|\^/| 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(1.0)/c(x)/c(x)/c(x));
> end;
exact_soln_y := proc(x) return c(1.0)/(c(x)*c(x)*c(x)) end proc
> next_delta := proc()
> global glob_nxt, x_delta;
> x_delta := [ 0.001 + 0.00004 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.000 + 0.000 * I ];
> glob_nxt := glob_nxt + 1;
> it := x_delta[glob_nxt];
> return it;
> end;
Warning, `it` is implicitly declared local to procedure `next_delta`
next_delta := proc()
local it;
global glob_nxt, x_delta;
x_delta := [0.001 + 0.00004*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0. + 0.*I];
glob_nxt := glob_nxt + 1;
it := x_delta[glob_nxt];
return it
end proc
#END USER DEF BLOCK
#END BLOCK 3
#END USER FUNCTION BLOCK
# before write_aux functions
# Begin Function number 2
> display_poles := proc()
> local rad_given;
> global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ;
> if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1
> rad_given := float_abs(array_x[1] - (array_given_rad_poles[1,1] + array_given_rad_poles[1,2] * I ));
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," ");
> omniout_complex(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," ");
> if ((float_abs(rad_given) < float_abs(glob_least_given_sing)) and
> (float_abs(rad_given) > 0.0)) then # if number 2
> glob_least_given_sing := rad_given;
> fi;# end if 2;
> elif
> (glob_type_given_pole = 3) then # if number 2
> omniout_str(ALWAYS,"NO POLE (given) for Equation 1");
> elif
> (glob_type_given_pole = 5) then # if number 3
> omniout_str(ALWAYS,"SOME POLE (given) for Equation 1");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 1");
> fi;# end if 3;
> if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," ");
> if ((float_abs(array_rad_test_poles[1,1]) < glob_least_ratio_sing)) then # if number 4
> glob_least_ratio_sing := array_rad_test_poles[1,1];
> fi;# end if 4;
> omniout_complex(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," ");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," ");
> if ((float_abs(array_rad_test_poles[1,2]) < glob_least_3_sing)) then # if number 4
> glob_least_3_sing := array_rad_test_poles[1,2];
> fi;# end if 4;
> omniout_complex(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," ");
> if ((float_abs(array_rad_test_poles[1,3]) < glob_least_6_sing)) then # if number 4
> glob_least_6_sing := array_rad_test_poles[1,3];
> fi;# end if 4;
> omniout_complex(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1");
> fi;# end if 3
> ;
> end;
display_poles := proc()
local rad_given;
global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float,
glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord,
glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
glob_least_3_sing, glob_least_6_sing, glob_least_given_sing,
glob_least_ratio_sing, array_x;
if glob_type_given_pole = 1 or glob_type_given_pole = 2 then
rad_given := float_abs(array_x[1] - array_given_rad_poles[1, 1]
- array_given_rad_poles[1, 2]*I);
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 1 ", 4,
rad_given, 4, " ");
omniout_complex(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles[1, 1], 4, " ");
if float_abs(rad_given) < float_abs(glob_least_given_sing) and
0. < float_abs(rad_given) then glob_least_given_sing := rad_given
end if
elif glob_type_given_pole = 3 then
omniout_str(ALWAYS, "NO POLE (given) for Equation 1")
elif glob_type_given_pole = 5 then
omniout_str(ALWAYS, "SOME POLE (given) for Equation 1")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 1")
end if;
if array_rad_test_poles[1, 1] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (ratio test) for eq 1 ", 4,
array_rad_test_poles[1, 1], 4, " ");
if float_abs(array_rad_test_poles[1, 1]) < glob_least_ratio_sing
then glob_least_ratio_sing := array_rad_test_poles[1, 1]
end if;
omniout_complex(ALWAYS,
"Order of pole (ratio test) ", 4,
array_ord_test_poles[1, 1], 4, " ")
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 2] and
array_rad_test_poles[1, 2] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 1 ", 4,
array_rad_test_poles[1, 2], 4, " ");
if float_abs(array_rad_test_poles[1, 2]) < glob_least_3_sing then
glob_least_3_sing := array_rad_test_poles[1, 2]
end if;
omniout_complex(ALWAYS,
"Order of pole (three term test) ", 4,
array_ord_test_poles[1, 2], 4, " ")
else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 3] and
array_rad_test_poles[1, 3] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 1 ", 4,
array_rad_test_poles[1, 3], 4, " ");
if float_abs(array_rad_test_poles[1, 3]) < glob_least_6_sing then
glob_least_6_sing := array_rad_test_poles[1, 3]
end if;
omniout_complex(ALWAYS,
"Order of pole (six term test) ", 4,
array_ord_test_poles[1, 3], 4, " ")
else omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 1")
end if
end proc
# End Function number 2
# Begin Function number 3
> my_check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 3
> ret := glob__1;
> else
> ret := glob__m1;
> fi;# end if 3;
> ret;;
> end;
my_check_sign := proc(x0, xf)
local ret;
if x0 < xf then ret := glob__1 else ret := glob__m1 end if; ret
end proc
# End Function number 3
# Begin Function number 4
> est_size_answer := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_3D0,
#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,
> 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_3D0,
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, 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_3D0,
#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,
> 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_3D0,
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, 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_3D0,
#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,
> 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_3D0,
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, 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_3D0,
#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,
> 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_3D0,
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, 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_3D0,
#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,
> 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_3D0,
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, 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_3D0,
#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,
> 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_3D0,
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, 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_3D0,
#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,
> 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_3D0,
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, 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_3D0,
#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,
> 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 neg ID_CONST $eq_no = 1
> array_tmp1[1] := neg(array_const_3D0[1]);
> #emit pre div CONST - LINEAR $eq_no = 1 i = 1
> array_tmp2[1] := array_tmp1[1] / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 1
> array_tmp3[1] := array_tmp2[1] / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 1
> array_tmp4[1] := array_tmp3[1] / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 1
> array_tmp5[1] := array_tmp4[1] / array_x[1];
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp6[1] := array_const_0D0[1] + array_tmp5[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_tmp6[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 div CONST - LINEAR $eq_no = 1 i = 2
> array_tmp2[2] := neg(array_tmp2[1])* array_x[2] / array_x[1];
> #emit pre div CONST - LINEAR $eq_no = 1 i = 3
> #emit pre div CONST - LINEAR $eq_no = 1 i = 4
> #emit pre div CONST - LINEAR $eq_no = 1 i = 5
> #emit pre div FULL - LINEAR $eq_no = 1 i = 2
> array_tmp3[2] := (array_tmp2[2] - array_tmp3[1] * array_x[2]) / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 2
> array_tmp4[2] := (array_tmp3[2] - array_tmp4[1] * array_x[2]) / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 2
> array_tmp5[2] := (array_tmp4[2] - array_tmp5[1] * array_x[2]) / array_x[1];
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp6[2] := array_tmp5[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_tmp6[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
> array_tmp2[3] := neg(array_tmp2[2])* array_x[2] / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 3
> array_tmp3[3] := (array_tmp2[3] - array_tmp3[2] * array_x[2]) / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 3
> array_tmp4[3] := (array_tmp3[3] - array_tmp4[2] * array_x[2]) / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 3
> array_tmp5[3] := (array_tmp4[3] - array_tmp5[2] * array_x[2]) / array_x[1];
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp6[3] := array_tmp5[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_tmp6[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
> array_tmp2[4] := neg(array_tmp2[3])* array_x[2] / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 4
> array_tmp3[4] := (array_tmp2[4] - array_tmp3[3] * array_x[2]) / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 4
> array_tmp4[4] := (array_tmp3[4] - array_tmp4[3] * array_x[2]) / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 4
> array_tmp5[4] := (array_tmp4[4] - array_tmp5[3] * array_x[2]) / array_x[1];
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp6[4] := array_tmp5[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_tmp6[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
> array_tmp2[5] := neg(array_tmp2[4])* array_x[2] / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 5
> array_tmp3[5] := (array_tmp2[5] - array_tmp3[4] * array_x[2]) / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 5
> array_tmp4[5] := (array_tmp3[5] - array_tmp4[4] * array_x[2]) / array_x[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 5
> array_tmp5[5] := (array_tmp4[5] - array_tmp5[4] * array_x[2]) / array_x[1];
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp6[5] := array_tmp5[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_tmp6[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 div CONST LINEAR (NOP) $eq_no = 1 i = 1
> array_tmp2[kkk] := array_tmp1[1] * array_x[kkk];
> #emit div FULL LINEAR $eq_no = 1 i = 1
> array_tmp3[kkk] := neg(ats(kkk,array_x,array_tmp3,2)) / array_x[1];
> #emit div FULL LINEAR $eq_no = 1 i = 1
> array_tmp4[kkk] := neg(ats(kkk,array_x,array_tmp4,2)) / array_x[1];
> #emit div FULL LINEAR $eq_no = 1 i = 1
> array_tmp5[kkk] := neg(ats(kkk,array_x,array_tmp5,2)) / array_x[1];
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp6[kkk] := array_tmp5[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_tmp6[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_3D0,
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, 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] := neg(array_const_3D0[1]);
array_tmp2[1] := array_tmp1[1]/array_x[1];
array_tmp3[1] := array_tmp2[1]/array_x[1];
array_tmp4[1] := array_tmp3[1]/array_x[1];
array_tmp5[1] := array_tmp4[1]/array_x[1];
array_tmp6[1] := array_const_0D0[1] + array_tmp5[1];
if not array_y_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp6[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_tmp2[2] := neg(array_tmp2[1])*array_x[2]/array_x[1];
array_tmp3[2] := (-array_x[2]*array_tmp3[1] + array_tmp2[2])/array_x[1]
;
array_tmp4[2] := (-array_x[2]*array_tmp4[1] + array_tmp3[2])/array_x[1]
;
array_tmp5[2] := (-array_x[2]*array_tmp5[1] + array_tmp4[2])/array_x[1]
;
array_tmp6[2] := array_tmp5[2];
if not array_y_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp6[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_tmp2[3] := neg(array_tmp2[2])*array_x[2]/array_x[1];
array_tmp3[3] := (-array_x[2]*array_tmp3[2] + array_tmp2[3])/array_x[1]
;
array_tmp4[3] := (-array_x[2]*array_tmp4[2] + array_tmp3[3])/array_x[1]
;
array_tmp5[3] := (-array_x[2]*array_tmp5[2] + array_tmp4[3])/array_x[1]
;
array_tmp6[3] := array_tmp5[3];
if not array_y_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp6[3])*expt(glob_h, c(1))*c(factorial_3(2, 3));
if 4 <= ATS_MAX_TERMS then
array_y[4] := temporary; array_y_higher[1, 4] := temporary
end if;
temporary := c(temporary)*c(3)/c(glob_h);
array_y_higher[2, 3] := c(temporary)
end if
end if;
kkk := 4;
array_tmp2[4] := neg(array_tmp2[3])*array_x[2]/array_x[1];
array_tmp3[4] := (-array_x[2]*array_tmp3[3] + array_tmp2[4])/array_x[1]
;
array_tmp4[4] := (-array_x[2]*array_tmp4[3] + array_tmp3[4])/array_x[1]
;
array_tmp5[4] := (-array_x[2]*array_tmp5[3] + array_tmp4[4])/array_x[1]
;
array_tmp6[4] := array_tmp5[4];
if not array_y_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp6[4])*expt(glob_h, c(1))*c(factorial_3(3, 4));
if 5 <= ATS_MAX_TERMS then
array_y[5] := temporary; array_y_higher[1, 5] := temporary
end if;
temporary := c(temporary)*c(4)/c(glob_h);
array_y_higher[2, 4] := c(temporary)
end if
end if;
kkk := 5;
array_tmp2[5] := neg(array_tmp2[4])*array_x[2]/array_x[1];
array_tmp3[5] := (-array_x[2]*array_tmp3[4] + array_tmp2[5])/array_x[1]
;
array_tmp4[5] := (-array_x[2]*array_tmp4[4] + array_tmp3[5])/array_x[1]
;
array_tmp5[5] := (-array_x[2]*array_tmp5[4] + array_tmp4[5])/array_x[1]
;
array_tmp6[5] := array_tmp5[5];
if not array_y_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp6[5])*expt(glob_h, c(1))*c(factorial_3(4, 5));
if 6 <= ATS_MAX_TERMS then
array_y[6] := temporary; array_y_higher[1, 6] := temporary
end if;
temporary := c(temporary)*c(5)/c(glob_h);
array_y_higher[2, 5] := c(temporary)
end if
end if;
kkk := 6;
while kkk <= ATS_MAX_TERMS do
array_tmp2[kkk] := array_tmp1[1]*array_x[kkk];
array_tmp3[kkk] := neg(ats(kkk, array_x, array_tmp3, 2))/array_x[1]
;
array_tmp4[kkk] := neg(ats(kkk, array_x, array_tmp4, 2))/array_x[1]
;
array_tmp5[kkk] := neg(ats(kkk, array_x, array_tmp5, 2))/array_x[1]
;
array_tmp6[kkk] := array_tmp5[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_tmp6[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_3D0,
> #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,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> ATS_MAX_TERMS := 20;
> # before first input block
> #BEGIN FIRST INPUT BLOCK
> #BEGIN BLOCK 1
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=20;
> #END BLOCK 1
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> # before generate arrays
> array_y_init:= Array(0..(20),[]);
> array_norms:= Array(0..(20),[]);
> array_fact_1:= Array(0..(20),[]);
> array_1st_rel_error:= Array(0..(2),[]);
> array_last_rel_error:= Array(0..(2),[]);
> array_est_rel_error:= Array(0..(2),[]);
> array_max_est_error:= Array(0..(2),[]);
> array_type_pole:= Array(0..(2),[]);
> array_type_real_pole:= Array(0..(2),[]);
> array_type_complex_pole:= Array(0..(2),[]);
> array_est_digits:= Array(0..(2),[]);
> array_y:= Array(0..(20),[]);
> array_x:= Array(0..(20),[]);
> array_tmp0:= Array(0..(20),[]);
> array_tmp1:= Array(0..(20),[]);
> array_tmp2:= Array(0..(20),[]);
> array_tmp3:= Array(0..(20),[]);
> array_tmp4:= Array(0..(20),[]);
> array_tmp5:= Array(0..(20),[]);
> array_tmp6:= Array(0..(20),[]);
> array_m1:= Array(0..(20),[]);
> array_y_higher := Array(0..(2) ,(0..20+ 1),[]);
> array_y_higher_work := Array(0..(2) ,(0..20+ 1),[]);
> array_y_higher_work2 := Array(0..(2) ,(0..20+ 1),[]);
> array_y_set_initial := Array(0..(2) ,(0..20+ 1),[]);
> array_given_rad_poles := Array(0..(2) ,(0..3+ 1),[]);
> array_given_ord_poles := Array(0..(2) ,(0..3+ 1),[]);
> array_rad_test_poles := Array(0..(2) ,(0..4+ 1),[]);
> array_ord_test_poles := Array(0..(2) ,(0..4+ 1),[]);
> array_fact_2 := Array(0..(20) ,(0..20+ 1),[]);
> # before generate constants
> # before generate globals definition
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> # before generate const definition
> # before arrays initialized
> term := 1;
> while (term <= 20) do # do number 1
> array_y_init[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_norms[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_fact_1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_1st_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_last_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_est_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_max_est_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_real_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_complex_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_est_digits[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_y[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_x[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp0[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp3[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp4[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp5[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp6[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_m1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 20) do # do number 2
> array_y_higher[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 20) do # do number 2
> array_y_higher_work[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 20) do # do number 2
> array_y_higher_work2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 20) do # do number 2
> array_y_set_initial[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_rad_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_ord_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_rad_test_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_ord_test_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=20) do # do number 1
> term := 1;
> while (term <= 20) do # do number 2
> array_fact_2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> # before symbols initialized
> #BEGIN SYMBOLS INITIALIZATED
> zero_ats_ar(array_y);
> zero_ats_ar(array_x);
> zero_ats_ar(array_tmp0);
> zero_ats_ar(array_tmp1);
> zero_ats_ar(array_tmp2);
> zero_ats_ar(array_tmp3);
> zero_ats_ar(array_tmp4);
> zero_ats_ar(array_tmp5);
> zero_ats_ar(array_tmp6);
> 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_3D0);
> array_const_3D0[1] := c(3.0);
> zero_ats_ar(array_m1);
> array_m1[1] := glob__m1;
> #END SYMBOLS INITIALIZATED
> # before generate factorials init
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= ATS_MAX_TERMS) do # do number 1
> jjjf := 0;
> while (jjjf <= ATS_MAX_TERMS) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Table
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> glob_yes_pole := 4;
> glob_no_pole := 3;
> glob_not_given := 0;
> glob_no_sing_tests := 4;
> glob_ratio_test := 1;
> glob_three_term_test := 2;
> glob_six_term_test := 3;
> glob_log_10 := log(c(10.0));
> MAX_UNCHANGED := 10;
> glob__small := c(0.1e-50);
> glob_small_float := c(0.1e-50);
> glob_smallish_float := c(0.1e-60);
> glob_large_float := c(1.0e100);
> glob_larger_float := c(1.1e100);
> glob__m2 := c(-2);
> glob__m1 := c(-1);
> glob__0 := c(0);
> glob__1 := c(1);
> glob__2 := c(2);
> glob__3 := c(3);
> glob__4 := c(4);
> glob__5 := c(5);
> glob__8 := c(8);
> glob__10 := c(10);
> glob__100 := c(100);
> glob__pi := c(0.0);
> glob__0_5 := c(0.5);
> glob__0_8 := c(0.8);
> glob__m0_8 := c(-0.8);
> glob__0_25 := c(0.25);
> glob__0_125 := c(0.125);
> glob_h := 0.1;
> glob_nxt := 1;
> glob_prec := c(1.0e-16);
> glob_check_sign := c(1.0);
> glob_desired_digits_correct := c(8.0);
> glob_max_estimated_step_error := c(0.0);
> glob_ratio_of_radius := c(0.1);
> glob_percent_done := c(0.0);
> glob_total_exp_sec := c(0.1);
> glob_optimal_expect_sec := c(0.1);
> glob_estimated_size_answer := c(100.0);
> glob_almost_1 := c(0.9990);
> glob_clock_sec := c(0.0);
> glob_clock_start_sec := c(0.0);
> glob_disp_incr := c(0.1);
> glob_diff_rc_fm := c(0.1);
> glob_diff_rc_fmm1 := c(0.1);
> glob_diff_rc_fmm2 := c(0.1);
> glob_diff_ord_fm := c(0.1);
> glob_diff_ord_fmm1 := c(0.1);
> glob_diff_ord_fmm2 := c(0.1);
> glob_six_term_ord_save := c(0.1);
> glob_guess_error_rc := c(0.1);
> glob_guess_error_ord := c(0.1);
> glob_least_given_sing := c(9.9e200);
> glob_least_ratio_sing := c(9.9e200);
> glob_least_3_sing := c(9.9e100);
> glob_least_6_sing := c(9.9e100);
> glob_last_good_h := c(0.1);
> glob_max_h := c(0.1);
> glob_min_h := c(0.000001);
> glob_display_interval := c(0.1);
> glob_abserr := c(0.1e-10);
> glob_relerr := c(0.1e-10);
> glob_min_pole_est := c(0.1e+10);
> glob_max_rel_trunc_err := c(0.1e-10);
> glob_max_trunc_err := c(0.1e-10);
> glob_max_hours := c(0.0);
> glob_optimal_clock_start_sec := c(0.0);
> glob_optimal_start := c(0.0);
> glob_upper_ratio_limit := c(1.0001);
> glob_lower_ratio_limit := c(0.9999);
> glob_max_sec := c(10000.0);
> glob_orig_start_sec := c(0.0);
> glob_normmax := c(0.0);
> glob_max_minutes := c(0.0);
> glob_next_display := c(0.0);
> glob_est_digits := 1;
> glob_subiter_method := 3;
> glob_html_log := true;
> glob_min_good_digits := 99999;
> glob_good_digits := 0;
> glob_min_apfp_est_good_digits := 99999;
> glob_apfp_est_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> glob_h_reason := 0;
> glob_sec_in_minute := 60 ;
> glob_min_in_hour := 60;
> glob_hours_in_day := 24;
> glob_days_in_year := 365;
> glob_sec_in_hour := 3600;
> glob_sec_in_day := 86400;
> glob_sec_in_year := 31536000;
> glob_not_yet_finished := true;
> glob_initial_pass := true;
> glob_not_yet_start_msg := true;
> glob_reached_optimal_h := false;
> glob_optimal_done := false;
> glob_type_given_pole := 0;
> glob_optimize := false;
> glob_look_poles := false;
> glob_dump_closed_form := false;
> glob_max_iter := 10000;
> glob_no_eqs := 0;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_start := 0;
> glob_iter := 0;
> # before generate set diff initial
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> # before generate init omniout const
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> ATS_MAX_TERMS := 20;
> glob_iolevel := INFO;
> # set default block
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> glob_display_flag := true;
> glob_no_eqs := 1;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 10000;
> glob_max_hours := (0.0);
> glob_max_minutes := (15.0);
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/sing5postcpx.cpx#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = neg ( 3.0 ) / x / x / x / x ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=20;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := -1.1 + 0.1 * I;");
> omniout_str(ALWAYS,"x_end := 99.0 + 99.0 * I;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_h := c(0.001);");
> omniout_str(ALWAYS,"glob_min_h := c(0.001);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_type_given_pole := 1;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_rad_poles[1,1] := c(0.0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_rad_poles[1,2] := c(0.0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_ord_poles[1,1] := c(4.0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_ord_poles[1,2] := c(0.0);");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=8;");
> omniout_str(ALWAYS,"glob_max_minutes:=(3.0);");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"glob_max_iter:=10000;");
> omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);");
> omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);");
> omniout_str(ALWAYS,"glob_look_poles:=true;");
> omniout_str(ALWAYS,"glob_h:=c(0.001);");
> omniout_str(ALWAYS,"glob_display_interval:=c(0.01);");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"return(c(1.0)/c(x)/c(x)/c(x));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"next_delta := proc()");
> omniout_str(ALWAYS,"global glob_nxt, x_delta;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"x_delta := [ 0.001 + 0.00004 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.000 + 0.000 * I ];");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_nxt := glob_nxt + 1;");
> omniout_str(ALWAYS,"it := x_delta[glob_nxt];");
> omniout_str(ALWAYS,"return it;");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := glob__0;
> glob_smallish_float := glob__0;
> glob_large_float := c(1.0e100);
> glob_larger_float := c( 1.1e100);
> glob_almost_1 := c( 0.99);
> # before second block
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #BEGIN BLOCK 2
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := -1.1 + 0.1 * I;
> x_end := 99.0 + 99.0 * I;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_max_h := c(0.001);
> glob_min_h := c(0.001);
> glob_type_given_pole := 1;
> array_given_rad_poles[1,1] := c(0.0);
> array_given_rad_poles[1,2] := c(0.0);
> array_given_ord_poles[1,1] := c(4.0);
> array_given_ord_poles[1,2] := c(0.0);
> #END SECOND INPUT BLOCK
> #BEGIN OVERRIDE BLOCK
> glob_desired_digits_correct:=8;
> glob_max_minutes:=(3.0);
> glob_subiter_method:=3;
> glob_max_iter:=10000;
> glob_upper_ratio_limit:=c(1.000001);
> glob_lower_ratio_limit:=c(0.999999);
> glob_look_poles:=true;
> glob_h:=c(0.001);
> glob_display_interval:=c(0.01);
> #END OVERRIDE BLOCK
> #END BLOCK 2
> #END SECOND INPUT BLOCK
> #BEGIN INITS AFTER SECOND INPUT BLOCK
> glob_last_good_h := glob_h;
> glob_max_sec := (60.0) * (glob_max_minutes) + (3600.0) * (glob_max_hours);
> # after second input block
> found_h := true;
> glob_h := next_delta();
> #START ADJUST ALL SERIES
> if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 9
> h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius;
> omniout_str(ALWAYS,"SETTING H FOR POLE");
> glob_h_reason := 6;
> if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 10
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> h_new := glob_min_h;
> glob_h_reason := 5;
> fi;# end if 10;
> term := 1;
> ratio := c(1.0);
> while (term <= ATS_MAX_TERMS) do # do number 1
> array_y[term] := array_y[term]* ratio;
> array_y_higher[1,term] := array_y_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / float_abs(glob_h);
> term := term + 1;
> od;# end do number 1;
> glob_h := h_new;
> fi;# end if 9;
> #BOTTOM ADJUST ALL SERIES
> #END OPTIMIZE CODE
> if (glob_html_log) then # if number 9
> html_log_file := fopen("entry.html",WRITE,TEXT);
> fi;# end if 9;
> #BEGIN SOLUTION CODE
> found_h := true;
> if (found_h) then # if number 9
> omniout_str(ALWAYS,"START of Soultion");
> #Start Series -- INITIALIZE FOR SOLUTION
> array_x[1] := c(x_start);
> array_x[2] := c(glob_h);
> glob_next_display := c(x_start);
> glob_min_pole_est := glob_larger_float;
> glob_least_given_sing := glob_larger_float;
> glob_least_ratio_sing := glob_larger_float;
> glob_least_3_sing := glob_larger_float;
> glob_least_6_sing := glob_larger_float;
> order_diff := 1;
> #Start Series array_y
> term_no := 1;
> while (term_no <= order_diff) do # do number 1
> array_y[term_no] := array_y_init[term_no] * expt(glob_h , c(term_no - 1)) / c(factorial_1(term_no - 1));
> term_no := term_no + 1;
> od;# end do number 1;
> rows := order_diff;
> r_order := 1;
> while (r_order <= rows) do # do number 1
> term_no := 1;
> while (term_no <= (rows - r_order + 1)) do # do number 2
> it := term_no + r_order - 1;
> if (term_no < ATS_MAX_TERMS) then # if number 10
> array_y_higher[r_order,term_no] := array_y_init[it]* expt(glob_h , c(term_no - 1)) / (c(factorial_1(term_no - 1)));
> fi;# end if 10;
> term_no := term_no + 1;
> od;# end do number 2;
> r_order := r_order + 1;
> od;# end do number 1
> ;
> current_iter := 1;
> glob_clock_start_sec := elapsed_time_seconds();
> glob_clock_sec := elapsed_time_seconds();
> glob_iter := 0;
> omniout_str(DEBUGL," ");
> glob_reached_optimal_h := true;
> found_h := true;
> glob_h := next_delta();
> #START ADJUST ALL SERIES
> if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 10
> h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius;
> omniout_str(ALWAYS,"SETTING H FOR POLE");
> glob_h_reason := 6;
> if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 11
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> h_new := glob_min_h;
> glob_h_reason := 5;
> fi;# end if 11;
> term := 1;
> ratio := c(1.0);
> while (term <= ATS_MAX_TERMS) do # do number 1
> array_y[term] := array_y[term]* ratio;
> array_y_higher[1,term] := array_y_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / float_abs(glob_h);
> term := term + 1;
> od;# end do number 1;
> glob_h := h_new;
> fi;# end if 10;
> #BOTTOM ADJUST ALL SERIES
> #END OPTIMIZE CODE
> glob_optimal_clock_start_sec := elapsed_time_seconds();
> while ((glob_iter < glob_max_iter) and ((glob_iter < 10) or ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0))))) do # do number 1
> #left paren 0001C
> if (true) then # if number 10
> omniout_str(INFO," ");
> fi;# end if 10;
> found_h := true;
> glob_h := next_delta();
> #START ADJUST ALL SERIES
> if (float_abs(glob_min_pole_est) * glob_ratio_of_radius < float_abs(glob_h)) then # if number 10
> h_new := glob_check_sign * glob_min_pole_est * glob_ratio_of_radius;
> omniout_str(ALWAYS,"SETTING H FOR POLE");
> glob_h_reason := 6;
> if (glob_check_sign * glob_min_h > glob_check_sign * h_new) then # if number 11
> omniout_str(ALWAYS,"SETTING H FOR MIN H");
> h_new := glob_min_h;
> glob_h_reason := 5;
> fi;# end if 11;
> term := 1;
> ratio := c(1.0);
> while (term <= ATS_MAX_TERMS) do # do number 2
> array_y[term] := array_y[term]* ratio;
> array_y_higher[1,term] := array_y_higher[1,term]* ratio;
> array_x[term] := array_x[term]* ratio;
> ratio := ratio * h_new / float_abs(glob_h);
> term := term + 1;
> od;# end do number 2;
> glob_h := h_new;
> fi;# end if 10;
> #BOTTOM ADJUST ALL SERIES
> #END OPTIMIZE CODE
> glob_iter := glob_iter + 1;
> glob_clock_sec := elapsed_time_seconds();
> atomall();
> if ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0))) then # if number 10
> display_alot(current_iter);
> fi;# end if 10;
> if ((glob_look_poles) and ( not ((Re(glob_h) = 0.0) and (Im(glob_h) = 0.0)))) then # if number 10
> check_for_pole();
> fi;# end if 10;
> if (true) then # if number 10
> glob_next_display := glob_next_display + glob_display_interval;
> fi;# end if 10;
> array_x[1] := array_x[1] + glob_h;
> array_x[2] := glob_h;
> #Jump Series array_y;
> order_diff := 2;
> #START PART 1 SUM AND ADJUST
> #START SUM AND ADJUST EQ =1
> #sum_and_adjust array_y
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 2;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[2,iii] := array_y_higher[2,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 2;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 2;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 1;
> calc_term := 2;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #BEFORE ADJUST SUBSERIES EQ =1
> ord := 1;
> calc_term := 1;
> #adjust_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> array_y_higher_work[1,iii] := array_y_higher[1,iii] / expt(glob_h , c(calc_term - 1)) / c(factorial_3(iii - calc_term , iii - 1));
> iii := iii - 1;
> od;# end do number 2;
> #AFTER ADJUST SUBSERIES EQ =1
> #BEFORE SUM SUBSERIES EQ =1
> temp_sum := glob__0;
> ord := 1;
> calc_term := 1;
> #sum_subseriesarray_y
> iii := ATS_MAX_TERMS;
> while (iii >= calc_term) do # do number 2
> temp_sum := temp_sum + array_y_higher_work[ord,iii];
> iii := iii - 1;
> od;# end do number 2;
> array_y_higher_work2[ord,calc_term] := temp_sum * expt(glob_h , c(calc_term - 1)) / c(factorial_1(calc_term - 1));
> #AFTER SUM SUBSERIES EQ =1
> #END SUM AND ADJUST EQ =1
> #END PART 1
> #START PART 2 MOVE TERMS to REGULAR Array
> term_no := ATS_MAX_TERMS;
> while (term_no >= 1) do # do number 2
> array_y[term_no] := array_y_higher_work2[1,term_no];
> ord := 1;
> while (ord <= order_diff) do # do number 3
> array_y_higher[ord,term_no] := array_y_higher_work2[ord,term_no];
> ord := ord + 1;
> od;# end do number 3;
> term_no := term_no - 1;
> od;# end do number 2;
> #END PART 2 HEVE MOVED TERMS to REGULAR Array
> ;
> od;# end do number 1;#right paren 0001C
> omniout_str(ALWAYS,"Finished!");
> if (glob_iter >= glob_max_iter) then # if number 10
> omniout_str(ALWAYS,"Maximum Iterations Reached before Solution Completed!");
> fi;# end if 10;
> if (elapsed_time_seconds() - (glob_orig_start_sec) >= (glob_max_sec )) then # if number 10
> omniout_str(ALWAYS,"Maximum Time Reached before Solution Completed!");
> fi;# end if 10;
> glob_clock_sec := elapsed_time_seconds();
> omniout_str(INFO,"diff ( y , x , 1 ) = neg ( 3.0 ) / x / x / x / x ; ");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 10
> logstart(html_log_file);
> logitem_str(html_log_file,"2017-11-26T16:24:17-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"sing5")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = neg ( 3.0 ) / x / x / x / x ; ")
> ;
> logitem_complex(html_log_file,x_start)
> ;
> logitem_complex(html_log_file,x_end)
> ;
> logitem_complex(html_log_file,array_x[1])
> ;
> logitem_complex(html_log_file,glob_h)
> ;
> logitem_h_reason(html_log_file)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> glob_desired_digits_correct := 0.0;
> logitem_float(html_log_file,glob_desired_digits_correct)
> ;
> if (array_est_digits[1] <> -16) then # if number 11
> logitem_integer(html_log_file,array_est_digits[1])
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_min_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_min_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> logitem_integer(html_log_file,ATS_MAX_TERMS)
> ;
> if (glob_type_given_pole = 0) then # if number 11
> logitem_str(html_log_file,"Not Given")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 4) then # if number 12
> logitem_str(html_log_file,"No Solution")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 5) then # if number 13
> logitem_str(html_log_file,"Some Pole")
> ;
> logitem_str(html_log_file,"????")
> ;
> elif
> (glob_type_given_pole = 3) then # if number 14
> logitem_str(html_log_file,"No Pole")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 1) then # if number 15
> logitem_str(html_log_file,"Real Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> elif
> (glob_type_given_pole = 2) then # if number 16
> logitem_str(html_log_file,"Complex Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> fi;# end if 16;
> if (glob_least_ratio_sing < glob_large_float) then # if number 16
> glob_least_ratio_sing := 0;
> logitem_float(html_log_file,glob_least_ratio_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_3_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_3_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_6_sing < glob_large_float) then # if number 16
> glob_least_6_sing := 0.0;
> logitem_float(html_log_file,glob_least_6_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_time(html_log_file,(glob_clock_sec))
> ;
> if (c(glob_percent_done) < glob__100) then # if number 16
> logitem_time(html_log_file,(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 16;
> log_revs(html_log_file," 309 | ")
> ;
> logitem_str(html_log_file,"sing5 diffeq.mxt")
> ;
> logitem_str(html_log_file,"sing5 maple results")
> ;
> logitem_str(html_log_file,"Poor Accuracy")
> ;
> 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_3D0,
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, array_m1, array_y_higher,
array_y_higher_work, array_y_higher_work2, array_y_set_initial,
array_given_rad_poles, array_given_ord_poles, array_rad_test_poles,
array_ord_test_poles, array_fact_2, ATS_MAX_TERMS, glob_last;
ATS_MAX_TERMS := 20;
Digits := 32;
max_terms := 20;
glob_html_log := true;
array_y_init := Array(0 .. 20, []);
array_norms := Array(0 .. 20, []);
array_fact_1 := Array(0 .. 20, []);
array_1st_rel_error := Array(0 .. 2, []);
array_last_rel_error := Array(0 .. 2, []);
array_est_rel_error := Array(0 .. 2, []);
array_max_est_error := Array(0 .. 2, []);
array_type_pole := Array(0 .. 2, []);
array_type_real_pole := Array(0 .. 2, []);
array_type_complex_pole := Array(0 .. 2, []);
array_est_digits := Array(0 .. 2, []);
array_y := Array(0 .. 20, []);
array_x := Array(0 .. 20, []);
array_tmp0 := Array(0 .. 20, []);
array_tmp1 := Array(0 .. 20, []);
array_tmp2 := Array(0 .. 20, []);
array_tmp3 := Array(0 .. 20, []);
array_tmp4 := Array(0 .. 20, []);
array_tmp5 := Array(0 .. 20, []);
array_tmp6 := Array(0 .. 20, []);
array_m1 := Array(0 .. 20, []);
array_y_higher := Array(0 .. 2, 0 .. 21, []);
array_y_higher_work := Array(0 .. 2, 0 .. 21, []);
array_y_higher_work2 := Array(0 .. 2, 0 .. 21, []);
array_y_set_initial := Array(0 .. 2, 0 .. 21, []);
array_given_rad_poles := Array(0 .. 2, 0 .. 4, []);
array_given_ord_poles := Array(0 .. 2, 0 .. 4, []);
array_rad_test_poles := Array(0 .. 2, 0 .. 5, []);
array_ord_test_poles := Array(0 .. 2, 0 .. 5, []);
array_fact_2 := Array(0 .. 20, 0 .. 21, []);
term := 1;
while term <= 20 do array_y_init[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 20 do array_norms[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 20 do array_fact_1[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_1st_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do
array_last_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_est_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_max_est_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_type_pole[term] := 0; term := term + 1 end do;
term := 1;
while term <= 2 do array_type_real_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 2 do array_type_complex_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 2 do array_est_digits[term] := 0; term := term + 1 end do
;
term := 1;
while term <= 20 do array_y[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_x[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_tmp0[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_tmp1[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_tmp2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_tmp3[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_tmp4[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_tmp5[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_tmp6[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_m1[term] := c(0.); term := term + 1 end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 20 do
array_y_higher[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 20 do
array_y_higher_work[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 20 do
array_y_higher_work2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 20 do
array_y_set_initial[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_rad_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_ord_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 4 do
array_rad_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 4 do
array_ord_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 20 do
term := 1;
while term <= 20 do
array_fact_2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
zero_ats_ar(array_y);
zero_ats_ar(array_x);
zero_ats_ar(array_tmp0);
zero_ats_ar(array_tmp1);
zero_ats_ar(array_tmp2);
zero_ats_ar(array_tmp3);
zero_ats_ar(array_tmp4);
zero_ats_ar(array_tmp5);
zero_ats_ar(array_tmp6);
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_3D0);
array_const_3D0[1] := c(3.0);
zero_ats_ar(array_m1);
array_m1[1] := glob__m1;
iiif := 0;
while iiif <= ATS_MAX_TERMS do
jjjf := 0;
while jjjf <= ATS_MAX_TERMS do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
glob_yes_pole := 4;
glob_no_pole := 3;
glob_not_given := 0;
glob_no_sing_tests := 4;
glob_ratio_test := 1;
glob_three_term_test := 2;
glob_six_term_test := 3;
glob_log_10 := log(c(10.0));
MAX_UNCHANGED := 10;
glob__small := c(0.1*10^(-50));
glob_small_float := c(0.1*10^(-50));
glob_smallish_float := c(0.1*10^(-60));
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob__m2 := c(-2);
glob__m1 := c(-1);
glob__0 := c(0);
glob__1 := c(1);
glob__2 := c(2);
glob__3 := c(3);
glob__4 := c(4);
glob__5 := c(5);
glob__8 := c(8);
glob__10 := c(10);
glob__100 := c(100);
glob__pi := c(0.);
glob__0_5 := c(0.5);
glob__0_8 := c(0.8);
glob__m0_8 := c(-0.8);
glob__0_25 := c(0.25);
glob__0_125 := c(0.125);
glob_h := 0.1;
glob_nxt := 1;
glob_prec := c(0.10*10^(-15));
glob_check_sign := c(1.0);
glob_desired_digits_correct := c(8.0);
glob_max_estimated_step_error := c(0.);
glob_ratio_of_radius := c(0.1);
glob_percent_done := c(0.);
glob_total_exp_sec := c(0.1);
glob_optimal_expect_sec := c(0.1);
glob_estimated_size_answer := c(100.0);
glob_almost_1 := c(0.9990);
glob_clock_sec := c(0.);
glob_clock_start_sec := c(0.);
glob_disp_incr := c(0.1);
glob_diff_rc_fm := c(0.1);
glob_diff_rc_fmm1 := c(0.1);
glob_diff_rc_fmm2 := c(0.1);
glob_diff_ord_fm := c(0.1);
glob_diff_ord_fmm1 := c(0.1);
glob_diff_ord_fmm2 := c(0.1);
glob_six_term_ord_save := c(0.1);
glob_guess_error_rc := c(0.1);
glob_guess_error_ord := c(0.1);
glob_least_given_sing := c(0.99*10^201);
glob_least_ratio_sing := c(0.99*10^201);
glob_least_3_sing := c(0.99*10^101);
glob_least_6_sing := c(0.99*10^101);
glob_last_good_h := c(0.1);
glob_max_h := c(0.1);
glob_min_h := c(0.1*10^(-5));
glob_display_interval := c(0.1);
glob_abserr := c(0.1*10^(-10));
glob_relerr := c(0.1*10^(-10));
glob_min_pole_est := c(0.1*10^10);
glob_max_rel_trunc_err := c(0.1*10^(-10));
glob_max_trunc_err := c(0.1*10^(-10));
glob_max_hours := c(0.);
glob_optimal_clock_start_sec := c(0.);
glob_optimal_start := c(0.);
glob_upper_ratio_limit := c(1.0001);
glob_lower_ratio_limit := c(0.9999);
glob_max_sec := c(10000.0);
glob_orig_start_sec := c(0.);
glob_normmax := c(0.);
glob_max_minutes := c(0.);
glob_next_display := c(0.);
glob_est_digits := 1;
glob_subiter_method := 3;
glob_html_log := true;
glob_min_good_digits := 99999;
glob_good_digits := 0;
glob_min_apfp_est_good_digits := 99999;
glob_apfp_est_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
glob_h_reason := 0;
glob_sec_in_minute := 60;
glob_min_in_hour := 60;
glob_hours_in_day := 24;
glob_days_in_year := 365;
glob_sec_in_hour := 3600;
glob_sec_in_day := 86400;
glob_sec_in_year := 31536000;
glob_not_yet_finished := true;
glob_initial_pass := true;
glob_not_yet_start_msg := true;
glob_reached_optimal_h := false;
glob_optimal_done := false;
glob_type_given_pole := 0;
glob_optimize := false;
glob_look_poles := false;
glob_dump_closed_form := false;
glob_max_iter := 10000;
glob_no_eqs := 0;
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_start := 0;
glob_iter := 0;
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
ATS_MAX_TERMS := 20;
glob_iolevel := INFO;
glob_orig_start_sec := elapsed_time_seconds();
glob_display_flag := true;
glob_no_eqs := 1;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 10000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/sing5postcpx.cpx#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = neg ( 3.0 ) /\
x / x / x / x ; ");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=20;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := -1.1 + 0.1 * I;");
omniout_str(ALWAYS, "x_end := 99.0 + 99.0 * I;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_h := c(0.001);");
omniout_str(ALWAYS, "glob_min_h := c(0.001);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_type_given_pole := 1;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_rad_poles[1,1] := c(0.0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_rad_poles[1,2] := c(0.0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_ord_poles[1,1] := c(4.0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_ord_poles[1,2] := c(0.0);");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=8;");
omniout_str(ALWAYS, "glob_max_minutes:=(3.0);");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "glob_max_iter:=10000;");
omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);");
omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);");
omniout_str(ALWAYS, "glob_look_poles:=true;");
omniout_str(ALWAYS, "glob_h:=c(0.001);");
omniout_str(ALWAYS, "glob_display_interval:=c(0.01);");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "return(c(1.0)/c(x)/c(x)/c(x));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "next_delta := proc()");
omniout_str(ALWAYS, "global glob_nxt, x_delta;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "x_delta := [ 0.001 + 0.00004 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
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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, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.000 + 0.000 * I ];");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_nxt := glob_nxt + 1;");
omniout_str(ALWAYS, "it := x_delta[glob_nxt];");
omniout_str(ALWAYS, "return it;");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := glob__0;
glob_smallish_float := glob__0;
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob_almost_1 := c(0.99);
x_start := -1.1 + 0.1*I;
x_end := 99.0 + 99.0*I;
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_h := c(0.001);
glob_min_h := c(0.001);
glob_type_given_pole := 1;
array_given_rad_poles[1, 1] := c(0.);
array_given_rad_poles[1, 2] := c(0.);
array_given_ord_poles[1, 1] := c(4.0);
array_given_ord_poles[1, 2] := c(0.);
glob_desired_digits_correct := 8;
glob_max_minutes := 3.0;
glob_subiter_method := 3;
glob_max_iter := 10000;
glob_upper_ratio_limit := c(1.000001);
glob_lower_ratio_limit := c(0.999999);
glob_look_poles := true;
glob_h := c(0.001);
glob_display_interval := c(0.01);
glob_last_good_h := glob_h;
glob_max_sec := 60.0*glob_max_minutes + 3600.0*glob_max_hours;
found_h := true;
glob_h := next_delta();
if
float_abs(glob_min_pole_est)*glob_ratio_of_radius < float_abs(glob_h)
then
h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius;
omniout_str(ALWAYS, "SETTING H FOR POLE");
glob_h_reason := 6;
if glob_check_sign*h_new < glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
h_new := glob_min_h;
glob_h_reason := 5
end if;
term := 1;
ratio := c(1.0);
while term <= ATS_MAX_TERMS do
array_y[term] := array_y[term]*ratio;
array_y_higher[1, term] := array_y_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/float_abs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
if glob_html_log then html_log_file := fopen("entry.html", WRITE, TEXT)
end if;
found_h := true;
if found_h then
omniout_str(ALWAYS, "START of Soultion");
array_x[1] := c(x_start);
array_x[2] := c(glob_h);
glob_next_display := c(x_start);
glob_min_pole_est := glob_larger_float;
glob_least_given_sing := glob_larger_float;
glob_least_ratio_sing := glob_larger_float;
glob_least_3_sing := glob_larger_float;
glob_least_6_sing := glob_larger_float;
order_diff := 1;
term_no := 1;
while term_no <= order_diff do
array_y[term_no] := array_y_init[term_no]*
expt(glob_h, c(term_no - 1))/c(factorial_1(term_no - 1));
term_no := term_no + 1
end do;
rows := order_diff;
r_order := 1;
while r_order <= rows do
term_no := 1;
while term_no <= rows - r_order + 1 do
it := term_no + r_order - 1;
if term_no < ATS_MAX_TERMS then
array_y_higher[r_order, term_no] := array_y_init[it]*
expt(glob_h, c(term_no - 1))/
c(factorial_1(term_no - 1))
end if;
term_no := term_no + 1
end do;
r_order := r_order + 1
end do;
current_iter := 1;
glob_clock_start_sec := elapsed_time_seconds();
glob_clock_sec := elapsed_time_seconds();
glob_iter := 0;
omniout_str(DEBUGL, " ");
glob_reached_optimal_h := true;
found_h := true;
glob_h := next_delta();
if float_abs(glob_min_pole_est)*glob_ratio_of_radius <
float_abs(glob_h) then
h_new := glob_check_sign*glob_min_pole_est*glob_ratio_of_radius
;
omniout_str(ALWAYS, "SETTING H FOR POLE");
glob_h_reason := 6;
if glob_check_sign*h_new < glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
h_new := glob_min_h;
glob_h_reason := 5
end if;
term := 1;
ratio := c(1.0);
while term <= ATS_MAX_TERMS do
array_y[term] := array_y[term]*ratio;
array_y_higher[1, term] := array_y_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/float_abs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
glob_optimal_clock_start_sec := elapsed_time_seconds();
while glob_iter < glob_max_iter and
(glob_iter < 10 or not (Re(glob_h) = 0. and Im(glob_h) = 0.)) do
omniout_str(INFO, " ");
found_h := true;
glob_h := next_delta();
if float_abs(glob_min_pole_est)*glob_ratio_of_radius <
float_abs(glob_h) then
h_new :=
glob_check_sign*glob_min_pole_est*glob_ratio_of_radius;
omniout_str(ALWAYS, "SETTING H FOR POLE");
glob_h_reason := 6;
if glob_check_sign*h_new < glob_check_sign*glob_min_h then
omniout_str(ALWAYS, "SETTING H FOR MIN H");
h_new := glob_min_h;
glob_h_reason := 5
end if;
term := 1;
ratio := c(1.0);
while term <= ATS_MAX_TERMS do
array_y[term] := array_y[term]*ratio;
array_y_higher[1, term] :=
array_y_higher[1, term]*ratio;
array_x[term] := array_x[term]*ratio;
ratio := ratio*h_new/float_abs(glob_h);
term := term + 1
end do;
glob_h := h_new
end if;
glob_iter := glob_iter + 1;
glob_clock_sec := elapsed_time_seconds();
atomall();
if not (Re(glob_h) = 0. and Im(glob_h) = 0.) then
display_alot(current_iter)
end if;
if
glob_look_poles and not (Re(glob_h) = 0. and Im(glob_h) = 0.)
then check_for_pole()
end if;
glob_next_display := glob_next_display + glob_display_interval;
array_x[1] := array_x[1] + glob_h;
array_x[2] := glob_h;
order_diff := 2;
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[2, iii] := array_y_higher[2, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 2;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 2;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
ord := 1;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
array_y_higher_work[1, iii] := array_y_higher[1, iii]/(
expt(glob_h, c(calc_term - 1))*
c(factorial_3(iii - calc_term, iii - 1)));
iii := iii - 1
end do;
temp_sum := glob__0;
ord := 1;
calc_term := 1;
iii := ATS_MAX_TERMS;
while calc_term <= iii do
temp_sum := temp_sum + array_y_higher_work[ord, iii];
iii := iii - 1
end do;
array_y_higher_work2[ord, calc_term] := temp_sum*
expt(glob_h, c(calc_term - 1))/
c(factorial_1(calc_term - 1));
term_no := ATS_MAX_TERMS;
while 1 <= term_no do
array_y[term_no] := array_y_higher_work2[1, term_no];
ord := 1;
while ord <= order_diff do
array_y_higher[ord, term_no] :=
array_y_higher_work2[ord, term_no];
ord := ord + 1
end do;
term_no := term_no - 1
end do
end do;
omniout_str(ALWAYS, "Finished!");
if glob_max_iter <= glob_iter then omniout_str(ALWAYS,
"Maximum Iterations Reached before Solution Completed!")
end if;
if glob_max_sec <= elapsed_time_seconds() - glob_orig_start_sec
then omniout_str(ALWAYS,
"Maximum Time Reached before Solution Completed!")
end if;
glob_clock_sec := elapsed_time_seconds();
omniout_str(INFO, "diff ( y , x , 1 ) = neg ( 3.0 ) \
/ x / x / x / x ; ");
omniout_int(INFO, "Iterations ", 32, glob_iter,
4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2017-11-26T16:24:17-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"sing5");
logitem_str(html_log_file, "diff ( y , x , 1 ) = ne\
g ( 3.0 ) / x / x / x / x ; ");
logitem_complex(html_log_file, x_start);
logitem_complex(html_log_file, x_end);
logitem_complex(html_log_file, array_x[1]);
logitem_complex(html_log_file, glob_h);
logitem_h_reason(html_log_file);
logitem_integer(html_log_file, Digits);
glob_desired_digits_correct := 0.;
logitem_float(html_log_file, glob_desired_digits_correct);
if array_est_digits[1] <> -16 then
logitem_integer(html_log_file, array_est_digits[1])
else logitem_str(html_log_file, "Unknown")
end if;
if glob_min_good_digits <> -16 then
logitem_integer(html_log_file, glob_min_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
if glob_good_digits <> -16 then
logitem_integer(html_log_file, glob_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
logitem_integer(html_log_file, ATS_MAX_TERMS);
if glob_type_given_pole = 0 then
logitem_str(html_log_file, "Not Given");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 4 then
logitem_str(html_log_file, "No Solution");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 5 then
logitem_str(html_log_file, "Some Pole");
logitem_str(html_log_file, "????")
elif glob_type_given_pole = 3 then
logitem_str(html_log_file, "No Pole");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 1 then
logitem_str(html_log_file, "Real Sing");
logitem_float(html_log_file, glob_least_given_sing)
elif glob_type_given_pole = 2 then
logitem_str(html_log_file, "Complex Sing");
logitem_float(html_log_file, glob_least_given_sing)
end if;
if glob_least_ratio_sing < glob_large_float then
glob_least_ratio_sing := 0;
logitem_float(html_log_file, glob_least_ratio_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_3_sing < glob_large_float then
logitem_float(html_log_file, glob_least_3_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_6_sing < glob_large_float then
glob_least_6_sing := 0.;
logitem_float(html_log_file, glob_least_6_sing)
else logitem_str(html_log_file, "NONE")
end if;
logitem_integer(html_log_file, glob_iter);
logitem_time(html_log_file, glob_clock_sec);
if c(glob_percent_done) < glob__100 then
logitem_time(html_log_file, glob_total_exp_sec); 0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 309 | ");
logitem_str(html_log_file,
"sing5 diffeq.mxt");
logitem_str(html_log_file,
"sing5 maple results")
;
logitem_str(html_log_file, "Poor Accuracy");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end if
end proc
# End Function number 12
> main();
memory used=3.9MB, alloc=40.3MB, time=0.08
##############ECHO OF PROBLEM#################
##############temp/sing5postcpx.cpx#################
diff ( y , x , 1 ) = neg ( 3.0 ) / x / x / x / x ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=20;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := -1.1 + 0.1 * I;
x_end := 99.0 + 99.0 * I;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_h := c(0.001);
glob_min_h := c(0.001);
glob_type_given_pole := 1;
array_given_rad_poles[1,1] := c(0.0);
array_given_rad_poles[1,2] := c(0.0);
array_given_ord_poles[1,1] := c(4.0);
array_given_ord_poles[1,2] := c(0.0);
#END SECOND INPUT BLOCK
#BEGIN OVERRIDE BLOCK
glob_desired_digits_correct:=8;
glob_max_minutes:=(3.0);
glob_subiter_method:=3;
glob_max_iter:=10000;
glob_upper_ratio_limit:=c(1.000001);
glob_lower_ratio_limit:=c(0.999999);
glob_look_poles:=true;
glob_h:=c(0.001);
glob_display_interval:=c(0.01);
#END OVERRIDE BLOCK
!
#BEGIN USER DEF BLOCK
exact_soln_y := proc(x)
return(c(1.0)/c(x)/c(x)/c(x));
end;
next_delta := proc()
global glob_nxt, x_delta;
x_delta := [ 0.001 + 0.00004 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.000 + 0.000 * I ];
glob_nxt := glob_nxt + 1;
it := x_delta[glob_nxt];
return it;
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = -1.1 0.1
h = 0.0001 0.005
y[1] (numeric) = -0.714817539794 -0.199355893225
y[1] (closed_form) = -0.714817539794 -0.199355893225
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 1.105
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.381
Order of pole (three term test) = 6.795e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0999 0.105
h = 0.0001 0.003
y[1] (numeric) = -0.71136408545 -0.208820511104
y[1] (closed_form) = -0.711347641449 -0.208812631546
absolute error = 1.823e-05
relative error = 0.00246 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.105
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6632
Order of pole (three term test) = 6.383e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0998 0.108
h = 0.001 0.001
y[1] (numeric) = -0.709257449737 -0.21447895692
y[1] (closed_form) = -0.709260641056 -0.214480673719
absolute error = 3.624e-06
relative error = 0.0004891 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.105
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5207
Order of pole (three term test) = 1.913e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0988 0.109
h = 0.001 0.003
y[1] (numeric) = -0.710334487206 -0.217110841881
y[1] (closed_form) = -0.710348881996 -0.217114058172
absolute error = 1.475e-05
relative error = 0.001986 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.104
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.469
Order of pole (three term test) = 1.165e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0978 0.112
h = 0.0001 0.004
y[1] (numeric) = -0.709850838814 -0.223484655234
y[1] (closed_form) = -0.709842429756 -0.223483746919
absolute error = 8.458e-06
relative error = 0.001137 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.103
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.396
Order of pole (three term test) = 7.448e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0977 0.116
h = 0.003 0.006
y[1] (numeric) = -0.706789664049 -0.230989659859
y[1] (closed_form) = -0.706774595329 -0.230970158053
absolute error = 2.465e-05
relative error = 0.003315 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.104
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.851
Order of pole (three term test) = 5.847e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0947 0.122
h = 0.0001 0.005
y[1] (numeric) = -0.707267618069 -0.244529588235
y[1] (closed_form) = -0.707197836135 -0.24457746166
absolute error = 8.462e-05
relative error = 0.01131 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.101
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8212
Order of pole (three term test) = 3.617e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0946 0.127
h = 0.0001 0.003
y[1] (numeric) = -0.702950618096 -0.2538095755
y[1] (closed_form) = -0.702924860879 -0.25382135644
absolute error = 2.832e-05
relative error = 0.00379 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.102
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6614
Order of pole (three term test) = 5.859e-30 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=36.0MB, alloc=40.3MB, time=0.47
x[1] = -1.0945 0.13
h = 0.001 0.001
y[1] (numeric) = -0.70036409565 -0.259336071196
y[1] (closed_form) = -0.700357144061 -0.259359544728
absolute error = 2.448e-05
relative error = 0.003278 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.102
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5193
Order of pole (three term test) = 1.135e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0935 0.131
h = 0.001 0.003
y[1] (numeric) = -0.701232680234 -0.262075075787
y[1] (closed_form) = -0.701236865798 -0.262101213077
absolute error = 2.647e-05
relative error = 0.003536 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.101
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.463
Order of pole (three term test) = 1.519e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0925 0.134
h = 0.0001 0.004
y[1] (numeric) = -0.700221563441 -0.268454332807
y[1] (closed_form) = -0.700203193324 -0.268473965125
absolute error = 2.689e-05
relative error = 0.003585 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.101
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.393
Order of pole (three term test) = 7.849e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0924 0.138
h = 0.003 0.006
y[1] (numeric) = -0.696522162102 -0.275758426215
y[1] (closed_form) = -0.696498998707 -0.275758642098
absolute error = 2.316e-05
relative error = 0.003092 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.101
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.846
Order of pole (three term test) = 7.640e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0894 0.144
h = 0.0001 0.005
y[1] (numeric) = -0.695889950439 -0.289425005993
y[1] (closed_form) = -0.695804754703 -0.289487423323
absolute error = 0.0001056
relative error = 0.01401 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.099
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8192
Order of pole (three term test) = 1.500e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0893 0.149
h = 0.0001 0.003
y[1] (numeric) = -0.69078182673 -0.298403519818
y[1] (closed_form) = -0.690744658119 -0.298434164613
absolute error = 4.817e-05
relative error = 0.006402 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.099
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6599
Order of pole (three term test) = 5.447e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0892 0.152
h = 0.001 0.001
y[1] (numeric) = -0.687725663464 -0.303747729078
y[1] (closed_form) = -0.687706205458 -0.303792074845
absolute error = 4.843e-05
relative error = 0.006441 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.1
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5181
Order of pole (three term test) = 1.036e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0882 0.153
h = 0.001 0.003
y[1] (numeric) = -0.688373352896 -0.306573115137
y[1] (closed_form) = -0.688364821134 -0.306621288733
absolute error = 4.892e-05
relative error = 0.006492 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.099
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.457
Order of pole (three term test) = 7.065e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0872 0.156
h = 0.0001 0.004
y[1] (numeric) = -0.686830640187 -0.3129034684
y[1] (closed_form) = -0.686800097584 -0.312942771337
absolute error = 4.978e-05
relative error = 0.006595 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.098
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.39
Order of pole (three term test) = 5.333e-31 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0871 0.16
h = 0.003 0.006
y[1] (numeric) = -0.682509668785 -0.319939532444
y[1] (closed_form) = -0.682476313036 -0.319958822158
absolute error = 3.853e-05
relative error = 0.005112 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.099
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.842
Order of pole (three term test) = 6.901e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0841 0.166
h = 0.0001 0.005
y[1] (numeric) = -0.680747623073 -0.333619088881
y[1] (closed_form) = -0.680645515316 -0.33369446943
absolute error = 0.0001269
relative error = 0.01674 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.097
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8176
Order of pole (three term test) = 2.520e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.084 0.171
h = 0.0001 0.003
y[1] (numeric) = -0.674875399394 -0.342212740656
y[1] (closed_form) = -0.674824804535 -0.342261187062
absolute error = 7.005e-05
relative error = 0.009258 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.097
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6587
Order of pole (three term test) = 7.260e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0839 0.174
h = 0.001 0.001
y[1] (numeric) = -0.671366136367 -0.347325303658
y[1] (closed_form) = -0.671331903067 -0.347389332702
absolute error = 7.261e-05
relative error = 0.009605 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.098
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5172
Order of pole (three term test) = 1.094e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0829 0.175
h = 0.001 0.003
y[1] (numeric) = -0.671782987406 -0.350214676036
y[1] (closed_form) = -0.67175932415 -0.350283675861
absolute error = 7.294e-05
relative error = 0.009628 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.097
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.453
Order of pole (three term test) = 2.003e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0819 0.178
h = 0.0001 0.004
y[1] (numeric) = -0.669711268499 -0.356440963756
y[1] (closed_form) = -0.66966643524 -0.356498784962
absolute error = 7.317e-05
relative error = 0.009644 %
Correct digits = 4
memory used=82.2MB, alloc=44.3MB, time=1.06
Radius of convergence (given) for eq 1 = 1.096
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.387
Order of pole (three term test) = 6.730e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0818 0.182
h = 0.003 0.006
y[1] (numeric) = -0.664793795451 -0.363143604535
y[1] (closed_form) = -0.66474821066 -0.363181059348
absolute error = 5.900e-05
relative error = 0.007789 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.097
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.839
Order of pole (three term test) = 4.797e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0788 0.188
h = 0.0001 0.005
y[1] (numeric) = -0.661896246173 -0.376719502055
y[1] (closed_form) = -0.661775927073 -0.376806083641
absolute error = 0.0001482
relative error = 0.01947 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.095
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8164
Order of pole (three term test) = 3.000e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0787 0.193
h = 0.0001 0.003
y[1] (numeric) = -0.655297412942 -0.384847951406
y[1] (closed_form) = -0.655231499226 -0.384912882179
absolute error = 9.252e-05
relative error = 0.01218 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.096
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6577
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0786 0.196
h = 0.001 0.001
y[1] (numeric) = -0.651357768931 -0.389681399813
y[1] (closed_form) = -0.651306631482 -0.389763631085
absolute error = 9.684e-05
relative error = 0.01276 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.096
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5165
Order of pole (three term test) = 9.361e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0776 0.197
h = 0.0001 0.004
y[1] (numeric) = -0.651536586016 -0.392611062178
y[1] (closed_form) = -0.651495519877 -0.392699364973
absolute error = 9.738e-05
relative error = 0.0128 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.095
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.099
Order of pole (three term test) = 1.129e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0775 0.201
h = 0.003 0.006
y[1] (numeric) = -0.646156271171 -0.398993621902
y[1] (closed_form) = -0.646096969702 -0.399037872033
absolute error = 7.399e-05
relative error = 0.009744 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.096
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.838
Order of pole (three term test) = 1.891e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0745 0.207
h = 0.0001 0.005
y[1] (numeric) = -0.642290953799 -0.412372772463
y[1] (closed_form) = -0.642152549182 -0.412459495091
absolute error = 0.0001633
relative error = 0.0214 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.094
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8158
Order of pole (three term test) = 1.789e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0744 0.212
h = 0.0001 0.003
y[1] (numeric) = -0.635111137989 -0.420032046612
y[1] (closed_form) = -0.635029035322 -0.420101980561
absolute error = 0.0001078
relative error = 0.01416 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.095
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6573
Order of pole (three term test) = 4.802e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0743 0.215
h = 0.001 0.001
y[1] (numeric) = -0.630827791591 -0.424584687879
y[1] (closed_form) = -0.630758912364 -0.424673221429
absolute error = 0.0001122
relative error = 0.01475 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.096
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5162
Order of pole (three term test) = 1.655e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0733 0.216
h = 0.001 0.003
y[1] (numeric) = -0.630798114566 -0.427526456561
y[1] (closed_form) = -0.630738755859 -0.427621951421
absolute error = 0.0001124
relative error = 0.01476 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.095
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.448
Order of pole (three term test) = 6.271e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0723 0.219
h = 0.0001 0.004
y[1] (numeric) = -0.627775175658 -0.433407646706
y[1] (closed_form) = -0.627696991241 -0.433487986267
absolute error = 0.0001121
relative error = 0.0147 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.094
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.385
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0722 0.223
h = 0.003 0.006
y[1] (numeric) = -0.621847850989 -0.439320764735
y[1] (closed_form) = -0.621772842938 -0.439380791589
absolute error = 9.607e-05
relative error = 0.01262 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.095
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.836
Order of pole (three term test) = 2.317e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0692 0.229
h = 0.0001 0.005
y[1] (numeric) = -0.616876451679 -0.452378659463
y[1] (closed_form) = -0.616718054029 -0.452472917095
absolute error = 0.0001843
relative error = 0.0241 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.093
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8152
Order of pole (three term test) = 4.293e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0691 0.234
h = 0.0001 0.003
y[1] (numeric) = -0.609066793022 -0.459437229646
y[1] (closed_form) = -0.608966322688 -0.459520563811
absolute error = 0.0001305
relative error = 0.01711 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.094
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6569
Order of pole (three term test) = 4.703e-30 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=128.2MB, alloc=44.3MB, time=1.64
x[1] = -1.069 0.237
h = 0.001 0.001
y[1] (numeric) = -0.604411223106 -0.463630928156
y[1] (closed_form) = -0.604322022024 -0.463734185255
absolute error = 0.0001365
relative error = 0.01791 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.095
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5159
Order of pole (three term test) = 4.528e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.068 0.238
h = 0.001 0.003
y[1] (numeric) = -0.604138337356 -0.466566812391
y[1] (closed_form) = -0.604057913129 -0.466677997521
absolute error = 0.0001372
relative error = 0.01798 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.094
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.447
Order of pole (three term test) = 1.232e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.067 0.241
h = 0.0001 0.004
y[1] (numeric) = -0.600632094266 -0.472190698446
y[1] (closed_form) = -0.600534462304 -0.472284820389
absolute error = 0.0001356
relative error = 0.01775 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.094
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.384
Order of pole (three term test) = 1.745e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0669 0.245
h = 0.003 0.006
y[1] (numeric) = -0.594224190268 -0.477604212776
y[1] (closed_form) = -0.594131825976 -0.477678412022
absolute error = 0.0001185
relative error = 0.01554 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.095
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.835
Order of pole (three term test) = 4.481e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0639 0.251
h = 0.0001 0.005
y[1] (numeric) = -0.588182434833 -0.490227279384
y[1] (closed_form) = -0.588003434859 -0.490326970589
absolute error = 0.0002049
relative error = 0.02676 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.093
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8149
Order of pole (three term test) = 1.424e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0638 0.256
h = 0.0001 0.003
y[1] (numeric) = -0.579807055953 -0.496621746727
y[1] (closed_form) = -0.579686872371 -0.496716552199
absolute error = 0.0001531
relative error = 0.02005 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.094
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6567
Order of pole (three term test) = 1.477e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0637 0.259
h = 0.001 0.001
y[1] (numeric) = -0.574817614135 -0.500419271191
y[1] (closed_form) = -0.574706592168 -0.500535073643
absolute error = 0.0001604
relative error = 0.02105 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.095
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5158
Order of pole (three term test) = 8.964e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0627 0.26
h = 0.001 0.003
y[1] (numeric) = -0.57430300096 -0.503324177362
y[1] (closed_form) = -0.574199896561 -0.503448777029
absolute error = 0.0001617
relative error = 0.02118 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.094
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.446
Order of pole (three term test) = 6.130e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0617 0.263
h = 0.0001 0.004
y[1] (numeric) = -0.570341813907 -0.50864172297
y[1] (closed_form) = -0.570223347044 -0.508747563142
absolute error = 0.0001589
relative error = 0.02079 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.094
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.384
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0616 0.267
h = 0.003 0.006
y[1] (numeric) = -0.563506907707 -0.513507966427
y[1] (closed_form) = -0.563395738529 -0.513594530671
absolute error = 0.0001409
relative error = 0.01848 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.095
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.835
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0586 0.273
h = 0.0001 0.005
y[1] (numeric) = -0.556444399546 -0.525587659476
y[1] (closed_form) = -0.556244452588 -0.525690633988
absolute error = 0.0002249
relative error = 0.02939 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.093
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.815
Order of pole (three term test) = 1.849e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0585 0.278
h = 0.0001 0.003
y[1] (numeric) = -0.547574890877 -0.531262975434
y[1] (closed_form) = -0.547433894644 -0.531367166511
absolute error = 0.0001753
relative error = 0.02298 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.094
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6569
Order of pole (three term test) = 4.795e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0584 0.281
h = 0.001 0.001
y[1] (numeric) = -0.542294281844 -0.534632088542
y[1] (closed_form) = -0.542160223527 -0.534758081527
absolute error = 0.000184
relative error = 0.02416 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.095
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5159
Order of pole (three term test) = 4.520e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0574 0.282
h = 0.001 0.003
y[1] (numeric) = -0.541542516447 -0.537481278469
y[1] (closed_form) = -0.541415415952 -0.537616824563
absolute error = 0.0001858
relative error = 0.02435 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.094
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.447
Order of pole (three term test) = 1.977e-29 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=174.3MB, alloc=44.3MB, time=2.22
x[1] = -1.0564 0.285
h = 0.0001 0.004
y[1] (numeric) = -0.537160622799 -0.542447299071
y[1] (closed_form) = -0.537020199667 -0.542562631709
absolute error = 0.0001817
relative error = 0.0238 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.094
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.384
Order of pole (three term test) = 7.871e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0563 0.289
h = 0.003 0.006
y[1] (numeric) = -0.529957797324 -0.546725589489
y[1] (closed_form) = -0.529826604195 -0.546822538265
absolute error = 0.0001631
relative error = 0.02142 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.095
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.836
Order of pole (three term test) = 1.284e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0533 0.295
h = 0.0001 0.005
y[1] (numeric) = -0.521937165517 -0.558160345525
y[1] (closed_form) = -0.521716193918 -0.558264442805
absolute error = 0.0002443
relative error = 0.03197 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.094
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8155
Order of pole (three term test) = 1.454e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0532 0.3
h = 0.0001 0.003
y[1] (numeric) = -0.51265130301 -0.563070804889
y[1] (closed_form) = -0.512488661309 -0.563182176048
absolute error = 0.0001971
relative error = 0.02589 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.095
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6573
Order of pole (three term test) = 6.786e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0531 0.303
h = 0.001 0.001
y[1] (numeric) = -0.507125818616 -0.565984836754
y[1] (closed_form) = -0.506967815192 -0.566118532228
absolute error = 0.000207
relative error = 0.02724 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.096
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5163
Order of pole (three term test) = 4.621e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0521 0.304
h = 0.0001 0.004
y[1] (numeric) = -0.506144485018 -0.568754369133
y[1] (closed_form) = -0.505992396753 -0.568898247285
absolute error = 0.0002094
relative error = 0.0275 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.095
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.098
Order of pole (three term test) = 1.250e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.052 0.308
h = 0.003 0.006
y[1] (numeric) = -0.498688759206 -0.572526520486
y[1] (closed_form) = -0.498541901775 -0.572622976197
absolute error = 0.0001757
relative error = 0.02314 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.096
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.838
Order of pole (three term test) = 1.047e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.049 0.314
h = 0.0001 0.005
y[1] (numeric) = -0.489911816375 -0.583321281081
y[1] (closed_form) = -0.489675351726 -0.583416902644
absolute error = 0.0002551
relative error = 0.03349 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.095
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8163
Order of pole (three term test) = 1.497e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0489 0.319
h = 0.0001 0.003
y[1] (numeric) = -0.48034318766 -0.587540869643
y[1] (closed_form) = -0.480163857333 -0.587648841313
absolute error = 0.0002093
relative error = 0.02758 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.096
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.658
Order of pole (three term test) = 1.113e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0488 0.322
h = 0.001 0.001
y[1] (numeric) = -0.474651847965 -0.590044286617
y[1] (closed_form) = -0.474475145891 -0.590174772961
absolute error = 0.0002197
relative error = 0.02901 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.097
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5169
Order of pole (three term test) = 4.799e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0478 0.323
h = 0.001 0.003
y[1] (numeric) = -0.473482480112 -0.592724441012
y[1] (closed_form) = -0.473310738784 -0.592865529714
absolute error = 0.0002223
relative error = 0.0293 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.096
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.452
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0468 0.326
h = 0.0001 0.004
y[1] (numeric) = -0.468431561692 -0.596928736414
y[1] (closed_form) = -0.468250690259 -0.597047659728
absolute error = 0.0002165
relative error = 0.02853 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.096
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.387
Order of pole (three term test) = 1.959e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0467 0.33
h = 0.003 0.006
y[1] (numeric) = -0.460723486833 -0.600028923184
y[1] (closed_form) = -0.460555050492 -0.600131731155
absolute error = 0.0001973
relative error = 0.02609 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.097
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.84
Order of pole (three term test) = 7.845e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0437 0.336
h = 0.0001 0.005
y[1] (numeric) = -0.451136381422 -0.610015358957
y[1] (closed_form) = -0.450879464578 -0.610108191084
absolute error = 0.0002732
relative error = 0.03601 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.096
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8174
Order of pole (three term test) = 1.593e-29 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=220.4MB, alloc=44.3MB, time=2.80
x[1] = -1.0436 0.341
h = 0.0001 0.003
y[1] (numeric) = -0.441307876125 -0.613413388656
y[1] (closed_form) = -0.441106131029 -0.613524253242
absolute error = 0.0002302
relative error = 0.03046 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.098
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.659
Order of pole (three term test) = 1.593e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0435 0.344
h = 0.001 0.001
y[1] (numeric) = -0.435464544231 -0.615428922524
y[1] (closed_form) = -0.435263100851 -0.615562286461
absolute error = 0.0002416
relative error = 0.03205 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.099
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5177
Order of pole (three term test) = 7.043e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0425 0.345
h = 0.001 0.003
y[1] (numeric) = -0.434087388992 -0.617988573138
y[1] (closed_form) = -0.433889763611 -0.618132909638
absolute error = 0.0002447
relative error = 0.0324 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.098
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.455
Order of pole (three term test) = 1.380e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0415 0.348
h = 0.0001 0.004
y[1] (numeric) = -0.428740448218 -0.621740640175
y[1] (closed_form) = -0.428536068657 -0.621862166194
absolute error = 0.0002378
relative error = 0.03148 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.098
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.389
Order of pole (three term test) = 3.948e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0414 0.352
h = 0.003 0.006
y[1] (numeric) = -0.420854078961 -0.62418147314
y[1] (closed_form) = -0.420663610131 -0.624288362504
absolute error = 0.0002184
relative error = 0.02901 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.099
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.843
Order of pole (three term test) = 5.126e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0384 0.358
h = 0.0001 0.005
y[1] (numeric) = -0.410549246497 -0.633287176292
y[1] (closed_form) = -0.410272520231 -0.633375235507
absolute error = 0.0002904
relative error = 0.03848 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.098
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8188
Order of pole (three term test) = 4.958e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0383 0.363
h = 0.0001 0.003
y[1] (numeric) = -0.400548023882 -0.635848062202
y[1] (closed_form) = -0.400323847855 -0.635959499329
absolute error = 0.0002503
relative error = 0.03331 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.1
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6602
Order of pole (three term test) = 5.524e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0382 0.366
h = 0.001 0.001
y[1] (numeric) = -0.394604323926 -0.637366892671
y[1] (closed_form) = -0.394378165719 -0.637500531204
absolute error = 0.0002627
relative error = 0.03504 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.101
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5186
Order of pole (three term test) = 1.512e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0372 0.367
h = 0.001 0.003
y[1] (numeric) = -0.393034467173 -0.639786603434
y[1] (closed_form) = -0.392810959458 -0.639931439289
absolute error = 0.0002663
relative error = 0.03547 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.1
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.46
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0362 0.37
h = 0.0001 0.004
y[1] (numeric) = -0.387441546233 -0.643062601157
y[1] (closed_form) = -0.387213696234 -0.643184281904
absolute error = 0.0002583
relative error = 0.03441 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.1
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.392
Order of pole (three term test) = 1.129e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0361 0.374
h = 0.003 0.006
y[1] (numeric) = -0.379446347949 -0.64483532367
y[1] (closed_form) = -0.379233677729 -0.644943998601
absolute error = 0.0002388
relative error = 0.03192 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.102
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.847
Order of pole (three term test) = 7.741e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0331 0.38
h = 0.0001 0.005
y[1] (numeric) = -0.368523414887 -0.653000384261
y[1] (closed_form) = -0.36822774191 -0.65308181091
absolute error = 0.0003067
relative error = 0.0409 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.101
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8206
Order of pole (three term test) = 1.772e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.033 0.385
h = 0.0001 0.003
y[1] (numeric) = -0.358436929922 -0.654719425041
y[1] (closed_form) = -0.358190589437 -0.654829152709
absolute error = 0.0002697
relative error = 0.03613 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.102
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6617
Order of pole (three term test) = 1.201e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0329 0.388
h = 0.001 0.001
y[1] (numeric) = -0.352444589767 -0.655739153866
y[1] (closed_form) = -0.352194064701 -0.655870514956
absolute error = 0.0002829
relative error = 0.038 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.103
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5198
Order of pole (three term test) = 5.756e-30 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=266.6MB, alloc=44.3MB, time=3.38
x[1] = -1.0319 0.389
h = 0.001 0.003
y[1] (numeric) = -0.350699186034 -0.658001682867
y[1] (closed_form) = -0.350450140275 -0.658144320518
absolute error = 0.000287
relative error = 0.03849 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.103
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.466
Order of pole (three term test) = 1.361e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0309 0.392
h = 0.0001 0.004
y[1] (numeric) = -0.344912267776 -0.66078428984
y[1] (closed_form) = -0.344661284385 -0.660903726183
absolute error = 0.000278
relative error = 0.03729 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.103
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.396
Order of pole (three term test) = 1.015e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0308 0.396
h = 0.003 0.006
y[1] (numeric) = -0.336877417568 -0.661888727517
y[1] (closed_form) = -0.336642659976 -0.661996908278
absolute error = 0.0002585
relative error = 0.0348 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.104
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.851
Order of pole (three term test) = 3.745e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0278 0.402
h = 0.0001 0.005
y[1] (numeric) = -0.325441273414 -0.669066458034
y[1] (closed_form) = -0.325127712556 -0.669139542723
absolute error = 0.000322
relative error = 0.04328 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.104
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8228
Order of pole (three term test) = 1.924e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0277 0.407
h = 0.0001 0.003
y[1] (numeric) = -0.315355735628 -0.669949614264
y[1] (closed_form) = -0.315087767843 -0.670055427857
absolute error = 0.0002881
relative error = 0.03891 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.105
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6635
Order of pole (three term test) = 9.147e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0276 0.41
h = 0.001 0.001
y[1] (numeric) = -0.30936568211 -0.670474121939
y[1] (closed_form) = -0.309091444527 -0.670600749355
absolute error = 0.0003021
relative error = 0.04091 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.106
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5213
Order of pole (three term test) = 1.404e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0266 0.411
h = 0.0001 0.004
y[1] (numeric) = -0.307463595321 -0.672564657345
y[1] (closed_form) = -0.307189682639 -0.672702498334
absolute error = 0.0003066
relative error = 0.04146 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.106
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.129
Order of pole (three term test) = 2.157e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0265 0.415
h = 0.003 0.006
y[1] (numeric) = -0.299447713905 -0.673128328184
y[1] (closed_form) = -0.2991997188 -0.673228873757
absolute error = 0.0002676
relative error = 0.03632 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.107
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.856
Order of pole (three term test) = 8.658e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0235 0.421
h = 0.0001 0.005
y[1] (numeric) = -0.287668625785 -0.679424850052
y[1] (closed_form) = -0.287346200771 -0.679484153707
absolute error = 0.0003278
relative error = 0.04444 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.107
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8251
Order of pole (three term test) = 9.410e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0234 0.426
h = 0.0001 0.003
y[1] (numeric) = -0.277660580858 -0.679602439311
y[1] (closed_form) = -0.277380132527 -0.679697790069
absolute error = 0.0002962
relative error = 0.04035 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.109
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6654
Order of pole (three term test) = 1.585e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0233 0.429
h = 0.001 0.001
y[1] (numeric) = -0.271717759269 -0.679709193265
y[1] (closed_form) = -0.271429377737 -0.679824446338
absolute error = 0.0003106
relative error = 0.04243 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.11
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5228
Order of pole (three term test) = 6.889e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0223 0.43
h = 0.001 0.003
y[1] (numeric) = -0.269699172237 -0.681640267879
y[1] (closed_form) = -0.269410153048 -0.681766558129
absolute error = 0.0003154
relative error = 0.04303 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.109
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.48
Order of pole (three term test) = 9.528e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0213 0.433
h = 0.0001 0.004
y[1] (numeric) = -0.263698321943 -0.683480541557
y[1] (closed_form) = -0.26341167264 -0.683584330259
absolute error = 0.0003049
relative error = 0.04161 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.109
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.404
Order of pole (three term test) = 1.246e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0212 0.437
h = 0.003 0.006
y[1] (numeric) = -0.255775478915 -0.683370562166
y[1] (closed_form) = -0.255506353272 -0.683466557475
absolute error = 0.0002857
relative error = 0.03916 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.111
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.862
Order of pole (three term test) = 1.319e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0182 0.443
h = 0.0001 0.005
y[1] (numeric) = -0.243685730307 -0.68863048589
y[1] (closed_form) = -0.243347830576 -0.688678754138
absolute error = 0.0003413
relative error = 0.04673 %
Correct digits = 3
memory used=312.7MB, alloc=44.3MB, time=3.97
Radius of convergence (given) for eq 1 = 1.11
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8278
Order of pole (three term test) = 6.621e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0181 0.448
h = 0.0001 0.003
y[1] (numeric) = -0.233830483533 -0.688010845633
y[1] (closed_form) = -0.23353008543 -0.688098519191
absolute error = 0.0003129
relative error = 0.04307 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.112
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6676
Order of pole (three term test) = 1.583e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.018 0.451
h = 0.001 0.001
y[1] (numeric) = -0.227979502685 -0.687645793844
y[1] (closed_form) = -0.227669386899 -0.687752149815
absolute error = 0.0003278
relative error = 0.04525 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.113
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5246
Order of pole (three term test) = 8.153e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.017 0.452
h = 0.001 0.003
y[1] (numeric) = -0.225842654087 -0.689384573205
y[1] (closed_form) = -0.225530828891 -0.689501658697
absolute error = 0.0003331
relative error = 0.04591 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.113
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.489
Order of pole (three term test) = 2.120e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.016 0.455
h = 0.0001 0.004
y[1] (numeric) = -0.219798624721 -0.690718859285
y[1] (closed_form) = -0.21949133108 -0.690814179027
absolute error = 0.0003217
relative error = 0.04439 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.113
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.409
Order of pole (three term test) = 9.864e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0159 0.459
h = 0.003 0.006
y[1] (numeric) = -0.212021772233 -0.68998514839
y[1] (closed_form) = -0.211732370926 -0.69007457281
absolute error = 0.0003029
relative error = 0.04196 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.115
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.869
Order of pole (three term test) = 8.024e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0129 0.465
h = 0.0001 0.005
y[1] (numeric) = -0.199730229245 -0.694200662404
y[1] (closed_form) = -0.199378316022 -0.694236719232
absolute error = 0.0003538
relative error = 0.04898 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.115
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8309
Order of pole (three term test) = 3.729e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0128 0.47
h = 0.0001 0.003
y[1] (numeric) = -0.190102719251 -0.692816923757
y[1] (closed_form) = -0.189783565298 -0.692895123289
absolute error = 0.0003286
relative error = 0.04574 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.117
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6702
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0127 0.473
h = 0.001 0.001
y[1] (numeric) = -0.18438770952 -0.691999890159
y[1] (closed_form) = -0.184057247344 -0.692095378237
absolute error = 0.000344
relative error = 0.04803 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.118
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5266
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0117 0.474
h = 0.001 0.003
y[1] (numeric) = -0.182154153606 -0.693539236275
y[1] (closed_form) = -0.181820977143 -0.693645029698
absolute error = 0.0003496
relative error = 0.04875 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.117
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.498
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0107 0.477
h = 0.0001 0.004
y[1] (numeric) = -0.176117528322 -0.694375026307
y[1] (closed_form) = -0.175790896321 -0.694460021415
absolute error = 0.0003375
relative error = 0.04711 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.118
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.414
Order of pole (three term test) = 3.468e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0106 0.481
h = 0.003 0.006
y[1] (numeric) = -0.168544254136 -0.693046522877
y[1] (closed_form) = -0.168235650633 -0.693127508074
absolute error = 0.0003191
relative error = 0.04473 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.119
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.876
Order of pole (three term test) = 4.256e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0076 0.487
h = 0.0001 0.005
y[1] (numeric) = -0.156157589612 -0.696222782519
y[1] (closed_form) = -0.155793206819 -0.696245657245
absolute error = 0.0003651
relative error = 0.05117 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.119
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8343
Order of pole (three term test) = 6.021e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0075 0.492
h = 0.0001 0.003
y[1] (numeric) = -0.146826676367 -0.694115863622
y[1] (closed_form) = -0.146490136929 -0.694182983482
absolute error = 0.0003432
relative error = 0.04837 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.121
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.673
Order of pole (three term test) = 2.040e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0074 0.495
h = 0.001 0.001
y[1] (numeric) = -0.141288148818 -0.692871224598
y[1] (closed_form) = -0.140938921129 -0.69295409765
absolute error = 0.0003589
relative error = 0.05076 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.122
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5288
Order of pole (three term test) = 9.961e-31 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=359.0MB, alloc=44.3MB, time=4.55
x[1] = -1.0064 0.496
h = 0.001 0.003
y[1] (numeric) = -0.13897962703 -0.694206720561
y[1] (closed_form) = -0.138626760382 -0.694299371507
absolute error = 0.0003648
relative error = 0.05153 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.122
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.509
Order of pole (three term test) = 4.122e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0054 0.499
h = 0.0001 0.004
y[1] (numeric) = -0.132998601266 -0.694557173256
y[1] (closed_form) = -0.132654117309 -0.694630196443
absolute error = 0.0003521
relative error = 0.04979 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.122
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.42
Order of pole (three term test) = 3.559e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0053 0.503
h = 0.003 0.006
y[1] (numeric) = -0.12568138147 -0.692668633569
y[1] (closed_form) = -0.125354839912 -0.692739488695
absolute error = 0.0003341
relative error = 0.04746 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.124
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.885
Order of pole (three term test) = 1.048e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0023 0.509
h = 0.0001 0.005
y[1] (numeric) = -0.113302399839 -0.694823000489
y[1] (closed_form) = -0.112927143794 -0.694831929805
absolute error = 0.0003754
relative error = 0.05332 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.124
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8381
Order of pole (three term test) = 1.869e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0022 0.514
h = 0.0001 0.003
y[1] (numeric) = -0.10433003674 -0.692040499176
y[1] (closed_form) = -0.103977626421 -0.692095141938
absolute error = 0.0003566
relative error = 0.05096 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.126
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.676
Order of pole (three term test) = 2.360e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0021 0.517
h = 0.001 0.001
y[1] (numeric) = -0.0990044048379 -0.690396527889
y[1] (closed_form) = -0.0986381476223 -0.69046528059
absolute error = 0.0003727
relative error = 0.05343 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.128
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5313
Order of pole (three term test) = 1.159e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0011 0.518
h = 0.0001 0.004
y[1] (numeric) = -0.0966424731973 -0.691526401658
y[1] (closed_form) = -0.0962717432822 -0.691604316223
absolute error = 0.0003788
relative error = 0.05425 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.127
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.189
Order of pole (three term test) = 1.990e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.001 0.522
h = 0.003 0.006
y[1] (numeric) = -0.0895704594449 -0.689209617783
y[1] (closed_form) = -0.089236306907 -0.689268473369
absolute error = 0.0003393
relative error = 0.04882 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.129
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.893
Order of pole (three term test) = 7.598e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.998 0.528
h = 0.0001 0.005
y[1] (numeric) = -0.0772880449597 -0.690508531291
y[1] (closed_form) = -0.0769114509916 -0.690503012996
absolute error = 0.0003766
relative error = 0.05421 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.129
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8417
Order of pole (three term test) = 5.644e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9979 0.533
h = 0.0001 0.003
y[1] (numeric) = -0.0686753599943 -0.687191988922
y[1] (closed_form) = -0.0683173039708 -0.687232891843
absolute error = 0.0003604
relative error = 0.05218 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.131
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.679
Order of pole (three term test) = 1.360e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9978 0.536
h = 0.001 0.001
y[1] (numeric) = -0.0635629862567 -0.68523242974
y[1] (closed_form) = -0.0631902881689 -0.685285957348
absolute error = 0.0003765
relative error = 0.05471 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.133
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5336
Order of pole (three term test) = 1.331e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9968 0.537
h = 0.001 0.003
y[1] (numeric) = -0.0611743782239 -0.686185519687
y[1] (closed_form) = -0.0607965772597 -0.686247611582
absolute error = 0.0003829
relative error = 0.05557 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.132
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.532
Order of pole (three term test) = 5.814e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9958 0.54
h = 0.0001 0.004
y[1] (numeric) = -0.0554193686892 -0.685686894413
y[1] (closed_form) = -0.0550528221385 -0.685731985308
absolute error = 0.0003693
relative error = 0.05368 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.133
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.433
Order of pole (three term test) = 1.068e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9957 0.544
h = 0.003 0.006
y[1] (numeric) = -0.0487039212911 -0.682869132787
y[1] (closed_form) = -0.0483545981566 -0.682915267229
absolute error = 0.0003524
relative error = 0.05147 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.135
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.902
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=405.3MB, alloc=44.3MB, time=5.13
x[1] = -0.9927 0.55
h = 0.0001 0.005
y[1] (numeric) = -0.0366047594343 -0.683208495986
y[1] (closed_form) = -0.0362203074665 -0.683188171335
absolute error = 0.000385
relative error = 0.05627 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.135
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8461
Order of pole (three term test) = 4.704e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9926 0.555
h = 0.0001 0.003
y[1] (numeric) = -0.0284448483641 -0.679319152456
y[1] (closed_form) = -0.0280740195013 -0.679345587502
absolute error = 0.0003718
relative error = 0.05468 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.137
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6826
Order of pole (three term test) = 1.606e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9925 0.558
h = 0.001 0.001
y[1] (numeric) = -0.0236006752075 -0.677021137335
y[1] (closed_form) = -0.0232144679557 -0.677058444724
absolute error = 0.000388
relative error = 0.05727 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.139
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5364
Order of pole (three term test) = 1.582e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9915 0.559
h = 0.001 0.003
y[1] (numeric) = -0.0211970757815 -0.677772106556
y[1] (closed_form) = -0.0208051209357 -0.677817240586
absolute error = 0.0003945
relative error = 0.05818 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.138
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.545
Order of pole (three term test) = 4.544e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9905 0.562
h = 0.0001 0.004
y[1] (numeric) = -0.0156164717328 -0.676852434098
y[1] (closed_form) = -0.0152370154058 -0.676882138962
absolute error = 0.0003806
relative error = 0.05622 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.139
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.441
Order of pole (three term test) = 5.663e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9904 0.566
h = 0.003 0.006
y[1] (numeric) = -0.00927383302956 -0.673598287225
y[1] (closed_form) = -0.00891097121247 -0.673630608872
absolute error = 0.0003643
relative error = 0.05408 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.141
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.912
Order of pole (three term test) = 1.060e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9874 0.572
h = 0.0001 0.005
y[1] (numeric) = 0.00255788306627 -0.673024274875
y[1] (closed_form) = 0.00294860234031 -0.672988945791
absolute error = 0.0003923
relative error = 0.05829 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.141
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8507
Order of pole (three term test) = 5.606e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9873 0.577
h = 0.0001 0.003
y[1] (numeric) = 0.010225580632 -0.66862209841
y[1] (closed_form) = 0.0106074421209 -0.668633308027
absolute error = 0.000382
relative error = 0.05713 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.144
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6864
Order of pole (three term test) = 2.712e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9872 0.58
h = 0.001 0.001
y[1] (numeric) = 0.0147784358631 -0.666021077568
y[1] (closed_form) = 0.0151761896613 -0.666041392625
absolute error = 0.0003983
relative error = 0.05978 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.145
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5394
Order of pole (three term test) = 5.949e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9862 0.581
h = 0.001 0.003
y[1] (numeric) = 0.01717779899 -0.666574842271
y[1] (closed_form) = 0.0175818386606 -0.666602203259
absolute error = 0.000405
relative error = 0.06073 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.145
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.559
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9852 0.584
h = 0.0001 0.004
y[1] (numeric) = 0.0225503446525 -0.665263503676
y[1] (closed_form) = 0.0229408637363 -0.665277084474
absolute error = 0.0003908
relative error = 0.0587 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.145
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.449
Order of pole (three term test) = 7.913e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9851 0.588
h = 0.003 0.006
y[1] (numeric) = 0.028491503616 -0.661621306354
y[1] (closed_form) = 0.0288662064245 -0.661638946549
absolute error = 0.0003751
relative error = 0.05664 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.147
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.923
Order of pole (three term test) = 9.007e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9821 0.594
h = 0.0001 0.005
y[1] (numeric) = 0.0399799123512 -0.660187663558
y[1] (closed_form) = 0.0403753553656 -0.660137308742
absolute error = 0.0003986
relative error = 0.06027 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.148
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8557
Order of pole (three term test) = 7.048e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.982 0.599
h = 0.0001 0.003
y[1] (numeric) = 0.0471241235702 -0.655334646893
y[1] (closed_form) = 0.0475152598972 -0.655330095483
absolute error = 0.0003912
relative error = 0.05953 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.15
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6904
Order of pole (three term test) = 6.544e-30 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=451.6MB, alloc=44.3MB, time=5.72
x[1] = -0.9819 0.602
h = 0.001 0.001
y[1] (numeric) = 0.0513673518532 -0.652467229344
y[1] (closed_form) = 0.0517746805374 -0.652470030979
absolute error = 0.0004073
relative error = 0.06223 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.152
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5426
Order of pole (three term test) = 6.817e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9809 0.603
h = 0.001 0.003
y[1] (numeric) = 0.0537445463916 -0.652830627202
y[1] (closed_form) = 0.0541585922846 -0.652839666587
absolute error = 0.0004141
relative error = 0.06322 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.151
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.575
Order of pole (three term test) = 9.952e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9799 0.606
h = 0.0001 0.004
y[1] (numeric) = 0.0588799393113 -0.651159550487
y[1] (closed_form) = 0.0592796639735 -0.651156503855
absolute error = 0.0003997
relative error = 0.06114 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.152
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.458
Order of pole (three term test) = 1.643e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9798 0.61
h = 0.003 0.006
y[1] (numeric) = 0.0643973924505 -0.64717886692
y[1] (closed_form) = 0.0647822047098 -0.647181178877
absolute error = 0.0003848
relative error = 0.05917 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.154
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.935
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9768 0.616
h = 0.0001 0.005
y[1] (numeric) = 0.0754755419204 -0.644945492794
y[1] (closed_form) = 0.0758742312989 -0.644880252773
absolute error = 0.000404
relative error = 0.06222 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.155
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8609
Order of pole (three term test) = 8.212e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9767 0.621
h = 0.0001 0.003
y[1] (numeric) = 0.0820730305335 -0.639704517411
y[1] (closed_form) = 0.0824716955106 -0.639683883219
absolute error = 0.0003992
relative error = 0.06189 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.157
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6947
Order of pole (three term test) = 2.820e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9766 0.624
h = 0.001 0.001
y[1] (numeric) = 0.085993048861 -0.63660780612
y[1] (closed_form) = 0.0864080046106 -0.636592813311
absolute error = 0.0004152
relative error = 0.06463 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.159
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.546
Order of pole (three term test) = 1.109e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9756 0.625
h = 0.0001 0.004
y[1] (numeric) = 0.0883316192385 -0.636789340402
y[1] (closed_form) = 0.0887536183586 -0.63677976448
absolute error = 0.0004221
relative error = 0.06565 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.159
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.278
Order of pole (three term test) = 1.460e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9755 0.629
h = 0.003 0.006
y[1] (numeric) = 0.093490022839 -0.632569613437
y[1] (closed_form) = 0.093876107529 -0.632559339733
absolute error = 0.0003862
relative error = 0.0604 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.161
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.946
Order of pole (three term test) = 1.306e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9725 0.635
h = 0.0001 0.005
y[1] (numeric) = 0.104160011825 -0.629705273532
y[1] (closed_form) = 0.104554352238 -0.629628481789
absolute error = 0.0004017
relative error = 0.06295 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.161
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8659
Order of pole (three term test) = 9.867e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9724 0.64
h = 0.0001 0.003
y[1] (numeric) = 0.110270614656 -0.624187355995
y[1] (closed_form) = 0.110668346857 -0.62415376649
absolute error = 0.0003991
relative error = 0.06297 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.164
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6987
Order of pole (three term test) = 4.798e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9723 0.643
h = 0.001 0.001
y[1] (numeric) = 0.113902897542 -0.620926895521
y[1] (closed_form) = 0.11431683604 -0.620897526112
absolute error = 0.000415
relative error = 0.06573 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.166
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5492
Order of pole (three term test) = 1.204e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9713 0.644
h = 0.001 0.003
y[1] (numeric) = 0.116194269063 -0.620960468459
y[1] (closed_form) = 0.116615440554 -0.620935807443
absolute error = 0.0004219
relative error = 0.06678 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.165
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.606
Order of pole (three term test) = 1.035e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9703 0.647
h = 0.0001 0.004
y[1] (numeric) = 0.120823596337 -0.618714235126
y[1] (closed_form) = 0.121229545571 -0.618680663336
absolute error = 0.0004073
relative error = 0.06461 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.166
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.476
Order of pole (three term test) = 2.424e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9702 0.651
h = 0.003 0.006
y[1] (numeric) = 0.125512180669 -0.614241633671
y[1] (closed_form) = 0.125905162179 -0.614215416229
absolute error = 0.0003939
relative error = 0.06282 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.168
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.959
Order of pole (three term test) = 3.224e-30 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=497.7MB, alloc=44.3MB, time=6.31
x[1] = -0.9672 0.657
h = 0.0001 0.005
y[1] (numeric) = 0.135672871447 -0.610701092491
y[1] (closed_form) = 0.136067942584 -0.61061006501
absolute error = 0.0004054
relative error = 0.06481 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.169
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8717
Order of pole (three term test) = 1.565e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9671 0.662
h = 0.0001 0.003
y[1] (numeric) = 0.141214554229 -0.604911125015
y[1] (closed_form) = 0.141616686273 -0.604861399572
absolute error = 0.0004052
relative error = 0.06523 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.172
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7034
Order of pole (three term test) = 4.704e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.967 0.665
h = 0.001 0.001
y[1] (numeric) = 0.144510711123 -0.601489700575
y[1] (closed_form) = 0.144928816126 -0.601442619751
absolute error = 0.0004207
relative error = 0.06801 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.174
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5529
Order of pole (three term test) = 9.269e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.966 0.666
h = 0.001 0.003
y[1] (numeric) = 0.146737331506 -0.601360897042
y[1] (closed_form) = 0.147162811471 -0.601317716669
absolute error = 0.0004277
relative error = 0.06908 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.173
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.624
Order of pole (three term test) = 1.163e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.965 0.669
h = 0.0001 0.004
y[1] (numeric) = 0.151072369766 -0.598854345927
y[1] (closed_form) = 0.151482418104 -0.598803918816
absolute error = 0.0004131
relative error = 0.06689 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.174
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.486
Order of pole (three term test) = 6.031e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9649 0.673
h = 0.003 0.006
y[1] (numeric) = 0.155307961766 -0.594184358323
y[1] (closed_form) = 0.155706171308 -0.594142139194
absolute error = 0.0004004
relative error = 0.0652 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.176
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.972
Order of pole (three term test) = 4.017e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9619 0.679
h = 0.0001 0.005
y[1] (numeric) = 0.164919055965 -0.59003730211
y[1] (closed_form) = 0.165313647357 -0.589932545953
absolute error = 0.0004083
relative error = 0.06664 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.177
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8778
Order of pole (three term test) = 1.534e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9618 0.684
h = 0.0001 0.003
y[1] (numeric) = 0.169889534289 -0.584035175881
y[1] (closed_form) = 0.170294489618 -0.583969527989
absolute error = 0.0004102
relative error = 0.06744 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.18
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7084
Order of pole (three term test) = 5.266e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9617 0.687
h = 0.001 0.001
y[1] (numeric) = 0.172848281741 -0.580488072069
y[1] (closed_form) = 0.173268824444 -0.580423590106
absolute error = 0.0004255
relative error = 0.07024 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.182
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5568
Order of pole (three term test) = 1.038e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9607 0.688
h = 0.001 0.003
y[1] (numeric) = 0.174998517889 -0.580208658328
y[1] (closed_form) = 0.17542648747 -0.580147291545
absolute error = 0.0004323
relative error = 0.07133 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.182
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.642
Order of pole (three term test) = 7.211e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9597 0.691
h = 0.0001 0.004
y[1] (numeric) = 0.179027846106 -0.577477218792
y[1] (closed_form) = 0.179440356319 -0.577410213776
absolute error = 0.0004179
relative error = 0.06912 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.183
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.496
Order of pole (three term test) = 1.892e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9596 0.695
h = 0.003 0.006
y[1] (numeric) = 0.182810661628 -0.572656596047
y[1] (closed_form) = 0.183212497295 -0.572598496566
absolute error = 0.000406
relative error = 0.06753 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.185
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.986
Order of pole (three term test) = 1.071e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9566 0.701
h = 0.0001 0.005
y[1] (numeric) = 0.191840927086 -0.567973674628
y[1] (closed_form) = 0.192233937726 -0.567855790346
absolute error = 0.0004103
relative error = 0.06844 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.186
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8841
Order of pole (three term test) = 1.924e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9565 0.706
h = 0.0001 0.003
y[1] (numeric) = 0.196244198116 -0.561816719451
y[1] (closed_form) = 0.196650494872 -0.561735515995
absolute error = 0.0004143
relative error = 0.06962 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.189
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7136
Order of pole (three term test) = 6.646e-30 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=544.0MB, alloc=44.3MB, time=6.90
x[1] = -0.9564 0.709
h = 0.001 0.001
y[1] (numeric) = 0.198867935361 -0.558177701898
y[1] (closed_form) = 0.199289301604 -0.558096295194
absolute error = 0.0004292
relative error = 0.07242 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.191
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5609
Order of pole (three term test) = 6.559e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9554 0.71
h = 0.001 0.003
y[1] (numeric) = 0.200931905648 -0.557760085102
y[1] (closed_form) = 0.20136066832 -0.557681040408
absolute error = 0.000436
relative error = 0.07353 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.19
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.662
Order of pole (three term test) = 9.115e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9544 0.713
h = 0.0001 0.004
y[1] (numeric) = 0.204648273536 -0.554838692776
y[1] (closed_form) = 0.205061714021 -0.554755544363
absolute error = 0.0004217
relative error = 0.0713 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.191
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.507
Order of pole (three term test) = 1.437e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9543 0.717
h = 0.003 0.006
y[1] (numeric) = 0.207983299823 -0.549911954691
y[1] (closed_form) = 0.20838724489 -0.549838257847
absolute error = 0.0004106
relative error = 0.06983 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.194
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.001
Order of pole (three term test) = 1.318e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9513 0.723
h = 0.0001 0.005
y[1] (numeric) = 0.216410183547 -0.54476365043
y[1] (closed_form) = 0.216800625889 -0.544633314216
absolute error = 0.0004116
relative error = 0.07022 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.195
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8908
Order of pole (three term test) = 4.890e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9512 0.728
h = 0.0001 0.003
y[1] (numeric) = 0.220255870396 -0.538506034648
y[1] (closed_form) = 0.220662134414 -0.538409776146
absolute error = 0.0004175
relative error = 0.07175 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.198
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7189
Order of pole (three term test) = 1.196e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9511 0.731
h = 0.001 0.001
y[1] (numeric) = 0.222550293406 -0.534807001139
y[1] (closed_form) = 0.222970997066 -0.534709288964
absolute error = 0.0004319
relative error = 0.07455 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.2
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5652
Order of pole (three term test) = 8.517e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9501 0.732
h = 0.0001 0.004
y[1] (numeric) = 0.224519844553 -0.534263987092
y[1] (closed_form) = 0.224947840281 -0.534167923643
absolute error = 0.0004386
relative error = 0.07568 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.199
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.393
Order of pole (three term test) = 1.026e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.95 0.736
h = 0.003 0.006
y[1] (numeric) = 0.227495260745 -0.529282360729
y[1] (closed_form) = 0.22789559821 -0.529198436532
absolute error = 0.000409
relative error = 0.07099 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.202
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.015
Order of pole (three term test) = 8.879e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.947 0.742
h = 0.0001 0.005
y[1] (numeric) = 0.235386540221 -0.523796440755
y[1] (closed_form) = 0.235769826379 -0.523658882137
absolute error = 0.0004072
relative error = 0.07091 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.203
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8969
Order of pole (three term test) = 6.087e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9469 0.747
h = 0.0001 0.003
y[1] (numeric) = 0.238763379574 -0.517499186088
y[1] (closed_form) = 0.239164329042 -0.517393341853
absolute error = 0.0004147
relative error = 0.07275 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.206
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7239
Order of pole (three term test) = 1.075e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9468 0.75
h = 0.001 0.001
y[1] (numeric) = 0.240780880558 -0.513776182863
y[1] (closed_form) = 0.241195640438 -0.513667917279
absolute error = 0.0004287
relative error = 0.07554 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.208
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5691
Order of pole (three term test) = 3.124e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9458 0.751
h = 0.001 0.003
y[1] (numeric) = 0.242662627387 -0.513136850833
y[1] (closed_form) = 0.243084529376 -0.513029658965
absolute error = 0.0004353
relative error = 0.07668 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.208
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.7
Order of pole (three term test) = 1.478e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9448 0.754
h = 0.0001 0.004
y[1] (numeric) = 0.245789052834 -0.50995517078
y[1] (closed_form) = 0.246196279906 -0.509846479276
absolute error = 0.0004215
relative error = 0.07444 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.209
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.529
Order of pole (three term test) = 1.619e-29 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=590.2MB, alloc=44.3MB, time=7.49
x[1] = -0.9447 0.758
h = 0.0001 0.004
y[1] (numeric) = 0.248318088251 -0.504945098259
y[1] (closed_form) = 0.248717994446 -0.504846482793
absolute error = 0.0004119
relative error = 0.07319 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.211
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.211
Order of pole (three term test) = 1.434e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9446 0.762
h = 0.003 0.006
y[1] (numeric) = 0.250767417867 -0.49995897156
y[1] (closed_form) = 0.251167324063 -0.499860356094
absolute error = 0.0004119
relative error = 0.07363 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.214
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.035
Order of pole (three term test) = 6.345e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9416 0.768
h = 0.0001 0.005
y[1] (numeric) = 0.257916476126 -0.49410644928
y[1] (closed_form) = 0.258295233115 -0.493958620739
absolute error = 0.0004066
relative error = 0.07294 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.215
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9059
Order of pole (three term test) = 5.916e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9415 0.773
h = 0.0001 0.003
y[1] (numeric) = 0.260678561796 -0.487820854858
y[1] (closed_form) = 0.261076983688 -0.48770141415
absolute error = 0.0004159
relative error = 0.07519 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.218
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7312
Order of pole (three term test) = 1.562e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9414 0.776
h = 0.001 0.001
y[1] (numeric) = 0.262332904683 -0.484103881464
y[1] (closed_form) = 0.26274417759 -0.483980872171
absolute error = 0.0004293
relative error = 0.07795 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.22
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5748
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9404 0.777
h = 0.001 0.003
y[1] (numeric) = 0.264087616162 -0.483351137795
y[1] (closed_form) = 0.264505749274 -0.483228485835
absolute error = 0.0004358
relative error = 0.0791 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.22
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.728
Order of pole (three term test) = 1.997e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9394 0.78
h = 0.0001 0.004
y[1] (numeric) = 0.26684447554 -0.480070596762
y[1] (closed_form) = 0.267248580181 -0.479947878941
absolute error = 0.0004223
relative error = 0.07688 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.221
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.545
Order of pole (three term test) = 1.177e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9393 0.784
h = 0.003 0.006
y[1] (numeric) = 0.268893545755 -0.475084896391
y[1] (closed_form) = 0.269291648498 -0.474972387154
absolute error = 0.0004137
relative error = 0.07577 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.223
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.051
Order of pole (three term test) = 1.412e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9363 0.79
h = 0.0001 0.005
y[1] (numeric) = 0.275421225906 -0.468970001622
y[1] (closed_form) = 0.275795156569 -0.468812094182
absolute error = 0.0004059
relative error = 0.07463 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.225
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9133
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9362 0.795
h = 0.0001 0.003
y[1] (numeric) = 0.277684133301 -0.462723336865
y[1] (closed_form) = 0.278079133063 -0.462591016641
absolute error = 0.0004166
relative error = 0.07718 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.228
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7372
Order of pole (three term test) = 6.410e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9361 0.798
h = 0.001 0.001
y[1] (numeric) = 0.279043557842 -0.459028547944
y[1] (closed_form) = 0.27945056598 -0.458891795305
absolute error = 0.0004294
relative error = 0.07991 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.23
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5795
Order of pole (three term test) = 3.731e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9351 0.799
h = 0.001 0.003
y[1] (numeric) = 0.280689627931 -0.45818964983
y[1] (closed_form) = 0.281103225385 -0.458052695569
absolute error = 0.0004357
relative error = 0.08107 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.23
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.75
Order of pole (three term test) = 3.115e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9341 0.802
h = 0.0001 0.004
y[1] (numeric) = 0.283141430964 -0.454846315238
y[1] (closed_form) = 0.283541608126 -0.454710408598
absolute error = 0.0004226
relative error = 0.07887 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.231
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.558
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.934 0.806
h = 0.003 0.006
y[1] (numeric) = 0.284801641969 -0.449903107467
y[1] (closed_form) = 0.285196886056 -0.449777435231
absolute error = 0.0004147
relative error = 0.07787 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.234
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.068
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.931 0.812
h = 0.0001 0.005
y[1] (numeric) = 0.290714145873 -0.443586551793
y[1] (closed_form) = 0.291082714508 -0.443419379695
absolute error = 0.0004047
relative error = 0.0763 %
Correct digits = 3
memory used=636.5MB, alloc=44.3MB, time=8.08
Radius of convergence (given) for eq 1 = 1.235
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.921
Order of pole (three term test) = 1.588e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9309 0.817
h = 0.0001 0.003
y[1] (numeric) = 0.292502887517 -0.437416524115
y[1] (closed_form) = 0.292893591793 -0.437272155962
absolute error = 0.0004165
relative error = 0.07914 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.239
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7434
Order of pole (three term test) = 7.801e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9308 0.82
h = 0.001 0.001
y[1] (numeric) = 0.293582102043 -0.433766133721
y[1] (closed_form) = 0.293983936176 -0.433616594152
absolute error = 0.0004288
relative error = 0.08184 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.24
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5844
Order of pole (three term test) = 9.771e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9298 0.821
h = 0.001 0.003
y[1] (numeric) = 0.295117549276 -0.432853400567
y[1] (closed_form) = 0.295525664092 -0.432703155544
absolute error = 0.0004349
relative error = 0.083 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.24
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.774
Order of pole (three term test) = 4.817e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9288 0.824
h = 0.0001 0.004
y[1] (numeric) = 0.297272820546 -0.429473997209
y[1] (closed_form) = 0.297668194646 -0.429325796962
absolute error = 0.0004222
relative error = 0.08082 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.242
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.571
Order of pole (three term test) = 2.713e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9287 0.828
h = 0.003 0.006
y[1] (numeric) = 0.29856471058 -0.424601839291
y[1] (closed_form) = 0.298956165494 -0.424463798452
absolute error = 0.0004151
relative error = 0.07995 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.244
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.086
Order of pole (three term test) = 1.230e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9257 0.834
h = 0.0001 0.005
y[1] (numeric) = 0.303873589988 -0.41814052358
y[1] (closed_form) = 0.304236361969 -0.417964903297
absolute error = 0.000403
relative error = 0.07796 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.246
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9289
Order of pole (three term test) = 9.390e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9256 0.839
h = 0.0001 0.003
y[1] (numeric) = 0.305215344386 -0.412080485325
y[1] (closed_form) = 0.305601004125 -0.411924938286
absolute error = 0.0004158
relative error = 0.08108 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.249
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7498
Order of pole (three term test) = 7.262e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9255 0.842
h = 0.001 0.001
y[1] (numeric) = 0.306030325894 -0.408494150267
y[1] (closed_form) = 0.306426216739 -0.408332813584
absolute error = 0.0004275
relative error = 0.08374 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.251
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5895
Order of pole (three term test) = 6.435e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9245 0.843
h = 0.001 0.003
y[1] (numeric) = 0.307454415383 -0.407519422061
y[1] (closed_form) = 0.307856248822 -0.407356931763
absolute error = 0.0004334
relative error = 0.08489 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.251
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.798
Order of pole (three term test) = 4.489e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9235 0.846
h = 0.0001 0.004
y[1] (numeric) = 0.309323693731 -0.404128444702
y[1] (closed_form) = 0.309713520452 -0.403968879758
absolute error = 0.0004212
relative error = 0.08275 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.252
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.585
Order of pole (three term test) = 1.239e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9234 0.85
h = 0.003 0.006
y[1] (numeric) = 0.31026932501 -0.399352454236
y[1] (closed_form) = 0.310656184252 -0.399202885161
absolute error = 0.0004148
relative error = 0.082 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.255
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.104
Order of pole (three term test) = 6.370e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9204 0.856
h = 0.0001 0.005
y[1] (numeric) = 0.314990734897 -0.392799135912
y[1] (closed_form) = 0.315347370283 -0.392615875847
absolute error = 0.000401
relative error = 0.07962 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.257
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.937
Order of pole (three term test) = 7.416e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9203 0.861
h = 0.0001 0.003
y[1] (numeric) = 0.315914243837 -0.386878131157
y[1] (closed_form) = 0.316294230441 -0.38671229603
absolute error = 0.0004146
relative error = 0.08299 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.26
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7564
Order of pole (three term test) = 4.489e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9202 0.864
h = 0.001 0.001
y[1] (numeric) = 0.316481885474 -0.383372979356
y[1] (closed_form) = 0.316871198212 -0.383200851491
absolute error = 0.0004257
relative error = 0.08561 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.262
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5947
Order of pole (three term test) = 1.348e-29 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=682.6MB, alloc=44.3MB, time=8.67
x[1] = -0.9192 0.865
h = 0.0001 0.004
y[1] (numeric) = 0.317794998499 -0.382347515112
y[1] (closed_form) = 0.318189894037 -0.382173840652
absolute error = 0.0004314
relative error = 0.08675 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.262
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.571
Order of pole (three term test) = 1.577e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9191 0.869
h = 0.003 0.006
y[1] (numeric) = 0.318474788715 -0.377666957371
y[1] (closed_form) = 0.318855251491 -0.377511689135
absolute error = 0.0004109
relative error = 0.08316 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.265
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.121
Order of pole (three term test) = 1.371e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9161 0.875
h = 0.0001 0.005
y[1] (numeric) = 0.322706113473 -0.371080031148
y[1] (closed_form) = 0.323055419008 -0.370894369061
absolute error = 0.0003956
relative error = 0.08043 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.267
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9444
Order of pole (three term test) = 4.767e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.916 0.88
h = 0.0001 0.003
y[1] (numeric) = 0.32329546075 -0.365303252054
y[1] (closed_form) = 0.323668276409 -0.36513281884
absolute error = 0.0004099
relative error = 0.08401 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.27
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7624
Order of pole (three term test) = 7.821e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9159 0.883
h = 0.001 0.001
y[1] (numeric) = 0.323665387829 -0.361882476256
y[1] (closed_form) = 0.324046750849 -0.361705414889
absolute error = 0.0004205
relative error = 0.08658 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.272
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.5994
Order of pole (three term test) = 1.097e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9149 0.884
h = 0.001 0.003
y[1] (numeric) = 0.324883601434 -0.360823151773
y[1] (closed_form) = 0.325270221805 -0.360644253215
absolute error = 0.000426
relative error = 0.08772 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.272
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.845
Order of pole (three term test) = 7.659e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9139 0.887
h = 0.0001 0.004
y[1] (numeric) = 0.326254597829 -0.357470973602
y[1] (closed_form) = 0.32663067652 -0.357296326582
absolute error = 0.0004147
relative error = 0.08566 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.274
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.611
Order of pole (three term test) = 1.034e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9138 0.891
h = 0.003 0.006
y[1] (numeric) = 0.326619667071 -0.352932745895
y[1] (closed_form) = 0.326994363199 -0.352767587092
absolute error = 0.0004095
relative error = 0.08513 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.276
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.14
Order of pole (three term test) = 7.704e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9108 0.897
h = 0.0001 0.005
y[1] (numeric) = 0.330303852571 -0.346339997793
y[1] (closed_form) = 0.330646625472 -0.346148151344
absolute error = 0.0003928
relative error = 0.08206 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.278
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.953
Order of pole (three term test) = 2.122e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9107 0.902
h = 0.0001 0.003
y[1] (numeric) = 0.330530976521 -0.340744905386
y[1] (closed_form) = 0.330897260966 -0.340565856962
absolute error = 0.0004077
relative error = 0.08586 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.282
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7693
Order of pole (three term test) = 7.392e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9106 0.905
h = 0.001 0.001
y[1] (numeric) = 0.330686490365 -0.337430498666
y[1] (closed_form) = 0.331060438197 -0.337244514005
absolute error = 0.0004176
relative error = 0.08837 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.284
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6049
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9096 0.906
h = 0.001 0.003
y[1] (numeric) = 0.33179706785 -0.33633955939
y[1] (closed_form) = 0.332175891843 -0.336151443116
absolute error = 0.000423
relative error = 0.0895 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.284
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.871
Order of pole (three term test) = 1.449e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9086 0.909
h = 0.0001 0.004
y[1] (numeric) = 0.332920355458 -0.333032953568
y[1] (closed_form) = 0.333289444062 -0.332849651469
absolute error = 0.0004121
relative error = 0.08749 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.285
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.626
Order of pole (three term test) = 1.920e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9085 0.913
h = 0.003 0.006
y[1] (numeric) = 0.333006913059 -0.328644203048
y[1] (closed_form) = 0.333375369494 -0.328470039576
absolute error = 0.0004075
relative error = 0.08708 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.288
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.159
Order of pole (three term test) = 3.667e-30 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=729.0MB, alloc=44.3MB, time=9.26
x[1] = -0.9055 0.919
h = 0.0001 0.005
y[1] (numeric) = 0.336169294348 -0.322085646159
y[1] (closed_form) = 0.336505424842 -0.321888356159
absolute error = 0.0003898
relative error = 0.0837 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.29
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9618
Order of pole (three term test) = 3.322e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9054 0.924
h = 0.0001 0.003
y[1] (numeric) = 0.336064504331 -0.31668978184
y[1] (closed_form) = 0.336423939168 -0.316502998144
absolute error = 0.0004051
relative error = 0.0877 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.294
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7765
Order of pole (three term test) = 3.970e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9053 0.927
h = 0.001 0.001
y[1] (numeric) = 0.336023420598 -0.313492121762
y[1] (closed_form) = 0.336389659137 -0.313298186942
absolute error = 0.0004144
relative error = 0.09015 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.296
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6105
Order of pole (three term test) = 1.261e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9043 0.928
h = 0.001 0.003
y[1] (numeric) = 0.337029198507 -0.312378794886
y[1] (closed_form) = 0.337399928739 -0.312182483441
absolute error = 0.0004195
relative error = 0.09126 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.296
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.897
Order of pole (three term test) = 1.377e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9033 0.931
h = 0.0001 0.004
y[1] (numeric) = 0.337919824244 -0.309133382498
y[1] (closed_form) = 0.338281627059 -0.308942346787
absolute error = 0.0004091
relative error = 0.08931 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.297
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.641
Order of pole (three term test) = 1.096e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9032 0.935
h = 0.003 0.006
y[1] (numeric) = 0.33775183506 -0.304906918216
y[1] (closed_form) = 0.338113683221 -0.304724627884
absolute error = 0.0004052
relative error = 0.08902 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.3
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.179
Order of pole (three term test) = 6.943e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9002 0.941
h = 0.0001 0.005
y[1] (numeric) = 0.340419719802 -0.298418110094
y[1] (closed_form) = 0.340749163827 -0.298216083161
absolute error = 0.0003865
relative error = 0.08534 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.302
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9708
Order of pole (three term test) = 1.384e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9001 0.946
h = 0.0001 0.003
y[1] (numeric) = 0.340013070121 -0.29323542719
y[1] (closed_form) = 0.340365430426 -0.293041765046
absolute error = 0.0004021
relative error = 0.08952 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.306
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7838
Order of pole (three term test) = 4.016e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9 0.949
h = 0.001 0.001
y[1] (numeric) = 0.339793057462 -0.290162785374
y[1] (closed_form) = 0.340151393549 -0.289961841742
absolute error = 0.0004108
relative error = 0.09192 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.308
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6162
Order of pole (three term test) = 1.352e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.899 0.95
h = 0.001 0.003
y[1] (numeric) = 0.340697488829 -0.289035526842
y[1] (closed_form) = 0.341059933908 -0.288832007959
absolute error = 0.0004157
relative error = 0.09301 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.308
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.925
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.898 0.953
h = 0.0001 0.004
y[1] (numeric) = 0.341370951732 -0.285864755446
y[1] (closed_form) = 0.341725269067 -0.285666879466
absolute error = 0.0004058
relative error = 0.09112 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.309
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.657
Order of pole (three term test) = 4.932e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8979 0.957
h = 0.003 0.006
y[1] (numeric) = 0.340972073757 -0.28181062692
y[1] (closed_form) = 0.341327041776 -0.281621069457
absolute error = 0.0004024
relative error = 0.09094 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.312
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.2
Order of pole (three term test) = 6.632e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8949 0.963
h = 0.0001 0.005
y[1] (numeric) = 0.343174173001 -0.275422777248
y[1] (closed_form) = 0.343496944575 -0.275216682139
absolute error = 0.000383
relative error = 0.08701 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.315
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9801
Order of pole (three term test) = 1.162e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8948 0.968
h = 0.0001 0.003
y[1] (numeric) = 0.342495131106 -0.270463909693
y[1] (closed_form) = 0.342840276852 -0.270264195222
absolute error = 0.0003988
relative error = 0.09134 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.318
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7912
Order of pole (three term test) = 7.249e-30 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=775.3MB, alloc=44.3MB, time=9.85
x[1] = -0.8947 0.971
h = 0.001 0.001
y[1] (numeric) = 0.342113517091 -0.267522609033
y[1] (closed_form) = 0.342463848403 -0.267315558416
absolute error = 0.0004069
relative error = 0.09367 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.32
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6221
Order of pole (three term test) = 1.799e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8937 0.972
h = 0.0001 0.004
y[1] (numeric) = 0.342920554972 -0.266389096298
y[1] (closed_form) = 0.343274618668 -0.266179314855
absolute error = 0.0004115
relative error = 0.09474 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.32
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.736
Order of pole (three term test) = 1.834e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8936 0.976
h = 0.003 0.006
y[1] (numeric) = 0.34235032901 -0.262481902356
y[1] (closed_form) = 0.342698806722 -0.26228993039
absolute error = 0.0003979
relative error = 0.09219 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.323
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.219
Order of pole (three term test) = 1.786e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8906 0.982
h = 0.0001 0.005
y[1] (numeric) = 0.344176809715 -0.256207811876
y[1] (closed_form) = 0.344493504583 -0.256001885623
absolute error = 0.0003778
relative error = 0.08801 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.326
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9883
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8905 0.987
h = 0.0001 0.003
y[1] (numeric) = 0.343289027831 -0.251450570476
y[1] (closed_form) = 0.343627505361 -0.251249454372
absolute error = 0.0003937
relative error = 0.09249 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.329
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7979
Order of pole (three term test) = 1.006e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8904 0.99
h = 0.001 0.001
y[1] (numeric) = 0.34278344197 -0.248627675094
y[1] (closed_form) = 0.343126458973 -0.248419238446
absolute error = 0.0004014
relative error = 0.09475 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.332
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6273
Order of pole (three term test) = 1.490e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8894 0.991
h = 0.001 0.003
y[1] (numeric) = 0.343510149778 -0.24749542551
y[1] (closed_form) = 0.343856581432 -0.247284160218
absolute error = 0.0004058
relative error = 0.0958 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.332
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.978
Order of pole (three term test) = 6.595e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8884 0.994
h = 0.0001 0.004
y[1] (numeric) = 0.343822514713 -0.244494482124
y[1] (closed_form) = 0.344162258673 -0.24428930789
absolute error = 0.0003969
relative error = 0.09404 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.333
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.687
Order of pole (three term test) = 1.226e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8883 0.998
h = 0.003 0.006
y[1] (numeric) = 0.343057154133 -0.240781353552
y[1] (closed_form) = 0.343398484025 -0.240583639604
absolute error = 0.0003945
relative error = 0.09408 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.336
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.24
Order of pole (three term test) = 4.714e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8853 1.004
h = 0.0001 0.005
y[1] (numeric) = 0.344473552254 -0.234654950238
y[1] (closed_form) = 0.344783737041 -0.234446089791
absolute error = 0.0003739
relative error = 0.08969 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.339
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9979
Order of pole (three term test) = 9.306e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8852 1.009
h = 0.0001 0.003
y[1] (numeric) = 0.343365786627 -0.230133131513
y[1] (closed_form) = 0.343696993813 -0.229927398582
absolute error = 0.0003899
relative error = 0.09429 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.342
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8056
Order of pole (three term test) = 4.348e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8851 1.012
h = 0.001 0.001
y[1] (numeric) = 0.342729430864 -0.227448537853
y[1] (closed_form) = 0.343064469189 -0.227235546888
absolute error = 0.000397
relative error = 0.09648 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.344
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6334
Order of pole (three term test) = 7.177e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8841 1.013
h = 0.001 0.003
y[1] (numeric) = 0.343367138206 -0.226322220295
y[1] (closed_form) = 0.343705235459 -0.226106315555
absolute error = 0.0004012
relative error = 0.09751 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.345
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.006
Order of pole (three term test) = 7.735e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8831 1.016
h = 0.0001 0.004
y[1] (numeric) = 0.343507228396 -0.223423204547
y[1] (closed_form) = 0.343839371195 -0.223213529427
absolute error = 0.0003928
relative error = 0.09582 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.346
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.703
Order of pole (three term test) = 2.672e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.883 1.02
h = 0.003 0.006
y[1] (numeric) = 0.342574976466 -0.219897653525
y[1] (closed_form) = 0.342909116335 -0.219694964028
absolute error = 0.0003908
relative error = 0.09596 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.349
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.262
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=821.6MB, alloc=44.3MB, time=10.43
x[1] = -0.88 1.026
h = 0.0001 0.005
y[1] (numeric) = 0.343611338718 -0.213938740676
y[1] (closed_form) = 0.343915153412 -0.213727494887
absolute error = 0.00037
relative error = 0.09139 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.352
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.008
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8799 1.031
h = 0.0001 0.003
y[1] (numeric) = 0.342309999245 -0.209655084735
y[1] (closed_form) = 0.342633990376 -0.20944544392
absolute error = 0.0003859
relative error = 0.0961 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.355
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8135
Order of pole (three term test) = 4.417e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8798 1.034
h = 0.001 0.001
y[1] (numeric) = 0.341558418134 -0.207110477759
y[1] (closed_form) = 0.341885579321 -0.206893692723
absolute error = 0.0003925
relative error = 0.09821 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.358
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6396
Order of pole (three term test) = 9.045e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8788 1.035
h = 0.001 0.003
y[1] (numeric) = 0.342111934641 -0.205995609618
y[1] (closed_form) = 0.342441813728 -0.205775858378
absolute error = 0.0003964
relative error = 0.09921 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.358
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.036
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8778 1.038
h = 0.0001 0.004
y[1] (numeric) = 0.342094981555 -0.203204698921
y[1] (closed_form) = 0.342419606196 -0.202991250708
absolute error = 0.0003885
relative error = 0.0976 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.359
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.72
Order of pole (three term test) = 1.761e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8777 1.042
h = 0.003 0.006
y[1] (numeric) = 0.34101636212 -0.199868236306
y[1] (closed_form) = 0.341343333624 -0.199661295786
absolute error = 0.000387
relative error = 0.09785 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.362
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.284
Order of pole (three term test) = 1.556e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8747 1.048
h = 0.0001 0.005
y[1] (numeric) = 0.341702478445 -0.194093096487
y[1] (closed_form) = 0.342000094608 -0.193879971212
absolute error = 0.0003661
relative error = 0.09311 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.365
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.018
Order of pole (three term test) = 1.938e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8746 1.053
h = 0.0001 0.003
y[1] (numeric) = 0.340232598981 -0.190048137929
y[1] (closed_form) = 0.340549480228 -0.189835251558
absolute error = 0.0003818
relative error = 0.09791 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.369
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8216
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8745 1.056
h = 0.001 0.001
y[1] (numeric) = 0.339380533613 -0.187643905205
y[1] (closed_form) = 0.33969997232 -0.187424031927
absolute error = 0.0003878
relative error = 0.09995 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.371
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.646
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8735 1.057
h = 0.001 0.003
y[1] (numeric) = 0.339854803978 -0.186545303167
y[1] (closed_form) = 0.340176636119 -0.18632244035
absolute error = 0.0003915
relative error = 0.1009 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.371
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.066
Order of pole (three term test) = 1.192e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8725 1.06
h = 0.0001 0.004
y[1] (numeric) = 0.339695597591 -0.183867133406
y[1] (closed_form) = 0.340012838627 -0.183650589404
absolute error = 0.0003841
relative error = 0.09939 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.373
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.737
Order of pole (three term test) = 3.859e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8724 1.064
h = 0.003 0.006
y[1] (numeric) = 0.338490014381 -0.180719608265
y[1] (closed_form) = 0.338809894766 -0.18050909641
absolute error = 0.0003829
relative error = 0.09975 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.376
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.307
Order of pole (three term test) = 9.756e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8694 1.07
h = 0.0001 0.005
y[1] (numeric) = 0.338855122903 -0.175141273384
y[1] (closed_form) = 0.339146737886 -0.174926731884
absolute error = 0.000362
relative error = 0.09487 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.379
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.028
Order of pole (three term test) = 5.955e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8693 1.075
h = 0.0001 0.003
y[1] (numeric) = 0.337240263517 -0.171333618538
y[1] (closed_form) = 0.337550185143 -0.171118100988
absolute error = 0.0003775
relative error = 0.09975 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.383
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8298
Order of pole (three term test) = 8.358e-30 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=868.0MB, alloc=44.3MB, time=11.02
x[1] = -0.8692 1.078
h = 0.001 0.001
y[1] (numeric) = 0.336301593967 -0.169069012363
y[1] (closed_form) = 0.336613509308 -0.168846701421
absolute error = 0.000383
relative error = 0.1017 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.385
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6524
Order of pole (three term test) = 8.263e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8682 1.079
h = 0.0001 0.004
y[1] (numeric) = 0.336701626881 -0.16799082992
y[1] (closed_form) = 0.33701562911 -0.167765531705
absolute error = 0.0003865
relative error = 0.1027 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.385
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.918
Order of pole (three term test) = 2.201e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8681 1.083
h = 0.003 0.006
y[1] (numeric) = 0.335406087056 -0.16499685351
y[1] (closed_form) = 0.335720457516 -0.164786252729
absolute error = 0.0003784
relative error = 0.1012 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.388
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.327
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8651 1.089
h = 0.0001 0.005
y[1] (numeric) = 0.335520194085 -0.159599444969
y[1] (closed_form) = 0.335807334952 -0.159386485604
absolute error = 0.0003575
relative error = 0.09617 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.391
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.037
Order of pole (three term test) = 4.457e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.865 1.094
h = 0.0001 0.003
y[1] (numeric) = 0.333801008701 -0.155995033884
y[1] (closed_form) = 0.334105593853 -0.15578018047
absolute error = 0.0003727
relative error = 0.1011 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.395
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8371
Order of pole (three term test) = 1.101e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8649 1.097
h = 0.001 0.001
y[1] (numeric) = 0.33279985601 -0.153850085584
y[1] (closed_form) = 0.333105991233 -0.153628635111
absolute error = 0.0003778
relative error = 0.103 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.397
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6582
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8639 1.098
h = 0.001 0.003
y[1] (numeric) = 0.333140300934 -0.152793132946
y[1] (closed_form) = 0.333448274618 -0.152568718434
absolute error = 0.0003811
relative error = 0.1039 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.397
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.124
Order of pole (three term test) = 1.534e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8629 1.101
h = 0.0001 0.004
y[1] (numeric) = 0.332755240076 -0.150333725306
y[1] (closed_form) = 0.333059750704 -0.150115523474
absolute error = 0.0003746
relative error = 0.1025 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.399
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.77
Order of pole (three term test) = 8.168e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8628 1.105
h = 0.003 0.006
y[1] (numeric) = 0.331363140277 -0.147533587051
y[1] (closed_form) = 0.331670691284 -0.147320552568
absolute error = 0.0003741
relative error = 0.1031 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.402
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.35
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8598 1.111
h = 0.0001 0.005
y[1] (numeric) = 0.33120845077 -0.142349210842
y[1] (closed_form) = 0.331490012977 -0.142135584444
absolute error = 0.0003534
relative error = 0.09799 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.405
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.047
Order of pole (three term test) = 9.719e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8597 1.116
h = 0.0001 0.003
y[1] (numeric) = 0.329383952978 -0.138975035418
y[1] (closed_form) = 0.329681956854 -0.138758562702
absolute error = 0.0003683
relative error = 0.103 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.409
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8455
Order of pole (three term test) = 1.697e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8596 1.119
h = 0.001 0.001
y[1] (numeric) = 0.328319585136 -0.13696568416
y[1] (closed_form) = 0.328618665005 -0.136742857213
absolute error = 0.000373
relative error = 0.1048 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.411
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6648
Order of pole (three term test) = 1.056e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8586 1.12
h = 0.001 0.003
y[1] (numeric) = 0.328595111353 -0.135935199878
y[1] (closed_form) = 0.328895758817 -0.135709449795
absolute error = 0.000376
relative error = 0.1057 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.411
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.156
Order of pole (three term test) = 1.079e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8576 1.123
h = 0.0001 0.004
y[1] (numeric) = 0.328106837321 -0.133594443338
y[1] (closed_form) = 0.328404569457 -0.133374796231
absolute error = 0.00037
relative error = 0.1044 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.413
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.788
Order of pole (three term test) = 2.521e-29 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=914.2MB, alloc=44.3MB, time=11.60
x[1] = -0.8575 1.127
h = 0.003 0.006
y[1] (numeric) = 0.326636561958 -0.130975332185
y[1] (closed_form) = 0.326937487087 -0.130760407958
absolute error = 0.0003698
relative error = 0.105 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.416
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.374
Order of pole (three term test) = 9.718e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8545 1.133
h = 0.0001 0.005
y[1] (numeric) = 0.326239516132 -0.126009269117
y[1] (closed_form) = 0.326515742927 -0.125795323271
absolute error = 0.0003494
relative error = 0.09985 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.419
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.058
Order of pole (three term test) = 8.493e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8544 1.138
h = 0.0001 0.003
y[1] (numeric) = 0.324328794081 -0.122859843861
y[1] (closed_form) = 0.32462045415 -0.122642228734
absolute error = 0.0003639
relative error = 0.1049 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.423
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8541
Order of pole (three term test) = 4.689e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8543 1.141
h = 0.001 0.001
y[1] (numeric) = 0.323212475914 -0.120982927576
y[1] (closed_form) = 0.323504784056 -0.120759219556
absolute error = 0.0003681
relative error = 0.1066 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.425
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6716
Order of pole (three term test) = 2.084e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8533 1.142
h = 0.001 0.003
y[1] (numeric) = 0.323427959218 -0.11998140612
y[1] (closed_form) = 0.323721583568 -0.119754832407
absolute error = 0.0003709
relative error = 0.1075 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.426
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.188
Order of pole (three term test) = 5.850e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8523 1.145
h = 0.0001 0.004
y[1] (numeric) = 0.322848764444 -0.117759354055
y[1] (closed_form) = 0.323139979869 -0.117538741869
absolute error = 0.0003653
relative error = 0.1063 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.427
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.806
Order of pole (three term test) = 1.247e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8522 1.149
h = 0.003 0.006
y[1] (numeric) = 0.321314983307 -0.115316633906
y[1] (closed_form) = 0.321609503861 -0.115100316738
absolute error = 0.0003654
relative error = 0.107 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.431
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.398
Order of pole (three term test) = 1.192e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8492 1.155
h = 0.0001 0.005
y[1] (numeric) = 0.320700774119 -0.110571977703
y[1] (closed_form) = 0.320971916959 -0.110358022872
absolute error = 0.0003454
relative error = 0.1018 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.434
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.069
Order of pole (three term test) = 8.751e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8491 1.16
h = 0.0001 0.003
y[1] (numeric) = 0.318721358242 -0.107640818063
y[1] (closed_form) = 0.31900693104 -0.107422491476
absolute error = 0.0003595
relative error = 0.1068 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.438
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8628
Order of pole (three term test) = 1.046e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.849 1.163
h = 0.001 0.001
y[1] (numeric) = 0.317563442733 -0.105892583208
y[1] (closed_form) = 0.317849280021 -0.105668438529
absolute error = 0.0003632
relative error = 0.1084 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.44
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6784
Order of pole (three term test) = 6.447e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.848 1.164
h = 0.001 0.003
y[1] (numeric) = 0.317723633346 -0.104922026588
y[1] (closed_form) = 0.318010554872 -0.104695087449
absolute error = 0.0003658
relative error = 0.1093 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.44
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.22
Order of pole (three term test) = 4.049e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.847 1.167
h = 0.0001 0.004
y[1] (numeric) = 0.317065058535 -0.102817873591
y[1] (closed_form) = 0.317350036632 -0.102596728383
absolute error = 0.0003607
relative error = 0.1082 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.442
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.825
Order of pole (three term test) = 1.526e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8469 1.171
h = 0.003 0.006
y[1] (numeric) = 0.315481217925 -0.100546176258
y[1] (closed_form) = 0.315769577042 -0.100328916858
absolute error = 0.000361
relative error = 0.109 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.445
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.423
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8439 1.177
h = 0.0001 0.005
y[1] (numeric) = 0.314673704275 -0.0960240908122
y[1] (closed_form) = 0.314940019448 -0.0958104023525
absolute error = 0.0003414
relative error = 0.1037 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.448
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.08
Order of pole (three term test) = 3.455e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8438 1.182
h = 0.0001 0.003
y[1] (numeric) = 0.312641599404 -0.0933039096912
y[1] (closed_form) = 0.312921355471 -0.09308525841
absolute error = 0.0003551
relative error = 0.1088 %
Correct digits = 3
memory used=960.5MB, alloc=44.3MB, time=12.19
Radius of convergence (given) for eq 1 = 1.452
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8717
Order of pole (three term test) = 1.764e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8437 1.185
h = 0.001 0.001
y[1] (numeric) = 0.311451546016 -0.091680126388
y[1] (closed_form) = 0.311731225202 -0.0914559408164
absolute error = 0.0003584
relative error = 0.1103 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.455
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6854
Order of pole (three term test) = 2.017e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8427 1.186
h = 0.0001 0.004
y[1] (numeric) = 0.31156103843 -0.090742089499
y[1] (closed_form) = 0.311841588984 -0.0905151919667
absolute error = 0.0003608
relative error = 0.1111 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.455
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.116
Order of pole (three term test) = 3.505e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8426 1.19
h = 0.003 0.006
y[1] (numeric) = 0.309945665725 -0.0886059122776
y[1] (closed_form) = 0.310229869407 -0.0883899080628
absolute error = 0.000357
relative error = 0.1107 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.458
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.445
Order of pole (three term test) = 1.782e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8396 1.196
h = 0.0001 0.005
y[1] (numeric) = 0.308992445883 -0.0842769887718
y[1] (closed_form) = 0.309255764759 -0.0840654484172
absolute error = 0.0003378
relative error = 0.1054 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.461
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.089
Order of pole (three term test) = 1.651e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8395 1.201
h = 0.0001 0.003
y[1] (numeric) = 0.306929057548 -0.0817324896532
y[1] (closed_form) = 0.307204977819 -0.0815155713523
absolute error = 0.000351
relative error = 0.1104 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.465
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8795
Order of pole (three term test) = 5.352e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8394 1.204
h = 0.001 0.001
y[1] (numeric) = 0.305719660513 -0.080212401709
y[1] (closed_form) = 0.305995245534 -0.0799902010383
absolute error = 0.000354
relative error = 0.1119 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.468
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6915
Order of pole (three term test) = 5.343e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8384 1.205
h = 0.001 0.003
y[1] (numeric) = 0.305789461432 -0.0793038259353
y[1] (closed_form) = 0.306065750628 -0.0790789938251
absolute error = 0.0003562
relative error = 0.1127 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.468
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.282
Order of pole (three term test) = 1.111e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8374 1.208
h = 0.0001 0.004
y[1] (numeric) = 0.305012619007 -0.0774151270125
y[1] (closed_form) = 0.305287722896 -0.0771957200436
absolute error = 0.0003519
relative error = 0.1117 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.47
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.86
Order of pole (three term test) = 1.212e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8373 1.212
h = 0.003 0.006
y[1] (numeric) = 0.303369220979 -0.0754457532241
y[1] (closed_form) = 0.303647760148 -0.0752295249671
absolute error = 0.0003526
relative error = 0.1127 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.473
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.47
Order of pole (three term test) = 9.665e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8343 1.218
h = 0.0001 0.005
y[1] (numeric) = 0.302263338555 -0.071337009786
y[1] (closed_form) = 0.30252231217 -0.0711261590338
absolute error = 0.000334
relative error = 0.1075 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.476
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.101
Order of pole (three term test) = 6.731e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8342 1.223
h = 0.0001 0.003
y[1] (numeric) = 0.300173050497 -0.0689882373055
y[1] (closed_form) = 0.300443683197 -0.0687716002331
absolute error = 0.0003467
relative error = 0.1125 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.48
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8886
Order of pole (three term test) = 1.051e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8341 1.226
h = 0.001 0.001
y[1] (numeric) = 0.298946778054 -0.0675837216357
y[1] (closed_form) = 0.299216806333 -0.0673620923037
absolute error = 0.0003493
relative error = 0.1139 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.483
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.6986
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8331 1.227
h = 0.001 0.003
y[1] (numeric) = 0.298973946855 -0.0667094700828
y[1] (closed_form) = 0.299244500593 -0.0664853066636
absolute error = 0.0003514
relative error = 0.1146 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.483
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.316
Order of pole (three term test) = 2.074e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8321 1.23
h = 0.0001 0.004
y[1] (numeric) = 0.298146475227 -0.0649325675504
y[1] (closed_form) = 0.298416198128 -0.0647136137756
absolute error = 0.0003474
relative error = 0.1138 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.485
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.879
Order of pole (three term test) = 2.820e-30 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1006.7MB, alloc=44.3MB, time=12.77
x[1] = -0.832 1.234
h = 0.003 0.006
y[1] (numeric) = 0.296484958134 -0.0631159786721
y[1] (closed_form) = 0.296758110547 -0.0628998547104
absolute error = 0.0003483
relative error = 0.1148 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.488
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.495
Order of pole (three term test) = 1.163e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.829 1.24
h = 0.0001 0.005
y[1] (numeric) = 0.295246216694 -0.0592243700795
y[1] (closed_form) = 0.295501100028 -0.0590143958762
absolute error = 0.0003302
relative error = 0.1096 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.492
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.112
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8289 1.245
h = 0.0001 0.003
y[1] (numeric) = 0.29314096388 -0.0570626730606
y[1] (closed_form) = 0.29340659623 -0.0568465897194
absolute error = 0.0003424
relative error = 0.1146 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.496
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8977
Order of pole (three term test) = 1.077e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8288 1.248
h = 0.001 0.001
y[1] (numeric) = 0.291904889207 -0.0557686837133
y[1] (closed_form) = 0.292169683101 -0.0555478974401
absolute error = 0.0003448
relative error = 0.1159 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.498
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7058
Order of pole (three term test) = 1.025e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8278 1.249
h = 0.001 0.003
y[1] (numeric) = 0.291893460047 -0.0549292736306
y[1] (closed_form) = 0.29215861793 -0.0547060559754
absolute error = 0.0003466
relative error = 0.1166 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.498
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.351
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8268 1.252
h = 0.0001 0.004
y[1] (numeric) = 0.291023958366 -0.0532611161406
y[1] (closed_form) = 0.291288604242 -0.0530428834401
absolute error = 0.000343
relative error = 0.1159 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.5
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.898
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8267 1.256
h = 0.003 0.006
y[1] (numeric) = 0.289353410585 -0.0515904011128
y[1] (closed_form) = 0.289621458466 -0.0513746712851
absolute error = 0.0003441
relative error = 0.117 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.504
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.521
Order of pole (three term test) = 1.864e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8237 1.262
h = 0.0001 0.005
y[1] (numeric) = 0.28800019545 -0.0479118071257
y[1] (closed_form) = 0.288251239196 -0.047702869801
absolute error = 0.0003266
relative error = 0.1118 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.507
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.123
Order of pole (three term test) = 8.475e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8236 1.267
h = 0.0001 0.003
y[1] (numeric) = 0.285890625253 -0.0459283146067
y[1] (closed_form) = 0.286151544107 -0.0457130223413
absolute error = 0.0003383
relative error = 0.1167 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.511
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.907
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8235 1.27
h = 0.001 0.001
y[1] (numeric) = 0.284651065697 -0.0447396713621
y[1] (closed_form) = 0.284910944602 -0.044519962207
absolute error = 0.0003403
relative error = 0.118 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.514
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7131
Order of pole (three term test) = 8.545e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8225 1.271
h = 0.001 0.003
y[1] (numeric) = 0.284604855907 -0.0439353339204
y[1] (closed_form) = 0.284864953723 -0.0437132998011
absolute error = 0.000342
relative error = 0.1187 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.514
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.385
Order of pole (three term test) = 2.003e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8215 1.274
h = 0.0001 0.004
y[1] (numeric) = 0.283701198851 -0.0423725175399
y[1] (closed_form) = 0.283961069759 -0.0421552377456
absolute error = 0.0003387
relative error = 0.118 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.516
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.918
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8214 1.278
h = 0.003 0.006
y[1] (numeric) = 0.282029712546 -0.0408406230307
y[1] (closed_form) = 0.282292939372 -0.0406255411146
absolute error = 0.0003399
relative error = 0.1192 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.519
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.547
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8184 1.284
h = 0.0001 0.005
y[1] (numeric) = 0.280579014743 -0.0373700293341
y[1] (closed_form) = 0.280826463793 -0.0371622647787
absolute error = 0.0003231
relative error = 0.1141 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.523
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.135
Order of pole (three term test) = 5.717e-30 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1053.1MB, alloc=44.3MB, time=13.36
x[1] = -0.8183 1.289
h = 0.0001 0.003
y[1] (numeric) = 0.278474564153 -0.0355557596582
y[1] (closed_form) = 0.278731053466 -0.0353414632179
absolute error = 0.0003342
relative error = 0.119 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.527
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9164
Order of pole (three term test) = 2.004e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8182 1.292
h = 0.001 0.001
y[1] (numeric) = 0.277237126099 -0.0344672122224
y[1] (closed_form) = 0.277492403927 -0.0342487795647
absolute error = 0.000336
relative error = 0.1202 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.529
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7205
Order of pole (three term test) = 1.782e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8172 1.293
h = 0.0001 0.004
y[1] (numeric) = 0.277159731233 -0.0336979287606
y[1] (closed_form) = 0.277415098366 -0.0334772798332
absolute error = 0.0003375
relative error = 0.1208 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.53
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.328
Order of pole (three term test) = 6.272e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8171 1.297
h = 0.003 0.006
y[1] (numeric) = 0.275493035518 -0.0322742672409
y[1] (closed_form) = 0.275753407607 -0.0320610319469
absolute error = 0.0003365
relative error = 0.1212 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.533
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.57
Order of pole (three term test) = 9.583e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8141 1.303
h = 0.0001 0.005
y[1] (numeric) = 0.273973379136 -0.028979047541
y[1] (closed_form) = 0.274218998447 -0.0287734816936
absolute error = 0.0003203
relative error = 0.1162 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.536
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.145
Order of pole (three term test) = 1.079e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.814 1.308
h = 0.0001 0.003
y[1] (numeric) = 0.271881896731 -0.0273030388862
y[1] (closed_form) = 0.272135869397 -0.0270908473585
absolute error = 0.0003309
relative error = 0.121 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.541
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9247
Order of pole (three term test) = 9.588e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8139 1.311
h = 0.001 0.001
y[1] (numeric) = 0.270651372555 -0.0262963298627
y[1] (closed_form) = 0.270904011361 -0.0260802397031
absolute error = 0.0003324
relative error = 0.1222 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.543
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.727
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8129 1.312
h = 0.001 0.003
y[1] (numeric) = 0.270550256527 -0.0255573562108
y[1] (closed_form) = 0.270802886046 -0.0253391455217
absolute error = 0.0003338
relative error = 0.1227 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.543
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.451
Order of pole (three term test) = 8.306e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8119 1.315
h = 0.0001 0.004
y[1] (numeric) = 0.269602784424 -0.0241808219445
y[1] (closed_form) = 0.26985563191 -0.0239669274799
absolute error = 0.0003312
relative error = 0.1222 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.545
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.955
Order of pole (three term test) = 1.992e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8118 1.319
h = 0.003 0.006
y[1] (numeric) = 0.267949389206 -0.0228881376655
y[1] (closed_form) = 0.268205464104 -0.0226759318355
absolute error = 0.0003326
relative error = 0.1236 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.549
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.597
Order of pole (three term test) = 3.998e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8088 1.325
h = 0.0001 0.005
y[1] (numeric) = 0.266360211323 -0.0197895928715
y[1] (closed_form) = 0.266602673209 -0.0195853920993
absolute error = 0.000317
relative error = 0.1186 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.552
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.157
Order of pole (three term test) = 1.657e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8087 1.33
h = 0.0001 0.003
y[1] (numeric) = 0.264288354639 -0.0182660284974
y[1] (closed_form) = 0.26453841308 -0.0180551325542
absolute error = 0.0003271
relative error = 0.1234 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.557
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9343
Order of pole (three term test) = 1.333e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8086 1.333
h = 0.001 0.001
y[1] (numeric) = 0.263068588949 -0.0173495934999
y[1] (closed_form) = 0.263317190942 -0.0171350650354
absolute error = 0.0003284
relative error = 0.1244 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.559
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7345
Order of pole (three term test) = 7.342e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8076 1.334
h = 0.001 0.003
y[1] (numeric) = 0.262942378853 -0.0166450509238
y[1] (closed_form) = 0.263190868177 -0.0164285115288
absolute error = 0.0003296
relative error = 0.125 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.559
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.487
Order of pole (three term test) = 1.155e-29 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1099.4MB, alloc=44.3MB, time=13.94
x[1] = -0.8066 1.337
h = 0.0001 0.004
y[1] (numeric) = 0.261979486927 -0.0153627643918
y[1] (closed_form) = 0.262228394136 -0.0151503082164
absolute error = 0.0003272
relative error = 0.1246 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.561
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.976
Order of pole (three term test) = 1.380e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8065 1.341
h = 0.003 0.006
y[1] (numeric) = 0.260343276042 -0.0141885580309
y[1] (closed_form) = 0.26059532678 -0.0139775462356
absolute error = 0.0003287
relative error = 0.126 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.565
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.623
Order of pole (three term test) = 5.633e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8035 1.347
h = 0.0001 0.005
y[1] (numeric) = 0.258697809789 -0.0112799809291
y[1] (closed_form) = 0.258937336431 -0.0110772227231
absolute error = 0.0003138
relative error = 0.1211 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.568
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.169
Order of pole (three term test) = 1.483e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8034 1.352
h = 0.0001 0.003
y[1] (numeric) = 0.256651996973 -0.00990004452386
y[1] (closed_form) = 0.256898406128 -0.00969056973217
absolute error = 0.0003234
relative error = 0.1258 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.573
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9439
Order of pole (three term test) = 5.143e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8033 1.355
h = 0.001 0.001
y[1] (numeric) = 0.255446820523 -0.00906871703011
y[1] (closed_form) = 0.255691673551 -0.0088558664766
absolute error = 0.0003244
relative error = 0.1268 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.575
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7422
Order of pole (three term test) = 5.104e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8023 1.356
h = 0.001 0.003
y[1] (numeric) = 0.255298475956 -0.00839805155259
y[1] (closed_form) = 0.25554312562 -0.00818329885768
absolute error = 0.0003255
relative error = 0.1273 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.576
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.523
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8013 1.359
h = 0.0001 0.004
y[1] (numeric) = 0.254325525384 -0.00720590780136
y[1] (closed_form) = 0.254570767108 -0.00699500821244
absolute error = 0.0003235
relative error = 0.127 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.578
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.996
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8012 1.363
h = 0.003 0.006
y[1] (numeric) = 0.252711334312 -0.00614325121983
y[1] (closed_form) = 0.252959626867 -0.00593357163705
absolute error = 0.000325
relative error = 0.1284 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.581
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.651
Order of pole (three term test) = 1.650e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7982 1.369
h = 0.0001 0.005
y[1] (numeric) = 0.251021609475 -0.00341758462136
y[1] (closed_form) = 0.251258413866 -0.00321632972864
absolute error = 0.0003108
relative error = 0.1237 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.585
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.181
Order of pole (three term test) = 1.437e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7981 1.374
h = 0.0001 0.003
y[1] (numeric) = 0.249007356981 -0.00217263696567
y[1] (closed_form) = 0.249250372699 -0.00196468585989
absolute error = 0.0003198
relative error = 0.1283 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.589
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9537
Order of pole (three term test) = 7.702e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.798 1.377
h = 0.001 0.001
y[1] (numeric) = 0.247820069386 -0.00142135030135
y[1] (closed_form) = 0.248061449943 -0.00121027000478
absolute error = 0.0003207
relative error = 0.1293 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.592
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7498
Order of pole (three term test) = 1.419e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.797 1.378
h = 0.001 0.003
y[1] (numeric) = 0.24765233598 -0.000783873422737
y[1] (closed_form) = 0.247893434202 -0.0005709981873
absolute error = 0.0003216
relative error = 0.1297 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.592
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.56
Order of pole (three term test) = 1.004e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.796 1.381
h = 0.0001 0.004
y[1] (numeric) = 0.246674123316 0.000322284626619
y[1] (closed_form) = 0.246915964074 0.000531532494631
absolute error = 0.0003198
relative error = 0.1295 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.594
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.017
Order of pole (three term test) = 5.332e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7959 1.385
h = 0.003 0.006
y[1] (numeric) = 0.24508609608 0.0012801666358
y[1] (closed_form) = 0.245330888087 0.00148839984326
absolute error = 0.0003214
relative error = 0.131 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.597
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.678
Order of pole (three term test) = 1.013e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7929 1.391
h = 0.0001 0.005
y[1] (numeric) = 0.243363002494 0.00383022537642
y[1] (closed_form) = 0.243597288045 0.00402993120777
absolute error = 0.0003079
relative error = 0.1264 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.601
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.194
Order of pole (three term test) = 2.855e-30 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1145.7MB, alloc=44.3MB, time=14.53
x[1] = -0.7928 1.396
h = 0.0001 0.003
y[1] (numeric) = 0.24138500158 0.00494860011877
y[1] (closed_form) = 0.241624869754 0.00515494578261
absolute error = 0.0003164
relative error = 0.1309 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.605
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9636
Order of pole (three term test) = 9.941e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7927 1.399
h = 0.001 0.001
y[1] (numeric) = 0.240218415975 0.00562478529564
y[1] (closed_form) = 0.240456588461 0.00583402436957
absolute error = 0.000317
relative error = 0.1318 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.608
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7576
Order of pole (three term test) = 1.977e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7917 1.4
h = 0.003 0.006
y[1] (numeric) = 0.240033831993 0.00622987300517
y[1] (closed_form) = 0.240271653953 0.00644080204382
absolute error = 0.0003179
relative error = 0.1323 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.608
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.629
Order of pole (three term test) = 1.924e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7887 1.406
h = 0.0001 0.005
y[1] (numeric) = 0.238284802466 0.00867475089482
y[1] (closed_form) = 0.238517300067 0.00886634595758
absolute error = 0.0003013
relative error = 0.1262 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.612
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.202
Order of pole (three term test) = 3.554e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7886 1.411
h = 0.0001 0.003
y[1] (numeric) = 0.236331122153 0.00970977700383
y[1] (closed_form) = 0.236568791836 0.00990796957662
absolute error = 0.0003095
relative error = 0.1307 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.616
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9702
Order of pole (three term test) = 2.474e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7885 1.414
h = 0.001 0.001
y[1] (numeric) = 0.235178428474 0.0103364982599
y[1] (closed_form) = 0.235414364919 0.0105374295617
absolute error = 0.0003099
relative error = 0.1315 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.619
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7628
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7875 1.415
h = 0.001 0.003
y[1] (numeric) = 0.234982832741 0.010920172001
y[1] (closed_form) = 0.235218374969 0.0111227240496
absolute error = 0.0003107
relative error = 0.1319 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.619
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.621
Order of pole (three term test) = 1.737e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7865 1.418
h = 0.0001 0.004
y[1] (numeric) = 0.234003227742 0.0118905531007
y[1] (closed_form) = 0.234239723576 0.0120898429648
absolute error = 0.0003093
relative error = 0.1319 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.622
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.052
Order of pole (three term test) = 4.611e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7864 1.422
h = 0.003 0.006
y[1] (numeric) = 0.232464744172 0.0126855861472
y[1] (closed_form) = 0.232704016453 0.0128841701374
absolute error = 0.0003109
relative error = 0.1334 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.625
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.724
Order of pole (three term test) = 6.192e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7834 1.428
h = 0.0001 0.005
y[1] (numeric) = 0.230703054831 0.0149565249524
y[1] (closed_form) = 0.230933354126 0.0151465186802
absolute error = 0.0002986
relative error = 0.129 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.629
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.214
Order of pole (three term test) = 1.397e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7833 1.433
h = 0.0001 0.003
y[1] (numeric) = 0.228792073131 0.0158784986881
y[1] (closed_form) = 0.229026984983 0.0160749834686
absolute error = 0.0003063
relative error = 0.1334 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.633
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9802
Order of pole (three term test) = 3.437e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7832 1.436
h = 0.001 0.001
y[1] (numeric) = 0.22766396094 0.0164380600861
y[1] (closed_form) = 0.227897106068 0.0166370664787
absolute error = 0.0003065
relative error = 0.1341 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.636
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7706
Order of pole (three term test) = 1.713e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7822 1.437
h = 0.001 0.003
y[1] (numeric) = 0.227455375203 0.0169908344471
y[1] (closed_form) = 0.227688074149 0.0171913612772
absolute error = 0.0003072
relative error = 0.1345 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.636
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.658
Order of pole (three term test) = 1.073e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7812 1.44
h = 0.0001 0.004
y[1] (numeric) = 0.226480992693 0.0178862860496
y[1] (closed_form) = 0.226714741442 0.018083759775
absolute error = 0.000306
relative error = 0.1345 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.638
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.073
Order of pole (three term test) = 6.437e-30 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1192.0MB, alloc=44.3MB, time=15.12
x[1] = -0.7811 1.444
h = 0.003 0.006
y[1] (numeric) = 0.224976991731 0.0185936996704
y[1] (closed_form) = 0.225213406377 0.018790626476
absolute error = 0.0003077
relative error = 0.1361 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.642
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.752
Order of pole (three term test) = 1.050e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7781 1.45
h = 0.0001 0.005
y[1] (numeric) = 0.223206258404 0.0207090146332
y[1] (closed_form) = 0.223434536469 0.0208973940712
absolute error = 0.000296
relative error = 0.1319 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.646
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.227
Order of pole (three term test) = 6.860e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.778 1.455
h = 0.0001 0.003
y[1] (numeric) = 0.221340795855 0.0215256064593
y[1] (closed_form) = 0.221573166817 0.0217203476153
absolute error = 0.0003032
relative error = 0.1362 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.65
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9903
Order of pole (three term test) = 1.285e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7779 1.458
h = 0.001 0.001
y[1] (numeric) = 0.22023897375 0.0220225184758
y[1] (closed_form) = 0.220469557923 0.0222195756478
absolute error = 0.0003033
relative error = 0.1369 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.653
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7786
Order of pole (three term test) = 2.365e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7769 1.459
h = 0.001 0.003
y[1] (numeric) = 0.220019421048 0.0225453969251
y[1] (closed_form) = 0.220249515497 0.0227438776393
absolute error = 0.0003039
relative error = 0.1372 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.653
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.696
Order of pole (three term test) = 7.451e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7759 1.462
h = 0.0001 0.004
y[1] (numeric) = 0.219053292458 0.0233699734591
y[1] (closed_form) = 0.219284516101 0.0235656023841
absolute error = 0.0003029
relative error = 0.1373 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.655
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.094
Order of pole (three term test) = 1.778e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7758 1.466
h = 0.003 0.006
y[1] (numeric) = 0.217585857057 0.0239957500029
y[1] (closed_form) = 0.217819634531 0.0241909754927
absolute error = 0.0003046
relative error = 0.139 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.659
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.781
Order of pole (three term test) = 1.246e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7728 1.472
h = 0.0001 0.005
y[1] (numeric) = 0.215813339697 0.025962973154
y[1] (closed_form) = 0.216039763698 0.0261497348865
absolute error = 0.0002935
relative error = 0.1349 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.663
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.239
Order of pole (three term test) = 9.521e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7727 1.477
h = 0.0001 0.003
y[1] (numeric) = 0.21399564509 0.0266815309108
y[1] (closed_form) = 0.214225680729 0.0268745061735
absolute error = 0.0003003
relative error = 0.1391 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.667
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.001
Order of pole (three term test) = 7.402e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7726 1.48
h = 0.001 0.001
y[1] (numeric) = 0.21292148342 0.0271201172563
y[1] (closed_form) = 0.213149723979 0.0273152144437
absolute error = 0.0003003
relative error = 0.1397 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.67
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7866
Order of pole (three term test) = 3.281e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7716 1.481
h = 0.0001 0.004
y[1] (numeric) = 0.212692811389 0.0276141467728
y[1] (closed_form) = 0.2129205263 0.0278105742819
absolute error = 0.0003007
relative error = 0.1401 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.67
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.725
Order of pole (three term test) = 1.444e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7715 1.485
h = 0.003 0.006
y[1] (numeric) = 0.211256637051 0.0281774834063
y[1] (closed_form) = 0.211489235208 0.02837084259
absolute error = 0.0003025
relative error = 0.1418 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.673
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.806
Order of pole (three term test) = 1.656e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7685 1.491
h = 0.0001 0.005
y[1] (numeric) = 0.20948940624 0.0300232819601
y[1] (closed_form) = 0.209715281815 0.0302082858157
absolute error = 0.000292
relative error = 0.1378 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.677
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.251
Order of pole (three term test) = 1.545e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7684 1.496
h = 0.0001 0.003
y[1] (numeric) = 0.20771529203 0.0306636806406
y[1] (closed_form) = 0.207944396509 0.0308547529925
absolute error = 0.0002983
relative error = 0.1419 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.682
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.009
Order of pole (three term test) = 8.811e-30 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1238.2MB, alloc=44.3MB, time=15.72
x[1] = -0.7683 1.499
h = 0.001 0.001
y[1] (numeric) = 0.206666432823 0.0310557229382
y[1] (closed_form) = 0.206893745487 0.0312487593314
absolute error = 0.0002982
relative error = 0.1425 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.684
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7936
Order of pole (three term test) = 8.720e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7673 1.5
h = 0.001 0.003
y[1] (numeric) = 0.206431590195 0.0315257001572
y[1] (closed_form) = 0.206658352862 0.031719989399
absolute error = 0.0002986
relative error = 0.1428 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.685
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.767
Order of pole (three term test) = 2.457e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7663 1.503
h = 0.0001 0.004
y[1] (numeric) = 0.205488295143 0.0322290280173
y[1] (closed_form) = 0.205716293453 0.0324208185195
absolute error = 0.0002979
relative error = 0.1431 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.687
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.135
Order of pole (three term test) = 1.511e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7662 1.507
h = 0.003 0.006
y[1] (numeric) = 0.204093802088 0.0327184052957
y[1] (closed_form) = 0.204324143757 0.0329100202984
absolute error = 0.0002996
relative error = 0.1448 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.691
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.834
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7632 1.513
h = 0.0001 0.005
y[1] (numeric) = 0.20233605102 0.0344299296333
y[1] (closed_form) = 0.202560357595 0.0346133324345
absolute error = 0.0002897
relative error = 0.141 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.695
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.263
Order of pole (three term test) = 3.923e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7631 1.518
h = 0.0001 0.003
y[1] (numeric) = 0.200612491567 0.0349850874073
y[1] (closed_form) = 0.200839612977 0.0351743851205
absolute error = 0.0002957
relative error = 0.145 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.699
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.02
Order of pole (three term test) = 8.200e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.763 1.521
h = 0.001 0.001
y[1] (numeric) = 0.199593014882 0.0353263396449
y[1] (closed_form) = 0.199818354047 0.0355174284149
absolute error = 0.0002955
relative error = 0.1456 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.702
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8017
Order of pole (three term test) = 8.538e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.762 1.522
h = 0.001 0.003
y[1] (numeric) = 0.199352044895 0.0357695046118
y[1] (closed_form) = 0.199576810297 0.0359617603631
absolute error = 0.0002958
relative error = 0.1459 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.702
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.806
Order of pole (three term test) = 2.553e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.761 1.525
h = 0.0001 0.004
y[1] (numeric) = 0.198423564169 0.0364130213534
y[1] (closed_form) = 0.198649605441 0.0366029553302
absolute error = 0.0002952
relative error = 0.1462 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.704
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.157
Order of pole (three term test) = 3.211e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7609 1.529
h = 0.003 0.006
y[1] (numeric) = 0.197069284924 0.0368364386563
y[1] (closed_form) = 0.197297558472 0.0370263019039
absolute error = 0.0002969
relative error = 0.1479 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.708
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.863
Order of pole (three term test) = 6.805e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7579 1.535
h = 0.0001 0.005
y[1] (numeric) = 0.195326070972 0.0384208586268
y[1] (closed_form) = 0.195548948322 0.0386026777555
absolute error = 0.0002876
relative error = 0.1443 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.712
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.276
Order of pole (three term test) = 2.429e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7578 1.54
h = 0.0001 0.003
y[1] (numeric) = 0.193654000141 0.0388971509801
y[1] (closed_form) = 0.19387931174 0.0390846818204
absolute error = 0.0002931
relative error = 0.1482 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.716
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.03
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7577 1.543
h = 0.001 0.001
y[1] (numeric) = 0.192664496674 0.0391913718833
y[1] (closed_form) = 0.192888043401 0.0393805317053
absolute error = 0.0002928
relative error = 0.1487 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.719
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8099
Order of pole (three term test) = 4.176e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7567 1.544
h = 0.001 0.003
y[1] (numeric) = 0.192418799875 0.0396088258339
y[1] (closed_form) = 0.19264175466 0.0397990708041
absolute error = 0.0002931
relative error = 0.149 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.719
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.845
Order of pole (three term test) = 1.229e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7557 1.547
h = 0.0001 0.004
y[1] (numeric) = 0.191506820688 0.0401961504679
y[1] (closed_form) = 0.191731080592 0.0403842418828
absolute error = 0.0002927
relative error = 0.1494 %
Correct digits = 3
memory used=1284.5MB, alloc=44.3MB, time=16.31
Radius of convergence (given) for eq 1 = 1.722
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.178
Order of pole (three term test) = 7.024e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7556 1.551
h = 0.003 0.006
y[1] (numeric) = 0.190193403305 0.040558562535
y[1] (closed_form) = 0.190419786063 0.0407466763216
absolute error = 0.0002943
relative error = 0.1512 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.725
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.892
Order of pole (three term test) = 8.419e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7526 1.557
h = 0.0001 0.005
y[1] (numeric) = 0.188469130874 0.0420228603097
y[1] (closed_form) = 0.188690709764 0.0422031185445
absolute error = 0.0002856
relative error = 0.1477 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.729
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.289
Order of pole (three term test) = 1.008e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7525 1.562
h = 0.0001 0.003
y[1] (numeric) = 0.186849119314 0.0424263224979
y[1] (closed_form) = 0.187072783529 0.0426121021641
absolute error = 0.0002908
relative error = 0.1515 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.734
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.041
Order of pole (three term test) = 1.649e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7524 1.565
h = 0.001 0.001
y[1] (numeric) = 0.185889963848 0.0426770725769
y[1] (closed_form) = 0.186111887213 0.0428643297251
absolute error = 0.0002904
relative error = 0.152 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.736
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8181
Order of pole (three term test) = 3.463e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7514 1.566
h = 0.001 0.003
y[1] (numeric) = 0.185640803676 0.0430699174834
y[1] (closed_form) = 0.185862121894 0.0432581820069
absolute error = 0.0002906
relative error = 0.1523 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.737
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.884
Order of pole (three term test) = 1.627e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7504 1.569
h = 0.0001 0.004
y[1] (numeric) = 0.184746738296 0.0436045315664
y[1] (closed_form) = 0.184969381158 0.043790802016
absolute error = 0.0002903
relative error = 0.1527 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.739
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.201
Order of pole (three term test) = 1.360e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7503 1.573
h = 0.003 0.006
y[1] (numeric) = 0.183474555501 0.0439106254914
y[1] (closed_form) = 0.183699213981 0.0440970006541
absolute error = 0.0002919
relative error = 0.1545 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.743
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.922
Order of pole (three term test) = 5.816e-31 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7473 1.579
h = 0.0001 0.005
y[1] (numeric) = 0.181773032263 0.0452615725369
y[1] (closed_form) = 0.181993434776 0.0454402972124
absolute error = 0.0002838
relative error = 0.1513 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.747
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.302
Order of pole (three term test) = 3.250e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7472 1.584
h = 0.0001 0.003
y[1] (numeric) = 0.180205331632 0.0455979034914
y[1] (closed_form) = 0.180427500377 0.0457819544583
absolute error = 0.0002885
relative error = 0.155 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.751
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.051
Order of pole (three term test) = 1.734e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7471 1.587
h = 0.001 0.001
y[1] (numeric) = 0.179276709035 0.0458085470836
y[1] (closed_form) = 0.179497166562 0.0459939342297
absolute error = 0.000288
relative error = 0.1555 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.754
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8264
Order of pole (three term test) = 5.747e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7461 1.588
h = 0.0001 0.004
y[1] (numeric) = 0.179025221382 0.0461778780954
y[1] (closed_form) = 0.179245064963 0.0463641988897
absolute error = 0.0002882
relative error = 0.1557 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.755
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.964
Order of pole (three term test) = 1.563e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.746 1.592
h = 0.003 0.006
y[1] (numeric) = 0.177786946934 0.0464412758206
y[1] (closed_form) = 0.178011013159 0.0466260268642
absolute error = 0.0002904
relative error = 0.1578 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.758
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.948
Order of pole (three term test) = 2.309e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.743 1.598
h = 0.0001 0.005
y[1] (numeric) = 0.176108882881 0.0477002253783
y[1] (closed_form) = 0.176329128221 0.0478775187938
absolute error = 0.0002827
relative error = 0.1547 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.762
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.314
Order of pole (three term test) = 3.687e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7429 1.603
h = 0.0001 0.003
y[1] (numeric) = 0.174586911019 0.0479837054427
y[1] (closed_form) = 0.17480867279 0.0481661514178
absolute error = 0.0002872
relative error = 0.1584 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.767
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.06
Order of pole (three term test) = 7.682e-30 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1330.9MB, alloc=44.3MB, time=16.89
x[1] = -0.7428 1.606
h = 0.001 0.001
y[1] (numeric) = 0.173685017504 0.0481627371699
y[1] (closed_form) = 0.173905098868 0.0483464059746
absolute error = 0.0002867
relative error = 0.1588 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.769
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8337
Order of pole (three term test) = 1.075e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7418 1.607
h = 0.001 0.003
y[1] (numeric) = 0.173432608069 0.0485126837408
y[1] (closed_form) = 0.173652071854 0.0486972258929
absolute error = 0.0002867
relative error = 0.159 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.77
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.958
Order of pole (three term test) = 1.072e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7408 1.61
h = 0.0001 0.004
y[1] (numeric) = 0.172575340133 0.0489582322531
y[1] (closed_form) = 0.172796141231 0.049141054181
absolute error = 0.0002867
relative error = 0.1596 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.772
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.242
Order of pole (three term test) = 2.507e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7407 1.614
h = 0.003 0.006
y[1] (numeric) = 0.171380624457 0.0491715972298
y[1] (closed_form) = 0.171603248135 0.0493546502013
absolute error = 0.0002882
relative error = 0.1614 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.776
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.977
Order of pole (three term test) = 1.067e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7377 1.62
h = 0.0001 0.005
y[1] (numeric) = 0.169730912329 0.0503292092045
y[1] (closed_form) = 0.169950186171 0.0505050307464
absolute error = 0.0002811
relative error = 0.1585 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.78
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.327
Order of pole (three term test) = 8.639e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7376 1.625
h = 0.0001 0.003
y[1] (numeric) = 0.168260947788 0.0505552862065
y[1] (closed_form) = 0.168481469655 0.0507360613677
absolute error = 0.0002851
relative error = 0.1621 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.785
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.071
Order of pole (three term test) = 5.901e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7375 1.628
h = 0.001 0.001
y[1] (numeric) = 0.167389470889 0.0506999602718
y[1] (closed_form) = 0.167608349904 0.050881834864
absolute error = 0.0002846
relative error = 0.1625 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.787
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8421
Order of pole (three term test) = 4.107e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7365 1.629
h = 0.001 0.003
y[1] (numeric) = 0.167136527019 0.0510284019408
y[1] (closed_form) = 0.16735478645 0.0512110835725
absolute error = 0.0002846
relative error = 0.1626 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.788
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.998
Order of pole (three term test) = 6.397e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7355 1.632
h = 0.0001 0.004
y[1] (numeric) = 0.166299891299 0.0514304087458
y[1] (closed_form) = 0.166519485887 0.0516115052387
absolute error = 0.0002846
relative error = 0.1633 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.79
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.265
Order of pole (three term test) = 1.092e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7354 1.636
h = 0.003 0.006
y[1] (numeric) = 0.165146201508 0.051599422898
y[1] (closed_form) = 0.165367519864 0.0517808066877
absolute error = 0.0002862
relative error = 0.1651 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.794
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.007
Order of pole (three term test) = 1.490e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7324 1.642
h = 0.0001 0.005
y[1] (numeric) = 0.163527227651 0.0526617785779
y[1] (closed_form) = 0.163745629232 0.0528361646172
absolute error = 0.0002795
relative error = 0.1624 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.798
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.34
Order of pole (three term test) = 3.499e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7323 1.647
h = 0.0001 0.003
y[1] (numeric) = 0.162108824375 0.0528352281982
y[1] (closed_form) = 0.162328230269 0.0530143688817
absolute error = 0.0002832
relative error = 0.1659 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.802
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.082
Order of pole (three term test) = 5.713e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7322 1.65
h = 0.001 0.001
y[1] (numeric) = 0.161267532124 0.0529483693167
y[1] (closed_form) = 0.161485335923 0.0531284949891
absolute error = 0.0002826
relative error = 0.1663 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.805
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8505
Order of pole (three term test) = 2.397e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7312 1.651
h = 0.001 0.003
y[1] (numeric) = 0.161014875025 0.0532563489194
y[1] (closed_form) = 0.161232060265 0.0534372191598
absolute error = 0.0002826
relative error = 0.1664 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.806
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.038
Order of pole (three term test) = 6.761e-30 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1377.2MB, alloc=44.3MB, time=17.48
x[1] = -0.7302 1.654
h = 0.0001 0.004
y[1] (numeric) = 0.160199459372 0.0536177293548
y[1] (closed_form) = 0.160417971819 0.0537971414495
absolute error = 0.0002827
relative error = 0.1671 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.808
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.288
Order of pole (three term test) = 1.502e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7301 1.658
h = 0.003 0.006
y[1] (numeric) = 0.159086400336 0.0537460940999
y[1] (closed_form) = 0.159306541125 0.0539258420999
absolute error = 0.0002842
relative error = 0.169 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.812
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.037
Order of pole (three term test) = 2.842e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7271 1.664
h = 0.0001 0.005
y[1] (numeric) = 0.157500142196 0.0547190198071
y[1] (closed_form) = 0.157717763523 0.0548920087727
absolute error = 0.000278
relative error = 0.1665 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.816
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.354
Order of pole (three term test) = 4.812e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.727 1.669
h = 0.0001 0.003
y[1] (numeric) = 0.156132671944 0.0548443154893
y[1] (closed_form) = 0.156351076863 0.0550218613366
absolute error = 0.0002815
relative error = 0.1698 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.82
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.093
Order of pole (three term test) = 1.242e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7269 1.672
h = 0.001 0.001
y[1] (numeric) = 0.15532122305 0.0549285714176
y[1] (closed_form) = 0.155538069164 0.0551069963138
absolute error = 0.0002808
relative error = 0.1702 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.823
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.859
Order of pole (three term test) = 1.647e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7259 1.673
h = 0.001 0.003
y[1] (numeric) = 0.155069580105 0.0552171059363
y[1] (closed_form) = 0.155285811314 0.0553962166534
absolute error = 0.0002808
relative error = 0.1703 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.824
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.078
Order of pole (three term test) = 1.095e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7249 1.676
h = 0.0001 0.004
y[1] (numeric) = 0.154275810962 0.0555406286397
y[1] (closed_form) = 0.154493356436 0.0557184003776
absolute error = 0.0002809
relative error = 0.1711 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.826
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.311
Order of pole (three term test) = 1.664e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7248 1.68
h = 0.003 0.006
y[1] (numeric) = 0.153202850618 0.0556318097764
y[1] (closed_form) = 0.153421932545 0.0558099590779
absolute error = 0.0002824
relative error = 0.173 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.83
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.068
Order of pole (three term test) = 3.903e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7218 1.686
h = 0.0001 0.005
y[1] (numeric) = 0.151650917688 0.0565208738117
y[1] (closed_form) = 0.151867843918 0.0566925057072
absolute error = 0.0002766
relative error = 0.1706 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.834
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.367
Order of pole (three term test) = 6.608e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7217 1.691
h = 0.0001 0.003
y[1] (numeric) = 0.150333597661 0.0566021984423
y[1] (closed_form) = 0.150551108117 0.0567781917236
absolute error = 0.0002798
relative error = 0.1739 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.839
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.104
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7216 1.694
h = 0.001 0.001
y[1] (numeric) = 0.149551557827 0.0566600466719
y[1] (closed_form) = 0.149767554707 0.0568368211069
absolute error = 0.0002791
relative error = 0.1742 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.841
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8675
Order of pole (three term test) = 7.532e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7206 1.695
h = 0.0001 0.004
y[1] (numeric) = 0.149301570316 0.0569301243409
y[1] (closed_form) = 0.149516958212 0.0571075294492
absolute error = 0.000279
relative error = 0.1743 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.842
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.211
Order of pole (three term test) = 6.636e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7205 1.699
h = 0.003 0.006
y[1] (numeric) = 0.14826097793 0.0569933734556
y[1] (closed_form) = 0.148479849256 0.0571701806999
absolute error = 0.0002814
relative error = 0.1768 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.845
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.094
Order of pole (three term test) = 5.137e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7175 1.705
h = 0.0001 0.005
y[1] (numeric) = 0.146740540405 0.0578149425481
y[1] (closed_form) = 0.146957541038 0.0579854451244
absolute error = 0.000276
relative error = 0.1747 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.85
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.379
Order of pole (three term test) = 1.195e-29 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1423.4MB, alloc=44.3MB, time=18.08
x[1] = -0.7174 1.71
h = 0.0001 0.003
y[1] (numeric) = 0.145466122646 0.0578621374316
y[1] (closed_form) = 0.145683554077 0.0580368335513
absolute error = 0.0002789
relative error = 0.1779 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.854
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.113
Order of pole (three term test) = 1.003e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7173 1.713
h = 0.001 0.001
y[1] (numeric) = 0.144709266645 0.0578994557511
y[1] (closed_form) = 0.14492522563 0.0580748554155
absolute error = 0.0002782
relative error = 0.1782 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.857
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.875
Order of pole (three term test) = 1.401e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7163 1.714
h = 0.001 0.003
y[1] (numeric) = 0.144461361642 0.0581544427743
y[1] (closed_form) = 0.144676718902 0.0583304285228
absolute error = 0.0002781
relative error = 0.1783 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.858
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.154
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7153 1.717
h = 0.0001 0.004
y[1] (numeric) = 0.14370890889 0.0584146600674
y[1] (closed_form) = 0.14392554427 0.058589508492
absolute error = 0.0002784
relative error = 0.1792 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.86
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.354
Order of pole (three term test) = 4.816e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7152 1.721
h = 0.003 0.006
y[1] (numeric) = 0.142709119678 0.0584455655031
y[1] (closed_form) = 0.142927129915 0.0586208517057
absolute error = 0.0002797
relative error = 0.1811 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.864
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.125
Order of pole (three term test) = 1.115e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7122 1.727
h = 0.0001 0.005
y[1] (numeric) = 0.141225091562 0.0591929578895
y[1] (closed_form) = 0.141441538129 0.0593621814439
absolute error = 0.0002747
relative error = 0.1791 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.868
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.393
Order of pole (three term test) = 2.779e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7121 1.732
h = 0.0001 0.003
y[1] (numeric) = 0.139998996875 0.0592032216787
y[1] (closed_form) = 0.140215710447 0.0593764499367
absolute error = 0.0002774
relative error = 0.1822 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.873
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.124
Order of pole (three term test) = 1.399e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.712 1.735
h = 0.001 0.001
y[1] (numeric) = 0.139270518329 0.0592183064782
y[1] (closed_form) = 0.139485806872 0.0593921541615
absolute error = 0.0002767
relative error = 0.1825 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.875
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8836
Order of pole (three term test) = 1.362e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.711 1.736
h = 0.001 0.003
y[1] (numeric) = 0.139025246591 0.0594565973171
y[1] (closed_form) = 0.139239942659 0.0596309822859
absolute error = 0.0002766
relative error = 0.1826 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.876
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.195
Order of pole (three term test) = 9.561e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.71 1.739
h = 0.0001 0.004
y[1] (numeric) = 0.138294899557 0.059686089041
y[1] (closed_form) = 0.138510850373 0.0598594350869
absolute error = 0.0002769
relative error = 0.1835 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.878
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.377
Order of pole (three term test) = 1.628e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7099 1.743
h = 0.003 0.006
y[1] (numeric) = 0.137333077578 0.0596884999664
y[1] (closed_form) = 0.137550321941 0.0598623090378
absolute error = 0.0002782
relative error = 0.1855 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.882
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.155
Order of pole (three term test) = 7.105e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7069 1.749
h = 0.0001 0.005
y[1] (numeric) = 0.135886218217 0.0603665470694
y[1] (closed_form) = 0.136102178361 0.0605345338674
absolute error = 0.0002736
relative error = 0.1837 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.886
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.406
Order of pole (three term test) = 5.430e-31 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7068 1.754
h = 0.0001 0.003
y[1] (numeric) = 0.13470735284 0.0603432997049
y[1] (closed_form) = 0.134923433262 0.0605151067419
absolute error = 0.0002761
relative error = 0.1867 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.891
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.135
Order of pole (three term test) = 1.876e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7067 1.757
h = 0.001 0.001
y[1] (numeric) = 0.134006628984 0.0603381806893
y[1] (closed_form) = 0.134221332416 0.0605105297942
absolute error = 0.0002753
relative error = 0.187 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.894
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8922
Order of pole (three term test) = 3.705e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7057 1.758
h = 0.001 0.003
y[1] (numeric) = 0.133764424551 0.060560670123
y[1] (closed_form) = 0.13397854617 0.0607335109058
absolute error = 0.0002752
relative error = 0.1871 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.894
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.236
Order of pole (three term test) = 9.421e-30 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1469.8MB, alloc=44.3MB, time=18.66
x[1] = -0.7047 1.761
h = 0.0001 0.004
y[1] (numeric) = 0.133056146924 0.0607616636439
y[1] (closed_form) = 0.133271497347 0.0609335572815
absolute error = 0.0002755
relative error = 0.188 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.897
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.4
Order of pole (three term test) = 6.963e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7046 1.765
h = 0.003 0.006
y[1] (numeric) = 0.13213141265 0.0607382266347
y[1] (closed_form) = 0.132347979002 0.0609106038545
absolute error = 0.0002768
relative error = 0.19 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.9
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.186
Order of pole (three term test) = 1.868e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7016 1.771
h = 0.0001 0.005
y[1] (numeric) = 0.130722244058 0.0613515108296
y[1] (closed_form) = 0.130937780005 0.0615183033438
absolute error = 0.0002725
relative error = 0.1884 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.905
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.42
Order of pole (three term test) = 8.156e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7015 1.776
h = 0.0001 0.003
y[1] (numeric) = 0.129589441603 0.0612979310257
y[1] (closed_form) = 0.129804966816 0.0614683641779
absolute error = 0.0002748
relative error = 0.1913 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.91
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.146
Order of pole (three term test) = 2.573e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7014 1.779
h = 0.001 0.001
y[1] (numeric) = 0.128915805177 0.0612744961165
y[1] (closed_form) = 0.129130001711 0.061445400316
absolute error = 0.000274
relative error = 0.1916 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.912
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.901
Order of pole (three term test) = 9.112e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7004 1.78
h = 0.001 0.003
y[1] (numeric) = 0.128677041661 0.0614820445046
y[1] (closed_form) = 0.128890668218 0.0616533978157
absolute error = 0.0002739
relative error = 0.1917 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.913
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.277
Order of pole (three term test) = 1.611e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6994 1.783
h = 0.0001 0.004
y[1] (numeric) = 0.127990711169 0.0616566372311
y[1] (closed_form) = 0.128205538489 0.0618271288784
absolute error = 0.0002743
relative error = 0.1927 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.915
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.423
Order of pole (three term test) = 2.687e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6993 1.787
h = 0.003 0.006
y[1] (numeric) = 0.127102131515 0.061609811643
y[1] (closed_form) = 0.127318100807 0.0617808032212
absolute error = 0.0002755
relative error = 0.1947 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.919
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.217
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6963 1.793
h = 0.0001 0.005
y[1] (numeric) = 0.125730965719 0.0621626721059
y[1] (closed_form) = 0.125946134625 0.0623283127658
absolute error = 0.0002715
relative error = 0.1932 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.923
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.434
Order of pole (three term test) = 1.011e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6962 1.798
h = 0.0001 0.003
y[1] (numeric) = 0.124643003013 0.0620817102395
y[1] (closed_form) = 0.124858044619 0.0622508171824
absolute error = 0.0002736
relative error = 0.1961 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.928
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.157
Order of pole (three term test) = 2.093e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6961 1.801
h = 0.001 0.001
y[1] (numeric) = 0.123995751674 0.0620417130522
y[1] (closed_form) = 0.124209512876 0.062211225947
absolute error = 0.0002728
relative error = 0.1964 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.931
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9097
Order of pole (three term test) = 1.379e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6951 1.802
h = 0.0001 0.004
y[1] (numeric) = 0.123760747862 0.0622351459021
y[1] (closed_form) = 0.123973951884 0.0624050682332
absolute error = 0.0002726
relative error = 0.1964 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.931
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.465
Order of pole (three term test) = 8.582e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.695 1.806
h = 0.003 0.006
y[1] (numeric) = 0.122901045371 0.0621709500007
y[1] (closed_form) = 0.123117036818 0.0623408693659
absolute error = 0.0002748
relative error = 0.1991 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.935
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.244
Order of pole (three term test) = 3.706e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.692 1.812
h = 0.0001 0.005
y[1] (numeric) = 0.121563352901 0.0626755480621
y[1] (closed_form) = 0.121778721536 0.0628403164854
absolute error = 0.0002712
relative error = 0.1979 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.94
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.446
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1516.1MB, alloc=44.3MB, time=19.27
x[1] = -0.6919 1.817
h = 0.0001 0.003
y[1] (numeric) = 0.120513256602 0.0625737277627
y[1] (closed_form) = 0.120728410239 0.0627418156368
absolute error = 0.000273
relative error = 0.2007 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.944
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.167
Order of pole (three term test) = 9.119e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6918 1.82
h = 0.001 0.001
y[1] (numeric) = 0.119888304821 0.0625210838891
y[1] (closed_form) = 0.120102220073 0.0626895266959
absolute error = 0.0002723
relative error = 0.201 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.947
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9173
Order of pole (three term test) = 7.739e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6908 1.821
h = 0.001 0.003
y[1] (numeric) = 0.119656909909 0.062703049932
y[1] (closed_form) = 0.119870280044 0.0628718703888
absolute error = 0.0002721
relative error = 0.201 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.948
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.355
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6898 1.824
h = 0.0001 0.004
y[1] (numeric) = 0.119011106943 0.0628339290916
y[1] (closed_form) = 0.119225620632 0.06300203093
absolute error = 0.0002725
relative error = 0.2021 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.95
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.467
Order of pole (three term test) = 1.690e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6897 1.828
h = 0.003 0.006
y[1] (numeric) = 0.118187402265 0.0627499319177
y[1] (closed_form) = 0.118402929746 0.0629185536213
absolute error = 0.0002737
relative error = 0.2041 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.954
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.276
Order of pole (three term test) = 4.507e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6867 1.834
h = 0.0001 0.005
y[1] (numeric) = 0.116887772948 0.0632015559518
y[1] (closed_form) = 0.117102868021 0.0633652511996
absolute error = 0.0002703
relative error = 0.203 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.958
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.46
Order of pole (three term test) = 1.048e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6866 1.839
h = 0.0001 0.003
y[1] (numeric) = 0.115880106534 0.0630772636266
y[1] (closed_form) = 0.116094893734 0.0632441145778
absolute error = 0.000272
relative error = 0.2057 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.963
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.178
Order of pole (three term test) = 8.761e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6865 1.842
h = 0.001 0.001
y[1] (numeric) = 0.115280149837 0.063010979292
y[1] (closed_form) = 0.11549374615 0.063178130061
absolute error = 0.0002712
relative error = 0.206 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.966
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9262
Order of pole (three term test) = 6.110e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6855 1.843
h = 0.001 0.003
y[1] (numeric) = 0.11505297057 0.063180275408
y[1] (closed_form) = 0.115266035825 0.06334776914
absolute error = 0.000271
relative error = 0.2061 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.966
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.397
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6845 1.846
h = 0.0001 0.004
y[1] (numeric) = 0.114428369518 0.0632900762935
y[1] (closed_form) = 0.114642546513 0.0634569206559
absolute error = 0.0002715
relative error = 0.2072 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.969
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.491
Order of pole (three term test) = 8.278e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6844 1.85
h = 0.003 0.006
y[1] (numeric) = 0.113637933441 0.0631887697472
y[1] (closed_form) = 0.113853060406 0.0633561406547
absolute error = 0.0002726
relative error = 0.2092 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.973
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.307
Order of pole (three term test) = 3.059e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6814 1.856
h = 0.0001 0.005
y[1] (numeric) = 0.112376211427 0.0635911015732
y[1] (closed_form) = 0.112591077369 0.0637537648254
absolute error = 0.0002695
relative error = 0.2083 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.977
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.474
Order of pole (three term test) = 2.439e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6813 1.861
h = 0.0001 0.003
y[1] (numeric) = 0.111409662995 0.0634467034301
y[1] (closed_form) = 0.111624139419 0.0636123644912
absolute error = 0.000271
relative error = 0.2109 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.982
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.189
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6812 1.864
h = 0.001 0.001
y[1] (numeric) = 0.110833942532 0.0633681881642
y[1] (closed_form) = 0.111047274901 0.0635340987672
absolute error = 0.0002703
relative error = 0.2112 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.985
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.935
Order of pole (three term test) = 8.286e-30 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1562.5MB, alloc=44.3MB, time=19.86
x[1] = -0.6802 1.865
h = 0.001 0.003
y[1] (numeric) = 0.110611168662 0.0635255399427
y[1] (closed_form) = 0.1108239845 0.0636917612881
absolute error = 0.00027
relative error = 0.2113 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.985
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.439
Order of pole (three term test) = 1.169e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6792 1.868
h = 0.0001 0.004
y[1] (numeric) = 0.110007416087 0.0636159045587
y[1] (closed_form) = 0.110221311129 0.0637815407236
absolute error = 0.0002705
relative error = 0.2124 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.988
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.515
Order of pole (three term test) = 1.341e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6791 1.872
h = 0.003 0.006
y[1] (numeric) = 0.109249211083 0.0634991182305
y[1] (closed_form) = 0.109463995621 0.063665284931
absolute error = 0.0002716
relative error = 0.2144 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.991
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.339
Order of pole (three term test) = 8.304e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6761 1.878
h = 0.0001 0.005
y[1] (numeric) = 0.10802511493 0.063855626428
y[1] (closed_form) = 0.108239792298 0.0640172981601
absolute error = 0.0002687
relative error = 0.2137 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.996
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.488
Order of pole (three term test) = 9.915e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.676 1.883
h = 0.0001 0.003
y[1] (numeric) = 0.107098360782 0.0636933078264
y[1] (closed_form) = 0.107312577237 0.0638578254121
absolute error = 0.0002701
relative error = 0.2163 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.001
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.201
Order of pole (three term test) = 1.138e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6759 1.886
h = 0.001 0.001
y[1] (numeric) = 0.106546109432 0.063603864495
y[1] (closed_form) = 0.106759227838 0.0637685858413
absolute error = 0.0002694
relative error = 0.2166 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.003
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9439
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6749 1.887
h = 0.001 0.003
y[1] (numeric) = 0.106327893869 0.0637499636071
y[1] (closed_form) = 0.106540510609 0.0639149658001
absolute error = 0.0002691
relative error = 0.2166 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.004
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.481
Order of pole (three term test) = 3.166e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6739 1.89
h = 0.0001 0.004
y[1] (numeric) = 0.105744597008 0.0638224289051
y[1] (closed_form) = 0.105958259947 0.0639869053476
absolute error = 0.0002696
relative error = 0.2178 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.007
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.539
Order of pole (three term test) = 2.108e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6738 1.894
h = 0.003 0.006
y[1] (numeric) = 0.105017578083 0.0636918523528
y[1] (closed_form) = 0.105232073291 0.0638568609471
absolute error = 0.0002706
relative error = 0.2199 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.01
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.37
Order of pole (three term test) = 1.742e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6708 1.9
h = 0.0001 0.005
y[1] (numeric) = 0.103830717883 0.0640058009608
y[1] (closed_form) = 0.104045243635 0.0641665208339
absolute error = 0.0002681
relative error = 0.2193 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.015
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.502
Order of pole (three term test) = 4.999e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6707 1.905
h = 0.0001 0.003
y[1] (numeric) = 0.102942430798 0.0638275777452
y[1] (closed_form) = 0.103156433581 0.06399099749
absolute error = 0.0002693
relative error = 0.2218 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.02
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.212
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6706 1.908
h = 0.001 0.001
y[1] (numeric) = 0.102412878123 0.0637284091654
y[1] (closed_form) = 0.102625827904 0.0638919910579
absolute error = 0.0002685
relative error = 0.2221 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.022
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9528
Order of pole (three term test) = 7.583e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6696 1.909
h = 0.0001 0.004
y[1] (numeric) = 0.102199340737 0.0638639140529
y[1] (closed_form) = 0.10241180394 0.0640277490839
absolute error = 0.0002683
relative error = 0.2221 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.023
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.724
Order of pole (three term test) = 4.010e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6695 1.913
h = 0.003 0.006
y[1] (numeric) = 0.101497067322 0.0637232692683
y[1] (closed_form) = 0.101711715922 0.0638874406663
absolute error = 0.0002702
relative error = 0.225 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.027
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.398
Order of pole (three term test) = 7.324e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6665 1.919
h = 0.0001 0.005
y[1] (numeric) = 0.100342332646 0.064003483623
y[1] (closed_form) = 0.100557116063 0.064163539894
absolute error = 0.0002679
relative error = 0.2246 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.031
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.514
Order of pole (three term test) = 5.921e-30 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1609.0MB, alloc=44.3MB, time=20.46
x[1] = -0.6664 1.924
h = 0.0001 0.003
y[1] (numeric) = 0.0994862562311 0.063813499853
y[1] (closed_form) = 0.0997004717339 0.063976134512
absolute error = 0.000269
relative error = 0.227 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.036
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.222
Order of pole (three term test) = 5.993e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6663 1.927
h = 0.001 0.001
y[1] (numeric) = 0.0989757235887 0.0637071095045
y[1] (closed_form) = 0.0991889244529 0.0638698741136
absolute error = 0.0002682
relative error = 0.2274 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.039
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9606
Order of pole (three term test) = 3.936e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6653 1.928
h = 0.001 0.003
y[1] (numeric) = 0.0987664024921 0.0638340548483
y[1] (closed_form) = 0.0989791301583 0.0639970505773
absolute error = 0.000268
relative error = 0.2274 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.04
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.561
Order of pole (three term test) = 1.111e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6643 1.931
h = 0.0001 0.004
y[1] (numeric) = 0.0982201916313 0.0638771974757
y[1] (closed_form) = 0.0984339030001 0.0640397659633
absolute error = 0.0002685
relative error = 0.2287 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.042
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.584
Order of pole (three term test) = 2.090e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6642 1.935
h = 0.003 0.006
y[1] (numeric) = 0.0975485439703 0.0637253563247
y[1] (closed_form) = 0.0977629893935 0.0638884540171
absolute error = 0.0002694
relative error = 0.2307 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.046
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.43
Order of pole (three term test) = 1.966e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6612 1.941
h = 0.0001 0.005
y[1] (numeric) = 0.0964300492366 0.0639685636814
y[1] (closed_form) = 0.0966447406629 0.0641277397828
absolute error = 0.0002673
relative error = 0.2304 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.051
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.529
Order of pole (three term test) = 3.915e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6611 1.946
h = 0.0001 0.003
y[1] (numeric) = 0.095609964781 0.0637659964475
y[1] (closed_form) = 0.0958240413389 0.0639276161016
absolute error = 0.0002682
relative error = 0.2329 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.055
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.234
Order of pole (three term test) = 6.021e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.661 1.949
h = 0.001 0.001
y[1] (numeric) = 0.0951206907732 0.06365186521
y[1] (closed_form) = 0.0953337956548 0.0638135801375
absolute error = 0.0002675
relative error = 0.2332 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.058
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9696
Order of pole (three term test) = 2.652e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.66 1.95
h = 0.001 0.003
y[1] (numeric) = 0.0949161877609 0.0637693566126
y[1] (closed_form) = 0.0951288346567 0.0639312786731
absolute error = 0.0002673
relative error = 0.2332 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.059
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.603
Order of pole (three term test) = 7.110e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.659 1.953
h = 0.0001 0.004
y[1] (numeric) = 0.094389135945 0.0637984574187
y[1] (closed_form) = 0.0946027333899 0.0639599996205
absolute error = 0.0002678
relative error = 0.2345 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.061
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.608
Order of pole (three term test) = 2.226e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6589 1.957
h = 0.003 0.006
y[1] (numeric) = 0.0937456807501 0.0636369512775
y[1] (closed_form) = 0.0939599636746 0.0637990190339
absolute error = 0.0002687
relative error = 0.2366 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.065
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.462
Order of pole (three term test) = 1.350e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6559 1.963
h = 0.0001 0.005
y[1] (numeric) = 0.092662807908 0.0638458788206
y[1] (closed_form) = 0.0928774354021 0.0640042116143
absolute error = 0.0002667
relative error = 0.2365 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.07
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.543
Order of pole (three term test) = 4.217e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6558 1.968
h = 0.0001 0.003
y[1] (numeric) = 0.0918774156684 0.0636323176387
y[1] (closed_form) = 0.0920913884234 0.0637929649897
absolute error = 0.0002676
relative error = 0.2388 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.074
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.245
Order of pole (three term test) = 1.097e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6557 1.971
h = 0.001 0.001
y[1] (numeric) = 0.0914086429149 0.0635113963681
y[1] (closed_form) = 0.0916216857552 0.0636721076495
absolute error = 0.0002669
relative error = 0.2392 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.077
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9787
Order of pole (three term test) = 1.035e-29 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1655.4MB, alloc=44.3MB, time=21.06
x[1] = -0.6547 1.972
h = 0.001 0.003
y[1] (numeric) = 0.0912090019789 0.0636200017598
y[1] (closed_form) = 0.09142160201 0.0637808980086
absolute error = 0.0002666
relative error = 0.2392 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.078
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.646
Order of pole (three term test) = 5.871e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6537 1.975
h = 0.0001 0.004
y[1] (numeric) = 0.0907006238858 0.0636362402598
y[1] (closed_form) = 0.0909141415557 0.0637968003327
absolute error = 0.0002672
relative error = 0.2405 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.08
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.632
Order of pole (three term test) = 1.894e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6536 1.979
h = 0.003 0.006
y[1] (numeric) = 0.0900843398016 0.0634662976385
y[1] (closed_form) = 0.0902984971574 0.0636273782065
absolute error = 0.000268
relative error = 0.2426 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.084
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.494
Order of pole (three term test) = 9.587e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6506 1.985
h = 0.0001 0.005
y[1] (numeric) = 0.0890364137265 0.0636435023623
y[1] (closed_form) = 0.0892510026699 0.0638010276433
absolute error = 0.0002662
relative error = 0.2426 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.089
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.557
Order of pole (three term test) = 5.669e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6505 1.99
h = 0.0001 0.003
y[1] (numeric) = 0.0882844325678 0.0634204065982
y[1] (closed_form) = 0.0884983333099 0.0635801231797
absolute error = 0.000267
relative error = 0.245 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.094
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.257
Order of pole (three term test) = 4.869e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6504 1.993
h = 0.001 0.001
y[1] (numeric) = 0.0878354136969 0.0632935691311
y[1] (closed_form) = 0.0880484250346 0.0634533213755
absolute error = 0.0002663
relative error = 0.2453 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.096
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9877
Order of pole (three term test) = 1.170e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6494 1.994
h = 0.001 0.003
y[1] (numeric) = 0.0876406576909 0.0633938268559
y[1] (closed_form) = 0.0878532412933 0.0635537436064
absolute error = 0.000266
relative error = 0.2453 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.097
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.689
Order of pole (three term test) = 1.483e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6484 1.997
h = 0.0001 0.004
y[1] (numeric) = 0.087150455663 0.0633983020707
y[1] (closed_form) = 0.0873639243624 0.063557922873
absolute error = 0.0002665
relative error = 0.2467 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.1
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.657
Order of pole (three term test) = 1.272e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6483 2.001
h = 0.003 0.006
y[1] (numeric) = 0.0865603367721 0.0632210508211
y[1] (closed_form) = 0.0867744020215 0.0633811858447
absolute error = 0.0002673
relative error = 0.2488 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.103
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.526
Order of pole (three term test) = 5.344e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6453 2.007
h = 0.0001 0.005
y[1] (numeric) = 0.0855466353998 0.0633689281764
y[1] (closed_form) = 0.0857612087015 0.0635256806402
absolute error = 0.0002657
relative error = 0.249 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.108
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.572
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6452 2.012
h = 0.0001 0.003
y[1] (numeric) = 0.0848268065484 0.0631376360249
y[1] (closed_form) = 0.0850406639737 0.0632964621484
absolute error = 0.0002664
relative error = 0.2513 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.113
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.268
Order of pole (three term test) = 1.460e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6451 2.015
h = 0.001 0.001
y[1] (numeric) = 0.084396806477 0.0630056844428
y[1] (closed_form) = 0.0846098137207 0.0631645207962
absolute error = 0.0002657
relative error = 0.2516 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.116
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9968
Order of pole (three term test) = 6.457e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6441 2.016
h = 0.0001 0.004
y[1] (numeric) = 0.0842069395743 0.0630981043352
y[1] (closed_form) = 0.0844195339966 0.0632570863257
absolute error = 0.0002655
relative error = 0.2516 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.116
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.988
Order of pole (three term test) = 8.009e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.644 2.02
h = 0.003 0.006
y[1] (numeric) = 0.0836374937066 0.0629156869116
y[1] (closed_form) = 0.0838517776497 0.0630751787117
absolute error = 0.0002671
relative error = 0.2546 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.12
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.555
Order of pole (three term test) = 8.715e-30 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1701.7MB, alloc=44.3MB, time=21.64
x[1] = -0.641 2.026
h = 0.0001 0.005
y[1] (numeric) = 0.0826529578018 0.063040516632
y[1] (closed_form) = 0.0828678059256 0.0631967697775
absolute error = 0.0002657
relative error = 0.2549 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.125
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.584
Order of pole (three term test) = 2.452e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6409 2.031
h = 0.0001 0.003
y[1] (numeric) = 0.0819598939949 0.0628035177123
y[1] (closed_form) = 0.0821740079299 0.0629617474
absolute error = 0.0002662
relative error = 0.2572 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.13
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.278
Order of pole (three term test) = 8.414e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6408 2.034
h = 0.001 0.001
y[1] (numeric) = 0.0815457359771 0.0626679701468
y[1] (closed_form) = 0.0817590327041 0.0628261907154
absolute error = 0.0002656
relative error = 0.2576 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.133
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.005
Order of pole (three term test) = 8.276e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6398 2.035
h = 0.001 0.003
y[1] (numeric) = 0.0813601537907 0.0627540888032
y[1] (closed_form) = 0.081573050569 0.0629124401355
absolute error = 0.0002653
relative error = 0.2576 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.133
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.77
Order of pole (three term test) = 2.612e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6388 2.038
h = 0.0001 0.004
y[1] (numeric) = 0.0809025346349 0.0627395460504
y[1] (closed_form) = 0.0811162568952 0.0628976675064
absolute error = 0.0002659
relative error = 0.259 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.136
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.702
Order of pole (three term test) = 2.083e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6387 2.042
h = 0.003 0.006
y[1] (numeric) = 0.0803585495811 0.0625516651866
y[1] (closed_form) = 0.0805727948824 0.0627102861021
absolute error = 0.0002666
relative error = 0.2611 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.14
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.587
Order of pole (three term test) = 1.237e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6357 2.048
h = 0.0001 0.005
y[1] (numeric) = 0.0794067756612 0.062651214234
y[1] (closed_form) = 0.0796216444568 0.0628067563423
absolute error = 0.0002653
relative error = 0.2616 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.144
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.599
Order of pole (three term test) = 9.839e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6356 2.053
h = 0.0001 0.003
y[1] (numeric) = 0.0787435786639 0.0624082009892
y[1] (closed_form) = 0.0789576948155 0.0625656121188
absolute error = 0.0002658
relative error = 0.2638 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.149
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.29
Order of pole (three term test) = 1.125e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6355 2.056
h = 0.001 0.001
y[1] (numeric) = 0.0783471027964 0.0622688493456
y[1] (closed_form) = 0.0785604384855 0.0624262305924
absolute error = 0.0002651
relative error = 0.2642 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.152
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.014
Order of pole (three term test) = 1.106e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6345 2.057
h = 0.001 0.003
y[1] (numeric) = 0.0781663699414 0.0623480063872
y[1] (closed_form) = 0.0783793201586 0.062505502211
absolute error = 0.0002649
relative error = 0.2642 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.153
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.813
Order of pole (three term test) = 7.806e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6335 2.06
h = 0.0001 0.004
y[1] (numeric) = 0.0777254570497 0.0623244345462
y[1] (closed_form) = 0.0779392018202 0.0624817320854
absolute error = 0.0002654
relative error = 0.2657 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.155
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.727
Order of pole (three term test) = 5.314e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6334 2.064
h = 0.003 0.006
y[1] (numeric) = 0.0772048578803 0.0621319652336
y[1] (closed_form) = 0.0774190894965 0.0622897534226
absolute error = 0.0002661
relative error = 0.2678 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.159
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.62
Order of pole (three term test) = 5.535e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6304 2.07
h = 0.0001 0.005
y[1] (numeric) = 0.0762850376907 0.0622082125729
y[1] (closed_form) = 0.0764999440235 0.0623630750844
absolute error = 0.0002649
relative error = 0.2684 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.164
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.613
Order of pole (three term test) = 7.007e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6303 2.075
h = 0.0001 0.003
y[1] (numeric) = 0.075650529018 0.0619602221737
y[1] (closed_form) = 0.0758646685272 0.0621168513611
absolute error = 0.0002653
relative error = 0.2706 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.169
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.302
Order of pole (three term test) = 6.006e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6302 2.078
h = 0.001 0.001
y[1] (numeric) = 0.0752710453423 0.0618176900295
y[1] (closed_form) = 0.0754844398101 0.0619742707989
absolute error = 0.0002647
relative error = 0.271 %
Correct digits = 3
memory used=1748.2MB, alloc=44.3MB, time=22.23
Radius of convergence (given) for eq 1 = 2.171
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.023
Order of pole (three term test) = 1.483e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6292 2.079
h = 0.001 0.003
y[1] (numeric) = 0.0750951244972 0.0618903197224
y[1] (closed_form) = 0.0753081476923 0.0620470001859
absolute error = 0.0002644
relative error = 0.271 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.172
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.857
Order of pole (three term test) = 7.511e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6282 2.082
h = 0.0001 0.004
y[1] (numeric) = 0.0746704051448 0.061858549018
y[1] (closed_form) = 0.0748841926503 0.0620150601638
absolute error = 0.000265
relative error = 0.2725 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.175
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.752
Order of pole (three term test) = 1.669e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6281 2.086
h = 0.003 0.006
y[1] (numeric) = 0.0741722685764 0.0616622926877
y[1] (closed_form) = 0.0743865089258 0.0618192850436
absolute error = 0.0002656
relative error = 0.2746 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.179
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.652
Order of pole (three term test) = 2.938e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6251 2.092
h = 0.0001 0.005
y[1] (numeric) = 0.0732835764558 0.0617170871098
y[1] (closed_form) = 0.0734985353915 0.0618713003312
absolute error = 0.0002646
relative error = 0.2754 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.183
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.628
Order of pole (three term test) = 1.174e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.625 2.097
h = 0.0001 0.003
y[1] (numeric) = 0.072676608911 0.0614650657452
y[1] (closed_form) = 0.0728907906725 0.0616209483021
absolute error = 0.0002649
relative error = 0.2775 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.188
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.313
Order of pole (three term test) = 8.947e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6249 2.1
h = 0.001 0.001
y[1] (numeric) = 0.0723134452515 0.0613199226547
y[1] (closed_form) = 0.0725269160725 0.061475740303
absolute error = 0.0002643
relative error = 0.278 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.191
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.032
Order of pole (three term test) = 4.396e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6239 2.101
h = 0.001 0.003
y[1] (numeric) = 0.0721422879473 0.061386435077
y[1] (closed_form) = 0.0723554013887 0.0615423387499
absolute error = 0.0002641
relative error = 0.278 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.192
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.901
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6229 2.104
h = 0.0001 0.004
y[1] (numeric) = 0.0717332515722 0.0613472361382
y[1] (closed_form) = 0.0719470998162 0.0615029970216
absolute error = 0.0002646
relative error = 0.2795 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.194
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.776
Order of pole (three term test) = 7.697e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6228 2.108
h = 0.003 0.006
y[1] (numeric) = 0.0712566791921 0.0611479238903
y[1] (closed_form) = 0.0714709483582 0.0613041560292
absolute error = 0.0002652
relative error = 0.2816 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.198
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.685
Order of pole (three term test) = 1.252e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6198 2.114
h = 0.0001 0.005
y[1] (numeric) = 0.0703982777086 0.0611829914483
y[1] (closed_form) = 0.0706133026591 0.06133658456
absolute error = 0.0002642
relative error = 0.2825 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.203
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.642
Order of pole (three term test) = 4.662e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6197 2.119
h = 0.0001 0.003
y[1] (numeric) = 0.0698177366144 0.0609278010317
y[1] (closed_form) = 0.0700319774613 0.0610829709674
absolute error = 0.0002645
relative error = 0.2847 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.208
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.325
Order of pole (three term test) = 1.357e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6196 2.122
h = 0.001 0.001
y[1] (numeric) = 0.0694702393578 0.0607805664722
y[1] (closed_form) = 0.0696838020554 0.0609356568823
absolute error = 0.0002639
relative error = 0.2851 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.211
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.042
Order of pole (three term test) = 9.427e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6186 2.123
h = 0.0001 0.004
y[1] (numeric) = 0.0693037875024 0.0608413486172
y[1] (closed_form) = 0.069517006385 0.0609965125109
absolute error = 0.0002637
relative error = 0.2851 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.211
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.256
Order of pole (three term test) = 1.630e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6185 2.127
h = 0.003 0.006
y[1] (numeric) = 0.0688442046493 0.0606400664709
y[1] (closed_form) = 0.0690587168801 0.060795810199
absolute error = 0.0002651
relative error = 0.2881 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.215
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.714
Order of pole (three term test) = 1.251e-30 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1794.5MB, alloc=44.3MB, time=22.82
x[1] = -0.6155 2.133
h = 0.0001 0.005
y[1] (numeric) = 0.0680114095663 0.0606597946531
y[1] (closed_form) = 0.0682267031711 0.0608130152737
absolute error = 0.0002642
relative error = 0.2891 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.22
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.655
Order of pole (three term test) = 1.989e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6154 2.138
h = 0.0001 0.003
y[1] (numeric) = 0.0674527735871 0.0604028042555
y[1] (closed_form) = 0.0676672806048 0.0605575257652
absolute error = 0.0002645
relative error = 0.2913 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.225
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.335
Order of pole (three term test) = 3.666e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6153 2.141
h = 0.001 0.001
y[1] (numeric) = 0.0671182700014 0.060254326288
y[1] (closed_form) = 0.0673321262061 0.0604089574388
absolute error = 0.0002639
relative error = 0.2917 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.228
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.05
Order of pole (three term test) = 1.705e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6143 2.142
h = 0.001 0.003
y[1] (numeric) = 0.0669558779839 0.0603105240268
y[1] (closed_form) = 0.0671694019048 0.0604652188648
absolute error = 0.0002637
relative error = 0.2918 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.228
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.983
Order of pole (three term test) = 4.247e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6133 2.145
h = 0.0001 0.004
y[1] (numeric) = 0.0665747496828 0.0602595379574
y[1] (closed_form) = 0.0667889553245 0.0604141331398
absolute error = 0.0002642
relative error = 0.2933 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.231
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.823
Order of pole (three term test) = 8.773e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6132 2.149
h = 0.003 0.006
y[1] (numeric) = 0.0661360195805 0.0600564984982
y[1] (closed_form) = 0.0663505920359 0.0602115450591
absolute error = 0.0002647
relative error = 0.2955 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.235
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.747
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6102 2.155
h = 0.0001 0.005
y[1] (numeric) = 0.0653319245905 0.0600593990536
y[1] (closed_form) = 0.0655473049084 0.0602120510298
absolute error = 0.000264
relative error = 0.2966 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.24
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.67
Order of pole (three term test) = 1.345e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6101 2.16
h = 0.0001 0.003
y[1] (numeric) = 0.0647977220782 0.0598006280172
y[1] (closed_form) = 0.0650123142261 0.0599546969082
absolute error = 0.0002642
relative error = 0.2987 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.245
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.347
Order of pole (three term test) = 4.862e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.61 2.163
h = 0.001 0.001
y[1] (numeric) = 0.0644777149489 0.0596508971835
y[1] (closed_form) = 0.0646916866683 0.0598048641565
absolute error = 0.0002636
relative error = 0.2992 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.247
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.059
Order of pole (three term test) = 4.432e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.609 2.164
h = 0.001 0.003
y[1] (numeric) = 0.0643198952704 0.0597020261083
y[1] (closed_form) = 0.0645335476027 0.0598560461137
absolute error = 0.0002634
relative error = 0.2992 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.248
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.027
Order of pole (three term test) = 2.377e-31 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.608 2.167
h = 0.0001 0.004
y[1] (numeric) = 0.0639530103079 0.0596455141884
y[1] (closed_form) = 0.0641673171594 0.0597994550294
absolute error = 0.0002639
relative error = 0.3008 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.251
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.848
Order of pole (three term test) = 8.945e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6079 2.171
h = 0.003 0.006
y[1] (numeric) = 0.0635334122139 0.0594411573371
y[1] (closed_form) = 0.0637480593158 0.0595955386787
absolute error = 0.0002644
relative error = 0.303 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.255
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.78
Order of pole (three term test) = 4.400e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6049 2.177
h = 0.0001 0.005
y[1] (numeric) = 0.0627571726422 0.0594286435771
y[1] (closed_form) = 0.0629726490866 0.0595807529352
absolute error = 0.0002638
relative error = 0.3042 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.259
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.684
Order of pole (three term test) = 8.736e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6048 2.182
h = 0.0001 0.003
y[1] (numeric) = 0.0622463865923 0.0591687464624
y[1] (closed_form) = 0.0624610757259 0.0593221930695
absolute error = 0.0002639
relative error = 0.3063 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.264
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.359
Order of pole (three term test) = 6.435e-30 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1840.7MB, alloc=44.3MB, time=23.42
x[1] = -0.6047 2.185
h = 0.001 0.001
y[1] (numeric) = 0.0619402784141 0.0590181588518
y[1] (closed_form) = 0.0621543762557 0.059171493432
absolute error = 0.0002633
relative error = 0.3069 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.267
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.068
Order of pole (three term test) = 6.032e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6037 2.186
h = 0.001 0.003
y[1] (numeric) = 0.061786952819 0.0590645457622
y[1] (closed_form) = 0.0620007438014 0.0592179236327
absolute error = 0.0002631
relative error = 0.3069 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.268
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.071
Order of pole (three term test) = 9.933e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6027 2.189
h = 0.0001 0.004
y[1] (numeric) = 0.0614338252357 0.0590030821315
y[1] (closed_form) = 0.0616482443696 0.0591563995078
absolute error = 0.0002636
relative error = 0.3085 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.27
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.873
Order of pole (three term test) = 1.585e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6026 2.193
h = 0.003 0.006
y[1] (numeric) = 0.0610325635462 0.0587979135728
y[1] (closed_form) = 0.0612472980431 0.0589516603929
absolute error = 0.0002641
relative error = 0.3107 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.274
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.813
Order of pole (three term test) = 1.455e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5996 2.199
h = 0.0001 0.005
y[1] (numeric) = 0.0602833387529 0.0587713019559
y[1] (closed_form) = 0.0604989195575 0.0589228936665
absolute error = 0.0002635
relative error = 0.3121 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.279
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.699
Order of pole (three term test) = 7.305e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5995 2.204
h = 0.0001 0.003
y[1] (numeric) = 0.0597949864961 0.0585108711411
y[1] (closed_form) = 0.0600097830054 0.0586637245627
absolute error = 0.0002636
relative error = 0.3141 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.284
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.371
Order of pole (three term test) = 3.158e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5994 2.207
h = 0.001 0.001
y[1] (numeric) = 0.0595021995721 0.0583597857872
y[1] (closed_form) = 0.0597164327061 0.0585125183965
absolute error = 0.0002631
relative error = 0.3147 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.287
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.077
Order of pole (three term test) = 8.663e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5984 2.208
h = 0.001 0.003
y[1] (numeric) = 0.0593532847608 0.0584017384607
y[1] (closed_form) = 0.0595672231879 0.0585545054637
absolute error = 0.0002629
relative error = 0.3147 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.288
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.115
Order of pole (three term test) = 5.468e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5974 2.211
h = 0.0001 0.004
y[1] (numeric) = 0.0590134377297 0.0583358541569
y[1] (closed_form) = 0.0592279787827 0.0584885776512
absolute error = 0.0002633
relative error = 0.3164 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.29
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.898
Order of pole (three term test) = 1.693e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5973 2.215
h = 0.003 0.006
y[1] (numeric) = 0.0586297438441 0.0581303315094
y[1] (closed_form) = 0.0588445769537 0.0582834732762
absolute error = 0.0002638
relative error = 0.3185 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.294
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.846
Order of pole (three term test) = 1.153e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5943 2.221
h = 0.0001 0.005
y[1] (numeric) = 0.0579067001002 0.0580908475833
y[1] (closed_form) = 0.0581223924202 0.0582419455856
absolute error = 0.0002634
relative error = 0.3201 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.299
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.714
Order of pole (three term test) = 1.364e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5942 2.226
h = 0.0001 0.003
y[1] (numeric) = 0.0574398332309 0.0578304180882
y[1] (closed_form) = 0.0576547461681 0.0579827062135
absolute error = 0.0002634
relative error = 0.3221 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.304
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.383
Order of pole (three term test) = 1.042e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5941 2.229
h = 0.001 0.001
y[1] (numeric) = 0.0571598096699 0.0576791598182
y[1] (closed_form) = 0.0573741859595 0.0578313195515
absolute error = 0.0002629
relative error = 0.3227 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.307
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.087
Order of pole (three term test) = 1.192e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5931 2.23
h = 0.0001 0.004
y[1] (numeric) = 0.0570152182064 0.0577169679862
y[1] (closed_form) = 0.0572293115614 0.0578691540002
absolute error = 0.0002627
relative error = 0.3227 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.308
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.529
Order of pole (three term test) = 9.009e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.593 2.234
h = 0.003 0.006
y[1] (numeric) = 0.056645339099 0.0575114904991
y[1] (closed_form) = 0.056860415484 0.0576642647294
absolute error = 0.0002638
relative error = 0.3258 %
Correct digits = 2
memory used=1887.2MB, alloc=44.3MB, time=24.00
Radius of convergence (given) for eq 1 = 2.311
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.875
Order of pole (three term test) = 1.092e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.59 2.24
h = 0.0001 0.005
y[1] (numeric) = 0.0559443056533 0.0574621411831
y[1] (closed_form) = 0.056160248179 0.057612963313
absolute error = 0.0002634
relative error = 0.3274 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.316
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.727
Order of pole (three term test) = 8.661e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5899 2.245
h = 0.0001 0.003
y[1] (numeric) = 0.0554951915114 0.0572023419695
y[1] (closed_form) = 0.0557103610134 0.0573542957157
absolute error = 0.0002634
relative error = 0.3294 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.321
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.393
Order of pole (three term test) = 3.969e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5898 2.248
h = 0.001 0.001
y[1] (numeric) = 0.0552257199093 0.0570513141743
y[1] (closed_form) = 0.0554403749159 0.0572031341863
absolute error = 0.0002629
relative error = 0.33 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.324
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.095
Order of pole (three term test) = 7.784e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5888 2.249
h = 0.001 0.003
y[1] (numeric) = 0.0550848222547 0.0570858238368
y[1] (closed_form) = 0.055299204239 0.0572376638631
absolute error = 0.0002627
relative error = 0.3301 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.325
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.198
Order of pole (three term test) = 6.602e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5878 2.252
h = 0.0001 0.004
y[1] (numeric) = 0.0547684922918 0.0570131365308
y[1] (closed_form) = 0.0549834314924 0.0571649603184
absolute error = 0.0002632
relative error = 0.3318 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.327
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.945
Order of pole (three term test) = 1.002e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5877 2.256
h = 0.003 0.006
y[1] (numeric) = 0.0544155277105 0.0568082125858
y[1] (closed_form) = 0.0546307196347 0.056960433505
absolute error = 0.0002636
relative error = 0.334 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.331
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.908
Order of pole (three term test) = 7.494e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5847 2.262
h = 0.0001 0.005
y[1] (numeric) = 0.0537391382037 0.0567480389301
y[1] (closed_form) = 0.0539552027493 0.0568984093057
absolute error = 0.0002632
relative error = 0.3357 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.336
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.742
Order of pole (three term test) = 5.097e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5846 2.267
h = 0.0001 0.003
y[1] (numeric) = 0.0533098299936 0.0564890887365
y[1] (closed_form) = 0.053525129305 0.0566405260422
absolute error = 0.0002632
relative error = 0.3378 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.341
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.405
Order of pole (three term test) = 8.871e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5845 2.27
h = 0.001 0.001
y[1] (numeric) = 0.0530521329109 0.0563384042737
y[1] (closed_form) = 0.05326694232 0.0564897022138
absolute error = 0.0002627
relative error = 0.3384 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.344
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.104
Order of pole (three term test) = 1.740e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5835 2.271
h = 0.001 0.003
y[1] (numeric) = 0.052915384623 0.0563692626042
y[1] (closed_form) = 0.0531299320638 0.056520573747
absolute error = 0.0002625
relative error = 0.3384 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.345
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.243
Order of pole (three term test) = 9.630e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5825 2.274
h = 0.0001 0.004
y[1] (numeric) = 0.0526110234543 0.0562934555096
y[1] (closed_form) = 0.0528261050113 0.0564447632617
absolute error = 0.000263
relative error = 0.3402 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.347
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.97
Order of pole (three term test) = 1.279e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5824 2.278
h = 0.003 0.006
y[1] (numeric) = 0.0522735718708 0.0560892453925
y[1] (closed_form) = 0.0524888868816 0.0562409390813
absolute error = 0.0002634
relative error = 0.3424 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.351
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.942
Order of pole (three term test) = 8.443e-31 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5794 2.284
h = 0.0001 0.005
y[1] (numeric) = 0.0516210255973 0.0560192431822
y[1] (closed_form) = 0.0518372167405 0.0561691829372
absolute error = 0.0002631
relative error = 0.3442 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.356
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.757
Order of pole (three term test) = 7.807e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5793 2.289
h = 0.0001 0.003
y[1] (numeric) = 0.0512106716597 0.0557615370925
y[1] (closed_form) = 0.0514261066402 0.0559124825471
absolute error = 0.0002631
relative error = 0.3463 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.361
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.417
Order of pole (three term test) = 7.223e-30 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1933.5MB, alloc=44.3MB, time=24.60
x[1] = -0.5792 2.292
h = 0.001 0.001
y[1] (numeric) = 0.0509642473084 0.0556114372026
y[1] (closed_form) = 0.0511792158899 0.0557622385783
absolute error = 0.0002626
relative error = 0.3469 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.364
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.114
Order of pole (three term test) = 7.080e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5782 2.293
h = 0.001 0.003
y[1] (numeric) = 0.0508315534804 0.0556388873715
y[1] (closed_form) = 0.0510462707686 0.0557896957654
absolute error = 0.0002624
relative error = 0.347 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.365
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.288
Order of pole (three term test) = 6.320e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5772 2.296
h = 0.0001 0.004
y[1] (numeric) = 0.0505387263176 0.0555603507225
y[1] (closed_form) = 0.0507539554505 0.0557111673338
absolute error = 0.0002628
relative error = 0.3487 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.367
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.996
Order of pole (three term test) = 3.352e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5771 2.3
h = 0.003 0.006
y[1] (numeric) = 0.0502161219003 0.0553571595385
y[1] (closed_form) = 0.050431566471 0.0555083509579
absolute error = 0.0002632
relative error = 0.351 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.371
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.976
Order of pole (three term test) = 1.772e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5741 2.306
h = 0.0001 0.005
y[1] (numeric) = 0.0495866326288 0.0552782538438
y[1] (closed_form) = 0.049802954194 0.0554277831924
absolute error = 0.000263
relative error = 0.3529 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.376
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.772
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.574 2.311
h = 0.0001 0.003
y[1] (numeric) = 0.0491944138923 0.0550221452617
y[1] (closed_form) = 0.0494099894712 0.0551726223715
absolute error = 0.0002629
relative error = 0.355 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.381
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.429
Order of pole (three term test) = 2.994e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5739 2.314
h = 0.001 0.001
y[1] (numeric) = 0.0489587794284 0.0548728462496
y[1] (closed_form) = 0.0491739110582 0.0550231753996
absolute error = 0.0002625
relative error = 0.3557 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.384
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.123
Order of pole (three term test) = 6.560e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5729 2.315
h = 0.001 0.003
y[1] (numeric) = 0.0488300436799 0.0548971168311
y[1] (closed_form) = 0.0490449343155 0.0550474473941
absolute error = 0.0002623
relative error = 0.3557 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.385
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.333
Order of pole (three term test) = 4.141e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5719 2.318
h = 0.0001 0.004
y[1] (numeric) = 0.048548327524 0.0548162102131
y[1] (closed_form) = 0.0487637085501 0.0549665594581
absolute error = 0.0002627
relative error = 0.3575 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.388
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.021
Order of pole (three term test) = 1.103e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5718 2.322
h = 0.003 0.006
y[1] (numeric) = 0.0482399299591 0.0546143108422
y[1] (closed_form) = 0.0484555095858 0.0547650238662
absolute error = 0.000263
relative error = 0.3597 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.391
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.009
Order of pole (three term test) = 2.901e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5688 2.328
h = 0.0001 0.005
y[1] (numeric) = 0.0476327271865 0.0545273605655
y[1] (closed_form) = 0.0478491823145 0.0546764988328
absolute error = 0.0002629
relative error = 0.3618 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.396
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.787
Order of pole (three term test) = 3.218e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5687 2.333
h = 0.0001 0.003
y[1] (numeric) = 0.0472578564999 0.0542731645986
y[1] (closed_form) = 0.0474735767623 0.0544231958224
absolute error = 0.0002628
relative error = 0.3638 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.401
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.441
Order of pole (three term test) = 8.760e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5686 2.336
h = 0.001 0.001
y[1] (numeric) = 0.0470325476565 0.0541248598385
y[1] (closed_form) = 0.0472478454031 0.0542747399748
absolute error = 0.0002623
relative error = 0.3646 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.404
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.133
Order of pole (three term test) = 3.838e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5676 2.337
h = 0.0001 0.004
y[1] (numeric) = 0.0469076726472 0.0541461656144
y[1] (closed_form) = 0.047122739328 0.0542960420936
absolute error = 0.0002621
relative error = 0.3646 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.405
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.804
Order of pole (three term test) = 3.383e-30 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1979.8MB, alloc=44.3MB, time=25.19
x[1] = -0.5675 2.341
h = 0.003 0.006
y[1] (numeric) = 0.0466104329578 0.0539455255539
y[1] (closed_form) = 0.0468262427553 0.0540959640336
absolute error = 0.0002631
relative error = 0.3677 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.409
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.038
Order of pole (three term test) = 3.660e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5645 2.347
h = 0.0001 0.005
y[1] (numeric) = 0.0460218924797 0.0538525444986
y[1] (closed_form) = 0.0462385738418 0.0540014798333
absolute error = 0.0002629
relative error = 0.3698 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.414
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.8
Order of pole (three term test) = 1.478e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5644 2.352
h = 0.0001 0.003
y[1] (numeric) = 0.0456613206778 0.0536004147236
y[1] (closed_form) = 0.0458772779971 0.0537501983778
absolute error = 0.0002628
relative error = 0.3719 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.419
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.452
Order of pole (three term test) = 2.964e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5643 2.355
h = 0.001 0.001
y[1] (numeric) = 0.045444527308 0.0534532203065
y[1] (closed_form) = 0.045660079801 0.0536028509686
absolute error = 0.0002624
relative error = 0.3726 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.422
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.141
Order of pole (three term test) = 9.676e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5633 2.356
h = 0.001 0.003
y[1] (numeric) = 0.0453229292266 0.0534721805055
y[1] (closed_form) = 0.04553825896 0.0536218036553
absolute error = 0.0002622
relative error = 0.3727 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.422
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.417
Order of pole (three term test) = 1.366e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5623 2.359
h = 0.0001 0.004
y[1] (numeric) = 0.0450608228585 0.0533878457716
y[1] (closed_form) = 0.0452766050893 0.0535375041024
absolute error = 0.0002626
relative error = 0.3745 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.425
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.068
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5622 2.363
h = 0.003 0.006
y[1] (numeric) = 0.0447772201137 0.0531891291966
y[1] (closed_form) = 0.0449931726398 0.0533391309722
absolute error = 0.0002629
relative error = 0.3768 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.429
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.072
Order of pole (three term test) = 7.556e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5592 2.369
h = 0.0001 0.005
y[1] (numeric) = 0.0442095690441 0.0530895314827
y[1] (closed_form) = 0.0444263880006 0.053238109456
absolute error = 0.0002628
relative error = 0.3791 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.434
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.815
Order of pole (three term test) = 1.902e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5591 2.374
h = 0.0001 0.003
y[1] (numeric) = 0.0438649601627 0.0528398008039
y[1] (closed_form) = 0.0440810675481 0.0529891777262
absolute error = 0.0002627
relative error = 0.3811 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.439
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.464
Order of pole (three term test) = 6.444e-31 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.559 2.377
h = 0.001 0.001
y[1] (numeric) = 0.0436576747967 0.0526939006751
y[1] (closed_form) = 0.0438733969883 0.0528431226801
absolute error = 0.0002623
relative error = 0.3819 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.442
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.15
Order of pole (three term test) = 6.310e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.558 2.378
h = 0.001 0.003
y[1] (numeric) = 0.0435397530809 0.0527102604545
y[1] (closed_form) = 0.0437552617626 0.0528594707603
absolute error = 0.0002621
relative error = 0.382 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.443
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.462
Order of pole (three term test) = 9.081e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.557 2.381
h = 0.0001 0.004
y[1] (numeric) = 0.0432876110682 0.0526244290943
y[1] (closed_form) = 0.0435035530568 0.052773682259
absolute error = 0.0002625
relative error = 0.3838 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.445
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.094
Order of pole (three term test) = 6.675e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5569 2.385
h = 0.003 0.006
y[1] (numeric) = 0.0430165171214 0.0524276229769
y[1] (closed_form) = 0.0432326155592 0.0525772089961
absolute error = 0.0002628
relative error = 0.3861 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.449
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.106
Order of pole (three term test) = 6.964e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5539 2.391
h = 0.0001 0.005
y[1] (numeric) = 0.0424690355195 0.0523221012764
y[1] (closed_form) = 0.0426859935985 0.0524703388345
absolute error = 0.0002628
relative error = 0.3885 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.454
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.83
Order of pole (three term test) = 1.654e-29 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2026.1MB, alloc=44.3MB, time=25.78
x[1] = -0.5538 2.396
h = 0.0001 0.003
y[1] (numeric) = 0.0421396898226 0.052074992149
y[1] (closed_form) = 0.0423559493726 0.0522239819933
absolute error = 0.0002626
relative error = 0.3906 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.459
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.476
Order of pole (three term test) = 7.385e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5537 2.399
h = 0.001 0.001
y[1] (numeric) = 0.0419414991756 0.051930524102
y[1] (closed_form) = 0.0421573922533 0.0520793576659
absolute error = 0.0002622
relative error = 0.3914 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.462
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.16
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5527 2.4
h = 0.001 0.003
y[1] (numeric) = 0.041827156197 0.0519444629084
y[1] (closed_form) = 0.042042844664 0.0520932810104
absolute error = 0.000262
relative error = 0.3914 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.463
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.507
Order of pole (three term test) = 1.174e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5517 2.403
h = 0.0001 0.004
y[1] (numeric) = 0.0415846026282 0.0518573950969
y[1] (closed_form) = 0.0418007059637 0.052006262905
absolute error = 0.0002624
relative error = 0.3933 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.466
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.12
Order of pole (three term test) = 1.267e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5516 2.407
h = 0.003 0.006
y[1] (numeric) = 0.0413254704987 0.0516626710593
y[1] (closed_form) = 0.041541717362 0.0518118613187
absolute error = 0.0002627
relative error = 0.3956 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.469
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.14
Order of pole (three term test) = 5.731e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5486 2.413
h = 0.0001 0.005
y[1] (numeric) = 0.0407974569828 0.0515518671034
y[1] (closed_form) = 0.0410145552473 0.0516997804224
absolute error = 0.0002627
relative error = 0.3981 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.475
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.845
Order of pole (three term test) = 1.604e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5485 2.418
h = 0.0001 0.003
y[1] (numeric) = 0.0404827035263 0.0513075745735
y[1] (closed_form) = 0.0406991167677 0.051456196086
absolute error = 0.0002625
relative error = 0.4002 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.479
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.488
Order of pole (three term test) = 1.091e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5484 2.421
h = 0.001 0.001
y[1] (numeric) = 0.0402932111334 0.05116465993
y[1] (closed_form) = 0.0405092757495 0.0513131243043
absolute error = 0.0002622
relative error = 0.401 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.482
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.17
Order of pole (three term test) = 1.068e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5474 2.422
h = 0.001 0.003
y[1] (numeric) = 0.040182349764 0.0511763461902
y[1] (closed_form) = 0.0403982183257 0.0513247917306
absolute error = 0.000262
relative error = 0.4011 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.483
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.552
Order of pole (three term test) = 1.537e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5464 2.425
h = 0.0001 0.004
y[1] (numeric) = 0.0399490208453 0.0510882805916
y[1] (closed_form) = 0.0401652865694 0.0512367819227
absolute error = 0.0002623
relative error = 0.403 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.486
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.145
Order of pole (three term test) = 5.646e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5463 2.429
h = 0.003 0.006
y[1] (numeric) = 0.0397013260522 0.0508957890564
y[1] (closed_form) = 0.0399177232504 0.0510446026368
absolute error = 0.0002626
relative error = 0.4053 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.49
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.174
Order of pole (three term test) = 1.177e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5433 2.435
h = 0.0001 0.005
y[1] (numeric) = 0.039192098146 0.0507802970228
y[1] (closed_form) = 0.0394093372399 0.050927901539
absolute error = 0.0002626
relative error = 0.4079 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.495
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.86
Order of pole (three term test) = 5.891e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5432 2.44
h = 0.0001 0.003
y[1] (numeric) = 0.0388912938983 0.0505389910575
y[1] (closed_form) = 0.0391078618436 0.0506872621127
absolute error = 0.0002625
relative error = 0.41 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.5
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.5
Order of pole (three term test) = 7.083e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5431 2.443
h = 0.001 0.001
y[1] (numeric) = 0.0387101196145 0.050397736052
y[1] (closed_form) = 0.0389263559421 0.0505458495645
absolute error = 0.0002621
relative error = 0.4108 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.503
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.179
Order of pole (three term test) = 1.402e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5421 2.444
h = 0.0001 0.004
y[1] (numeric) = 0.0386026434971 0.0504073278073
y[1] (closed_form) = 0.0388186919927 0.0505554194734
absolute error = 0.0002619
relative error = 0.4109 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.503
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.083
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2072.5MB, alloc=44.3MB, time=26.38
x[1] = -0.542 2.448
h = 0.003 0.006
y[1] (numeric) = 0.0383639242196 0.0502167769935
y[1] (closed_form) = 0.038580531954 0.0503653868514
absolute error = 0.0002627
relative error = 0.414 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.507
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.204
Order of pole (three term test) = 1.475e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.539 2.454
h = 0.0001 0.005
y[1] (numeric) = 0.0378703814666 0.0500979045262
y[1] (closed_form) = 0.0380878212776 0.0502453608264
absolute error = 0.0002627
relative error = 0.4167 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.512
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.873
Order of pole (three term test) = 5.217e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5389 2.459
h = 0.0001 0.003
y[1] (numeric) = 0.0375810520577 0.0498594440843
y[1] (closed_form) = 0.0377978333513 0.0500075330939
absolute error = 0.0002625
relative error = 0.4188 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.517
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.511
Order of pole (three term test) = 1.774e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5388 2.462
h = 0.001 0.001
y[1] (numeric) = 0.0374067241641 0.0497197853524
y[1] (closed_form) = 0.0376231878325 0.0498677169874
absolute error = 0.0002622
relative error = 0.4197 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.52
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.187
Order of pole (three term test) = 1.811e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5378 2.463
h = 0.001 0.003
y[1] (numeric) = 0.0373021081294 0.049727732079
y[1] (closed_form) = 0.0375183908137 0.0498756396331
absolute error = 0.000262
relative error = 0.4198 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.521
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.637
Order of pole (three term test) = 8.828e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5368 2.466
h = 0.0001 0.004
y[1] (numeric) = 0.0370850230205 0.0496384779187
y[1] (closed_form) = 0.0373016717448 0.0497864505742
absolute error = 0.0002624
relative error = 0.4217 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.524
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.193
Order of pole (three term test) = 9.170e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5367 2.47
h = 0.003 0.006
y[1] (numeric) = 0.0368572587373 0.049450598187
y[1] (closed_form) = 0.0370740187479 0.0495988645624
absolute error = 0.0002626
relative error = 0.4241 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.528
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.238
Order of pole (three term test) = 8.545e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5337 2.476
h = 0.0001 0.005
y[1] (numeric) = 0.0363812767693 0.049328019861
y[1] (closed_form) = 0.0365988574703 0.0494751942112
absolute error = 0.0002627
relative error = 0.4268 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.533
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.888
Order of pole (three term test) = 1.351e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5336 2.481
h = 0.0001 0.003
y[1] (numeric) = 0.0361047698412 0.0490927958434
y[1] (closed_form) = 0.0363217063393 0.049240565455
absolute error = 0.0002625
relative error = 0.429 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.538
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.523
Order of pole (three term test) = 8.278e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5335 2.484
h = 0.001 0.001
y[1] (numeric) = 0.0359380934792 0.0489549544938
y[1] (closed_form) = 0.036154727886 0.0491025670373
absolute error = 0.0002621
relative error = 0.4299 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.541
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.197
Order of pole (three term test) = 1.004e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5325 2.485
h = 0.001 0.003
y[1] (numeric) = 0.0358366846091 0.0489610740735
y[1] (closed_form) = 0.0360531456539 0.0491086601135
absolute error = 0.000262
relative error = 0.43 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.541
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.683
Order of pole (three term test) = 3.168e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5315 2.488
h = 0.0001 0.004
y[1] (numeric) = 0.0356278471752 0.0488713956005
y[1] (closed_form) = 0.0358446585404 0.0490190509813
absolute error = 0.0002623
relative error = 0.432 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.544
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.219
Order of pole (three term test) = 1.840e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5314 2.492
h = 0.003 0.006
y[1] (numeric) = 0.035410136731 0.0486860717654
y[1] (closed_form) = 0.0356270495198 0.0488340113072
absolute error = 0.0002626
relative error = 0.4344 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.548
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.272
Order of pole (three term test) = 1.105e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5284 2.498
h = 0.0001 0.005
y[1] (numeric) = 0.0349510884516 0.0485602628467
y[1] (closed_form) = 0.0351688097174 0.0487071687243
absolute error = 0.0002626
relative error = 0.4372 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.553
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.903
Order of pole (three term test) = 8.734e-30 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2118.8MB, alloc=44.3MB, time=26.97
x[1] = -0.5283 2.503
h = 0.0001 0.003
y[1] (numeric) = 0.0346868360819 0.0483283851126
y[1] (closed_form) = 0.0349039276086 0.0484758508934
absolute error = 0.0002624
relative error = 0.4393 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.558
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.535
Order of pole (three term test) = 4.195e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5282 2.506
h = 0.001 0.001
y[1] (numeric) = 0.0345274750894 0.0481924311389
y[1] (closed_form) = 0.0347442793175 0.0483397404864
absolute error = 0.0002621
relative error = 0.4403 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.561
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.207
Order of pole (three term test) = 6.485e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5272 2.507
h = 0.001 0.003
y[1] (numeric) = 0.0344291805153 0.0481968551354
y[1] (closed_form) = 0.0346458186965 0.0483441358395
absolute error = 0.000262
relative error = 0.4404 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.562
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.728
Order of pole (three term test) = 4.093e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5262 2.51
h = 0.0001 0.004
y[1] (numeric) = 0.0342282726599 0.0481069216668
y[1] (closed_form) = 0.0344452460915 0.0482542754048
absolute error = 0.0002623
relative error = 0.4424 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.565
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.245
Order of pole (three term test) = 4.334e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5261 2.514
h = 0.003 0.006
y[1] (numeric) = 0.0340201720361 0.0479242382499
y[1] (closed_form) = 0.034237237704 0.0480718668247
absolute error = 0.0002625
relative error = 0.4448 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.568
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.306
Order of pole (three term test) = 2.854e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5231 2.52
h = 0.0001 0.005
y[1] (numeric) = 0.0335774495119 0.0477956376801
y[1] (closed_form) = 0.0337953107424 0.0479422879335
absolute error = 0.0002626
relative error = 0.4477 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.574
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.919
Order of pole (three term test) = 3.382e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.523 2.525
h = 0.0001 0.003
y[1] (numeric) = 0.0333249081941 0.0475671984465
y[1] (closed_form) = 0.0335421542378 0.047714375224
absolute error = 0.0002624
relative error = 0.4499 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.579
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.548
Order of pole (three term test) = 5.413e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5229 2.528
h = 0.001 0.001
y[1] (numeric) = 0.033172540725 0.047433191182
y[1] (closed_form) = 0.0333895135536 0.0475802124524
absolute error = 0.0002621
relative error = 0.4509 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.582
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.216
Order of pole (three term test) = 1.496e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5219 2.529
h = 0.001 0.003
y[1] (numeric) = 0.0330772690763 0.0474360429296
y[1] (closed_form) = 0.0332940828761 0.0475830336758
absolute error = 0.0002619
relative error = 0.451 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.582
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.774
Order of pole (three term test) = 1.056e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5209 2.532
h = 0.0001 0.004
y[1] (numeric) = 0.032883983996 0.0473460088528
y[1] (closed_form) = 0.0331011186042 0.0474930758262
absolute error = 0.0002623
relative error = 0.453 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.585
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.271
Order of pole (three term test) = 5.588e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5208 2.536
h = 0.003 0.006
y[1] (numeric) = 0.032685068237 0.0471660367239
y[1] (closed_form) = 0.0329022865266 0.0473133694487
absolute error = 0.0002625
relative error = 0.4554 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.589
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.34
Order of pole (three term test) = 1.839e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5178 2.542
h = 0.0001 0.005
y[1] (numeric) = 0.0322580825678 0.0470350495978
y[1] (closed_form) = 0.0324760829189 0.0471814564733
absolute error = 0.0002626
relative error = 0.4585 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.594
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.934
Order of pole (three term test) = 1.460e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5177 2.547
h = 0.0001 0.003
y[1] (numeric) = 0.0320167323189 0.0468101250212
y[1] (closed_form) = 0.0322341320694 0.0469570269148
absolute error = 0.0002624
relative error = 0.4607 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.599
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.56
Order of pole (three term test) = 4.931e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5176 2.55
h = 0.001 0.001
y[1] (numeric) = 0.0318710503283 0.0466781140814
y[1] (closed_form) = 0.0320881902698 0.046824861652
absolute error = 0.0002621
relative error = 0.4617 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.602
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.226
Order of pole (three term test) = 1.077e-29 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2165.2MB, alloc=44.3MB, time=27.57
x[1] = -0.5166 2.551
h = 0.0001 0.004
y[1] (numeric) = 0.0317787118576 0.0466795091719
y[1] (closed_form) = 0.0319956995007 0.0468262245753
absolute error = 0.0002619
relative error = 0.4619 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.603
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.364
Order of pole (three term test) = 1.699e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5165 2.555
h = 0.003 0.006
y[1] (numeric) = 0.0315870004352 0.0465018117957
y[1] (closed_form) = 0.0318044071962 0.0466489943568
absolute error = 0.0002625
relative error = 0.465 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.607
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.37
Order of pole (three term test) = 1.224e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5135 2.561
h = 0.0001 0.005
y[1] (numeric) = 0.0311731257899 0.0463692489216
y[1] (closed_form) = 0.0313913020188 0.0465155484403
absolute error = 0.0002627
relative error = 0.4681 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.612
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.947
Order of pole (three term test) = 1.817e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5134 2.566
h = 0.0001 0.003
y[1] (numeric) = 0.0309409665316 0.0461475247409
y[1] (closed_form) = 0.0311585550526 0.0462942937548
absolute error = 0.0002625
relative error = 0.4703 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.617
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.571
Order of pole (three term test) = 1.226e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5133 2.569
h = 0.001 0.001
y[1] (numeric) = 0.0308007782463 0.0460173400152
y[1] (closed_form) = 0.0310181179606 0.0461639560577
absolute error = 0.0002622
relative error = 0.4714 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.62
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.234
Order of pole (three term test) = 1.340e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5123 2.57
h = 0.001 0.003
y[1] (numeric) = 0.0307109096188 0.0460176017722
y[1] (closed_form) = 0.0309281026215 0.0461641844839
absolute error = 0.000262
relative error = 0.4716 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.621
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.86
Order of pole (three term test) = 8.453e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5113 2.573
h = 0.0001 0.004
y[1] (numeric) = 0.0305310273179 0.045927827467
y[1] (closed_form) = 0.0307485158264 0.0460744910061
absolute error = 0.0002623
relative error = 0.4736 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.623
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.319
Order of pole (three term test) = 5.728e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5112 2.577
h = 0.003 0.006
y[1] (numeric) = 0.0303481000699 0.0457531455982
y[1] (closed_form) = 0.0305656579899 0.0459000585418
absolute error = 0.0002625
relative error = 0.476 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.627
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.405
Order of pole (three term test) = 1.316e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5082 2.583
h = 0.0001 0.005
y[1] (numeric) = 0.0299489124548 0.0456188612169
y[1] (closed_form) = 0.0301672255458 0.0457649386158
absolute error = 0.0002627
relative error = 0.4792 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.633
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.963
Order of pole (three term test) = 3.453e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5081 2.588
h = 0.0001 0.003
y[1] (numeric) = 0.0297270357732 0.045400749989
y[1] (closed_form) = 0.0299447756633 0.0455472685973
absolute error = 0.0002624
relative error = 0.4815 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.637
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.583
Order of pole (three term test) = 1.761e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.508 2.591
h = 0.001 0.001
y[1] (numeric) = 0.0295929944044 0.0452726276709
y[1] (closed_form) = 0.0298104977105 0.0454189948853
absolute error = 0.0002622
relative error = 0.4826 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.64
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.244
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.507 2.592
h = 0.001 0.003
y[1] (numeric) = 0.0295058954349 0.0452716277928
y[1] (closed_form) = 0.0297232582486 0.0454179604205
absolute error = 0.000262
relative error = 0.4827 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.641
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.906
Order of pole (three term test) = 5.427e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.506 2.595
h = 0.0001 0.004
y[1] (numeric) = 0.0293328170152 0.0451821184013
y[1] (closed_form) = 0.0295504625738 0.0453285338518
absolute error = 0.0002623
relative error = 0.4848 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.644
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.345
Order of pole (three term test) = 4.060e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5059 2.599
h = 0.003 0.006
y[1] (numeric) = 0.0291579575901 0.0450102813564
y[1] (closed_form) = 0.0293756655972 0.0451569378264
absolute error = 0.0002625
relative error = 0.4873 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.648
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.439
Order of pole (three term test) = 4.609e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5029 2.605
h = 0.0001 0.005
y[1] (numeric) = 0.0287729216337 0.0448745962592
y[1] (closed_form) = 0.0289913701945 0.0450204622014
absolute error = 0.0002627
relative error = 0.4905 %
Correct digits = 2
memory used=2211.4MB, alloc=44.3MB, time=28.16
Radius of convergence (given) for eq 1 = 2.653
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.978
Order of pole (three term test) = 6.115e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5028 2.61
h = 0.0001 0.003
y[1] (numeric) = 0.0285608701561 0.0446601361008
y[1] (closed_form) = 0.0287787599356 0.0448064165642
absolute error = 0.0002624
relative error = 0.4928 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.658
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.595
Order of pole (three term test) = 1.030e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5027 2.613
h = 0.001 0.001
y[1] (numeric) = 0.0284327044396 0.0445341027244
y[1] (closed_form) = 0.0286503692648 0.0446802335489
absolute error = 0.0002622
relative error = 0.4939 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.661
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.254
Order of pole (three term test) = 9.863e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5017 2.614
h = 0.001 0.003
y[1] (numeric) = 0.028348290605 0.0445319371328
y[1] (closed_form) = 0.0285658208973 0.0446780322995
absolute error = 0.000262
relative error = 0.4941 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.662
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.952
Order of pole (three term test) = 1.872e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5007 2.617
h = 0.0001 0.004
y[1] (numeric) = 0.0281817505862 0.0444427991852
y[1] (closed_form) = 0.028399551407 0.044588978818
absolute error = 0.0002623
relative error = 0.4962 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.664
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.371
Order of pole (three term test) = 3.680e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5006 2.621
h = 0.003 0.006
y[1] (numeric) = 0.0280146012623 0.0442738359609
y[1] (closed_form) = 0.0282324580585 0.0444202484708
absolute error = 0.0002625
relative error = 0.4987 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.668
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.474
Order of pole (three term test) = 4.839e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4976 2.627
h = 0.0001 0.005
y[1] (numeric) = 0.027643199596 0.0441370452513
y[1] (closed_form) = 0.0278617820835 0.0442827098943
absolute error = 0.0002627
relative error = 0.5021 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.674
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.993
Order of pole (three term test) = 1.151e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4975 2.632
h = 0.0001 0.003
y[1] (numeric) = 0.0274405361389 0.04392626323
y[1] (closed_form) = 0.0276585741449 0.0440723172159
absolute error = 0.0002624
relative error = 0.5044 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.679
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.608
Order of pole (three term test) = 1.350e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4974 2.635
h = 0.001 0.001
y[1] (numeric) = 0.027317986683 0.0438023386053
y[1] (closed_form) = 0.0275358107984 0.0439482448618
absolute error = 0.0002622
relative error = 0.5055 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.682
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.263
Order of pole (three term test) = 2.525e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4964 2.636
h = 0.001 0.003
y[1] (numeric) = 0.027236175379 0.0437990971208
y[1] (closed_form) = 0.0274538706709 0.0439449668173
absolute error = 0.000262
relative error = 0.5057 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.682
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.998
Order of pole (three term test) = 1.782e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4954 2.639
h = 0.0001 0.004
y[1] (numeric) = 0.0270759182645 0.0437104268939
y[1] (closed_form) = 0.0272938723924 0.0438563823794
absolute error = 0.0002623
relative error = 0.5078 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.685
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.397
Order of pole (three term test) = 1.053e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4953 2.643
h = 0.003 0.006
y[1] (numeric) = 0.0269161370783 0.0435443579324
y[1] (closed_form) = 0.0271341411666 0.0436905383933
absolute error = 0.0002625
relative error = 0.5104 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.689
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.508
Order of pole (three term test) = 6.191e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4923 2.649
h = 0.0001 0.005
y[1] (numeric) = 0.0265578699821 0.0434067328168
y[1] (closed_form) = 0.0267765847224 0.0435522058351
absolute error = 0.0002627
relative error = 0.5138 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.694
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.009
Order of pole (three term test) = 9.874e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4922 2.654
h = 0.0001 0.003
y[1] (numeric) = 0.0263641767367 0.0431996460098
y[1] (closed_form) = 0.0265823611465 0.0433454846202
absolute error = 0.0002624
relative error = 0.5161 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.699
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.62
Order of pole (three term test) = 3.307e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4921 2.657
h = 0.001 0.001
y[1] (numeric) = 0.0262469955493 0.0430778438567
y[1] (closed_form) = 0.0264649765928 0.0432235367801
absolute error = 0.0002622
relative error = 0.5173 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.702
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.273
Order of pole (three term test) = 1.614e-30 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2257.7MB, alloc=44.3MB, time=28.76
x[1] = -0.4911 2.658
h = 0.0001 0.004
y[1] (numeric) = 0.0261677061305 0.0430736105672
y[1] (closed_form) = 0.0263855638191 0.0432192661825
absolute error = 0.0002621
relative error = 0.5175 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.703
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.648
Order of pole (three term test) = 4.267e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.491 2.662
h = 0.003 0.006
y[1] (numeric) = 0.0260137027254 0.0429099291578
y[1] (closed_form) = 0.0262318731605 0.0430559997558
absolute error = 0.0002626
relative error = 0.5208 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.707
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.538
Order of pole (three term test) = 1.083e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.488 2.668
h = 0.0001 0.005
y[1] (numeric) = 0.0256663604187 0.0427719346564
y[1] (closed_form) = 0.025885228018 0.0429173307226
absolute error = 0.0002628
relative error = 0.5243 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.712
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.022
Order of pole (three term test) = 1.350e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4879 2.673
h = 0.0001 0.003
y[1] (numeric) = 0.0254800239435 0.0425681357583
y[1] (closed_form) = 0.025698373516 0.0427138782213
absolute error = 0.0002625
relative error = 0.5266 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.717
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.631
Order of pole (three term test) = 2.061e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4878 2.676
h = 0.001 0.001
y[1] (numeric) = 0.0253672479579 0.0424482274551
y[1] (closed_form) = 0.0255854027844 0.0425938261982
absolute error = 0.0002623
relative error = 0.5279 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.72
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.282
Order of pole (three term test) = 2.082e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4868 2.677
h = 0.001 0.003
y[1] (numeric) = 0.0252900767836 0.0424432324377
y[1] (closed_form) = 0.0255081127832 0.0425887934031
absolute error = 0.0002622
relative error = 0.5281 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.721
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.084
Order of pole (three term test) = 6.040e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4858 2.68
h = 0.0001 0.004
y[1] (numeric) = 0.0251408558075 0.0423557249526
y[1] (closed_form) = 0.0253591302033 0.0425013732877
absolute error = 0.0002624
relative error = 0.5302 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.724
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.446
Order of pole (three term test) = 1.052e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4857 2.684
h = 0.003 0.006
y[1] (numeric) = 0.0249938914895 0.0421951488545
y[1] (closed_form) = 0.0252122058588 0.0423410080355
absolute error = 0.0002626
relative error = 0.5328 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.728
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.573
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4827 2.69
h = 0.0001 0.005
y[1] (numeric) = 0.0246587969132 0.0420567611704
y[1] (closed_form) = 0.0248777932583 0.0422019823804
absolute error = 0.0002628
relative error = 0.5364 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.733
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.037
Order of pole (three term test) = 7.698e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4826 2.695
h = 0.0001 0.003
y[1] (numeric) = 0.0244807021031 0.0418566614818
y[1] (closed_form) = 0.0246991942176 0.0420022077855
absolute error = 0.0002625
relative error = 0.5388 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.738
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.643
Order of pole (three term test) = 7.855e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4825 2.698
h = 0.001 0.001
y[1] (numeric) = 0.0243728616824 0.0417388842787
y[1] (closed_form) = 0.0245911686369 0.0418842890969
absolute error = 0.0002623
relative error = 0.54 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.741
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.291
Order of pole (three term test) = 9.164e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4815 2.699
h = 0.001 0.003
y[1] (numeric) = 0.0242980667786 0.0417330389361
y[1] (closed_form) = 0.0245162599494 0.0418784054771
absolute error = 0.0002622
relative error = 0.5403 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.742
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.13
Order of pole (three term test) = 7.172e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4805 2.702
h = 0.0001 0.004
y[1] (numeric) = 0.0241544495133 0.0416462220288
y[1] (closed_form) = 0.0243728707787 0.0417916765037
absolute error = 0.0002624
relative error = 0.5424 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.744
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.472
Order of pole (three term test) = 9.476e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4804 2.706
h = 0.003 0.006
y[1] (numeric) = 0.0240139564867 0.0414885549935
y[1] (closed_form) = 0.02423241286 0.0416342130926
absolute error = 0.0002626
relative error = 0.545 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.748
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.608
Order of pole (three term test) = 1.760e-29 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2304.1MB, alloc=44.3MB, time=29.34
x[1] = -0.4774 2.712
h = 0.0001 0.005
y[1] (numeric) = 0.023690658468 0.0413499860297
y[1] (closed_form) = 0.0239097816073 0.041495040794
absolute error = 0.0002628
relative error = 0.5487 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.754
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.053
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4773 2.717
h = 0.0001 0.003
y[1] (numeric) = 0.0235204387191 0.0411535793588
y[1] (closed_form) = 0.023739071214 0.0412989391269
absolute error = 0.0002625
relative error = 0.5512 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.759
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.656
Order of pole (three term test) = 3.317e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4772 2.72
h = 0.001 0.001
y[1] (numeric) = 0.0234173160309 0.041037932734
y[1] (closed_form) = 0.0236357724823 0.0411831533338
absolute error = 0.0002623
relative error = 0.5524 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.762
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.301
Order of pole (three term test) = 1.730e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4762 2.721
h = 0.001 0.003
y[1] (numeric) = 0.0233448225335 0.041031306627
y[1] (closed_form) = 0.0235631700294 0.0411764885682
absolute error = 0.0002622
relative error = 0.5527 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.762
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.177
Order of pole (three term test) = 4.564e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4752 2.724
h = 0.0001 0.004
y[1] (numeric) = 0.023206589368 0.0409452439047
y[1] (closed_form) = 0.0234251551051 0.0410905141235
absolute error = 0.0002624
relative error = 0.5549 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.765
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.499
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4751 2.728
h = 0.003 0.006
y[1] (numeric) = 0.0230722807568 0.0407904806196
y[1] (closed_form) = 0.0232908770893 0.0409359474697
absolute error = 0.0002626
relative error = 0.5575 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.769
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.642
Order of pole (three term test) = 1.705e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4721 2.734
h = 0.0001 0.005
y[1] (numeric) = 0.0227603441905 0.0406519242491
y[1] (closed_form) = 0.0229795921009 0.0407968205758
absolute error = 0.0002628
relative error = 0.5613 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.774
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.068
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.472 2.739
h = 0.0001 0.003
y[1] (numeric) = 0.0225976493268 0.0404591977485
y[1] (closed_form) = 0.0228164199537 0.0406043801349
absolute error = 0.0002626
relative error = 0.5637 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.779
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.668
Order of pole (three term test) = 1.265e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4719 2.742
h = 0.001 0.001
y[1] (numeric) = 0.0224990362238 0.0403456770896
y[1] (closed_form) = 0.0227176394766 0.0404907226931
absolute error = 0.0002623
relative error = 0.5651 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.782
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.311
Order of pole (three term test) = 6.167e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4709 2.743
h = 0.001 0.003
y[1] (numeric) = 0.0224287712793 0.040338335279
y[1] (closed_form) = 0.0226472701982 0.0404833419498
absolute error = 0.0002622
relative error = 0.5653 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.783
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.223
Order of pole (three term test) = 5.829e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4699 2.746
h = 0.0001 0.004
y[1] (numeric) = 0.0222957111552 0.0402530833867
y[1] (closed_form) = 0.0225144188914 0.0403981784794
absolute error = 0.0002625
relative error = 0.5675 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.786
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.525
Order of pole (three term test) = 3.064e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4698 2.75
h = 0.003 0.006
y[1] (numeric) = 0.0221673129068 0.0401012133835
y[1] (closed_form) = 0.0223860470556 0.0402464983396
absolute error = 0.0002626
relative error = 0.5702 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.79
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.677
Order of pole (three term test) = 2.011e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4668 2.756
h = 0.0001 0.005
y[1] (numeric) = 0.021866318319 0.039962846733
y[1] (closed_form) = 0.0220856889183 0.0401075922464
absolute error = 0.0002628
relative error = 0.574 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.795
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.084
Order of pole (three term test) = 3.167e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4667 2.761
h = 0.0001 0.003
y[1] (numeric) = 0.0217108138903 0.0397737816
y[1] (closed_form) = 0.0219297203282 0.0399187953109
absolute error = 0.0002626
relative error = 0.5765 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.8
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.681
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4666 2.764
h = 0.001 0.001
y[1] (numeric) = 0.0216165114999 0.0396623786251
y[1] (closed_form) = 0.0218352588076 0.0398072579937
absolute error = 0.0002624
relative error = 0.5779 %
Correct digits = 2
memory used=2350.6MB, alloc=44.3MB, time=29.93
Radius of convergence (given) for eq 1 = 2.803
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.321
Order of pole (three term test) = 5.321e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4656 2.765
h = 0.0001 0.004
y[1] (numeric) = 0.0215484042598 0.0396543819471
y[1] (closed_form) = 0.0217670516569 0.0397992222063
absolute error = 0.0002623
relative error = 0.5782 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.804
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.933
Order of pole (three term test) = 1.896e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4655 2.769
h = 0.003 0.006
y[1] (numeric) = 0.0214246401162 0.0395048757802
y[1] (closed_form) = 0.0216435197118 0.0396500810845
absolute error = 0.0002627
relative error = 0.5815 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.808
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.707
Order of pole (three term test) = 5.525e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4625 2.775
h = 0.0001 0.005
y[1] (numeric) = 0.0211327348832 0.0393669261931
y[1] (closed_form) = 0.0213522376384 0.0395116173121
absolute error = 0.0002629
relative error = 0.5854 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.813
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.097
Order of pole (three term test) = 7.012e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4624 2.78
h = 0.0001 0.003
y[1] (numeric) = 0.0209831202176 0.0391810740239
y[1] (closed_form) = 0.0212021701036 0.039326018938
absolute error = 0.0002627
relative error = 0.5879 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.818
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.692
Order of pole (three term test) = 1.470e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4623 2.783
h = 0.001 0.001
y[1] (numeric) = 0.0208923508518 0.0390715330226
y[1] (closed_form) = 0.0211112483488 0.0392163458219
absolute error = 0.0002625
relative error = 0.5893 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.821
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.329
Order of pole (three term test) = 5.765e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4613 2.784
h = 0.001 0.003
y[1] (numeric) = 0.0208260525681 0.0390630429293
y[1] (closed_form) = 0.0210448538101 0.0392078165875
absolute error = 0.0002624
relative error = 0.5896 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.822
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.31
Order of pole (three term test) = 9.435e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4603 2.787
h = 0.0001 0.004
y[1] (numeric) = 0.0207020736547 0.0389794850194
y[1] (closed_form) = 0.0209210672645 0.0391243468017
absolute error = 0.0002626
relative error = 0.5918 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.825
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.574
Order of pole (three term test) = 3.375e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4602 2.791
h = 0.003 0.006
y[1] (numeric) = 0.0205839514988 0.0388330187037
y[1] (closed_form) = 0.0208029646173 0.0389780582979
absolute error = 0.0002627
relative error = 0.5946 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.829
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.742
Order of pole (three term test) = 4.427e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4572 2.797
h = 0.0001 0.005
y[1] (numeric) = 0.020302246098 0.0386955433191
y[1] (closed_form) = 0.0205218674661 0.0388400968258
absolute error = 0.0002629
relative error = 0.5985 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.834
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.113
Order of pole (three term test) = 7.789e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4571 2.802
h = 0.0001 0.003
y[1] (numeric) = 0.0201592394417 0.0385133002663
y[1] (closed_form) = 0.0203784205805 0.0386580915581
absolute error = 0.0002627
relative error = 0.6011 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.839
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.704
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.457 2.805
h = 0.001 0.001
y[1] (numeric) = 0.0200724342559 0.0384058509446
y[1] (closed_form) = 0.0202914705112 0.0385505126296
absolute error = 0.0002625
relative error = 0.6025 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.842
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.339
Order of pole (three term test) = 8.269e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.456 2.806
h = 0.001 0.003
y[1] (numeric) = 0.0200081665161 0.0383968080293
y[1] (closed_form) = 0.0202271105911 0.0385414305515
absolute error = 0.0002624
relative error = 0.6028 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.843
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.357
Order of pole (three term test) = 1.144e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.455 2.809
h = 0.0001 0.004
y[1] (numeric) = 0.0198888010676 0.0383141870567
y[1] (closed_form) = 0.0201079292213 0.0384588973835
absolute error = 0.0002626
relative error = 0.6051 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.846
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.601
Order of pole (three term test) = 9.059e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4549 2.813
h = 0.003 0.006
y[1] (numeric) = 0.0197758715489 0.0381705574742
y[1] (closed_form) = 0.0199950158544 0.0383154394662
absolute error = 0.0002627
relative error = 0.6079 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.85
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.777
Order of pole (three term test) = 3.960e-30 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2397.0MB, alloc=44.3MB, time=30.52
x[1] = -0.4519 2.819
h = 0.0001 0.005
y[1] (numeric) = 0.0195039889323 0.0380336920175
y[1] (closed_form) = 0.019723726723 0.038178114535
absolute error = 0.0002629
relative error = 0.6119 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.855
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.128
Order of pole (three term test) = 1.123e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4518 2.824
h = 0.0001 0.003
y[1] (numeric) = 0.0193672972024 0.0378550257681
y[1] (closed_form) = 0.0195866071402 0.0379996709784
absolute error = 0.0002627
relative error = 0.6145 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.86
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.717
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4517 2.827
h = 0.001 0.001
y[1] (numeric) = 0.0192842817455 0.0377496514668
y[1] (closed_form) = 0.0195034539362 0.0378941696028
absolute error = 0.0002625
relative error = 0.616 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.863
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.349
Order of pole (three term test) = 1.070e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4507 2.828
h = 0.001 0.003
y[1] (numeric) = 0.0192219793908 0.0377401058814
y[1] (closed_form) = 0.0194410633003 0.0378845849059
absolute error = 0.0002624
relative error = 0.6163 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.864
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.403
Order of pole (three term test) = 1.445e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4497 2.831
h = 0.0001 0.004
y[1] (numeric) = 0.0191070467444 0.0376584564628
y[1] (closed_form) = 0.0193263068072 0.0378030228398
absolute error = 0.0002626
relative error = 0.6186 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.866
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.627
Order of pole (three term test) = 1.207e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4496 2.835
h = 0.003 0.006
y[1] (numeric) = 0.0189990803802 0.0375176380655
y[1] (closed_form) = 0.0192183534913 0.0376623701673
absolute error = 0.0002627
relative error = 0.6214 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.87
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.812
Order of pole (three term test) = 5.002e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4466 2.841
h = 0.0001 0.005
y[1] (numeric) = 0.0187366574048 0.0373815057046
y[1] (closed_form) = 0.0189565094057 0.0375258035378
absolute error = 0.000263
relative error = 0.6255 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.876
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.144
Order of pole (three term test) = 3.934e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4465 2.846
h = 0.0001 0.003
y[1] (numeric) = 0.0186060007493 0.0372063801791
y[1] (closed_form) = 0.0188254370047 0.0373508864791
absolute error = 0.0002627
relative error = 0.6282 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.881
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.729
Order of pole (three term test) = 1.878e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4464 2.849
h = 0.001 0.001
y[1] (numeric) = 0.0185266083873 0.0371030618881
y[1] (closed_form) = 0.018745913681 0.0372474436621
absolute error = 0.0002626
relative error = 0.6297 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.884
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.359
Order of pole (three term test) = 1.035e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4454 2.85
h = 0.001 0.003
y[1] (numeric) = 0.0184662081862 0.0370930604774
y[1] (closed_form) = 0.0186854289291 0.0372374032571
absolute error = 0.0002625
relative error = 0.63 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.885
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.45
Order of pole (three term test) = 1.064e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4444 2.853
h = 0.0001 0.004
y[1] (numeric) = 0.0183555348603 0.037012412565
y[1] (closed_form) = 0.0185749241798 0.0371568421263
absolute error = 0.0002627
relative error = 0.6323 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.887
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.653
Order of pole (three term test) = 1.444e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4443 2.857
h = 0.003 0.006
y[1] (numeric) = 0.0182523124985 0.036874376887
y[1] (closed_form) = 0.0184717119992 0.0370189664338
absolute error = 0.0002628
relative error = 0.6351 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.891
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.847
Order of pole (three term test) = 6.310e-31 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4413 2.863
h = 0.0001 0.005
y[1] (numeric) = 0.017998999485 0.0367390891455
y[1] (closed_form) = 0.0182189634688 0.0368832682962
absolute error = 0.000263
relative error = 0.6393 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.897
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.16
Order of pole (three term test) = 7.015e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4412 2.868
h = 0.0001 0.003
y[1] (numeric) = 0.0178741106963 0.0365674649551
y[1] (closed_form) = 0.018093670769 0.0367118391643
absolute error = 0.0002628
relative error = 0.642 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.902
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.742
Order of pole (three term test) = 9.760e-30 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=2443.4MB, alloc=44.3MB, time=31.11
x[1] = -0.4411 2.871
h = 0.001 0.001
y[1] (numeric) = 0.017798182269 0.0364661815891
y[1] (closed_form) = 0.0180176178314 0.0366104338284
absolute error = 0.0002626
relative error = 0.6436 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.905
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.369
Order of pole (three term test) = 1.990e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4401 2.872
h = 0.001 0.003
y[1] (numeric) = 0.0177396228871 0.0364557680952
y[1] (closed_form) = 0.0179589774679 0.0365999815166
absolute error = 0.0002625
relative error = 0.6439 %
Correct digits = 2
Radius of convergence (given) for eq 1 = 2.906
Order of pole (given) = 4 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.497
Order of pole (three term test) = 6.898e-30 0
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff ( y , x , 1 ) = neg ( 3.0 ) / x / x / x / x ;
Iterations = 754
Total Elapsed Time = 31 Seconds
Expected Time Remaining = 0 Seconds
Optimized Time Remaining = 0 Seconds
Expected Total Time = 31 Seconds
> quit
memory used=2451.4MB, alloc=44.3MB, time=31.21