|\^/| 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(6.0) ) / ( c(x) - c(6.0) ));
> end;
exact_soln_y :=
proc(x) return c(1.0)/((c(x) - c(6.0))*(c(x) - c(6.0))) 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_2D0,
> array_const_6D0,
#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_tmp7,
> array_tmp8,
> 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_2D0,
array_const_6D0, 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_tmp7, array_tmp8, 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_2D0,
> array_const_6D0,
#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_tmp7,
> array_tmp8,
> 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_2D0,
array_const_6D0, 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_tmp7, array_tmp8, 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_2D0,
> array_const_6D0,
#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_tmp7,
> array_tmp8,
> 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_2D0,
array_const_6D0, 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_tmp7, array_tmp8, 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_2D0,
> array_const_6D0,
#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_tmp7,
> array_tmp8,
> 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_2D0,
array_const_6D0, 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_tmp7, array_tmp8, 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_2D0,
> array_const_6D0,
#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_tmp7,
> array_tmp8,
> 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_2D0,
array_const_6D0, 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_tmp7, array_tmp8, 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_2D0,
> array_const_6D0,
#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_tmp7,
> array_tmp8,
> 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_2D0,
array_const_6D0, 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_tmp7, array_tmp8, 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_2D0,
> array_const_6D0,
#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_tmp7,
> array_tmp8,
> 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_2D0,
array_const_6D0, 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_tmp7, array_tmp8, 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_2D0,
> array_const_6D0,
#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_tmp7,
> array_tmp8,
> 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_2D0[1]);
> #emit pre sub LINEAR - CONST $eq_no = 1 i = 1
> array_tmp2[1] := array_x[1] - array_const_6D0[1];
> #emit pre div CONST - LINEAR $eq_no = 1 i = 1
> array_tmp3[1] := array_tmp1[1] / array_tmp2[1];
> #emit pre sub LINEAR - CONST $eq_no = 1 i = 1
> array_tmp4[1] := array_x[1] - array_const_6D0[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 1
> array_tmp5[1] := array_tmp3[1] / array_tmp4[1];
> #emit pre sub LINEAR - CONST $eq_no = 1 i = 1
> array_tmp6[1] := array_x[1] - array_const_6D0[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 1
> array_tmp7[1] := array_tmp5[1] / array_tmp6[1];
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp8[1] := array_const_0D0[1] + array_tmp7[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_tmp8[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 sub LINEAR - CONST $eq_no = 1 i = 2
> array_tmp2[2] := array_x[2];
> #emit pre div CONST - LINEAR $eq_no = 1 i = 2
> array_tmp3[2] := neg(array_tmp3[1])* array_tmp2[2] / array_tmp2[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 sub LINEAR - CONST $eq_no = 1 i = 2
> array_tmp4[2] := array_x[2];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 2
> array_tmp5[2] := (array_tmp3[2] - array_tmp5[1] * array_tmp4[2]) / array_tmp4[1];
> #emit pre sub LINEAR - CONST $eq_no = 1 i = 2
> array_tmp6[2] := array_x[2];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 2
> array_tmp7[2] := (array_tmp5[2] - array_tmp7[1] * array_tmp6[2]) / array_tmp6[1];
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp8[2] := array_tmp7[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_tmp8[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_tmp3[3] := neg(array_tmp3[2])* array_tmp2[2] / array_tmp2[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 3
> array_tmp5[3] := (array_tmp3[3] - array_tmp5[2] * array_tmp4[2]) / array_tmp4[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 3
> array_tmp7[3] := (array_tmp5[3] - array_tmp7[2] * array_tmp6[2]) / array_tmp6[1];
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp8[3] := array_tmp7[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_tmp8[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_tmp3[4] := neg(array_tmp3[3])* array_tmp2[2] / array_tmp2[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 4
> array_tmp5[4] := (array_tmp3[4] - array_tmp5[3] * array_tmp4[2]) / array_tmp4[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 4
> array_tmp7[4] := (array_tmp5[4] - array_tmp7[3] * array_tmp6[2]) / array_tmp6[1];
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp8[4] := array_tmp7[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_tmp8[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_tmp3[5] := neg(array_tmp3[4])* array_tmp2[2] / array_tmp2[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 5
> array_tmp5[5] := (array_tmp3[5] - array_tmp5[4] * array_tmp4[2]) / array_tmp4[1];
> #emit pre div FULL - LINEAR $eq_no = 1 i = 5
> array_tmp7[5] := (array_tmp5[5] - array_tmp7[4] * array_tmp6[2]) / array_tmp6[1];
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp8[5] := array_tmp7[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_tmp8[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_tmp3[kkk] := array_tmp1[1] * array_tmp2[kkk];
> #emit div FULL LINEAR $eq_no = 1 i = 1
> array_tmp5[kkk] := neg(ats(kkk,array_tmp4,array_tmp5,2)) / array_tmp4[1];
> #emit div FULL LINEAR $eq_no = 1 i = 1
> array_tmp7[kkk] := neg(ats(kkk,array_tmp6,array_tmp7,2)) / array_tmp6[1];
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp8[kkk] := array_tmp7[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_tmp8[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_2D0,
array_const_6D0, 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_tmp7, array_tmp8, 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_2D0[1]);
array_tmp2[1] := array_x[1] - array_const_6D0[1];
array_tmp3[1] := array_tmp1[1]/array_tmp2[1];
array_tmp4[1] := array_x[1] - array_const_6D0[1];
array_tmp5[1] := array_tmp3[1]/array_tmp4[1];
array_tmp6[1] := array_x[1] - array_const_6D0[1];
array_tmp7[1] := array_tmp5[1]/array_tmp6[1];
array_tmp8[1] := array_const_0D0[1] + array_tmp7[1];
if not array_y_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp8[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] := array_x[2];
array_tmp3[2] := neg(array_tmp3[1])*array_tmp2[2]/array_tmp2[1];
array_tmp4[2] := array_x[2];
array_tmp5[2] :=
(-array_tmp4[2]*array_tmp5[1] + array_tmp3[2])/array_tmp4[1];
array_tmp6[2] := array_x[2];
array_tmp7[2] :=
(-array_tmp6[2]*array_tmp7[1] + array_tmp5[2])/array_tmp6[1];
array_tmp8[2] := array_tmp7[2];
if not array_y_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp8[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
if 3 <= ATS_MAX_TERMS then
array_y[3] := temporary; array_y_higher[1, 3] := temporary
end if;
temporary := c(temporary)*c(2)/c(glob_h);
array_y_higher[2, 2] := c(temporary)
end if
end if;
kkk := 3;
array_tmp3[3] := neg(array_tmp3[2])*array_tmp2[2]/array_tmp2[1];
array_tmp5[3] :=
(-array_tmp4[2]*array_tmp5[2] + array_tmp3[3])/array_tmp4[1];
array_tmp7[3] :=
(-array_tmp6[2]*array_tmp7[2] + array_tmp5[3])/array_tmp6[1];
array_tmp8[3] := array_tmp7[3];
if not array_y_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp8[3])*expt(glob_h, c(1))*c(factorial_3(2, 3));
if 4 <= ATS_MAX_TERMS then
array_y[4] := temporary; array_y_higher[1, 4] := temporary
end if;
temporary := c(temporary)*c(3)/c(glob_h);
array_y_higher[2, 3] := c(temporary)
end if
end if;
kkk := 4;
array_tmp3[4] := neg(array_tmp3[3])*array_tmp2[2]/array_tmp2[1];
array_tmp5[4] :=
(-array_tmp4[2]*array_tmp5[3] + array_tmp3[4])/array_tmp4[1];
array_tmp7[4] :=
(-array_tmp6[2]*array_tmp7[3] + array_tmp5[4])/array_tmp6[1];
array_tmp8[4] := array_tmp7[4];
if not array_y_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp8[4])*expt(glob_h, c(1))*c(factorial_3(3, 4));
if 5 <= ATS_MAX_TERMS then
array_y[5] := temporary; array_y_higher[1, 5] := temporary
end if;
temporary := c(temporary)*c(4)/c(glob_h);
array_y_higher[2, 4] := c(temporary)
end if
end if;
kkk := 5;
array_tmp3[5] := neg(array_tmp3[4])*array_tmp2[2]/array_tmp2[1];
array_tmp5[5] :=
(-array_tmp4[2]*array_tmp5[4] + array_tmp3[5])/array_tmp4[1];
array_tmp7[5] :=
(-array_tmp6[2]*array_tmp7[4] + array_tmp5[5])/array_tmp6[1];
array_tmp8[5] := array_tmp7[5];
if not array_y_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp8[5])*expt(glob_h, c(1))*c(factorial_3(4, 5));
if 6 <= ATS_MAX_TERMS then
array_y[6] := temporary; array_y_higher[1, 6] := temporary
end if;
temporary := c(temporary)*c(5)/c(glob_h);
array_y_higher[2, 5] := c(temporary)
end if
end if;
kkk := 6;
while kkk <= ATS_MAX_TERMS do
array_tmp3[kkk] := array_tmp1[1]*array_tmp2[kkk];
array_tmp5[kkk] :=
neg(ats(kkk, array_tmp4, array_tmp5, 2))/array_tmp4[1];
array_tmp7[kkk] :=
neg(ats(kkk, array_tmp6, array_tmp7, 2))/array_tmp6[1];
array_tmp8[kkk] := array_tmp7[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_tmp8[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_2D0,
> array_const_6D0,
> #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_tmp7,
> array_tmp8,
> 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:=30;
> 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_tmp7:= Array(0..(20),[]);
> array_tmp8:= 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_tmp7[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 20) do # do number 1
> array_tmp8[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_tmp7);
> zero_ats_ar(array_tmp8);
> 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_2D0);
> array_const_2D0[1] := c(2.0);
> zero_ats_ar(array_const_6D0);
> array_const_6D0[1] := c(6.0);
> 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/sing6postcpx.cpx#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = neg ( 2.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=30;");
> 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 := 2.1 + 0.1 * I;");
> omniout_str(ALWAYS,"x_end := 99.0 + 99.0 * I;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_type_given_pole := 1;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_rad_poles[1,1] := c(6.0);");
> 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(3.0);");
> 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(6.0) ) / ( c(x) - c(6.0) ));");
> 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 := 2.1 + 0.1 * I;
> x_end := 99.0 + 99.0 * I;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_type_given_pole := 1;
> array_given_rad_poles[1,1] := c(6.0);
> array_given_rad_poles[1,2] := c(0.0);
> array_given_ord_poles[1,1] := c(3.0);
> 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 ( 2.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; ");
> 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,"2017-11-26T16:24:49-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"sing6")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = neg ( 2.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; ")
> ;
> 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,"sing6 diffeq.mxt")
> ;
> logitem_str(html_log_file,"sing6 maple results")
> ;
> logitem_str(html_log_file,"OK")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 15;
> if (glob_html_log) then # if number 15
> fclose(html_log_file);
> fi;# end if 15
> ;
> ;;
> end;
> # End Function number 12
> #END OUTFILEMAIN
> end;
Warning, `h_new` is implicitly declared local to procedure `main`
Warning, `ratio` is implicitly declared local to procedure `main`
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max,
term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order,
sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it,
last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err,
estimated_step_error, min_value, est_answer, found_h, repeat_it, h_new,
ratio;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_6D0, 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_tmp7, array_tmp8, 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 := 30;
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_tmp7 := Array(0 .. 20, []);
array_tmp8 := 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_tmp7[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 20 do array_tmp8[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_tmp7);
zero_ats_ar(array_tmp8);
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_2D0);
array_const_2D0[1] := c(2.0);
zero_ats_ar(array_const_6D0);
array_const_6D0[1] := c(6.0);
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/sing6postcpx.cpx#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = neg ( 2.0 ) / \
( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ; \
");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=30;");
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 := 2.1 + 0.1 * I;");
omniout_str(ALWAYS, "x_end := 99.0 + 99.0 * I;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_type_given_pole := 1;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_rad_poles[1,1] := c(6.0);");
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(3.0);");
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(6.0) ) / ( c(x) - c(6.0) ));");
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,");
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omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.000 + 0.000 * I ];");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_nxt := glob_nxt + 1;");
omniout_str(ALWAYS, "it := x_delta[glob_nxt];");
omniout_str(ALWAYS, "return it;");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := glob__0;
glob_smallish_float := glob__0;
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob_almost_1 := c(0.99);
x_start := 2.1 + 0.1*I;
x_end := 99.0 + 99.0*I;
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_type_given_pole := 1;
array_given_rad_poles[1, 1] := c(6.0);
array_given_rad_poles[1, 2] := c(0.);
array_given_ord_poles[1, 1] := c(3.0);
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 ( 2.0 ) /\
( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 \
) ; ");
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, "2017-11-26T16:24:49-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"sing6");
logitem_str(html_log_file, "diff ( y , x , 1 ) = ne\
g ( 2.0 ) / ( x - 6.0 ) / ( x - 6.0 ) \
/ ( x - 6.0 ) ; ");
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,
"sing6 diffeq.mxt");
logitem_str(html_log_file,
"sing6 maple results")
;
logitem_str(html_log_file, "OK");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end if
end proc
# End Function number 12
> main();
memory used=3.9MB, alloc=40.3MB, time=0.08
##############ECHO OF PROBLEM#################
##############temp/sing6postcpx.cpx#################
diff ( y , x , 1 ) = neg ( 2.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=30;
max_terms:=20;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 2.1 + 0.1 * I;
x_end := 99.0 + 99.0 * I;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_type_given_pole := 1;
array_given_rad_poles[1,1] := c(6.0);
array_given_rad_poles[1,2] := c(0.0);
array_given_ord_poles[1,1] := c(3.0);
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(6.0) ) / ( c(x) - c(6.0) ));
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] = 2.1 0.1
h = 0.0001 0.005
y[1] (numeric) = 0.0656166845961 0.0033671719727
y[1] (closed_form) = 0.0656166845961 0.0033671719727
absolute error = 0
relative error = 0 %
Correct digits = 28
Radius of convergence (given) for eq 1 = 3.901
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.876
Order of pole (three term test) = 1.358e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1001 0.105
h = 0.0001 0.003
y[1] (numeric) = 0.0656068449068 0.00353533163166
y[1] (closed_form) = 0.0656067803786 0.00353532609315
absolute error = 6.477e-08
relative error = 9.857e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 3.901
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.342
Order of pole (three term test) = 1.785e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1002 0.108
h = 0.001 0.001
y[1] (numeric) = 0.0656018572616 0.00363630907876
y[1] (closed_form) = 0.0656018702466 0.00363630952707
absolute error = 1.299e-08
relative error = 1.978e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 3.901
Order of pole (given) = 3 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) = 1.664e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1012 0.109
h = 0.001 0.003
y[1] (numeric) = 0.0656325873365 0.00367270555364
y[1] (closed_form) = 0.0656326392491 0.00367269604465
absolute error = 5.278e-08
relative error = 8.029e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 3.9
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.721
Order of pole (three term test) = 9.436e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1022 0.112
h = 0.0001 0.004
y[1] (numeric) = 0.0656576757237 0.00377634486587
y[1] (closed_form) = 0.0656576473737 0.00377635234382
absolute error = 2.932e-08
relative error = 4.458e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 3.899
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.934
Order of pole (three term test) = 5.814e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1023 0.116
h = 0.003 0.006
y[1] (numeric) = 0.065649263148 0.0039110974409
y[1] (closed_form) = 0.0656491873934 0.00391105358949
absolute error = 8.753e-08
relative error = 0.0001331 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 3.899
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.537
Order of pole (three term test) = 7.294e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1053 0.122
h = 0.0001 0.005
y[1] (numeric) = 0.0657316877679 0.00412182279105
y[1] (closed_form) = 0.0657315323504 0.00412207534135
absolute error = 2.965e-07
relative error = 0.0004503 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.897
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.905
Order of pole (three term test) = 1.494e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1054 0.127
h = 0.0001 0.003
y[1] (numeric) = 0.0657187887821 0.00429056740708
y[1] (closed_form) = 0.0657187186765 0.00429063926746
absolute error = 1.004e-07
relative error = 0.0001524 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 3.897
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.339
Order of pole (three term test) = 3.378e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1055 0.13
h = 0.001 0.001
y[1] (numeric) = 0.0657120570041 0.00439180511158
y[1] (closed_form) = 0.0657120646238 0.00439188475542
absolute error = 8.001e-08
relative error = 0.0001215 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 3.897
Order of pole (given) = 3 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) = 9.552e-28 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=32.5MB, alloc=40.3MB, time=0.42
x[1] = 2.1065 0.131
h = 0.001 0.003
y[1] (numeric) = 0.0657422693997 0.00442885147022
y[1] (closed_form) = 0.0657423163491 0.00442892200097
absolute error = 8.473e-08
relative error = 0.0001286 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 3.896
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.711
Order of pole (three term test) = 4.938e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1075 0.134
h = 0.0001 0.004
y[1] (numeric) = 0.0657656699995 0.00453327395712
y[1] (closed_form) = 0.0657656359382 0.00453335971752
absolute error = 9.228e-08
relative error = 0.00014 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 3.895
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.928
Order of pole (three term test) = 1.255e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1076 0.138
h = 0.003 0.006
y[1] (numeric) = 0.0657549220173 0.00466834032541
y[1] (closed_form) = 0.0657548415129 0.00466837344414
absolute error = 8.705e-08
relative error = 0.0001321 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 3.895
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.53
Order of pole (three term test) = 7.042e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1106 0.144
h = 0.0001 0.005
y[1] (numeric) = 0.0658340172749 0.00488118849125
y[1] (closed_form) = 0.0658338499785 0.00488151750464
absolute error = 3.691e-07
relative error = 0.0005591 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.892
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.902
Order of pole (three term test) = 1.839e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1107 0.149
h = 0.0001 0.003
y[1] (numeric) = 0.0658181819608 0.00505027710195
y[1] (closed_form) = 0.0658181044865 0.00505042658291
absolute error = 1.684e-07
relative error = 0.0002551 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 3.892
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.336
Order of pole (three term test) = 8.156e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1108 0.152
h = 0.001 0.001
y[1] (numeric) = 0.0658096923615 0.00515173635473
y[1] (closed_form) = 0.0658096927744 0.0051518954317
absolute error = 1.591e-07
relative error = 0.000241 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 3.892
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.834
Order of pole (three term test) = 4.613e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1118 0.153
h = 0.001 0.003
y[1] (numeric) = 0.0658393699312 0.00518942364016
y[1] (closed_form) = 0.065839410054 0.00518957446434
absolute error = 1.561e-07
relative error = 0.0002363 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 3.891
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.701
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1128 0.156
h = 0.0001 0.004
y[1] (numeric) = 0.0658610573625 0.00529459417432
y[1] (closed_form) = 0.0658610157727 0.00529475843987
absolute error = 1.694e-07
relative error = 0.0002565 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 3.89
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.922
Order of pole (three term test) = 1.626e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1129 0.16
h = 0.003 0.006
y[1] (numeric) = 0.0658479565094 0.00542992229213
y[1] (closed_form) = 0.0658478694807 0.00543003262412
absolute error = 1.405e-07
relative error = 0.0002127 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 3.89
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.522
Order of pole (three term test) = 1.388e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1159 0.166
h = 0.0001 0.005
y[1] (numeric) = 0.0659236592645 0.00564482639619
y[1] (closed_form) = 0.065923478291 0.00564523190892
absolute error = 4.441e-07
relative error = 0.0006711 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.888
Order of pole (given) = 3 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) = 1.559e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.116 0.171
h = 0.0001 0.003
y[1] (numeric) = 0.065904866999 0.0058141932216
y[1] (closed_form) = 0.0659047803484 0.00581442049483
absolute error = 2.432e-07
relative error = 0.0003676 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.888
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.333
Order of pole (three term test) = 5.685e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1161 0.174
h = 0.001 0.001
y[1] (numeric) = 0.0658946069245 0.00591583471297
y[1] (closed_form) = 0.0658945982718 0.00591607340902
absolute error = 2.389e-07
relative error = 0.000361 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.888
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.832
Order of pole (three term test) = 1.601e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1171 0.175
h = 0.001 0.003
y[1] (numeric) = 0.065923732686 0.00595415342906
y[1] (closed_form) = 0.0659237641009 0.0059543847481
absolute error = 2.334e-07
relative error = 0.0003527 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.887
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.691
Order of pole (three term test) = 6.188e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1181 0.178
h = 0.0001 0.004
y[1] (numeric) = 0.0659436824375 0.00606003596714
y[1] (closed_form) = 0.0659436314855 0.00606027890967
absolute error = 2.482e-07
relative error = 0.0003748 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.886
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.917
Order of pole (three term test) = 5.646e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1182 0.182
h = 0.003 0.006
y[1] (numeric) = 0.0659282126471 0.00619557301193
y[1] (closed_form) = 0.0659281173027 0.00619576075101
absolute error = 2.106e-07
relative error = 0.000318 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.886
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.515
Order of pole (three term test) = 5.923e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1212 0.188
h = 0.0001 0.005
y[1] (numeric) = 0.0660004613407 0.00641246401183
y[1] (closed_form) = 0.0660002648818 0.00641294600871
absolute error = 5.205e-07
relative error = 0.0007849 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.883
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.895
Order of pole (three term test) = 4.769e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1213 0.193
h = 0.0001 0.003
y[1] (numeric) = 0.0659786932798 0.00658204233369
y[1] (closed_form) = 0.0659785956309 0.00658234752003
absolute error = 3.204e-07
relative error = 0.0004833 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.883
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.331
Order of pole (three term test) = 1.526e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1214 0.196
h = 0.001 0.001
y[1] (numeric) = 0.0659666511379 0.00668382618526
y[1] (closed_form) = 0.0659666315459 0.00668414463381
absolute error = 3.191e-07
relative error = 0.0004812 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.884
Order of pole (given) = 3 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) = 2.878e-28 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=78.5MB, alloc=44.3MB, time=1.01
x[1] = 2.1224 0.197
h = 0.0001 0.004
y[1] (numeric) = 0.0659952082929 0.00672276629904
y[1] (closed_form) = 0.0659952291027 0.00672307826111
absolute error = 3.127e-07
relative error = 0.0004713 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.883
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.99
Order of pole (three term test) = 4.987e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1225 0.201
h = 0.003 0.006
y[1] (numeric) = 0.0659777900236 0.00685843073627
y[1] (closed_form) = 0.065977663376 0.00685866756483
absolute error = 2.686e-07
relative error = 0.0004049 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.883
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.509
Order of pole (three term test) = 4.489e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1255 0.207
h = 0.0001 0.005
y[1] (numeric) = 0.066046995042 0.00707693296849
y[1] (closed_form) = 0.0660467611146 0.00707746300608
absolute error = 5.794e-07
relative error = 0.0008722 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.88
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.893
Order of pole (three term test) = 5.006e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1256 0.212
h = 0.0001 0.003
y[1] (numeric) = 0.0660226503948 0.00724660351893
y[1] (closed_form) = 0.0660225191059 0.00724695813828
absolute error = 3.781e-07
relative error = 0.0005693 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.88
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.329
Order of pole (three term test) = 8.924e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1257 0.215
h = 0.001 0.001
y[1] (numeric) = 0.0660090648165 0.00734845617057
y[1] (closed_form) = 0.066009011571 0.00734882564404
absolute error = 3.733e-07
relative error = 0.000562 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.88
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.828
Order of pole (three term test) = 1.465e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1267 0.216
h = 0.001 0.003
y[1] (numeric) = 0.0660371120079 0.00738791567928
y[1] (closed_form) = 0.0660370994218 0.00738827944769
absolute error = 3.640e-07
relative error = 0.0005478 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.879
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.674
Order of pole (three term test) = 1.569e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1277 0.219
h = 0.0001 0.004
y[1] (numeric) = 0.0660537588108 0.00749500277926
y[1] (closed_form) = 0.0660536627939 0.00749537470843
absolute error = 3.841e-07
relative error = 0.0005778 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.878
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.907
Order of pole (three term test) = 5.769e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1278 0.223
h = 0.003 0.006
y[1] (numeric) = 0.0660338421849 0.00763075691054
y[1] (closed_form) = 0.0660337038483 0.00763107135097
absolute error = 3.435e-07
relative error = 0.0005168 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.879
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.503
Order of pole (three term test) = 1.019e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1308 0.229
h = 0.0001 0.005
y[1] (numeric) = 0.0660994839731 0.00785111126333
y[1] (closed_form) = 0.0660992311771 0.00785171759621
absolute error = 6.569e-07
relative error = 0.0009869 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.876
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.89
Order of pole (three term test) = 1.351e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1309 0.234
h = 0.0001 0.003
y[1] (numeric) = 0.066072134167 0.00802086668569
y[1] (closed_form) = 0.0660719884566 0.0080212992828
absolute error = 4.565e-07
relative error = 0.0006858 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.876
Order of pole (given) = 3 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) = 2.143e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.131 0.237
h = 0.001 0.001
y[1] (numeric) = 0.0660567483549 0.00812278598701
y[1] (closed_form) = 0.0660566806481 0.00812323529582
absolute error = 4.544e-07
relative error = 0.0006827 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.876
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.826
Order of pole (three term test) = 4.080e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.132 0.238
h = 0.001 0.003
y[1] (numeric) = 0.0660841963732 0.00816284661265
y[1] (closed_form) = 0.0660841696149 0.00816329113221
absolute error = 4.453e-07
relative error = 0.0006688 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.875
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.665
Order of pole (three term test) = 5.660e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.133 0.241
h = 0.0001 0.004
y[1] (numeric) = 0.0660990409704 0.00827053751655
y[1] (closed_form) = 0.0660989302704 0.00827098830323
absolute error = 4.642e-07
relative error = 0.0006968 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.875
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.902
Order of pole (three term test) = 4.797e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1331 0.245
h = 0.003 0.006
y[1] (numeric) = 0.0660767181336 0.00840634542356
y[1] (closed_form) = 0.0660765662783 0.00840673752383
absolute error = 4.205e-07
relative error = 0.0006313 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.875
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.496
Order of pole (three term test) = 6.025e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1361 0.251
h = 0.0001 0.005
y[1] (numeric) = 0.0661387401423 0.00862847692288
y[1] (closed_form) = 0.0661384666518 0.00862915938553
absolute error = 7.352e-07
relative error = 0.001102 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.872
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.887
Order of pole (three term test) = 4.456e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1362 0.256
h = 0.0001 0.003
y[1] (numeric) = 0.0661083716645 0.00879824815221
y[1] (closed_form) = 0.066108209679 0.00879875869797
absolute error = 5.356e-07
relative error = 0.0008031 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.872
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.324
Order of pole (three term test) = 2.080e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1363 0.259
h = 0.001 0.001
y[1] (numeric) = 0.0660911772093 0.00890019279902
y[1] (closed_form) = 0.0660910931338 0.00890072192163
absolute error = 5.358e-07
relative error = 0.0008034 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.872
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.824
Order of pole (three term test) = 1.320e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1373 0.26
h = 0.001 0.003
y[1] (numeric) = 0.0661180098972 0.00894084299561
y[1] (closed_form) = 0.066117967034 0.0089413682574
absolute error = 5.270e-07
relative error = 0.0007899 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.871
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.657
Order of pole (three term test) = 1.840e-27 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=124.3MB, alloc=44.3MB, time=1.58
x[1] = 2.1383 0.263
h = 0.0001 0.004
y[1] (numeric) = 0.0661310314853 0.0090490983782
y[1] (closed_form) = 0.066130904222 0.00904962798988
absolute error = 5.447e-07
relative error = 0.000816 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.871
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.898
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1384 0.267
h = 0.003 0.006
y[1] (numeric) = 0.0661062920955 0.0091849046719
y[1] (closed_form) = 0.0661061248813 0.0091853744276
absolute error = 4.986e-07
relative error = 0.0007471 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.871
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.49
Order of pole (three term test) = 5.849e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1414 0.273
h = 0.0001 0.005
y[1] (numeric) = 0.0661646396752 0.00940873635869
y[1] (closed_form) = 0.0661643436611 0.00940949473217
absolute error = 8.141e-07
relative error = 0.001218 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.868
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.884
Order of pole (three term test) = 1.273e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1415 0.278
h = 0.0001 0.003
y[1] (numeric) = 0.0661312409474 0.00957845361859
y[1] (closed_form) = 0.0661310608252 0.00957904203026
absolute error = 6.154e-07
relative error = 0.0009209 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.869
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.322
Order of pole (three term test) = 2.581e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1416 0.281
h = 0.001 0.001
y[1] (numeric) = 0.0661122305951 0.00968038187326
y[1] (closed_form) = 0.0661121282349 0.00968099073266
absolute error = 6.174e-07
relative error = 0.000924 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.869
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.823
Order of pole (three term test) = 3.846e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1426 0.282
h = 0.001 0.003
y[1] (numeric) = 0.0661384320547 0.00972160957462
y[1] (closed_form) = 0.066138371145 0.00972221551345
absolute error = 6.090e-07
relative error = 0.000911 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.868
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.648
Order of pole (three term test) = 1.788e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1436 0.285
h = 0.0001 0.004
y[1] (numeric) = 0.0661496108724 0.00983038932832
y[1] (closed_form) = 0.0661494651576 0.00983099767788
absolute error = 6.256e-07
relative error = 0.0009354 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.867
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.893
Order of pole (three term test) = 1.430e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1437 0.289
h = 0.003 0.006
y[1] (numeric) = 0.0661224461428 0.00996613806758
y[1] (closed_form) = 0.0661222617208 0.00996668542126
absolute error = 5.776e-07
relative error = 0.0008638 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.867
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.483
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1467 0.295
h = 0.0001 0.005
y[1] (numeric) = 0.0661770666232 0.010191591053
y[1] (closed_form) = 0.0661767462554 0.0101924250645
absolute error = 8.934e-07
relative error = 0.001334 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.865
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.881
Order of pole (three term test) = 1.304e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1468 0.3
h = 0.0001 0.003
y[1] (numeric) = 0.0661406280367 0.010361183919
y[1] (closed_form) = 0.0661404279103 0.0103618500596
absolute error = 6.956e-07
relative error = 0.001039 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.865
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.32
Order of pole (three term test) = 6.604e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1469 0.303
h = 0.001 0.001
y[1] (numeric) = 0.0661197957099 0.0104630536483
y[1] (closed_form) = 0.0661196731427 0.0104637421114
absolute error = 6.993e-07
relative error = 0.001045 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.865
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.821
Order of pole (three term test) = 3.739e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1479 0.304
h = 0.0001 0.004
y[1] (numeric) = 0.0661453503224 0.0105048462743
y[1] (closed_form) = 0.0661452694177 0.0105055327681
absolute error = 6.912e-07
relative error = 0.001032 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.864
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.93
Order of pole (three term test) = 1.080e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.148 0.308
h = 0.003 0.006
y[1] (numeric) = 0.0661161969199 0.0106405022507
y[1] (closed_form) = 0.0661159752168 0.0106410958463
absolute error = 6.336e-07
relative error = 0.0009462 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.864
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.479
Order of pole (three term test) = 1.112e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.151 0.314
h = 0.0001 0.005
y[1] (numeric) = 0.0661675506294 0.0108672409811
y[1] (closed_form) = 0.0661671868773 0.0108681192902
absolute error = 9.507e-07
relative error = 0.001418 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.862
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.879
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1511 0.319
h = 0.0001 0.003
y[1] (numeric) = 0.0661284919016 0.0110366336034
y[1] (closed_form) = 0.066128252074 0.0110373460006
absolute error = 7.517e-07
relative error = 0.001121 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.862
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.318
Order of pole (three term test) = 1.293e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1512 0.322
h = 0.001 0.001
y[1] (numeric) = 0.0661060887132 0.0111383971639
y[1] (closed_form) = 0.0661059262035 0.0111391334957
absolute error = 7.541e-07
relative error = 0.001125 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.862
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.82
Order of pole (three term test) = 1.364e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1522 0.323
h = 0.001 0.003
y[1] (numeric) = 0.0661310677455 0.0111806576444
y[1] (closed_form) = 0.0661309470479 0.0111813928359
absolute error = 7.450e-07
relative error = 0.001111 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.861
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.634
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1532 0.326
h = 0.0001 0.004
y[1] (numeric) = 0.0661387636217 0.0112902813815
y[1] (closed_form) = 0.0661385575347 0.0112910153199
absolute error = 7.623e-07
relative error = 0.001136 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.861
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.885
Order of pole (three term test) = 4.306e-28 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=170.2MB, alloc=44.3MB, time=2.16
x[1] = 2.1533 0.33
h = 0.003 0.006
y[1] (numeric) = 0.0661070702355 0.0114257433961
y[1] (closed_form) = 0.0661068278696 0.0114264143174
absolute error = 7.134e-07
relative error = 0.001063 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.861
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.473
Order of pole (three term test) = 5.412e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1563 0.336
h = 0.0001 0.005
y[1] (numeric) = 0.0661546053611 0.0116539511304
y[1] (closed_form) = 0.066154213858 0.0116549044042
absolute error = 1.031e-06
relative error = 0.001534 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.858
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.876
Order of pole (three term test) = 8.786e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1564 0.341
h = 0.0001 0.003
y[1] (numeric) = 0.0661124951018 0.0118230867579
y[1] (closed_form) = 0.0661122317883 0.0118238764609
absolute error = 8.324e-07
relative error = 0.001239 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.859
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.316
Order of pole (three term test) = 2.518e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1565 0.344
h = 0.001 0.001
y[1] (numeric) = 0.06608826234 0.0119247124356
y[1] (closed_form) = 0.0660880760384 0.0119255279494
absolute error = 8.365e-07
relative error = 0.001246 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.859
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.818
Order of pole (three term test) = 1.188e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1575 0.345
h = 0.001 0.003
y[1] (numeric) = 0.066112566435 0.0119675129119
y[1] (closed_form) = 0.0661124221073 0.0119683282545
absolute error = 8.280e-07
relative error = 0.001232 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.858
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.627
Order of pole (three term test) = 1.154e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1585 0.348
h = 0.0001 0.004
y[1] (numeric) = 0.0661183695561 0.0120775420634
y[1] (closed_form) = 0.0661181395925 0.0120783541615
absolute error = 8.440e-07
relative error = 0.001256 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.857
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.881
Order of pole (three term test) = 5.933e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1586 0.352
h = 0.003 0.006
y[1] (numeric) = 0.0660842352038 0.0122127838641
y[1] (closed_form) = 0.066083970312 0.0122135318988
absolute error = 7.936e-07
relative error = 0.001181 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.857
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.467
Order of pole (three term test) = 5.274e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1616 0.358
h = 0.0001 0.005
y[1] (numeric) = 0.0661279051786 0.0124423765556
y[1] (closed_form) = 0.066127484102 0.012443404366
absolute error = 1.111e-06
relative error = 0.001651 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.855
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.874
Order of pole (three term test) = 8.563e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1617 0.363
h = 0.0001 0.003
y[1] (numeric) = 0.066082739591 0.0126111833007
y[1] (closed_form) = 0.0660824509179 0.012612050015
absolute error = 9.135e-07
relative error = 0.001358 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.855
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.314
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1618 0.366
h = 0.001 0.001
y[1] (numeric) = 0.066056674652 0.0127126280638
y[1] (closed_form) = 0.0660564626288 0.0127135224634
absolute error = 9.192e-07
relative error = 0.001366 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.856
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.817
Order of pole (three term test) = 1.159e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1628 0.367
h = 0.001 0.003
y[1] (numeric) = 0.0660802891013 0.0127559545315
y[1] (closed_form) = 0.066080119186 0.0127568497375
absolute error = 9.112e-07
relative error = 0.001354 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.855
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.619
Order of pole (three term test) = 1.798e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1638 0.37
h = 0.0001 0.004
y[1] (numeric) = 0.0660841840327 0.0128663462977
y[1] (closed_form) = 0.0660839282923 0.012867236253
absolute error = 9.260e-07
relative error = 0.001375 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.854
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.876
Order of pole (three term test) = 1.309e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1639 0.374
h = 0.003 0.006
y[1] (numeric) = 0.066047606176 0.0130013103245
y[1] (closed_form) = 0.0660473168938 0.0130021352053
absolute error = 8.741e-07
relative error = 0.001299 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.854
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.462
Order of pole (three term test) = 9.706e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1669 0.38
h = 0.0001 0.005
y[1] (numeric) = 0.0660873666994 0.0132322022428
y[1] (closed_form) = 0.0660869142331 0.0132333041074
absolute error = 1.191e-06
relative error = 0.001767 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.852
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.872
Order of pole (three term test) = 8.354e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.167 0.385
h = 0.0001 0.003
y[1] (numeric) = 0.0660391440683 0.0134006078314
y[1] (closed_form) = 0.0660388281628 0.0134015512066
absolute error = 9.949e-07
relative error = 0.001476 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.852
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.312
Order of pole (three term test) = 2.678e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1671 0.388
h = 0.001 0.001
y[1] (numeric) = 0.0660112455925 0.0135018284084
y[1] (closed_form) = 0.0660110059191 0.0135028013401
absolute error = 1.002e-06
relative error = 0.001487 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.852
Order of pole (given) = 3 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) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1681 0.389
h = 0.001 0.003
y[1] (numeric) = 0.0660341560398 0.0135456663815
y[1] (closed_form) = 0.0660339585805 0.0135466411046
absolute error = 9.945e-07
relative error = 0.001475 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.852
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.612
Order of pole (three term test) = 1.569e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1691 0.392
h = 0.0001 0.004
y[1] (numeric) = 0.0660361285366 0.0136563773503
y[1] (closed_form) = 0.0660358451205 0.0136573448034
absolute error = 1.008e-06
relative error = 0.001495 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.851
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.873
Order of pole (three term test) = 1.199e-27 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=216.2MB, alloc=44.3MB, time=2.74
x[1] = 2.1692 0.396
h = 0.003 0.006
y[1] (numeric) = 0.0659971063066 0.0137910057525
y[1] (closed_form) = 0.0659967907698 0.013791907157
absolute error = 9.550e-07
relative error = 0.001416 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.851
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.457
Order of pole (three term test) = 7.246e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1722 0.402
h = 0.0001 0.005
y[1] (numeric) = 0.0660329154131 0.0140231095563
y[1] (closed_form) = 0.0660324297491 0.0140242849381
absolute error = 1.272e-06
relative error = 0.001884 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.849
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.869
Order of pole (three term test) = 3.284e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1723 0.407
h = 0.0001 0.003
y[1] (numeric) = 0.0659816361274 0.0141910413985
y[1] (closed_form) = 0.0659812911201 0.0141920610285
absolute error = 1.076e-06
relative error = 0.001595 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.849
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.31
Order of pole (three term test) = 1.498e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1724 0.41
h = 0.001 0.001
y[1] (numeric) = 0.0659519040133 0.0142919943208
y[1] (closed_form) = 0.0659516347641 0.0142930453728
absolute error = 1.085e-06
relative error = 0.001608 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.849
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.814
Order of pole (three term test) = 1.105e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1734 0.411
h = 0.0001 0.004
y[1] (numeric) = 0.0659740964735 0.0143363288416
y[1] (closed_form) = 0.065973869516 0.0143373826766
absolute error = 1.078e-06
relative error = 0.001597 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.849
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.89
Order of pole (three term test) = 3.831e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1735 0.415
h = 0.003 0.006
y[1] (numeric) = 0.0659330763948 0.014470635829
y[1] (closed_form) = 0.0659327179228 0.0144715797405
absolute error = 1.010e-06
relative error = 0.001496 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.849
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.453
Order of pole (three term test) = 9.310e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1765 0.421
h = 0.0001 0.005
y[1] (numeric) = 0.0659654394891 0.0147036639628
y[1] (closed_form) = 0.0659649050034 0.0147048790114
absolute error = 1.327e-06
relative error = 0.001964 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.847
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.868
Order of pole (three term test) = 1.202e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1766 0.426
h = 0.0001 0.003
y[1] (numeric) = 0.0659115378939 0.0148710933397
y[1] (closed_form) = 0.0659111475033 0.0148721551441
absolute error = 1.131e-06
relative error = 0.001674 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.847
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.309
Order of pole (three term test) = 1.201e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1767 0.429
h = 0.001 0.001
y[1] (numeric) = 0.0658802322292 0.0149717591266
y[1] (closed_form) = 0.0658799171216 0.0149728539461
absolute error = 1.139e-06
relative error = 0.001686 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.847
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.813
Order of pole (three term test) = 1.086e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1777 0.43
h = 0.001 0.003
y[1] (numeric) = 0.0659017901036 0.0150164999575
y[1] (closed_form) = 0.0659015173197 0.0150175984187
absolute error = 1.132e-06
relative error = 0.001675 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.846
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.601
Order of pole (three term test) = 1.623e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1787 0.433
h = 0.0001 0.004
y[1] (numeric) = 0.0659001491126 0.0151276641679
y[1] (closed_form) = 0.065899790308 0.0151287515743
absolute error = 1.145e-06
relative error = 0.001694 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.846
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.866
Order of pole (three term test) = 3.837e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1788 0.437
h = 0.003 0.006
y[1] (numeric) = 0.0658565875843 0.0152614842614
y[1] (closed_form) = 0.0658561994018 0.0152625039266
absolute error = 1.091e-06
relative error = 0.001614 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.846
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.448
Order of pole (three term test) = 1.079e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1818 0.443
h = 0.0001 0.005
y[1] (numeric) = 0.0658849286969 0.0154955572974
y[1] (closed_form) = 0.065884357685 0.0154968446981
absolute error = 1.408e-06
relative error = 0.002081 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.844
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.866
Order of pole (three term test) = 7.155e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1819 0.448
h = 0.0001 0.003
y[1] (numeric) = 0.0658279777068 0.0156623773293
y[1] (closed_form) = 0.0658275547577 0.0156635144615
absolute error = 1.213e-06
relative error = 0.001793 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.844
Order of pole (given) = 3 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) = 2.262e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.182 0.451
h = 0.001 0.001
y[1] (numeric) = 0.0657948421254 0.0157626942357
y[1] (closed_form) = 0.065794493881 0.0157638662321
absolute error = 1.223e-06
relative error = 0.001807 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.845
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.811
Order of pole (three term test) = 1.240e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.183 0.452
h = 0.001 0.003
y[1] (numeric) = 0.0658156572289 0.0158079024096
y[1] (closed_form) = 0.065815351332 0.0158090790488
absolute error = 1.216e-06
relative error = 0.001796 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.844
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.595
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.184 0.455
h = 0.0001 0.004
y[1] (numeric) = 0.0658120603905 0.0159192584841
y[1] (closed_form) = 0.0658116685105 0.015920422024
absolute error = 1.228e-06
relative error = 0.001813 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.843
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.863
Order of pole (three term test) = 8.398e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1841 0.459
h = 0.003 0.006
y[1] (numeric) = 0.0657660620632 0.0160525764264
y[1] (closed_form) = 0.0657656423183 0.0160536713637
absolute error = 1.173e-06
relative error = 0.001732 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.843
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.444
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=262.2MB, alloc=44.3MB, time=3.32
x[1] = 2.1871 0.465
h = 0.0001 0.005
y[1] (numeric) = 0.0657903462826 0.0162876028679
y[1] (closed_form) = 0.065789736971 0.0162889619286
absolute error = 1.489e-06
relative error = 0.002198 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.841
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.864
Order of pole (three term test) = 1.718e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1872 0.47
h = 0.0001 0.003
y[1] (numeric) = 0.0657303524068 0.0164537404923
y[1] (closed_form) = 0.0657298950506 0.0164549523859
absolute error = 1.295e-06
relative error = 0.001912 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.842
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.306
Order of pole (three term test) = 1.102e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1873 0.473
h = 0.001 0.001
y[1] (numeric) = 0.0656953904682 0.0165536647425
y[1] (closed_form) = 0.0656950071823 0.0165549133382
absolute error = 1.306e-06
relative error = 0.001928 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.842
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.81
Order of pole (three term test) = 2.083e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1883 0.474
h = 0.001 0.003
y[1] (numeric) = 0.0657154499801 0.0165993240218
y[1] (closed_form) = 0.0657151090364 0.0166005782649
absolute error = 1.300e-06
relative error = 0.001918 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.841
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.589
Order of pole (three term test) = 2.891e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1893 0.477
h = 0.0001 0.004
y[1] (numeric) = 0.0657098878831 0.0167108265771
y[1] (closed_form) = 0.065709461054 0.0167120656714
absolute error = 1.311e-06
relative error = 0.001933 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.84
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.859
Order of pole (three term test) = 1.562e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1894 0.481
h = 0.003 0.006
y[1] (numeric) = 0.0656614584756 0.0168435839625
y[1] (closed_form) = 0.0656610053244 0.0168447536346
absolute error = 1.254e-06
relative error = 0.00185 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.841
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.439
Order of pole (three term test) = 6.550e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1924 0.487
h = 0.0001 0.005
y[1] (numeric) = 0.0656816534656 0.017079471008
y[1] (closed_form) = 0.0656810040962 0.0170809009832
absolute error = 1.571e-06
relative error = 0.002314 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.839
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.862
Order of pole (three term test) = 1.065e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1925 0.492
h = 0.0001 0.003
y[1] (numeric) = 0.0656186253768 0.0172448531331
y[1] (closed_form) = 0.0656181317759 0.0172461391657
absolute error = 1.378e-06
relative error = 0.00203 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.839
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.304
Order of pole (three term test) = 1.129e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1926 0.495
h = 0.001 0.001
y[1] (numeric) = 0.0655818419356 0.0173443409253
y[1] (closed_form) = 0.0655814217148 0.0173456654845
absolute error = 1.390e-06
relative error = 0.002048 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.839
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.809
Order of pole (three term test) = 9.193e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1936 0.496
h = 0.001 0.003
y[1] (numeric) = 0.0656011334735 0.0173904346478
y[1] (closed_form) = 0.06560075556 0.017391765862
absolute error = 1.384e-06
relative error = 0.002039 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.839
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.583
Order of pole (three term test) = 1.446e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1946 0.499
h = 0.0001 0.004
y[1] (numeric) = 0.0655935980106 0.0175020378897
y[1] (closed_form) = 0.0655931343699 0.0175033519025
absolute error = 1.393e-06
relative error = 0.002053 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.838
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.856
Order of pole (three term test) = 1.805e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1947 0.503
h = 0.003 0.006
y[1] (numeric) = 0.0655427449732 0.0176341763088
y[1] (closed_form) = 0.0655422565817 0.0176354201228
absolute error = 1.336e-06
relative error = 0.001969 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.838
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.435
Order of pole (three term test) = 6.427e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1977 0.509
h = 0.0001 0.005
y[1] (numeric) = 0.0655588210273 0.0178708299384
y[1] (closed_form) = 0.0655581298596 0.0178723300289
absolute error = 1.652e-06
relative error = 0.002431 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.836
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.86
Order of pole (three term test) = 1.686e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1978 0.514
h = 0.0001 0.003
y[1] (numeric) = 0.065492769571 0.0180353835186
y[1] (closed_form) = 0.0654922379005 0.0180367430122
absolute error = 1.460e-06
relative error = 0.002149 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.837
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.303
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1979 0.517
h = 0.001 0.001
y[1] (numeric) = 0.0654541707817 0.0181343910703
y[1] (closed_form) = 0.0654537117457 0.0181357908998
absolute error = 1.473e-06
relative error = 0.002169 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.837
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.808
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1989 0.518
h = 0.0001 0.004
y[1] (numeric) = 0.065472682418 0.0181809021637
y[1] (closed_form) = 0.0654722656247 0.0181823096574
absolute error = 1.468e-06
relative error = 0.00216 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.836
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.85
Order of pole (three term test) = 8.695e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.199 0.522
h = 0.003 0.006
y[1] (numeric) = 0.0654198551522 0.0183124872862
y[1] (closed_form) = 0.0654193186502 0.0183137690305
absolute error = 1.389e-06
relative error = 0.002045 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.837
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.432
Order of pole (three term test) = 4.484e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.202 0.528
h = 0.0001 0.005
y[1] (numeric) = 0.065432356435 0.018549675116
y[1] (closed_form) = 0.065431611644 0.0185512094314
absolute error = 1.706e-06
relative error = 0.002508 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.835
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.859
Order of pole (three term test) = 2.089e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2021 0.533
h = 0.0001 0.003
y[1] (numeric) = 0.0653637239633 0.0187134213142
y[1] (closed_form) = 0.0653631417663 0.0187148180503
absolute error = 1.513e-06
relative error = 0.002226 %
Correct digits = 5
memory used=308.2MB, alloc=44.3MB, time=3.89
Radius of convergence (given) for eq 1 = 3.835
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.302
Order of pole (three term test) = 2.159e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2022 0.536
h = 0.001 0.001
y[1] (numeric) = 0.0653235749358 0.0188119589794
y[1] (closed_form) = 0.065323064666 0.0188133975853
absolute error = 1.526e-06
relative error = 0.002245 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.835
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.807
Order of pole (three term test) = 5.940e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2032 0.537
h = 0.001 0.003
y[1] (numeric) = 0.0653414013787 0.0188588058834
y[1] (closed_form) = 0.0653409332601 0.0188602530214
absolute error = 1.521e-06
relative error = 0.002236 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.835
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.574
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2042 0.54
h = 0.0001 0.004
y[1] (numeric) = 0.0653301770132 0.018970449703
y[1] (closed_form) = 0.0653296236482 0.0189718758228
absolute error = 1.530e-06
relative error = 0.002249 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.834
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.851
Order of pole (three term test) = 4.950e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2043 0.544
h = 0.003 0.006
y[1] (numeric) = 0.0652748489592 0.0191012525734
y[1] (closed_form) = 0.065274273846 0.0191026071871
absolute error = 1.472e-06
relative error = 0.002164 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.834
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.429
Order of pole (three term test) = 9.855e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2073 0.55
h = 0.0001 0.005
y[1] (numeric) = 0.0652831843533 0.0193390288229
y[1] (closed_form) = 0.0652823945896 0.0193406316064
absolute error = 1.787e-06
relative error = 0.002624 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.832
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.857
Order of pole (three term test) = 1.014e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2074 0.555
h = 0.0001 0.003
y[1] (numeric) = 0.0652115553577 0.019501811134
y[1] (closed_form) = 0.0652109317467 0.0195032799008
absolute error = 1.596e-06
relative error = 0.002344 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.833
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.301
Order of pole (three term test) = 2.060e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2075 0.558
h = 0.001 0.001
y[1] (numeric) = 0.0651696064243 0.0195997874087
y[1] (closed_form) = 0.0651690538928 0.01960129982
absolute error = 1.610e-06
relative error = 0.002366 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.833
Order of pole (given) = 3 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) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2085 0.559
h = 0.001 0.003
y[1] (numeric) = 0.0651866322496 0.0196470187462
y[1] (closed_form) = 0.065186121749 0.0196485406989
absolute error = 1.605e-06
relative error = 0.002358 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.832
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.57
Order of pole (three term test) = 4.056e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2095 0.562
h = 0.0001 0.004
y[1] (numeric) = 0.0651734192462 0.0197586303365
y[1] (closed_form) = 0.0651728238317 0.0197601292222
absolute error = 1.613e-06
relative error = 0.002368 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.832
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.849
Order of pole (three term test) = 1.033e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2096 0.566
h = 0.003 0.006
y[1] (numeric) = 0.0651156991691 0.0198886478307
y[1] (closed_form) = 0.0651150836505 0.0198900745631
absolute error = 1.554e-06
relative error = 0.002282 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.832
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.425
Order of pole (three term test) = 1.788e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2126 0.572
h = 0.0001 0.005
y[1] (numeric) = 0.0651198467756 0.0201269155254
y[1] (closed_form) = 0.0651190103599 0.0201285858285
absolute error = 1.868e-06
relative error = 0.002741 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.83
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.856
Order of pole (three term test) = 3.158e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2127 0.577
h = 0.0001 0.003
y[1] (numeric) = 0.0650452383311 0.0202886614894
y[1] (closed_form) = 0.0650445715298 0.0202902014513
absolute error = 1.678e-06
relative error = 0.002463 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.831
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.299
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2128 0.58
h = 0.001 0.001
y[1] (numeric) = 0.0650014993764 0.0203860329166
y[1] (closed_form) = 0.0650009027528 0.0203876182768
absolute error = 1.694e-06
relative error = 0.002487 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.831
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.805
Order of pole (three term test) = 9.588e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2138 0.581
h = 0.001 0.003
y[1] (numeric) = 0.0650177140476 0.0204336305311
y[1] (closed_form) = 0.0650171593046 0.0204352264406
absolute error = 1.690e-06
relative error = 0.002479 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.831
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.565
Order of pole (three term test) = 1.331e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2148 0.584
h = 0.0001 0.004
y[1] (numeric) = 0.065002509497 0.0205451629543
y[1] (closed_form) = 0.0650018702338 0.0205467337534
absolute error = 1.696e-06
relative error = 0.002488 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.83
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.846
Order of pole (three term test) = 3.541e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2149 0.588
h = 0.003 0.006
y[1] (numeric) = 0.0649424115608 0.0206743372456
y[1] (closed_form) = 0.0649417538602 0.0206758352913
absolute error = 1.636e-06
relative error = 0.002401 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.83
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.422
Order of pole (three term test) = 6.408e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2179 0.594
h = 0.0001 0.005
y[1] (numeric) = 0.0649423522891 0.0209129985486
y[1] (closed_form) = 0.0649414675672 0.0209147353718
absolute error = 1.949e-06
relative error = 0.002857 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.828
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.854
Order of pole (three term test) = 3.111e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.218 0.599
h = 0.0001 0.003
y[1] (numeric) = 0.0648647836453 0.0210736360507
y[1] (closed_form) = 0.0648640718982 0.0210752463181
absolute error = 1.761e-06
relative error = 0.002581 %
Correct digits = 5
memory used=354.1MB, alloc=44.3MB, time=4.45
Radius of convergence (given) for eq 1 = 3.829
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.298
Order of pole (three term test) = 1.414e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2181 0.602
h = 0.001 0.001
y[1] (numeric) = 0.0648192658565 0.0211703593713
y[1] (closed_form) = 0.0648186233316 0.0211720167678
absolute error = 1.778e-06
relative error = 0.002607 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.83
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.804
Order of pole (three term test) = 9.451e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2191 0.603
h = 0.001 0.003
y[1] (numeric) = 0.0648346593497 0.0212183047571
y[1] (closed_form) = 0.0648340585252 0.0212199737084
absolute error = 1.774e-06
relative error = 0.0026 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.829
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.561
Order of pole (three term test) = 1.338e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2201 0.606
h = 0.0001 0.004
y[1] (numeric) = 0.0648174617209 0.0213297108894
y[1] (closed_form) = 0.064816776831 0.0213313526942
absolute error = 1.779e-06
relative error = 0.002607 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.828
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.844
Order of pole (three term test) = 6.893e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2202 0.61
h = 0.003 0.006
y[1] (numeric) = 0.0647550018251 0.0214579844475
y[1] (closed_form) = 0.0647543001856 0.0214595529467
absolute error = 1.718e-06
relative error = 0.002519 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.829
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.419
Order of pole (three term test) = 5.897e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2232 0.616
h = 0.0001 0.005
y[1] (numeric) = 0.0647507194305 0.0216969407563
y[1] (closed_form) = 0.0647497847749 0.0216987430498
absolute error = 2.030e-06
relative error = 0.002973 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.827
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.853
Order of pole (three term test) = 9.704e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2233 0.621
h = 0.0001 0.003
y[1] (numeric) = 0.0646702120046 0.0218563981053
y[1] (closed_form) = 0.0646694535789 0.0218580777348
absolute error = 1.843e-06
relative error = 0.0027 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.827
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.297
Order of pole (three term test) = 1.085e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2234 0.624
h = 0.001 0.001
y[1] (numeric) = 0.0646229278672 0.0219524303047
y[1] (closed_form) = 0.0646222376554 0.0219541587692
absolute error = 1.861e-06
relative error = 0.002727 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.828
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.803
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2244 0.625
h = 0.0001 0.004
y[1] (numeric) = 0.0646374906852 0.022000704624
y[1] (closed_form) = 0.0646368419634 0.0220024456455
absolute error = 1.858e-06
relative error = 0.002721 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.827
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.83
Order of pole (three term test) = 8.248e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2245 0.629
h = 0.003 0.006
y[1] (numeric) = 0.0645731137019 0.0221281954313
y[1] (closed_form) = 0.0645723594037 0.0221297965187
absolute error = 1.770e-06
relative error = 0.002593 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.828
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.417
Order of pole (three term test) = 1.252e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2275 0.635
h = 0.0001 0.005
y[1] (numeric) = 0.06456518347 0.0223672756867
y[1] (closed_form) = 0.0645641911668 0.0223691060607
absolute error = 2.082e-06
relative error = 0.003047 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.826
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.852
Order of pole (three term test) = 3.042e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2276 0.64
h = 0.0001 0.003
y[1] (numeric) = 0.0644821804467 0.0225256255518
y[1] (closed_form) = 0.0644813670398 0.0225273367313
absolute error = 1.895e-06
relative error = 0.002774 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.826
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.297
Order of pole (three term test) = 1.977e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2277 0.643
h = 0.001 0.001
y[1] (numeric) = 0.0644333958052 0.0226210078193
y[1] (closed_form) = 0.0644326496825 0.0226227692678
absolute error = 1.913e-06
relative error = 0.002801 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.827
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.803
Order of pole (three term test) = 9.245e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2287 0.644
h = 0.001 0.003
y[1] (numeric) = 0.0644472328046 0.0226695399095
y[1] (closed_form) = 0.0644465279551 0.0226713147712
absolute error = 1.910e-06
relative error = 0.002795 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.826
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.555
Order of pole (three term test) = 2.568e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2297 0.647
h = 0.0001 0.004
y[1] (numeric) = 0.064426330042 0.0227805614675
y[1] (closed_form) = 0.0644255421593 0.0227823054283
absolute error = 1.914e-06
relative error = 0.0028 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.825
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.84
Order of pole (three term test) = 7.317e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2298 0.651
h = 0.003 0.006
y[1] (numeric) = 0.0643595356523 0.0229069795175
y[1] (closed_form) = 0.0643587342164 0.0229086492965
absolute error = 1.852e-06
relative error = 0.002711 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.826
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.414
Order of pole (three term test) = 4.124e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2328 0.657
h = 0.0001 0.005
y[1] (numeric) = 0.064347360948 0.0231461694944
y[1] (closed_form) = 0.0643463157736 0.0231480632359
absolute error = 2.163e-06
relative error = 0.003163 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.824
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.851
Order of pole (three term test) = 1.503e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2329 0.662
h = 0.0001 0.003
y[1] (numeric) = 0.0642614655649 0.0233032075137
y[1] (closed_form) = 0.0642606023342 0.0233049861399
absolute error = 1.977e-06
relative error = 0.002892 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.825
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.296
Order of pole (three term test) = 1.063e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.233 0.665
h = 0.001 0.001
y[1] (numeric) = 0.0642109417456 0.0233978196153
y[1] (closed_form) = 0.0642101446949 0.0233996501644
absolute error = 1.997e-06
relative error = 0.002921 %
Correct digits = 5
memory used=400.0MB, alloc=44.3MB, time=5.04
Radius of convergence (given) for eq 1 = 3.825
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.802
Order of pole (three term test) = 9.185e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.234 0.666
h = 0.001 0.003
y[1] (numeric) = 0.0642239320749 0.0234466446667
y[1] (closed_form) = 0.0642231760314 0.0234484896213
absolute error = 1.994e-06
relative error = 0.002916 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.824
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.552
Order of pole (three term test) = 1.269e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.235 0.669
h = 0.0001 0.004
y[1] (numeric) = 0.0642010401086 0.0235574045693
y[1] (closed_form) = 0.0642002016604 0.0235592166211
absolute error = 1.997e-06
relative error = 0.00292 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.824
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.838
Order of pole (three term test) = 7.235e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2351 0.673
h = 0.003 0.006
y[1] (numeric) = 0.0641319394274 0.023682759755
y[1] (closed_form) = 0.0641310891641 0.0236844972147
absolute error = 1.934e-06
relative error = 0.002829 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.825
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.412
Order of pole (three term test) = 9.119e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2381 0.679
h = 0.0001 0.005
y[1] (numeric) = 0.0641155123241 0.0239219592493
y[1] (closed_form) = 0.0641144127379 0.0239239151701
absolute error = 2.244e-06
relative error = 0.003279 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.823
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.85
Order of pole (three term test) = 6.649e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2382 0.684
h = 0.0001 0.003
y[1] (numeric) = 0.0640267521235 0.0240776153961
y[1] (closed_form) = 0.064025837412 0.0240794603767
absolute error = 2.059e-06
relative error = 0.00301 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.823
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.295
Order of pole (three term test) = 9.562e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2383 0.687
h = 0.001 0.001
y[1] (numeric) = 0.0639745052832 0.0241714152888
y[1] (closed_form) = 0.063973655597 0.0241733138156
absolute error = 2.080e-06
relative error = 0.003041 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.824
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.802
Order of pole (three term test) = 1.809e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2393 0.688
h = 0.001 0.003
y[1] (numeric) = 0.0639866410226 0.0242205136212
y[1] (closed_form) = 0.063985832048 0.0242224275396
absolute error = 2.078e-06
relative error = 0.003037 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.823
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.549
Order of pole (three term test) = 1.256e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2403 0.691
h = 0.0001 0.004
y[1] (numeric) = 0.0639617637163 0.0243309645018
y[1] (closed_form) = 0.0639608730254 0.0243328435313
absolute error = 2.079e-06
relative error = 0.003039 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.823
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.837
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2404 0.695
h = 0.003 0.006
y[1] (numeric) = 0.0638903792529 0.0244552010385
y[1] (closed_form) = 0.0638894784996 0.0244570051165
absolute error = 2.016e-06
relative error = 0.002948 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.823
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.41
Order of pole (three term test) = 4.038e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2434 0.701
h = 0.0001 0.005
y[1] (numeric) = 0.0638696947759 0.0246943094718
y[1] (closed_form) = 0.0638685392707 0.0246963263371
absolute error = 2.324e-06
relative error = 0.003394 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.821
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.849
Order of pole (three term test) = 1.062e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2435 0.706
h = 0.0001 0.003
y[1] (numeric) = 0.0637780994092 0.0248485144409
y[1] (closed_form) = 0.0637771315899 0.0248504246331
absolute error = 2.141e-06
relative error = 0.003128 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.822
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.294
Order of pole (three term test) = 1.630e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2436 0.709
h = 0.001 0.001
y[1] (numeric) = 0.0637241469693 0.0249414605045
y[1] (closed_form) = 0.0637232429712 0.0249434258342
absolute error = 2.163e-06
relative error = 0.003161 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.823
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.801
Order of pole (three term test) = 9.651e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2446 0.71
h = 0.001 0.003
y[1] (numeric) = 0.0637354207712 0.0249908121784
y[1] (closed_form) = 0.0637345571595 0.0249927938781
absolute error = 2.162e-06
relative error = 0.003158 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.822
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.546
Order of pole (three term test) = 1.245e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2456 0.713
h = 0.0001 0.004
y[1] (numeric) = 0.063708563395 0.0251009067237
y[1] (closed_form) = 0.063707618815 0.0251028515663
absolute error = 2.162e-06
relative error = 0.003157 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.822
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.835
Order of pole (three term test) = 3.173e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2457 0.717
h = 0.003 0.006
y[1] (numeric) = 0.0636349193375 0.0252239694227
y[1] (closed_form) = 0.0636339664605 0.0252258390059
absolute error = 2.098e-06
relative error = 0.003066 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.822
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.408
Order of pole (three term test) = 5.659e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2487 0.723
h = 0.0001 0.005
y[1] (numeric) = 0.0636099754816 0.0254628859465
y[1] (closed_form) = 0.0636087625856 0.0254649624763
absolute error = 2.405e-06
relative error = 0.00351 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 3 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) = 4.128e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2488 0.728
h = 0.0001 0.003
y[1] (numeric) = 0.0635155766869 0.0256155712301
y[1] (closed_form) = 0.0635145541646 0.0256175454416
absolute error = 2.223e-06
relative error = 0.003246 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.821
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.294
Order of pole (three term test) = 9.392e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2489 0.731
h = 0.001 0.001
y[1] (numeric) = 0.0634599373203 0.0257076223131
y[1] (closed_form) = 0.0634589773665 0.0257096532192
absolute error = 2.246e-06
relative error = 0.003281 %
Correct digits = 4
memory used=446.1MB, alloc=44.3MB, time=5.61
Radius of convergence (given) for eq 1 = 3.822
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.801
Order of pole (three term test) = 9.935e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2499 0.732
h = 0.0001 0.004
y[1] (numeric) = 0.0634703424187 0.0257572071492
y[1] (closed_form) = 0.063469422497 0.0257592553952
absolute error = 2.245e-06
relative error = 0.003278 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.821
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.81
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.25 0.736
h = 0.003 0.006
y[1] (numeric) = 0.0633948715176 0.0258792658745
y[1] (closed_form) = 0.0633938621927 0.0258811620451
absolute error = 2.148e-06
relative error = 0.003137 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.822
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.407
Order of pole (three term test) = 5.632e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.253 0.742
h = 0.0001 0.005
y[1] (numeric) = 0.0633662659253 0.0261178856092
y[1] (closed_form) = 0.0633649922541 0.0261199835092
absolute error = 2.454e-06
relative error = 0.003581 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 3 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) = 2.906e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2531 0.747
h = 0.0001 0.003
y[1] (numeric) = 0.063269500219 0.0262691757618
y[1] (closed_form) = 0.0632684190806 0.0262711751891
absolute error = 2.273e-06
relative error = 0.003318 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.821
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.293
Order of pole (three term test) = 1.322e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2532 0.75
h = 0.001 0.001
y[1] (numeric) = 0.0632124360174 0.0263604041443
y[1] (closed_form) = 0.0632114163136 0.0263624615623
absolute error = 2.296e-06
relative error = 0.003353 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.821
Order of pole (given) = 3 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) = 3.540e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2542 0.751
h = 0.001 0.003
y[1] (numeric) = 0.0632220859516 0.0264101629051
y[1] (closed_form) = 0.0632211059402 0.0264122384855
absolute error = 2.295e-06
relative error = 0.00335 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.543
Order of pole (three term test) = 4.916e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2552 0.754
h = 0.0001 0.004
y[1] (numeric) = 0.0631915685391 0.0265194454856
y[1] (closed_form) = 0.0631905091308 0.0265214806125
absolute error = 2.294e-06
relative error = 0.003348 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.833
Order of pole (three term test) = 9.914e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2553 0.758
h = 0.0001 0.004
y[1] (numeric) = 0.0631138054553 0.0266401531936
y[1] (closed_form) = 0.0631127410646 0.026642112648
absolute error = 2.230e-06
relative error = 0.003255 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.821
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.821
Order of pole (three term test) = 1.111e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2554 0.762
h = 0.003 0.006
y[1] (numeric) = 0.0630357071959 0.0267604783043
y[1] (closed_form) = 0.0630346428051 0.0267624377587
absolute error = 2.230e-06
relative error = 0.003256 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.821
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.407
Order of pole (three term test) = 1.193e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2584 0.768
h = 0.0001 0.005
y[1] (numeric) = 0.0630021294106 0.0269984846449
y[1] (closed_form) = 0.0630007951192 0.0270006384392
absolute error = 2.534e-06
relative error = 0.003696 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 3 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) = 1.298e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2585 0.773
h = 0.0001 0.003
y[1] (numeric) = 0.062902218604 0.0271477388545
y[1] (closed_form) = 0.0629010795353 0.0271497995553
absolute error = 2.355e-06
relative error = 0.003437 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.821
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.293
Order of pole (three term test) = 9.342e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2586 0.776
h = 0.001 0.001
y[1] (numeric) = 0.0628432601675 0.0272377650501
y[1] (closed_form) = 0.0628421809043 0.0272398854332
absolute error = 2.379e-06
relative error = 0.003474 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.821
Order of pole (given) = 3 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) = 1.250e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2596 0.777
h = 0.001 0.003
y[1] (numeric) = 0.0628518713489 0.0272877176568
y[1] (closed_form) = 0.0628508312615 0.0272898573003
absolute error = 2.379e-06
relative error = 0.003472 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.542
Order of pole (three term test) = 1.228e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2606 0.78
h = 0.0001 0.004
y[1] (numeric) = 0.0628190794012 0.0273963475153
y[1] (closed_form) = 0.0628179610657 0.0273984445098
absolute error = 2.377e-06
relative error = 0.003468 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.833
Order of pole (three term test) = 4.894e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2607 0.784
h = 0.003 0.006
y[1] (numeric) = 0.0627388122347 0.0275154127332
y[1] (closed_form) = 0.0627376910223 0.0275174339418
absolute error = 2.311e-06
relative error = 0.003374 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.821
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.405
Order of pole (three term test) = 4.825e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2637 0.79
h = 0.0001 0.005
y[1] (numeric) = 0.0627009922141 0.0277529210758
y[1] (closed_form) = 0.0626995963687 0.0277551303207
absolute error = 2.613e-06
relative error = 0.003811 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.847
Order of pole (three term test) = 1.633e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2638 0.795
h = 0.0001 0.003
y[1] (numeric) = 0.0625983899345 0.0279004553206
y[1] (closed_form) = 0.0625971916026 0.0279025760599
absolute error = 2.436e-06
relative error = 0.003554 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.293
Order of pole (three term test) = 9.293e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2639 0.798
h = 0.001 0.001
y[1] (numeric) = 0.0625378106252 0.0279894661464
y[1] (closed_form) = 0.062536670709 0.0279916480095
absolute error = 2.462e-06
relative error = 0.003593 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 3 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) = 1.244e-27 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=492.1MB, alloc=44.3MB, time=6.19
x[1] = 2.2649 0.799
h = 0.001 0.003
y[1] (numeric) = 0.0625455372495 0.0280395892164
y[1] (closed_form) = 0.0625444360682 0.0280417912758
absolute error = 2.462e-06
relative error = 0.003592 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.541
Order of pole (three term test) = 2.519e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2659 0.802
h = 0.0001 0.004
y[1] (numeric) = 0.0625108030109 0.0281476740269
y[1] (closed_form) = 0.0625096245619 0.028149831566
absolute error = 2.458e-06
relative error = 0.003586 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.833
Order of pole (three term test) = 3.255e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.266 0.806
h = 0.003 0.006
y[1] (numeric) = 0.0624283929703 0.0282653516129
y[1] (closed_form) = 0.0624272134397 0.0282674332703
absolute error = 2.393e-06
relative error = 0.003491 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.404
Order of pole (three term test) = 9.605e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.269 0.812
h = 0.0001 0.005
y[1] (numeric) = 0.062386340767 0.0285022612396
y[1] (closed_form) = 0.0623848820556 0.0285045244869
absolute error = 2.693e-06
relative error = 0.003926 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.818
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.847
Order of pole (three term test) = 2.931e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2691 0.817
h = 0.0001 0.003
y[1] (numeric) = 0.0622810868189 0.0286480110751
y[1] (closed_form) = 0.0622798277768 0.0286501904743
absolute error = 2.517e-06
relative error = 0.003671 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.292
Order of pole (three term test) = 9.254e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2692 0.82
h = 0.001 0.001
y[1] (numeric) = 0.0622189101511 0.0287359677771
y[1] (closed_form) = 0.0622177080916 0.0287382097007
absolute error = 2.544e-06
relative error = 0.003712 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 3 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) = 1.239e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2702 0.821
h = 0.001 0.003
y[1] (numeric) = 0.0622257478909 0.0287862404057
y[1] (closed_form) = 0.0622245840976 0.0287885034489
absolute error = 2.545e-06
relative error = 0.003712 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.54
Order of pole (three term test) = 1.241e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2712 0.824
h = 0.0001 0.004
y[1] (numeric) = 0.0621890836524 0.0288937339505
y[1] (closed_form) = 0.0621878436277 0.0288959506306
absolute error = 2.540e-06
relative error = 0.003704 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.832
Order of pole (three term test) = 1.889e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2713 0.828
h = 0.003 0.006
y[1] (numeric) = 0.0621045629931 0.029009972693
y[1] (closed_form) = 0.0621033236853 0.0290121134489
absolute error = 2.474e-06
relative error = 0.003609 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.404
Order of pole (three term test) = 3.920e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2743 0.834
h = 0.0001 0.005
y[1] (numeric) = 0.0620582916465 0.0292461831495
y[1] (closed_form) = 0.0620567688 0.0292484989126
absolute error = 2.772e-06
relative error = 0.00404 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.818
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.846
Order of pole (three term test) = 6.404e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2744 0.839
h = 0.0001 0.003
y[1] (numeric) = 0.061950427756 0.0293900852932
y[1] (closed_form) = 0.061949106597 0.0293923219304
absolute error = 2.598e-06
relative error = 0.003788 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.292
Order of pole (three term test) = 9.631e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2745 0.842
h = 0.001 0.001
y[1] (numeric) = 0.0618866783976 0.0294769498044
y[1] (closed_form) = 0.0618854127464 0.0294792503245
absolute error = 2.626e-06
relative error = 0.00383 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 3 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) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2755 0.843
h = 0.001 0.003
y[1] (numeric) = 0.0618926235439 0.0295273509539
y[1] (closed_form) = 0.0618913956627 0.029529673503
absolute error = 2.627e-06
relative error = 0.003831 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.539
Order of pole (three term test) = 1.307e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2765 0.846
h = 0.0001 0.004
y[1] (numeric) = 0.0618540429691 0.029634207369
y[1] (closed_form) = 0.0618527399476 0.0296364817428
absolute error = 2.621e-06
relative error = 0.003822 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.818
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.831
Order of pole (three term test) = 6.925e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2766 0.85
h = 0.003 0.006
y[1] (numeric) = 0.0617674454704 0.0297489570023
y[1] (closed_form) = 0.0617661449658 0.0297511554624
absolute error = 2.554e-06
relative error = 0.003726 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 3 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) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2796 0.856
h = 0.0001 0.005
y[1] (numeric) = 0.0617169709979 0.0299843682042
y[1] (closed_form) = 0.0617153827916 0.0299867349594
absolute error = 2.850e-06
relative error = 0.004154 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.818
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.846
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2797 0.861
h = 0.0001 0.003
y[1] (numeric) = 0.0616065407716 0.0301263606042
y[1] (closed_form) = 0.0616051561308 0.0301286530155
absolute error = 2.678e-06
relative error = 0.003905 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.292
Order of pole (three term test) = 9.337e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2798 0.864
h = 0.001 0.001
y[1] (numeric) = 0.0615412445202 0.0302120955855
y[1] (closed_form) = 0.0615399138723 0.0302144531946
absolute error = 2.707e-06
relative error = 0.003949 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.799
Order of pole (three term test) = 1.743e-28 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=538.1MB, alloc=44.3MB, time=6.76
x[1] = 2.2808 0.865
h = 0.0001 0.004
y[1] (numeric) = 0.0615462939869 0.0302626041072
y[1] (closed_form) = 0.0615450005859 0.0302649846399
absolute error = 2.709e-06
relative error = 0.00395 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.818
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.8
Order of pole (three term test) = 7.565e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2809 0.869
h = 0.003 0.006
y[1] (numeric) = 0.0614580265882 0.0303760961359
y[1] (closed_form) = 0.0614566662009 0.0303783130041
absolute error = 2.601e-06
relative error = 0.003794 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 3 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) = 7.824e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2839 0.875
h = 0.0001 0.005
y[1] (numeric) = 0.0614039604297 0.0306106898291
y[1] (closed_form) = 0.0614023089987 0.0306130690699
absolute error = 2.896e-06
relative error = 0.004221 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.818
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.846
Order of pole (three term test) = 6.395e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.284 0.88
h = 0.0001 0.003
y[1] (numeric) = 0.0612913812395 0.0307509598555
y[1] (closed_form) = 0.0612899348192 0.0307532689328
absolute error = 2.725e-06
relative error = 0.003973 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.292
Order of pole (three term test) = 9.216e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2841 0.883
h = 0.001 0.001
y[1] (numeric) = 0.0612247890215 0.030835675273
y[1] (closed_form) = 0.061223395244 0.0308380506251
absolute error = 2.754e-06
relative error = 0.004018 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.799
Order of pole (three term test) = 9.400e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2851 0.884
h = 0.001 0.003
y[1] (numeric) = 0.0612290645898 0.0308862485055
y[1] (closed_form) = 0.0612277075775 0.0308886475322
absolute error = 2.756e-06
relative error = 0.004019 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.539
Order of pole (three term test) = 4.851e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2861 0.887
h = 0.0001 0.004
y[1] (numeric) = 0.0611869680335 0.0309917763367
y[1] (closed_form) = 0.0611855380734 0.0309941239178
absolute error = 2.749e-06
relative error = 0.004008 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.818
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.831
Order of pole (three term test) = 9.287e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2862 0.891
h = 0.003 0.006
y[1] (numeric) = 0.0610966201087 0.0311036010445
y[1] (closed_form) = 0.0610951960107 0.0311058728953
absolute error = 2.681e-06
relative error = 0.003911 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 3 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) = 8.742e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2892 0.897
h = 0.0001 0.005
y[1] (numeric) = 0.0610383896839 0.0313372108698
y[1] (closed_form) = 0.0610366707548 0.0313396381609
absolute error = 2.974e-06
relative error = 0.004335 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.818
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.846
Order of pole (three term test) = 9.040e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2893 0.902
h = 0.0001 0.003
y[1] (numeric) = 0.0609233308529 0.0314754597607
y[1] (closed_form) = 0.0609218185462 0.0314778217669
absolute error = 2.805e-06
relative error = 0.00409 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.292
Order of pole (three term test) = 9.260e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2894 0.905
h = 0.001 0.001
y[1] (numeric) = 0.060855243084 0.0315589785818
y[1] (closed_form) = 0.060853781835 0.031561408092
absolute error = 2.835e-06
relative error = 0.004136 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.799
Order of pole (three term test) = 9.112e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2904 0.906
h = 0.001 0.003
y[1] (numeric) = 0.0608586191551 0.0316096195947
y[1] (closed_form) = 0.0608571940998 0.031612073644
absolute error = 2.838e-06
relative error = 0.004138 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.539
Order of pole (three term test) = 4.851e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2914 0.909
h = 0.0001 0.004
y[1] (numeric) = 0.0608146533378 0.0317143816943
y[1] (closed_form) = 0.0608131565757 0.0317167825841
absolute error = 2.829e-06
relative error = 0.004125 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.818
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.831
Order of pole (three term test) = 6.924e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2915 0.913
h = 0.003 0.006
y[1] (numeric) = 0.060722333871 0.0318245796567
y[1] (closed_form) = 0.060720844764 0.0318269049792
absolute error = 2.761e-06
relative error = 0.004028 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 3 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) = 5.531e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2945 0.919
h = 0.0001 0.005
y[1] (numeric) = 0.0606599636205 0.0320571072049
y[1] (closed_form) = 0.0606581761021 0.0320595809264
absolute error = 3.052e-06
relative error = 0.004448 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.818
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.846
Order of pole (three term test) = 4.046e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2946 0.924
h = 0.0001 0.003
y[1] (numeric) = 0.0605424738652 0.0321932768116
y[1] (closed_form) = 0.0605408944356 0.0321956901719
absolute error = 2.884e-06
relative error = 0.004206 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.292
Order of pole (three term test) = 9.222e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2947 0.927
h = 0.001 0.001
y[1] (numeric) = 0.060472919415 0.0322755640103
y[1] (closed_form) = 0.0604713894225 0.0322780460562
absolute error = 2.916e-06
relative error = 0.004254 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 3 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) = 8.910e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2957 0.928
h = 0.001 0.003
y[1] (numeric) = 0.0604753947039 0.0323262514675
y[1] (closed_form) = 0.0604739003081 0.0323287588997
absolute error = 2.919e-06
relative error = 0.004257 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.539
Order of pole (three term test) = 3.642e-28 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=584.1MB, alloc=44.3MB, time=7.34
x[1] = 2.2967 0.931
h = 0.0001 0.004
y[1] (numeric) = 0.0604295784461 0.0324302038055
y[1] (closed_form) = 0.0604280136345 0.0324326564018
absolute error = 2.909e-06
relative error = 0.004242 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.832
Order of pole (three term test) = 9.804e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2968 0.935
h = 0.003 0.006
y[1] (numeric) = 0.0603353267516 0.0325387289202
y[1] (closed_form) = 0.0603337713824 0.0325411061655
absolute error = 2.841e-06
relative error = 0.004144 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 3 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) = 1.751e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2998 0.941
h = 0.0001 0.005
y[1] (numeric) = 0.0602688440178 0.0327700765566
y[1] (closed_form) = 0.0602669868676 0.0327725950577
absolute error = 3.129e-06
relative error = 0.004561 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.818
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.846
Order of pole (three term test) = 4.053e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2999 0.946
h = 0.0001 0.003
y[1] (numeric) = 0.0601489737499 0.0329041102072
y[1] (closed_form) = 0.0601473260079 0.032906573311
absolute error = 2.963e-06
relative error = 0.004322 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.292
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3 0.949
h = 0.001 0.001
y[1] (numeric) = 0.0600779825078 0.0329851316336
y[1] (closed_form) = 0.0600763825485 0.032987664556
absolute error = 2.996e-06
relative error = 0.004371 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 3 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) = 8.755e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.301 0.95
h = 0.001 0.003
y[1] (numeric) = 0.0600795563618 0.0330358441743
y[1] (closed_form) = 0.0600779913778 0.0330384033117
absolute error = 3.000e-06
relative error = 0.004375 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.54
Order of pole (three term test) = 6.083e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.302 0.953
h = 0.0001 0.004
y[1] (numeric) = 0.0600319097766 0.0331389433057
y[1] (closed_form) = 0.0600302757164 0.0331414459703
absolute error = 2.989e-06
relative error = 0.004359 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.832
Order of pole (three term test) = 4.394e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3021 0.957
h = 0.003 0.006
y[1] (numeric) = 0.0599357665084 0.0332457506652
y[1] (closed_form) = 0.05993414367 0.0332481782477
absolute error = 2.920e-06
relative error = 0.00426 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.404
Order of pole (three term test) = 1.963e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3051 0.963
h = 0.0001 0.005
y[1] (numeric) = 0.0598652015056 0.0334758216318
y[1] (closed_form) = 0.0598632737309 0.033478383233
absolute error = 3.206e-06
relative error = 0.004674 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.818
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.847
Order of pole (three term test) = 1.285e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3052 0.968
h = 0.0001 0.003
y[1] (numeric) = 0.0597430027778 0.0336076641906
y[1] (closed_form) = 0.0597412855827 0.0336101753933
absolute error = 3.042e-06
relative error = 0.004438 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.293
Order of pole (three term test) = 9.268e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3053 0.971
h = 0.001 0.001
y[1] (numeric) = 0.0596706056209 0.0336873866065
y[1] (closed_form) = 0.0596689345218 0.0336899687106
absolute error = 3.076e-06
relative error = 0.004489 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 3 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) = 1.242e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3063 0.972
h = 0.0001 0.004
y[1] (numeric) = 0.0596712780205 0.0337381028674
y[1] (closed_form) = 0.0596696412512 0.0337407119962
absolute error = 3.080e-06
relative error = 0.004493 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.81
Order of pole (three term test) = 7.775e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3064 0.976
h = 0.003 0.006
y[1] (numeric) = 0.0595736216791 0.0338434700847
y[1] (closed_form) = 0.0595719372331 0.0338459091181
absolute error = 2.964e-06
relative error = 0.004326 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.405
Order of pole (three term test) = 1.186e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3094 0.982
h = 0.0001 0.005
y[1] (numeric) = 0.0594995859155 0.0340723173143
y[1] (closed_form) = 0.0594975940786 0.0340748840332
absolute error = 3.249e-06
relative error = 0.004738 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.819
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.847
Order of pole (three term test) = 1.556e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3095 0.987
h = 0.0001 0.003
y[1] (numeric) = 0.0593754527852 0.0342022040543
y[1] (closed_form) = 0.0593736723567 0.034204724713
absolute error = 3.086e-06
relative error = 0.004504 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.293
Order of pole (three term test) = 9.319e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3096 0.99
h = 0.001 0.001
y[1] (numeric) = 0.0593018869135 0.0342807662012
y[1] (closed_form) = 0.0593001510928 0.034283358632
absolute error = 3.120e-06
relative error = 0.004555 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.821
Order of pole (given) = 3 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) = 8.832e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3106 0.991
h = 0.001 0.003
y[1] (numeric) = 0.0593017841396 0.0343314578454
y[1] (closed_form) = 0.0593000820652 0.0343340779739
absolute error = 3.124e-06
relative error = 0.00456 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.542
Order of pole (three term test) = 1.228e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3116 0.994
h = 0.0001 0.004
y[1] (numeric) = 0.0592508009617 0.0344328347412
y[1] (closed_form) = 0.0592490324471 0.0344353954791
absolute error = 3.112e-06
relative error = 0.004541 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.833
Order of pole (three term test) = 9.537e-28 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=630.0MB, alloc=44.3MB, time=7.91
x[1] = 2.3117 0.998
h = 0.003 0.006
y[1] (numeric) = 0.0591512721895 0.0345363091904
y[1] (closed_form) = 0.0591495181761 0.0345387955066
absolute error = 3.043e-06
relative error = 0.004442 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.821
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.406
Order of pole (three term test) = 4.622e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3147 1.004
h = 0.0001 0.005
y[1] (numeric) = 0.0590732190258 0.0347637028241
y[1] (closed_form) = 0.0590711548734 0.0347663094367
absolute error = 3.325e-06
relative error = 0.004851 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 3 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) = 8.727e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3148 1.009
h = 0.0001 0.003
y[1] (numeric) = 0.0589468590774 0.0348913008213
y[1] (closed_form) = 0.0589450072263 0.0348938664215
absolute error = 3.164e-06
relative error = 0.004619 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.821
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.293
Order of pole (three term test) = 1.199e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3149 1.012
h = 0.001 0.001
y[1] (numeric) = 0.0588719476276 0.0349685050447
y[1] (closed_form) = 0.0588701386435 0.0349711434039
absolute error = 3.199e-06
relative error = 0.004672 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.822
Order of pole (given) = 3 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) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3159 1.013
h = 0.001 0.003
y[1] (numeric) = 0.0588709452976 0.0350191607455
y[1] (closed_form) = 0.0588691693717 0.035021827574
absolute error = 3.204e-06
relative error = 0.004678 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.821
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.544
Order of pole (three term test) = 9.871e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3169 1.016
h = 0.0001 0.004
y[1] (numeric) = 0.0588181967535 0.0351195640702
y[1] (closed_form) = 0.0588163558577 0.0351221699936
absolute error = 3.191e-06
relative error = 0.004657 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.821
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.834
Order of pole (three term test) = 1.576e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.317 1.02
h = 0.003 0.006
y[1] (numeric) = 0.0587169001915 0.0352211998333
y[1] (closed_form) = 0.0587150755435 0.0352237317526
absolute error = 3.121e-06
relative error = 0.004558 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.822
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.407
Order of pole (three term test) = 7.970e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.32 1.026
h = 0.0001 0.005
y[1] (numeric) = 0.0586348678408 0.0354470462069
y[1] (closed_form) = 0.0586327305278 0.0354496909618
absolute error = 3.400e-06
relative error = 0.004963 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.82
Order of pole (given) = 3 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) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3201 1.031
h = 0.0001 0.003
y[1] (numeric) = 0.0585063374823 0.0355723050413
y[1] (closed_form) = 0.0585044132129 0.0355749138512
absolute error = 3.242e-06
relative error = 0.004734 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.822
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.294
Order of pole (three term test) = 1.150e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3202 1.034
h = 0.001 0.001
y[1] (numeric) = 0.0584301139552 0.035648120904
y[1] (closed_form) = 0.0584282307851 0.0356508034069
absolute error = 3.278e-06
relative error = 0.004788 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.822
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.801
Order of pole (three term test) = 9.986e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3212 1.035
h = 0.001 0.003
y[1] (numeric) = 0.0584282138521 0.0356987194229
y[1] (closed_form) = 0.0584263630304 0.0357014311454
absolute error = 3.283e-06
relative error = 0.004795 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.822
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.545
Order of pole (three term test) = 6.208e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3222 1.038
h = 0.0001 0.004
y[1] (numeric) = 0.0583737248122 0.0357981084206
y[1] (closed_form) = 0.0583718105337 0.0358007577692
absolute error = 3.269e-06
relative error = 0.004773 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.821
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.835
Order of pole (three term test) = 3.173e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3223 1.042
h = 0.003 0.006
y[1] (numeric) = 0.0582707058434 0.0358978656346
y[1] (closed_form) = 0.0582688095443 0.0359004414477
absolute error = 3.199e-06
relative error = 0.004673 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.822
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.408
Order of pole (three term test) = 5.673e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3253 1.048
h = 0.0001 0.005
y[1] (numeric) = 0.0581847352354 0.0361220723414
y[1] (closed_form) = 0.0581825239695 0.0361247534654
absolute error = 3.475e-06
relative error = 0.005075 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.821
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.849
Order of pole (three term test) = 2.940e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3254 1.053
h = 0.0001 0.003
y[1] (numeric) = 0.0580540922852 0.0362449433329
y[1] (closed_form) = 0.0580520946544 0.0362475935937
absolute error = 3.319e-06
relative error = 0.004849 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.822
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.294
Order of pole (three term test) = 1.518e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3255 1.056
h = 0.001 0.001
y[1] (numeric) = 0.0579765910323 0.0363193414322
y[1] (closed_form) = 0.0579746327083 0.0363220662663
absolute error = 3.356e-06
relative error = 0.004905 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.823
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.801
Order of pole (three term test) = 1.098e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3265 1.057
h = 0.001 0.003
y[1] (numeric) = 0.0579737955641 0.0363698616147
y[1] (closed_form) = 0.0579718688576 0.0363726163964
absolute error = 3.362e-06
relative error = 0.004912 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.823
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.547
Order of pole (three term test) = 5.002e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3275 1.06
h = 0.0001 0.004
y[1] (numeric) = 0.0579175920671 0.0364681963247
y[1] (closed_form) = 0.0579156034579 0.0364708873107
absolute error = 3.346e-06
relative error = 0.004889 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.822
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.837
Order of pole (three term test) = 9.588e-28 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=676.0MB, alloc=44.3MB, time=8.48
x[1] = 2.3276 1.064
h = 0.003 0.006
y[1] (numeric) = 0.0578128971841 0.0365660365279
y[1] (closed_form) = 0.0578109282692 0.0365686544975
absolute error = 3.276e-06
relative error = 0.004789 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.823
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.41
Order of pole (three term test) = 5.716e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3306 1.07
h = 0.0001 0.005
y[1] (numeric) = 0.0577230319154 0.0367885125123
y[1] (closed_form) = 0.057720745958 0.0367912282126
absolute error = 3.550e-06
relative error = 0.005186 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.822
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.849
Order of pole (three term test) = 6.625e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3307 1.075
h = 0.0001 0.003
y[1] (numeric) = 0.0575903355383 0.0369089487677
y[1] (closed_form) = 0.0575882636562 0.0369116386953
absolute error = 3.395e-06
relative error = 0.004964 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.824
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.295
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3308 1.078
h = 0.001 0.001
y[1] (numeric) = 0.0575115917233 0.0369819007632
y[1] (closed_form) = 0.0575095573328 0.03698466609
absolute error = 3.433e-06
relative error = 0.005021 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.824
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.802
Order of pole (three term test) = 1.058e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3318 1.079
h = 0.0001 0.004
y[1] (numeric) = 0.0575079039188 0.0370323215607
y[1] (closed_form) = 0.0575059003947 0.0370351175404
absolute error = 3.440e-06
relative error = 0.005029 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.824
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.82
Order of pole (three term test) = 1.114e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3319 1.083
h = 0.003 0.006
y[1] (numeric) = 0.0574018767977 0.0371285639419
y[1] (closed_form) = 0.0573998455607 0.0371311862427
absolute error = 3.317e-06
relative error = 0.004852 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.825
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.412
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3349 1.089
h = 0.0001 0.005
y[1] (numeric) = 0.0573087181081 0.0373494327249
y[1] (closed_form) = 0.057306368315 0.0373521461722
absolute error = 3.589e-06
relative error = 0.005247 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.823
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.85
Order of pole (three term test) = 6.690e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.335 1.094
h = 0.0001 0.003
y[1] (numeric) = 0.0571743322945 0.037467713609
y[1] (closed_form) = 0.057172196774 0.0374704056712
absolute error = 3.436e-06
relative error = 0.005027 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.825
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.296
Order of pole (three term test) = 6.763e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3351 1.097
h = 0.001 0.001
y[1] (numeric) = 0.0570945653382 0.0375393847662
y[1] (closed_form) = 0.0570924657208 0.0375421528725
absolute error = 3.474e-06
relative error = 0.005085 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.826
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.802
Order of pole (three term test) = 9.566e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3361 1.098
h = 0.001 0.003
y[1] (numeric) = 0.0570901138584 0.0375896926891
y[1] (closed_form) = 0.0570880444374 0.0375924920273
absolute error = 3.481e-06
relative error = 0.005093 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.825
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.553
Order of pole (three term test) = 1.274e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3371 1.101
h = 0.0001 0.004
y[1] (numeric) = 0.0570308069746 0.0376859425097
y[1] (closed_form) = 0.0570286786613 0.0376886755558
absolute error = 3.464e-06
relative error = 0.005067 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.825
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.84
Order of pole (three term test) = 3.256e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3372 1.105
h = 0.003 0.006
y[1] (numeric) = 0.0569231447817 0.0377800995786
y[1] (closed_form) = 0.0569210392961 0.0377827607256
absolute error = 3.393e-06
relative error = 0.004967 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.826
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.414
Order of pole (three term test) = 9.211e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3402 1.111
h = 0.0001 0.005
y[1] (numeric) = 0.0568261805094 0.0379990727066
y[1] (closed_form) = 0.0568237548167 0.0380018173406
absolute error = 3.663e-06
relative error = 0.005358 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.825
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.851
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3403 1.116
h = 0.0001 0.003
y[1] (numeric) = 0.056689855222 0.0381148372407
y[1] (closed_form) = 0.0566876439613 0.0381175655806
absolute error = 3.512e-06
relative error = 0.005141 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.826
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.296
Order of pole (three term test) = 2.928e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3404 1.119
h = 0.001 0.001
y[1] (numeric) = 0.0566089134686 0.0381850129165
y[1] (closed_form) = 0.0566067362589 0.0381878180231
absolute error = 3.551e-06
relative error = 0.0052 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.827
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.803
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3414 1.12
h = 0.001 0.003
y[1] (numeric) = 0.0566035771689 0.0382351826972
y[1] (closed_form) = 0.0566014293694 0.0382380196965
absolute error = 3.558e-06
relative error = 0.005209 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.826
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.556
Order of pole (three term test) = 2.574e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3424 1.123
h = 0.0001 0.004
y[1] (numeric) = 0.0565426369299 0.0383302690084
y[1] (closed_form) = 0.0565404318991 0.038333038436
absolute error = 3.540e-06
relative error = 0.005182 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.826
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.841
Order of pole (three term test) = 7.357e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3425 1.127
h = 0.003 0.006
y[1] (numeric) = 0.0564334378852 0.0384224076865
y[1] (closed_form) = 0.0564312573396 0.0384251058738
absolute error = 3.469e-06
relative error = 0.005081 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.827
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.416
Order of pole (three term test) = 8.326e-28 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=721.8MB, alloc=44.3MB, time=9.05
x[1] = 2.3455 1.133
h = 0.0001 0.005
y[1] (numeric) = 0.0563327189295 0.0386393984968
y[1] (closed_form) = 0.0563302167549 0.0386421724793
absolute error = 3.736e-06
relative error = 0.005469 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.826
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.852
Order of pole (three term test) = 1.366e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3456 1.138
h = 0.0001 0.003
y[1] (numeric) = 0.0561945167902 0.0387526051453
y[1] (closed_form) = 0.0561922290566 0.0387553679183
absolute error = 3.587e-06
relative error = 0.005255 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.827
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.297
Order of pole (three term test) = 9.868e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3457 1.141
h = 0.001 0.001
y[1] (numeric) = 0.0561124374933 0.0388212601872
y[1] (closed_form) = 0.0561101819413 0.0388241003934
absolute error = 3.627e-06
relative error = 0.005315 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.828
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.804
Order of pole (three term test) = 9.360e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3467 1.142
h = 0.001 0.003
y[1] (numeric) = 0.0561062211449 0.0388712712062
y[1] (closed_form) = 0.0561039941992 0.0388741439413
absolute error = 3.635e-06
relative error = 0.005325 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.828
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.559
Order of pole (three term test) = 7.809e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3477 1.145
h = 0.0001 0.004
y[1] (numeric) = 0.0560436777874 0.0389651574912
y[1] (closed_form) = 0.0560413953055 0.0389679614266
absolute error = 3.615e-06
relative error = 0.005297 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.828
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.843
Order of pole (three term test) = 4.707e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3478 1.149
h = 0.003 0.006
y[1] (numeric) = 0.0559329921511 0.0390552450597
y[1] (closed_form) = 0.0559307357885 0.0390579784612
absolute error = 3.544e-06
relative error = 0.005196 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.829
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.419
Order of pole (three term test) = 9.417e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3508 1.155
h = 0.0001 0.005
y[1] (numeric) = 0.0558285718514 0.0392701685805
y[1] (closed_form) = 0.0558259926677 0.0392729700611
absolute error = 3.808e-06
relative error = 0.005579 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.828
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.854
Order of pole (three term test) = 4.371e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3509 1.16
h = 0.0001 0.003
y[1] (numeric) = 0.0556885565639 0.0393807777471
y[1] (closed_form) = 0.0556861916805 0.0393835730912
absolute error = 3.662e-06
relative error = 0.005368 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.829
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.298
Order of pole (three term test) = 9.988e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.351 1.163
h = 0.001 0.001
y[1] (numeric) = 0.0556053776319 0.0394478881573
y[1] (closed_form) = 0.0556030430457 0.0394507615444
absolute error = 3.702e-06
relative error = 0.00543 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.83
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.804
Order of pole (three term test) = 9.476e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.352 1.164
h = 0.001 0.003
y[1] (numeric) = 0.0555982866018 0.0394977199835
y[1] (closed_form) = 0.0555959798012 0.0395006265105
absolute error = 3.711e-06
relative error = 0.005441 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.829
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.562
Order of pole (three term test) = 1.318e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.353 1.167
h = 0.0001 0.004
y[1] (numeric) = 0.0555341713678 0.0395903707002
y[1] (closed_form) = 0.055531810758 0.0395932072525
absolute error = 3.690e-06
relative error = 0.005411 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.829
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.845
Order of pole (three term test) = 4.316e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3531 1.171
h = 0.003 0.006
y[1] (numeric) = 0.0554220502454 0.0396783759973
y[1] (closed_form) = 0.0554197173643 0.0396811427682
absolute error = 3.619e-06
relative error = 0.00531 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.83
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.422
Order of pole (three term test) = 9.354e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3561 1.177
h = 0.0001 0.005
y[1] (numeric) = 0.0553139843147 0.0398911490281
y[1] (closed_form) = 0.0553113276504 0.0398939761464
absolute error = 3.879e-06
relative error = 0.005689 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.829
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.855
Order of pole (three term test) = 9.394e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3562 1.182
h = 0.0001 0.003
y[1] (numeric) = 0.0551722205927 0.0399991230889
y[1] (closed_form) = 0.055169777939 0.0400019491264
absolute error = 3.735e-06
relative error = 0.005481 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.831
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.299
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3563 1.185
h = 0.001 0.001
y[1] (numeric) = 0.0550879805462 0.0400646660439
y[1] (closed_form) = 0.0550855662922 0.0400675706773
absolute error = 3.777e-06
relative error = 0.005545 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.832
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.805
Order of pole (three term test) = 1.358e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3573 1.186
h = 0.0001 0.004
y[1] (numeric) = 0.0550800207891 0.0401142984546
y[1] (closed_form) = 0.0550776334842 0.0401172368132
absolute error = 3.786e-06
relative error = 0.005556 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.831
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.84
Order of pole (three term test) = 1.668e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3574 1.19
h = 0.003 0.006
y[1] (numeric) = 0.0549667675321 0.0402005766843
y[1] (closed_form) = 0.054964372633 0.040203340679
absolute error = 3.657e-06
relative error = 0.00537 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.832
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.425
Order of pole (three term test) = 1.038e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3604 1.196
h = 0.0001 0.005
y[1] (numeric) = 0.0548556368687 0.0404113909506
y[1] (closed_form) = 0.0548529176344 0.0404142086231
absolute error = 3.916e-06
relative error = 0.005747 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.831
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.856
Order of pole (three term test) = 9.548e-28 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=767.9MB, alloc=44.3MB, time=9.62
x[1] = 2.3605 1.201
h = 0.0001 0.003
y[1] (numeric) = 0.054712452653 0.0405170484382
y[1] (closed_form) = 0.0547099470017 0.0405198693584
absolute error = 3.773e-06
relative error = 0.005542 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.833
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.3
Order of pole (three term test) = 1.047e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3606 1.204
h = 0.001 0.001
y[1] (numeric) = 0.0546273495355 0.0405812128084
y[1] (closed_form) = 0.0546248706361 0.0405841127319
absolute error = 3.815e-06
relative error = 0.005606 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.833
Order of pole (given) = 3 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) = 9.742e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3616 1.205
h = 0.001 0.003
y[1] (numeric) = 0.0546186499162 0.0406306473083
y[1] (closed_form) = 0.0546161972273 0.0406335814297
absolute error = 3.824e-06
relative error = 0.005618 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.833
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.57
Order of pole (three term test) = 1.355e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3626 1.208
h = 0.0001 0.004
y[1] (numeric) = 0.0545517118949 0.0407208899972
y[1] (closed_form) = 0.0545492087013 0.0407237521228
absolute error = 3.802e-06
relative error = 0.005586 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.833
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.85
Order of pole (three term test) = 1.550e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3627 1.212
h = 0.003 0.006
y[1] (numeric) = 0.054437083948 0.0408049275423
y[1] (closed_form) = 0.0544346113965 0.040807721425
absolute error = 3.731e-06
relative error = 0.005484 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.834
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.428
Order of pole (three term test) = 6.205e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3657 1.218
h = 0.0001 0.005
y[1] (numeric) = 0.0543224183364 0.0410134422111
y[1] (closed_form) = 0.0543196209147 0.0410162820345
absolute error = 3.986e-06
relative error = 0.005856 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.833
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.857
Order of pole (three term test) = 5.035e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3658 1.223
h = 0.0001 0.003
y[1] (numeric) = 0.0541776089329 0.0411164007261
y[1] (closed_form) = 0.0541750245309 0.0411192488059
absolute error = 3.846e-06
relative error = 0.005655 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.834
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.301
Order of pole (three term test) = 1.047e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3659 1.226
h = 0.001 0.001
y[1] (numeric) = 0.0540915180977 0.0411789588314
y[1] (closed_form) = 0.0540889585317 0.0411818863606
absolute error = 3.889e-06
relative error = 0.00572 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.835
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.807
Order of pole (three term test) = 1.033e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3669 1.227
h = 0.001 0.003
y[1] (numeric) = 0.0540819625972 0.0412281569967
y[1] (closed_form) = 0.0540794283786 0.0412311192599
absolute error = 3.898e-06
relative error = 0.005733 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.835
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.575
Order of pole (three term test) = 2.751e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3679 1.23
h = 0.0001 0.004
y[1] (numeric) = 0.0540135476686 0.0413170685181
y[1] (closed_form) = 0.0540109647525 0.041319957767
absolute error = 3.875e-06
relative error = 0.005699 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.835
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.852
Order of pole (three term test) = 1.113e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.368 1.234
h = 0.003 0.006
y[1] (numeric) = 0.0538976348933 0.0413989440932
y[1] (closed_form) = 0.053895084149 0.0414017659782
absolute error = 3.804e-06
relative error = 0.005597 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.836
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.431
Order of pole (three term test) = 9.966e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.371 1.24
h = 0.0001 0.005
y[1] (numeric) = 0.0537794964173 0.04160508148
y[1] (closed_form) = 0.0537766204962 0.0416079415758
absolute error = 4.056e-06
relative error = 0.005965 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.835
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.859
Order of pole (three term test) = 6.550e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3711 1.245
h = 0.0001 0.003
y[1] (numeric) = 0.0536331289999 0.0417053092007
y[1] (closed_form) = 0.05363046539 0.0417081825301
absolute error = 3.918e-06
relative error = 0.005767 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.837
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.303
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3712 1.248
h = 0.001 0.001
y[1] (numeric) = 0.0535460904631 0.0417662416749
y[1] (closed_form) = 0.0535434497662 0.0417691948423
absolute error = 3.962e-06
relative error = 0.005834 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.837
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.808
Order of pole (three term test) = 1.124e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3722 1.249
h = 0.001 0.003
y[1] (numeric) = 0.05353568666 0.0418151839956
y[1] (closed_form) = 0.0535330704343 0.0418181724062
absolute error = 3.972e-06
relative error = 0.005847 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.837
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.579
Order of pole (three term test) = 1.405e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3732 1.252
h = 0.0001 0.004
y[1] (numeric) = 0.0534658295725 0.0419027328724
y[1] (closed_form) = 0.0534631664807 0.0419056473062
absolute error = 3.948e-06
relative error = 0.005812 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.837
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.855
Order of pole (three term test) = 3.578e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3733 1.256
h = 0.003 0.006
y[1] (numeric) = 0.0533486857719 0.041982421546
y[1] (closed_form) = 0.053346056351 0.0419852695371
absolute error = 3.876e-06
relative error = 0.00571 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.838
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.435
Order of pole (three term test) = 6.408e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3763 1.262
h = 0.0001 0.005
y[1] (numeric) = 0.053227138603 0.0421861060215
y[1] (closed_form) = 0.0532241839259 0.0421889845088
absolute error = 4.125e-06
relative error = 0.006074 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.837
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.861
Order of pole (three term test) = 7.448e-28 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=813.9MB, alloc=44.3MB, time=10.20
x[1] = 2.3764 1.267
h = 0.0001 0.003
y[1] (numeric) = 0.0530792810695 0.0422835731939
y[1] (closed_form) = 0.0530765378518 0.0422864698552
absolute error = 3.989e-06
relative error = 0.005879 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.839
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.304
Order of pole (three term test) = 1.083e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3765 1.27
h = 0.001 0.001
y[1] (numeric) = 0.0529913352894 0.0423428619034
y[1] (closed_form) = 0.0529886130564 0.0423458387339
absolute error = 4.034e-06
relative error = 0.005947 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.84
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.809
Order of pole (three term test) = 3.068e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3775 1.271
h = 0.001 0.003
y[1] (numeric) = 0.0529800913095 0.0423915291525
y[1] (closed_form) = 0.0529773926595 0.0423945417081
absolute error = 4.045e-06
relative error = 0.005961 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.839
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.584
Order of pole (three term test) = 1.597e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3785 1.274
h = 0.0001 0.004
y[1] (numeric) = 0.0529088276242 0.0424776850245
y[1] (closed_form) = 0.0529060839618 0.0424806226976
absolute error = 4.020e-06
relative error = 0.005924 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.839
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.858
Order of pole (three term test) = 8.141e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3786 1.278
h = 0.003 0.006
y[1] (numeric) = 0.0527905071602 0.0425551635201
y[1] (closed_form) = 0.0527877986359 0.0425580357124
absolute error = 3.948e-06
relative error = 0.005822 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.84
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.438
Order of pole (three term test) = 1.031e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3816 1.284
h = 0.0001 0.005
y[1] (numeric) = 0.0526656174772 0.0427563215756
y[1] (closed_form) = 0.0526625838434 0.0427592165728
absolute error = 4.193e-06
relative error = 0.006182 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.839
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.862
Order of pole (three term test) = 1.696e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3817 1.289
h = 0.0001 0.003
y[1] (numeric) = 0.0525163383746 0.0428510005305
y[1] (closed_form) = 0.0525135152065 0.0428539186007
absolute error = 4.060e-06
relative error = 0.00599 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.841
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.305
Order of pole (three term test) = 1.097e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3818 1.292
h = 0.001 0.001
y[1] (numeric) = 0.0524275262062 0.0429086285849
y[1] (closed_form) = 0.0524247220915 0.0429116270978
absolute error = 4.105e-06
relative error = 0.00606 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.842
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.81
Order of pole (three term test) = 1.062e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3828 1.293
h = 0.0001 0.004
y[1] (numeric) = 0.0524154507109 0.0429570018368
y[1] (closed_form) = 0.0524126692799 0.0429600365291
absolute error = 4.117e-06
relative error = 0.006074 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.841
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.87
Order of pole (three term test) = 9.050e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3829 1.297
h = 0.003 0.006
y[1] (numeric) = 0.0522962121792 0.0430326549884
y[1] (closed_form) = 0.0522934429334 0.0430355174809
absolute error = 3.983e-06
relative error = 0.005881 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.843
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.442
Order of pole (three term test) = 9.392e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3859 1.303
h = 0.0001 0.005
y[1] (numeric) = 0.0521685310831 0.0432315424797
y[1] (closed_form) = 0.0521654371247 0.0432344211864
absolute error = 4.226e-06
relative error = 0.006237 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.842
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.864
Order of pole (three term test) = 3.454e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.386 1.308
h = 0.0001 0.003
y[1] (numeric) = 0.0520181172935 0.0433237850636
y[1] (closed_form) = 0.0520152327762 0.0433266910092
absolute error = 4.095e-06
relative error = 0.006048 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.843
Order of pole (given) = 3 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) = 1.123e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3861 1.311
h = 0.001 0.001
y[1] (numeric) = 0.0519286123845 0.04337996146
y[1] (closed_form) = 0.0519257452548 0.043382948015
absolute error = 4.140e-06
relative error = 0.006119 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.844
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.811
Order of pole (three term test) = 5.306e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3871 1.312
h = 0.001 0.003
y[1] (numeric) = 0.0519158322864 0.0434280569819
y[1] (closed_form) = 0.0519129870531 0.0434310800741
absolute error = 4.151e-06
relative error = 0.006133 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.844
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.595
Order of pole (three term test) = 1.484e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3881 1.315
h = 0.0001 0.004
y[1] (numeric) = 0.0518420658969 0.043511528196
y[1] (closed_form) = 0.0518391791616 0.0435144748958
absolute error = 4.125e-06
relative error = 0.006095 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.844
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.864
Order of pole (three term test) = 1.069e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3882 1.319
h = 0.003 0.006
y[1] (numeric) = 0.0517217291907 0.0435848253688
y[1] (closed_form) = 0.0517188802221 0.0435877084987
absolute error = 4.053e-06
relative error = 0.005993 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.845
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.446
Order of pole (three term test) = 4.789e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3912 1.325
h = 0.0001 0.005
y[1] (numeric) = 0.0515908345957 0.0437810563519
y[1] (closed_form) = 0.0515876614762 0.0437839480712
absolute error = 4.293e-06
relative error = 0.006345 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.844
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.866
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3913 1.33
h = 0.0001 0.003
y[1] (numeric) = 0.051439128524 0.043870465659
y[1] (closed_form) = 0.0514361635945 0.0438733894245
absolute error = 4.164e-06
relative error = 0.006159 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.846
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.308
Order of pole (three term test) = 1.140e-27 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=859.8MB, alloc=44.3MB, time=10.76
x[1] = 2.3914 1.333
h = 0.001 0.001
y[1] (numeric) = 0.0513488343159 0.0439249538039
y[1] (closed_form) = 0.0513458848429 0.0439279583458
absolute error = 4.210e-06
relative error = 0.006231 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.847
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.812
Order of pole (three term test) = 3.249e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3924 1.334
h = 0.001 0.003
y[1] (numeric) = 0.0513352404155 0.0439727210915
y[1] (closed_form) = 0.051332311922 0.0439757625729
absolute error = 4.222e-06
relative error = 0.006246 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.846
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.601
Order of pole (three term test) = 1.757e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3934 1.337
h = 0.0001 0.004
y[1] (numeric) = 0.051260173579 0.044054719275
y[1] (closed_form) = 0.0512572054887 0.0440576836235
absolute error = 4.195e-06
relative error = 0.006206 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.846
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.867
Order of pole (three term test) = 7.714e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3935 1.341
h = 0.003 0.006
y[1] (numeric) = 0.0511388184829 0.0441257495893
y[1] (closed_form) = 0.0511358895279 0.0441286514388
absolute error = 4.123e-06
relative error = 0.006104 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.848
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.451
Order of pole (three term test) = 4.888e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3965 1.347
h = 0.0001 0.005
y[1] (numeric) = 0.0510047818204 0.0443192569716
y[1] (closed_form) = 0.0510015294961 0.044322159831
absolute error = 4.359e-06
relative error = 0.006452 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.847
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.868
Order of pole (three term test) = 3.597e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3966 1.352
h = 0.0001 0.003
y[1] (numeric) = 0.0508518534248 0.0444058113691
y[1] (closed_form) = 0.0508488079044 0.0444087510272
absolute error = 4.233e-06
relative error = 0.00627 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.849
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.31
Order of pole (three term test) = 1.165e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3967 1.355
h = 0.001 0.001
y[1] (numeric) = 0.0507608116431 0.044458597973
y[1] (closed_form) = 0.0507577796506 0.0444616185178
absolute error = 4.280e-06
relative error = 0.006343 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.85
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.814
Order of pole (three term test) = 1.564e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3977 1.356
h = 0.001 0.003
y[1] (numeric) = 0.050746414056 0.0445060190631
y[1] (closed_form) = 0.050743402118 0.0445090769212
absolute error = 4.292e-06
relative error = 0.006359 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.849
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.607
Order of pole (three term test) = 3.078e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3987 1.359
h = 0.0001 0.004
y[1] (numeric) = 0.0506700850515 0.0445865183843
y[1] (closed_form) = 0.0506670354358 0.0445894984274
absolute error = 4.264e-06
relative error = 0.006317 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.849
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.87
Order of pole (three term test) = 1.581e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3988 1.363
h = 0.003 0.006
y[1] (numeric) = 0.050547767498 0.0446552650547
y[1] (closed_form) = 0.0505447583498 0.0446581837056
absolute error = 4.192e-06
relative error = 0.006215 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.851
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.455
Order of pole (three term test) = 3.996e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4018 1.369
h = 0.0001 0.005
y[1] (numeric) = 0.0504106618764 0.0448459840814
y[1] (closed_form) = 0.0504073303579 0.0448488962152
absolute error = 4.425e-06
relative error = 0.006558 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.85
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.87
Order of pole (three term test) = 1.875e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4019 1.374
h = 0.0001 0.003
y[1] (numeric) = 0.0502565814708 0.0449296640578
y[1] (closed_form) = 0.0502534552374 0.0449326176834
absolute error = 4.301e-06
relative error = 0.00638 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.852
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.312
Order of pole (three term test) = 1.331e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.402 1.377
h = 0.001 0.001
y[1] (numeric) = 0.0501648340628 0.0449807370971
y[1] (closed_form) = 0.0501617194333 0.0449837716633
absolute error = 4.349e-06
relative error = 0.006454 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.852
Order of pole (given) = 3 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) = 1.599e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.403 1.378
h = 0.001 0.003
y[1] (numeric) = 0.0501496433869 0.0450277943916
y[1] (closed_form) = 0.0501465478797 0.0450308666166
absolute error = 4.361e-06
relative error = 0.006471 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.852
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.613
Order of pole (three term test) = 1.101e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.404 1.381
h = 0.0001 0.004
y[1] (numeric) = 0.0500720910927 0.0451067702347
y[1] (closed_form) = 0.0500689598391 0.045109764021
absolute error = 4.332e-06
relative error = 0.006428 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.852
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.874
Order of pole (three term test) = 8.070e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4041 1.385
h = 0.003 0.006
y[1] (numeric) = 0.0499488672789 0.0451732181693
y[1] (closed_form) = 0.0499457777875 0.0451761517044
absolute error = 4.260e-06
relative error = 0.006326 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.853
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.46
Order of pole (three term test) = 6.130e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4071 1.391
h = 0.0001 0.005
y[1] (numeric) = 0.0498087673944 0.0453610864705
y[1] (closed_form) = 0.049805356746 0.0453640060215
absolute error = 4.490e-06
relative error = 0.006664 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.853
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.872
Order of pole (three term test) = 3.836e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4072 1.396
h = 0.0001 0.003
y[1] (numeric) = 0.0496536055723 0.0454418746372
y[1] (closed_form) = 0.0496503985604 0.0454448403096
absolute error = 4.368e-06
relative error = 0.00649 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.854
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.314
Order of pole (three term test) = 1.487e-27 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=905.7MB, alloc=44.3MB, time=11.34
x[1] = 2.4073 1.399
h = 0.001 0.001
y[1] (numeric) = 0.0495611946621 0.0454912233558
y[1] (closed_form) = 0.0495579973366 0.0454942699665
absolute error = 4.416e-06
relative error = 0.006565 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.855
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.816
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4083 1.4
h = 0.003 0.006
y[1] (numeric) = 0.0495452219623 0.0455378996369
y[1] (closed_form) = 0.0495420428208 0.0455409842234
absolute error = 4.430e-06
relative error = 0.006583 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.855
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 18.29
Order of pole (three term test) = 1.132e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4113 1.406
h = 0.0001 0.005
y[1] (numeric) = 0.0494031047392 0.0457241213396
y[1] (closed_form) = 0.0493995333563 0.0457269106462
absolute error = 4.532e-06
relative error = 0.006732 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.854
Order of pole (given) = 3 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) = 1.142e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4114 1.411
h = 0.0001 0.003
y[1] (numeric) = 0.0492471667938 0.0458029364051
y[1] (closed_form) = 0.0492437979539 0.0458057750239
absolute error = 4.405e-06
relative error = 0.00655 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.856
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.314
Order of pole (three term test) = 3.699e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4115 1.414
h = 0.001 0.001
y[1] (numeric) = 0.0491542802617 0.0458511088532
y[1] (closed_form) = 0.0491509197922 0.0458540284245
absolute error = 4.452e-06
relative error = 0.006623 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.857
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.817
Order of pole (three term test) = 1.223e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4125 1.415
h = 0.001 0.003
y[1] (numeric) = 0.0491377661725 0.0458975326089
y[1] (closed_form) = 0.0491344232457 0.0459004903813
absolute error = 4.464e-06
relative error = 0.006638 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.856
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.623
Order of pole (three term test) = 6.521e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4135 1.418
h = 0.0001 0.004
y[1] (numeric) = 0.0490581991806 0.045973913225
y[1] (closed_form) = 0.049054823776 0.04597679159
absolute error = 4.436e-06
relative error = 0.006598 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.857
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.88
Order of pole (three term test) = 1.506e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4136 1.422
h = 0.003 0.006
y[1] (numeric) = 0.0489335151121 0.0460364713621
y[1] (closed_form) = 0.0489301835975 0.0460392914447
absolute error = 4.365e-06
relative error = 0.006497 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.858
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.468
Order of pole (three term test) = 5.296e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4166 1.428
h = 0.0001 0.005
y[1] (numeric) = 0.0487884597591 0.0462194644716
y[1] (closed_form) = 0.0487848094288 0.0462222580805
absolute error = 4.597e-06
relative error = 0.00684 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.857
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.876
Order of pole (three term test) = 1.234e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4167 1.433
h = 0.0001 0.003
y[1] (numeric) = 0.0486315596549 0.0462953614017
y[1] (closed_form) = 0.0486281100044 0.0462982088385
absolute error = 4.473e-06
relative error = 0.006662 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.859
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.316
Order of pole (three term test) = 1.320e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4168 1.436
h = 0.001 0.001
y[1] (numeric) = 0.0485380807955 0.0463417931797
y[1] (closed_form) = 0.0485346376118 0.0463447214731
absolute error = 4.520e-06
relative error = 0.006735 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.86
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.819
Order of pole (three term test) = 1.401e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4178 1.437
h = 0.001 0.003
y[1] (numeric) = 0.0485208039629 0.0463878074589
y[1] (closed_form) = 0.048517377375 0.0463907742223
absolute error = 4.532e-06
relative error = 0.006752 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.86
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.631
Order of pole (three term test) = 1.680e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4188 1.44
h = 0.0001 0.004
y[1] (numeric) = 0.0484401202817 0.0464626035464
y[1] (closed_form) = 0.0484366631708 0.0464654904364
absolute error = 4.504e-06
relative error = 0.00671 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.86
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.884
Order of pole (three term test) = 8.564e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4189 1.444
h = 0.003 0.006
y[1] (numeric) = 0.0483146816061 0.0465228293461
y[1] (closed_form) = 0.0483112695746 0.0465256591801
absolute error = 4.433e-06
relative error = 0.006609 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.861
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.474
Order of pole (three term test) = 1.214e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4219 1.45
h = 0.0001 0.005
y[1] (numeric) = 0.0481668385513 0.0467028142347
y[1] (closed_form) = 0.0481631094795 0.0467056103191
absolute error = 4.661e-06
relative error = 0.006947 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.861
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.878
Order of pole (three term test) = 8.950e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.422 1.455
h = 0.0001 0.003
y[1] (numeric) = 0.048009047315 0.0467757813329
y[1] (closed_form) = 0.0480055169379 0.0467786356863
absolute error = 4.540e-06
relative error = 0.006773 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.863
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.318
Order of pole (three term test) = 2.600e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4221 1.458
h = 0.001 0.001
y[1] (numeric) = 0.0479150185369 0.0468204650835
y[1] (closed_form) = 0.0479114927347 0.046823400143
absolute error = 4.588e-06
relative error = 0.006848 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.864
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.82
Order of pole (three term test) = 1.233e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4231 1.459
h = 0.001 0.003
y[1] (numeric) = 0.0478969912136 0.0468660537488
y[1] (closed_form) = 0.0478934810567 0.0468690275187
absolute error = 4.600e-06
relative error = 0.006865 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.863
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.638
Order of pole (three term test) = 1.715e-28 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=951.8MB, alloc=44.3MB, time=11.92
x[1] = 2.4241 1.462
h = 0.0001 0.004
y[1] (numeric) = 0.0478152315706 0.0469392452787
y[1] (closed_form) = 0.0478116928498 0.0469421387677
absolute error = 4.571e-06
relative error = 0.006822 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.863
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.888
Order of pole (three term test) = 9.828e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4242 1.466
h = 0.003 0.006
y[1] (numeric) = 0.047689094985 0.0469971298817
y[1] (closed_form) = 0.0476856024922 0.0469999675697
absolute error = 4.500e-06
relative error = 0.006721 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.865
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.479
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4272 1.472
h = 0.0001 0.005
y[1] (numeric) = 0.0475385440481 0.0471740532878
y[1] (closed_form) = 0.0475347364918 0.047176850036
absolute error = 4.724e-06
relative error = 0.007054 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.864
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.881
Order of pole (three term test) = 8.220e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4273 1.477
h = 0.0001 0.003
y[1] (numeric) = 0.047379932711 0.0472440809636
y[1] (closed_form) = 0.0473763217458 0.0472469403433
absolute error = 4.606e-06
relative error = 0.006884 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.866
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.32
Order of pole (three term test) = 1.332e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4274 1.48
h = 0.001 0.001
y[1] (numeric) = 0.0472853964351 0.0472870105879
y[1] (closed_form) = 0.0472817881661 0.0472899504695
absolute error = 4.654e-06
relative error = 0.00696 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.867
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.822
Order of pole (three term test) = 1.318e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4284 1.481
h = 0.0001 0.004
y[1] (numeric) = 0.047266631281 0.0473321579314
y[1] (closed_form) = 0.0472630377047 0.0473351367351
absolute error = 4.668e-06
relative error = 0.006978 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.866
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.94
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4285 1.485
h = 0.003 0.006
y[1] (numeric) = 0.0471399697064 0.0473881215074
y[1] (closed_form) = 0.047136420942 0.04739093822
absolute error = 4.531e-06
relative error = 0.006778 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.868
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.485
Order of pole (three term test) = 8.088e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4315 1.491
h = 0.0001 0.005
y[1] (numeric) = 0.0469871899988 0.047562338051
y[1] (closed_form) = 0.0469833281148 0.0475651077348
absolute error = 4.752e-06
relative error = 0.007108 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.867
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.883
Order of pole (three term test) = 1.520e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4316 1.496
h = 0.0001 0.003
y[1] (numeric) = 0.0468279647067 0.0476298208703
y[1] (closed_form) = 0.04682429746 0.0476326568483
absolute error = 4.636e-06
relative error = 0.006941 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.869
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.322
Order of pole (three term test) = 8.202e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4317 1.499
h = 0.001 0.001
y[1] (numeric) = 0.046733046511 0.0476712313147
y[1] (closed_form) = 0.046729380359 0.047674147554
absolute error = 4.685e-06
relative error = 0.007017 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.87
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.823
Order of pole (three term test) = 1.299e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4327 1.5
h = 0.001 0.003
y[1] (numeric) = 0.0467136621964 0.0477159779648
y[1] (closed_form) = 0.0467100099139 0.0477189332745
absolute error = 4.698e-06
relative error = 0.007036 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.87
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.653
Order of pole (three term test) = 3.617e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4337 1.503
h = 0.0001 0.004
y[1] (numeric) = 0.0466300297395 0.0477861231792
y[1] (closed_form) = 0.0466263525462 0.0477889976284
absolute error = 4.667e-06
relative error = 0.006991 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.87
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.897
Order of pole (three term test) = 9.271e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4338 1.507
h = 0.003 0.006
y[1] (numeric) = 0.0465027733748 0.0478396267989
y[1] (closed_form) = 0.0464991444195 0.0478424478657
absolute error = 4.596e-06
relative error = 0.00689 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.872
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.491
Order of pole (three term test) = 5.882e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4368 1.513
h = 0.0001 0.005
y[1] (numeric) = 0.0463474378682 0.0480106905557
y[1] (closed_form) = 0.0463434981328 0.048013457582
absolute error = 4.814e-06
relative error = 0.007215 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.871
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.886
Order of pole (three term test) = 8.676e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4369 1.518
h = 0.0001 0.003
y[1] (numeric) = 0.0461875244669 0.0480752225115
y[1] (closed_form) = 0.0461837770545 0.0480780600376
absolute error = 4.700e-06
relative error = 0.007051 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.873
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.325
Order of pole (three term test) = 1.414e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.437 1.521
h = 0.001 0.001
y[1] (numeric) = 0.0460921776305 0.0481148713083
y[1] (closed_form) = 0.0460884294644 0.0481177887938
absolute error = 4.750e-06
relative error = 0.007129 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.874
Order of pole (given) = 3 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) = 1.337e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.438 1.522
h = 0.001 0.003
y[1] (numeric) = 0.0460720802424 0.0481591487523
y[1] (closed_form) = 0.0460683449918 0.048162105467
absolute error = 4.764e-06
relative error = 0.007148 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.874
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.662
Order of pole (three term test) = 7.896e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.439 1.525
h = 0.0001 0.004
y[1] (numeric) = 0.0459874904916 0.048227639641
y[1] (closed_form) = 0.0459837322898 0.0482305152541
absolute error = 4.732e-06
relative error = 0.007101 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.874
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.902
Order of pole (three term test) = 1.067e-27 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=997.8MB, alloc=44.3MB, time=12.50
x[1] = 2.4391 1.529
h = 0.003 0.006
y[1] (numeric) = 0.0458596981754 0.0482787866181
y[1] (closed_form) = 0.0458559892387 0.0482816101763
absolute error = 4.661e-06
relative error = 0.007 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.875
Order of pole (given) = 3 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) = 6.055e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4421 1.535
h = 0.0001 0.005
y[1] (numeric) = 0.0457018897029 0.0484466517118
y[1] (closed_form) = 0.0456978725146 0.0484494143213
absolute error = 4.875e-06
relative error = 0.00732 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.875
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.889
Order of pole (three term test) = 8.935e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4422 1.54
h = 0.0001 0.003
y[1] (numeric) = 0.0455413588132 0.048508229159
y[1] (closed_form) = 0.0455375315252 0.0485110663856
absolute error = 4.764e-06
relative error = 0.00716 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.877
Order of pole (given) = 3 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) = 2.028e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4423 1.543
h = 0.001 0.001
y[1] (numeric) = 0.0454456255391 0.0485461137631
y[1] (closed_form) = 0.0454417956675 0.0485490305958
absolute error = 4.814e-06
relative error = 0.00724 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.878
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.827
Order of pole (three term test) = 1.405e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4433 1.544
h = 0.001 0.003
y[1] (numeric) = 0.0454248288016 0.0485899075879
y[1] (closed_form) = 0.0454210108918 0.0485928637804
absolute error = 4.829e-06
relative error = 0.007259 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.877
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.67
Order of pole (three term test) = 4.287e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4443 1.547
h = 0.0001 0.004
y[1] (numeric) = 0.0453393237013 0.0486567290533
y[1] (closed_form) = 0.0453354847965 0.0486596039607
absolute error = 4.796e-06
relative error = 0.007211 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.878
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.906
Order of pole (three term test) = 3.932e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4444 1.551
h = 0.003 0.006
y[1] (numeric) = 0.0452110517385 0.0487055169377
y[1] (closed_form) = 0.0452072630824 0.0487083411399
absolute error = 4.725e-06
relative error = 0.007111 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.879
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.504
Order of pole (three term test) = 1.872e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4474 1.557
h = 0.0001 0.005
y[1] (numeric) = 0.0450508540128 0.0488701401064
y[1] (closed_form) = 0.045046759818 0.048872896561
absolute error = 4.936e-06
relative error = 0.007426 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.879
Order of pole (given) = 3 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) = 4.605e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4475 1.562
h = 0.0001 0.003
y[1] (numeric) = 0.0448897759852 0.0489287614428
y[1] (closed_form) = 0.0448858691631 0.0489315965403
absolute error = 4.827e-06
relative error = 0.00727 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.881
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.329
Order of pole (three term test) = 4.481e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4476 1.565
h = 0.001 0.001
y[1] (numeric) = 0.044793698324 0.0489648805309
y[1] (closed_form) = 0.0447897871085 0.0489677948306
absolute error = 4.878e-06
relative error = 0.00735 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.882
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.829
Order of pole (three term test) = 1.420e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4486 1.566
h = 0.001 0.003
y[1] (numeric) = 0.0447722163002 0.049008176793
y[1] (closed_form) = 0.0447683160943 0.0490111305553
absolute error = 4.892e-06
relative error = 0.00737 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.881
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.679
Order of pole (three term test) = 7.128e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4496 1.569
h = 0.0001 0.004
y[1] (numeric) = 0.0446858380028 0.0490733150194
y[1] (closed_form) = 0.0446819187527 0.0490761873699
absolute error = 4.859e-06
relative error = 0.007321 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.882
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.911
Order of pole (three term test) = 1.036e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4497 1.573
h = 0.003 0.006
y[1] (numeric) = 0.0445571424653 0.049119742985
y[1] (closed_form) = 0.0445532744036 0.0491225660009
absolute error = 4.789e-06
relative error = 0.007221 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.883
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.51
Order of pole (three term test) = 7.271e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4527 1.579
h = 0.0001 0.005
y[1] (numeric) = 0.0443946399839 0.0492810835947
y[1] (closed_form) = 0.0443904692755 0.0492838321789
absolute error = 4.995e-06
relative error = 0.007531 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.883
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.895
Order of pole (three term test) = 1.573e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4528 1.584
h = 0.0001 0.003
y[1] (numeric) = 0.0442330848296 0.0493367492385
y[1] (closed_form) = 0.0442290988655 0.0493395803968
absolute error = 4.889e-06
relative error = 0.007378 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.885
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.332
Order of pole (three term test) = 1.549e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4529 1.587
h = 0.001 0.001
y[1] (numeric) = 0.0441367046392 0.0493711026956
y[1] (closed_form) = 0.0441327124933 0.0493740126028
absolute error = 4.940e-06
relative error = 0.00746 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.886
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.831
Order of pole (three term test) = 2.931e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4539 1.588
h = 0.0001 0.004
y[1] (numeric) = 0.0441145517131 0.04941388793
y[1] (closed_form) = 0.044110569627 0.0494168373749
absolute error = 4.955e-06
relative error = 0.007481 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.885
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.99
Order of pole (three term test) = 1.274e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.454 1.592
h = 0.003 0.006
y[1] (numeric) = 0.0439855548982 0.0494583859
y[1] (closed_form) = 0.0439816342138 0.0494611822952
absolute error = 4.816e-06
relative error = 0.007276 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.887
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.517
Order of pole (three term test) = 6.660e-28 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1043.8MB, alloc=44.3MB, time=13.08
x[1] = 2.457 1.598
h = 0.0001 0.005
y[1] (numeric) = 0.043821176463 0.0496168443952
y[1] (closed_form) = 0.0438169558386 0.0496195607386
absolute error = 5.019e-06
relative error = 0.007582 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.887
Order of pole (given) = 3 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) = 1.094e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4571 1.603
h = 0.0001 0.003
y[1] (numeric) = 0.0436593015331 0.0496699631797
y[1] (closed_form) = 0.0436552632675 0.0496727653703
absolute error = 4.915e-06
relative error = 0.007433 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.889
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.334
Order of pole (three term test) = 7.940e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4572 1.606
h = 0.001 0.001
y[1] (numeric) = 0.0435627152891 0.0497027947306
y[1] (closed_form) = 0.043558669327 0.0497056752205
absolute error = 4.967e-06
relative error = 0.007515 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.89
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.833
Order of pole (three term test) = 7.551e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4582 1.607
h = 0.001 0.003
y[1] (numeric) = 0.0435400029186 0.0497451219249
y[1] (closed_form) = 0.043535966201 0.0497480419838
absolute error = 4.982e-06
relative error = 0.007536 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.889
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.697
Order of pole (three term test) = 1.695e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4592 1.61
h = 0.0001 0.004
y[1] (numeric) = 0.0434521328974 0.049807086438
y[1] (closed_form) = 0.0434480807445 0.0498099250217
absolute error = 4.947e-06
relative error = 0.007485 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.89
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.922
Order of pole (three term test) = 5.393e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4593 1.614
h = 0.003 0.006
y[1] (numeric) = 0.0433228254622 0.0498491229483
y[1] (closed_form) = 0.0433188261112 0.0498519148074
absolute error = 4.877e-06
relative error = 0.007385 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.891
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.524
Order of pole (three term test) = 6.847e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4623 1.62
h = 0.0001 0.005
y[1] (numeric) = 0.0431563016728 0.0500042313209
y[1] (closed_form) = 0.0431520055922 0.0500069366738
absolute error = 5.077e-06
relative error = 0.007686 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.891
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.901
Order of pole (three term test) = 1.882e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4624 1.625
h = 0.0001 0.003
y[1] (numeric) = 0.0429940787005 0.0500544013006
y[1] (closed_form) = 0.0429899621741 0.0500571962478
absolute error = 4.976e-06
relative error = 0.007541 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.893
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.337
Order of pole (three term test) = 1.641e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4625 1.628
h = 0.001 0.001
y[1] (numeric) = 0.0428972671325 0.0500854706626
y[1] (closed_form) = 0.0428931411662 0.050088343367
absolute error = 5.028e-06
relative error = 0.007624 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.894
Order of pole (given) = 3 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) = 3.123e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4635 1.629
h = 0.001 0.003
y[1] (numeric) = 0.0428739115617 0.0501272632523
y[1] (closed_form) = 0.0428697938972 0.05013017555
absolute error = 5.043e-06
relative error = 0.007646 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.894
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.706
Order of pole (three term test) = 2.174e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4645 1.632
h = 0.0001 0.004
y[1] (numeric) = 0.0427852897879 0.0501875125666
y[1] (closed_form) = 0.0427811586125 0.0501903434218
absolute error = 5.008e-06
relative error = 0.007594 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.894
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.927
Order of pole (three term test) = 5.576e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4646 1.636
h = 0.003 0.006
y[1] (numeric) = 0.0426557173687 0.050227196244
y[1] (closed_form) = 0.0426516398069 0.0502299817948
absolute error = 4.938e-06
relative error = 0.007494 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.896
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.531
Order of pole (three term test) = 7.082e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4676 1.642
h = 0.0001 0.005
y[1] (numeric) = 0.0424871344108 0.0503789214208
y[1] (closed_form) = 0.0424827634938 0.0503816141406
absolute error = 5.134e-06
relative error = 0.00779 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.895
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.904
Order of pole (three term test) = 5.233e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4677 1.647
h = 0.0001 0.003
y[1] (numeric) = 0.0423246320509 0.050426148639
y[1] (closed_form) = 0.042320437794 0.0504289345981
absolute error = 5.035e-06
relative error = 0.007648 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.897
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.339
Order of pole (three term test) = 1.868e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4678 1.65
h = 0.001 0.001
y[1] (numeric) = 0.0422276362328 0.0504554590635
y[1] (closed_form) = 0.0422234308183 0.0504583221917
absolute error = 5.088e-06
relative error = 0.007733 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.899
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.837
Order of pole (three term test) = 1.616e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4688 1.651
h = 0.001 0.003
y[1] (numeric) = 0.0422036526543 0.0504967049951
y[1] (closed_form) = 0.0421994546042 0.0504996077139
absolute error = 5.104e-06
relative error = 0.007755 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.898
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.716
Order of pole (three term test) = 3.870e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4698 1.654
h = 0.0001 0.004
y[1] (numeric) = 0.0421143216462 0.0505552302141
y[1] (closed_form) = 0.0421101119967 0.0505580515774
absolute error = 5.068e-06
relative error = 0.007702 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.898
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.933
Order of pole (three term test) = 1.154e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4699 1.658
h = 0.003 0.006
y[1] (numeric) = 0.0419845389009 0.0505925663049
y[1] (closed_form) = 0.0419803836317 0.0505953437985
absolute error = 4.998e-06
relative error = 0.007602 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.9
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.539
Order of pole (three term test) = 7.331e-28 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1089.7MB, alloc=44.3MB, time=13.66
x[1] = 2.4729 1.664
h = 0.0001 0.005
y[1] (numeric) = 0.0418139833798 0.0507408778542
y[1] (closed_form) = 0.0418095382883 0.0507435563262
absolute error = 5.190e-06
relative error = 0.007893 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.9
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.907
Order of pole (three term test) = 1.212e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.473 1.669
h = 0.0001 0.003
y[1] (numeric) = 0.0416512696993 0.0507851702629
y[1] (closed_form) = 0.0416469982886 0.0507879455147
absolute error = 5.094e-06
relative error = 0.007755 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.902
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.342
Order of pole (three term test) = 5.277e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4731 1.672
h = 0.001 0.001
y[1] (numeric) = 0.0415541303627 0.0508127261444
y[1] (closed_form) = 0.041549846104 0.0508155779323
absolute error = 5.147e-06
relative error = 0.007841 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.903
Order of pole (given) = 3 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) = 1.707e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4741 1.673
h = 0.001 0.003
y[1] (numeric) = 0.041529534218 0.0508534138677
y[1] (closed_form) = 0.0415252563918 0.0508563052171
absolute error = 5.163e-06
relative error = 0.007864 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.903
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.727
Order of pole (three term test) = 7.235e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4751 1.676
h = 0.0001 0.004
y[1] (numeric) = 0.0414395364856 0.050910207353
y[1] (closed_form) = 0.0414352489576 0.0509130174873
absolute error = 5.126e-06
relative error = 0.007809 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.903
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.939
Order of pole (three term test) = 8.456e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4752 1.68
h = 0.003 0.006
y[1] (numeric) = 0.0413095975885 0.050945202618
y[1] (closed_form) = 0.041305365162 0.0509479703302
absolute error = 5.057e-06
relative error = 0.00771 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.905
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.546
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4782 1.686
h = 0.0001 0.005
y[1] (numeric) = 0.0411371564365 0.0510900727443
y[1] (closed_form) = 0.0411326378734 0.0510927353825
absolute error = 5.245e-06
relative error = 0.007996 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.905
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.911
Order of pole (three term test) = 5.616e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4783 1.691
h = 0.0001 0.003
y[1] (numeric) = 0.0409742988543 0.05113144017
y[1] (closed_form) = 0.0409699509114 0.0511342030222
absolute error = 5.152e-06
relative error = 0.007862 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.907
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.345
Order of pole (three term test) = 3.647e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4784 1.694
h = 0.001 0.001
y[1] (numeric) = 0.0408770563526 0.0511572470258
y[1] (closed_form) = 0.0408726938998 0.0511600857375
absolute error = 5.205e-06
relative error = 0.007948 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.908
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.841
Order of pole (three term test) = 5.205e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4794 1.695
h = 0.0001 0.004
y[1] (numeric) = 0.0408518633123 0.0511973654987
y[1] (closed_form) = 0.040847506367 0.0512002437167
absolute error = 5.222e-06
relative error = 0.007972 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.907
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.06
Order of pole (three term test) = 1.509e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4795 1.699
h = 0.003 0.006
y[1] (numeric) = 0.0407218402126 0.051230452347
y[1] (closed_form) = 0.0407175594515 0.0512331884754
absolute error = 5.080e-06
relative error = 0.007763 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.909
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.554
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4825 1.705
h = 0.0001 0.005
y[1] (numeric) = 0.0405478871632 0.0513723189113
y[1] (closed_form) = 0.0405433236255 0.0513749449162
absolute error = 5.265e-06
relative error = 0.008045 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.909
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.914
Order of pole (three term test) = 1.643e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4826 1.71
h = 0.0001 0.003
y[1] (numeric) = 0.0403849938129 0.051411177248
y[1] (closed_form) = 0.0403805981602 0.0514139062987
absolute error = 5.174e-06
relative error = 0.007914 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.911
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.347
Order of pole (three term test) = 8.435e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4827 1.713
h = 0.001 0.001
y[1] (numeric) = 0.0402877152338 0.0514354832779
y[1] (closed_form) = 0.0402833036732 0.0514382875523
absolute error = 5.227e-06
relative error = 0.008001 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.912
Order of pole (given) = 3 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) = 1.804e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4837 1.714
h = 0.001 0.003
y[1] (numeric) = 0.0402620280659 0.0514750964554
y[1] (closed_form) = 0.0402576212237 0.0514779401571
absolute error = 5.245e-06
relative error = 0.008026 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.912
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.747
Order of pole (three term test) = 7.903e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4847 1.717
h = 0.0001 0.004
y[1] (numeric) = 0.0401709234397 0.0515286447753
y[1] (closed_form) = 0.0401665103794 0.0515314076848
absolute error = 5.207e-06
relative error = 0.007969 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.912
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.95
Order of pole (three term test) = 6.415e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4848 1.721
h = 0.003 0.006
y[1] (numeric) = 0.0400408639379 0.0515593070119
y[1] (closed_form) = 0.0400365071829 0.0515620302282
absolute error = 5.138e-06
relative error = 0.00787 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.914
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.562
Order of pole (three term test) = 8.151e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4878 1.727
h = 0.0001 0.005
y[1] (numeric) = 0.0398651878327 0.0516976884554
y[1] (closed_form) = 0.0398605522536 0.051700295766
absolute error = 5.319e-06
relative error = 0.008147 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.914
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.918
Order of pole (three term test) = 1.348e-27 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1135.7MB, alloc=44.3MB, time=14.23
x[1] = 2.4879 1.732
h = 0.0001 0.003
y[1] (numeric) = 0.0397022739393 0.0517336457399
y[1] (closed_form) = 0.0396978030461 0.0517363593267
absolute error = 5.230e-06
relative error = 0.00802 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.916
Order of pole (given) = 3 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) = 6.193e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.488 1.735
h = 0.001 0.001
y[1] (numeric) = 0.039604966061 0.0517562163931
y[1] (closed_form) = 0.0396004776549 0.0517590044495
absolute error = 5.284e-06
relative error = 0.008108 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.917
Order of pole (given) = 3 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) = 3.728e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.489 1.736
h = 0.001 0.003
y[1] (numeric) = 0.0395787118203 0.0517952413308
y[1] (closed_form) = 0.0395742272226 0.0517980687121
absolute error = 5.301e-06
relative error = 0.008133 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.917
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.758
Order of pole (three term test) = 5.804e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.49 1.739
h = 0.0001 0.004
y[1] (numeric) = 0.0394870617025 0.0518470434207
y[1] (closed_form) = 0.0394825727335 0.051849790298
absolute error = 5.263e-06
relative error = 0.008075 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.917
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.956
Order of pole (three term test) = 6.663e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4901 1.743
h = 0.003 0.006
y[1] (numeric) = 0.0393569977985 0.0518753929023
y[1] (closed_form) = 0.0393525657261 0.0518781015607
absolute error = 5.194e-06
relative error = 0.007977 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.919
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.57
Order of pole (three term test) = 8.468e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4931 1.749
h = 0.0001 0.005
y[1] (numeric) = 0.0391796859721 0.0520102689099
y[1] (closed_form) = 0.0391749791637 0.0520128560296
absolute error = 5.371e-06
relative error = 0.008248 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.919
Order of pole (given) = 3 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) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4932 1.754
h = 0.0001 0.003
y[1] (numeric) = 0.039016816763 0.0520433401145
y[1] (closed_form) = 0.0390122713725 0.0520460366297
absolute error = 5.285e-06
relative error = 0.008125 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.921
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.353
Order of pole (three term test) = 7.339e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4933 1.757
h = 0.001 0.001
y[1] (numeric) = 0.0389195186547 0.0520641839924
y[1] (closed_form) = 0.0389149541782 0.0520669541831
absolute error = 5.339e-06
relative error = 0.008214 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.922
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.848
Order of pole (three term test) = 4.332e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4943 1.758
h = 0.001 0.003
y[1] (numeric) = 0.0388927135578 0.0521026111225
y[1] (closed_form) = 0.0388881519888 0.0521054205108
absolute error = 5.357e-06
relative error = 0.00824 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.922
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.769
Order of pole (three term test) = 8.095e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4953 1.761
h = 0.0001 0.004
y[1] (numeric) = 0.0388005600219 0.0521526640932
y[1] (closed_form) = 0.0387959959077 0.0521553933154
absolute error = 5.318e-06
relative error = 0.008181 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.922
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.963
Order of pole (three term test) = 1.392e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4954 1.765
h = 0.003 0.006
y[1] (numeric) = 0.0386705435725 0.0521787131442
y[1] (closed_form) = 0.0386660369011 0.0521814056285
absolute error = 5.250e-06
relative error = 0.008083 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.924
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.579
Order of pole (three term test) = 1.761e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4984 1.771
h = 0.0001 0.005
y[1] (numeric) = 0.0384916833397 0.0523100659821
y[1] (closed_form) = 0.0384869061499 0.0523126314475
absolute error = 5.422e-06
relative error = 0.008349 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.924
Order of pole (given) = 3 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) = 3.258e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4985 1.776
h = 0.0001 0.003
y[1] (numeric) = 0.0383289231799 0.0523402678029
y[1] (closed_form) = 0.0383243040754 0.0523429456701
absolute error = 5.339e-06
relative error = 0.00823 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.926
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.357
Order of pole (three term test) = 4.735e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4986 1.779
h = 0.001 0.001
y[1] (numeric) = 0.0382316734041 0.0523593945402
y[1] (closed_form) = 0.0382270336735 0.0523621452506
absolute error = 5.394e-06
relative error = 0.00832 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.927
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.85
Order of pole (three term test) = 4.507e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4996 1.78
h = 0.001 0.003
y[1] (numeric) = 0.0382043338245 0.0523972148133
y[1] (closed_form) = 0.03819969611 0.0524000045698
absolute error = 5.412e-06
relative error = 0.008346 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.927
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.781
Order of pole (three term test) = 1.431e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5006 1.783
h = 0.0001 0.004
y[1] (numeric) = 0.038111718737 0.0524455169713
y[1] (closed_form) = 0.0381070802815 0.0524482269483
absolute error = 5.372e-06
relative error = 0.008286 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.927
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.969
Order of pole (three term test) = 1.442e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5007 1.787
h = 0.003 0.006
y[1] (numeric) = 0.0379818008989 0.0524692792804
y[1] (closed_form) = 0.0379772203871 0.0524719540054
absolute error = 5.304e-06
relative error = 0.008189 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.929
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.587
Order of pole (three term test) = 1.296e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5037 1.793
h = 0.0001 0.005
y[1] (numeric) = 0.0378014794681 0.0525970937745
y[1] (closed_form) = 0.0377966327791 0.0525996361561
absolute error = 5.473e-06
relative error = 0.00845 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.929
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.929
Order of pole (three term test) = 2.714e-27 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1181.7MB, alloc=44.3MB, time=14.81
x[1] = 2.5038 1.798
h = 0.0001 0.003
y[1] (numeric) = 0.03763889181 0.0526244445875
y[1] (closed_form) = 0.0376341998132 0.0526271022633
absolute error = 5.392e-06
relative error = 0.008335 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.931
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.36
Order of pole (three term test) = 3.118e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5039 1.801
h = 0.001 0.001
y[1] (numeric) = 0.037541728392 0.0526418648269
y[1] (closed_form) = 0.0375370142629 0.0526445944765
absolute error = 5.447e-06
relative error = 0.008425 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.933
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.853
Order of pole (three term test) = 2.968e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5049 1.802
h = 0.0001 0.004
y[1] (numeric) = 0.0375138708409 0.0526790697132
y[1] (closed_form) = 0.0375091578473 0.0526818382336
absolute error = 5.466e-06
relative error = 0.008452 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.932
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.13
Order of pole (three term test) = 7.304e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.505 1.806
h = 0.003 0.006
y[1] (numeric) = 0.0373840746623 0.0527009732621
y[1] (closed_form) = 0.0373794506057 0.0527036121941
absolute error = 5.324e-06
relative error = 0.00824 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.934
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.596
Order of pole (three term test) = 1.024e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.508 1.812
h = 0.0001 0.005
y[1] (numeric) = 0.0372026075193 0.0528257158566
y[1] (closed_form) = 0.0371977211769 0.0528282180425
absolute error = 5.490e-06
relative error = 0.008497 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.934
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.933
Order of pole (three term test) = 1.492e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5081 1.817
h = 0.0001 0.003
y[1] (numeric) = 0.0370402520557 0.0528506316476
y[1] (closed_form) = 0.0370355174072 0.0528532514841
absolute error = 5.411e-06
relative error = 0.008384 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.936
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.363
Order of pole (three term test) = 5.118e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5082 1.82
h = 0.001 0.001
y[1] (numeric) = 0.0369432131267 0.0528665938975
y[1] (closed_form) = 0.0369384550885 0.0528692849135
absolute error = 5.466e-06
relative error = 0.008476 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.938
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.855
Order of pole (three term test) = 4.872e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5092 1.821
h = 0.001 0.003
y[1] (numeric) = 0.0369149304956 0.0529032567452
y[1] (closed_form) = 0.0369101728462 0.0529059864523
absolute error = 5.485e-06
relative error = 0.008503 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.937
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.804
Order of pole (three term test) = 4.293e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5102 1.824
h = 0.0001 0.004
y[1] (numeric) = 0.0368215879795 0.0529482962338
y[1] (closed_form) = 0.0368168328766 0.052950947027
absolute error = 5.444e-06
relative error = 0.008441 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.938
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.982
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5103 1.828
h = 0.003 0.006
y[1] (numeric) = 0.0366920140204 0.0529678469874
y[1] (closed_form) = 0.0366873176564 0.052970465306
absolute error = 5.377e-06
relative error = 0.008345 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.939
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.605
Order of pole (three term test) = 1.011e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5133 1.834
h = 0.0001 0.005
y[1] (numeric) = 0.0365092474936 0.0530890307582
y[1] (closed_form) = 0.0365042933959 0.0530915073047
absolute error = 5.539e-06
relative error = 0.008596 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.94
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.937
Order of pole (three term test) = 2.280e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5134 1.839
h = 0.0001 0.003
y[1] (numeric) = 0.0363471797436 0.0531111347807
y[1] (closed_form) = 0.0363423738473 0.0531137316548
absolute error = 5.463e-06
relative error = 0.008488 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.942
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.366
Order of pole (three term test) = 8.606e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5135 1.842
h = 0.001 0.001
y[1] (numeric) = 0.0362502962467 0.053125413364
y[1] (closed_form) = 0.0362454655207 0.0531280804837
absolute error = 5.518e-06
relative error = 0.00858 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.943
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.858
Order of pole (three term test) = 5.082e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5145 1.843
h = 0.001 0.003
y[1] (numeric) = 0.0362215267591 0.0531614465348
y[1] (closed_form) = 0.0362166955627 0.0531641521278
absolute error = 5.537e-06
relative error = 0.008608 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.943
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.816
Order of pole (three term test) = 4.478e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5155 1.846
h = 0.0001 0.004
y[1] (numeric) = 0.0361278409557 0.0532047373001
y[1] (closed_form) = 0.0361230140386 0.0532073644981
absolute error = 5.496e-06
relative error = 0.008545 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.943
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.989
Order of pole (three term test) = 8.132e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5156 1.85
h = 0.003 0.006
y[1] (numeric) = 0.0359985075258 0.0532220482668
y[1] (closed_form) = 0.035993739721 0.0532246444813
absolute error = 5.429e-06
relative error = 0.008449 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.945
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.614
Order of pole (three term test) = 1.463e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5186 1.856
h = 0.0001 0.005
y[1] (numeric) = 0.03581452803 0.0533396652082
y[1] (closed_form) = 0.0358095071489 0.0533421147874
absolute error = 5.587e-06
relative error = 0.008695 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.945
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.941
Order of pole (three term test) = 7.663e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5187 1.861
h = 0.0001 0.003
y[1] (numeric) = 0.0356528085567 0.0533589803802
y[1] (closed_form) = 0.0356479323364 0.0533615528478
absolute error = 5.513e-06
relative error = 0.008591 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.948
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.369
Order of pole (three term test) = 7.804e-28 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1227.7MB, alloc=44.3MB, time=15.38
x[1] = 2.5188 1.864
h = 0.001 0.001
y[1] (numeric) = 0.0355561168142 0.0533715886662
y[1] (closed_form) = 0.0355512143607 0.0533742304126
absolute error = 5.569e-06
relative error = 0.008684 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.949
Order of pole (given) = 3 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) = 1.678e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5198 1.865
h = 0.001 0.003
y[1] (numeric) = 0.0355268772683 0.0534069851155
y[1] (closed_form) = 0.0355219734979 0.0534096650953
absolute error = 5.588e-06
relative error = 0.008712 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.948
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.829
Order of pole (three term test) = 6.902e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5208 1.868
h = 0.0001 0.004
y[1] (numeric) = 0.035432888883 0.053448529906
y[1] (closed_form) = 0.0354279910972 0.0534511320537
absolute error = 5.546e-06
relative error = 0.008649 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.949
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.997
Order of pole (three term test) = 8.491e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5209 1.872
h = 0.003 0.006
y[1] (numeric) = 0.0353038440646 0.0534636196937
y[1] (closed_form) = 0.0352990057206 0.053466192348
absolute error = 5.480e-06
relative error = 0.008553 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.951
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.624
Order of pole (three term test) = 1.080e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5239 1.878
h = 0.0001 0.005
y[1] (numeric) = 0.0351187375927 0.0535776642451
y[1] (closed_form) = 0.0351136509287 0.053580085566
absolute error = 5.634e-06
relative error = 0.008794 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.951
Order of pole (given) = 3 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) = 1.790e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.524 1.883
h = 0.0001 0.003
y[1] (numeric) = 0.0349574258726 0.0535942149841
y[1] (closed_form) = 0.0349524802853 0.0535967616371
absolute error = 5.563e-06
relative error = 0.008694 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.953
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.373
Order of pole (three term test) = 1.841e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5241 1.886
h = 0.001 0.001
y[1] (numeric) = 0.034860961565 0.0536051672429
y[1] (closed_form) = 0.0348559883783 0.0536077821767
absolute error = 5.619e-06
relative error = 0.008787 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.955
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.863
Order of pole (three term test) = 6.507e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5251 1.887
h = 0.001 0.003
y[1] (numeric) = 0.0348312688271 0.0536399204417
y[1] (closed_form) = 0.0348262934898 0.0536425733476
absolute error = 5.638e-06
relative error = 0.008816 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.954
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.842
Order of pole (three term test) = 6.907e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5261 1.89
h = 0.0001 0.004
y[1] (numeric) = 0.0347370181827 0.0536797231073
y[1] (closed_form) = 0.0347320505071 0.0536822987865
absolute error = 5.596e-06
relative error = 0.008752 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.955
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.004
Order of pole (three term test) = 1.255e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5262 1.894
h = 0.003 0.006
y[1] (numeric) = 0.034608309182 0.0536926115078
y[1] (closed_form) = 0.0346034012341 0.0536951591816
absolute error = 5.530e-06
relative error = 0.008657 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.957
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.633
Order of pole (three term test) = 1.129e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5292 1.9
h = 0.0001 0.005
y[1] (numeric) = 0.0344221612281 0.0538030805177
y[1] (closed_form) = 0.0344170098093 0.0538054723265
absolute error = 5.680e-06
relative error = 0.008892 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.957
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.95
Order of pole (three term test) = 1.183e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5293 1.905
h = 0.0001 0.003
y[1] (numeric) = 0.0342613156118 0.0538168926908
y[1] (closed_form) = 0.0342563016458 0.0538194121584
absolute error = 5.611e-06
relative error = 0.008796 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.959
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.376
Order of pole (three term test) = 6.086e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5294 1.908
h = 0.001 0.001
y[1] (numeric) = 0.0341651137545 0.0538262040638
y[1] (closed_form) = 0.0341600708609 0.0538287907843
absolute error = 5.668e-06
relative error = 0.00889 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.96
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.866
Order of pole (three term test) = 1.296e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5304 1.909
h = 0.0001 0.004
y[1] (numeric) = 0.0341349847407 0.0538603079969
y[1] (closed_form) = 0.0341299388765 0.0538629324073
absolute error = 5.688e-06
relative error = 0.008919 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.96
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.2
Order of pole (three term test) = 4.512e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5305 1.913
h = 0.003 0.006
y[1] (numeric) = 0.0340065881924 0.0538714122058
y[1] (closed_form) = 0.0340016418485 0.0538739206741
absolute error = 5.546e-06
relative error = 0.008706 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.962
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.642
Order of pole (three term test) = 1.314e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5335 1.919
h = 0.0001 0.005
y[1] (numeric) = 0.0338196543898 0.053978791765
y[1] (closed_form) = 0.0338144688694 0.0539811406614
absolute error = 5.693e-06
relative error = 0.008937 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.962
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.954
Order of pole (three term test) = 1.233e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5336 1.924
h = 0.0001 0.003
y[1] (numeric) = 0.0336592879945 0.0539902749315
y[1] (closed_form) = 0.0336542367536 0.0539927533516
absolute error = 5.627e-06
relative error = 0.008844 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.965
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.38
Order of pole (three term test) = 1.203e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5337 1.927
h = 0.001 0.001
y[1] (numeric) = 0.0335633588455 0.0539981903337
y[1] (closed_form) = 0.0335582775772 0.0540007350841
absolute error = 5.683e-06
relative error = 0.008938 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.966
Order of pole (given) = 3 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) = 3.819e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5347 1.928
h = 0.001 0.003
y[1] (numeric) = 0.0335328756936 0.0540317260512
y[1] (closed_form) = 0.0335277907638 0.0540343082228
absolute error = 5.703e-06
relative error = 0.008968 %
Correct digits = 4
memory used=1273.8MB, alloc=44.3MB, time=15.96
Radius of convergence (given) for eq 1 = 3.966
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.867
Order of pole (three term test) = 2.027e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5357 1.931
h = 0.0001 0.004
y[1] (numeric) = 0.0334382635159 0.0540682989413
y[1] (closed_form) = 0.0334331892804 0.054070805141
absolute error = 5.659e-06
relative error = 0.008902 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.966
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.018
Order of pole (three term test) = 4.836e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5358 1.935
h = 0.003 0.006
y[1] (numeric) = 0.0333103275201 0.0540771529242
y[1] (closed_form) = 0.0333053134127 0.0540796338783
absolute error = 5.594e-06
relative error = 0.008808 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.968
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.652
Order of pole (three term test) = 3.691e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5388 1.941
h = 0.0001 0.005
y[1] (numeric) = 0.0331225097101 0.0541809583556
y[1] (closed_form) = 0.0331172614289 0.0541832755213
absolute error = 5.737e-06
relative error = 0.009034 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.968
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.958
Order of pole (three term test) = 2.041e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5389 1.946
h = 0.0001 0.003
y[1] (numeric) = 0.032962714526 0.0541897554355
y[1] (closed_form) = 0.0329575968396 0.0541922042323
absolute error = 5.673e-06
relative error = 0.008945 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.971
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.383
Order of pole (three term test) = 1.260e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.539 1.949
h = 0.001 0.001
y[1] (numeric) = 0.0328671109326 0.0541960607397
y[1] (closed_form) = 0.0328619619631 0.0541985747882
absolute error = 5.730e-06
relative error = 0.00904 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.972
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.871
Order of pole (three term test) = 6.325e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.54 1.95
h = 0.001 0.003
y[1] (numeric) = 0.0328362231134 0.0542289375555
y[1] (closed_form) = 0.0328310696894 0.0542314887061
absolute error = 5.750e-06
relative error = 0.009071 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.972
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.881
Order of pole (three term test) = 5.575e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.541 1.953
h = 0.0001 0.004
y[1] (numeric) = 0.0327414615433 0.05426378567
y[1] (closed_form) = 0.0327363204026 0.0542662615683
absolute error = 5.706e-06
relative error = 0.009004 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.972
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.026
Order of pole (three term test) = 5.065e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5411 1.957
h = 0.003 0.006
y[1] (numeric) = 0.0326139910245 0.0542705015889
y[1] (closed_form) = 0.0326089101764 0.0542729537148
absolute error = 5.642e-06
relative error = 0.00891 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.974
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.663
Order of pole (three term test) = 1.289e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5441 1.963
h = 0.0001 0.005
y[1] (numeric) = 0.0324253728428 0.0543707364016
y[1] (closed_form) = 0.0324200628979 0.0543730206927
absolute error = 5.780e-06
relative error = 0.009131 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.974
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.963
Order of pole (three term test) = 2.183e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5442 1.968
h = 0.0001 0.003
y[1] (numeric) = 0.0322662037861 0.0543768771123
y[1] (closed_form) = 0.032261020724 0.0543792950248
absolute error = 5.719e-06
relative error = 0.009045 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.977
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.387
Order of pole (three term test) = 6.959e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5443 1.971
h = 0.001 0.001
y[1] (numeric) = 0.0321709587324 0.0543815897763
y[1] (closed_form) = 0.0321657431709 0.0543840718363
absolute error = 5.776e-06
relative error = 0.009142 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.978
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.874
Order of pole (three term test) = 9.376e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5453 1.972
h = 0.001 0.003
y[1] (numeric) = 0.0321396832047 0.054413803124
y[1] (closed_form) = 0.0321344624108 0.0544163219481
absolute error = 5.797e-06
relative error = 0.009172 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.978
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.895
Order of pole (three term test) = 1.307e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5463 1.975
h = 0.0001 0.004
y[1] (numeric) = 0.0320448107803 0.054446934336
y[1] (closed_form) = 0.0320396038263 0.0544493786648
absolute error = 5.752e-06
relative error = 0.009105 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.979
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.034
Order of pole (three term test) = 2.443e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5464 1.979
h = 0.003 0.006
y[1] (numeric) = 0.031917849277 0.0544515361619
y[1] (closed_form) = 0.0319127027386 0.0544539581838
absolute error = 5.688e-06
relative error = 0.009012 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.98
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.673
Order of pole (three term test) = 9.191e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5494 1.985
h = 0.0001 0.005
y[1] (numeric) = 0.0317285135855 0.0545482061107
y[1] (closed_form) = 0.0317231430957 0.0545504564223
absolute error = 5.823e-06
relative error = 0.009227 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.981
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.968
Order of pole (three term test) = 3.009e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5495 1.99
h = 0.0001 0.003
y[1] (numeric) = 0.0315700243167 0.0545517214195
y[1] (closed_form) = 0.0315647769741 0.0545541072257
absolute error = 5.764e-06
relative error = 0.009146 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.983
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.391
Order of pole (three term test) = 1.177e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5496 1.993
h = 0.001 0.001
y[1] (numeric) = 0.0314751700426 0.0545548596535
y[1] (closed_form) = 0.0314698890244 0.0545573084793
absolute error = 5.821e-06
relative error = 0.009242 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.985
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.877
Order of pole (three term test) = 6.221e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5506 1.994
h = 0.001 0.003
y[1] (numeric) = 0.0314435237503 0.0545864054645
y[1] (closed_form) = 0.0314382367374 0.054588890698
absolute error = 5.842e-06
relative error = 0.009274 %
Correct digits = 4
memory used=1319.8MB, alloc=44.3MB, time=16.54
Radius of convergence (given) for eq 1 = 3.984
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.909
Order of pole (three term test) = 6.130e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5516 1.997
h = 0.0001 0.004
y[1] (numeric) = 0.0313485784801 0.0546178286285
y[1] (closed_form) = 0.0313433068303 0.0546202401597
absolute error = 5.797e-06
relative error = 0.009205 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.985
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.042
Order of pole (three term test) = 1.246e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5517 2.001
h = 0.003 0.006
y[1] (numeric) = 0.0312221685224 0.0546203413163
y[1] (closed_form) = 0.0312169573705 0.0546227319973
absolute error = 5.733e-06
relative error = 0.009113 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.987
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.684
Order of pole (three term test) = 2.962e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5547 2.007
h = 0.0001 0.005
y[1] (numeric) = 0.031032197344 0.054713454354
y[1] (closed_form) = 0.0310267674482 0.0547156696207
absolute error = 5.864e-06
relative error = 0.009323 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.987
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.973
Order of pole (three term test) = 2.106e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5548 2.012
h = 0.0001 0.003
y[1] (numeric) = 0.0308744402392 0.0547143764246
y[1] (closed_form) = 0.0308691297357 0.0547167289424
absolute error = 5.808e-06
relative error = 0.009245 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.99
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.395
Order of pole (three term test) = 3.427e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5549 2.015
h = 0.001 0.001
y[1] (numeric) = 0.0307800082242 0.0547159591599
y[1] (closed_form) = 0.030774662909 0.054718373547
absolute error = 5.865e-06
relative error = 0.009343 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.991
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.88
Order of pole (three term test) = 9.797e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5559 2.016
h = 0.0001 0.004
y[1] (numeric) = 0.03074800808 0.0547468338575
y[1] (closed_form) = 0.0307426560239 0.0547492842784
absolute error = 5.886e-06
relative error = 0.009375 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.991
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.29
Order of pole (three term test) = 9.295e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.556 2.02
h = 0.003 0.006
y[1] (numeric) = 0.0306220832544 0.0547476581714
y[1] (closed_form) = 0.0306168390726 0.0547500070449
absolute error = 5.746e-06
relative error = 0.00916 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.993
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.694
Order of pole (three term test) = 1.482e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.559 2.026
h = 0.0001 0.005
y[1] (numeric) = 0.0304316722657 0.0548377112921
y[1] (closed_form) = 0.0304262139086 0.0548398817634
absolute error = 5.874e-06
relative error = 0.009366 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.993
Order of pole (given) = 3 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) = 1.719e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5591 2.031
h = 0.0001 0.003
y[1] (numeric) = 0.0302746166731 0.0548364373655
y[1] (closed_form) = 0.0302692744446 0.0548387464618
absolute error = 5.820e-06
relative error = 0.009291 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.996
Order of pole (given) = 3 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) = 8.011e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5592 2.034
h = 0.001 0.001
y[1] (numeric) = 0.0301805909492 0.0548367023916
y[1] (closed_form) = 0.0301752129779 0.0548390723376
absolute error = 5.877e-06
relative error = 0.009389 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.997
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.883
Order of pole (three term test) = 1.080e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5602 2.035
h = 0.001 0.003
y[1] (numeric) = 0.0301483077724 0.0548669929825
y[1] (closed_form) = 0.0301429224357 0.0548693986183
absolute error = 5.898e-06
relative error = 0.009421 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.997
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.937
Order of pole (three term test) = 1.064e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5612 2.038
h = 0.0001 0.004
y[1] (numeric) = 0.0300533462435 0.0548952648583
y[1] (closed_form) = 0.0300479790021 0.0548975983749
absolute error = 5.853e-06
relative error = 0.009352 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.997
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.058
Order of pole (three term test) = 1.101e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5613 2.042
h = 0.003 0.006
y[1] (numeric) = 0.0299280963772 0.0548939674758
y[1] (closed_form) = 0.029922789664 0.0548962828251
absolute error = 5.790e-06
relative error = 0.00926 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.999
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.705
Order of pole (three term test) = 1.817e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5643 2.048
h = 0.0001 0.005
y[1] (numeric) = 0.0297371999265 0.0549804851152
y[1] (closed_form) = 0.0297316843423 0.0549826186784
absolute error = 5.914e-06
relative error = 0.009461 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.982
Order of pole (three term test) = 1.180e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5644 2.053
h = 0.0001 0.003
y[1] (numeric) = 0.0295809700389 0.0549766813863
y[1] (closed_form) = 0.0295755668043 0.0549789551154
absolute error = 5.862e-06
relative error = 0.00939 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.002
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.402
Order of pole (three term test) = 1.584e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5645 2.056
h = 0.001 0.001
y[1] (numeric) = 0.0294874228282 0.0549754283023
y[1] (closed_form) = 0.0294819827908 0.0549777616938
absolute error = 5.919e-06
relative error = 0.009489 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.004
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.886
Order of pole (three term test) = 8.027e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5655 2.057
h = 0.001 0.003
y[1] (numeric) = 0.0294548171637 0.0550050426134
y[1] (closed_form) = 0.0294493690456 0.0550074112901
absolute error = 5.941e-06
relative error = 0.009521 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.003
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.952
Order of pole (three term test) = 6.408e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5665 2.06
h = 0.0001 0.004
y[1] (numeric) = 0.0293598882228 0.0550316373771
y[1] (closed_form) = 0.029354459623 0.0550339348219
absolute error = 5.895e-06
relative error = 0.009451 %
Correct digits = 4
memory used=1365.7MB, alloc=44.3MB, time=17.11
Radius of convergence (given) for eq 1 = 4.004
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.066
Order of pole (three term test) = 1.501e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5666 2.064
h = 0.003 0.006
y[1] (numeric) = 0.0292353054825 0.0550283277624
y[1] (closed_form) = 0.0292299373809 0.0550306084643
absolute error = 5.833e-06
relative error = 0.00936 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.006
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.716
Order of pole (three term test) = 1.711e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5696 2.07
h = 0.0001 0.005
y[1] (numeric) = 0.0290440028302 0.0551113238717
y[1] (closed_form) = 0.0290384312067 0.0551134195751
absolute error = 5.953e-06
relative error = 0.009556 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.007
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.987
Order of pole (three term test) = 3.652e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5697 2.075
h = 0.0001 0.003
y[1] (numeric) = 0.0288886472037 0.0551050256129
y[1] (closed_form) = 0.0288831841424 0.0551072629085
absolute error = 5.903e-06
relative error = 0.009488 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.009
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.406
Order of pole (three term test) = 1.587e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5698 2.078
h = 0.001 0.001
y[1] (numeric) = 0.0287956077203 0.0551022752257
y[1] (closed_form) = 0.0287901068373 0.0551045709785
absolute error = 5.961e-06
relative error = 0.009587 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.011
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.89
Order of pole (three term test) = 1.269e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5708 2.079
h = 0.001 0.003
y[1] (numeric) = 0.0287626963017 0.0551312110524
y[1] (closed_form) = 0.02875718664 0.0551335416702
absolute error = 5.982e-06
relative error = 0.009621 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.01
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.967
Order of pole (three term test) = 1.581e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5718 2.082
h = 0.0001 0.004
y[1] (numeric) = 0.0286678356648 0.0551561410812
y[1] (closed_form) = 0.0286623469081 0.0551584013846
absolute error = 5.936e-06
relative error = 0.009549 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.011
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.075
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5719 2.086
h = 0.003 0.006
y[1] (numeric) = 0.0285439584903 0.0551508475729
y[1] (closed_form) = 0.028538530164 0.0551530925444
absolute error = 5.874e-06
relative error = 0.009459 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.013
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.728
Order of pole (three term test) = 3.449e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5749 2.092
h = 0.0001 0.005
y[1] (numeric) = 0.0283523278305 0.055230338101
y[1] (closed_form) = 0.0283467013698 0.0552323950328
absolute error = 5.991e-06
relative error = 0.00965 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.013
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.992
Order of pole (three term test) = 1.288e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.575 2.097
h = 0.0001 0.003
y[1] (numeric) = 0.0281978936509 0.0552215815724
y[1] (closed_form) = 0.0281923719606 0.055223781409
absolute error = 5.944e-06
relative error = 0.009586 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.016
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.41
Order of pole (three term test) = 1.320e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5751 2.1
h = 0.001 0.001
y[1] (numeric) = 0.0281053902958 0.0552173552855
y[1] (closed_form) = 0.0280998298062 0.0552196123576
absolute error = 6.001e-06
relative error = 0.009686 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.017
Order of pole (given) = 3 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) = 5.797e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5761 2.101
h = 0.001 0.003
y[1] (numeric) = 0.0280721897681 0.0552456108893
y[1] (closed_form) = 0.028066619819 0.0552479023914
absolute error = 6.023e-06
relative error = 0.009719 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.017
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.983
Order of pole (three term test) = 1.111e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5771 2.104
h = 0.0001 0.004
y[1] (numeric) = 0.0279774325053 0.0552688894044
y[1] (closed_form) = 0.0279718848111 0.0552711115383
absolute error = 5.976e-06
relative error = 0.009647 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.018
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.084
Order of pole (three term test) = 5.706e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5772 2.108
h = 0.003 0.006
y[1] (numeric) = 0.02785429824 0.0552616411157
y[1] (closed_form) = 0.0278488108715 0.0552638493144
absolute error = 5.915e-06
relative error = 0.009558 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.02
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.739
Order of pole (three term test) = 7.490e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5802 2.114
h = 0.0001 0.005
y[1] (numeric) = 0.027662416648 0.0553376439542
y[1] (closed_form) = 0.0276567365652 0.0553396612425
absolute error = 6.028e-06
relative error = 0.009743 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.02
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.997
Order of pole (three term test) = 1.910e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5803 2.119
h = 0.0001 0.003
y[1] (numeric) = 0.0275089497139 0.0553264663487
y[1] (closed_form) = 0.0275033706089 0.0553286277418
absolute error = 5.983e-06
relative error = 0.009683 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.023
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.415
Order of pole (three term test) = 4.398e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5804 2.122
h = 0.001 0.001
y[1] (numeric) = 0.0274170100648 0.0553207861298
y[1] (closed_form) = 0.0274113912241 0.0553230035219
absolute error = 6.041e-06
relative error = 0.009784 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.024
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.896
Order of pole (three term test) = 1.024e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5814 2.123
h = 0.0001 0.004
y[1] (numeric) = 0.0273835369702 0.0553483602305
y[1] (closed_form) = 0.0273779080069 0.0553506116033
absolute error = 6.063e-06
relative error = 0.009818 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.024
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.39
Order of pole (three term test) = 1.460e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5815 2.127
h = 0.003 0.006
y[1] (numeric) = 0.0272610402102 0.055339536676
y[1] (closed_form) = 0.0272555252599 0.0553417012642
absolute error = 5.925e-06
relative error = 0.009604 %
Correct digits = 4
memory used=1411.8MB, alloc=44.3MB, time=17.68
Radius of convergence (given) for eq 1 = 4.026
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.75
Order of pole (three term test) = 8.518e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5845 2.133
h = 0.0001 0.005
y[1] (numeric) = 0.0270690446727 0.0554125514346
y[1] (closed_form) = 0.0270633417269 0.0554145228424
absolute error = 6.034e-06
relative error = 0.009784 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.027
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.002
Order of pole (three term test) = 1.478e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5846 2.138
h = 0.0001 0.003
y[1] (numeric) = 0.0269164741363 0.0553993325404
y[1] (closed_form) = 0.0269108688934 0.0554014489515
absolute error = 5.991e-06
relative error = 0.009728 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.029
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.418
Order of pole (three term test) = 1.031e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5847 2.141
h = 0.001 0.001
y[1] (numeric) = 0.026825058108 0.0553924259698
y[1] (closed_form) = 0.0268194123712 0.0553945972941
absolute error = 6.049e-06
relative error = 0.009828 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.031
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.899
Order of pole (three term test) = 4.398e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5857 2.142
h = 0.001 0.003
y[1] (numeric) = 0.0267913716854 0.055419409793
y[1] (closed_form) = 0.0267857152752 0.055421614693
absolute error = 6.071e-06
relative error = 0.009863 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.031
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.013
Order of pole (three term test) = 1.226e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5867 2.145
h = 0.0001 0.004
y[1] (numeric) = 0.026696917087 0.0554396553687
y[1] (closed_form) = 0.0266912853322 0.0554417927478
absolute error = 6.024e-06
relative error = 0.00979 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.031
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.101
Order of pole (three term test) = 1.577e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5868 2.149
h = 0.003 0.006
y[1] (numeric) = 0.0265752832187 0.0554288594958
y[1] (closed_form) = 0.0265697114831 0.0554309854945
absolute error = 5.964e-06
relative error = 0.009702 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.033
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.762
Order of pole (three term test) = 8.284e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5898 2.155
h = 0.0001 0.005
y[1] (numeric) = 0.0263831767559 0.0554984257167
y[1] (closed_form) = 0.0263774224885 0.0555003559796
absolute error = 6.069e-06
relative error = 0.009877 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.034
Order of pole (given) = 3 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) = 4.483e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5899 2.16
h = 0.0001 0.003
y[1] (numeric) = 0.0262316544787 0.0554828577564
y[1] (closed_form) = 0.0262259941308 0.0554849340164
absolute error = 6.029e-06
relative error = 0.009824 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.037
Order of pole (given) = 3 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) = 9.736e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.59 2.163
h = 0.001 0.001
y[1] (numeric) = 0.0261408509749 0.0554745398266
y[1] (closed_form) = 0.0261351492736 0.0554766697398
absolute error = 6.087e-06
relative error = 0.009925 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.038
Order of pole (given) = 3 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) = 4.641e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.591 2.164
h = 0.001 0.003
y[1] (numeric) = 0.0261069224499 0.055500841149
y[1] (closed_form) = 0.0261012094459 0.0555030041644
absolute error = 6.109e-06
relative error = 0.00996 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.038
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.029
Order of pole (three term test) = 1.447e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.592 2.167
h = 0.0001 0.004
y[1] (numeric) = 0.0260126676244 0.0555194778185
y[1] (closed_form) = 0.0260069805174 0.055521574333
absolute error = 6.061e-06
relative error = 0.009886 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.039
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.11
Order of pole (three term test) = 1.665e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5921 2.171
h = 0.003 0.006
y[1] (numeric) = 0.025891876959 0.0555068147412
y[1] (closed_form) = 0.0258862496659 0.0555089012249
absolute error = 6.002e-06
relative error = 0.009799 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.041
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.774
Order of pole (three term test) = 7.648e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5951 2.177
h = 0.0001 0.005
y[1] (numeric) = 0.0256997331584 0.0555729555415
y[1] (closed_form) = 0.0256939288137 0.0555748439015
absolute error = 6.104e-06
relative error = 0.009969 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.041
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.013
Order of pole (three term test) = 1.699e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5952 2.182
h = 0.0001 0.003
y[1] (numeric) = 0.0255493008886 0.0555550780609
y[1] (closed_form) = 0.0255435866893 0.0555571133031
absolute error = 6.066e-06
relative error = 0.00992 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.044
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.427
Order of pole (three term test) = 1.854e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5953 2.185
h = 0.001 0.001
y[1] (numeric) = 0.0254591350809 0.0555453721655
y[1] (closed_form) = 0.0254533787098 0.05554745979
absolute error = 6.123e-06
relative error = 0.01002 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.046
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.906
Order of pole (three term test) = 1.471e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5963 2.186
h = 0.001 0.003
y[1] (numeric) = 0.0254249806241 0.0555709909689
y[1] (closed_form) = 0.0254192123393 0.0555731112102
absolute error = 6.146e-06
relative error = 0.01006 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.045
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.045
Order of pole (three term test) = 6.836e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5973 2.189
h = 0.0001 0.004
y[1] (numeric) = 0.0253309579638 0.0555880349222
y[1] (closed_form) = 0.0253252167794 0.0555900897056
absolute error = 6.098e-06
relative error = 0.009982 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.046
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.119
Order of pole (three term test) = 1.760e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5974 2.193
h = 0.003 0.006
y[1] (numeric) = 0.0252110434995 0.055573536325
y[1] (closed_form) = 0.0252053618899 0.0555755824092
absolute error = 6.039e-06
relative error = 0.009896 %
Correct digits = 4
memory used=1457.7MB, alloc=44.3MB, time=18.26
Radius of convergence (given) for eq 1 = 4.048
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.787
Order of pole (three term test) = 6.723e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6004 2.199
h = 0.0001 0.005
y[1] (numeric) = 0.025018934653 0.0556362765395
y[1] (closed_form) = 0.0250130814831 0.0556381222783
absolute error = 6.137e-06
relative error = 0.01006 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.049
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.018
Order of pole (three term test) = 3.351e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6005 2.204
h = 0.0001 0.003
y[1] (numeric) = 0.0248696327079 0.0556161298089
y[1] (closed_form) = 0.0248638659218 0.0556181232077
absolute error = 6.102e-06
relative error = 0.01002 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.051
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.432
Order of pole (three term test) = 1.215e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6006 2.207
h = 0.001 0.001
y[1] (numeric) = 0.0247801289173 0.0556050597815
y[1] (closed_form) = 0.0247743191821 0.0556071042823
absolute error = 6.159e-06
relative error = 0.01012 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.053
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.91
Order of pole (three term test) = 5.181e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6016 2.208
h = 0.001 0.003
y[1] (numeric) = 0.0247457645473 0.055629996472
y[1] (closed_form) = 0.0247399423059 0.0556320730928
absolute error = 6.181e-06
relative error = 0.01015 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.053
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.062
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6026 2.211
h = 0.0001 0.004
y[1] (numeric) = 0.0246520057147 0.0556454645959
y[1] (closed_form) = 0.0246462117383 0.0556474768234
absolute error = 6.133e-06
relative error = 0.01008 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.053
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.129
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6027 2.215
h = 0.003 0.006
y[1] (numeric) = 0.0245329993073 0.0556291627285
y[1] (closed_form) = 0.0245272646342 0.0556311675693
absolute error = 6.075e-06
relative error = 0.009992 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.056
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.799
Order of pole (three term test) = 1.920e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6057 2.221
h = 0.0001 0.005
y[1] (numeric) = 0.0243409963723 0.0556885288494
y[1] (closed_form) = 0.0243350956357 0.055690331288
absolute error = 6.170e-06
relative error = 0.01015 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.056
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.024
Order of pole (three term test) = 1.786e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6058 2.226
h = 0.0001 0.003
y[1] (numeric) = 0.0241928636317 0.0556661538103
y[1] (closed_form) = 0.0241870455332 0.055668104581
absolute error = 6.136e-06
relative error = 0.01011 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.059
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.436
Order of pole (three term test) = 2.072e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6059 2.229
h = 0.001 0.001
y[1] (numeric) = 0.0241040453248 0.0556537438926
y[1] (closed_form) = 0.0240981835405 0.0556557444771
absolute error = 6.194e-06
relative error = 0.01021 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.061
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.913
Order of pole (three term test) = 7.751e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6069 2.23
h = 0.0001 0.004
y[1] (numeric) = 0.0240694868967 0.0556779992909
y[1] (closed_form) = 0.0240636120323 0.0556800314877
absolute error = 6.216e-06
relative error = 0.01025 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.06
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.49
Order of pole (three term test) = 8.213e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.607 2.234
h = 0.003 0.006
y[1] (numeric) = 0.0239512487092 0.0556602484943
y[1] (closed_form) = 0.0239454918607 0.0556622086859
absolute error = 6.081e-06
relative error = 0.01004 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.062
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.811
Order of pole (three term test) = 5.572e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.61 2.24
h = 0.0001 0.005
y[1] (numeric) = 0.0237594324468 0.055716735129
y[1] (closed_form) = 0.0237535142887 0.0557184913439
absolute error = 6.173e-06
relative error = 0.01019 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.063
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.029
Order of pole (three term test) = 2.597e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6101 2.245
h = 0.0001 0.003
y[1] (numeric) = 0.0236123620202 0.0556924898256
y[1] (closed_form) = 0.0236065232846 0.0556943948235
absolute error = 6.142e-06
relative error = 0.01015 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.066
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.44
Order of pole (three term test) = 5.441e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6102 2.248
h = 0.001 0.001
y[1] (numeric) = 0.0235241674522 0.0556789548056
y[1] (closed_form) = 0.0235182844449 0.055680908495
absolute error = 6.199e-06
relative error = 0.01026 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.067
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.916
Order of pole (three term test) = 1.153e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6112 2.249
h = 0.001 0.003
y[1] (numeric) = 0.0234894626433 0.0557026226787
y[1] (closed_form) = 0.0234835660832 0.0557046075289
absolute error = 6.222e-06
relative error = 0.01029 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.067
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.094
Order of pole (three term test) = 1.679e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6122 2.252
h = 0.0001 0.004
y[1] (numeric) = 0.0233962947136 0.0557152097528
y[1] (closed_form) = 0.0233904284686 0.055717132256
absolute error = 6.173e-06
relative error = 0.01022 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.068
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.147
Order of pole (three term test) = 4.628e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6123 2.256
h = 0.003 0.006
y[1] (numeric) = 0.0232790793934 0.0556956516735
y[1] (closed_form) = 0.0232732718481 0.0556975691753
absolute error = 6.116e-06
relative error = 0.01013 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.07
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.824
Order of pole (three term test) = 1.319e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6153 2.262
h = 0.0001 0.005
y[1] (numeric) = 0.0230874970426 0.0557488185192
y[1] (closed_form) = 0.0230815336794 0.0557505302888
absolute error = 6.204e-06
relative error = 0.01028 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.071
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.035
Order of pole (three term test) = 3.928e-28 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1503.8MB, alloc=44.3MB, time=18.83
x[1] = 2.6154 2.267
h = 0.0001 0.003
y[1] (numeric) = 0.0229416638238 0.0557224231187
y[1] (closed_form) = 0.0229357761759 0.055724284152
absolute error = 6.175e-06
relative error = 0.01025 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.074
Order of pole (given) = 3 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) = 9.519e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6155 2.27
h = 0.001 0.001
y[1] (numeric) = 0.0228541958227 0.0557075945516
y[1] (closed_form) = 0.022848263242 0.0557095029773
absolute error = 6.232e-06
relative error = 0.01035 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.075
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.92
Order of pole (three term test) = 1.366e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6165 2.271
h = 0.001 0.003
y[1] (numeric) = 0.022819325965 0.0557305839121
y[1] (closed_form) = 0.0228133792927 0.0557325229733
absolute error = 6.255e-06
relative error = 0.01039 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.075
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.112
Order of pole (three term test) = 9.933e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6175 2.274
h = 0.0001 0.004
y[1] (numeric) = 0.0227265080688 0.0557416473843
y[1] (closed_form) = 0.0227205927642 0.0557435252163
absolute error = 6.206e-06
relative error = 0.01031 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.076
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.157
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6176 2.278
h = 0.003 0.006
y[1] (numeric) = 0.022610285192 0.0557203813721
y[1] (closed_form) = 0.0226044282282 0.0557222554566
absolute error = 6.149e-06
relative error = 0.01023 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.078
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.837
Order of pole (three term test) = 2.795e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6206 2.284
h = 0.0001 0.005
y[1] (numeric) = 0.022419003682 0.0557702593077
y[1] (closed_form) = 0.0224129963833 0.055771926064
absolute error = 6.234e-06
relative error = 0.01037 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.079
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.041
Order of pole (three term test) = 2.081e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6207 2.289
h = 0.0001 0.003
y[1] (numeric) = 0.0222744424157 0.0557417563657
y[1] (closed_form) = 0.0222685071495 0.0557435727655
absolute error = 6.207e-06
relative error = 0.01034 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.082
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.45
Order of pole (three term test) = 7.309e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6208 2.292
h = 0.001 0.001
y[1] (numeric) = 0.0221877219878 0.0557256594786
y[1] (closed_form) = 0.0221817411677 0.0557275219677
absolute error = 6.264e-06
relative error = 0.01044 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.083
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.924
Order of pole (three term test) = 7.236e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6218 2.293
h = 0.001 0.003
y[1] (numeric) = 0.0221527024049 0.0557479722751
y[1] (closed_form) = 0.0221467069734 0.0557498648657
absolute error = 6.287e-06
relative error = 0.01048 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.083
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.13
Order of pole (three term test) = 1.058e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6228 2.296
h = 0.0001 0.004
y[1] (numeric) = 0.0220602632646 0.0557575314228
y[1] (closed_form) = 0.022054300214 0.0557593639181
absolute error = 6.238e-06
relative error = 0.0104 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.084
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.167
Order of pole (three term test) = 2.324e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6229 2.3
h = 0.003 0.006
y[1] (numeric) = 0.0219450602437 0.0557345915034
y[1] (closed_form) = 0.0219391551462 0.0557364214833
absolute error = 6.182e-06
relative error = 0.01032 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.086
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.85
Order of pole (three term test) = 8.888e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6259 2.306
h = 0.0001 0.005
y[1] (numeric) = 0.0217541450438 0.0557812128278
y[1] (closed_form) = 0.0217480950805 0.0557828340403
absolute error = 6.263e-06
relative error = 0.01046 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.087
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.047
Order of pole (three term test) = 6.979e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.626 2.311
h = 0.0001 0.003
y[1] (numeric) = 0.0216108890317 0.0557506453706
y[1] (closed_form) = 0.0216049074453 0.0557524165083
absolute error = 6.238e-06
relative error = 0.01043 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.09
Order of pole (given) = 3 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) = 4.318e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6261 2.314
h = 0.001 0.001
y[1] (numeric) = 0.0215249363244 0.0557333056797
y[1] (closed_form) = 0.0215189086028 0.0557351216006
absolute error = 6.295e-06
relative error = 0.01054 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.091
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.928
Order of pole (three term test) = 4.805e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6271 2.315
h = 0.001 0.003
y[1] (numeric) = 0.0214897821369 0.0557549442354
y[1] (closed_form) = 0.0214837393029 0.0557567897158
absolute error = 6.318e-06
relative error = 0.01057 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.091
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.148
Order of pole (three term test) = 9.623e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6281 2.318
h = 0.0001 0.004
y[1] (numeric) = 0.0213977496918 0.0557630188827
y[1] (closed_form) = 0.0213917402126 0.0557648054163
absolute error = 6.269e-06
relative error = 0.0105 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.092
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.177
Order of pole (three term test) = 4.931e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6282 2.322
h = 0.003 0.006
y[1] (numeric) = 0.0212835927896 0.0557384394456
y[1] (closed_form) = 0.0212776408483 0.0557402246736
absolute error = 6.214e-06
relative error = 0.01041 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.094
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.864
Order of pole (three term test) = 9.429e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6312 2.328
h = 0.0001 0.005
y[1] (numeric) = 0.0210931078827 0.0557818378153
y[1] (closed_form) = 0.0210870165264 0.0557834129915
absolute error = 6.292e-06
relative error = 0.01055 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.095
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.053
Order of pole (three term test) = 2.001e-27 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1549.7MB, alloc=44.3MB, time=19.41
x[1] = 2.6313 2.333
h = 0.0001 0.003
y[1] (numeric) = 0.0209511889866 0.0557492492905
y[1] (closed_form) = 0.0209451623815 0.0557509745769
absolute error = 6.269e-06
relative error = 0.01053 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.098
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.459
Order of pole (three term test) = 3.055e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6314 2.336
h = 0.001 0.001
y[1] (numeric) = 0.0208660232899 0.055730692571
y[1] (closed_form) = 0.0208599500075 0.055732461333
absolute error = 6.326e-06
relative error = 0.01063 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.099
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.931
Order of pole (three term test) = 7.322e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6324 2.337
h = 0.0001 0.004
y[1] (numeric) = 0.0208307494063 0.055751659573
y[1] (closed_form) = 0.0208246605294 0.0557534573452
absolute error = 6.349e-06
relative error = 0.01067 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.099
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.6
Order of pole (three term test) = 8.978e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6325 2.341
h = 0.003 0.006
y[1] (numeric) = 0.0207174692188 0.0557257667793
y[1] (closed_form) = 0.0207115003577 0.0557275070307
absolute error = 6.217e-06
relative error = 0.01046 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.101
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.876
Order of pole (three term test) = 1.483e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6355 2.347
h = 0.0001 0.005
y[1] (numeric) = 0.0205274425994 0.0557664250138
y[1] (closed_form) = 0.02052133901 0.0557679542945
absolute error = 6.292e-06
relative error = 0.01059 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.102
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.058
Order of pole (three term test) = 1.747e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6356 2.352
h = 0.0001 0.003
y[1] (numeric) = 0.0203867224299 0.0557321483153
y[1] (closed_form) = 0.0203806804959 0.0557338277471
absolute error = 6.271e-06
relative error = 0.01057 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.105
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.464
Order of pole (three term test) = 1.140e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6357 2.355
h = 0.001 0.001
y[1] (numeric) = 0.020302263035 0.0557125745059
y[1] (closed_form) = 0.0202961740039 0.0557142962815
absolute error = 6.328e-06
relative error = 0.01067 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.107
Order of pole (given) = 3 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) = 1.537e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6367 2.356
h = 0.001 0.003
y[1] (numeric) = 0.0202669058402 0.0557329646903
y[1] (closed_form) = 0.0202608008216 0.0557347149925
absolute error = 6.351e-06
relative error = 0.01071 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.106
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.182
Order of pole (three term test) = 1.309e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6377 2.359
h = 0.0001 0.004
y[1] (numeric) = 0.0201757189118 0.0557383371279
y[1] (closed_form) = 0.020169648942 0.0557400306651
absolute error = 6.302e-06
relative error = 0.01063 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.107
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.197
Order of pole (three term test) = 1.139e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6378 2.363
h = 0.003 0.006
y[1] (numeric) = 0.0200635931165 0.055710812689
y[1] (closed_form) = 0.0200575798275 0.0557125071047
absolute error = 6.247e-06
relative error = 0.01055 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.11
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.89
Order of pole (three term test) = 4.980e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6408 2.369
h = 0.0001 0.005
y[1] (numeric) = 0.0198741113764 0.0557483147162
y[1] (closed_form) = 0.0198679687622 0.0557497971576
absolute error = 6.319e-06
relative error = 0.01068 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.111
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.064
Order of pole (three term test) = 1.174e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6409 2.374
h = 0.0001 0.003
y[1] (numeric) = 0.0197347832682 0.055712099087
y[1] (closed_form) = 0.019728698747 0.0557137316911
absolute error = 6.300e-06
relative error = 0.01066 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.113
Order of pole (given) = 3 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) = 8.562e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.641 2.377
h = 0.001 0.001
y[1] (numeric) = 0.0196511441927 0.0556913570054
y[1] (closed_form) = 0.0196450121043 0.0556930306463
absolute error = 6.356e-06
relative error = 0.01076 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.115
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.939
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.642 2.378
h = 0.001 0.003
y[1] (numeric) = 0.0196156944073 0.0557110817387
y[1] (closed_form) = 0.0196095458847 0.0557127833454
absolute error = 6.380e-06
relative error = 0.0108 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.115
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.201
Order of pole (three term test) = 5.698e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.643 2.381
h = 0.0001 0.004
y[1] (numeric) = 0.0195249894615 0.0557150294321
y[1] (closed_form) = 0.0195188768494 0.055716675456
absolute error = 6.330e-06
relative error = 0.01072 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.116
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.208
Order of pole (three term test) = 6.564e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6431 2.385
h = 0.003 0.006
y[1] (numeric) = 0.0194139781793 0.0556859657814
y[1] (closed_form) = 0.0194079217594 0.0556876138263
absolute error = 6.277e-06
relative error = 0.01064 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.118
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.904
Order of pole (three term test) = 8.369e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6461 2.391
h = 0.0001 0.005
y[1] (numeric) = 0.0192251009142 0.0557203487807
y[1] (closed_form) = 0.0192189205414 0.0557217839951
absolute error = 6.345e-06
relative error = 0.01076 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.119
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.071
Order of pole (three term test) = 2.012e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6462 2.396
h = 0.0001 0.003
y[1] (numeric) = 0.0190871926383 0.0556822385862
y[1] (closed_form) = 0.019081066833 0.0556838238848
absolute error = 6.328e-06
relative error = 0.01075 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.122
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.474
Order of pole (three term test) = 1.287e-27 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1595.7MB, alloc=44.3MB, time=19.99
x[1] = 2.6463 2.399
h = 0.001 0.001
y[1] (numeric) = 0.0190043907352 0.0556603545777
y[1] (closed_form) = 0.0189982169305 0.0556619796079
absolute error = 6.384e-06
relative error = 0.01085 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.123
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.943
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6473 2.4
h = 0.001 0.003
y[1] (numeric) = 0.0189688626112 0.0556794175247
y[1] (closed_form) = 0.0189626719445 0.0556810699542
absolute error = 6.407e-06
relative error = 0.01089 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.123
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.22
Order of pole (three term test) = 1.714e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6483 2.403
h = 0.0001 0.004
y[1] (numeric) = 0.0188786645009 0.0556819621114
y[1] (closed_form) = 0.0188725105677 0.0556835601499
absolute error = 6.358e-06
relative error = 0.01081 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.124
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.218
Order of pole (three term test) = 3.490e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6484 2.407
h = 0.003 0.006
y[1] (numeric) = 0.0187687895929 0.0556513946642
y[1] (closed_form) = 0.0187626913394 0.0556529958418
absolute error = 6.305e-06
relative error = 0.01074 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.126
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.918
Order of pole (three term test) = 3.583e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6514 2.413
h = 0.0001 0.005
y[1] (numeric) = 0.0185805748361 0.0556826969331
y[1] (closed_form) = 0.018574357967 0.0556840845686
absolute error = 6.370e-06
relative error = 0.01085 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.127
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.077
Order of pole (three term test) = 6.639e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6515 2.418
h = 0.0001 0.003
y[1] (numeric) = 0.0184441127513 0.0556427367746
y[1] (closed_form) = 0.0184379469635 0.0556442743276
absolute error = 6.355e-06
relative error = 0.01084 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.13
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.479
Order of pole (three term test) = 9.686e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6516 2.421
h = 0.001 0.001
y[1] (numeric) = 0.0183621640317 0.0556197373331
y[1] (closed_form) = 0.0183559498499 0.0556213133153
absolute error = 6.411e-06
relative error = 0.01095 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.132
Order of pole (given) = 3 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) = 9.243e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6526 2.422
h = 0.001 0.003
y[1] (numeric) = 0.0183265715789 0.0556381424791
y[1] (closed_form) = 0.0183203401259 0.0556397452896
absolute error = 6.434e-06
relative error = 0.01098 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.132
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.239
Order of pole (three term test) = 1.290e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6536 2.425
h = 0.0001 0.004
y[1] (numeric) = 0.01823690435 0.0556393059959
y[1] (closed_form) = 0.0182307104146 0.0556408556152
absolute error = 6.385e-06
relative error = 0.0109 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.133
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.229
Order of pole (three term test) = 4.255e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6537 2.429
h = 0.003 0.006
y[1] (numeric) = 0.0181281865543 0.055607270345
y[1] (closed_form) = 0.0181220477636 0.0556088241969
absolute error = 6.332e-06
relative error = 0.01083 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.135
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.932
Order of pole (three term test) = 1.327e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6567 2.435
h = 0.0001 0.005
y[1] (numeric) = 0.0179406907619 0.0556355312382
y[1] (closed_form) = 0.0179344386543 0.0556368709779
absolute error = 6.394e-06
relative error = 0.01094 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.136
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.083
Order of pole (three term test) = 1.265e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6568 2.44
h = 0.0001 0.003
y[1] (numeric) = 0.017805699826 0.055593765907
y[1] (closed_form) = 0.0177994953547 0.0555952553118
absolute error = 6.381e-06
relative error = 0.01093 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.139
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.484
Order of pole (three term test) = 1.031e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6569 2.443
h = 0.001 0.001
y[1] (numeric) = 0.0177246194658 0.0555696776472
y[1] (closed_form) = 0.0177183662425 0.055571204183
absolute error = 6.437e-06
relative error = 0.01104 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.141
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.951
Order of pole (three term test) = 9.841e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6579 2.444
h = 0.0001 0.004
y[1] (numeric) = 0.0176889764449 0.0555874292873
y[1] (closed_form) = 0.0176827055601 0.055588982076
absolute error = 6.460e-06
relative error = 0.01107 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.14
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.71
Order of pole (three term test) = 6.862e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.658 2.448
h = 0.003 0.006
y[1] (numeric) = 0.0175812217852 0.0555542213093
y[1] (closed_form) = 0.0175750710874 0.055555730501
absolute error = 6.333e-06
relative error = 0.01087 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.143
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.945
Order of pole (three term test) = 6.999e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.661 2.454
h = 0.0001 0.005
y[1] (numeric) = 0.0173944244222 0.0555799060134
y[1] (closed_form) = 0.0173881649389 0.0555812007759
absolute error = 6.392e-06
relative error = 0.01098 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.144
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.089
Order of pole (three term test) = 1.606e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6611 2.459
h = 0.0001 0.003
y[1] (numeric) = 0.017260739501 0.0555366407326
y[1] (closed_form) = 0.0172545247279 0.0555380848358
absolute error = 6.380e-06
relative error = 0.01097 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.147
Order of pole (given) = 3 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) = 4.364e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6612 2.462
h = 0.001 0.001
y[1] (numeric) = 0.017180430652 0.0555116472141
y[1] (closed_form) = 0.0171741668632 0.055513127331
absolute error = 6.436e-06
relative error = 0.01108 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.148
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.954
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1641.8MB, alloc=44.3MB, time=20.57
x[1] = 2.6622 2.463
h = 0.001 0.003
y[1] (numeric) = 0.0171447626382 0.0555288396211
y[1] (closed_form) = 0.0171384808736 0.0555303454887
absolute error = 6.460e-06
relative error = 0.01112 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.148
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.276
Order of pole (three term test) = 1.453e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6632 2.466
h = 0.0001 0.004
y[1] (numeric) = 0.0170561602981 0.0555275001485
y[1] (closed_form) = 0.0170499173936 0.0555289550828
absolute error = 6.410e-06
relative error = 0.01104 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.149
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.25
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6633 2.47
h = 0.003 0.006
y[1] (numeric) = 0.0169496634877 0.0554928420187
y[1] (closed_form) = 0.0169434746631 0.0554943031462
absolute error = 6.359e-06
relative error = 0.01096 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.151
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.96
Order of pole (three term test) = 6.752e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6663 2.476
h = 0.0001 0.005
y[1] (numeric) = 0.016763685411 0.0555155618089
y[1] (closed_form) = 0.016757393016 0.0555168081921
absolute error = 6.415e-06
relative error = 0.01106 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.153
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.096
Order of pole (three term test) = 1.127e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6664 2.481
h = 0.0001 0.003
y[1] (numeric) = 0.0166315138558 0.0554705753141
y[1] (closed_form) = 0.0166252628091 0.055471970633
absolute error = 6.405e-06
relative error = 0.01106 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.156
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.494
Order of pole (three term test) = 1.300e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6665 2.484
h = 0.001 0.001
y[1] (numeric) = 0.0165520990867 0.0554445428907
y[1] (closed_form) = 0.0165457987334 0.0554459729357
absolute error = 6.461e-06
relative error = 0.01117 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.157
Order of pole (given) = 3 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) = 1.115e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6675 2.485
h = 0.001 0.003
y[1] (numeric) = 0.0165164053687 0.0554610907249
y[1] (closed_form) = 0.0165100866836 0.0554625459393
absolute error = 6.484e-06
relative error = 0.01121 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.157
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.295
Order of pole (three term test) = 1.556e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6685 2.488
h = 0.0001 0.004
y[1] (numeric) = 0.0164283979543 0.0554584354216
y[1] (closed_form) = 0.0164221188044 0.0554598409184
absolute error = 6.435e-06
relative error = 0.01112 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.158
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.261
Order of pole (three term test) = 3.991e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6686 2.492
h = 0.003 0.006
y[1] (numeric) = 0.0163231110385 0.0554224117758
y[1] (closed_form) = 0.0163168853745 0.0554238244863
absolute error = 6.384e-06
relative error = 0.01105 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.16
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.975
Order of pole (three term test) = 1.610e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6716 2.498
h = 0.0001 0.005
y[1] (numeric) = 0.0161380041276 0.0554422086761
y[1] (closed_form) = 0.016131680059 0.0554434064602
absolute error = 6.436e-06
relative error = 0.01115 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.162
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.102
Order of pole (three term test) = 1.140e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6717 2.503
h = 0.0001 0.003
y[1] (numeric) = 0.016007366959 0.0553955460442
y[1] (closed_form) = 0.0160010809238 0.05539689228
absolute error = 6.429e-06
relative error = 0.01115 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.164
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.5
Order of pole (three term test) = 1.265e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6718 2.506
h = 0.001 0.001
y[1] (numeric) = 0.0159288590972 0.0553685015228
y[1] (closed_form) = 0.0159225234995 0.0553698812039
absolute error = 6.484e-06
relative error = 0.01125 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.166
Order of pole (given) = 3 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) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6728 2.507
h = 0.001 0.003
y[1] (numeric) = 0.0158931526889 0.055384409898
y[1] (closed_form) = 0.0158867984217 0.0553858141649
absolute error = 6.508e-06
relative error = 0.01129 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.166
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.315
Order of pole (three term test) = 1.652e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6738 2.51
h = 0.0001 0.004
y[1] (numeric) = 0.0158057611193 0.0553804620599
y[1] (closed_form) = 0.0157994470248 0.0553818178281
absolute error = 6.458e-06
relative error = 0.01121 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.167
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.273
Order of pole (three term test) = 9.519e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6739 2.514
h = 0.003 0.006
y[1] (numeric) = 0.0157017005944 0.0553431088332
y[1] (closed_form) = 0.0156954393731 0.05534447281
absolute error = 6.408e-06
relative error = 0.01114 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.169
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.99
Order of pole (three term test) = 7.681e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6769 2.52
h = 0.0001 0.005
y[1] (numeric) = 0.0155175151201 0.0553600256925
y[1] (closed_form) = 0.0155111606079 0.0553611746901
absolute error = 6.458e-06
relative error = 0.01123 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.171
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.109
Order of pole (three term test) = 1.672e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.677 2.525
h = 0.0001 0.003
y[1] (numeric) = 0.0153884320131 0.0553117320245
y[1] (closed_form) = 0.0153821122678 0.0553130289135
absolute error = 6.451e-06
relative error = 0.01124 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.173
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.505
Order of pole (three term test) = 1.330e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6771 2.528
h = 0.001 0.001
y[1] (numeric) = 0.0153108430824 0.0552837022343
y[1] (closed_form) = 0.0153044735532 0.0552850312955
absolute error = 6.507e-06
relative error = 0.01134 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.175
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.967
Order of pole (three term test) = 1.361e-27 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1687.8MB, alloc=44.3MB, time=21.14
x[1] = 2.6781 2.529
h = 0.001 0.003
y[1] (numeric) = 0.0152751367282 0.0552989765294
y[1] (closed_form) = 0.0152687482099 0.0553003295909
absolute error = 6.530e-06
relative error = 0.01138 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.175
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.336
Order of pole (three term test) = 8.816e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6791 2.532
h = 0.0001 0.004
y[1] (numeric) = 0.0151883811166 0.0552937597125
y[1] (closed_form) = 0.0151820333713 0.0552950654966
absolute error = 6.481e-06
relative error = 0.0113 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.176
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.284
Order of pole (three term test) = 9.089e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6792 2.536
h = 0.003 0.006
y[1] (numeric) = 0.0150855624102 0.0552551128508
y[1] (closed_form) = 0.0150792669077 0.0552564278121
absolute error = 6.431e-06
relative error = 0.01123 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.178
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.005
Order of pole (three term test) = 5.798e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6822 2.542
h = 0.0001 0.005
y[1] (numeric) = 0.014902347032 0.0552691932839
y[1] (closed_form) = 0.0148959632967 0.0552702933398
absolute error = 6.478e-06
relative error = 0.01132 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.18
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.116
Order of pole (three term test) = 1.369e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6823 2.547
h = 0.0001 0.003
y[1] (numeric) = 0.0147748363325 0.0552193136655
y[1] (closed_form) = 0.0147684841479 0.0552205609783
absolute error = 6.473e-06
relative error = 0.01132 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.183
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.51
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6824 2.55
h = 0.001 0.001
y[1] (numeric) = 0.0146981775636 0.0551903254334
y[1] (closed_form) = 0.0146917754073 0.0551916036542
absolute error = 6.529e-06
relative error = 0.01143 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.184
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.971
Order of pole (three term test) = 1.366e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6834 2.551
h = 0.0001 0.004
y[1] (numeric) = 0.0146624837342 0.0552049712809
y[1] (closed_form) = 0.0146560622872 0.0552062729154
absolute error = 6.552e-06
relative error = 0.01147 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.184
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.84
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6835 2.555
h = 0.003 0.006
y[1] (numeric) = 0.0145606932616 0.0551652951258
y[1] (closed_form) = 0.014554390548 0.0551665663101
absolute error = 6.430e-06
relative error = 0.01127 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.187
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.019
Order of pole (three term test) = 1.375e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6865 2.561
h = 0.0001 0.005
y[1] (numeric) = 0.0143783837111 0.0551769818402
y[1] (closed_form) = 0.014371997069 0.0551780383405
absolute error = 6.473e-06
relative error = 0.01135 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.188
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.122
Order of pole (three term test) = 1.655e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6866 2.566
h = 0.0001 0.003
y[1] (numeric) = 0.0142522583394 0.0551257921546
y[1] (closed_form) = 0.0142459005295 0.055126995271
absolute error = 6.471e-06
relative error = 0.01136 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.191
Order of pole (given) = 3 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) = 1.506e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6867 2.569
h = 0.001 0.001
y[1] (numeric) = 0.0141764196007 0.055096011639
y[1] (closed_form) = 0.0141700116988 0.0550972445812
absolute error = 6.525e-06
relative error = 0.01147 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.193
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.975
Order of pole (three term test) = 5.723e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6877 2.57
h = 0.001 0.003
y[1] (numeric) = 0.0141407537169 0.0551101215815
y[1] (closed_form) = 0.0141343262859 0.0551113774283
absolute error = 6.549e-06
relative error = 0.01151 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.192
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.374
Order of pole (three term test) = 8.234e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6887 2.573
h = 0.0001 0.004
y[1] (numeric) = 0.0140552467036 0.0551026150681
y[1] (closed_form) = 0.014048861051 0.055103825918
absolute error = 6.499e-06
relative error = 0.01143 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.193
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.306
Order of pole (three term test) = 1.544e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6888 2.577
h = 0.003 0.006
y[1] (numeric) = 0.0139547905909 0.055061671808
y[1] (closed_form) = 0.0139484559536 0.0550628935594
absolute error = 6.451e-06
relative error = 0.01136 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.196
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.034
Order of pole (three term test) = 9.290e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6918 2.583
h = 0.0001 0.005
y[1] (numeric) = 0.0137735368511 0.0550706056298
y[1] (closed_form) = 0.013767123231 0.0550716129963
absolute error = 6.492e-06
relative error = 0.01144 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.197
Order of pole (given) = 3 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) = 4.907e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6919 2.588
h = 0.0001 0.003
y[1] (numeric) = 0.0136490140163 0.0550179138956
y[1] (closed_form) = 0.0136426261102 0.0550190671133
absolute error = 6.491e-06
relative error = 0.01145 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.2
Order of pole (given) = 3 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) = 1.791e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.692 2.591
h = 0.001 0.001
y[1] (numeric) = 0.0135741239445 0.0549872248847
y[1] (closed_form) = 0.0135676858192 0.0549884066829
absolute error = 6.546e-06
relative error = 0.01156 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.202
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.98
Order of pole (three term test) = 1.537e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.693 2.592
h = 0.001 0.003
y[1] (numeric) = 0.0135384929756 0.055000717637
y[1] (closed_form) = 0.0135320350525 0.0550019217522
absolute error = 6.569e-06
relative error = 0.0116 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.202
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.395
Order of pole (three term test) = 4.270e-28 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1733.8MB, alloc=44.3MB, time=21.72
x[1] = 2.694 2.595
h = 0.0001 0.004
y[1] (numeric) = 0.0134536747522 0.0549920109356
y[1] (closed_form) = 0.0134472591042 0.0549931712751
absolute error = 6.520e-06
relative error = 0.01152 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.203
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.318
Order of pole (three term test) = 7.784e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6941 2.599
h = 0.003 0.006
y[1] (numeric) = 0.0133544983928 0.0549498767956
y[1] (closed_form) = 0.0133481330849 0.0549510489294
absolute error = 6.472e-06
relative error = 0.01145 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.205
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.05
Order of pole (three term test) = 7.024e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6971 2.605
h = 0.0001 0.005
y[1] (numeric) = 0.0131743445074 0.0549561031966
y[1] (closed_form) = 0.0131679050989 0.0549570613614
absolute error = 6.510e-06
relative error = 0.01152 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.207
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.136
Order of pole (three term test) = 5.249e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6972 2.61
h = 0.0001 0.003
y[1] (numeric) = 0.0130514388603 0.0549019542291
y[1] (closed_form) = 0.0130450221017 0.0549030574134
absolute error = 6.511e-06
relative error = 0.01154 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.21
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.527
Order of pole (three term test) = 3.832e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6973 2.613
h = 0.001 0.001
y[1] (numeric) = 0.0129775064786 0.0548703834094
y[1] (closed_form) = 0.0129710394053 0.0548715139401
absolute error = 6.565e-06
relative error = 0.01164 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.211
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.984
Order of pole (three term test) = 1.636e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6983 2.614
h = 0.001 0.003
y[1] (numeric) = 0.0129419220905 0.0548832652631
y[1] (closed_form) = 0.0129354349678 0.0548844175234
absolute error = 6.589e-06
relative error = 0.01168 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.211
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.417
Order of pole (three term test) = 1.938e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6993 2.617
h = 0.0001 0.004
y[1] (numeric) = 0.0128578096942 0.054873382674
y[1] (closed_form) = 0.0128513653082 0.0548744923776
absolute error = 6.539e-06
relative error = 0.0116 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.212
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.33
Order of pole (three term test) = 1.178e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6994 2.621
h = 0.003 0.006
y[1] (numeric) = 0.0127599245289 0.0548300933411
y[1] (closed_form) = 0.012753529794 0.0548312157054
absolute error = 6.492e-06
relative error = 0.01153 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.215
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.066
Order of pole (three term test) = 1.011e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7024 2.627
h = 0.0001 0.005
y[1] (numeric) = 0.0125809129378 0.0548336583415
y[1] (closed_form) = 0.0125744489184 0.0548345672659
absolute error = 6.528e-06
relative error = 0.0116 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.216
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.143
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7025 2.632
h = 0.0001 0.003
y[1] (numeric) = 0.0124596378768 0.0547780967975
y[1] (closed_form) = 0.0124531934985 0.0547791498452
absolute error = 6.530e-06
relative error = 0.01162 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.219
Order of pole (given) = 3 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) = 1.556e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7026 2.635
h = 0.001 0.001
y[1] (numeric) = 0.0123866714601 0.054745670768
y[1] (closed_form) = 0.0123801767026 0.0547467499399
absolute error = 6.584e-06
relative error = 0.01173 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.221
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.989
Order of pole (three term test) = 1.401e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7036 2.636
h = 0.001 0.003
y[1] (numeric) = 0.0123511450329 0.0547579482244
y[1] (closed_form) = 0.0123446299914 0.0547590485392
absolute error = 6.607e-06
relative error = 0.01177 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.221
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.438
Order of pole (three term test) = 7.731e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7046 2.639
h = 0.0001 0.004
y[1] (numeric) = 0.0122677547183 0.0547469141806
y[1] (closed_form) = 0.0122612828403 0.054747973155
absolute error = 6.558e-06
relative error = 0.01169 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.222
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.342
Order of pole (three term test) = 6.428e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7047 2.643
h = 0.003 0.006
y[1] (numeric) = 0.0121711711952 0.0547025052083
y[1] (closed_form) = 0.0121647482663 0.0547035776831
absolute error = 6.512e-06
relative error = 0.01162 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.224
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.082
Order of pole (three term test) = 1.617e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7077 2.649
h = 0.0001 0.005
y[1] (numeric) = 0.0119933427403 0.0547034553229
y[1] (closed_form) = 0.0119868552748 0.0547043149966
absolute error = 6.544e-06
relative error = 0.01169 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.226
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.15
Order of pole (three term test) = 1.203e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7078 2.654
h = 0.0001 0.003
y[1] (numeric) = 0.0118737104335 0.0546465256665
y[1] (closed_form) = 0.0118672396566 0.0546475285055
absolute error = 6.548e-06
relative error = 0.01171 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.229
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.538
Order of pole (three term test) = 1.001e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7079 2.657
h = 0.001 0.001
y[1] (numeric) = 0.0118017175214 0.0546132709181
y[1] (closed_form) = 0.0117951963308 0.0546142986716
absolute error = 6.602e-06
relative error = 0.01182 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.231
Order of pole (given) = 3 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) = 5.930e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7089 2.658
h = 0.0001 0.004
y[1] (numeric) = 0.0117662601473 0.0546249506772
y[1] (closed_form) = 0.0117597184551 0.0546259989881
absolute error = 6.625e-06
relative error = 0.01186 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.23
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.97
Order of pole (three term test) = 1.707e-27 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1779.8MB, alloc=44.3MB, time=22.29
x[1] = 2.709 2.662
h = 0.003 0.006
y[1] (numeric) = 0.0116707498691 0.0545796544004
y[1] (closed_form) = 0.0116643240529 0.0545806844656
absolute error = 6.508e-06
relative error = 0.01166 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.233
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.096
Order of pole (three term test) = 4.959e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.712 2.668
h = 0.0001 0.005
y[1] (numeric) = 0.0114940016957 0.0545784060206
y[1] (closed_form) = 0.011487515364 0.0545792239752
absolute error = 6.538e-06
relative error = 0.01172 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.234
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.157
Order of pole (three term test) = 7.454e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7121 2.673
h = 0.0001 0.003
y[1] (numeric) = 0.0113758078186 0.0545203539164
y[1] (closed_form) = 0.0113693356924 0.0545213141296
absolute error = 6.543e-06
relative error = 0.01175 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.237
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.543
Order of pole (three term test) = 7.527e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7122 2.676
h = 0.001 0.001
y[1] (numeric) = 0.0113046677972 0.0544864186557
y[1] (closed_form) = 0.0112981452652 0.054487402753
absolute error = 6.596e-06
relative error = 0.01185 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.239
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.997
Order of pole (three term test) = 2.819e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7132 2.677
h = 0.001 0.003
y[1] (numeric) = 0.0112692855307 0.0544975904425
y[1] (closed_form) = 0.0112627423299 0.0544985945921
absolute error = 6.620e-06
relative error = 0.0119 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.239
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.479
Order of pole (three term test) = 6.223e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7142 2.68
h = 0.0001 0.004
y[1] (numeric) = 0.0111872924775 0.0544844882164
y[1] (closed_form) = 0.0111807931298 0.0544854532818
absolute error = 6.571e-06
relative error = 0.01181 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.24
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.365
Order of pole (three term test) = 7.213e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7143 2.684
h = 0.003 0.006
y[1] (numeric) = 0.0110931678326 0.0544381056682
y[1] (closed_form) = 0.0110867160872 0.0544390857173
absolute error = 6.526e-06
relative error = 0.01175 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.243
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.113
Order of pole (three term test) = 1.024e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7173 2.69
h = 0.0001 0.005
y[1] (numeric) = 0.0109176740034 0.0544343305334
y[1] (closed_form) = 0.0109111663563 0.0544350993047
absolute error = 6.553e-06
relative error = 0.0118 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.244
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.164
Order of pole (three term test) = 7.828e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7174 2.695
h = 0.0001 0.003
y[1] (numeric) = 0.0108011418034 0.0543749925419
y[1] (closed_form) = 0.0107946455175 0.0543759025058
absolute error = 6.560e-06
relative error = 0.01183 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.247
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.549
Order of pole (three term test) = 5.004e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7175 2.698
h = 0.001 0.001
y[1] (numeric) = 0.0107309870929 0.0543402775714
y[1] (closed_form) = 0.0107244404203 0.0543412102354
absolute error = 6.613e-06
relative error = 0.01194 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.249
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.002
Order of pole (three term test) = 7.704e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7185 2.699
h = 0.001 0.003
y[1] (numeric) = 0.0106956936633 0.0543508647427
y[1] (closed_form) = 0.0106891261348 0.0543518168771
absolute error = 6.636e-06
relative error = 0.01198 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.249
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.501
Order of pole (three term test) = 9.434e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7195 2.702
h = 0.0001 0.004
y[1] (numeric) = 0.0106144646422 0.0543366816407
y[1] (closed_form) = 0.0106079412975 0.0543375958932
absolute error = 6.587e-06
relative error = 0.0119 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.25
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.378
Order of pole (three term test) = 8.033e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7196 2.706
h = 0.003 0.006
y[1] (numeric) = 0.0105216657895 0.0542892802757
y[1] (closed_form) = 0.0105151893137 0.0542902102756
absolute error = 6.543e-06
relative error = 0.01183 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.252
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.129
Order of pole (three term test) = 1.002e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7226 2.712
h = 0.0001 0.005
y[1] (numeric) = 0.0103474626215 0.0542830260082
y[1] (closed_form) = 0.0103409347834 0.0542837456629
absolute error = 6.567e-06
relative error = 0.01188 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.254
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.171
Order of pole (three term test) = 7.346e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7227 2.717
h = 0.0001 0.003
y[1] (numeric) = 0.0102326008783 0.0542224458527
y[1] (closed_form) = 0.0102260816162 0.0542233055792
absolute error = 6.576e-06
relative error = 0.01192 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.257
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.555
Order of pole (three term test) = 7.589e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7228 2.72
h = 0.001 0.001
y[1] (numeric) = 0.0101634369913 0.0541869772405
y[1] (closed_form) = 0.0101568673895 0.0541878584975
absolute error = 6.628e-06
relative error = 0.01202 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.259
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.007
Order of pole (three term test) = 3.241e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7238 2.721
h = 0.001 0.003
y[1] (numeric) = 0.0101282426577 0.0541969870003
y[1] (closed_form) = 0.0101216520287 0.0541978871483
absolute error = 6.652e-06
relative error = 0.01206 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.259
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.523
Order of pole (three term test) = 1.319e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7248 2.724
h = 0.0001 0.004
y[1] (numeric) = 0.0100477909735 0.0541817477364
y[1] (closed_form) = 0.0100412448269 0.0541826111983
absolute error = 6.603e-06
relative error = 0.01198 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.26
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.39
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1825.8MB, alloc=44.3MB, time=22.86
x[1] = 2.7249 2.728
h = 0.003 0.006
y[1] (numeric) = 0.00995632470097 0.0541333623391
y[1] (closed_form) = 0.0099498246804 0.0541342422858
absolute error = 6.559e-06
relative error = 0.01192 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.262
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.146
Order of pole (three term test) = 1.059e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7279 2.734
h = 0.0001 0.005
y[1] (numeric) = 0.00978344695346 0.0541246768582
y[1] (closed_form) = 0.00977690003416 0.0541253474883
absolute error = 6.581e-06
relative error = 0.01197 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.264
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.179
Order of pole (three term test) = 9.621e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.728 2.739
h = 0.0001 0.003
y[1] (numeric) = 0.00967026330837 0.0540628979504
y[1] (closed_form) = 0.00966372223922 0.0540637074791
absolute error = 6.591e-06
relative error = 0.012 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.267
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.561
Order of pole (three term test) = 1.038e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7281 2.742
h = 0.001 0.001
y[1] (numeric) = 0.0096020950763 0.0540267015852
y[1] (closed_form) = 0.00959550374147 0.0540275314899
absolute error = 6.643e-06
relative error = 0.01211 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.269
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.011
Order of pole (three term test) = 5.499e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7291 2.743
h = 0.001 0.003
y[1] (numeric) = 0.0095670098057 0.0540361412942
y[1] (closed_form) = 0.00956039728824 0.0540369895134
absolute error = 6.667e-06
relative error = 0.01215 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.269
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.545
Order of pole (three term test) = 6.944e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7301 2.746
h = 0.0001 0.004
y[1] (numeric) = 0.00948734802141 0.0540198706028
y[1] (closed_form) = 0.00948078025304 0.0540206833246
absolute error = 6.618e-06
relative error = 0.01207 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.27
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.403
Order of pole (three term test) = 8.857e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7302 2.75
h = 0.003 0.006
y[1] (numeric) = 0.00939722021521 0.0539705357038
y[1] (closed_form) = 0.00939069782158 0.0539713656213
absolute error = 6.575e-06
relative error = 0.012 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.272
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.163
Order of pole (three term test) = 2.262e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7332 2.756
h = 0.0001 0.005
y[1] (numeric) = 0.00922570110389 0.053959467177
y[1] (closed_form) = 0.00921913619748 0.0539600888992
absolute error = 6.594e-06
relative error = 0.01205 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.274
Order of pole (given) = 3 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) = 8.461e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7333 2.761
h = 0.0001 0.003
y[1] (numeric) = 0.00911420208457 0.0538965325896
y[1] (closed_form) = 0.00910764036282 0.0538972919874
absolute error = 6.606e-06
relative error = 0.01208 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.277
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.567
Order of pole (three term test) = 2.977e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7334 2.764
h = 0.001 0.001
y[1] (numeric) = 0.00904703367228 0.0538596341642
y[1] (closed_form) = 0.00904042178504 0.053860412799
absolute error = 6.658e-06
relative error = 0.01219 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.279
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.016
Order of pole (three term test) = 5.280e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7344 2.765
h = 0.0001 0.004
y[1] (numeric) = 0.00901206713945 0.0538685113292
y[1] (closed_form) = 0.00900543392949 0.0538693077053
absolute error = 6.681e-06
relative error = 0.01223 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.279
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 12.11
Order of pole (three term test) = 3.256e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7345 2.769
h = 0.003 0.006
y[1] (numeric) = 0.00892303910745 0.0538184274735
y[1] (closed_form) = 0.00891651774011 0.0538192167483
absolute error = 6.569e-06
relative error = 0.01204 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.281
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.178
Order of pole (three term test) = 1.204e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7375 2.775
h = 0.0001 0.005
y[1] (numeric) = 0.00875274249785 0.0538053631206
y[1] (closed_form) = 0.00874618231496 0.0538059452878
absolute error = 6.586e-06
relative error = 0.01208 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.283
Order of pole (given) = 3 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) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7376 2.78
h = 0.0001 0.003
y[1] (numeric) = 0.00864271101928 0.0537414881285
y[1] (closed_form) = 0.00863615179066 0.0537422068496
absolute error = 6.598e-06
relative error = 0.01212 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.286
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.573
Order of pole (three term test) = 1.178e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7377 2.783
h = 0.001 0.001
y[1] (numeric) = 0.00857641400623 0.0537040177708
y[1] (closed_form) = 0.00856980473202 0.0537047547631
absolute error = 6.650e-06
relative error = 0.01223 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.288
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.02
Order of pole (three term test) = 1.142e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7387 2.784
h = 0.001 0.003
y[1] (numeric) = 0.00854156377997 0.053712418398
y[1] (closed_form) = 0.00853493308129 0.0537131726394
absolute error = 6.673e-06
relative error = 0.01227 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.288
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.588
Order of pole (three term test) = 4.713e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7397 2.787
h = 0.0001 0.004
y[1] (numeric) = 0.00846341434422 0.0536943040032
y[1] (closed_form) = 0.00845682879483 0.0536950249394
absolute error = 6.625e-06
relative error = 0.01219 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.289
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.427
Order of pole (three term test) = 1.013e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7398 2.791
h = 0.003 0.006
y[1] (numeric) = 0.00837580012631 0.053643309316
y[1] (closed_form) = 0.00836925852629 0.0536440486923
absolute error = 6.583e-06
relative error = 0.01213 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.292
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.195
Order of pole (three term test) = 1.830e-27 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1871.8MB, alloc=44.3MB, time=23.44
x[1] = 2.7428 2.797
h = 0.0001 0.005
y[1] (numeric) = 0.00820691932532 0.0536279524001
y[1] (closed_form) = 0.0082003431465 0.0536284859522
absolute error = 6.598e-06
relative error = 0.01216 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.293
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.201
Order of pole (three term test) = 9.683e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7429 2.802
h = 0.0001 0.003
y[1] (numeric) = 0.0080985812414 0.0535630009321
y[1] (closed_form) = 0.00809200346533 0.0535636697292
absolute error = 6.612e-06
relative error = 0.01221 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.296
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.579
Order of pole (three term test) = 4.475e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.743 2.805
h = 0.001 0.001
y[1] (numeric) = 0.00803328977606 0.0535248757784
y[1] (closed_form) = 0.00802666210096 0.0535255617383
absolute error = 6.663e-06
relative error = 0.01231 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.298
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.025
Order of pole (three term test) = 5.960e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.744 2.806
h = 0.001 0.003
y[1] (numeric) = 0.00799857541987 0.0535327282912
y[1] (closed_form) = 0.00799192620793 0.0535334309343
absolute error = 6.686e-06
relative error = 0.01235 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.298
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.611
Order of pole (three term test) = 4.220e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.745 2.809
h = 0.0001 0.004
y[1] (numeric) = 0.00792124752521 0.0535136532751
y[1] (closed_form) = 0.00791464364233 0.0535143237763
absolute error = 6.638e-06
relative error = 0.01227 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.299
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.44
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7451 2.813
h = 0.003 0.006
y[1] (numeric) = 0.00783498341556 0.0534618063127
y[1] (closed_form) = 0.00782842271147 0.0534624958906
absolute error = 6.597e-06
relative error = 0.01221 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.302
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.212
Order of pole (three term test) = 5.562e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7481 2.819
h = 0.0001 0.005
y[1] (numeric) = 0.00766754730989 0.0534442054393
y[1] (closed_form) = 0.00766095618233 0.053444690559
absolute error = 6.609e-06
relative error = 0.01224 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.304
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.208
Order of pole (three term test) = 1.041e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7482 2.824
h = 0.0001 0.003
y[1] (numeric) = 0.00756090611103 0.0533782194442
y[1] (closed_form) = 0.0075543108962 0.053378838457
absolute error = 6.624e-06
relative error = 0.01229 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.307
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.585
Order of pole (three term test) = 6.803e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7483 2.827
h = 0.001 0.001
y[1] (numeric) = 0.00749662253877 0.053339464534
y[1] (closed_form) = 0.00748997759532 0.0533400996182
absolute error = 6.675e-06
relative error = 0.01239 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.309
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.03
Order of pole (three term test) = 1.378e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7493 2.828
h = 0.001 0.003
y[1] (numeric) = 0.00746205289182 0.0533467767977
y[1] (closed_form) = 0.00745538631363 0.0533474280035
absolute error = 6.698e-06
relative error = 0.01244 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.309
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.634
Order of pole (three term test) = 6.417e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7503 2.831
h = 0.0001 0.004
y[1] (numeric) = 0.00738555633674 0.0533267657724
y[1] (closed_form) = 0.00737893523826 0.0533273859895
absolute error = 6.650e-06
relative error = 0.01235 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.31
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.453
Order of pole (three term test) = 7.024e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7504 2.835
h = 0.003 0.006
y[1] (numeric) = 0.00730064493636 0.0532740998803
y[1] (closed_form) = 0.00729406624086 0.053274739785
absolute error = 6.610e-06
relative error = 0.01229 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.312
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.23
Order of pole (three term test) = 1.525e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7534 2.841
h = 0.0001 0.005
y[1] (numeric) = 0.00713468093513 0.053254303729
y[1] (closed_form) = 0.00712807588898 0.0532547406207
absolute error = 6.619e-06
relative error = 0.01232 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.314
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.216
Order of pole (three term test) = 1.119e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7535 2.846
h = 0.0001 0.003
y[1] (numeric) = 0.00702973909965 0.053187324722
y[1] (closed_form) = 0.00702312753797 0.053187894114
absolute error = 6.636e-06
relative error = 0.01237 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.317
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.591
Order of pole (three term test) = 8.181e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7536 2.849
h = 0.001 0.001
y[1] (numeric) = 0.0069664651592 0.0531479648419
y[1] (closed_form) = 0.00695980406235 0.0531485492314
absolute error = 6.687e-06
relative error = 0.01247 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.319
Order of pole (given) = 3 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) = 3.495e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7546 2.85
h = 0.001 0.003
y[1] (numeric) = 0.0069320487708 0.0531547448293
y[1] (closed_form) = 0.00692536595545 0.0531553447833
absolute error = 6.710e-06
relative error = 0.01252 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.319
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.658
Order of pole (three term test) = 2.183e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7556 2.853
h = 0.0001 0.004
y[1] (numeric) = 0.00685639266568 0.0531338223306
y[1] (closed_form) = 0.0068497554523 0.0531343924384
absolute error = 6.662e-06
relative error = 0.01243 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.32
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.467
Order of pole (three term test) = 1.356e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7557 2.857
h = 0.003 0.006
y[1] (numeric) = 0.00677283577506 0.0530803705043
y[1] (closed_form) = 0.00676624018434 0.0530809608854
absolute error = 6.622e-06
relative error = 0.01238 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.323
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.248
Order of pole (three term test) = 1.608e-28 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1917.9MB, alloc=44.3MB, time=24.01
x[1] = 2.7587 2.863
h = 0.0001 0.005
y[1] (numeric) = 0.00660836982951 0.0530584277874
y[1] (closed_form) = 0.00660175187752 0.0530588166761
absolute error = 6.629e-06
relative error = 0.0124 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.325
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.224
Order of pole (three term test) = 4.818e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7588 2.868
h = 0.0001 0.003
y[1] (numeric) = 0.00650512885058 0.0529904968283
y[1] (closed_form) = 0.00649850201681 0.0529910167862
absolute error = 6.647e-06
relative error = 0.01245 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.328
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.598
Order of pole (three term test) = 1.113e-27 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7589 2.871
h = 0.001 0.001
y[1] (numeric) = 0.00644286569002 0.052950556499
y[1] (closed_form) = 0.0064361895367 0.0529510903982
absolute error = 6.697e-06
relative error = 0.01256 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.33
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.04
Order of pole (three term test) = 3.761e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7599 2.872
h = 0.001 0.003
y[1] (numeric) = 0.00640861082094 0.0529568122806
y[1] (closed_form) = 0.00640191287915 0.0529573611922
absolute error = 6.720e-06
relative error = 0.0126 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.33
Order of pole (given) = 3 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.682
Order of pole (three term test) = 5.253e-28 0
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff ( y , x , 1 ) = neg ( 2.0 ) / ( x - 6.0 ) / ( x - 6.0 ) / ( x - 6.0 ) ;
Iterations = 754
Total Elapsed Time = 24 Seconds
Expected Time Remaining = 0 Seconds
Optimized Time Remaining = 0 Seconds
Expected Total Time = 24 Seconds
> quit
memory used=1928.9MB, alloc=44.3MB, time=24.14