
relative error = 0.001862 %
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 = 2.861
Order of pole (three term test) = 31.88 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4071 1.391
h = 0.0001 0.005
y[1] (numeric) = -3.54570425959 0.650175607487
y[1] (closed_form) = -3.54570565869 0.65024761577
absolute error = 7.202e-05
relative error = 0.001998 %
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 = 1.279
Order of pole (three term test) = 31.88 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4072 1.396
h = 0.0001 0.003
y[1] (numeric) = -3.54845252585 0.652637500701
y[1] (closed_form) = -3.54845314725 0.652706386099
absolute error = 6.889e-05
relative error = 0.001909 %
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 = 1.033
Order of pole (three term test) = 31.88 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4073 1.399
h = 0.001 0.001
y[1] (numeric) = -3.55008804912 0.654135889406
y[1] (closed_form) = -3.55008741708 0.654204647249
absolute error = 6.876e-05
relative error = 0.001905 %
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 = 0.8127
Order of pole (three term test) = 31.88 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4083 1.4
h = 0.003 0.006
y[1] (numeric) = -3.5501692282 0.655178779021
y[1] (closed_form) = -3.5501680046 0.655247265027
absolute error = 6.850e-05
relative error = 0.001897 %
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 = 8.19
Order of pole (three term test) = 31.88 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4113 1.406
h = 0.0001 0.005
y[1] (numeric) = -3.55209679745 0.659753532775
y[1] (closed_form) = -3.55210021227 0.659828018064
absolute error = 7.456e-05
relative error = 0.002064 %
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 = 1.294
Order of pole (three term test) = 31.88 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4114 1.411
h = 0.0001 0.003
y[1] (numeric) = -3.55487565089 0.662226993279
y[1] (closed_form) = -3.55487829042 0.662298351042
absolute error = 7.141e-05
relative error = 0.001975 %
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 = 1.045
Order of pole (three term test) = 31.88 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4115 1.414
h = 0.001 0.001
y[1] (numeric) = -3.55652944716 0.663732573695
y[1] (closed_form) = -3.55653083186 0.663803802398
absolute error = 7.124e-05
relative error = 0.001969 %
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 = 0.8223
Order of pole (three term test) = 31.88 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4125 1.415
h = 0.001 0.003
y[1] (numeric) = -3.55661459842 0.664783821068
y[1] (closed_form) = -3.55661539113 0.664854776965
absolute error = 7.096e-05
relative error = 0.001961 %
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 = 3.906
Order of pole (three term test) = 31.88 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4135 1.418
h = 0.0001 0.004
y[1] (numeric) = -3.55783541364 0.666802946261
y[1] (closed_form) = -3.55783743511 0.666874408976
absolute error = 7.149e-05
relative error = 0.001975 %
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 = 2.216
Order of pole (three term test) = 31.88 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4136 1.422
h = 0.003 0.006
y[1] (numeric) = -3.56006621556 0.6687966957
y[1] (closed_form) = -3.56006914606 0.668867484258
absolute error = 7.085e-05
relative error = 0.001956 %
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 = 2.944
Order of pole (three term test) = 31.88 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4166 1.428
h = 0.0001 0.005
y[1] (numeric) = -3.56204390371 0.673416869552
y[1] (closed_form) = -3.56204718237 0.673492616299
absolute error = 7.582e-05
relative error = 0.002091 %
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 = 1.316
Order of pole (three term test) = 31.87 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4167 1.433
h = 0.0001 0.003
y[1] (numeric) = -3.5648678274 0.675905578459
y[1] (closed_form) = -3.56487033404 0.675978190724
absolute error = 7.266e-05
relative error = 0.002002 %
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 = 1.063
Order of pole (three term test) = 31.87 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4168 1.436
h = 0.001 0.001
y[1] (numeric) = -3.56654856354 0.677420677484
y[1] (closed_form) = -3.56654981322 0.677493158558
absolute error = 7.249e-05
relative error = 0.001997 %
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 = 0.8364
Order of pole (three term test) = 31.87 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4178 1.437
h = 0.001 0.003
y[1] (numeric) = -3.56663992005 0.67848387369
y[1] (closed_form) = -3.56664057705 0.678556080557
absolute error = 7.221e-05
relative error = 0.001989 %
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 = 3.973
Order of pole (three term test) = 31.87 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4188 1.44
h = 0.0001 0.004
y[1] (numeric) = -3.56788509052 0.680520693506
y[1] (closed_form) = -3.56788697781 0.68059340999
absolute error = 7.274e-05
relative error = 0.002003 %
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 = 2.254
Order of pole (three term test) = 31.87 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4189 1.444
h = 0.003 0.006
y[1] (numeric) = -3.57015191801 0.682526856173
y[1] (closed_form) = -3.57015471703 0.682598898616
absolute error = 7.210e-05
relative error = 0.001984 %
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 = 2.995
Order of pole (three term test) = 31.87 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4219 1.45
h = 0.0001 0.005
y[1] (numeric) = -3.57217545979 0.687191550776
y[1] (closed_form) = -3.57217860011 0.687268561218
absolute error = 7.707e-05
relative error = 0.002119 %
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 = 1.338
Order of pole (three term test) = 31.87 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.422 1.455
h = 0.0001 0.003
y[1] (numeric) = -3.57504451466 0.689695604765
y[1] (closed_form) = -3.57504688629 0.689769473658
absolute error = 7.391e-05
relative error = 0.00203 %
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 = 1.081
Order of pole (three term test) = 31.87 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4221 1.458
h = 0.001 0.001
y[1] (numeric) = -3.57675222668 0.691220280974
y[1] (closed_form) = -3.57675333917 0.691294016518
absolute error = 7.374e-05
relative error = 0.002024 %
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 = 0.8506
Order of pole (three term test) = 31.87 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4231 1.459
h = 0.001 0.003
y[1] (numeric) = -3.57684978197 0.692295457794
y[1] (closed_form) = -3.57685030108 0.692368917714
absolute error = 7.346e-05
relative error = 0.002016 %
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 = 4.04
Order of pole (three term test) = 31.87 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=776.0MB, alloc=52.3MB, time=9.17
x[1] = 0.4241 1.462
h = 0.0001 0.004
y[1] (numeric) = -3.57811932652 0.6943500423
y[1] (closed_form) = -3.57812107747 0.694424014671
absolute error = 7.399e-05
relative error = 0.00203 %
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 = 2.292
Order of pole (three term test) = 31.87 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4242 1.466
h = 0.003 0.006
y[1] (numeric) = -3.58042222843 0.696368696195
y[1] (closed_form) = -3.58042489386 0.696441994638
absolute error = 7.335e-05
relative error = 0.002011 %
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 = 3.045
Order of pole (three term test) = 31.87 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4272 1.472
h = 0.0001 0.005
y[1] (numeric) = -3.5824916427 0.701078065091
y[1] (closed_form) = -3.58249464251 0.701156341501
absolute error = 7.833e-05
relative error = 0.002146 %
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 = 1.361
Order of pole (three term test) = 31.87 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4273 1.477
h = 0.0001 0.003
y[1] (numeric) = -3.58540589084 0.703597562071
y[1] (closed_form) = -3.58540812529 0.703672689754
absolute error = 7.516e-05
relative error = 0.002057 %
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 = 1.099
Order of pole (three term test) = 31.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4274 1.48
h = 0.001 0.001
y[1] (numeric) = -3.58714061543 0.705131874783
y[1] (closed_form) = -3.58714158853 0.705206866937
absolute error = 7.500e-05
relative error = 0.002051 %
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 = 0.8649
Order of pole (three term test) = 31.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4284 1.481
h = 0.0001 0.004
y[1] (numeric) = -3.58724436303 0.706219064476
y[1] (closed_form) = -3.58724474204 0.706293779568
absolute error = 7.472e-05
relative error = 0.002044 %
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 = 5.198
Order of pole (three term test) = 31.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4285 1.485
h = 0.003 0.006
y[1] (numeric) = -3.58957682338 0.708247935918
y[1] (closed_form) = -3.58957980239 0.708322144315
absolute error = 7.427e-05
relative error = 0.00203 %
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 = 3.089
Order of pole (three term test) = 31.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4315 1.491
h = 0.0001 0.005
y[1] (numeric) = -3.59168627348 0.712995336798
y[1] (closed_form) = -3.59168958095 0.713074531956
absolute error = 7.926e-05
relative error = 0.002165 %
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 = 1.38
Order of pole (three term test) = 31.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4316 1.496
h = 0.0001 0.003
y[1] (numeric) = -3.59463965864 0.715527666567
y[1] (closed_form) = -3.59464220357 0.715603706691
absolute error = 7.608e-05
relative error = 0.002076 %
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 = 1.115
Order of pole (three term test) = 31.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4317 1.499
h = 0.001 0.001
y[1] (numeric) = -3.59639778039 0.717069999756
y[1] (closed_form) = -3.59639906201 0.71714590248
absolute error = 7.591e-05
relative error = 0.00207 %
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 = 0.8773
Order of pole (three term test) = 31.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4327 1.5
h = 0.001 0.003
y[1] (numeric) = -3.59650699658 0.718167482265
y[1] (closed_form) = -3.59650768346 0.718243106684
absolute error = 7.563e-05
relative error = 0.002062 %
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 = 4.168
Order of pole (three term test) = 31.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4337 1.503
h = 0.0001 0.004
y[1] (numeric) = -3.59782216087 0.720255021587
y[1] (closed_form) = -3.59782408259 0.72033116381
absolute error = 7.617e-05
relative error = 0.002076 %
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 = 2.364
Order of pole (three term test) = 31.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4338 1.507
h = 0.003 0.006
y[1] (numeric) = -3.60019247302 0.722296698604
y[1] (closed_form) = -3.60019531447 0.722372167058
absolute error = 7.552e-05
relative error = 0.002057 %
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 = 3.141
Order of pole (three term test) = 31.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4368 1.513
h = 0.0001 0.005
y[1] (numeric) = -3.60234783441 0.727089064967
y[1] (closed_form) = -3.60235099726 0.727169530449
absolute error = 8.053e-05
relative error = 0.002191 %
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 = 1.403
Order of pole (three term test) = 31.86 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4369 1.518
h = 0.0001 0.003
y[1] (numeric) = -3.60534653261 0.729637022431
y[1] (closed_form) = -3.60534893631 0.729714325496
absolute error = 7.734e-05
relative error = 0.002103 %
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 = 1.134
Order of pole (three term test) = 31.85 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.437 1.521
h = 0.001 0.001
y[1] (numeric) = -3.6071317377 0.731189104051
y[1] (closed_form) = -3.60713287581 0.731266267487
absolute error = 7.717e-05
relative error = 0.002097 %
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 = 0.8919
Order of pole (three term test) = 31.85 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.438 1.522
h = 0.001 0.003
y[1] (numeric) = -3.60724713455 0.7322986608
y[1] (closed_form) = -3.60724767718 0.73237554446
absolute error = 7.689e-05
relative error = 0.002089 %
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 = 4.237
Order of pole (three term test) = 31.85 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.439 1.525
h = 0.0001 0.004
y[1] (numeric) = -3.60858673014 0.734404170312
y[1] (closed_form) = -3.60858850925 0.734481574716
absolute error = 7.742e-05
relative error = 0.002102 %
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 = 2.403
Order of pole (three term test) = 31.85 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4391 1.529
h = 0.003 0.006
y[1] (numeric) = -3.61099326245 0.736458566563
y[1] (closed_form) = -3.61099596415 0.736535297292
absolute error = 7.678e-05
relative error = 0.002083 %
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 = 3.193
Order of pole (three term test) = 31.85 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4421 1.535
h = 0.0001 0.005
y[1] (numeric) = -3.61319455594 0.741296058114
y[1] (closed_form) = -3.61319757191 0.741377796299
absolute error = 8.179e-05
relative error = 0.002218 %
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 = 1.427
Order of pole (three term test) = 31.85 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4422 1.54
h = 0.0001 0.003
y[1] (numeric) = -3.61623863256 0.743859744713
y[1] (closed_form) = -3.6162408928 0.743938312988
absolute error = 7.860e-05
relative error = 0.002129 %
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 = 1.153
Order of pole (three term test) = 31.85 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4423 1.543
h = 0.001 0.001
y[1] (numeric) = -3.6180509596 0.745421636233
y[1] (closed_form) = -3.61805195194 0.745500062625
absolute error = 7.843e-05
relative error = 0.002123 %
Correct digits = 5
memory used=819.9MB, alloc=52.3MB, time=9.70
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9066
Order of pole (three term test) = 31.85 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4433 1.544
h = 0.001 0.003
y[1] (numeric) = -3.61817253063 0.746543300845
y[1] (closed_form) = -3.61817292672 0.74662144597
absolute error = 7.815e-05
relative error = 0.002115 %
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 = 4.307
Order of pole (three term test) = 31.85 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4443 1.547
h = 0.0001 0.004
y[1] (numeric) = -3.61953657811 0.748666854324
y[1] (closed_form) = -3.61953821234 0.748745523169
absolute error = 7.869e-05
relative error = 0.002129 %
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 = 2.443
Order of pole (three term test) = 31.85 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4444 1.551
h = 0.003 0.006
y[1] (numeric) = -3.62197938295 0.750734051644
y[1] (closed_form) = -3.62198194268 0.750812046904
absolute error = 7.804e-05
relative error = 0.00211 %
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 = 3.246
Order of pole (three term test) = 31.85 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4474 1.557
h = 0.0001 0.005
y[1] (numeric) = -3.62422663002 0.755616830258
y[1] (closed_form) = -3.62422949682 0.755699843562
absolute error = 8.306e-05
relative error = 0.002244 %
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 = 1.45
Order of pole (three term test) = 31.85 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4475 1.562
h = 0.0001 0.003
y[1] (numeric) = -3.62731615157 0.758196348685
y[1] (closed_form) = -3.62731826609 0.758276184474
absolute error = 7.986e-05
relative error = 0.002155 %
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 = 1.172
Order of pole (three term test) = 31.84 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4476 1.565
h = 0.001 0.001
y[1] (numeric) = -3.62915563987 0.759768112334
y[1] (closed_form) = -3.62915648413 0.75984780396
absolute error = 7.970e-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 = 0.9215
Order of pole (three term test) = 31.84 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4486 1.566
h = 0.001 0.003
y[1] (numeric) = -3.62928337856 0.760901918909
y[1] (closed_form) = -3.62928362582 0.76098132776
absolute error = 7.941e-05
relative error = 0.002141 %
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 = 4.377
Order of pole (three term test) = 31.84 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4496 1.569
h = 0.0001 0.004
y[1] (numeric) = -3.63067189898 0.763043591102
y[1] (closed_form) = -3.63067338606 0.763123526687
absolute error = 7.995e-05
relative error = 0.002155 %
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 = 2.483
Order of pole (three term test) = 31.84 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4497 1.573
h = 0.003 0.006
y[1] (numeric) = -3.63315102964 0.765123672334
y[1] (closed_form) = -3.63315344518 0.765202934418
absolute error = 7.930e-05
relative error = 0.002136 %
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 = 3.299
Order of pole (three term test) = 31.84 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4527 1.579
h = 0.0001 0.005
y[1] (numeric) = -3.63544425244 0.770051902064
y[1] (closed_form) = -3.63544696775 0.770136192942
absolute error = 8.433e-05
relative error = 0.002269 %
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 = 1.474
Order of pole (three term test) = 31.84 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4528 1.584
h = 0.0001 0.003
y[1] (numeric) = -3.63857928658 0.772647356267
y[1] (closed_form) = -3.63858125309 0.772728461912
absolute error = 8.113e-05
relative error = 0.002181 %
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) = 31.84 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4529 1.587
h = 0.001 0.001
y[1] (numeric) = -3.64044597611 0.774229055038
y[1] (closed_form) = -3.64044666998 0.774310014215
absolute error = 8.096e-05
relative error = 0.002175 %
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 = 0.9366
Order of pole (three term test) = 31.84 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4539 1.588
h = 0.0001 0.004
y[1] (numeric) = -3.64057987595 0.775375038158
y[1] (closed_form) = -3.64057997203 0.775455713033
absolute error = 8.067e-05
relative error = 0.002167 %
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 = 5.629
Order of pole (three term test) = 31.84 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.454 1.592
h = 0.003 0.006
y[1] (numeric) = -3.64308877457 0.777465661284
y[1] (closed_form) = -3.64309149997 0.777545844356
absolute error = 8.023e-05
relative error = 0.002154 %
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 = 3.345
Order of pole (three term test) = 31.84 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.457 1.598
h = 0.0001 0.005
y[1] (numeric) = -3.6454221341 0.782432598824
y[1] (closed_form) = -3.64542515307 0.78251782016
absolute error = 8.527e-05
relative error = 0.002287 %
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 = 1.494
Order of pole (three term test) = 31.84 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4571 1.603
h = 0.0001 0.003
y[1] (numeric) = -3.64859659053 0.78504131095
y[1] (closed_form) = -3.64859886364 0.78512334028
absolute error = 8.206e-05
relative error = 0.002199 %
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 = 1.207
Order of pole (three term test) = 31.83 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4572 1.606
h = 0.001 0.001
y[1] (numeric) = -3.65048684589 0.786631287891
y[1] (closed_form) = -3.65048784423 0.786713168776
absolute error = 8.189e-05
relative error = 0.002193 %
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 = 0.9496
Order of pole (three term test) = 31.83 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4582 1.607
h = 0.001 0.003
y[1] (numeric) = -3.65062618943 0.78778770695
y[1] (closed_form) = -3.65062658929 0.787869302212
absolute error = 8.160e-05
relative error = 0.002185 %
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 = 4.511
Order of pole (three term test) = 31.83 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4592 1.61
h = 0.0001 0.004
y[1] (numeric) = -3.65206052381 0.78996300399
y[1] (closed_form) = -3.65206216676 0.79004513167
absolute error = 8.214e-05
relative error = 0.002198 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.558
Order of pole (three term test) = 31.83 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4593 1.614
h = 0.003 0.006
y[1] (numeric) = -3.65460754914 0.792066848879
y[1] (closed_form) = -3.65461012613 0.792148303166
absolute error = 8.150e-05
relative error = 0.002179 %
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 = 3.399
Order of pole (three term test) = 31.83 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4623 1.62
h = 0.0001 0.005
y[1] (numeric) = -3.65698692938 0.797079548338
y[1] (closed_form) = -3.65698979252 0.79716605194
absolute error = 8.655e-05
relative error = 0.002312 %
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 = 1.518
Order of pole (three term test) = 31.83 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=863.8MB, alloc=52.3MB, time=10.21
x[1] = 0.4624 1.625
h = 0.0001 0.003
y[1] (numeric) = -3.66020702861 0.799704392186
y[1] (closed_form) = -3.66020914942 0.799787695857
absolute error = 8.333e-05
relative error = 0.002224 %
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 = 1.227
Order of pole (three term test) = 31.83 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4625 1.628
h = 0.001 0.001
y[1] (numeric) = -3.66212456215 0.801304423011
y[1] (closed_form) = -3.66212540575 0.801387575884
absolute error = 8.316e-05
relative error = 0.002218 %
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 = 0.965
Order of pole (three term test) = 31.83 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4635 1.629
h = 0.001 0.003
y[1] (numeric) = -3.66227005512 0.802473084326
y[1] (closed_form) = -3.66227029941 0.802555950013
absolute error = 8.287e-05
relative error = 0.00221 %
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 = 4.584
Order of pole (three term test) = 31.83 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4645 1.632
h = 0.0001 0.004
y[1] (numeric) = -3.66372892607 0.804666719037
y[1] (closed_form) = -3.66373041524 0.804750120263
absolute error = 8.341e-05
relative error = 0.002224 %
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 = 2.599
Order of pole (three term test) = 31.83 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4646 1.636
h = 0.003 0.006
y[1] (numeric) = -3.6663124357 0.806783689762
y[1] (closed_form) = -3.66631486198 0.806866417664
absolute error = 8.276e-05
relative error = 0.002205 %
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 = 3.454
Order of pole (three term test) = 31.83 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4676 1.642
h = 0.0001 0.005
y[1] (numeric) = -3.66873786071 0.811842321456
y[1] (closed_form) = -3.66874056564 0.811930109884
absolute error = 8.783e-05
relative error = 0.002337 %
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 = 1.543
Order of pole (three term test) = 31.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4677 1.647
h = 0.0001 0.003
y[1] (numeric) = -3.67200367368 0.814483404584
y[1] (closed_form) = -3.67200563985 0.814567985045
absolute error = 8.460e-05
relative error = 0.002249 %
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 = 1.246
Order of pole (three term test) = 31.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4678 1.65
h = 0.001 0.001
y[1] (numeric) = -3.67394852733 0.816093554482
y[1] (closed_form) = -3.67394921379 0.816177981765
absolute error = 8.443e-05
relative error = 0.002243 %
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 = 0.9804
Order of pole (three term test) = 31.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4688 1.651
h = 0.001 0.003
y[1] (numeric) = -3.67410016317 0.817274494016
y[1] (closed_form) = -3.6741002495 0.817358632532
absolute error = 8.414e-05
relative error = 0.002235 %
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 = 4.657
Order of pole (three term test) = 31.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4698 1.654
h = 0.0001 0.004
y[1] (numeric) = -3.6755835935 0.819486544921
y[1] (closed_form) = -3.67558492651 0.819571222133
absolute error = 8.469e-05
relative error = 0.002249 %
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 = 2.641
Order of pole (three term test) = 31.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4699 1.658
h = 0.003 0.006
y[1] (numeric) = -3.67820364425 0.821616728245
y[1] (closed_form) = -3.67820591748 0.821700732197
absolute error = 8.403e-05
relative error = 0.00223 %
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 = 3.509
Order of pole (three term test) = 31.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4729 1.664
h = 0.0001 0.005
y[1] (numeric) = -3.68067513875 0.826721464695
y[1] (closed_form) = -3.68067768305 0.826810540547
absolute error = 8.911e-05
relative error = 0.002362 %
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 = 1.568
Order of pole (three term test) = 31.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.473 1.669
h = 0.0001 0.003
y[1] (numeric) = -3.68398673755 0.82937889594
y[1] (closed_form) = -3.68398854669 0.829464755677
absolute error = 8.588e-05
relative error = 0.002274 %
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 = 1.266
Order of pole (three term test) = 31.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4731 1.672
h = 0.001 0.001
y[1] (numeric) = -3.68595895392 0.830999230875
y[1] (closed_form) = -3.68595948081 0.831084935027
absolute error = 8.571e-05
relative error = 0.002268 %
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 = 0.9961
Order of pole (three term test) = 31.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4741 1.673
h = 0.001 0.003
y[1] (numeric) = -3.68611672605 0.832192485079
y[1] (closed_form) = -3.68611665198 0.832277898863
absolute error = 8.541e-05
relative error = 0.00226 %
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 = 4.731
Order of pole (three term test) = 31.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4751 1.676
h = 0.0001 0.004
y[1] (numeric) = -3.68762473901 0.834423031689
y[1] (closed_form) = -3.68762591347 0.834508987364
absolute error = 8.596e-05
relative error = 0.002274 %
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 = 2.683
Order of pole (three term test) = 31.82 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4752 1.68
h = 0.003 0.006
y[1] (numeric) = -3.69028138862 0.836566515403
y[1] (closed_form) = -3.69028350643 0.836651797877
absolute error = 8.531e-05
relative error = 0.002254 %
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 = 3.565
Order of pole (three term test) = 31.81 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4782 1.686
h = 0.0001 0.005
y[1] (numeric) = -3.69279897796 0.841717531344
y[1] (closed_form) = -3.69280135919 0.841807897256
absolute error = 9.040e-05
relative error = 0.002387 %
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 = 1.592
Order of pole (three term test) = 31.81 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4783 1.691
h = 0.0001 0.003
y[1] (numeric) = -3.69615643584 0.844391420827
y[1] (closed_form) = -3.69615808553 0.844478562362
absolute error = 8.716e-05
relative error = 0.002299 %
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 = 1.286
Order of pole (three term test) = 31.81 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4784 1.694
h = 0.001 0.001
y[1] (numeric) = -3.69815605819 0.846022007545
y[1] (closed_form) = -3.69815642307 0.846108991062
absolute error = 8.698e-05
relative error = 0.002293 %
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 = 1.012
Order of pole (three term test) = 31.81 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4794 1.695
h = 0.0001 0.004
y[1] (numeric) = -3.69831996003 0.847227613355
y[1] (closed_form) = -3.6983197231 0.847314304884
absolute error = 8.669e-05
relative error = 0.002285 %
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 = 6.082
Order of pole (three term test) = 31.81 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=907.8MB, alloc=52.3MB, time=10.73
x[1] = 0.4795 1.699
h = 0.003 0.006
y[1] (numeric) = -3.70100660484 0.849381982818
y[1] (closed_form) = -3.70100902867 0.849468198112
absolute error = 8.625e-05
relative error = 0.002271 %
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 = 3.614
Order of pole (three term test) = 31.81 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4825 1.705
h = 0.0001 0.005
y[1] (numeric) = -3.70356444605 0.854572426718
y[1] (closed_form) = -3.70356712679 0.854663735602
absolute error = 9.135e-05
relative error = 0.002403 %
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 = 1.614
Order of pole (three term test) = 31.81 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4826 1.71
h = 0.0001 0.003
y[1] (numeric) = -3.70696163527 0.85726002459
y[1] (closed_form) = -3.70696358752 0.857348101853
absolute error = 8.810e-05
relative error = 0.002315 %
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 = 1.304
Order of pole (three term test) = 31.81 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4827 1.713
h = 0.001 0.001
y[1] (numeric) = -3.70898500616 0.858899162573
y[1] (closed_form) = -3.70898567134 0.858987079734
absolute error = 8.792e-05
relative error = 0.002309 %
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 = 1.026
Order of pole (three term test) = 31.81 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4837 1.714
h = 0.001 0.003
y[1] (numeric) = -3.70915432671 0.860115357275
y[1] (closed_form) = -3.70915438931 0.860202981048
absolute error = 8.762e-05
relative error = 0.002301 %
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 = 4.872
Order of pole (three term test) = 31.81 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4847 1.717
h = 0.0001 0.004
y[1] (numeric) = -3.71070836828 0.862380241594
y[1] (closed_form) = -3.71070968294 0.862468413283
absolute error = 8.818e-05
relative error = 0.002315 %
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 = 2.763
Order of pole (three term test) = 31.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4848 1.721
h = 0.003 0.006
y[1] (numeric) = -3.71343343752 0.864548273809
y[1] (closed_form) = -3.71343570149 0.864635772355
absolute error = 8.753e-05
relative error = 0.002296 %
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 = 3.671
Order of pole (three term test) = 31.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4878 1.727
h = 0.0001 0.005
y[1] (numeric) = -3.71603742464 0.86978532794
y[1] (closed_form) = -3.71603993773 0.869877931916
absolute error = 9.264e-05
relative error = 0.002427 %
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 = 1.64
Order of pole (three term test) = 31.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4879 1.732
h = 0.0001 0.003
y[1] (numeric) = -3.71948061361 0.872489591493
y[1] (closed_form) = -3.7194824019 0.872578955376
absolute error = 8.938e-05
relative error = 0.00234 %
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 = 1.324
Order of pole (three term test) = 31.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.488 1.735
h = 0.001 0.001
y[1] (numeric) = -3.72153147365 0.874139107011
y[1] (closed_form) = -3.72153197222 0.87422830831
absolute error = 8.920e-05
relative error = 0.002333 %
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 = 1.042
Order of pole (three term test) = 31.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.489 1.736
h = 0.001 0.003
y[1] (numeric) = -3.72170691206 0.87536772343
y[1] (closed_form) = -3.72170680718 0.875456629685
absolute error = 8.891e-05
relative error = 0.002325 %
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 = 4.948
Order of pole (three term test) = 31.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.49 1.739
h = 0.0001 0.004
y[1] (numeric) = -3.72328560627 0.877651336111
y[1] (closed_form) = -3.72328675537 0.877740793587
absolute error = 8.946e-05
relative error = 0.002339 %
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 = 2.806
Order of pole (three term test) = 31.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4901 1.743
h = 0.003 0.006
y[1] (numeric) = -3.72604744563 0.879832924874
y[1] (closed_form) = -3.72604954731 0.87992170925
absolute error = 8.881e-05
relative error = 0.00232 %
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 = 3.728
Order of pole (three term test) = 31.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4931 1.749
h = 0.0001 0.005
y[1] (numeric) = -3.7286976059 0.885116770338
y[1] (closed_form) = -3.72869994882 0.885210672149
absolute error = 9.393e-05
relative error = 0.002451 %
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 = 1.665
Order of pole (three term test) = 31.8 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4932 1.754
h = 0.0001 0.003
y[1] (numeric) = -3.73218687117 0.887837813388
y[1] (closed_form) = -3.73218849301 0.887928466521
absolute error = 9.067e-05
relative error = 0.002363 %
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 = 1.345
Order of pole (three term test) = 31.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4933 1.757
h = 0.001 0.001
y[1] (numeric) = -3.73426526557 0.889497775432
y[1] (closed_form) = -3.73426559502 0.88958826347
absolute error = 9.049e-05
relative error = 0.002357 %
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 = 1.058
Order of pole (three term test) = 31.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4943 1.758
h = 0.001 0.003
y[1] (numeric) = -3.7344468152 0.890738851905
y[1] (closed_form) = -3.73444654031 0.890829043224
absolute error = 9.019e-05
relative error = 0.002349 %
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 = 5.026
Order of pole (three term test) = 31.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4953 1.761
h = 0.0001 0.004
y[1] (numeric) = -3.73605018707 0.893041276305
y[1] (closed_form) = -3.73605116811 0.893132022188
absolute error = 9.075e-05
relative error = 0.002362 %
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 = 2.85
Order of pole (three term test) = 31.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4954 1.765
h = 0.003 0.006
y[1] (numeric) = -3.73884885782 0.895236513416
y[1] (closed_form) = -3.73885079473 0.89532658624
absolute error = 9.009e-05
relative error = 0.002343 %
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 = 3.786
Order of pole (three term test) = 31.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4984 1.771
h = 0.0001 0.005
y[1] (numeric) = -3.74154521912 0.900567333562
y[1] (closed_form) = -3.74154738931 0.900662535988
absolute error = 9.523e-05
relative error = 0.002474 %
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 = 1.691
Order of pole (three term test) = 31.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4985 1.776
h = 0.0001 0.003
y[1] (numeric) = -3.74508063836 0.903305271231
y[1] (closed_form) = -3.74508209124 0.90339721628
absolute error = 9.196e-05
relative error = 0.002387 %
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 = 1.366
Order of pole (three term test) = 31.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4986 1.779
h = 0.001 0.001
y[1] (numeric) = -3.74718661305 0.904975749585
y[1] (closed_form) = -3.74718677082 0.905067527004
absolute error = 9.178e-05
relative error = 0.002381 %
Correct digits = 5
memory used=951.8MB, alloc=52.3MB, time=11.25
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.075
Order of pole (three term test) = 31.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4996 1.78
h = 0.001 0.003
y[1] (numeric) = -3.74737426724 0.906229324943
y[1] (closed_form) = -3.74737381977 0.906320803948
absolute error = 9.148e-05
relative error = 0.002373 %
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 = 5.104
Order of pole (three term test) = 31.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5006 1.783
h = 0.0001 0.004
y[1] (numeric) = -3.74900234222 0.908550645425
y[1] (closed_form) = -3.74900315266 0.908642682375
absolute error = 9.204e-05
relative error = 0.002386 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.894
Order of pole (three term test) = 31.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5007 1.787
h = 0.003 0.006
y[1] (numeric) = -3.75183790653 0.91075962374
y[1] (closed_form) = -3.75183967619 0.910850987665
absolute error = 9.138e-05
relative error = 0.002367 %
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 = 3.845
Order of pole (three term test) = 31.79 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5037 1.793
h = 0.0001 0.005
y[1] (numeric) = -3.75458049739 0.916137604167
y[1] (closed_form) = -3.75458249229 0.916234110025
absolute error = 9.653e-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 = 1.717
Order of pole (three term test) = 31.78 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5038 1.798
h = 0.0001 0.003
y[1] (numeric) = -3.75816214945 0.918892552892
y[1] (closed_form) = -3.75816343082 0.918985792562
absolute error = 9.325e-05
relative error = 0.00241 %
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 = 1.387
Order of pole (three term test) = 31.78 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5039 1.801
h = 0.001 0.001
y[1] (numeric) = -3.760295751 0.920573618141
y[1] (closed_form) = -3.76029573452 0.920666687616
absolute error = 9.307e-05
relative error = 0.002404 %
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 = 1.091
Order of pole (three term test) = 31.78 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5049 1.802
h = 0.0001 0.004
y[1] (numeric) = -3.76048950308 0.921839731709
y[1] (closed_form) = -3.76048888043 0.921932501055
absolute error = 9.277e-05
relative error = 0.002396 %
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 = 6.558
Order of pole (three term test) = 31.78 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.505 1.806
h = 0.003 0.006
y[1] (numeric) = -3.76335530762 0.924059959578
y[1] (closed_form) = -3.76335737932 0.924152268965
absolute error = 9.233e-05
relative error = 0.002383 %
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 = 3.896
Order of pole (three term test) = 31.78 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.508 1.812
h = 0.0001 0.005
y[1] (numeric) = -3.76613827948 0.929478133193
y[1] (closed_form) = -3.76614056959 0.929575595355
absolute error = 9.749e-05
relative error = 0.002513 %
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 = 1.74
Order of pole (three term test) = 31.78 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5081 1.817
h = 0.0001 0.003
y[1] (numeric) = -3.76975999577 0.932247266693
y[1] (closed_form) = -3.76976157553 0.932341454945
absolute error = 9.420e-05
relative error = 0.002426 %
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 = 1.406
Order of pole (three term test) = 31.78 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5082 1.82
h = 0.001 0.001
y[1] (numeric) = -3.77191754271 0.933937172064
y[1] (closed_form) = -3.77191782218 0.934031187925
absolute error = 9.402e-05
relative error = 0.002419 %
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 = 1.106
Order of pole (three term test) = 31.78 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5092 1.821
h = 0.001 0.003
y[1] (numeric) = -3.77211668826 0.935214037443
y[1] (closed_form) = -3.77211636075 0.935307751695
absolute error = 9.371e-05
relative error = 0.002411 %
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 = 5.252
Order of pole (three term test) = 31.78 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5102 1.824
h = 0.0001 0.004
y[1] (numeric) = -3.77379102675 0.937570452126
y[1] (closed_form) = -3.77379196097 0.937664730695
absolute error = 9.428e-05
relative error = 0.002425 %
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 = 2.978
Order of pole (three term test) = 31.78 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5103 1.828
h = 0.003 0.006
y[1] (numeric) = -3.77669557636 0.939804809113
y[1] (closed_form) = -3.77669747613 0.93989841467
absolute error = 9.362e-05
relative error = 0.002406 %
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 = 3.956
Order of pole (three term test) = 31.77 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5133 1.834
h = 0.0001 0.005
y[1] (numeric) = -3.7795248348 0.945270494031
y[1] (closed_form) = -3.77952694479 0.945369265002
absolute error = 9.879e-05
relative error = 0.002536 %
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 = 1.767
Order of pole (three term test) = 31.77 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5134 1.839
h = 0.0001 0.003
y[1] (numeric) = -3.7831929351 0.9480568578
y[1] (closed_form) = -3.78319433858 0.948152345834
absolute error = 9.550e-05
relative error = 0.002449 %
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 = 1.427
Order of pole (three term test) = 31.77 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5135 1.842
h = 0.001 0.001
y[1] (numeric) = -3.78537819828 0.94975748297
y[1] (closed_form) = -3.78537829866 0.949852795999
absolute error = 9.531e-05
relative error = 0.002442 %
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 = 1.123
Order of pole (three term test) = 31.77 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5145 1.843
h = 0.001 0.003
y[1] (numeric) = -3.78558342969 0.951046961131
y[1] (closed_form) = -3.78558292214 0.9511419708
absolute error = 9.501e-05
relative error = 0.002434 %
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 = 5.332
Order of pole (three term test) = 31.77 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5155 1.846
h = 0.0001 0.004
y[1] (numeric) = -3.78728254763 0.953422518515
y[1] (closed_form) = -3.78728330388 0.953518095994
absolute error = 9.558e-05
relative error = 0.002447 %
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 = 3.024
Order of pole (three term test) = 31.77 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5156 1.85
h = 0.003 0.006
y[1] (numeric) = -3.79022417489 0.955670887428
y[1] (closed_form) = -3.79022590015 0.955765791917
absolute error = 9.492e-05
relative error = 0.002428 %
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 = 4.017
Order of pole (three term test) = 31.77 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5186 1.856
h = 0.0001 0.005
y[1] (numeric) = -3.79309975028 0.961184275731
y[1] (closed_form) = -3.79310167749 0.961284358436
absolute error = 0.0001001
relative error = 0.002558 %
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 = 1.794
Order of pole (three term test) = 31.77 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=995.7MB, alloc=52.3MB, time=11.77
x[1] = 0.5187 1.861
h = 0.0001 0.003
y[1] (numeric) = -3.79681431673 0.963987989987
y[1] (closed_form) = -3.79681554132 0.964084780616
absolute error = 9.680e-05
relative error = 0.002471 %
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 = 1.449
Order of pole (three term test) = 31.76 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5188 1.864
h = 0.001 0.001
y[1] (numeric) = -3.79902734469 0.965699407838
y[1] (closed_form) = -3.79902726332 0.965796020819
absolute error = 9.661e-05
relative error = 0.002465 %
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 = 1.14
Order of pole (three term test) = 31.76 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5198 1.865
h = 0.001 0.003
y[1] (numeric) = -3.79923865522 0.967001539528
y[1] (closed_form) = -3.79923796497 0.967097847378
absolute error = 9.631e-05
relative error = 0.002457 %
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 = 5.414
Order of pole (three term test) = 31.76 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5208 1.868
h = 0.0001 0.004
y[1] (numeric) = -3.8009625798 0.969396327896
y[1] (closed_form) = -3.80096315543 0.969493207088
absolute error = 9.688e-05
relative error = 0.00247 %
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 = 3.07
Order of pole (three term test) = 31.76 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5209 1.872
h = 0.003 0.006
y[1] (numeric) = -3.80394135045 0.971658805693
y[1] (closed_form) = -3.8039428986 0.971755011913
absolute error = 9.622e-05
relative error = 0.002451 %
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 = 4.078
Order of pole (three term test) = 31.76 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5239 1.878
h = 0.0001 0.005
y[1] (numeric) = -3.80686327377 0.977220091746
y[1] (closed_form) = -3.80686501552 0.97732148915
absolute error = 0.0001014
relative error = 0.00258 %
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 = 1.821
Order of pole (three term test) = 31.76 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.524 1.883
h = 0.0001 0.003
y[1] (numeric) = -3.81062438967 0.980041278049
y[1] (closed_form) = -3.81062543273 0.980139374122
absolute error = 9.810e-05
relative error = 0.002493 %
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 = 1.471
Order of pole (three term test) = 31.76 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5241 1.886
h = 0.001 0.001
y[1] (numeric) = -3.81286523165 0.981763562278
y[1] (closed_form) = -3.81286496585 0.981861478032
absolute error = 9.792e-05
relative error = 0.002487 %
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 = 1.157
Order of pole (three term test) = 31.76 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5251 1.887
h = 0.001 0.003
y[1] (numeric) = -3.81308261452 0.983078388741
y[1] (closed_form) = -3.81308173886 0.983175997573
absolute error = 9.761e-05
relative error = 0.002479 %
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 = 5.496
Order of pole (three term test) = 31.76 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5261 1.89
h = 0.0001 0.004
y[1] (numeric) = -3.81483137337 0.985492497404
y[1] (closed_form) = -3.81483176573 0.98559068115
absolute error = 9.818e-05
relative error = 0.002492 %
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 = 3.117
Order of pole (three term test) = 31.76 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5262 1.894
h = 0.003 0.006
y[1] (numeric) = -3.81784735405 0.987769182124
y[1] (closed_form) = -3.81784872248 0.987866692911
absolute error = 9.752e-05
relative error = 0.002473 %
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 = 4.14
Order of pole (three term test) = 31.75 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5292 1.9
h = 0.0001 0.005
y[1] (numeric) = -3.82081565692 0.993378562586
y[1] (closed_form) = -3.82081721051 0.99348127769
absolute error = 0.0001027
relative error = 0.002602 %
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 = 1.849
Order of pole (three term test) = 31.75 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5293 1.905
h = 0.0001 0.003
y[1] (numeric) = -3.82462340673 0.99621734384
y[1] (closed_form) = -3.82462426558 0.996316748245
absolute error = 9.941e-05
relative error = 0.002515 %
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 = 1.494
Order of pole (three term test) = 31.75 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5294 1.908
h = 0.001 0.001
y[1] (numeric) = -3.82689211265 0.997950568961
y[1] (closed_form) = -3.8268916597 0.998049790347
absolute error = 9.922e-05
relative error = 0.002509 %
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 = 1.175
Order of pole (three term test) = 31.75 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5304 1.909
h = 0.0001 0.004
y[1] (numeric) = -3.82711556105 0.999278131945
y[1] (closed_form) = -3.82711449726 0.999377044598
absolute error = 9.892e-05
relative error = 0.002501 %
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 = 7.06
Order of pole (three term test) = 31.75 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5305 1.913
h = 0.003 0.006
y[1] (numeric) = -3.83016204484 1.00156645045
y[1] (closed_form) = -3.83016371117 1.00166492016
absolute error = 9.848e-05
relative error = 0.002488 %
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 = 4.194
Order of pole (three term test) = 31.75 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5335 1.919
h = 0.0001 0.005
y[1] (numeric) = -3.83317087159 1.00721683522
y[1] (closed_form) = -3.83317271591 1.00732052078
absolute error = 0.0001037
relative error = 0.002617 %
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 = 1.873
Order of pole (three term test) = 31.75 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5336 1.924
h = 0.0001 0.003
y[1] (numeric) = -3.83701904244 1.01007030418
y[1] (closed_form) = -3.83702019535 1.01017067084
absolute error = 0.0001004
relative error = 0.00253 %
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 = 1.513
Order of pole (three term test) = 31.75 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5337 1.927
h = 0.001 0.001
y[1] (numeric) = -3.83931190474 1.01181267442
y[1] (closed_form) = -3.83931174325 1.01191285575
absolute error = 0.0001002
relative error = 0.002523 %
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 = 1.19
Order of pole (three term test) = 31.74 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5347 1.928
h = 0.001 0.003
y[1] (numeric) = -3.83954072108 1.01315116224
y[1] (closed_form) = -3.83953994787 1.01325103328
absolute error = 9.987e-05
relative error = 0.002515 %
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 = 5.652
Order of pole (three term test) = 31.74 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5357 1.931
h = 0.0001 0.004
y[1] (numeric) = -3.84133599849 1.01560116608
y[1] (closed_form) = -3.84133649738 1.01570161876
absolute error = 0.0001005
relative error = 0.002528 %
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 = 3.205
Order of pole (three term test) = 31.74 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1039.7MB, alloc=52.3MB, time=12.28
x[1] = 0.5358 1.935
h = 0.003 0.006
y[1] (numeric) = -3.84442157095 1.01790410606
y[1] (closed_form) = -3.84442305262 1.01800388575
absolute error = 9.979e-05
relative error = 0.002509 %
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 = 4.258
Order of pole (three term test) = 31.74 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5388 1.941
h = 0.0001 0.005
y[1] (numeric) = -3.84747684013 1.02360295691
y[1] (closed_form) = -3.84747849121 1.02370796589
absolute error = 0.000105
relative error = 0.002638 %
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 = 1.901
Order of pole (three term test) = 31.74 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5389 1.946
h = 0.0001 0.003
y[1] (numeric) = -3.85137180663 1.02647425209
y[1] (closed_form) = -3.8513727703 1.02657593258
absolute error = 0.0001017
relative error = 0.002551 %
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 = 1.536
Order of pole (three term test) = 31.74 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.539 1.949
h = 0.001 0.001
y[1] (numeric) = -3.85369262846 1.02822770345
y[1] (closed_form) = -3.85369227474 1.02832919586
absolute error = 0.0001015
relative error = 0.002545 %
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 = 1.208
Order of pole (three term test) = 31.74 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.54 1.95
h = 0.001 0.003
y[1] (numeric) = -3.85392749811 1.0295790069
y[1] (closed_form) = -3.85392653165 1.02968018717
absolute error = 0.0001012
relative error = 0.002537 %
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 = 5.737
Order of pole (three term test) = 31.74 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.541 1.953
h = 0.0001 0.004
y[1] (numeric) = -3.8557476924 1.03204859188
y[1] (closed_form) = -3.85574800026 1.03215035748
absolute error = 0.0001018
relative error = 0.00255 %
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 = 3.253
Order of pole (three term test) = 31.74 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5411 1.957
h = 0.003 0.006
y[1] (numeric) = -3.85887067186 1.03436602443
y[1] (closed_form) = -3.85887196617 1.03446711704
absolute error = 0.0001011
relative error = 0.002531 %
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 = 4.322
Order of pole (three term test) = 31.74 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5441 1.963
h = 0.0001 0.005
y[1] (numeric) = -3.86197241688 1.04011354462
y[1] (closed_form) = -3.86197387192 1.04021988014
absolute error = 0.0001063
relative error = 0.002659 %
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 = 1.93
Order of pole (three term test) = 31.73 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5442 1.968
h = 0.0001 0.003
y[1] (numeric) = -3.86591426681 1.0430027928
y[1] (closed_form) = -3.86591503849 1.04310579013
absolute error = 0.000103
relative error = 0.002572 %
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 = 1.559
Order of pole (three term test) = 31.73 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5443 1.971
h = 0.001 0.001
y[1] (numeric) = -3.86826310005 1.04476740215
y[1] (closed_form) = -3.8682625513 1.04487020862
absolute error = 0.0001028
relative error = 0.002566 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.226
Order of pole (three term test) = 31.73 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5453 1.972
h = 0.001 0.003
y[1] (numeric) = -3.86850401611 1.04613156441
y[1] (closed_form) = -3.8685028536 1.04623405687
absolute error = 0.0001025
relative error = 0.002558 %
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 = 5.823
Order of pole (three term test) = 31.73 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5463 1.975
h = 0.0001 0.004
y[1] (numeric) = -3.87034915666 1.04862082386
y[1] (closed_form) = -3.8703492707 1.04872390537
absolute error = 0.0001031
relative error = 0.002571 %
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 = 3.302
Order of pole (three term test) = 31.73 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5464 1.979
h = 0.003 0.006
y[1] (numeric) = -3.87350961332 1.05095285121
y[1] (closed_form) = -3.87351071753 1.05105525973
absolute error = 0.0001024
relative error = 0.002552 %
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 = 4.386
Order of pole (three term test) = 31.73 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5494 1.985
h = 0.0001 0.005
y[1] (numeric) = -3.87665786821 1.05674924633
y[1] (closed_form) = -3.87665912439 1.05685691154
absolute error = 0.0001077
relative error = 0.00268 %
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 = 1.959
Order of pole (three term test) = 31.73 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5495 1.99
h = 0.0001 0.003
y[1] (numeric) = -3.8806466905 1.05965657567
y[1] (closed_form) = -3.88064726742 1.05976089286
absolute error = 0.0001043
relative error = 0.002593 %
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 = 1.582
Order of pole (three term test) = 31.72 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5496 1.993
h = 0.001 0.001
y[1] (numeric) = -3.88302358772 1.06143242071
y[1] (closed_form) = -3.88302284112 1.06153654424
absolute error = 0.0001041
relative error = 0.002587 %
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 = 1.244
Order of pole (three term test) = 31.72 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5506 1.994
h = 0.001 0.003
y[1] (numeric) = -3.88327054328 1.06280948549
y[1] (closed_form) = -3.88326918188 1.06291329311
absolute error = 0.0001038
relative error = 0.002579 %
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 = 5.91
Order of pole (three term test) = 31.72 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5516 1.997
h = 0.0001 0.004
y[1] (numeric) = -3.88514065987 1.06531851375
y[1] (closed_form) = -3.8851405773 1.06542291419
absolute error = 0.0001044
relative error = 0.002591 %
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 = 3.351
Order of pole (three term test) = 31.72 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5517 2.001
h = 0.003 0.006
y[1] (numeric) = -3.88833866488 1.06766523926
y[1] (closed_form) = -3.88833957622 1.0677689667
absolute error = 0.0001037
relative error = 0.002573 %
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 = 4.452
Order of pole (three term test) = 31.72 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5547 2.007
h = 0.0001 0.005
y[1] (numeric) = -3.89153346428 1.07351071724
y[1] (closed_form) = -3.89153451874 1.07361971531
absolute error = 0.000109
relative error = 0.0027 %
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 = 1.988
Order of pole (three term test) = 31.72 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5548 2.012
h = 0.0001 0.003
y[1] (numeric) = -3.89556934903 1.07643625726
y[1] (closed_form) = -3.89556972836 1.07654189739
absolute error = 0.0001056
relative error = 0.002614 %
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 = 1.606
Order of pole (three term test) = 31.72 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5549 2.015
h = 0.001 0.001
y[1] (numeric) = -3.89797436348 1.07822341654
y[1] (closed_form) = -3.89797341617 1.07832886016
memory used=1083.6MB, alloc=52.3MB, time=12.80
absolute error = 0.0001054
relative error = 0.002607 %
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 = 1.263
Order of pole (three term test) = 31.72 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5559 2.016
h = 0.0001 0.004
y[1] (numeric) = -3.89822735158 1.07961342803
y[1] (closed_form) = -3.89822578842 1.07971855384
absolute error = 0.0001051
relative error = 0.002599 %
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 = 7.589
Order of pole (three term test) = 31.72 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.556 2.02
h = 0.003 0.006
y[1] (numeric) = -3.90145614048 1.08197219249
y[1] (closed_form) = -3.90145734542 1.08207689314
absolute error = 0.0001047
relative error = 0.002586 %
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 = 4.509
Order of pole (three term test) = 31.72 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.559 2.026
h = 0.0001 0.005
y[1] (numeric) = -3.90469162013 1.08785953263
y[1] (closed_form) = -3.90469296068 1.08796951616
absolute error = 0.00011
relative error = 0.002714 %
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 = 2.013
Order of pole (three term test) = 31.71 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5591 2.031
h = 0.0001 0.003
y[1] (numeric) = -3.90876830676 1.09080029051
y[1] (closed_form) = -3.90876897564 1.0909069074
absolute error = 0.0001066
relative error = 0.002627 %
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 = 1.626
Order of pole (three term test) = 31.71 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5592 2.034
h = 0.001 0.001
y[1] (numeric) = -3.9111977028 1.09259691643
y[1] (closed_form) = -3.91119704229 1.09270333439
absolute error = 0.0001064
relative error = 0.002621 %
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 = 1.279
Order of pole (three term test) = 31.71 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5602 2.035
h = 0.001 0.003
y[1] (numeric) = -3.91145603287 1.09399803606
y[1] (closed_form) = -3.91145475557 1.09410413456
absolute error = 0.0001061
relative error = 0.002612 %
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 = 6.074
Order of pole (three term test) = 31.71 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5612 2.038
h = 0.0001 0.004
y[1] (numeric) = -3.91337294305 1.09654380586
y[1] (closed_form) = -3.91337294894 1.09665050427
absolute error = 0.0001067
relative error = 0.002625 %
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 = 3.444
Order of pole (three term test) = 31.71 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5613 2.042
h = 0.003 0.006
y[1] (numeric) = -3.91664118731 1.09891771078
y[1] (closed_form) = -3.9166421942 1.09902373612
absolute error = 0.000106
relative error = 0.002606 %
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 = 4.575
Order of pole (three term test) = 31.71 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5643 2.048
h = 0.0001 0.005
y[1] (numeric) = -3.91992328009 1.10485452649
y[1] (closed_form) = -3.91992441358 1.10496584896
absolute error = 0.0001113
relative error = 0.002734 %
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 = 2.043
Order of pole (three term test) = 31.71 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5644 2.053
h = 0.0001 0.003
y[1] (numeric) = -3.9240472015 1.10781373869
y[1] (closed_form) = -3.92404766752 1.10792168437
absolute error = 0.0001079
relative error = 0.002647 %
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 = 1.65
Order of pole (three term test) = 31.7 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5645 2.056
h = 0.001 0.001
y[1] (numeric) = -3.92650481663 1.10962182658
y[1] (closed_form) = -3.92650395007 1.10972957043
absolute error = 0.0001077
relative error = 0.002641 %
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 = 1.298
Order of pole (three term test) = 31.7 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5655 2.057
h = 0.001 0.003
y[1] (numeric) = -3.92676916675 1.11103597664
y[1] (closed_form) = -3.92676768232 1.11114339908
absolute error = 0.0001074
relative error = 0.002633 %
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 = 6.164
Order of pole (three term test) = 31.7 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5665 2.06
h = 0.0001 0.004
y[1] (numeric) = -3.92871114182 1.11360179064
y[1] (closed_form) = -3.92871094294 1.11370981688
absolute error = 0.000108
relative error = 0.002645 %
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 = 3.495
Order of pole (three term test) = 31.7 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5666 2.064
h = 0.003 0.006
y[1] (numeric) = -3.9320171443 1.11599069465
y[1] (closed_form) = -3.93201795029 1.1160980478
absolute error = 0.0001074
relative error = 0.002627 %
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 = 4.643
Order of pole (three term test) = 31.7 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5696 2.07
h = 0.0001 0.005
y[1] (numeric) = -3.9353458866 1.12197720059
y[1] (closed_form) = -3.9353468101 1.1220898653
absolute error = 0.0001127
relative error = 0.002753 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.073
Order of pole (three term test) = 31.7 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5697 2.075
h = 0.0001 0.003
y[1] (numeric) = -3.93951713624 1.12495500061
y[1] (closed_form) = -3.9395173965 1.12506427826
absolute error = 0.0001093
relative error = 0.002667 %
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 = 1.675
Order of pole (three term test) = 31.7 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5698 2.078
h = 0.001 0.001
y[1] (numeric) = -3.94200302567 1.12677463143
y[1] (closed_form) = -3.94200195013 1.12688370433
absolute error = 0.0001091
relative error = 0.002661 %
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 = 1.317
Order of pole (three term test) = 31.7 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5708 2.079
h = 0.001 0.003
y[1] (numeric) = -3.94227338879 1.12820185758
y[1] (closed_form) = -3.94227169428 1.1283106071
absolute error = 0.0001088
relative error = 0.002652 %
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 = 6.255
Order of pole (three term test) = 31.7 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5718 2.082
h = 0.0001 0.004
y[1] (numeric) = -3.94424046026 1.13078781424
y[1] (closed_form) = -3.94424005369 1.13089717148
absolute error = 0.0001094
relative error = 0.002665 %
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 = 3.547
Order of pole (three term test) = 31.69 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5719 2.086
h = 0.003 0.006
y[1] (numeric) = -3.94758429568 1.133191825
y[1] (closed_form) = -3.9475848979 1.13330050913
absolute error = 0.0001087
relative error = 0.002646 %
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 = 4.711
Order of pole (three term test) = 31.69 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5749 2.092
h = 0.0001 0.005
y[1] (numeric) = -3.9509597245 1.13922823819
y[1] (closed_form) = -3.95096043505 1.13934224848
absolute error = 0.000114
relative error = 0.002773 %
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 = 2.104
Order of pole (three term test) = 31.69 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1127.5MB, alloc=52.3MB, time=13.30
x[1] = 0.575 2.097
h = 0.0001 0.003
y[1] (numeric) = -3.95517839695 1.14222476096
y[1] (closed_form) = -3.95517844853 1.14233537379
absolute error = 0.0001106
relative error = 0.002687 %
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 = 1.699
Order of pole (three term test) = 31.69 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5751 2.1
h = 0.001 0.001
y[1] (numeric) = -3.95769261661 1.14405601652
y[1] (closed_form) = -3.95769132911 1.14416642165
absolute error = 0.0001104
relative error = 0.00268 %
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 = 1.336
Order of pole (three term test) = 31.69 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5761 2.101
h = 0.001 0.003
y[1] (numeric) = -3.95796898563 1.14549636495
y[1] (closed_form) = -3.95796707806 1.14560644471
absolute error = 0.0001101
relative error = 0.002672 %
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 = 6.347
Order of pole (three term test) = 31.69 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5771 2.104
h = 0.0001 0.004
y[1] (numeric) = -3.95996118545 1.14810256376
y[1] (closed_form) = -3.95996056823 1.14821325521
absolute error = 0.0001107
relative error = 0.002685 %
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 = 3.599
Order of pole (three term test) = 31.69 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5772 2.108
h = 0.003 0.006
y[1] (numeric) = -3.96334292944 1.15052179008
y[1] (closed_form) = -3.96334332498 1.15063180839
absolute error = 0.00011
relative error = 0.002666 %
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 = 4.78
Order of pole (three term test) = 31.69 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5802 2.114
h = 0.0001 0.005
y[1] (numeric) = -3.96676508239 1.15660832993
y[1] (closed_form) = -3.96676557698 1.15672368917
absolute error = 0.0001154
relative error = 0.002792 %
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 = 2.134
Order of pole (three term test) = 31.68 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5803 2.119
h = 0.0001 0.003
y[1] (numeric) = -3.97103127341 1.15962371177
y[1] (closed_form) = -3.97103111335 1.15973566305
absolute error = 0.000112
relative error = 0.002706 %
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 = 1.724
Order of pole (three term test) = 31.68 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5804 2.122
h = 0.001 0.001
y[1] (numeric) = -3.97357387988 1.16146667474
y[1] (closed_form) = -3.97357237743 1.16157841534
absolute error = 0.0001118
relative error = 0.002699 %
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 = 1.356
Order of pole (three term test) = 31.68 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5814 2.123
h = 0.0001 0.004
y[1] (numeric) = -3.97385624768 1.16292019216
y[1] (closed_form) = -3.97385412404 1.16303160537
absolute error = 0.0001114
relative error = 0.002691 %
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 = 8.148
Order of pole (three term test) = 31.68 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5815 2.127
h = 0.003 0.006
y[1] (numeric) = -3.97726907432 1.16535188404
y[1] (closed_form) = -3.97726975898 1.16546289071
absolute error = 0.000111
relative error = 0.002678 %
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 = 4.841
Order of pole (three term test) = 31.68 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5845 2.133
h = 0.0001 0.005
y[1] (numeric) = -3.98073207711 1.17148119158
y[1] (closed_form) = -3.98073285295 1.17159755212
absolute error = 0.0001164
relative error = 0.002804 %
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 = 2.161
Order of pole (three term test) = 31.68 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5846 2.138
h = 0.0001 0.003
y[1] (numeric) = -3.98503947499 1.17451234933
y[1] (closed_form) = -3.98503959979 1.17462529272
absolute error = 0.0001129
relative error = 0.002719 %
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 = 1.746
Order of pole (three term test) = 31.68 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5847 2.141
h = 0.001 0.001
y[1] (numeric) = -3.98760670255 1.17636511744
y[1] (closed_form) = -3.98760548205 1.1764778476
absolute error = 0.0001127
relative error = 0.002712 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.373
Order of pole (three term test) = 31.67 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5857 2.142
h = 0.001 0.003
y[1] (numeric) = -3.98789438578 1.17782993673
y[1] (closed_form) = -3.98789254309 1.17794233778
absolute error = 0.0001124
relative error = 0.002703 %
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 = 6.521
Order of pole (three term test) = 31.67 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5867 2.145
h = 0.0001 0.004
y[1] (numeric) = -3.98993367408 1.18047376978
y[1] (closed_form) = -3.98993312637 1.18058678997
absolute error = 0.000113
relative error = 0.002716 %
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 = 3.697
Order of pole (three term test) = 31.67 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5868 2.149
h = 0.003 0.006
y[1] (numeric) = -3.99338634593 1.18292114843
y[1] (closed_form) = -3.99338681848 1.18303349538
absolute error = 0.0001123
relative error = 0.002697 %
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 = 4.911
Order of pole (three term test) = 31.67 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5898 2.155
h = 0.0001 0.005
y[1] (numeric) = -3.99689614707 1.1891009968
y[1] (closed_form) = -3.99689670134 1.18921871272
absolute error = 0.0001177
relative error = 0.002823 %
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 = 2.193
Order of pole (three term test) = 31.67 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5899 2.16
h = 0.0001 0.003
y[1] (numeric) = -4.00125124649 1.19215126994
y[1] (closed_form) = -4.0012511541 1.19226555797
absolute error = 0.0001143
relative error = 0.002737 %
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 = 1.771
Order of pole (three term test) = 31.67 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.59 2.163
h = 0.001 0.001
y[1] (numeric) = -4.00384696901 1.1940159009
y[1] (closed_form) = -4.00384552795 1.19412997267
absolute error = 0.0001141
relative error = 0.00273 %
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 = 1.393
Order of pole (three term test) = 31.67 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.591 2.164
h = 0.001 0.003
y[1] (numeric) = -4.00414063821 1.19549397756
y[1] (closed_form) = -4.00413857381 1.19560771816
absolute error = 0.0001138
relative error = 0.002722 %
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 = 6.616
Order of pole (three term test) = 31.67 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.592 2.167
h = 0.0001 0.004
y[1] (numeric) = -4.00620514987 1.19815834299
y[1] (closed_form) = -4.00620438297 1.19827270683
absolute error = 0.0001144
relative error = 0.002735 %
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 = 3.751
Order of pole (three term test) = 31.67 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1171.5MB, alloc=52.3MB, time=13.82
x[1] = 0.5921 2.171
h = 0.003 0.006
y[1] (numeric) = -4.00969595316 1.20062125382
y[1] (closed_form) = -4.00969621058 1.20073494438
absolute error = 0.0001137
relative error = 0.002716 %
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 = 4.983
Order of pole (three term test) = 31.66 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5951 2.177
h = 0.0001 0.005
y[1] (numeric) = -4.01325259195 1.20685186931
y[1] (closed_form) = -4.01325292158 1.20697094408
absolute error = 0.0001191
relative error = 0.002841 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.225
Order of pole (three term test) = 31.66 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5952 2.182
h = 0.0001 0.003
y[1] (numeric) = -4.01765549202 1.20992139824
y[1] (closed_form) = -4.01765517941 1.21003703429
absolute error = 0.0001156
relative error = 0.002756 %
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 = 1.797
Order of pole (three term test) = 31.66 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5953 2.185
h = 0.001 0.001
y[1] (numeric) = -4.02027976808 1.2117979772
y[1] (closed_form) = -4.02027810338 1.21191339392
absolute error = 0.0001154
relative error = 0.002749 %
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 = 1.413
Order of pole (three term test) = 31.66 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5963 2.186
h = 0.001 0.003
y[1] (numeric) = -4.020579416 1.21328935942
y[1] (closed_form) = -4.02057712681 1.21340444289
absolute error = 0.0001151
relative error = 0.002741 %
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 = 6.712
Order of pole (three term test) = 31.66 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5973 2.189
h = 0.0001 0.004
y[1] (numeric) = -4.02266918468 1.21597436093
y[1] (closed_form) = -4.02266819551 1.21609007177
absolute error = 0.0001157
relative error = 0.002754 %
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 = 3.805
Order of pole (three term test) = 31.66 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5974 2.193
h = 0.003 0.006
y[1] (numeric) = -4.02619819862 1.21845291716
y[1] (closed_form) = -4.02619823791 1.21856795468
absolute error = 0.000115
relative error = 0.002735 %
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 = 5.055
Order of pole (three term test) = 31.66 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6004 2.199
h = 0.0001 0.005
y[1] (numeric) = -4.02980171498 1.22473452845
y[1] (closed_form) = -4.02980181685 1.22485496561
absolute error = 0.0001204
relative error = 0.002859 %
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 = 2.257
Order of pole (three term test) = 31.65 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6005 2.204
h = 0.0001 0.003
y[1] (numeric) = -4.03425251598 1.22782345504
y[1] (closed_form) = -4.03425198007 1.22794044251
absolute error = 0.000117
relative error = 0.002774 %
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 = 1.823
Order of pole (three term test) = 31.65 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6006 2.207
h = 0.001 0.001
y[1] (numeric) = -4.03690540486 1.22971206803
y[1] (closed_form) = -4.0369035134 1.22982883306
absolute error = 0.0001168
relative error = 0.002767 %
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 = 1.434
Order of pole (three term test) = 31.65 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6016 2.208
h = 0.001 0.003
y[1] (numeric) = -4.0372110242 1.23121680453
y[1] (closed_form) = -4.03720850708 1.23133323423
absolute error = 0.0001165
relative error = 0.002759 %
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 = 6.809
Order of pole (three term test) = 31.65 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6026 2.211
h = 0.0001 0.004
y[1] (numeric) = -4.03932608396 1.23392254689
y[1] (closed_form) = -4.03932486943 1.23403960813
absolute error = 0.0001171
relative error = 0.002772 %
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 = 3.86
Order of pole (three term test) = 31.65 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6027 2.215
h = 0.003 0.006
y[1] (numeric) = -4.04289338873 1.23641686291
y[1] (closed_form) = -4.04289320684 1.23653325078
absolute error = 0.0001164
relative error = 0.002753 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.128
Order of pole (three term test) = 31.65 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6057 2.221
h = 0.0001 0.005
y[1] (numeric) = -4.04654382314 1.24274970113
y[1] (closed_form) = -4.04654369411 1.24287150424
absolute error = 0.0001218
relative error = 0.002877 %
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 = 2.29
Order of pole (three term test) = 31.65 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6058 2.226
h = 0.0001 0.003
y[1] (numeric) = -4.05104262652 1.24585816869
y[1] (closed_form) = -4.05104186421 1.24597651102
absolute error = 0.0001183
relative error = 0.002792 %
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 = 1.849
Order of pole (three term test) = 31.64 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6059 2.229
h = 0.001 0.001
y[1] (numeric) = -4.05372418816 1.24775890261
y[1] (closed_form) = -4.05372206681 1.24787701938
absolute error = 0.0001181
relative error = 0.002785 %
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 = 1.454
Order of pole (three term test) = 31.64 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6069 2.23
h = 0.0001 0.004
y[1] (numeric) = -4.05403577159 1.24927704264
y[1] (closed_form) = -4.05403302339 1.24939482195
absolute error = 0.0001178
relative error = 0.002777 %
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 = 8.739
Order of pole (three term test) = 31.64 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.607 2.234
h = 0.003 0.006
y[1] (numeric) = -4.05763447584 1.25178427286
y[1] (closed_form) = -4.0576345784 1.25190166507
absolute error = 0.0001174
relative error = 0.002765 %
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 = 5.192
Order of pole (three term test) = 31.64 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.61 2.24
h = 0.0001 0.005
y[1] (numeric) = -4.0613259426 1.2581608329
y[1] (closed_form) = -4.06132608978 1.25828365403
absolute error = 0.0001228
relative error = 0.002889 %
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 = 2.318
Order of pole (three term test) = 31.64 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6101 2.245
h = 0.0001 0.003
y[1] (numeric) = -4.0658663821 1.26128566308
y[1] (closed_form) = -4.06586589977 1.26140501373
absolute error = 0.0001194
relative error = 0.002804 %
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 = 1.872
Order of pole (three term test) = 31.64 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6102 2.248
h = 0.001 0.001
y[1] (numeric) = -4.06857281865 1.26319655804
y[1] (closed_form) = -4.0685709742 1.26331568045
absolute error = 0.0001191
relative error = 0.002797 %
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 = 1.472
Order of pole (three term test) = 31.64 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6112 2.249
h = 0.001 0.003
y[1] (numeric) = -4.06888969032 1.26472620429
y[1] (closed_form) = -4.06888721796 1.26484498743
absolute error = 0.0001188
relative error = 0.002788 %
Correct digits = 5
memory used=1215.6MB, alloc=52.3MB, time=14.33
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.993
Order of pole (three term test) = 31.64 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6122 2.252
h = 0.0001 0.004
y[1] (numeric) = -4.07105215313 1.26747052094
y[1] (closed_form) = -4.07105098826 1.26758994346
absolute error = 0.0001194
relative error = 0.002801 %
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 = 3.965
Order of pole (three term test) = 31.63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6123 2.256
h = 0.003 0.006
y[1] (numeric) = -4.07469111575 1.26999401228
y[1] (closed_form) = -4.0746909914 1.2701127613
absolute error = 0.0001187
relative error = 0.002782 %
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 = 5.266
Order of pole (three term test) = 31.63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6153 2.262
h = 0.0001 0.005
y[1] (numeric) = -4.07842958025 1.27642223532
y[1] (closed_form) = -4.07842949063 1.27654642918
absolute error = 0.0001242
relative error = 0.002906 %
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 = 2.351
Order of pole (three term test) = 31.63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6154 2.267
h = 0.0001 0.003
y[1] (numeric) = -4.08301821577 1.27956687581
y[1] (closed_form) = -4.08301750122 1.27968758787
absolute error = 0.0001207
relative error = 0.002821 %
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 = 1.899
Order of pole (three term test) = 31.63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6155 2.27
h = 0.001 0.001
y[1] (numeric) = -4.08575343957 1.28149005504
y[1] (closed_form) = -4.08575135933 1.28161053568
absolute error = 0.0001205
relative error = 0.002814 %
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 = 1.493
Order of pole (three term test) = 31.63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6165 2.271
h = 0.001 0.003
y[1] (numeric) = -4.08607626214 1.28303319795
y[1] (closed_form) = -4.08607355278 1.28315333717
absolute error = 0.0001202
relative error = 0.002806 %
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 = 7.093
Order of pole (three term test) = 31.63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6175 2.274
h = 0.0001 0.004
y[1] (numeric) = -4.08826411719 1.28579856086
y[1] (closed_form) = -4.08826271797 1.28591934375
absolute error = 0.0001208
relative error = 0.002818 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.022
Order of pole (three term test) = 31.63 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6176 2.278
h = 0.003 0.006
y[1] (numeric) = -4.09194160652 1.28833814472
y[1] (closed_form) = -4.09194125213 1.28845825405
absolute error = 0.0001201
relative error = 0.0028 %
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 = 5.342
Order of pole (three term test) = 31.62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6206 2.284
h = 0.0001 0.005
y[1] (numeric) = -4.09572711092 1.2948182689
y[1] (closed_form) = -4.09572678127 1.29494383916
absolute error = 0.0001256
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 = 2.385
Order of pole (three term test) = 31.62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6207 2.289
h = 0.0001 0.003
y[1] (numeric) = -4.10036404729 1.29798286718
y[1] (closed_form) = -4.10036309734 1.29810494422
absolute error = 0.0001221
relative error = 0.002838 %
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 = 1.926
Order of pole (three term test) = 31.62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6208 2.292
h = 0.001 0.001
y[1] (numeric) = -4.10312812028 1.29991842016
y[1] (closed_form) = -4.10312580102 1.30004026255
absolute error = 0.0001219
relative error = 0.002831 %
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 = 1.515
Order of pole (three term test) = 31.62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6218 2.293
h = 0.001 0.003
y[1] (numeric) = -4.10345688628 1.30147511049
y[1] (closed_form) = -4.10345393668 1.30159660928
absolute error = 0.0001215
relative error = 0.002823 %
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 = 7.195
Order of pole (three term test) = 31.62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6228 2.296
h = 0.0001 0.004
y[1] (numeric) = -4.10567016933 1.3042616287
y[1] (closed_form) = -4.10566853255 1.3043837755
absolute error = 0.0001222
relative error = 0.002836 %
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 = 4.079
Order of pole (three term test) = 31.62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6229 2.3
h = 0.003 0.006
y[1] (numeric) = -4.10938626914 1.306817424
y[1] (closed_form) = -4.10938568154 1.3069388972
absolute error = 0.0001215
relative error = 0.002817 %
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 = 5.418
Order of pole (three term test) = 31.62 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6259 2.306
h = 0.0001 0.005
y[1] (numeric) = -4.11321885618 1.31334968993
y[1] (closed_form) = -4.11321828324 1.31347664031
absolute error = 0.000127
relative error = 0.00294 %
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 = 2.419
Order of pole (three term test) = 31.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.626 2.311
h = 0.0001 0.003
y[1] (numeric) = -4.1179041994 1.316534395
y[1] (closed_form) = -4.11790301081 1.3166578406
absolute error = 0.0001235
relative error = 0.002856 %
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 = 1.954
Order of pole (three term test) = 31.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6261 2.314
h = 0.001 0.001
y[1] (numeric) = -4.12069718421 1.31848241206
y[1] (closed_form) = -4.12069462268 1.31860561977
absolute error = 0.0001232
relative error = 0.002848 %
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 = 1.537
Order of pole (three term test) = 31.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6271 2.315
h = 0.001 0.003
y[1] (numeric) = -4.12103188612 1.32005270111
y[1] (closed_form) = -4.121028693 1.32017556302
absolute error = 0.0001229
relative error = 0.00284 %
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 = 7.297
Order of pole (three term test) = 31.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6281 2.318
h = 0.0001 0.004
y[1] (numeric) = -4.12327063335 1.32286048478
y[1] (closed_form) = -4.12326875576 1.32298399909
absolute error = 0.0001235
relative error = 0.002853 %
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 = 4.137
Order of pole (three term test) = 31.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6282 2.322
h = 0.003 0.006
y[1] (numeric) = -4.12702542836 1.32543261166
y[1] (closed_form) = -4.12702460434 1.3255554523
absolute error = 0.0001228
relative error = 0.002834 %
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 = 5.496
Order of pole (three term test) = 31.61 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6312 2.328
h = 0.0001 0.005
y[1] (numeric) = -4.13090514133 1.33201726241
y[1] (closed_form) = -4.1309043218 1.33214559667
absolute error = 0.0001283
relative error = 0.002957 %
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 = 2.454
Order of pole (three term test) = 31.61 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1259.5MB, alloc=52.3MB, time=14.84
x[1] = 0.6313 2.333
h = 0.0001 0.003
y[1] (numeric) = -4.13563899856 1.33522222475
y[1] (closed_form) = -4.13563756809 1.33534704255
absolute error = 0.0001248
relative error = 0.002872 %
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 = 1.982
Order of pole (three term test) = 31.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6314 2.336
h = 0.001 0.001
y[1] (numeric) = -4.13846095854 1.33718279716
y[1] (closed_form) = -4.13845815144 1.33730737379
absolute error = 0.0001246
relative error = 0.002865 %
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 = 1.558
Order of pole (three term test) = 31.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6324 2.337
h = 0.0001 0.004
y[1] (numeric) = -4.13880158878 1.33876673677
y[1] (closed_form) = -4.13879814883 1.33889096537
absolute error = 0.0001243
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 = 9.365
Order of pole (three term test) = 31.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6325 2.341
h = 0.003 0.006
y[1] (numeric) = -4.14258811825 1.34135224911
y[1] (closed_form) = -4.14258757382 1.34147611094
absolute error = 0.0001239
relative error = 0.002845 %
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 = 5.563
Order of pole (three term test) = 31.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6355 2.347
h = 0.0001 0.005
y[1] (numeric) = -4.14650905875 1.34798162546
y[1] (closed_form) = -4.14650851016 1.34811099532
absolute error = 0.0001294
relative error = 0.002967 %
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 = 2.484
Order of pole (three term test) = 31.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6356 2.352
h = 0.0001 0.003
y[1] (numeric) = -4.15128500572 1.35120356657
y[1] (closed_form) = -4.15128385013 1.35132940976
absolute error = 0.0001258
relative error = 0.002883 %
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 = 2.006
Order of pole (three term test) = 31.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6357 2.355
h = 0.001 0.001
y[1] (numeric) = -4.15413210886 1.35317467378
y[1] (closed_form) = -4.1541295734 1.353300273
absolute error = 0.0001256
relative error = 0.002875 %
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 = 1.578
Order of pole (three term test) = 31.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6367 2.356
h = 0.001 0.003
y[1] (numeric) = -4.15447799935 1.35477033475
y[1] (closed_form) = -4.15447482993 1.35489558403
absolute error = 0.0001253
relative error = 0.002867 %
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 = 7.492
Order of pole (three term test) = 31.6 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6377 2.359
h = 0.0001 0.004
y[1] (numeric) = -4.15676448372 1.35761768118
y[1] (closed_form) = -4.15676263501 1.3577435911
absolute error = 0.0001259
relative error = 0.00288 %
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 = 4.248
Order of pole (three term test) = 31.59 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6378 2.363
h = 0.003 0.006
y[1] (numeric) = -4.16059170811 1.36022005779
y[1] (closed_form) = -4.16059092126 1.36034529388
absolute error = 0.0001252
relative error = 0.002861 %
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 = 5.642
Order of pole (three term test) = 31.59 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6408 2.369
h = 0.0001 0.005
y[1] (numeric) = -4.16455985956 1.36690227741
y[1] (closed_form) = -4.16455905821 1.36703303829
absolute error = 0.0001308
relative error = 0.002983 %
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 = 2.519
Order of pole (three term test) = 31.59 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6409 2.374
h = 0.0001 0.003
y[1] (numeric) = -4.16938452494 1.37014475849
y[1] (closed_form) = -4.16938312136 1.3702719808
absolute error = 0.0001272
relative error = 0.002899 %
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 = 2.034
Order of pole (three term test) = 31.59 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.641 2.377
h = 0.001 0.001
y[1] (numeric) = -4.17226072406 1.37212859253
y[1] (closed_form) = -4.17225793685 1.37225556751
absolute error = 0.000127
relative error = 0.002892 %
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 = 1.6
Order of pole (three term test) = 31.59 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.642 2.378
h = 0.001 0.003
y[1] (numeric) = -4.17261252927 1.37373800202
y[1] (closed_form) = -4.17260910681 1.3738646248
absolute error = 0.0001267
relative error = 0.002883 %
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 = 7.598
Order of pole (three term test) = 31.59 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.643 2.381
h = 0.0001 0.004
y[1] (numeric) = -4.17492458506 1.37660693484
y[1] (closed_form) = -4.17492248611 1.37673422276
absolute error = 0.0001273
relative error = 0.002896 %
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 = 4.308
Order of pole (three term test) = 31.59 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6431 2.385
h = 0.003 0.006
y[1] (numeric) = -4.17879075363 1.3792259923
y[1] (closed_form) = -4.17878972107 1.37935260633
absolute error = 0.0001266
relative error = 0.002877 %
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 = 5.722
Order of pole (three term test) = 31.58 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6461 2.391
h = 0.0001 0.005
y[1] (numeric) = -4.18280616097 1.38596130542
y[1] (closed_form) = -4.18280510345 1.38609346118
absolute error = 0.0001322
relative error = 0.002999 %
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 = 2.555
Order of pole (three term test) = 31.58 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6462 2.396
h = 0.0001 0.003
y[1] (numeric) = -4.18767965531 1.38922448126
y[1] (closed_form) = -4.1876780004 1.38935308642
absolute error = 0.0001286
relative error = 0.002915 %
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 = 2.063
Order of pole (three term test) = 31.58 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6463 2.399
h = 0.001 0.001
y[1] (numeric) = -4.19058501575 1.39122113599
y[1] (closed_form) = -4.19058197341 1.39134949046
absolute error = 0.0001284
relative error = 0.002908 %
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 = 1.623
Order of pole (three term test) = 31.58 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6473 2.4
h = 0.001 0.003
y[1] (numeric) = -4.19094272794 1.39284434738
y[1] (closed_form) = -4.19093904906 1.39297234736
absolute error = 0.0001281
relative error = 0.0029 %
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 = 7.706
Order of pole (three term test) = 31.58 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6483 2.403
h = 0.0001 0.004
y[1] (numeric) = -4.193280393 1.39573498112
y[1] (closed_form) = -4.19327804046 1.39586365079
absolute error = 0.0001287
relative error = 0.002912 %
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 = 4.369
Order of pole (three term test) = 31.58 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1303.7MB, alloc=52.3MB, time=15.36
x[1] = 0.6484 2.407
h = 0.003 0.006
y[1] (numeric) = -4.1971855941 1.39837084422
y[1] (closed_form) = -4.19718431251 1.39849883994
absolute error = 0.000128
relative error = 0.002893 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.803
Order of pole (three term test) = 31.57 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6514 2.413
h = 0.0001 0.005
y[1] (numeric) = -4.20124830281 1.40515950362
y[1] (closed_form) = -4.20124698571 1.40529305817
absolute error = 0.0001336
relative error = 0.003015 %
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 = 2.591
Order of pole (three term test) = 31.57 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6515 2.418
h = 0.0001 0.003
y[1] (numeric) = -4.20617073786 1.40844353053
y[1] (closed_form) = -4.20616882823 1.40857352233
absolute error = 0.00013
relative error = 0.002931 %
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 = 2.092
Order of pole (three term test) = 31.57 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6516 2.421
h = 0.001 0.001
y[1] (numeric) = -4.20910532565 1.41045310075
y[1] (closed_form) = -4.20910202475 1.41058283845
absolute error = 0.0001298
relative error = 0.002924 %
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 = 1.646
Order of pole (three term test) = 31.57 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6526 2.422
h = 0.001 0.003
y[1] (numeric) = -4.20946893703 1.41209016796
y[1] (closed_form) = -4.20946499829 1.41221954887
absolute error = 0.0001294
relative error = 0.002915 %
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 = 7.815
Order of pole (three term test) = 31.57 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6536 2.425
h = 0.0001 0.004
y[1] (numeric) = -4.21183224964 1.41500261828
y[1] (closed_form) = -4.21182964009 1.41513267348
absolute error = 0.0001301
relative error = 0.002928 %
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 = 4.431
Order of pole (three term test) = 31.57 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6537 2.429
h = 0.003 0.006
y[1] (numeric) = -4.21577657254 1.41765541306
y[1] (closed_form) = -4.21577503856 1.41778479423
absolute error = 0.0001294
relative error = 0.002909 %
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 = 5.885
Order of pole (three term test) = 31.57 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6567 2.435
h = 0.0001 0.005
y[1] (numeric) = -4.21988662866 1.42449767404
y[1] (closed_form) = -4.21988504851 1.42463263134
absolute error = 0.000135
relative error = 0.00303 %
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 = 2.627
Order of pole (three term test) = 31.56 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6568 2.44
h = 0.0001 0.003
y[1] (numeric) = -4.22485811733 1.42780270987
y[1] (closed_form) = -4.22485594957 1.42793409214
absolute error = 0.0001314
relative error = 0.002946 %
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 = 2.122
Order of pole (three term test) = 31.56 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6569 2.443
h = 0.001 0.001
y[1] (numeric) = -4.2278219992 1.42982529131
y[1] (closed_form) = -4.2278184363 1.42995641604
absolute error = 0.0001312
relative error = 0.002939 %
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 = 1.669
Order of pole (three term test) = 31.56 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6579 2.444
h = 0.0001 0.004
y[1] (numeric) = -4.22819150193 1.4314762688
y[1] (closed_form) = -4.22818729985 1.43160703441
absolute error = 0.0001308
relative error = 0.002931 %
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 = 10.03
Order of pole (three term test) = 31.56 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.658 2.448
h = 0.003 0.006
y[1] (numeric) = -4.23216791252 1.43414294354
y[1] (closed_form) = -4.23216665305 1.43427336364
absolute error = 0.0001304
relative error = 0.002919 %
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 = 5.957
Order of pole (three term test) = 31.56 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.661 2.454
h = 0.0001 0.005
y[1] (numeric) = -4.23631940368 1.4410309846
y[1] (closed_form) = -4.23631808899 1.44116699598
absolute error = 0.000136
relative error = 0.00304 %
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 = 2.659
Order of pole (three term test) = 31.56 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6611 2.459
h = 0.0001 0.003
y[1] (numeric) = -4.24133346024 1.44435364561
y[1] (closed_form) = -4.24133156207 1.44448607123
absolute error = 0.0001324
relative error = 0.002956 %
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 = 2.148
Order of pole (three term test) = 31.55 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6612 2.462
h = 0.001 0.001
y[1] (numeric) = -4.24432276801 1.446387154
y[1] (closed_form) = -4.24431947128 1.44651931915
absolute error = 0.0001322
relative error = 0.002948 %
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 = 1.689
Order of pole (three term test) = 31.55 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6622 2.463
h = 0.001 0.003
y[1] (numeric) = -4.24469750207 1.44805007899
y[1] (closed_form) = -4.24469356499 1.448181883
absolute error = 0.0001319
relative error = 0.00294 %
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 = 8.021
Order of pole (three term test) = 31.55 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6632 2.466
h = 0.0001 0.004
y[1] (numeric) = -4.24710890528 1.45100313009
y[1] (closed_form) = -4.24710630285 1.45113561704
absolute error = 0.0001325
relative error = 0.002952 %
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 = 4.548
Order of pole (three term test) = 31.55 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6633 2.47
h = 0.003 0.006
y[1] (numeric) = -4.25112647087 1.45368730185
y[1] (closed_form) = -4.25112495273 1.45381911458
absolute error = 0.0001318
relative error = 0.002934 %
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 = 6.041
Order of pole (three term test) = 31.55 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6663 2.476
h = 0.0001 0.005
y[1] (numeric) = -4.25532539966 1.46062942578
y[1] (closed_form) = -4.25532381545 1.4607668474
absolute error = 0.0001374
relative error = 0.003055 %
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 = 2.697
Order of pole (three term test) = 31.55 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6664 2.481
h = 0.0001 0.003
y[1] (numeric) = -4.26038872503 1.46397339216
y[1] (closed_form) = -4.26038656234 1.46410721552
absolute error = 0.0001338
relative error = 0.002971 %
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 = 2.178
Order of pole (three term test) = 31.54 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6665 2.484
h = 0.001 0.001
y[1] (numeric) = -4.26340745408 1.4660200916
y[1] (closed_form) = -4.26340388888 1.46615365098
absolute error = 0.0001336
relative error = 0.002963 %
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 = 1.713
Order of pole (three term test) = 31.54 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6675 2.485
h = 0.001 0.003
y[1] (numeric) = -4.26378806538 1.46769702976
y[1] (closed_form) = -4.26378385848 1.46783022564
absolute error = 0.0001333
relative error = 0.002955 %
Correct digits = 5
memory used=1347.7MB, alloc=52.3MB, time=15.88
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.134
Order of pole (three term test) = 31.54 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6685 2.488
h = 0.0001 0.004
y[1] (numeric) = -4.26622522941 1.47067223426
y[1] (closed_form) = -4.2662223601 1.47080611779
absolute error = 0.0001339
relative error = 0.002968 %
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 = 4.612
Order of pole (three term test) = 31.54 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6686 2.492
h = 0.003 0.006
y[1] (numeric) = -4.27028217896 1.47337370398
y[1] (closed_form) = -4.27028039869 1.47350691321
absolute error = 0.0001332
relative error = 0.002949 %
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 = 6.126
Order of pole (three term test) = 31.54 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6716 2.498
h = 0.0001 0.005
y[1] (numeric) = -4.27452859299 1.48037017339
y[1] (closed_form) = -4.27452673571 1.48050900931
absolute error = 0.0001388
relative error = 0.003069 %
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 = 2.734
Order of pole (three term test) = 31.54 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6717 2.503
h = 0.0001 0.003
y[1] (numeric) = -4.27964130351 1.48373560742
y[1] (closed_form) = -4.27963887279 1.48387083246
absolute error = 0.0001352
relative error = 0.002986 %
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 = 2.208
Order of pole (three term test) = 31.54 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6718 2.506
h = 0.001 0.001
y[1] (numeric) = -4.28268952257 1.48579559632
y[1] (closed_form) = -4.28268568535 1.48593055384
absolute error = 0.000135
relative error = 0.002978 %
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 = 1.737
Order of pole (three term test) = 31.53 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6728 2.507
h = 0.001 0.003
y[1] (numeric) = -4.28307600309 1.4874866037
y[1] (closed_form) = -4.28307152281 1.48762119532
absolute error = 0.0001347
relative error = 0.00297 %
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 = 8.248
Order of pole (three term test) = 31.53 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6738 2.51
h = 0.0001 0.004
y[1] (numeric) = -4.28553896785 1.49048408173
y[1] (closed_form) = -4.28553582813 1.49061936579
absolute error = 0.0001353
relative error = 0.002982 %
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 = 4.676
Order of pole (three term test) = 31.53 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6739 2.514
h = 0.003 0.006
y[1] (numeric) = -4.2896353943 1.49320298023
y[1] (closed_form) = -4.28963334841 1.49333758991
absolute error = 0.0001346
relative error = 0.002964 %
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 = 6.211
Order of pole (three term test) = 31.53 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6769 2.52
h = 0.0001 0.005
y[1] (numeric) = -4.29392934173 1.50025406033
y[1] (closed_form) = -4.29392720779 1.50039431467
absolute error = 0.0001403
relative error = 0.003084 %
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 = 2.773
Order of pole (three term test) = 31.53 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.677 2.525
h = 0.0001 0.003
y[1] (numeric) = -4.2990915549 1.50364112586
y[1] (closed_form) = -4.29908885261 1.50377775654
absolute error = 0.0001367
relative error = 0.003 %
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 = 2.239
Order of pole (three term test) = 31.53 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6771 2.528
h = 0.001 0.001
y[1] (numeric) = -4.30216933343 1.50571450358
y[1] (closed_form) = -4.30216522061 1.50585086319
absolute error = 0.0001364
relative error = 0.002993 %
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 = 1.761
Order of pole (three term test) = 31.52 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6781 2.529
h = 0.001 0.003
y[1] (numeric) = -4.30256167508 1.50741963678
y[1] (closed_form) = -4.30255691782 1.50755562806
absolute error = 0.0001361
relative error = 0.002985 %
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 = 8.364
Order of pole (three term test) = 31.52 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6791 2.532
h = 0.0001 0.004
y[1] (numeric) = -4.30505048092 1.51043950965
y[1] (closed_form) = -4.30504706723 1.51057619819
absolute error = 0.0001367
relative error = 0.002997 %
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 = 4.742
Order of pole (three term test) = 31.52 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6792 2.536
h = 0.003 0.006
y[1] (numeric) = -4.30918647813 1.51317596903
y[1] (closed_form) = -4.30918416311 1.51331198311
absolute error = 0.000136
relative error = 0.002979 %
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 = 6.298
Order of pole (three term test) = 31.52 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6822 2.542
h = 0.0001 0.005
y[1] (numeric) = -4.31352800766 1.5202819276
y[1] (closed_form) = -4.31352559343 1.5204236045
absolute error = 0.0001417
relative error = 0.003098 %
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 = 2.812
Order of pole (three term test) = 31.52 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6823 2.547
h = 0.0001 0.003
y[1] (numeric) = -4.31873984218 1.52369079005
y[1] (closed_form) = -4.31873686475 1.52382883041
absolute error = 0.0001381
relative error = 0.003015 %
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 = 2.271
Order of pole (three term test) = 31.52 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6824 2.55
h = 0.001 0.001
y[1] (numeric) = -4.32184725032 1.52577765693
y[1] (closed_form) = -4.32184285828 1.52591542261
absolute error = 0.0001378
relative error = 0.003007 %
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 = 1.786
Order of pole (three term test) = 31.52 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6834 2.551
h = 0.0001 0.004
y[1] (numeric) = -4.32224544493 1.52749697308
y[1] (closed_form) = -4.32224040707 1.52763436799
absolute error = 0.0001375
relative error = 0.002999 %
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 = 10.73
Order of pole (three term test) = 31.52 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6835 2.555
h = 0.003 0.006
y[1] (numeric) = -4.32641390142 1.53024783079
y[1] (closed_form) = -4.3264118556 1.53038490244
absolute error = 0.0001371
relative error = 0.002987 %
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 = 6.374
Order of pole (three term test) = 31.51 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6865 2.561
h = 0.0001 0.005
y[1] (numeric) = -4.33079708551 1.53740067577
y[1] (closed_form) = -4.33079493102 1.53754342613
absolute error = 0.0001428
relative error = 0.003107 %
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 = 2.845
Order of pole (three term test) = 31.51 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6866 2.566
h = 0.0001 0.003
y[1] (numeric) = -4.33605199076 1.54082784092
y[1] (closed_form) = -4.33604927737 1.54096694349
absolute error = 0.0001391
relative error = 0.003023 %
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 = 2.298
Order of pole (three term test) = 31.51 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1391.6MB, alloc=52.3MB, time=16.39
x[1] = 0.6867 2.569
h = 0.001 0.001
y[1] (numeric) = -4.33918512211 1.54292604579
y[1] (closed_form) = -4.33918099053 1.54306487061
absolute error = 0.0001389
relative error = 0.003016 %
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 = 1.807
Order of pole (three term test) = 31.51 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6877 2.57
h = 0.001 0.003
y[1] (numeric) = -4.33958851807 1.54465754676
y[1] (closed_form) = -4.33958373943 1.54479599871
absolute error = 0.0001385
relative error = 0.003007 %
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 = 8.583
Order of pole (three term test) = 31.51 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6887 2.573
h = 0.0001 0.004
y[1] (numeric) = -4.34212578719 1.54771910916
y[1] (closed_form) = -4.34212235785 1.54785826742
absolute error = 0.0001392
relative error = 0.00302 %
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 = 4.866
Order of pole (three term test) = 31.51 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6888 2.577
h = 0.003 0.006
y[1] (numeric) = -4.34633588243 1.55048812711
y[1] (closed_form) = -4.34633356089 1.55062661069
absolute error = 0.0001385
relative error = 0.003001 %
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 = 6.463
Order of pole (three term test) = 31.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6918 2.583
h = 0.0001 0.005
y[1] (numeric) = -4.35076674387 1.55769635521
y[1] (closed_form) = -4.35076430232 1.55784053599
absolute error = 0.0001442
relative error = 0.00312 %
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 = 2.885
Order of pole (three term test) = 31.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6919 2.588
h = 0.0001 0.003
y[1] (numeric) = -4.35607149654 1.56114562788
y[1] (closed_form) = -4.35606850131 1.56128614776
absolute error = 0.0001406
relative error = 0.003037 %
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 = 2.33
Order of pole (three term test) = 31.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.692 2.591
h = 0.001 0.001
y[1] (numeric) = -4.3592343911 1.56325751031
y[1] (closed_form) = -4.35922997354 1.56339774877
absolute error = 0.0001403
relative error = 0.00303 %
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 = 1.832
Order of pole (three term test) = 31.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.693 2.592
h = 0.001 0.003
y[1] (numeric) = -4.35964362537 1.56500330215
y[1] (closed_form) = -4.35963855933 1.56514316525
absolute error = 0.00014
relative error = 0.003021 %
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 = 8.702
Order of pole (three term test) = 31.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.694 2.595
h = 0.0001 0.004
y[1] (numeric) = -4.36220685481 1.56808761248
y[1] (closed_form) = -4.36220314116 1.56822818684
absolute error = 0.0001406
relative error = 0.003034 %
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 = 4.934
Order of pole (three term test) = 31.5 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6941 2.599
h = 0.003 0.006
y[1] (numeric) = -4.36645679622 1.57087457507
y[1] (closed_form) = -4.36645419535 1.57101447467
absolute error = 0.0001399
relative error = 0.003015 %
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 = 6.553
Order of pole (three term test) = 31.49 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6971 2.605
h = 0.0001 0.005
y[1] (numeric) = -4.37093538525 1.57813846157
y[1] (closed_form) = -4.37093265291 1.57828407704
absolute error = 0.0001456
relative error = 0.003134 %
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 = 2.925
Order of pole (three term test) = 31.49 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6972 2.61
h = 0.0001 0.003
y[1] (numeric) = -4.37629010746 1.58161001174
y[1] (closed_form) = -4.37628682672 1.58175195306
absolute error = 0.000142
relative error = 0.003051 %
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 = 2.362
Order of pole (three term test) = 31.49 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6973 2.613
h = 0.001 0.001
y[1] (numeric) = -4.3794828374 1.58373567483
y[1] (closed_form) = -4.37947813014 1.58387733103
absolute error = 0.0001417
relative error = 0.003043 %
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 = 1.858
Order of pole (three term test) = 31.49 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6983 2.614
h = 0.001 0.003
y[1] (numeric) = -4.37989790163 1.58549581629
y[1] (closed_form) = -4.37989254446 1.58563709462
absolute error = 0.0001414
relative error = 0.003035 %
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 = 8.823
Order of pole (three term test) = 31.49 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6993 2.617
h = 0.0001 0.004
y[1] (numeric) = -4.38248713337 1.58860300043
y[1] (closed_form) = -4.38248313171 1.58874499502
absolute error = 0.0001421
relative error = 0.003047 %
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 = 5.002
Order of pole (three term test) = 31.49 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6994 2.621
h = 0.003 0.006
y[1] (numeric) = -4.3867770185 1.5914080447
y[1] (closed_form) = -4.38677413465 1.59154936444
absolute error = 0.0001413
relative error = 0.003029 %
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 = 6.644
Order of pole (three term test) = 31.48 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7024 2.627
h = 0.0001 0.005
y[1] (numeric) = -4.39130338585 1.59872786752
y[1] (closed_form) = -4.39130035897 1.59887492197
absolute error = 0.0001471
relative error = 0.003147 %
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 = 2.966
Order of pole (three term test) = 31.48 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7025 2.632
h = 0.0001 0.003
y[1] (numeric) = -4.39670820093 1.60222186678
y[1] (closed_form) = -4.39670463097 1.6023652337
absolute error = 0.0001434
relative error = 0.003065 %
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 = 2.395
Order of pole (three term test) = 31.48 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7026 2.635
h = 0.001 0.001
y[1] (numeric) = -4.39993083912 1.60436141459
y[1] (closed_form) = -4.39992583841 1.60450449266
absolute error = 0.0001432
relative error = 0.003057 %
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 = 1.884
Order of pole (three term test) = 31.48 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7036 2.636
h = 0.001 0.003
y[1] (numeric) = -4.40035172489 1.60613596498
y[1] (closed_form) = -4.40034607283 1.60627866266
absolute error = 0.0001428
relative error = 0.003049 %
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 = 8.946
Order of pole (three term test) = 31.48 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7046 2.639
h = 0.0001 0.004
y[1] (numeric) = -4.40296700132 1.60926615003
y[1] (closed_form) = -4.40296270793 1.609409569
absolute error = 0.0001435
relative error = 0.003061 %
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 = 5.072
Order of pole (three term test) = 31.48 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1435.7MB, alloc=52.3MB, time=16.91
x[1] = 0.7047 2.643
h = 0.003 0.006
y[1] (numeric) = -4.40729692866 1.61208941431
y[1] (closed_form) = -4.40729375815 1.61223215835
absolute error = 0.0001428
relative error = 0.003042 %
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 = 6.736
Order of pole (three term test) = 31.47 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7077 2.649
h = 0.0001 0.005
y[1] (numeric) = -4.4118711256 1.619465454
y[1] (closed_form) = -4.41186780038 1.61961395178
absolute error = 0.0001485
relative error = 0.00316 %
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 = 3.007
Order of pole (three term test) = 31.47 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7078 2.654
h = 0.0001 0.003
y[1] (numeric) = -4.41732615806 1.62298207557
y[1] (closed_form) = -4.41732229514 1.62312687233
absolute error = 0.0001448
relative error = 0.003078 %
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 = 2.428
Order of pole (three term test) = 31.47 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7079 2.657
h = 0.001 0.001
y[1] (numeric) = -4.42057877808 1.62513561317
y[1] (closed_form) = -4.42057348014 1.6252801173
absolute error = 0.0001446
relative error = 0.00307 %
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 = 1.91
Order of pole (three term test) = 31.47 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7089 2.658
h = 0.0001 0.004
y[1] (numeric) = -4.42100547689 1.62692463238
y[1] (closed_form) = -4.42099952614 1.62706875355
absolute error = 0.0001442
relative error = 0.003062 %
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 = 11.48
Order of pole (three term test) = 31.47 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.709 2.662
h = 0.003 0.006
y[1] (numeric) = -4.42536825353 1.62976283795
y[1] (closed_form) = -4.42536534667 1.62990665911
absolute error = 0.0001439
relative error = 0.00305 %
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 = 6.817
Order of pole (three term test) = 31.47 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.712 2.668
h = 0.0001 0.005
y[1] (numeric) = -4.42998433626 1.63718692338
y[1] (closed_form) = -4.4299812648 1.63733651494
absolute error = 0.0001496
relative error = 0.003168 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.043
Order of pole (three term test) = 31.46 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7121 2.673
h = 0.0001 0.003
y[1] (numeric) = -4.43548296711 1.64072255721
y[1] (closed_form) = -4.43547936244 1.64086843596
absolute error = 0.0001459
relative error = 0.003086 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.457
Order of pole (three term test) = 31.46 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7122 2.676
h = 0.001 0.001
y[1] (numeric) = -4.43876162231 1.64288786328
y[1] (closed_form) = -4.43875657888 1.64303344618
absolute error = 0.0001457
relative error = 0.003078 %
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 = 1.933
Order of pole (three term test) = 31.46 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7132 2.677
h = 0.001 0.003
y[1] (numeric) = -4.43919349126 1.64468931604
y[1] (closed_form) = -4.43918779372 1.64483451377
absolute error = 0.0001453
relative error = 0.003069 %
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 = 9.178
Order of pole (three term test) = 31.46 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7142 2.68
h = 0.0001 0.004
y[1] (numeric) = -4.44185762268 1.64786233134
y[1] (closed_form) = -4.44185328981 1.64800825985
absolute error = 0.000146
relative error = 0.003081 %
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 = 5.203
Order of pole (three term test) = 31.46 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7143 2.684
h = 0.003 0.006
y[1] (numeric) = -4.44626254564 1.65071939167
y[1] (closed_form) = -4.44625934521 1.65086464502
absolute error = 0.0001453
relative error = 0.003063 %
Correct digits = 5
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.911
Order of pole (three term test) = 31.46 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7173 2.69
h = 0.0001 0.005
y[1] (numeric) = -4.45092655811 1.65820022253
y[1] (closed_form) = -4.45092318121 1.65835126565
absolute error = 0.0001511
relative error = 0.003181 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.085
Order of pole (three term test) = 31.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7174 2.695
h = 0.0001 0.003
y[1] (numeric) = -4.45647564333 1.66175880383
y[1] (closed_form) = -4.4564717387 1.66190612039
absolute error = 0.0001474
relative error = 0.003098 %
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 = 2.491
Order of pole (three term test) = 31.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7175 2.698
h = 0.001 0.001
y[1] (numeric) = -4.45978442043 1.66393829692
y[1] (closed_form) = -4.45977907268 1.6640853138
absolute error = 0.0001471
relative error = 0.003091 %
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 = 1.959
Order of pole (three term test) = 31.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7185 2.699
h = 0.001 0.003
y[1] (numeric) = -4.46022208713 1.66575433152
y[1] (closed_form) = -4.46021608379 1.66590096064
absolute error = 0.0001468
relative error = 0.003082 %
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 = 9.305
Order of pole (three term test) = 31.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7195 2.702
h = 0.0001 0.004
y[1] (numeric) = -4.46291238839 1.66895071746
y[1] (closed_form) = -4.46290775297 1.66909808255
absolute error = 0.0001474
relative error = 0.003094 %
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 = 5.275
Order of pole (three term test) = 31.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7196 2.706
h = 0.003 0.006
y[1] (numeric) = -4.46735764229 1.67182639958
y[1] (closed_form) = -4.46735414452 1.67197308941
absolute error = 0.0001467
relative error = 0.003076 %
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 = 7.007
Order of pole (three term test) = 31.45 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7226 2.712
h = 0.0001 0.005
y[1] (numeric) = -4.47206963725 1.67936426409
y[1] (closed_form) = -4.47206595103 1.67951676323
absolute error = 0.0001525
relative error = 0.003193 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.128
Order of pole (three term test) = 31.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7227 2.717
h = 0.0001 0.003
y[1] (numeric) = -4.47766930481 1.68294597077
y[1] (closed_form) = -4.47766509637 1.68309472949
absolute error = 0.0001488
relative error = 0.003111 %
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 = 2.526
Order of pole (three term test) = 31.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7228 2.72
h = 0.001 0.001
y[1] (numeric) = -4.48100827941 1.68513975878
y[1] (closed_form) = -4.48100262346 1.68528821395
absolute error = 0.0001486
relative error = 0.003103 %
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 = 1.986
Order of pole (three term test) = 31.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7238 2.721
h = 0.001 0.003
y[1] (numeric) = -4.48145173515 1.68697043674
y[1] (closed_form) = -4.48144542211 1.68711850152
absolute error = 0.0001482
relative error = 0.003095 %
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 = 9.433
Order of pole (three term test) = 31.44 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1479.7MB, alloc=52.3MB, time=17.42
x[1] = 0.7248 2.724
h = 0.0001 0.004
y[1] (numeric) = -4.48416825027 1.69019032511
y[1] (closed_form) = -4.48416330842 1.69033913109
absolute error = 0.0001489
relative error = 0.003107 %
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 = 5.348
Order of pole (three term test) = 31.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7249 2.728
h = 0.003 0.006
y[1] (numeric) = -4.48865393731 1.69308477243
y[1] (closed_form) = -4.48865013837 1.69323290305
absolute error = 0.0001482
relative error = 0.003089 %
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 = 7.103
Order of pole (three term test) = 31.44 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7279 2.734
h = 0.0001 0.005
y[1] (numeric) = -4.49341396799 1.70067996151
y[1] (closed_form) = -4.49340996851 1.70083392118
absolute error = 0.000154
relative error = 0.003206 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.171
Order of pole (three term test) = 31.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.728 2.739
h = 0.0001 0.003
y[1] (numeric) = -4.49906434706 1.70428497313
y[1] (closed_form) = -4.49905983092 1.70443517838
absolute error = 0.0001503
relative error = 0.003123 %
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 = 2.561
Order of pole (three term test) = 31.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7281 2.742
h = 0.001 0.001
y[1] (numeric) = -4.50243359547 1.70649316497
y[1] (closed_form) = -4.50242762741 1.70664306277
absolute error = 0.00015
relative error = 0.003116 %
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 = 2.014
Order of pole (three term test) = 31.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7291 2.743
h = 0.001 0.003
y[1] (numeric) = -4.50288283146 1.70833854839
y[1] (closed_form) = -4.50287620479 1.70848805314
absolute error = 0.0001497
relative error = 0.003107 %
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 = 9.563
Order of pole (three term test) = 31.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7301 2.746
h = 0.0001 0.004
y[1] (numeric) = -4.50562560487 1.7115820722
y[1] (closed_form) = -4.50562035269 1.71173232342
absolute error = 0.0001503
relative error = 0.003119 %
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 = 5.422
Order of pole (three term test) = 31.43 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7302 2.75
h = 0.003 0.006
y[1] (numeric) = -4.51015182818 1.71449542947
y[1] (closed_form) = -4.51014772422 1.71464500525
absolute error = 0.0001496
relative error = 0.003101 %
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 = 7.201
Order of pole (three term test) = 31.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7332 2.756
h = 0.0001 0.005
y[1] (numeric) = -4.51495994834 1.72214823676
y[1] (closed_form) = -4.51495563162 1.7223036615
absolute error = 0.0001555
relative error = 0.003218 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.214
Order of pole (three term test) = 31.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7333 2.761
h = 0.0001 0.003
y[1] (numeric) = -4.52066116928 1.72577673457
y[1] (closed_form) = -4.52065634153 1.72592839076
absolute error = 0.0001517
relative error = 0.003136 %
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 = 2.596
Order of pole (three term test) = 31.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7334 2.764
h = 0.001 0.001
y[1] (numeric) = -4.52406076853 1.72799944017
y[1] (closed_form) = -4.52405448439 1.72815078496
absolute error = 0.0001515
relative error = 0.003128 %
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 = 2.041
Order of pole (three term test) = 31.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7344 2.765
h = 0.0001 0.004
y[1] (numeric) = -4.52451577589 1.7298595917
y[1] (closed_form) = -4.52450883162 1.73001054077
absolute error = 0.0001511
relative error = 0.00312 %
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 = 12.27
Order of pole (three term test) = 31.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7345 2.769
h = 0.003 0.006
y[1] (numeric) = -4.52907525709 1.73278845852
y[1] (closed_form) = -4.52907141099 1.7329391319
absolute error = 0.0001507
relative error = 0.003108 %
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 = 7.287
Order of pole (three term test) = 31.42 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7375 2.775
h = 0.0001 0.005
y[1] (numeric) = -4.53392550563 1.74049052514
y[1] (closed_form) = -4.53392143641 1.74064706491
absolute error = 0.0001566
relative error = 0.003224 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.253
Order of pole (three term test) = 31.41 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7376 2.78
h = 0.0001 0.003
y[1] (numeric) = -4.53967087761 1.74413877775
y[1] (closed_form) = -4.53966630207 1.74429153663
absolute error = 0.0001528
relative error = 0.003143 %
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 = 2.627
Order of pole (three term test) = 31.41 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7377 2.783
h = 0.001 0.001
y[1] (numeric) = -4.54309683877 1.74637370231
y[1] (closed_form) = -4.54309080291 1.74652614642
absolute error = 0.0001526
relative error = 0.003134 %
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 = 2.066
Order of pole (three term test) = 31.41 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7387 2.784
h = 0.001 0.003
y[1] (numeric) = -4.5435569837 1.74824654776
y[1] (closed_form) = -4.54355028635 1.74839859384
absolute error = 0.0001522
relative error = 0.003126 %
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 = 9.81
Order of pole (three term test) = 31.41 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7397 2.787
h = 0.0001 0.004
y[1] (numeric) = -4.54634902265 1.75153409582
y[1] (closed_form) = -4.54634370608 1.7516868983
absolute error = 0.0001529
relative error = 0.003138 %
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 = 5.562
Order of pole (three term test) = 31.41 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7398 2.791
h = 0.003 0.006
y[1] (numeric) = -4.55095118171 1.75448254417
y[1] (closed_form) = -4.55094702336 1.75463467097
absolute error = 0.0001522
relative error = 0.00312 %
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 = 7.387
Order of pole (three term test) = 31.41 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7428 2.797
h = 0.0001 0.005
y[1] (numeric) = -4.5558496246 1.76224278201
y[1] (closed_form) = -4.55584523073 1.76240079546
absolute error = 0.0001581
relative error = 0.003236 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.297
Order of pole (three term test) = 31.4 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7429 2.802
h = 0.0001 0.003
y[1] (numeric) = -4.56164608645 1.76591486095
y[1] (closed_form) = -4.56164119197 1.76606907915
absolute error = 0.0001543
relative error = 0.003154 %
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 = 2.663
Order of pole (three term test) = 31.4 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1523.8MB, alloc=52.3MB, time=17.93
x[1] = 0.743 2.805
h = 0.001 0.001
y[1] (numeric) = -4.56510254501 1.7681645056
y[1] (closed_form) = -4.56509618567 1.76831840501
absolute error = 0.000154
relative error = 0.003146 %
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 = 2.094
Order of pole (three term test) = 31.4 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.744 2.806
h = 0.001 0.003
y[1] (numeric) = -4.56556844533 1.77005223743
y[1] (closed_form) = -4.56556142294 1.77020573609
absolute error = 0.0001537
relative error = 0.003138 %
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 = 9.945
Order of pole (three term test) = 31.4 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.745 2.809
h = 0.0001 0.004
y[1] (numeric) = -4.56838687357 1.77336380776
y[1] (closed_form) = -4.56838123535 1.77351806823
absolute error = 0.0001544
relative error = 0.00315 %
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 = 5.638
Order of pole (three term test) = 31.4 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7451 2.813
h = 0.003 0.006
y[1] (numeric) = -4.57302987104 1.77633158637
y[1] (closed_form) = -4.5730253965 1.77648517107
absolute error = 0.0001536
relative error = 0.003132 %
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 = 7.489
Order of pole (three term test) = 31.39 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7481 2.819
h = 0.0001 0.005
y[1] (numeric) = -4.57797656346 1.7841502969
y[1] (closed_form) = -4.57797184086 1.7843097887
absolute error = 0.0001596
relative error = 0.003247 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.343
Order of pole (three term test) = 31.39 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7482 2.824
h = 0.0001 0.003
y[1] (numeric) = -4.58382424902 1.78784638826
y[1] (closed_form) = -4.58381903158 1.78800207029
absolute error = 0.0001558
relative error = 0.003166 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.699
Order of pole (three term test) = 31.39 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7483 2.827
h = 0.001 0.001
y[1] (numeric) = -4.58731128406 1.79011086585
y[1] (closed_form) = -4.58730459716 1.79026622505
absolute error = 0.0001555
relative error = 0.003158 %
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 = 2.123
Order of pole (three term test) = 31.39 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7493 2.828
h = 0.001 0.003
y[1] (numeric) = -4.58778293065 1.79201354838
y[1] (closed_form) = -4.58777557914 1.79216850408
absolute error = 0.0001551
relative error = 0.00315 %
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 = 10.08
Order of pole (three term test) = 31.39 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7503 2.831
h = 0.0001 0.004
y[1] (numeric) = -4.5906277942 1.79534927881
y[1] (closed_form) = -4.59062183029 1.7955050018
absolute error = 0.0001558
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 = 5.715
Order of pole (three term test) = 31.39 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7504 2.835
h = 0.003 0.006
y[1] (numeric) = -4.59531173694 1.79833653767
y[1] (closed_form) = -4.59530694222 1.79849158479
absolute error = 0.0001551
relative error = 0.003143 %
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 = 7.591
Order of pole (three term test) = 31.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7534 2.841
h = 0.0001 0.005
y[1] (numeric) = -4.60030673455 1.80621402513
y[1] (closed_form) = -4.60030167911 1.80637499998
absolute error = 0.0001611
relative error = 0.003259 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.388
Order of pole (three term test) = 31.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7535 2.846
h = 0.0001 0.003
y[1] (numeric) = -4.60620577887 1.80993431669
y[1] (closed_form) = -4.60620023441 1.81009146713
absolute error = 0.0001572
relative error = 0.003177 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.736
Order of pole (three term test) = 31.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7536 2.849
h = 0.001 0.001
y[1] (numeric) = -4.60972347016 1.81221374111
y[1] (closed_form) = -4.60971645162 1.81237056464
absolute error = 0.000157
relative error = 0.003169 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.152
Order of pole (three term test) = 31.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7546 2.85
h = 0.001 0.003
y[1] (numeric) = -4.61020085381 1.81413143927
y[1] (closed_form) = -4.61019316909 1.81428785652
absolute error = 0.0001566
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 = 10.22
Order of pole (three term test) = 31.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7556 2.853
h = 0.0001 0.004
y[1] (numeric) = -4.61307219912 1.81749146888
y[1] (closed_form) = -4.61306590544 1.81764865894
absolute error = 0.0001573
relative error = 0.003173 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.794
Order of pole (three term test) = 31.38 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7557 2.857
h = 0.003 0.006
y[1] (numeric) = -4.61779719496 1.82049835935
y[1] (closed_form) = -4.61779207601 1.82065487345
absolute error = 0.0001566
relative error = 0.003155 %
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 = 7.695
Order of pole (three term test) = 31.37 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7587 2.863
h = 0.0001 0.005
y[1] (numeric) = -4.62284055388 1.82843493077
y[1] (closed_form) = -4.62283516145 1.82859739341
absolute error = 0.0001626
relative error = 0.00327 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.435
Order of pole (three term test) = 31.37 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7588 2.868
h = 0.0001 0.003
y[1] (numeric) = -4.62879109322 1.83217961203
y[1] (closed_form) = -4.62878521765 1.8323382355
absolute error = 0.0001587
relative error = 0.003189 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.774
Order of pole (three term test) = 31.37 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7589 2.871
h = 0.001 0.001
y[1] (numeric) = -4.63233952126 1.83447409823
y[1] (closed_form) = -4.63233216695 1.83463239066
absolute error = 0.0001585
relative error = 0.00318 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.181
Order of pole (three term test) = 31.37 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7599 2.872
h = 0.001 0.003
y[1] (numeric) = -4.63282263269 1.83640687751
y[1] (closed_form) = -4.63281461058 1.83656476087
absolute error = 0.0001581
relative error = 0.003172 %
Correct digits = 4
NO POLE (given) for Equation 1
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.36
Order of pole (three term test) = 31.37 0
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) + sin ( 0.3 * x + 0.1 ) ;
Iterations = 754
Total Elapsed Time = 18 Seconds
Expected Time Remaining = 0 Seconds
Optimized Time Remaining = 0 Seconds
Expected Total Time = 18 Seconds
> quit
memory used=1566.2MB, alloc=52.3MB, time=18.40