|\^/| Maple 2016 (X86 64 LINUX)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2016
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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#BEGIN OUTFILE1
# before write maple top matter
# before write_ats library and user def block
#BEGIN ATS LIBRARY BLOCK
# Begin Function number 2
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s\n",str);
> fi;# end if 1;
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
# End Function number 2
# Begin Function number 3
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s",str);
> fi;# end if 1;
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
# End Function number 3
# Begin Function number 4
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> print(label,str);
> fi;# end if 1;
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
# End Function number 4
# Begin Function number 5
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 5
# Begin Function number 6
> omniout_complex := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> if vallen = 4 then
> printf("%-30s = %-20.4g %-20g %s \n",prelabel,Re(value), Im(value), postlabel);
> else
> printf("%-30s = %-20.12g %-20.12g %s \n",prelabel,Re(value),Im(value), postlabel);
> fi;# end if 0;
> fi;# end if -1;
> end;
omniout_complex := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then printf("%-30s = %-20.4g %-20g %s \n", prelabel,
Re(value), Im(value), postlabel)
else printf("%-30s = %-20.12g %-20.12g %s \n", prelabel, Re(value),
Im(value), postlabel)
end if
end if
end proc
# End Function number 6
# Begin Function number 7
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number -1
> if vallen = 5 then # if number 0
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;# end if 0;
> fi;# end if -1;
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 7
# Begin Function number 8
> logitem_time := proc(fd,secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> fprintf(fd,"| ");
> if (secs_in >= 0) then # if number -1
> years_int := int_trunc(secs_in / glob_sec_in_year);
> sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
> days_int := int_trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := sec_temp mod int_trunc(glob_sec_in_day) ;
> hours_int := int_trunc(sec_temp / glob_sec_in_hour);
> sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
> minutes_int := int_trunc(sec_temp / glob_sec_in_minute);
> sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
> if (years_int > 0) then # if number 0
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 1
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 2
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 3
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 3
> else
> fprintf(fd," 0.0 Seconds");
> fi;# end if 2
> fprintf(fd," | \n");
> end;
logitem_time := proc(fd, secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
fprintf(fd, "");
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, " 0.0 Seconds")
end if;
fprintf(fd, " | \n")
end proc
# End Function number 8
# Begin Function number 9
> omniout_timestr := proc(secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> if (secs_in >= 0) then # if number 2
> years_int := int_trunc(secs_in / glob_sec_in_year);
> sec_temp := (int_trunc(secs_in) mod int_trunc(glob_sec_in_year));
> days_int := int_trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_day)) ;
> hours_int := int_trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_hour));
> minutes_int := int_trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod int_trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 3
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 4
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 5
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 6
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 6
> else
> printf(" 0.0 Seconds\n");
> fi;# end if 5
> end;
omniout_timestr := proc(secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" 0.0 Seconds\n")
end if
end proc
# End Function number 9
# Begin Function number 10
> zero_ats_ar := proc(arr_a)
> global ATS_MAX_TERMS;
> local iii;
> iii := 1;
> while (iii <= ATS_MAX_TERMS) do # do number 1
> arr_a [iii] := glob__0;
> iii := iii + 1;
> od;# end do number 1
> end;
zero_ats_ar := proc(arr_a)
local iii;
global ATS_MAX_TERMS;
iii := 1;
while iii <= ATS_MAX_TERMS do arr_a[iii] := glob__0; iii := iii + 1
end do
end proc
# End Function number 10
# Begin Function number 11
> ats := proc(mmm_ats,arr_a,arr_b,jjj_ats)
> global ATS_MAX_TERMS;
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := glob__0;
> if (jjj_ats <= mmm_ats) then # if number 5
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> if ((lll_ats <= ATS_MAX_TERMS and (iii_ats <= ATS_MAX_TERMS) )) then # if number 6
> ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]);
> fi;# end if 6;
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 5;
> ret_ats;
> end;
ats := proc(mmm_ats, arr_a, arr_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
global ATS_MAX_TERMS;
ret_ats := glob__0;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
if lll_ats <= ATS_MAX_TERMS and iii_ats <= ATS_MAX_TERMS then
ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats])
end if;
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
# End Function number 11
# Begin Function number 12
> att := proc(mmm_att,arr_aa,arr_bb,jjj_att)
> global ATS_MAX_TERMS;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := glob__0;
> if (jjj_att < mmm_att) then # if number 5
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while ((iii_att < mmm_att) and (iii_att <= ATS_MAX_TERMS) ) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if ((lll_att <= ATS_MAX_TERMS and (iii_att <= ATS_MAX_TERMS) )) then # if number 6
> ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att);
> fi;# end if 6;
> iii_att := iii_att + 1;
> od;# end do number 1;
> ret_att := ret_att / c(mmm_att) ;
> fi;# end if 5;
> ret_att;
> end;
att := proc(mmm_att, arr_aa, arr_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global ATS_MAX_TERMS;
ret_att := glob__0;
if jjj_att < mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att < mmm_att and iii_att <= ATS_MAX_TERMS do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= ATS_MAX_TERMS and iii_att <= ATS_MAX_TERMS then
ret_att :=
ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])*c(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/c(mmm_att)
end if;
ret_att
end proc
# End Function number 12
# Begin Function number 13
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
# End Function number 13
# Begin Function number 14
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
# End Function number 14
# Begin Function number 15
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
# End Function number 15
# Begin Function number 16
> logitem_good_digits := proc(file,rel_error)
> global glob_small_float,glob_prec;
> local good_digits;
> fprintf(file,"");
> fprintf(file,"%d",glob_min_good_digits);
> fprintf(file," | ");
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float, glob_prec;
fprintf(file, "");
fprintf(file, "%d", glob_min_good_digits);
fprintf(file, " | ")
end proc
# End Function number 16
# Begin Function number 17
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
# End Function number 17
# Begin Function number 18
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
# End Function number 18
# Begin Function number 19
> logitem_complex := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g + %g I",Re(x),Im(x));
> fprintf(file," | ");
> end;
logitem_complex := proc(file, x)
fprintf(file, "");
fprintf(file, "%g + %g I", Re(x), Im(x));
fprintf(file, " | ")
end proc
# End Function number 19
# Begin Function number 20
> logitem_h_reason := proc(file)
> global glob_h_reason;
> fprintf(file,"");
> if (glob_h_reason = 1) then # if number 5
> fprintf(file,"Max H");
> elif
> (glob_h_reason = 2) then # if number 6
> fprintf(file,"Display Interval");
> elif
> (glob_h_reason = 3) then # if number 7
> fprintf(file,"Optimal");
> elif
> (glob_h_reason = 4) then # if number 8
> fprintf(file,"Pole Accuracy");
> elif
> (glob_h_reason = 5) then # if number 9
> fprintf(file,"Min H (Pole)");
> elif
> (glob_h_reason = 6) then # if number 10
> fprintf(file,"Pole");
> elif
> (glob_h_reason = 7) then # if number 11
> fprintf(file,"Opt Iter");
> else
> fprintf(file,"Impossible");
> fi;# end if 11
> fprintf(file," | ");
> end;
logitem_h_reason := proc(file)
global glob_h_reason;
fprintf(file, "");
if glob_h_reason = 1 then fprintf(file, "Max H")
elif glob_h_reason = 2 then fprintf(file, "Display Interval")
elif glob_h_reason = 3 then fprintf(file, "Optimal")
elif glob_h_reason = 4 then fprintf(file, "Pole Accuracy")
elif glob_h_reason = 5 then fprintf(file, "Min H (Pole)")
elif glob_h_reason = 6 then fprintf(file, "Pole")
elif glob_h_reason = 7 then fprintf(file, "Opt Iter")
else fprintf(file, "Impossible")
end if;
fprintf(file, " | ")
end proc
# End Function number 20
# Begin Function number 21
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
# End Function number 21
# Begin Function number 22
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file) fprintf(file, "\n") end proc
# End Function number 22
# Begin Function number 23
> chk_data := proc()
> global glob_max_iter,ALWAYS, ATS_MAX_TERMS;
> local errflag;
> errflag := false;
> if (glob_max_iter < 2) then # if number 11
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 11;
> if (errflag) then # if number 11
> quit;
> fi;# end if 11
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, ATS_MAX_TERMS;
errflag := false;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
# End Function number 23
# Begin Function number 24
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := c(clock_sec2);
> sub1 := c(t_end2-t_start2);
> sub2 := c(t2-t_start2);
> if (sub1 = glob__0) then # if number 11
> sec_left := glob__0;
> else
> if (sub2 > glob__0) then # if number 12
> rrr := (sub1/sub2);
> sec_left := rrr * c(ms2) - c(ms2);
> else
> sec_left := glob__0;
> fi;# end if 12
> fi;# end if 11;
> sec_left;
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := c(clock_sec2);
sub1 := c(t_end2 - t_start2);
sub2 := c(t2 - t_start2);
if sub1 = glob__0 then sec_left := glob__0
else
if glob__0 < sub2 then
rrr := sub1/sub2; sec_left := rrr*c(ms2) - c(ms2)
else sec_left := glob__0
end if
end if;
sec_left
end proc
# End Function number 24
# Begin Function number 25
> comp_percent := proc(t_end2,t_start2, t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub2 > glob_small_float) then # if number 11
> rrr := (glob__100*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 11;
> rrr;
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < sub2 then rrr := glob__100*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
# End Function number 25
# Begin Function number 26
> comp_rad_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 11
> ret := float_abs(term1 * glob_h / term2);
> else
> ret := glob_larger_float;
> fi;# end if 11;
> ret;
> #BOTTOM TWO TERM RADIUS ANALYSIS
> end;
comp_rad_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := float_abs(term1*glob_h/term2)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 26
# Begin Function number 27
> comp_ord_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM ORDER ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 11
> ret := glob__1 + float_abs(term2) * c(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(c(last_no));
> else
> ret := glob_larger_float;
> fi;# end if 11;
> ret;
> #BOTTOM TWO TERM ORDER ANALYSIS
> end;
comp_ord_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := glob__1 + float_abs(term2)*
c(last_no)*ln(float_abs(term1*glob_h/term2))/ln(c(last_no))
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 27
# Begin Function number 28
> c := proc(in_val)
> #To Force Conversion when needed
> local ret;
> ret := evalc(in_val);
> ret;
> #End Conversion
> end;
c := proc(in_val) local ret; ret := evalc(in_val); ret end proc
# End Function number 28
# Begin Function number 29
> comp_rad_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret,temp;
> temp := float_abs(term2*term2*c(last_no)+glob__m2*term2*term2-term1*term3*c(last_no)+term1*term3);
> if (float_abs(temp) > glob__0) then # if number 11
> ret := float_abs((term2*glob_h*term1)/(temp));
> else
> ret := glob_larger_float;
> fi;# end if 11;
> ret;
> #BOTTOM THREE TERM RADIUS ANALYSIS
> end;
comp_rad_from_three_terms := proc(term1, term2, term3, last_no)
local ret, temp;
global glob_h, glob_larger_float;
temp := float_abs(term2*term2*c(last_no) + glob__m2*term2*term2
- term1*term3*c(last_no) + term1*term3);
if glob__0 < float_abs(temp) then
ret := float_abs(term2*glob_h*term1/temp)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 29
# Begin Function number 30
> comp_ord_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM ORDER ANALYSIS
> local ret;
> ret := float_abs((glob__4*term1*term3*c(last_no)-glob__3*term1*term3-glob__4*term2*term2*c(last_no)+glob__4*term2*term2+term2*term2*c(last_no*last_no)-term1*term3*c(last_no*last_no))/(term2*term2*c(last_no)-glob__2*term2*term2-term1*term3*c(last_no)+term1*term3));
> ret;
> #TOP THREE TERM ORDER ANALYSIS
> end;
comp_ord_from_three_terms := proc(term1, term2, term3, last_no)
local ret;
ret := float_abs((glob__4*term1*term3*c(last_no) - glob__3*term1*term3
- glob__4*term2*term2*c(last_no) + glob__4*term2*term2
+ term2*term2*c(last_no*last_no) - term1*term3*c(last_no*last_no))
/(term2*term2*c(last_no) - glob__2*term2*term2
- term1*term3*c(last_no) + term1*term3));
ret
end proc
# End Function number 30
# Begin Function number 31
> comp_rad_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> #TOP SIX TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float,glob_six_term_ord_save;
> local ret,rm0,rm1,rm2,rm3,rm4,nr1,nr2,dr1,dr2,ds2,rad_c,ord_no,ds1,rcs;
> if ((term5 <> glob__0) and (term4 <> glob__0) and (term3 <> glob__0) and (term2 <> glob__0) and (term1 <> glob__0)) then # if number 11
> rm0 := term6/term5;
> rm1 := term5/term4;
> rm2 := term4/term3;
> rm3 := term3/term2;
> rm4 := term2/term1;
> nr1 := c(last_no-1)*rm0 - glob__2*c(last_no-2)*rm1 + c(last_no-3)*rm2;
> nr2 := c(last_no-2)*rm1 - glob__2*c(last_no-3)*rm2 + c(last_no-4)*rm3;
> dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
> dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
> ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
> ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
> if ((float_abs(nr1 * dr2 - nr2 * dr1) = glob__0) or (float_abs(dr1) = glob__0)) then # if number 12
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> else
> if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0) then # if number 13
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) -c(last_no)/glob__2;
> if (float_abs(rcs) <> glob__0) then # if number 14
> if (rcs > glob__0) then # if number 15
> rad_c := float_abs( sqrt(rcs) * float_abs(glob_h));
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 15
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 14
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 13
> fi;# end if 12
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 11;
> glob_six_term_ord_save := ord_no;
> rad_c;
> #BOTTOM SIX TERM RADIUS ANALYSIS
> end;
comp_rad_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
local ret, rm0, rm1, rm2, rm3, rm4, nr1, nr2, dr1, dr2, ds2, rad_c, ord_no,
ds1, rcs;
global glob_h, glob_larger_float, glob_six_term_ord_save;
if term5 <> glob__0 and term4 <> glob__0 and term3 <> glob__0 and
term2 <> glob__0 and term1 <> glob__0 then
rm0 := term6/term5;
rm1 := term5/term4;
rm2 := term4/term3;
rm3 := term3/term2;
rm4 := term2/term1;
nr1 := c(last_no - 1)*rm0 - glob__2*c(last_no - 2)*rm1
+ c(last_no - 3)*rm2;
nr2 := c(last_no - 2)*rm1 - glob__2*c(last_no - 3)*rm2
+ c(last_no - 4)*rm3;
dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
if
float_abs(nr1*dr2 - nr2*dr1) = glob__0 or float_abs(dr1) = glob__0
then rad_c := glob_larger_float; ord_no := glob_larger_float
else
if glob__0 < float_abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no :=
(rcs*nr1 - ds1)/(glob__2*dr1) - c(last_no)/glob__2;
if float_abs(rcs) <> glob__0 then
if glob__0 < rcs then
rad_c := float_abs(sqrt(rcs)*float_abs(glob_h))
else
rad_c := glob_larger_float;
ord_no := glob_larger_float
end if
else
rad_c := glob_larger_float; ord_no := glob_larger_float
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if;
glob_six_term_ord_save := ord_no;
rad_c
end proc
# End Function number 31
# Begin Function number 32
> comp_ord_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> global glob_six_term_ord_save;
> #TOP SIX TERM ORDER ANALYSIS
> #TOP SAVED FROM SIX TERM RADIUS ANALYSIS
> glob_six_term_ord_save;
> #BOTTOM SIX TERM ORDER ANALYSIS
> end;
comp_ord_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
global glob_six_term_ord_save;
glob_six_term_ord_save
end proc
# End Function number 32
# Begin Function number 33
> factorial_2 := proc(nnn)
> ret := nnn!;
> ret;;
> end;
Warning, `ret` is implicitly declared local to procedure `factorial_2`
factorial_2 := proc(nnn) local ret; ret := nnn!; ret end proc
# End Function number 33
# Begin Function number 34
> factorial_1 := proc(nnn)
> global ATS_MAX_TERMS,array_fact_1;
> local ret;
> if (nnn <= ATS_MAX_TERMS) then # if number 11
> if (array_fact_1[nnn] = 0) then # if number 12
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 12;
> else
> ret := factorial_2(nnn);
> fi;# end if 11;
> ret;
> end;
factorial_1 := proc(nnn)
local ret;
global ATS_MAX_TERMS, array_fact_1;
if nnn <= ATS_MAX_TERMS then
if array_fact_1[nnn] = 0 then
ret := factorial_2(nnn); array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := factorial_2(nnn)
end if;
ret
end proc
# End Function number 34
# Begin Function number 35
> factorial_3 := proc(mmm,nnn)
> global ATS_MAX_TERMS,array_fact_2;
> local ret;
> if ((nnn <= ATS_MAX_TERMS) and (mmm <= ATS_MAX_TERMS)) then # if number 11
> if (array_fact_2[mmm,nnn] = 0) then # if number 12
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 12;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 11;
> ret;
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global ATS_MAX_TERMS, array_fact_2;
if nnn <= ATS_MAX_TERMS and mmm <= ATS_MAX_TERMS then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := factorial_2(mmm)/factorial_2(nnn)
end if;
ret
end proc
# End Function number 35
# Begin Function number 36
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
# End Function number 36
# Begin Function number 37
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
# End Function number 37
# Begin Function number 38
> float_abs := proc(x)
> abs(x);
> end;
float_abs := proc(x) abs(x) end proc
# End Function number 38
# Begin Function number 39
> expt := proc(x,y)
> x^y;
> end;
expt := proc(x, y) x^y end proc
# End Function number 39
# Begin Function number 40
> neg := proc(x)
> -x;
> end;
neg := proc(x) -x end proc
# End Function number 40
# Begin Function number 41
> int_trunc := proc(x)
> trunc(x);
> end;
int_trunc := proc(x) trunc(x) end proc
# End Function number 41
# Begin Function number 42
> estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer)
> local desired_abs_gbl_error,range,estimated_steps,step_error;
> global glob_desired_digits_correct,ALWAYS,ATS_MAX_TERMS;
> omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
> desired_abs_gbl_error := expt(glob__10,c( -glob_desired_digits_correct)) * c(float_abs(c(estimated_answer)));
> omniout_float(ALWAYS,"estimated_h",32,estimated_h,32,"");
> omniout_float(ALWAYS,"estimated_answer",32,estimated_answer,32,"");
> omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,"");
> range := (x_end - x_start);
> omniout_float(ALWAYS,"range",32,range,32,"");
> estimated_steps := range / estimated_h;
> omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,"");
> step_error := (c(float_abs(desired_abs_gbl_error) /sqrt(c( estimated_steps))/c(ATS_MAX_TERMS)));
> omniout_float(ALWAYS,"step_error",32,step_error,32,"");
> (step_error);;
> end;
estimated_needed_step_error := proc(
x_start, x_end, estimated_h, estimated_answer)
local desired_abs_gbl_error, range, estimated_steps, step_error;
global glob_desired_digits_correct, ALWAYS, ATS_MAX_TERMS;
omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, "");
desired_abs_gbl_error :=
expt(glob__10, c(-glob_desired_digits_correct))*
c(float_abs(c(estimated_answer)));
omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, "");
omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, "")
;
omniout_float(ALWAYS, "desired_abs_gbl_error", 32,
desired_abs_gbl_error, 32, "");
range := x_end - x_start;
omniout_float(ALWAYS, "range", 32, range, 32, "");
estimated_steps := range/estimated_h;
omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, "");
step_error := c(float_abs(desired_abs_gbl_error)/(
sqrt(c(estimated_steps))*c(ATS_MAX_TERMS)));
omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
step_error
end proc
# End Function number 42
#END ATS LIBRARY BLOCK
#BEGIN USER FUNCTION BLOCK
#BEGIN BLOCK 3
#BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return(c(0.5) * c(x) + c(0.25) * ln(c(2.0) * c(x) + c(3.0)));
> end;
exact_soln_y :=
proc(x) return c(0.5)*c(x) + c(0.25)*ln(c(2.0)*c(x) + c(3.0)) 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_0D1,
> array_const_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local min_size;
> min_size := glob_estimated_size_answer;
> if (float_abs(array_y[1]) < min_size) then # if number 3
> min_size := float_abs(array_y[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> if (min_size < glob__1) then # if number 3
> min_size := glob__1;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> min_size;
> end;
est_size_answer := proc()
local min_size;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
min_size := glob_estimated_size_answer;
if float_abs(array_y[1]) < min_size then
min_size := float_abs(array_y[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if min_size < glob__1 then
min_size := glob__1;
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
min_size
end proc
# End Function number 4
# Begin Function number 5
> test_suggested_h := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> max_estimated_step_error := glob__small;
> no_terms := ATS_MAX_TERMS;
> hn_div_ho := glob__0_5;
> hn_div_ho_2 := glob__0_25;
> hn_div_ho_3 := glob__0_125;
> omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,"");
> omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,"");
> omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,"");
> est_tmp := float_abs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3);
> if (est_tmp >= max_estimated_step_error) then # if number 3
> max_estimated_step_error := est_tmp;
> fi;# end if 3;
> omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,"");
> max_estimated_step_error;
> end;
test_suggested_h := proc()
local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3,
no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
max_estimated_step_error := glob__small;
no_terms := ATS_MAX_TERMS;
hn_div_ho := glob__0_5;
hn_div_ho_2 := glob__0_25;
hn_div_ho_3 := glob__0_125;
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, "");
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, "");
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, "");
est_tmp := float_abs(array_y[no_terms - 3]
+ array_y[no_terms - 2]*hn_div_ho
+ array_y[no_terms - 1]*hn_div_ho_2
+ array_y[no_terms]*hn_div_ho_3);
if max_estimated_step_error <= est_tmp then
max_estimated_step_error := est_tmp
end if;
omniout_float(ALWAYS, "max_estimated_step_error", 32,
max_estimated_step_error, 32, "");
max_estimated_step_error
end proc
# End Function number 5
# Begin Function number 6
> track_estimated_error := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> no_terms := ATS_MAX_TERMS;
> hn_div_ho := glob__0_5;
> hn_div_ho_2 := glob__0_25;
> hn_div_ho_3 := glob__0_125;
> est_tmp := c(float_abs(array_y[no_terms-3])) + c(float_abs(array_y[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y[no_terms])) * c(hn_div_ho_3);
> if (glob_prec * c(float_abs(array_y[1])) > c(est_tmp)) then # if number 3
> est_tmp := c(glob_prec) * c(float_abs(array_y[1]));
> fi;# end if 3;
> if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 3
> array_max_est_error[1] := c(est_tmp);
> fi;# end if 3
> ;
> end;
track_estimated_error := proc()
local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
no_terms := ATS_MAX_TERMS;
hn_div_ho := glob__0_5;
hn_div_ho_2 := glob__0_25;
hn_div_ho_3 := glob__0_125;
est_tmp := c(float_abs(array_y[no_terms - 3]))
+ c(float_abs(array_y[no_terms - 2]))*c(hn_div_ho)
+ c(float_abs(array_y[no_terms - 1]))*c(hn_div_ho_2)
+ c(float_abs(array_y[no_terms]))*c(hn_div_ho_3);
if c(est_tmp) < glob_prec*c(float_abs(array_y[1])) then
est_tmp := c(glob_prec)*c(float_abs(array_y[1]))
end if;
if c(array_max_est_error[1]) <= c(est_tmp) then
array_max_est_error[1] := c(est_tmp)
end if
end proc
# End Function number 6
# Begin Function number 7
> reached_interval := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local ret;
> if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 3
> ret := true;
> else
> ret := false;
> fi;# end if 3;
> return(ret);
> end;
reached_interval := proc()
local ret;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
if glob_check_sign*glob_next_display - glob_h/glob__10 <=
glob_check_sign*array_x[1] then ret := true
else ret := false
end if;
return ret
end proc
# End Function number 7
# Begin Function number 8
> display_alot := proc(iter)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err;
> #TOP DISPLAY ALOT
> ind_var := array_x[1];
> omniout_complex(ALWAYS,"x[1] ",33,ind_var,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> omniout_complex(ALWAYS,"h ",33,glob_h,20," ");
> omniout_complex(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> closed_form_val_y := evalf(exact_soln_y(ind_var));
> omniout_complex(ALWAYS,"y[1] (closed_form) ",33,closed_form_val_y,20," ");
> abserr := float_abs(numeric_val - closed_form_val_y);
> if (float_abs(closed_form_val_y) > 0.0) then # if number 3
> relerr := abserr/float_abs(closed_form_val_y);
> if (float_abs(c(relerr)) > 0.0) then # if number 4
> glob_good_digits := round(-log10(relerr));
> else
> relerr := 0.0 ;
> glob_good_digits := Digits - 2;
> fi;# end if 4;
> else
> ;
> relerr := glob__m1 ;
> glob_good_digits := -16;
> fi;# end if 3;
> if (glob_good_digits < glob_min_good_digits) then # if number 3
> glob_min_good_digits := glob_good_digits;
> fi;# end if 3;
> omniout_float(ALWAYS,"absolute error ",4,abserr,4," ");
> omniout_float(ALWAYS,"relative error ",4,relerr * glob__100 ,4,"%");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> #BOTTOM DISPLAY ALOT
> end;
display_alot := proc(iter)
local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no,
est_rel_err;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
ind_var := array_x[1];
omniout_complex(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
omniout_complex(ALWAYS, "h ", 33, glob_h,
20, " ");
omniout_complex(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
closed_form_val_y := evalf(exact_soln_y(ind_var));
omniout_complex(ALWAYS, "y[1] (closed_form) ", 33,
closed_form_val_y, 20, " ");
abserr := float_abs(numeric_val - closed_form_val_y);
if 0. < float_abs(closed_form_val_y) then
relerr := abserr/float_abs(closed_form_val_y);
if 0. < float_abs(c(relerr)) then
glob_good_digits := round(-log10(relerr))
else relerr := 0.; glob_good_digits := Digits - 2
end if
else relerr := glob__m1; glob_good_digits := -16
end if;
if glob_good_digits < glob_min_good_digits then
glob_min_good_digits := glob_good_digits
end if;
omniout_float(ALWAYS, "absolute error ", 4, abserr, 4,
" ");
omniout_float(ALWAYS, "relative error ", 4,
relerr*glob__100, 4, "%");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ")
end proc
# End Function number 8
# Begin Function number 9
> prog_report := proc(x_start,x_end)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := (clock_sec1) - (glob_orig_start_sec);
> glob_clock_sec := (clock_sec1) - (glob_clock_start_sec);
> left_sec := (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1);
> expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h) ,( clock_sec1) - (glob_orig_start_sec));
> opt_clock_sec := ( clock_sec1) - (glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec));
> glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
> percent_done := comp_percent((x_end),(x_start),(array_x[1]) + (glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr((total_clock_sec));
> if (c(percent_done) < glob__100) then # if number 3
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr((expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr((glob_optimal_expect_sec));
> omniout_str_noeol(INFO,"Expected Total Time ");
> omniout_timestr((glob_total_exp_sec));
> fi;# end if 3;
> #BOTTOM PROGRESS REPORT
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec := clock_sec1 - glob_orig_start_sec;
glob_clock_sec := clock_sec1 - glob_clock_start_sec;
left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1;
expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h,
clock_sec1 - glob_orig_start_sec);
opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec;
glob_optimal_expect_sec :=
comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec)
;
glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h);
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(total_clock_sec);
if c(percent_done) < glob__100 then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(expect_sec);
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(glob_optimal_expect_sec);
omniout_str_noeol(INFO, "Expected Total Time ");
omniout_timestr(glob_total_exp_sec)
end if
end proc
# End Function number 9
# Begin Function number 10
> check_for_pole := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad, last_no;
> #TOP CHECK FOR POLE
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,1] := glob_larger_float;
> array_ord_test_poles[1,1] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 3
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 3;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 3
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 4
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 5
> found_sing := 0;
> fi;# end if 5;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 5
> if (rad_c < array_rad_test_poles[1,1]) then # if number 6
> array_rad_test_poles[1,1] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,1] := rad_c;
> array_ord_test_poles[1,1] := tmp_ord;
> fi;# end if 6;
> fi;# end if 5;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,2] := glob_larger_float;
> array_ord_test_poles[1,2] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 5
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 5;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 6
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 7
> found_sing := 0;
> fi;# end if 7;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 7
> if (rad_c < array_rad_test_poles[1,2]) then # if number 8
> array_rad_test_poles[1,2] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,2] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 9
> glob_min_pole_est := rad_c;
> fi;# end if 9;
> array_ord_test_poles[1,2] := tmp_ord;
> fi;# end if 8;
> fi;# end if 7;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,3] := glob_larger_float;
> array_ord_test_poles[1,3] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 7
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 7;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 8
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 9
> found_sing := 0;
> fi;# end if 9;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 9
> if (rad_c < array_rad_test_poles[1,3]) then # if number 10
> array_rad_test_poles[1,3] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,3] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 11
> glob_min_pole_est := rad_c;
> fi;# end if 11;
> array_ord_test_poles[1,3] := tmp_ord;
> fi;# end if 10;
> fi;# end if 9;
> #BOTTOM general radius test1
> ;
> if (true) then # if number 9
> display_poles();
> fi;# end if 9
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2,
term3, part1, part2, part3, part4, part5, part6, part7, part8, part9,
part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4,
found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio,
prev_tmp_rad, last_no;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 1] := glob_larger_float;
array_ord_test_poles[1, 1] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do
tmp_rad := comp_rad_from_ratio(array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 1] then
array_rad_test_poles[1, 1] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_ratio(array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
array_rad_test_poles[1, 1] := rad_c;
array_ord_test_poles[1, 1] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 2] := glob_larger_float;
array_ord_test_poles[1, 2] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do
tmp_rad := comp_rad_from_three_terms(
array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 2] then
array_rad_test_poles[1, 2] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_three_terms(
array_y_higher[1, last_no - 2],
array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
last_no);
array_rad_test_poles[1, 2] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 2] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 3] := glob_larger_float;
array_ord_test_poles[1, 3] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do
tmp_rad := comp_rad_from_six_terms(array_y_higher[1, last_no - 5],
array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3],
array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 3] then
array_rad_test_poles[1, 3] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_six_terms(
array_y_higher[1, last_no - 5],
array_y_higher[1, last_no - 4],
array_y_higher[1, last_no - 3],
array_y_higher[1, last_no - 2],
array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
last_no);
array_rad_test_poles[1, 3] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 3] := tmp_ord
end if
end if;
display_poles()
end proc
# End Function number 10
# Begin Function number 11
> atomall := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local kkk, order_d, adj2, adj3 , temporary, term;
> #TOP ATOMALL
> # before write maple main top matter
> # before generate constants assign
> # before generate globals assign
> #END OUTFILE1
> #BEGIN OUTFILE2
> #END OUTFILE2
> #BEGIN ATOMHDR1
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 1
> array_tmp1[1] := array_const_0D1[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp2[1] := array_tmp1[1] + array_const_0D2[1];
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 1
> array_tmp3[1] := array_const_0D2[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp4[1] := array_tmp3[1] + array_const_0D3[1];
> #emit pre div LINEAR - LINEAR $eq_no = 1 i = 1
> array_tmp5[1] := array_tmp2[1] / array_tmp4[1];
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp6[1] := array_const_0D0[1] + array_tmp5[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y_set_initial[1,2]) then # if number 1
> if (1 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp6[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
> if (2 <= ATS_MAX_TERMS) then # if number 3
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(1);
> array_y_higher[2,1] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
> array_tmp1[2] := array_const_0D1[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
> array_tmp3[2] := array_const_0D2[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp4[2] := array_tmp3[2];
> #emit pre div LINEAR - LINEAR $eq_no = 1 i = 2
> array_tmp5[2] := (array_tmp2[2] - array_tmp5[1] * array_tmp4[2]) / array_tmp4[1];
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp6[2] := array_tmp5[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y_set_initial[1,3]) then # if number 1
> if (2 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp6[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2));
> if (3 <= ATS_MAX_TERMS) then # if number 3
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y_higher[2,2] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre div LINEAR - LINEAR $eq_no = 1 i = 3
> array_tmp5[3] := neg( array_tmp5[2]) * array_tmp4[2] / array_tmp4[1];
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp6[3] := array_tmp5[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y_set_initial[1,4]) then # if number 1
> if (3 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp6[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3));
> if (4 <= ATS_MAX_TERMS) then # if number 3
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y_higher[2,3] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre div LINEAR - LINEAR $eq_no = 1 i = 4
> array_tmp5[4] := neg( array_tmp5[3]) * array_tmp4[2] / array_tmp4[1];
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp6[4] := array_tmp5[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y_set_initial[1,5]) then # if number 1
> if (4 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp6[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4));
> if (5 <= ATS_MAX_TERMS) then # if number 3
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y_higher[2,4] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre div LINEAR - LINEAR $eq_no = 1 i = 5
> array_tmp5[5] := neg( array_tmp5[4]) * array_tmp4[2] / array_tmp4[1];
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp6[5] := array_tmp5[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y_set_initial[1,6]) then # if number 1
> if (5 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp6[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5));
> if (6 <= ATS_MAX_TERMS) then # if number 3
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y_higher[2,5] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= ATS_MAX_TERMS) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit div LINEAR - LINEAR (NOP) $eq_no = 1 i = 1
> array_tmp5[kkk] := neg(array_tmp5[kkk-1]) * array_tmp4[2] / array_tmp4[1];
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp6[kkk] := array_tmp5[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1
> if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2
> temporary := c(array_tmp6[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
> array_y[kkk + order_d] := c(temporary);
> array_y_higher[1,kkk + order_d] := c(temporary);
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := c(temporary) / c(glob_h) * c(adj2);
> else
> temporary := c(temporary);
> fi;# end if 4;
> array_y_higher[adj3,term] := c(temporary);
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 1
> fi;# end if 2
> fi;# end if 1;
> kkk := kkk + 1;
> od;# end do number 1;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
array_tmp1[1] := array_const_0D1[1]*array_x[1];
array_tmp2[1] := array_tmp1[1] + array_const_0D2[1];
array_tmp3[1] := array_const_0D2[1]*array_x[1];
array_tmp4[1] := array_tmp3[1] + array_const_0D3[1];
array_tmp5[1] := array_tmp2[1]/array_tmp4[1];
array_tmp6[1] := array_const_0D0[1] + array_tmp5[1];
if not array_y_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp6[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
if 2 <= ATS_MAX_TERMS then
array_y[2] := temporary; array_y_higher[1, 2] := temporary
end if;
temporary := c(temporary)*c(1)/c(glob_h);
array_y_higher[2, 1] := c(temporary)
end if
end if;
kkk := 2;
array_tmp1[2] := array_const_0D1[1]*array_x[2];
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := array_const_0D2[1]*array_x[2];
array_tmp4[2] := array_tmp3[2];
array_tmp5[2] :=
(-array_tmp4[2]*array_tmp5[1] + array_tmp2[2])/array_tmp4[1];
array_tmp6[2] := array_tmp5[2];
if not array_y_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp6[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
if 3 <= ATS_MAX_TERMS then
array_y[3] := temporary; array_y_higher[1, 3] := temporary
end if;
temporary := c(temporary)*c(2)/c(glob_h);
array_y_higher[2, 2] := c(temporary)
end if
end if;
kkk := 3;
array_tmp5[3] := neg(array_tmp5[2])*array_tmp4[2]/array_tmp4[1];
array_tmp6[3] := array_tmp5[3];
if not array_y_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp6[3])*expt(glob_h, c(1))*c(factorial_3(2, 3));
if 4 <= ATS_MAX_TERMS then
array_y[4] := temporary; array_y_higher[1, 4] := temporary
end if;
temporary := c(temporary)*c(3)/c(glob_h);
array_y_higher[2, 3] := c(temporary)
end if
end if;
kkk := 4;
array_tmp5[4] := neg(array_tmp5[3])*array_tmp4[2]/array_tmp4[1];
array_tmp6[4] := array_tmp5[4];
if not array_y_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp6[4])*expt(glob_h, c(1))*c(factorial_3(3, 4));
if 5 <= ATS_MAX_TERMS then
array_y[5] := temporary; array_y_higher[1, 5] := temporary
end if;
temporary := c(temporary)*c(4)/c(glob_h);
array_y_higher[2, 4] := c(temporary)
end if
end if;
kkk := 5;
array_tmp5[5] := neg(array_tmp5[4])*array_tmp4[2]/array_tmp4[1];
array_tmp6[5] := array_tmp5[5];
if not array_y_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp6[5])*expt(glob_h, c(1))*c(factorial_3(4, 5));
if 6 <= ATS_MAX_TERMS then
array_y[6] := temporary; array_y_higher[1, 6] := temporary
end if;
temporary := c(temporary)*c(5)/c(glob_h);
array_y_higher[2, 5] := c(temporary)
end if
end if;
kkk := 6;
while kkk <= ATS_MAX_TERMS do
array_tmp5[kkk] :=
neg(array_tmp5[kkk - 1])*array_tmp4[2]/array_tmp4[1];
array_tmp6[kkk] := array_tmp5[kkk];
order_d := 1;
if kkk + order_d <= ATS_MAX_TERMS then
if not array_y_set_initial[1, kkk + order_d] then
temporary := c(array_tmp6[kkk])*expt(glob_h, c(order_d))*
c(factorial_3(kkk - 1, kkk + order_d - 1));
array_y[kkk + order_d] := c(temporary);
array_y_higher[1, kkk + order_d] := c(temporary);
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while
1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1
do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := c(temporary)*c(adj2)/c(glob_h)
else temporary := c(temporary)
end if;
array_y_higher[adj3, term] := c(temporary)
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
# End Function number 12
#END OUTFILE5
# Begin Function number 12
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it;
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
> array_const_0D3,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4,
> array_tmp5,
> array_tmp6,
> 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 := 30;
> # before first input block
> #BEGIN FIRST INPUT BLOCK
> #BEGIN BLOCK 1
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=30;
> #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..(30),[]);
> array_norms:= Array(0..(30),[]);
> array_fact_1:= Array(0..(30),[]);
> 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..(30),[]);
> array_x:= Array(0..(30),[]);
> array_tmp0:= Array(0..(30),[]);
> array_tmp1:= Array(0..(30),[]);
> array_tmp2:= Array(0..(30),[]);
> array_tmp3:= Array(0..(30),[]);
> array_tmp4:= Array(0..(30),[]);
> array_tmp5:= Array(0..(30),[]);
> array_tmp6:= Array(0..(30),[]);
> array_m1:= Array(0..(30),[]);
> array_y_higher := Array(0..(2) ,(0..30+ 1),[]);
> array_y_higher_work := Array(0..(2) ,(0..30+ 1),[]);
> array_y_higher_work2 := Array(0..(2) ,(0..30+ 1),[]);
> array_y_set_initial := Array(0..(2) ,(0..30+ 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..(30) ,(0..30+ 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 <= 30) do # do number 1
> array_y_init[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_norms[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) 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 <= 30) do # do number 1
> array_y[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_x[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp0[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp3[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp4[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp5[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) do # do number 1
> array_tmp6[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 30) 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 <= 30) 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 <= 30) 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 <= 30) 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 <= 30) 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 <=30) do # do number 1
> term := 1;
> while (term <= 30) do # do number 2
> array_fact_2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> # before symbols initialized
> #BEGIN SYMBOLS INITIALIZATED
> zero_ats_ar(array_y);
> zero_ats_ar(array_x);
> zero_ats_ar(array_tmp0);
> zero_ats_ar(array_tmp1);
> zero_ats_ar(array_tmp2);
> zero_ats_ar(array_tmp3);
> zero_ats_ar(array_tmp4);
> zero_ats_ar(array_tmp5);
> zero_ats_ar(array_tmp6);
> zero_ats_ar(array_m1);
> zero_ats_ar(array_const_1);
> array_const_1[1] := c(1);
> zero_ats_ar(array_const_0D0);
> array_const_0D0[1] := c(0.0);
> zero_ats_ar(array_const_0D1);
> array_const_0D1[1] := c(0.1);
> zero_ats_ar(array_const_0D2);
> array_const_0D2[1] := c(0.2);
> zero_ats_ar(array_const_0D3);
> array_const_0D3[1] := c(0.3);
> zero_ats_ar(array_m1);
> array_m1[1] := glob__m1;
> #END SYMBOLS INITIALIZATED
> # before generate factorials init
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= ATS_MAX_TERMS) do # do number 1
> jjjf := 0;
> while (jjjf <= ATS_MAX_TERMS) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Table
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> glob_yes_pole := 4;
> glob_no_pole := 3;
> glob_not_given := 0;
> glob_no_sing_tests := 4;
> glob_ratio_test := 1;
> glob_three_term_test := 2;
> glob_six_term_test := 3;
> glob_log_10 := log(c(10.0));
> MAX_UNCHANGED := 10;
> glob__small := c(0.1e-50);
> glob_small_float := c(0.1e-50);
> glob_smallish_float := c(0.1e-60);
> glob_large_float := c(1.0e100);
> glob_larger_float := c(1.1e100);
> glob__m2 := c(-2);
> glob__m1 := c(-1);
> glob__0 := c(0);
> glob__1 := c(1);
> glob__2 := c(2);
> glob__3 := c(3);
> glob__4 := c(4);
> glob__5 := c(5);
> glob__8 := c(8);
> glob__10 := c(10);
> glob__100 := c(100);
> glob__pi := c(0.0);
> glob__0_5 := c(0.5);
> glob__0_8 := c(0.8);
> glob__m0_8 := c(-0.8);
> glob__0_25 := c(0.25);
> glob__0_125 := c(0.125);
> glob_h := 0.1;
> glob_nxt := 1;
> glob_prec := c(1.0e-16);
> glob_check_sign := c(1.0);
> glob_desired_digits_correct := c(8.0);
> glob_max_estimated_step_error := c(0.0);
> glob_ratio_of_radius := c(0.1);
> glob_percent_done := c(0.0);
> glob_total_exp_sec := c(0.1);
> glob_optimal_expect_sec := c(0.1);
> glob_estimated_size_answer := c(100.0);
> glob_almost_1 := c(0.9990);
> glob_clock_sec := c(0.0);
> glob_clock_start_sec := c(0.0);
> glob_disp_incr := c(0.1);
> glob_diff_rc_fm := c(0.1);
> glob_diff_rc_fmm1 := c(0.1);
> glob_diff_rc_fmm2 := c(0.1);
> glob_diff_ord_fm := c(0.1);
> glob_diff_ord_fmm1 := c(0.1);
> glob_diff_ord_fmm2 := c(0.1);
> glob_six_term_ord_save := c(0.1);
> glob_guess_error_rc := c(0.1);
> glob_guess_error_ord := c(0.1);
> glob_least_given_sing := c(9.9e200);
> glob_least_ratio_sing := c(9.9e200);
> glob_least_3_sing := c(9.9e100);
> glob_least_6_sing := c(9.9e100);
> glob_last_good_h := c(0.1);
> glob_max_h := c(0.1);
> glob_min_h := c(0.000001);
> glob_display_interval := c(0.1);
> glob_abserr := c(0.1e-10);
> glob_relerr := c(0.1e-10);
> glob_min_pole_est := c(0.1e+10);
> glob_max_rel_trunc_err := c(0.1e-10);
> glob_max_trunc_err := c(0.1e-10);
> glob_max_hours := c(0.0);
> glob_optimal_clock_start_sec := c(0.0);
> glob_optimal_start := c(0.0);
> glob_upper_ratio_limit := c(1.0001);
> glob_lower_ratio_limit := c(0.9999);
> glob_max_sec := c(10000.0);
> glob_orig_start_sec := c(0.0);
> glob_normmax := c(0.0);
> glob_max_minutes := c(0.0);
> glob_next_display := c(0.0);
> glob_est_digits := 1;
> glob_subiter_method := 3;
> glob_html_log := true;
> glob_min_good_digits := 99999;
> glob_good_digits := 0;
> glob_min_apfp_est_good_digits := 99999;
> glob_apfp_est_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> glob_h_reason := 0;
> glob_sec_in_minute := 60 ;
> glob_min_in_hour := 60;
> glob_hours_in_day := 24;
> glob_days_in_year := 365;
> glob_sec_in_hour := 3600;
> glob_sec_in_day := 86400;
> glob_sec_in_year := 31536000;
> glob_not_yet_finished := true;
> glob_initial_pass := true;
> glob_not_yet_start_msg := true;
> glob_reached_optimal_h := false;
> glob_optimal_done := false;
> glob_type_given_pole := 0;
> glob_optimize := false;
> glob_look_poles := false;
> glob_dump_closed_form := false;
> glob_max_iter := 10000;
> glob_no_eqs := 0;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_start := 0;
> glob_iter := 0;
> # before generate set diff initial
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> # before generate init omniout const
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> ATS_MAX_TERMS := 30;
> 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/div_lin_linpostcpx.cpx#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) / ( 0.2 * x + 0.3 ) ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=30;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := 0.1 + 0.1 * I;");
> omniout_str(ALWAYS,"x_end := 99.0 + 99.0 * I;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_type_given_pole := 1;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_rad_poles[1,1] := c(-1.5);");
> 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(1.0);");
> 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,"");
> omniout_str(ALWAYS,"return(c(0.5) * c(x) + c(0.25) * ln(c(2.0) * c(x) + c(3.0)));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"next_delta := proc()");
> omniout_str(ALWAYS,"global glob_nxt, x_delta;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"x_delta := [ 0.001 + 0.00004 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.000 + 0.000 * I ];");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_nxt := glob_nxt + 1;");
> omniout_str(ALWAYS,"it := x_delta[glob_nxt];");
> omniout_str(ALWAYS,"return it;");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := glob__0;
> glob_smallish_float := glob__0;
> glob_large_float := c(1.0e100);
> glob_larger_float := c( 1.1e100);
> glob_almost_1 := c( 0.99);
> # before second block
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #BEGIN BLOCK 2
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := 0.1 + 0.1 * I;
> x_end := 99.0 + 99.0 * I;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_type_given_pole := 1;
> array_given_rad_poles[1,1] := c(-1.5);
> array_given_rad_poles[1,2] := c(0.0);
> array_given_ord_poles[1,1] := c(1.0);
> 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 ) = ( 0.1 * x + 0.2 ) / ( 0.2 * x + 0.3 ) ; ");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 10
> logstart(html_log_file);
> logitem_str(html_log_file,"2017-11-26T14:47:11-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"div_lin_lin")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) / ( 0.2 * x + 0.3 ) ; ")
> ;
> 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,"div_lin_lin diffeq.mxt")
> ;
> logitem_str(html_log_file,"div_lin_lin maple results")
> ;
> logitem_str(html_log_file,"OK")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 15;
> if (glob_html_log) then # if number 15
> fclose(html_log_file);
> fi;# end if 15
> ;
> ;;
> end;
> # End Function number 12
> #END OUTFILEMAIN
> end;
Warning, `h_new` is implicitly declared local to procedure `main`
Warning, `ratio` is implicitly declared local to procedure `main`
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max,
term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order,
sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it,
last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err,
estimated_step_error, min_value, est_answer, found_h, repeat_it, h_new,
ratio;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_const_0D3, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4, array_tmp5, array_tmp6,
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 := 30;
Digits := 32;
max_terms := 30;
glob_html_log := true;
array_y_init := Array(0 .. 30, []);
array_norms := Array(0 .. 30, []);
array_fact_1 := Array(0 .. 30, []);
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 .. 30, []);
array_x := Array(0 .. 30, []);
array_tmp0 := Array(0 .. 30, []);
array_tmp1 := Array(0 .. 30, []);
array_tmp2 := Array(0 .. 30, []);
array_tmp3 := Array(0 .. 30, []);
array_tmp4 := Array(0 .. 30, []);
array_tmp5 := Array(0 .. 30, []);
array_tmp6 := Array(0 .. 30, []);
array_m1 := Array(0 .. 30, []);
array_y_higher := Array(0 .. 2, 0 .. 31, []);
array_y_higher_work := Array(0 .. 2, 0 .. 31, []);
array_y_higher_work2 := Array(0 .. 2, 0 .. 31, []);
array_y_set_initial := Array(0 .. 2, 0 .. 31, []);
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 .. 30, 0 .. 31, []);
term := 1;
while term <= 30 do array_y_init[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 30 do array_norms[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 30 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 <= 30 do array_y[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_x[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp0[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp1[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp3[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp4[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp5[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_tmp6[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 30 do array_m1[term] := c(0.); term := term + 1 end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 30 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 <= 30 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 <= 30 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 <= 30 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 <= 30 do
term := 1;
while term <= 30 do
array_fact_2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
zero_ats_ar(array_y);
zero_ats_ar(array_x);
zero_ats_ar(array_tmp0);
zero_ats_ar(array_tmp1);
zero_ats_ar(array_tmp2);
zero_ats_ar(array_tmp3);
zero_ats_ar(array_tmp4);
zero_ats_ar(array_tmp5);
zero_ats_ar(array_tmp6);
zero_ats_ar(array_m1);
zero_ats_ar(array_const_1);
array_const_1[1] := c(1);
zero_ats_ar(array_const_0D0);
array_const_0D0[1] := c(0.);
zero_ats_ar(array_const_0D1);
array_const_0D1[1] := c(0.1);
zero_ats_ar(array_const_0D2);
array_const_0D2[1] := c(0.2);
zero_ats_ar(array_const_0D3);
array_const_0D3[1] := c(0.3);
zero_ats_ar(array_m1);
array_m1[1] := glob__m1;
iiif := 0;
while iiif <= ATS_MAX_TERMS do
jjjf := 0;
while jjjf <= ATS_MAX_TERMS do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
glob_yes_pole := 4;
glob_no_pole := 3;
glob_not_given := 0;
glob_no_sing_tests := 4;
glob_ratio_test := 1;
glob_three_term_test := 2;
glob_six_term_test := 3;
glob_log_10 := log(c(10.0));
MAX_UNCHANGED := 10;
glob__small := c(0.1*10^(-50));
glob_small_float := c(0.1*10^(-50));
glob_smallish_float := c(0.1*10^(-60));
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob__m2 := c(-2);
glob__m1 := c(-1);
glob__0 := c(0);
glob__1 := c(1);
glob__2 := c(2);
glob__3 := c(3);
glob__4 := c(4);
glob__5 := c(5);
glob__8 := c(8);
glob__10 := c(10);
glob__100 := c(100);
glob__pi := c(0.);
glob__0_5 := c(0.5);
glob__0_8 := c(0.8);
glob__m0_8 := c(-0.8);
glob__0_25 := c(0.25);
glob__0_125 := c(0.125);
glob_h := 0.1;
glob_nxt := 1;
glob_prec := c(0.10*10^(-15));
glob_check_sign := c(1.0);
glob_desired_digits_correct := c(8.0);
glob_max_estimated_step_error := c(0.);
glob_ratio_of_radius := c(0.1);
glob_percent_done := c(0.);
glob_total_exp_sec := c(0.1);
glob_optimal_expect_sec := c(0.1);
glob_estimated_size_answer := c(100.0);
glob_almost_1 := c(0.9990);
glob_clock_sec := c(0.);
glob_clock_start_sec := c(0.);
glob_disp_incr := c(0.1);
glob_diff_rc_fm := c(0.1);
glob_diff_rc_fmm1 := c(0.1);
glob_diff_rc_fmm2 := c(0.1);
glob_diff_ord_fm := c(0.1);
glob_diff_ord_fmm1 := c(0.1);
glob_diff_ord_fmm2 := c(0.1);
glob_six_term_ord_save := c(0.1);
glob_guess_error_rc := c(0.1);
glob_guess_error_ord := c(0.1);
glob_least_given_sing := c(0.99*10^201);
glob_least_ratio_sing := c(0.99*10^201);
glob_least_3_sing := c(0.99*10^101);
glob_least_6_sing := c(0.99*10^101);
glob_last_good_h := c(0.1);
glob_max_h := c(0.1);
glob_min_h := c(0.1*10^(-5));
glob_display_interval := c(0.1);
glob_abserr := c(0.1*10^(-10));
glob_relerr := c(0.1*10^(-10));
glob_min_pole_est := c(0.1*10^10);
glob_max_rel_trunc_err := c(0.1*10^(-10));
glob_max_trunc_err := c(0.1*10^(-10));
glob_max_hours := c(0.);
glob_optimal_clock_start_sec := c(0.);
glob_optimal_start := c(0.);
glob_upper_ratio_limit := c(1.0001);
glob_lower_ratio_limit := c(0.9999);
glob_max_sec := c(10000.0);
glob_orig_start_sec := c(0.);
glob_normmax := c(0.);
glob_max_minutes := c(0.);
glob_next_display := c(0.);
glob_est_digits := 1;
glob_subiter_method := 3;
glob_html_log := true;
glob_min_good_digits := 99999;
glob_good_digits := 0;
glob_min_apfp_est_good_digits := 99999;
glob_apfp_est_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
glob_h_reason := 0;
glob_sec_in_minute := 60;
glob_min_in_hour := 60;
glob_hours_in_day := 24;
glob_days_in_year := 365;
glob_sec_in_hour := 3600;
glob_sec_in_day := 86400;
glob_sec_in_year := 31536000;
glob_not_yet_finished := true;
glob_initial_pass := true;
glob_not_yet_start_msg := true;
glob_reached_optimal_h := false;
glob_optimal_done := false;
glob_type_given_pole := 0;
glob_optimize := false;
glob_look_poles := false;
glob_dump_closed_form := false;
glob_max_iter := 10000;
glob_no_eqs := 0;
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_start := 0;
glob_iter := 0;
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
ATS_MAX_TERMS := 30;
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/div_lin_linpostcpx.cpx#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = ( 0.1 * x + \
0.2 ) / ( 0.2 * x + 0.3 ) ; ");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=30;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := 0.1 + 0.1 * I;");
omniout_str(ALWAYS, "x_end := 99.0 + 99.0 * I;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_type_given_pole := 1;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_rad_poles[1,1] := c(-1.5);");
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(1.0);");
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, "");
omniout_str(ALWAYS,
"return(c(0.5) * c(x) + c(0.25) * ln(c(2.0) * c(x) + c(3.0)));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "next_delta := proc()");
omniout_str(ALWAYS, "global glob_nxt, x_delta;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "x_delta := [ 0.001 + 0.00004 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
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omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.000 + 0.000 * I ];");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_nxt := glob_nxt + 1;");
omniout_str(ALWAYS, "it := x_delta[glob_nxt];");
omniout_str(ALWAYS, "return it;");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := glob__0;
glob_smallish_float := glob__0;
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob_almost_1 := c(0.99);
x_start := 0.1 + 0.1*I;
x_end := 99.0 + 99.0*I;
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_type_given_pole := 1;
array_given_rad_poles[1, 1] := c(-1.5);
array_given_rad_poles[1, 2] := c(0.);
array_given_ord_poles[1, 1] := c(1.0);
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 ) = ( 0.1 * x +\
0.2 ) / ( 0.2 * x + 0.3 ) ; ");
omniout_int(INFO, "Iterations ", 32, glob_iter,
4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2017-11-26T14:47:11-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"div_lin_lin");
logitem_str(html_log_file, "diff ( y , x , 1 ) = (\
0.1 * x + 0.2 ) / ( 0.2 * x + 0.3 ) ; ");
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, "div_lin_lin diffeq.mxt");
logitem_str(html_log_file, "div_lin_lin 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/div_lin_linpostcpx.cpx#################
diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) / ( 0.2 * x + 0.3 ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 0.1 + 0.1 * I;
x_end := 99.0 + 99.0 * I;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_type_given_pole := 1;
array_given_rad_poles[1,1] := c(-1.5);
array_given_rad_poles[1,2] := c(0.0);
array_given_ord_poles[1,1] := c(1.0);
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(0.5) * c(x) + c(0.25) * ln(c(2.0) * c(x) + c(3.0)));
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,
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0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.000 + 0.000 * I ];
glob_nxt := glob_nxt + 1;
it := x_delta[glob_nxt];
return it;
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = 0.1 0.1
h = 0.0001 0.005
y[1] (numeric) = 0.341275032503 0.065604702499
y[1] (closed_form) = 0.341275032503 0.065604702499
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 1.603
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.004
Order of pole (three term test) = 2.767e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1001 0.105
h = 0.0001 0.003
y[1] (numeric) = 0.341390193683 0.0688817737926
y[1] (closed_form) = 0.341390434165 0.0688817378003
absolute error = 2.432e-07
relative error = 6.982e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 1.604
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9625
Order of pole (three term test) = 2.552e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1002 0.108
h = 0.001 0.001
y[1] (numeric) = 0.341487093677 0.0708473286816
y[1] (closed_form) = 0.341487046502 0.0708473413831
absolute error = 4.885e-08
relative error = 1.401e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 1.604
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7556
Order of pole (three term test) = 1.341e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1012 0.109
h = 0.001 0.003
y[1] (numeric) = 0.342153231334 0.0714921859663
y[1] (closed_form) = 0.342153051889 0.0714922707476
absolute error = 1.985e-07
relative error = 5.678e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 1.605
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.589
Order of pole (three term test) = 7.706e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1022 0.112
h = 0.0001 0.004
y[1] (numeric) = 0.342840452458 0.0734476391158
y[1] (closed_form) = 0.342840547877 0.0734475879594
absolute error = 1.083e-07
relative error = 3.088e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 1.606
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.032
Order of pole (three term test) = 3.304e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1023 0.116
h = 0.003 0.006
y[1] (numeric) = 0.342949939323 0.0760673733256
y[1] (closed_form) = 0.342950254857 0.0760674618237
absolute error = 3.277e-07
relative error = 9.329e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 1.606
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.693
Order of pole (three term test) = 1.694e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1053 0.122
h = 0.0001 0.005
y[1] (numeric) = 0.344984042956 0.0799641655914
y[1] (closed_form) = 0.3449843488 0.0799631113708
absolute error = 1.098e-06
relative error = 0.00031 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 1.61
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.2
Order of pole (three term test) = 4.840e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1054 0.127
h = 0.0001 0.003
y[1] (numeric) = 0.345109662786 0.0832362260261
y[1] (closed_form) = 0.345109853927 0.0832359014974
absolute error = 3.766e-07
relative error = 0.0001061 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 1.61
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9666
Order of pole (three term test) = 5.178e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1055 0.13
h = 0.001 0.001
y[1] (numeric) = 0.345212572676 0.0851991165446
y[1] (closed_form) = 0.34521248002 0.0851988479219
absolute error = 2.842e-07
relative error = 7.991e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 1.611
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7589
Order of pole (three term test) = 1.339e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1065 0.131
h = 0.001 0.003
y[1] (numeric) = 0.345879913121 0.0858411206414
y[1] (closed_form) = 0.345879691291 0.0858409269676
absolute error = 2.945e-07
relative error = 8.263e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 1.612
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.604
Order of pole (three term test) = 1.485e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1075 0.134
h = 0.0001 0.004
y[1] (numeric) = 0.346572384172 0.0877920789988
y[1] (closed_form) = 0.34657243114 0.0877917433098
absolute error = 3.390e-07
relative error = 9.481e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 1.613
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.041
Order of pole (three term test) = 1.803e-29 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=27.1MB, alloc=40.3MB, time=0.33
x[1] = 0.1076 0.138
h = 0.003 0.006
y[1] (numeric) = 0.346689856504 0.0904082837777
y[1] (closed_form) = 0.346690125304 0.090408080653
absolute error = 3.369e-07
relative error = 9.404e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 1.614
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.705
Order of pole (three term test) = 2.314e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1106 0.144
h = 0.0001 0.005
y[1] (numeric) = 0.348733505207 0.0942939793691
y[1] (closed_form) = 0.348733734181 0.0942926441582
absolute error = 1.355e-06
relative error = 0.000375 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.617
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.205
Order of pole (three term test) = 4.005e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1107 0.149
h = 0.0001 0.003
y[1] (numeric) = 0.348869004876 0.0975615687147
y[1] (closed_form) = 0.348869139431 0.0975609595362
absolute error = 6.239e-07
relative error = 0.0001722 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 1.618
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9709
Order of pole (three term test) = 4.260e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1108 0.152
h = 0.001 0.001
y[1] (numeric) = 0.348977799645 0.099521659986
y[1] (closed_form) = 0.348977654493 0.0995211136735
absolute error = 5.653e-07
relative error = 0.0001558 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 1.618
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7623
Order of pole (three term test) = 3.287e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1118 0.153
h = 0.001 0.003
y[1] (numeric) = 0.349646256472 0.10016080505
y[1] (closed_form) = 0.349645985314 0.100160336393
absolute error = 5.414e-07
relative error = 0.0001489 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 1.619
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.62
Order of pole (three term test) = 2.447e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1128 0.156
h = 0.0001 0.004
y[1] (numeric) = 0.350343810953 0.102107170746
y[1] (closed_form) = 0.350343802371 0.10210655432
absolute error = 6.165e-07
relative error = 0.0001689 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 1.62
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.05
Order of pole (three term test) = 4.627e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1129 0.16
h = 0.003 0.006
y[1] (numeric) = 0.350469102611 0.104719667713
y[1] (closed_form) = 0.350469317276 0.104719176793
absolute error = 5.358e-07
relative error = 0.0001465 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 1.621
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.717
Order of pole (three term test) = 2.744e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1159 0.166
h = 0.0001 0.005
y[1] (numeric) = 0.352521915958 0.108594117383
y[1] (closed_form) = 0.352522061503 0.108592506044
absolute error = 1.618e-06
relative error = 0.0004386 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.624
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.211
Order of pole (three term test) = 7.081e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.116 0.171
h = 0.0001 0.003
y[1] (numeric) = 0.352667086346 0.111857018019
y[1] (closed_form) = 0.352667157323 0.111856128311
absolute error = 8.925e-07
relative error = 0.0002412 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 1.625
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9754
Order of pole (three term test) = 2.353e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1161 0.174
h = 0.001 0.001
y[1] (numeric) = 0.35278163743 0.11381418198
y[1] (closed_form) = 0.352781433006 0.113813361838
absolute error = 8.452e-07
relative error = 0.000228 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 1.625
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7658
Order of pole (three term test) = 4.189e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1171 0.175
h = 0.001 0.003
y[1] (numeric) = 0.353451125222 0.114450465644
y[1] (closed_form) = 0.353450798021 0.114449725703
absolute error = 8.091e-07
relative error = 0.0002178 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 1.627
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.637
Order of pole (three term test) = 3.026e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1181 0.178
h = 0.0001 0.004
y[1] (numeric) = 0.35415359514 0.116392148727
y[1] (closed_form) = 0.354153524155 0.116391255588
absolute error = 8.960e-07
relative error = 0.0002403 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 1.628
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.06
Order of pole (three term test) = 2.757e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1182 0.182
h = 0.003 0.006
y[1] (numeric) = 0.354286535343 0.119000768544
y[1] (closed_form) = 0.354286688725 0.118999993898
absolute error = 7.897e-07
relative error = 0.0002113 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 1.628
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.73
Order of pole (three term test) = 3.159e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1212 0.188
h = 0.0001 0.005
y[1] (numeric) = 0.356348132496 0.122863840072
y[1] (closed_form) = 0.356348188342 0.122861957647
absolute error = 1.883e-06
relative error = 0.0004996 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.632
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.217
Order of pole (three term test) = 2.382e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1213 0.193
h = 0.0001 0.003
y[1] (numeric) = 0.356502759009 0.126121845662
y[1] (closed_form) = 0.356502759678 0.126120679759
absolute error = 1.166e-06
relative error = 0.0003083 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 1.633
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.98
Order of pole (three term test) = 9.806e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1214 0.196
h = 0.001 0.001
y[1] (numeric) = 0.356622934721 0.128075961115
y[1] (closed_form) = 0.35662266449 0.128074871213
absolute error = 1.123e-06
relative error = 0.0002963 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 1.633
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7695
Order of pole (three term test) = 2.530e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1224 0.197
h = 0.0001 0.004
y[1] (numeric) = 0.357293369211 0.128709384374
y[1] (closed_form) = 0.357292979483 0.128708377054
absolute error = 1.080e-06
relative error = 0.0002844 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 1.634
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.624
Order of pole (three term test) = 7.847e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1225 0.201
h = 0.003 0.006
y[1] (numeric) = 0.357432441142 0.131314725621
y[1] (closed_form) = 0.357432637354 0.131313731678
absolute error = 1.013e-06
relative error = 0.0002661 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 1.635
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.741
Order of pole (three term test) = 3.869e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1255 0.207
h = 0.0001 0.005
y[1] (numeric) = 0.359501431845 0.13516800859
y[1] (closed_form) = 0.359501506627 0.135165918151
absolute error = 2.092e-06
relative error = 0.0005446 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.639
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.222
Order of pole (three term test) = 3.652e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1256 0.212
h = 0.0001 0.003
y[1] (numeric) = 0.359664083805 0.13842175319
y[1] (closed_form) = 0.359664119784 0.138420374564
absolute error = 1.379e-06
relative error = 0.0003579 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.639
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.984
Order of pole (three term test) = 1.175e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1257 0.215
h = 0.001 0.001
y[1] (numeric) = 0.359789031628 0.140373217615
y[1] (closed_form) = 0.359788800653 0.140371920369
absolute error = 1.318e-06
relative error = 0.0003412 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.64
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7726
Order of pole (three term test) = 3.050e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1267 0.216
h = 0.001 0.003
y[1] (numeric) = 0.360460248513 0.141004191935
y[1] (closed_form) = 0.360459900871 0.141002979231
absolute error = 1.262e-06
relative error = 0.0003259 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.641
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.669
Order of pole (three term test) = 1.515e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1277 0.219
h = 0.0001 0.004
y[1] (numeric) = 0.361171472419 0.142937002931
y[1] (closed_form) = 0.361171368923 0.142935627718
absolute error = 1.379e-06
relative error = 0.000355 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.642
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.078
Order of pole (three term test) = 1.196e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1278 0.223
h = 0.003 0.006
y[1] (numeric) = 0.361318227192 0.145538074906
y[1] (closed_form) = 0.361318349468 0.145536805315
absolute error = 1.275e-06
relative error = 0.0003274 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.643
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.755
Order of pole (three term test) = 1.429e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1308 0.229
h = 0.0001 0.005
y[1] (numeric) = 0.363395296073 0.149379773415
y[1] (closed_form) = 0.363395270213 0.149377421613
absolute error = 2.352e-06
relative error = 0.0005986 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.647
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.228
Order of pole (three term test) = 2.793e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1309 0.234
h = 0.0001 0.003
y[1] (numeric) = 0.363566994767 0.152628266538
y[1] (closed_form) = 0.363566948575 0.152626620224
absolute error = 1.647e-06
relative error = 0.0004177 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.648
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9889
Order of pole (three term test) = 4.680e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.131 0.237
h = 0.001 0.001
y[1] (numeric) = 0.363697316528 0.154576473636
y[1] (closed_form) = 0.363697008206 0.154574914632
absolute error = 1.589e-06
relative error = 0.0004021 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.648
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7765
Order of pole (three term test) = 1.538e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.132 0.238
h = 0.001 0.003
y[1] (numeric) = 0.364369326778 0.155204596939
y[1] (closed_form) = 0.364368905139 0.15520312456
absolute error = 1.532e-06
relative error = 0.0003867 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.649
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.688
Order of pole (three term test) = 1.910e-29 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=71.1MB, alloc=52.3MB, time=0.87
x[1] = 0.133 0.241
h = 0.0001 0.004
y[1] (numeric) = 0.365084981886 0.157132508905
y[1] (closed_form) = 0.36508479775 0.157130869518
absolute error = 1.650e-06
relative error = 0.0004151 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.651
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.089
Order of pole (three term test) = 3.681e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1331 0.245
h = 0.003 0.006
y[1] (numeric) = 0.365238877632 0.159729267465
y[1] (closed_form) = 0.365238919587 0.159727726894
absolute error = 1.541e-06
relative error = 0.0003866 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.651
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.769
Order of pole (three term test) = 3.008e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1361 0.251
h = 0.0001 0.005
y[1] (numeric) = 0.367323647242 0.163559296148
y[1] (closed_form) = 0.367323515316 0.163556688437
absolute error = 2.611e-06
relative error = 0.0006494 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.655
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.234
Order of pole (three term test) = 3.222e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1362 0.256
h = 0.0001 0.003
y[1] (numeric) = 0.367504166036 0.166802363866
y[1] (closed_form) = 0.367504031718 0.16680045472
absolute error = 1.914e-06
relative error = 0.0004742 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.656
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.994
Order of pole (three term test) = 2.402e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1363 0.259
h = 0.001 0.001
y[1] (numeric) = 0.367639723288 0.1687472121
y[1] (closed_form) = 0.367639331811 0.16874539592
absolute error = 1.858e-06
relative error = 0.0004593 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.657
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7805
Order of pole (three term test) = 1.758e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1373 0.26
h = 0.001 0.003
y[1] (numeric) = 0.36831244668 0.169372494294
y[1] (closed_form) = 0.368311945262 0.169370766661
absolute error = 1.799e-06
relative error = 0.0004438 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.658
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.707
Order of pole (three term test) = 1.187e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1383 0.263
h = 0.0001 0.004
y[1] (numeric) = 0.369032363104 0.171295446914
y[1] (closed_form) = 0.369032092482 0.171293548095
absolute error = 1.918e-06
relative error = 0.0004714 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.659
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.099
Order of pole (three term test) = 1.983e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1384 0.267
h = 0.003 0.006
y[1] (numeric) = 0.369193216164 0.173887757872
y[1] (closed_form) = 0.369193171693 0.173885951161
absolute error = 1.807e-06
relative error = 0.0004429 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.66
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.783
Order of pole (three term test) = 2.300e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1414 0.273
h = 0.0001 0.005
y[1] (numeric) = 0.371285311837 0.177706046939
y[1] (closed_form) = 0.371285068718 0.17770318888
absolute error = 2.868e-06
relative error = 0.0006969 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.664
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.24
Order of pole (three term test) = 1.641e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1415 0.278
h = 0.0001 0.003
y[1] (numeric) = 0.371474421197 0.180943526599
y[1] (closed_form) = 0.371474193078 0.180941359625
absolute error = 2.179e-06
relative error = 0.0005273 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.665
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9993
Order of pole (three term test) = 3.381e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1416 0.281
h = 0.001 0.001
y[1] (numeric) = 0.371615073919 0.182884921253
y[1] (closed_form) = 0.37161459374 0.182882852623
absolute error = 2.124e-06
relative error = 0.0005127 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.665
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7847
Order of pole (three term test) = 8.802e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1426 0.282
h = 0.001 0.003
y[1] (numeric) = 0.372288431893 0.183507375087
y[1] (closed_form) = 0.372287845167 0.183505396769
absolute error = 2.063e-06
relative error = 0.0004972 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.667
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.727
Order of pole (three term test) = 3.092e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1436 0.285
h = 0.0001 0.004
y[1] (numeric) = 0.373012440226 0.185425315368
y[1] (closed_form) = 0.373012077542 0.185423162006
absolute error = 2.184e-06
relative error = 0.0005242 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.668
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.111
Order of pole (three term test) = 2.644e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1437 0.289
h = 0.003 0.006
y[1] (numeric) = 0.373180064908 0.188013053565
y[1] (closed_form) = 0.373179928183 0.188010985708
absolute error = 2.072e-06
relative error = 0.0004959 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.669
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.798
Order of pole (three term test) = 2.187e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1467 0.295
h = 0.0001 0.005
y[1] (numeric) = 0.375279115473 0.191819548327
y[1] (closed_form) = 0.375278756326 0.191816445571
absolute error = 3.123e-06
relative error = 0.0007411 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.673
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.247
Order of pole (three term test) = 5.311e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1468 0.3
h = 0.0001 0.003
y[1] (numeric) = 0.375476583585 0.195051288446
y[1] (closed_form) = 0.375476256267 0.195048868779
absolute error = 2.442e-06
relative error = 0.0005771 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.674
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.005
Order of pole (three term test) = 3.082e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1469 0.303
h = 0.001 0.001
y[1] (numeric) = 0.375622190549 0.196989141552
y[1] (closed_form) = 0.375621616385 0.196986825329
absolute error = 2.386e-06
relative error = 0.0005626 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.675
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7889
Order of pole (three term test) = 2.881e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1479 0.304
h = 0.0001 0.004
y[1] (numeric) = 0.376296106316 0.197608782474
y[1] (closed_form) = 0.376295429004 0.197606558174
absolute error = 2.325e-06
relative error = 0.0005471 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.676
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.741
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.148 0.308
h = 0.003 0.006
y[1] (numeric) = 0.37646913726 0.200192704519
y[1] (closed_form) = 0.376469014591 0.20019042442
absolute error = 2.283e-06
relative error = 0.0005355 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.677
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.811
Order of pole (three term test) = 3.619e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.151 0.314
h = 0.0001 0.005
y[1] (numeric) = 0.378574021407 0.203989091407
y[1] (closed_form) = 0.378573656451 0.20398579078
absolute error = 3.321e-06
relative error = 0.0007722 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.681
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.253
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1511 0.319
h = 0.0001 0.003
y[1] (numeric) = 0.378778568145 0.20721587403
y[1] (closed_form) = 0.378778249144 0.207213249414
absolute error = 2.644e-06
relative error = 0.0006124 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.682
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.009
Order of pole (three term test) = 7.581e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1512 0.322
h = 0.001 0.001
y[1] (numeric) = 0.378928369298 0.209150670041
y[1] (closed_form) = 0.37892780796 0.209148153101
absolute error = 2.579e-06
relative error = 0.0005958 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.682
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7926
Order of pole (three term test) = 3.125e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1522 0.323
h = 0.001 0.003
y[1] (numeric) = 0.379602738329 0.209767909458
y[1] (closed_form) = 0.379602076756 0.209765485748
absolute error = 2.512e-06
relative error = 0.0005793 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.683
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.764
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1532 0.326
h = 0.0001 0.004
y[1] (numeric) = 0.380333973827 0.211676450238
y[1] (closed_form) = 0.380333523701 0.211673845048
absolute error = 2.644e-06
relative error = 0.0006074 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.685
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.132
Order of pole (three term test) = 1.342e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1533 0.33
h = 0.003 0.006
y[1] (numeric) = 0.380513757301 0.214255452335
y[1] (closed_form) = 0.380513532227 0.214252920677
absolute error = 2.542e-06
relative error = 0.000582 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.686
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.826
Order of pole (three term test) = 3.419e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1563 0.336
h = 0.0001 0.005
y[1] (numeric) = 0.38262491747 0.218039977294
y[1] (closed_form) = 0.382624428198 0.218036442624
absolute error = 3.568e-06
relative error = 0.0008103 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.69
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.26
Order of pole (three term test) = 4.216e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1564 0.341
h = 0.0001 0.003
y[1] (numeric) = 0.382837389068 0.221260764947
y[1] (closed_form) = 0.382836961505 0.221257897425
absolute error = 2.899e-06
relative error = 0.0006557 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.691
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.015
Order of pole (three term test) = 5.996e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1565 0.344
h = 0.001 0.001
y[1] (numeric) = 0.38299188054 0.223191871648
y[1] (closed_form) = 0.382991216025 0.22318911639
absolute error = 2.834e-06
relative error = 0.0006394 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.692
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.7971
Order of pole (three term test) = 2.615e-29 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=115.1MB, alloc=52.3MB, time=1.38
x[1] = 0.1575 0.345
h = 0.001 0.003
y[1] (numeric) = 0.383666669233 0.223806332714
y[1] (closed_form) = 0.383665907881 0.223803672018
absolute error = 2.767e-06
relative error = 0.0006231 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.693
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.786
Order of pole (three term test) = 2.297e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1585 0.348
h = 0.0001 0.004
y[1] (numeric) = 0.384401518067 0.22570974632
y[1] (closed_form) = 0.384400961364 0.225706901164
absolute error = 2.899e-06
relative error = 0.0006504 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.695
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.144
Order of pole (three term test) = 1.777e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1586 0.352
h = 0.003 0.006
y[1] (numeric) = 0.384587536115 0.228283864196
y[1] (closed_form) = 0.384587203616 0.228281086327
absolute error = 2.798e-06
relative error = 0.0006256 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.696
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.843
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1616 0.358
h = 0.0001 0.005
y[1] (numeric) = 0.386704614475 0.232056512915
y[1] (closed_form) = 0.386703996879 0.23205275003
absolute error = 3.813e-06
relative error = 0.0008455 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.7
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.267
Order of pole (three term test) = 5.457e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1617 0.363
h = 0.0001 0.003
y[1] (numeric) = 0.386924775685 0.235271185207
y[1] (closed_form) = 0.386924234958 0.235268080199
absolute error = 3.152e-06
relative error = 0.000696 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.701
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.021
Order of pole (three term test) = 2.638e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1618 0.366
h = 0.001 0.001
y[1] (numeric) = 0.387083814642 0.237198533357
y[1] (closed_form) = 0.387083042417 0.237195544928
absolute error = 3.087e-06
relative error = 0.0006799 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.702
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8017
Order of pole (three term test) = 3.737e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1628 0.367
h = 0.001 0.003
y[1] (numeric) = 0.387758951708 0.237810238446
y[1] (closed_form) = 0.387758086032 0.237807345767
absolute error = 3.019e-06
relative error = 0.0006638 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.703
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.808
Order of pole (three term test) = 1.857e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1638 0.37
h = 0.0001 0.004
y[1] (numeric) = 0.388497249351 0.23970849832
y[1] (closed_form) = 0.388496581539 0.239705418495
absolute error = 3.151e-06
relative error = 0.0006903 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.704
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.157
Order of pole (three term test) = 2.273e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1639 0.374
h = 0.003 0.006
y[1] (numeric) = 0.38868931272 0.2422776405
y[1] (closed_form) = 0.388688868058 0.242274621857
absolute error = 3.051e-06
relative error = 0.0006662 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.705
Order of pole (given) = 1 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) = 1.852e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1669 0.38
h = 0.0001 0.005
y[1] (numeric) = 0.390811957233 0.246038411689
y[1] (closed_form) = 0.390811207585 0.246034426447
absolute error = 4.055e-06
relative error = 0.0008781 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.71
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.275
Order of pole (three term test) = 7.135e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.167 0.385
h = 0.0001 0.003
y[1] (numeric) = 0.391039572692 0.249246858708
y[1] (closed_form) = 0.391038914475 0.249243521704
absolute error = 3.401e-06
relative error = 0.0007335 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.711
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.027
Order of pole (three term test) = 2.649e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1671 0.388
h = 0.001 0.001
y[1] (numeric) = 0.391203016385 0.251170385361
y[1] (closed_form) = 0.391202132178 0.251167168982
absolute error = 3.336e-06
relative error = 0.0007175 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.712
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8064
Order of pole (three term test) = 2.190e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1681 0.389
h = 0.001 0.003
y[1] (numeric) = 0.391878432596 0.251779358977
y[1] (closed_form) = 0.391877458304 0.251776239393
absolute error = 3.268e-06
relative error = 0.0007016 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.713
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.83
Order of pole (three term test) = 3.078e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1691 0.392
h = 0.0001 0.004
y[1] (numeric) = 0.392620016509 0.253672444856
y[1] (closed_form) = 0.392619233323 0.253669135727
absolute error = 3.401e-06
relative error = 0.0007275 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.715
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.169
Order of pole (three term test) = 2.996e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1692 0.396
h = 0.003 0.006
y[1] (numeric) = 0.39281793609 0.256236528183
y[1] (closed_form) = 0.392817374806 0.25623327428
absolute error = 3.302e-06
relative error = 0.000704 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.716
Order of pole (given) = 1 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) = 3.627e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1722 0.402
h = 0.0001 0.005
y[1] (numeric) = 0.394945800989 0.25998543299
y[1] (closed_form) = 0.394944915834 0.259981231267
absolute error = 4.294e-06
relative error = 0.0009081 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.72
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.282
Order of pole (three term test) = 4.688e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1723 0.407
h = 0.0001 0.003
y[1] (numeric) = 0.39518063571 0.263187555057
y[1] (closed_form) = 0.395179855948 0.2631839916
absolute error = 3.648e-06
relative error = 0.0007683 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.721
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.033
Order of pole (three term test) = 1.559e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1724 0.41
h = 0.001 0.001
y[1] (numeric) = 0.395348341766 0.265107203409
y[1] (closed_form) = 0.395347341562 0.265103764355
absolute error = 3.582e-06
relative error = 0.0007524 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.722
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8113
Order of pole (three term test) = 1.355e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1734 0.411
h = 0.0001 0.004
y[1] (numeric) = 0.396023970007 0.265713472032
y[1] (closed_form) = 0.396022883061 0.265710130685
absolute error = 3.514e-06
relative error = 0.0007368 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.723
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.875
Order of pole (three term test) = 3.760e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1735 0.415
h = 0.003 0.006
y[1] (numeric) = 0.396226546818 0.268273370872
y[1] (closed_form) = 0.396225974645 0.268269916036
absolute error = 3.502e-06
relative error = 0.0007318 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.724
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.891
Order of pole (three term test) = 2.627e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1765 0.421
h = 0.0001 0.005
y[1] (numeric) = 0.398358774418 0.272012136183
y[1] (closed_form) = 0.398357862689 0.272007749731
absolute error = 4.480e-06
relative error = 0.0009288 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.729
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.289
Order of pole (three term test) = 1.673e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1766 0.426
h = 0.0001 0.003
y[1] (numeric) = 0.398599712475 0.275208823944
y[1] (closed_form) = 0.398598917798 0.275205067092
absolute error = 3.840e-06
relative error = 0.0007928 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.73
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.038
Order of pole (three term test) = 2.816e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1767 0.429
h = 0.001 0.001
y[1] (numeric) = 0.39877102092 0.277125141537
y[1] (closed_form) = 0.398770010559 0.277121512199
absolute error = 3.767e-06
relative error = 0.0007758 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.731
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8154
Order of pole (three term test) = 3.925e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1777 0.43
h = 0.001 0.003
y[1] (numeric) = 0.399446811326 0.27772910588
y[1] (closed_form) = 0.399445717066 0.277725574967
absolute error = 3.697e-06
relative error = 0.0007598 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.732
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.873
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1787 0.433
h = 0.0001 0.004
y[1] (numeric) = 0.400194147353 0.279612565463
y[1] (closed_form) = 0.40019323176 0.279608841197
absolute error = 3.835e-06
relative error = 0.0007856 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.734
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.194
Order of pole (three term test) = 2.809e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1788 0.437
h = 0.003 0.006
y[1] (numeric) = 0.400402524972 0.282167106207
y[1] (closed_form) = 0.400401828544 0.282163426471
absolute error = 3.745e-06
relative error = 0.0007646 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.735
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.908
Order of pole (three term test) = 1.834e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1818 0.443
h = 0.0001 0.005
y[1] (numeric) = 0.40253934721 0.285894053017
y[1] (closed_form) = 0.402538294185 0.285889460987
absolute error = 4.711e-06
relative error = 0.0009542 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.739
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.297
Order of pole (three term test) = 2.217e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1819 0.448
h = 0.0001 0.003
y[1] (numeric) = 0.402787070761 0.289084253893
y[1] (closed_form) = 0.402786147636 0.289080280957
absolute error = 4.079e-06
relative error = 0.0008227 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.741
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.045
Order of pole (three term test) = 1.847e-29 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=159.1MB, alloc=52.3MB, time=1.88
x[1] = 0.182 0.451
h = 0.001 0.001
y[1] (numeric) = 0.402962379086 0.290996601568
y[1] (closed_form) = 0.402961245868 0.290992759445
absolute error = 4.006e-06
relative error = 0.0008059 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.741
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8205
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.183 0.452
h = 0.001 0.003
y[1] (numeric) = 0.403638262022 0.291597914225
y[1] (closed_form) = 0.403637048187 0.291594171197
absolute error = 3.935e-06
relative error = 0.0007902 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.743
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.897
Order of pole (three term test) = 2.453e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.184 0.455
h = 0.0001 0.004
y[1] (numeric) = 0.404388432424 0.293476172571
y[1] (closed_form) = 0.404387390641 0.293472234565
absolute error = 4.073e-06
relative error = 0.0008153 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.744
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.207
Order of pole (three term test) = 3.959e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1841 0.459
h = 0.003 0.006
y[1] (numeric) = 0.404602130085 0.296025458364
y[1] (closed_form) = 0.40460130572 0.296021559376
absolute error = 3.985e-06
relative error = 0.0007949 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.746
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.926
Order of pole (three term test) = 3.179e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1871 0.465
h = 0.0001 0.005
y[1] (numeric) = 0.406743221186 0.299740630193
y[1] (closed_form) = 0.406742024158 0.299735838444
absolute error = 4.939e-06
relative error = 0.0009775 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.75
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.305
Order of pole (three term test) = 2.433e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1872 0.47
h = 0.0001 0.003
y[1] (numeric) = 0.406997498676 0.302924272269
y[1] (closed_form) = 0.406996443799 0.302920088877
absolute error = 4.314e-06
relative error = 0.0008504 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.751
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.051
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1873 0.473
h = 0.001 0.001
y[1] (numeric) = 0.407176666971 0.304832609839
y[1] (closed_form) = 0.407175407597 0.304828560308
absolute error = 4.241e-06
relative error = 0.0008338 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.752
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8256
Order of pole (three term test) = 4.517e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1883 0.474
h = 0.001 0.003
y[1] (numeric) = 0.407852581531 0.305431302183
y[1] (closed_form) = 0.407851244782 0.305427352292
absolute error = 4.170e-06
relative error = 0.0008184 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.754
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.921
Order of pole (three term test) = 6.415e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1893 0.477
h = 0.0001 0.004
y[1] (numeric) = 0.408605433493 0.307304361027
y[1] (closed_form) = 0.408604262252 0.307300214787
absolute error = 4.308e-06
relative error = 0.0008427 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.755
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.221
Order of pole (three term test) = 1.968e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1894 0.481
h = 0.003 0.006
y[1] (numeric) = 0.408824265954 0.309848338761
y[1] (closed_form) = 0.408823310234 0.309844226192
absolute error = 4.222e-06
relative error = 0.0008231 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.757
Order of pole (given) = 1 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) = 1.456e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1924 0.487
h = 0.0001 0.005
y[1] (numeric) = 0.410969307804 0.313551789257
y[1] (closed_form) = 0.410967964315 0.313546803621
absolute error = 5.163e-06
relative error = 0.0009989 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.761
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.313
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1925 0.492
h = 0.0001 0.003
y[1] (numeric) = 0.411229909686 0.316728809734
y[1] (closed_form) = 0.411228720006 0.316724421516
absolute error = 4.547e-06
relative error = 0.0008759 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.763
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.058
Order of pole (three term test) = 4.431e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1926 0.495
h = 0.001 0.001
y[1] (numeric) = 0.411412799379 0.318633102454
y[1] (closed_form) = 0.411411410792 0.318628850901
absolute error = 4.473e-06
relative error = 0.0008595 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.763
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8309
Order of pole (three term test) = 3.115e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1936 0.496
h = 0.001 0.003
y[1] (numeric) = 0.412088686872 0.319229207288
y[1] (closed_form) = 0.412087224108 0.319225055803
absolute error = 4.402e-06
relative error = 0.0008444 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.765
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.946
Order of pole (three term test) = 8.589e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1946 0.499
h = 0.0001 0.004
y[1] (numeric) = 0.412844070564 0.321097073429
y[1] (closed_form) = 0.412842766843 0.321092724466
absolute error = 4.540e-06
relative error = 0.0008681 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.767
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.235
Order of pole (three term test) = 2.637e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1947 0.503
h = 0.003 0.006
y[1] (numeric) = 0.413067854373 0.323635697179
y[1] (closed_form) = 0.413066764137 0.323631376705
absolute error = 4.456e-06
relative error = 0.0008492 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.768
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.964
Order of pole (three term test) = 1.381e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1977 0.509
h = 0.0001 0.005
y[1] (numeric) = 0.415216536771 0.327327489514
y[1] (closed_form) = 0.415215044602 0.327322315784
absolute error = 5.385e-06
relative error = 0.001018 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.772
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.321
Order of pole (three term test) = 5.289e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1978 0.514
h = 0.0001 0.003
y[1] (numeric) = 0.415483235857 0.330497834389
y[1] (closed_form) = 0.41548190857 0.330493246968
absolute error = 4.776e-06
relative error = 0.0008995 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.774
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.065
Order of pole (three term test) = 4.446e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1979 0.517
h = 0.001 0.001
y[1] (numeric) = 0.415669709917 0.332398052757
y[1] (closed_form) = 0.415668189295 0.332393604566
absolute error = 4.701e-06
relative error = 0.0008833 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.775
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8362
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.1989 0.518
h = 0.0001 0.004
y[1] (numeric) = 0.416345513874 0.33299160418
y[1] (closed_form) = 0.416343922224 0.332987256373
absolute error = 4.630e-06
relative error = 0.0008685 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.776
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.025
Order of pole (three term test) = 1.442e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.199 0.522
h = 0.003 0.006
y[1] (numeric) = 0.416573220564 0.335525827501
y[1] (closed_form) = 0.416572098728 0.335521320286
absolute error = 4.645e-06
relative error = 0.0008684 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.777
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.98
Order of pole (three term test) = 5.327e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.202 0.528
h = 0.0001 0.005
y[1] (numeric) = 0.418724932103 0.339207680795
y[1] (closed_form) = 0.418723396646 0.339202337282
absolute error = 5.560e-06
relative error = 0.001032 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.782
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.329
Order of pole (three term test) = 9.604e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2021 0.533
h = 0.0001 0.003
y[1] (numeric) = 0.418996779809 0.342372311755
y[1] (closed_form) = 0.418995418436 0.342367544999
absolute error = 4.957e-06
relative error = 0.0009162 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.784
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.071
Order of pole (three term test) = 1.608e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2022 0.536
h = 0.001 0.001
y[1] (numeric) = 0.419186279676 0.344269043794
y[1] (closed_form) = 0.419184729716 0.344264418357
absolute error = 4.878e-06
relative error = 0.0008993 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.785
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8408
Order of pole (three term test) = 1.045e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2032 0.537
h = 0.001 0.003
y[1] (numeric) = 0.419861998044 0.344860423655
y[1] (closed_form) = 0.419860379723 0.344855898823
absolute error = 4.806e-06
relative error = 0.0008845 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.786
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.993
Order of pole (three term test) = 2.676e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2042 0.54
h = 0.0001 0.004
y[1] (numeric) = 0.420621766175 0.346718687823
y[1] (closed_form) = 0.420620295122 0.346713963951
absolute error = 4.948e-06
relative error = 0.0009077 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.788
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.262
Order of pole (three term test) = 2.129e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2043 0.544
h = 0.003 0.006
y[1] (numeric) = 0.420854347005 0.34924730424
y[1] (closed_form) = 0.420853085367 0.349242599636
absolute error = 4.871e-06
relative error = 0.0008906 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.789
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.999
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2073 0.55
h = 0.0001 0.005
y[1] (numeric) = 0.42300914264 0.352917636794
y[1] (closed_form) = 0.423007454916 0.352912115812
absolute error = 5.773e-06
relative error = 0.001048 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.794
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.337
Order of pole (three term test) = 2.051e-29 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=203.1MB, alloc=52.3MB, time=2.39
x[1] = 0.2074 0.555
h = 0.0001 0.003
y[1] (numeric) = 0.423286672572 0.356075511297
y[1] (closed_form) = 0.423285168938 0.35607055572
absolute error = 5.179e-06
relative error = 0.0009362 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.795
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.078
Order of pole (three term test) = 6.198e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2075 0.558
h = 0.001 0.001
y[1] (numeric) = 0.423479506769 0.357968125761
y[1] (closed_form) = 0.423477820066 0.357963313643
absolute error = 5.099e-06
relative error = 0.0009196 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.796
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8463
Order of pole (three term test) = 4.061e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2085 0.559
h = 0.001 0.003
y[1] (numeric) = 0.424155041984 0.358557018056
y[1] (closed_form) = 0.424153289971 0.358552306662
absolute error = 5.027e-06
relative error = 0.000905 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.798
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.02
Order of pole (three term test) = 1.420e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2095 0.562
h = 0.0001 0.004
y[1] (numeric) = 0.424916930661 0.36041013293
y[1] (closed_form) = 0.424915319725 0.36040522201
absolute error = 5.168e-06
relative error = 0.0009276 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.8
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.277
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2096 0.566
h = 0.003 0.006
y[1] (numeric) = 0.425153950499 0.36293329916
y[1] (closed_form) = 0.425152546598 0.362928402807
absolute error = 5.094e-06
relative error = 0.0009112 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.801
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.019
Order of pole (three term test) = 3.955e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2126 0.572
h = 0.0001 0.005
y[1] (numeric) = 0.427311543605 0.366592198255
y[1] (closed_form) = 0.427309702035 0.366586505442
absolute error = 5.983e-06
relative error = 0.001063 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.806
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.346
Order of pole (three term test) = 1.966e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2127 0.577
h = 0.0001 0.003
y[1] (numeric) = 0.427594536904 0.36974328564
y[1] (closed_form) = 0.427592888871 0.36973814679
absolute error = 5.397e-06
relative error = 0.0009547 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.807
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.085
Order of pole (three term test) = 5.318e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2128 0.58
h = 0.001 0.001
y[1] (numeric) = 0.427790573733 0.371631766913
y[1] (closed_form) = 0.427788748106 0.371626773448
absolute error = 5.317e-06
relative error = 0.0009382 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.808
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.852
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2138 0.581
h = 0.001 0.003
y[1] (numeric) = 0.428465875634 0.372218208773
y[1] (closed_form) = 0.428463987689 0.372213316049
absolute error = 5.244e-06
relative error = 0.000924 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.81
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.046
Order of pole (three term test) = 4.199e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2148 0.584
h = 0.0001 0.004
y[1] (numeric) = 0.429229747699 0.374066198289
y[1] (closed_form) = 0.42922799475 0.374061105758
absolute error = 5.386e-06
relative error = 0.000946 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.812
Order of pole (given) = 1 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) = 3.913e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2149 0.588
h = 0.003 0.006
y[1] (numeric) = 0.429471032245 0.37658389364
y[1] (closed_form) = 0.429469483851 0.376578811146
absolute error = 5.313e-06
relative error = 0.0009302 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.813
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.039
Order of pole (three term test) = 2.069e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2179 0.594
h = 0.0001 0.005
y[1] (numeric) = 0.431631144723 0.380231453847
y[1] (closed_form) = 0.431629147934 0.380225594771
absolute error = 6.190e-06
relative error = 0.001076 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.818
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.355
Order of pole (three term test) = 1.195e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.218 0.599
h = 0.0001 0.003
y[1] (numeric) = 0.431919385977 0.383375730941
y[1] (closed_form) = 0.431917591625 0.383370414323
absolute error = 5.611e-06
relative error = 0.0009716 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.819
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.092
Order of pole (three term test) = 3.174e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2181 0.602
h = 0.001 0.001
y[1] (numeric) = 0.432118495915 0.38526006785
y[1] (closed_form) = 0.432116529391 0.385254898331
absolute error = 5.531e-06
relative error = 0.0009554 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.821
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8577
Order of pole (three term test) = 7.469e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2191 0.603
h = 0.001 0.003
y[1] (numeric) = 0.432793516516 0.385844097221
y[1] (closed_form) = 0.432791490607 0.38583902837
absolute error = 5.459e-06
relative error = 0.0009415 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.822
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.074
Order of pole (three term test) = 3.711e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2201 0.606
h = 0.0001 0.004
y[1] (numeric) = 0.433559238336 0.387686989123
y[1] (closed_form) = 0.433557341456 0.387681720377
absolute error = 5.600e-06
relative error = 0.0009628 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.824
Order of pole (given) = 1 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) = 5.105e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2202 0.61
h = 0.003 0.006
y[1] (numeric) = 0.433804616176 0.390199198763
y[1] (closed_form) = 0.433802921282 0.390193935692
absolute error = 5.529e-06
relative error = 0.0009477 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.825
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.06
Order of pole (three term test) = 2.474e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2232 0.616
h = 0.0001 0.005
y[1] (numeric) = 0.435966978521 0.39383552139
y[1] (closed_form) = 0.43596482534 0.393829501541
absolute error = 6.393e-06
relative error = 0.001088 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.83
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.364
Order of pole (three term test) = 2.087e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2233 0.621
h = 0.0001 0.003
y[1] (numeric) = 0.43626025598 0.396972972161
y[1] (closed_form) = 0.4362583136 0.396967483228
absolute error = 5.822e-06
relative error = 0.0009871 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.832
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.099
Order of pole (three term test) = 3.874e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2234 0.624
h = 0.001 0.001
y[1] (numeric) = 0.436462311802 0.398853157765
y[1] (closed_form) = 0.436460202613 0.398847817445
absolute error = 5.742e-06
relative error = 0.0009711 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.833
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8636
Order of pole (three term test) = 5.324e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2244 0.625
h = 0.0001 0.004
y[1] (numeric) = 0.437137005271 0.399434813301
y[1] (closed_form) = 0.437134839567 0.399429573486
absolute error = 5.670e-06
relative error = 0.0009575 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.834
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.189
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2245 0.629
h = 0.003 0.006
y[1] (numeric) = 0.437385614047 0.401942535628
y[1] (closed_form) = 0.437383871078 0.401937101659
absolute error = 5.707e-06
relative error = 0.0009607 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.836
Order of pole (given) = 1 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) = 1.746e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2275 0.635
h = 0.0001 0.005
y[1] (numeric) = 0.439549835889 0.40556929379
y[1] (closed_form) = 0.439547626532 0.405563119899
absolute error = 6.557e-06
relative error = 0.001096 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.841
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.372
Order of pole (three term test) = 3.000e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2276 0.64
h = 0.0001 0.003
y[1] (numeric) = 0.43984736317 0.408700917682
y[1] (closed_form) = 0.439845371531 0.40869526485
absolute error = 5.993e-06
relative error = 0.0009982 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.842
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.106
Order of pole (three term test) = 2.833e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2277 0.643
h = 0.001 0.001
y[1] (numeric) = 0.440051904155 0.410577560574
y[1] (closed_form) = 0.440049750257 0.410572057564
absolute error = 5.910e-06
relative error = 0.0009819 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.843
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8685
Order of pole (three term test) = 1.486e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2287 0.644
h = 0.001 0.003
y[1] (numeric) = 0.440726308598 0.411157199605
y[1] (closed_form) = 0.440724100609 0.411151796926
absolute error = 5.836e-06
relative error = 0.0009683 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.845
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.125
Order of pole (three term test) = 3.368e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2297 0.647
h = 0.0001 0.004
y[1] (numeric) = 0.441495188798 0.412990710329
y[1] (closed_form) = 0.441493099054 0.412985108009
absolute error = 5.979e-06
relative error = 0.0009891 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.847
Order of pole (given) = 1 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) = 2.875e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2298 0.651
h = 0.003 0.006
y[1] (numeric) = 0.441747803128 0.415492735853
y[1] (closed_form) = 0.441745910427 0.415487131507
absolute error = 5.915e-06
relative error = 0.0009754 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.848
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.099
Order of pole (three term test) = 2.393e-29 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=247.1MB, alloc=52.3MB, time=2.90
x[1] = 0.2328 0.657
h = 0.0001 0.005
y[1] (numeric) = 0.443913794977 0.419108458088
y[1] (closed_form) = 0.443911427479 0.419102133411
absolute error = 6.753e-06
relative error = 0.001106 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.853
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.382
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2329 0.662
h = 0.0001 0.003
y[1] (numeric) = 0.444215974837 0.422233241247
y[1] (closed_form) = 0.444213832459 0.422227426067
absolute error = 6.197e-06
relative error = 0.001011 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.855
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.113
Order of pole (three term test) = 8.452e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.233 0.665
h = 0.001 0.001
y[1] (numeric) = 0.444423231421 0.42410572902
y[1] (closed_form) = 0.444420932025 0.424100064821
absolute error = 6.113e-06
relative error = 0.0009951 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.856
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8745
Order of pole (three term test) = 2.885e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.234 0.666
h = 0.001 0.003
y[1] (numeric) = 0.445097228595 0.424683067172
y[1] (closed_form) = 0.445094877857 0.42467750299
absolute error = 6.040e-06
relative error = 0.0009819 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.858
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.153
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.235 0.669
h = 0.0001 0.004
y[1] (numeric) = 0.445867595731 0.426511577023
y[1] (closed_form) = 0.445865357623 0.426505813616
absolute error = 6.183e-06
relative error = 0.001002 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.86
Order of pole (given) = 1 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) = 1.765e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2351 0.673
h = 0.003 0.006
y[1] (numeric) = 0.446123830245 0.429008102358
y[1] (closed_form) = 0.446121786402 0.429002333039
absolute error = 6.121e-06
relative error = 0.0009889 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.861
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.12
Order of pole (three term test) = 1.714e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2381 0.679
h = 0.0001 0.005
y[1] (numeric) = 0.448291347259 0.432612906448
y[1] (closed_form) = 0.448288820966 0.432606436229
absolute error = 6.946e-06
relative error = 0.001115 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.866
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.391
Order of pole (three term test) = 1.598e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2382 0.684
h = 0.0001 0.003
y[1] (numeric) = 0.448597979327 0.435730851432
y[1] (closed_form) = 0.448595685061 0.435724879173
absolute error = 6.398e-06
relative error = 0.001023 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.868
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.121
Order of pole (three term test) = 2.896e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2383 0.687
h = 0.001 0.001
y[1] (numeric) = 0.448807831371 0.437599188132
y[1] (closed_form) = 0.448805385251 0.437593367833
absolute error = 6.313e-06
relative error = 0.001007 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.869
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8806
Order of pole (three term test) = 2.539e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2393 0.688
h = 0.001 0.003
y[1] (numeric) = 0.449481381413 0.438174265532
y[1] (closed_form) = 0.449478886634 0.43816854486
absolute error = 6.241e-06
relative error = 0.0009942 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.87
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.182
Order of pole (three term test) = 3.742e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2403 0.691
h = 0.0001 0.004
y[1] (numeric) = 0.450253115861 0.439997814713
y[1] (closed_form) = 0.450250728227 0.439991895389
absolute error = 6.383e-06
relative error = 0.001014 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.872
Order of pole (given) = 1 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) = 1.850e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2404 0.695
h = 0.003 0.006
y[1] (numeric) = 0.450512811577 0.442488845092
y[1] (closed_form) = 0.450510615373 0.442482916133
absolute error = 6.323e-06
relative error = 0.001001 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.874
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.142
Order of pole (three term test) = 2.024e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2434 0.701
h = 0.0001 0.005
y[1] (numeric) = 0.452681617521 0.446082853579
y[1] (closed_form) = 0.452678931947 0.446076242968
absolute error = 7.135e-06
relative error = 0.001123 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.879
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.401
Order of pole (three term test) = 1.101e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2435 0.706
h = 0.0001 0.003
y[1] (numeric) = 0.452992505703 0.449193968777
y[1] (closed_form) = 0.452990058578 0.449187844629
absolute error = 6.595e-06
relative error = 0.001034 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.881
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.129
Order of pole (three term test) = 6.563e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2436 0.709
h = 0.001 0.001
y[1] (numeric) = 0.453204835713 0.451058161886
y[1] (closed_form) = 0.453202241818 0.451052190507
absolute error = 6.510e-06
relative error = 0.001018 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.882
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8868
Order of pole (three term test) = 2.448e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2446 0.71
h = 0.001 0.003
y[1] (numeric) = 0.453877900773 0.451631018984
y[1] (closed_form) = 0.453875260836 0.451625146773
absolute error = 6.438e-06
relative error = 0.001006 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.884
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.212
Order of pole (three term test) = 2.432e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2456 0.713
h = 0.0001 0.004
y[1] (numeric) = 0.454650886602 0.453449650352
y[1] (closed_form) = 0.454648348457 0.453443580208
absolute error = 6.579e-06
relative error = 0.001025 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.886
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.386
Order of pole (three term test) = 5.297e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2457 0.717
h = 0.003 0.006
y[1] (numeric) = 0.454913888035 0.455935195537
y[1] (closed_form) = 0.454911538438 0.455929112198
absolute error = 6.521e-06
relative error = 0.001013 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.887
Order of pole (given) = 1 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) = 3.352e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2487 0.723
h = 0.0001 0.005
y[1] (numeric) = 0.45708375523 0.459518535257
y[1] (closed_form) = 0.457080910041 0.459511789305
absolute error = 7.321e-06
relative error = 0.00113 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.892
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.411
Order of pole (three term test) = 1.520e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2488 0.728
h = 0.0001 0.003
y[1] (numeric) = 0.45739870781 0.462622834559
y[1] (closed_form) = 0.457396107028 0.462616563633
absolute error = 6.789e-06
relative error = 0.001044 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.894
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.137
Order of pole (three term test) = 4.623e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2489 0.731
h = 0.001 0.001
y[1] (numeric) = 0.457613400992 0.464482894797
y[1] (closed_form) = 0.45761065844 0.464476777285
absolute error = 6.704e-06
relative error = 0.001028 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.896
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8931
Order of pole (three term test) = 5.350e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2499 0.732
h = 0.0001 0.004
y[1] (numeric) = 0.458285945193 0.465053572277
y[1] (closed_form) = 0.458283159146 0.465047553408
absolute error = 6.632e-06
relative error = 0.001016 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.897
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.367
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.25 0.736
h = 0.003 0.006
y[1] (numeric) = 0.458551545629 0.467534646726
y[1] (closed_form) = 0.458549135426 0.467528408959
absolute error = 6.687e-06
relative error = 0.001021 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.898
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.183
Order of pole (three term test) = 3.673e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.253 0.742
h = 0.0001 0.005
y[1] (numeric) = 0.460722275423 0.471108916748
y[1] (closed_form) = 0.460719364594 0.471102032513
absolute error = 7.474e-06
relative error = 0.001134 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.904
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.419
Order of pole (three term test) = 2.234e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2531 0.747
h = 0.0001 0.003
y[1] (numeric) = 0.461040657258 0.474207409632
y[1] (closed_form) = 0.461037995736 0.474200990699
absolute error = 6.949e-06
relative error = 0.001051 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.906
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.144
Order of pole (three term test) = 5.336e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2532 0.75
h = 0.001 0.001
y[1] (numeric) = 0.461257343758 0.476063949685
y[1] (closed_form) = 0.461254544693 0.476057684655
absolute error = 6.862e-06
relative error = 0.001035 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.907
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.8984
Order of pole (three term test) = 3.212e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2542 0.751
h = 0.001 0.003
y[1] (numeric) = 0.461929437659 0.476632776971
y[1] (closed_form) = 0.461926597243 0.476626610114
absolute error = 6.790e-06
relative error = 0.001023 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.908
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.267
Order of pole (three term test) = 5.640e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2552 0.754
h = 0.0001 0.004
y[1] (numeric) = 0.462704513352 0.47844239152
y[1] (closed_form) = 0.462701765113 0.478436028371
absolute error = 6.931e-06
relative error = 0.001041 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.91
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.417
Order of pole (three term test) = 2.586e-29 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=291.1MB, alloc=52.3MB, time=3.40
x[1] = 0.2553 0.758
h = 0.0001 0.004
y[1] (numeric) = 0.462973329283 0.480917805625
y[1] (closed_form) = 0.462970764164 0.480911423036
absolute error = 6.879e-06
relative error = 0.00103 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.912
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.912
Order of pole (three term test) = 4.291e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2554 0.762
h = 0.003 0.006
y[1] (numeric) = 0.463243038285 0.483392366784
y[1] (closed_form) = 0.463240473166 0.483385984195
absolute error = 6.879e-06
relative error = 0.001027 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.914
Order of pole (given) = 1 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) = 5.532e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2584 0.768
h = 0.0001 0.005
y[1] (numeric) = 0.465414903037 0.486954442141
y[1] (closed_form) = 0.465411830826 0.486947434713
absolute error = 7.651e-06
relative error = 0.001136 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.919
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.43
Order of pole (three term test) = 2.968e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2585 0.773
h = 0.0001 0.003
y[1] (numeric) = 0.465737879852 0.490045120663
y[1] (closed_form) = 0.465735063338 0.490038565483
absolute error = 7.135e-06
relative error = 0.001055 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.921
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.153
Order of pole (three term test) = 4.873e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2586 0.776
h = 0.001 0.001
y[1] (numeric) = 0.465957236965 0.491896923738
y[1] (closed_form) = 0.465954288559 0.491890523047
absolute error = 7.047e-06
relative error = 0.00104 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.922
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9056
Order of pole (three term test) = 9.112e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2596 0.777
h = 0.001 0.003
y[1] (numeric) = 0.466628720958 0.492463265082
y[1] (closed_form) = 0.466625734054 0.492456961902
absolute error = 6.975e-06
relative error = 0.001028 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.924
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.301
Order of pole (three term test) = 2.260e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2606 0.78
h = 0.0001 0.004
y[1] (numeric) = 0.467405064384 0.49426730634
y[1] (closed_form) = 0.467402163802 0.49426080798
absolute error = 7.116e-06
relative error = 0.001046 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.926
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.437
Order of pole (three term test) = 3.176e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2607 0.784
h = 0.003 0.006
y[1] (numeric) = 0.467677445628 0.496736450081
y[1] (closed_form) = 0.467674724779 0.496729928529
absolute error = 7.066e-06
relative error = 0.001036 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.927
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.231
Order of pole (three term test) = 7.358e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2637 0.79
h = 0.0001 0.005
y[1] (numeric) = 0.469849725559 0.500288253486
y[1] (closed_form) = 0.469846493373 0.500281125415
absolute error = 7.827e-06
relative error = 0.00114 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.933
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.441
Order of pole (three term test) = 2.831e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2638 0.795
h = 0.0001 0.003
y[1] (numeric) = 0.47017621124 0.503372180026
y[1] (closed_form) = 0.470173239383 0.503365493016
absolute error = 7.318e-06
relative error = 0.001062 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.935
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.161
Order of pole (three term test) = 7.256e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2639 0.798
h = 0.001 0.001
y[1] (numeric) = 0.470397599231 0.505219895436
y[1] (closed_form) = 0.470394500209 0.505213363109
absolute error = 7.230e-06
relative error = 0.001047 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.936
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9121
Order of pole (three term test) = 2.608e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2649 0.799
h = 0.001 0.003
y[1] (numeric) = 0.471068463067 0.505784179782
y[1] (closed_form) = 0.471065327887 0.505777744267
absolute error = 7.159e-06
relative error = 0.001036 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.937
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.332
Order of pole (three term test) = 3.279e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2659 0.802
h = 0.0001 0.004
y[1] (numeric) = 0.471845624959 0.507583493875
y[1] (closed_form) = 0.47184257129 0.507576864409
absolute error = 7.299e-06
relative error = 0.001053 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.939
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.454
Order of pole (three term test) = 8.659e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.266 0.806
h = 0.003 0.006
y[1] (numeric) = 0.472120720246 0.510047225717
y[1] (closed_form) = 0.472117843299 0.510040570116
absolute error = 7.251e-06
relative error = 0.001043 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.941
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.255
Order of pole (three term test) = 1.023e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.269 0.812
h = 0.0001 0.005
y[1] (numeric) = 0.474293221084 0.51358889736
y[1] (closed_form) = 0.474289829146 0.513581653281
absolute error = 7.999e-06
relative error = 0.001144 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.946
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.451
Order of pole (three term test) = 3.938e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2691 0.817
h = 0.0001 0.003
y[1] (numeric) = 0.474623042071 0.516666105035
y[1] (closed_form) = 0.474619914689 0.516659290945
absolute error = 7.497e-06
relative error = 0.001069 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.949
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.17
Order of pole (three term test) = 5.465e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2692 0.82
h = 0.001 0.001
y[1] (numeric) = 0.474846357294 0.518509754772
y[1] (closed_form) = 0.474843107379 0.518503095427
absolute error = 7.410e-06
relative error = 0.001054 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.95
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9187
Order of pole (three term test) = 8.807e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2702 0.821
h = 0.001 0.003
y[1] (numeric) = 0.475516572546 0.519072023067
y[1] (closed_form) = 0.475513288742 0.519065459787
absolute error = 7.339e-06
relative error = 0.001043 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.951
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.363
Order of pole (three term test) = 4.372e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2712 0.824
h = 0.0001 0.004
y[1] (numeric) = 0.476294455251 0.52086666326
y[1] (closed_form) = 0.476291248285 0.520859907362
absolute error = 7.478e-06
relative error = 0.00106 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.953
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.472
Order of pole (three term test) = 1.705e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2713 0.828
h = 0.003 0.006
y[1] (numeric) = 0.4765721274 0.523325012097
y[1] (closed_form) = 0.476569094132 0.523318227264
absolute error = 7.432e-06
relative error = 0.00105 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.955
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.278
Order of pole (three term test) = 4.508e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2743 0.834
h = 0.0001 0.005
y[1] (numeric) = 0.478744662886 0.526856694397
y[1] (closed_form) = 0.478741111537 0.526849338833
absolute error = 8.168e-06
relative error = 0.001147 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.961
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.462
Order of pole (three term test) = 4.178e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2744 0.839
h = 0.0001 0.003
y[1] (numeric) = 0.479077650268 0.529927220285
y[1] (closed_form) = 0.479074367315 0.529920283766
absolute error = 7.674e-06
relative error = 0.001074 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.963
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.178
Order of pole (three term test) = 3.627e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2745 0.842
h = 0.001 0.001
y[1] (numeric) = 0.479302791922 0.531766828651
y[1] (closed_form) = 0.479299390967 0.531760046814
absolute error = 7.587e-06
relative error = 0.00106 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.964
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9254
Order of pole (three term test) = 2.746e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2755 0.843
h = 0.001 0.003
y[1] (numeric) = 0.47997233188 0.532327121715
y[1] (closed_form) = 0.479968899235 0.532320435151
absolute error = 7.516e-06
relative error = 0.001049 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.965
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.395
Order of pole (three term test) = 1.829e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2765 0.846
h = 0.0001 0.004
y[1] (numeric) = 0.480750841295 0.53411714274
y[1] (closed_form) = 0.480747480954 0.534110264986
absolute error = 7.655e-06
relative error = 0.001065 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.968
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.49
Order of pole (three term test) = 1.810e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2766 0.85
h = 0.003 0.006
y[1] (numeric) = 0.481030956881 0.53657014051
y[1] (closed_form) = 0.481027767203 0.536563231165
absolute error = 7.610e-06
relative error = 0.001056 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.969
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.302
Order of pole (three term test) = 2.812e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2796 0.856
h = 0.0001 0.005
y[1] (numeric) = 0.483203348612 0.540091977761
y[1] (closed_form) = 0.4831996383 0.540084515127
absolute error = 8.334e-06
relative error = 0.00115 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.975
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.472
Order of pole (three term test) = 2.164e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2797 0.861
h = 0.0001 0.003
y[1] (numeric) = 0.483539338136 0.543155862621
y[1] (closed_form) = 0.483535899689 0.543148808227
absolute error = 7.848e-06
relative error = 0.001079 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.977
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.187
Order of pole (three term test) = 3.241e-29 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=335.1MB, alloc=52.3MB, time=3.90
x[1] = 0.2798 0.864
h = 0.001 0.001
y[1] (numeric) = 0.48376620826 0.544991456061
y[1] (closed_form) = 0.483762656242 0.544984556166
absolute error = 7.761e-06
relative error = 0.001065 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.978
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9321
Order of pole (three term test) = 1.846e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2808 0.865
h = 0.0001 0.004
y[1] (numeric) = 0.484435047876 0.545549814532
y[1] (closed_form) = 0.4844314663 0.545543009079
absolute error = 7.690e-06
relative error = 0.001054 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.98
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.601
Order of pole (three term test) = 1.594e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2809 0.869
h = 0.003 0.006
y[1] (numeric) = 0.48471707354 0.547998465417
y[1] (closed_form) = 0.484713812385 0.547991421777
absolute error = 7.762e-06
relative error = 0.001061 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.982
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.322
Order of pole (three term test) = 2.638e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2839 0.875
h = 0.0001 0.005
y[1] (numeric) = 0.486889319458 0.551511940653
y[1] (closed_form) = 0.486885535681 0.551504358465
absolute error = 8.474e-06
relative error = 0.001152 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.987
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.481
Order of pole (three term test) = 4.366e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.284 0.88
h = 0.0001 0.003
y[1] (numeric) = 0.487227843533 0.554570177576
y[1] (closed_form) = 0.487224334445 0.554562994477
absolute error = 7.994e-06
relative error = 0.001083 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.989
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.194
Order of pole (three term test) = 1.729e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2841 0.883
h = 0.001 0.001
y[1] (numeric) = 0.487456172547 0.556402356848
y[1] (closed_form) = 0.487452553624 0.556395328054
absolute error = 7.906e-06
relative error = 0.001069 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.991
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9379
Order of pole (three term test) = 4.551e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2851 0.884
h = 0.001 0.003
y[1] (numeric) = 0.488124412895 0.55695907373
y[1] (closed_form) = 0.488120766204 0.556952138657
absolute error = 7.835e-06
relative error = 0.001058 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.992
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.454
Order of pole (three term test) = 2.259e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2861 0.887
h = 0.0001 0.004
y[1] (numeric) = 0.488903903383 0.55874065454
y[1] (closed_form) = 0.488900320898 0.558733531113
absolute error = 7.974e-06
relative error = 0.001074 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.994
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.523
Order of pole (three term test) = 4.405e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2862 0.891
h = 0.003 0.006
y[1] (numeric) = 0.489188286072 0.561183815284
y[1] (closed_form) = 0.489184868628 0.561176655647
absolute error = 7.933e-06
relative error = 0.001066 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.996
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.347
Order of pole (three term test) = 3.850e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2892 0.897
h = 0.0001 0.005
y[1] (numeric) = 0.491360074861 0.564687715935
y[1] (closed_form) = 0.491356133177 0.564680034605
absolute error = 8.634e-06
relative error = 0.001153 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.001
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.492
Order of pole (three term test) = 3.173e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2893 0.902
h = 0.0001 0.003
y[1] (numeric) = 0.491701307231 0.567739394732
y[1] (closed_form) = 0.491697643051 0.567732101959
absolute error = 8.162e-06
relative error = 0.001087 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.004
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.203
Order of pole (three term test) = 1.203e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2894 0.905
h = 0.001 0.001
y[1] (numeric) = 0.491931189594 0.56956761235
y[1] (closed_form) = 0.491927419822 0.569560473499
absolute error = 8.073e-06
relative error = 0.001073 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.005
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9448
Order of pole (three term test) = 3.200e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2904 0.906
h = 0.001 0.003
y[1] (numeric) = 0.492598686755 0.570122469339
y[1] (closed_form) = 0.49259489122 0.570115423308
absolute error = 8.003e-06
relative error = 0.001062 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.007
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.487
Order of pole (three term test) = 6.416e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2914 0.909
h = 0.0001 0.004
y[1] (numeric) = 0.493378553174 0.571899593199
y[1] (closed_form) = 0.493374817696 0.571892360478
absolute error = 8.140e-06
relative error = 0.001078 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.009
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.542
Order of pole (three term test) = 1.743e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2915 0.913
h = 0.003 0.006
y[1] (numeric) = 0.493665017787 0.574337507691
y[1] (closed_form) = 0.493661444318 0.574330236485
absolute error = 8.102e-06
relative error = 0.00107 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.011
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.371
Order of pole (three term test) = 2.581e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2945 0.919
h = 0.0001 0.005
y[1] (numeric) = 0.495836192587 0.577831981748
y[1] (closed_form) = 0.495832093723 0.577824205374
absolute error = 8.790e-06
relative error = 0.001155 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.016
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.503
Order of pole (three term test) = 5.632e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2946 0.924
h = 0.0001 0.003
y[1] (numeric) = 0.496179982213 0.580877152311
y[1] (closed_form) = 0.49617616334 0.580869754123
absolute error = 8.326e-06
relative error = 0.00109 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.019
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.212
Order of pole (three term test) = 2.382e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2947 0.927
h = 0.001 0.001
y[1] (numeric) = 0.496411328006 0.582701440013
y[1] (closed_form) = 0.496407407681 0.582694195264
absolute error = 8.237e-06
relative error = 0.001076 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.02
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9517
Order of pole (three term test) = 4.546e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2957 0.928
h = 0.001 0.003
y[1] (numeric) = 0.497078061392 0.583254476963
y[1] (closed_form) = 0.497074117241 0.583247324106
absolute error = 8.168e-06
relative error = 0.001066 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.021
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.52
Order of pole (three term test) = 3.128e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2967 0.931
h = 0.0001 0.004
y[1] (numeric) = 0.497858222808 0.585027202805
y[1] (closed_form) = 0.497854334699 0.585019864986
absolute error = 8.304e-06
relative error = 0.001081 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.024
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.56
Order of pole (three term test) = 2.548e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2968 0.935
h = 0.003 0.006
y[1] (numeric) = 0.498146650284 0.587459912792
y[1] (closed_form) = 0.498142921162 0.587452534341
absolute error = 8.267e-06
relative error = 0.001073 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.026
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.396
Order of pole (three term test) = 7.229e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2998 0.941
h = 0.0001 0.005
y[1] (numeric) = 0.500317061423 0.590945108947
y[1] (closed_form) = 0.500312806191 0.590937241519
absolute error = 8.944e-06
relative error = 0.001155 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.031
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.514
Order of pole (three term test) = 1.966e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.2999 0.946
h = 0.0001 0.003
y[1] (numeric) = 0.500663261843 0.593983823866
y[1] (closed_form) = 0.500659288774 0.593976324419
absolute error = 8.487e-06
relative error = 0.001092 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.033
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.22
Order of pole (three term test) = 1.888e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3 0.949
h = 0.001 0.001
y[1] (numeric) = 0.500895983923 0.595804214942
y[1] (closed_form) = 0.500891913438 0.595796868359
absolute error = 8.399e-06
relative error = 0.001079 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.035
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9587
Order of pole (three term test) = 1.397e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.301 0.95
h = 0.001 0.003
y[1] (numeric) = 0.501561934397 0.596355471346
y[1] (closed_form) = 0.501557841958 0.596348215698
absolute error = 8.330e-06
relative error = 0.001069 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.036
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.553
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.302 0.953
h = 0.0001 0.004
y[1] (numeric) = 0.502342313131 0.598123858825
y[1] (closed_form) = 0.50233827285 0.598116420007
absolute error = 8.465e-06
relative error = 0.001084 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.038
Order of pole (given) = 1 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) = 8.551e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3021 0.957
h = 0.003 0.006
y[1] (numeric) = 0.502632588077 0.600551408106
y[1] (closed_form) = 0.502628703774 0.600543926629
absolute error = 8.430e-06
relative error = 0.001076 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.04
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.421
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3051 0.963
h = 0.0001 0.005
y[1] (numeric) = 0.504802092885 0.604027475496
y[1] (closed_form) = 0.504797682174 0.604019520894
absolute error = 9.096e-06
relative error = 0.001155 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.046
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.525
Order of pole (three term test) = 6.163e-29 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=379.2MB, alloc=52.3MB, time=4.41
x[1] = 0.3052 0.968
h = 0.0001 0.003
y[1] (numeric) = 0.505150562163 0.607059789826
y[1] (closed_form) = 0.505146435489 0.607052193171
absolute error = 8.645e-06
relative error = 0.001095 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.048
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.229
Order of pole (three term test) = 2.647e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3053 0.971
h = 0.001 0.001
y[1] (numeric) = 0.505384576134 0.608876318982
y[1] (closed_form) = 0.505380355976 0.60886887453
absolute error = 8.557e-06
relative error = 0.001081 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.05
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9658
Order of pole (three term test) = 2.629e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3063 0.972
h = 0.0001 0.004
y[1] (numeric) = 0.506049725955 0.609425833933
y[1] (closed_form) = 0.506045485651 0.609418479434
absolute error = 8.489e-06
relative error = 0.001072 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.051
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.804
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3064 0.976
h = 0.003 0.006
y[1] (numeric) = 0.506341436576 0.61184919925
y[1] (closed_form) = 0.506337475353 0.611841598916
absolute error = 8.571e-06
relative error = 0.001079 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.053
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.442
Order of pole (three term test) = 1.350e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3094 0.982
h = 0.0001 0.005
y[1] (numeric) = 0.508510158526 0.615317515505
y[1] (closed_form) = 0.508505670769 0.615309455417
absolute error = 9.225e-06
relative error = 0.001156 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.059
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.535
Order of pole (three term test) = 5.192e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3095 0.987
h = 0.0001 0.003
y[1] (numeric) = 0.508860545833 0.618344391039
y[1] (closed_form) = 0.508856343614 0.61833668042
absolute error = 8.781e-06
relative error = 0.001097 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.061
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.237
Order of pole (three term test) = 4.431e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3096 0.99
h = 0.001 0.001
y[1] (numeric) = 0.509095651726 0.620157638832
y[1] (closed_form) = 0.509091359335 0.620150079829
absolute error = 8.693e-06
relative error = 0.001083 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.063
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9718
Order of pole (three term test) = 1.652e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3106 0.991
h = 0.001 0.003
y[1] (numeric) = 0.50976011931 0.620705675971
y[1] (closed_form) = 0.50975580829 0.620698206078
absolute error = 8.625e-06
relative error = 0.001074 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.064
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.615
Order of pole (three term test) = 5.792e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3116 0.994
h = 0.0001 0.004
y[1] (numeric) = 0.510540756511 0.62246615206
y[1] (closed_form) = 0.510536490742 0.622458502432
absolute error = 8.759e-06
relative error = 0.001088 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.066
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.615
Order of pole (three term test) = 1.598e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3117 0.998
h = 0.003 0.006
y[1] (numeric) = 0.510834234574 0.624884240249
y[1] (closed_form) = 0.510830119253 0.624876544468
absolute error = 8.727e-06
relative error = 0.001081 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.068
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.468
Order of pole (three term test) = 2.842e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3147 1.004
h = 0.0001 0.005
y[1] (numeric) = 0.51300180092 0.628343704098
y[1] (closed_form) = 0.51299715948 0.628335563779
absolute error = 9.371e-06
relative error = 0.001155 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.074
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.546
Order of pole (three term test) = 5.151e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3148 1.009
h = 0.0001 0.003
y[1] (numeric) = 0.513354204129 0.631364285742
y[1] (closed_form) = 0.513349849583 0.631356485185
absolute error = 8.934e-06
relative error = 0.001098 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.076
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.246
Order of pole (three term test) = 3.095e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3149 1.012
h = 0.001 0.001
y[1] (numeric) = 0.513590451609 0.633173738593
y[1] (closed_form) = 0.513586010632 0.633166088845
absolute error = 8.845e-06
relative error = 0.001085 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.078
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.979
Order of pole (three term test) = 1.640e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3159 1.013
h = 0.001 0.003
y[1] (numeric) = 0.514254088607 0.633720105666
y[1] (closed_form) = 0.514249630692 0.633712544008
absolute error = 8.778e-06
relative error = 0.001076 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.079
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.65
Order of pole (three term test) = 5.692e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3169 1.016
h = 0.0001 0.004
y[1] (numeric) = 0.515034737511 0.635476416152
y[1] (closed_form) = 0.515030321328 0.635468676694
absolute error = 8.911e-06
relative error = 0.001089 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.082
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.634
Order of pole (three term test) = 2.342e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.317 1.02
h = 0.003 0.006
y[1] (numeric) = 0.515329752188 0.637889477442
y[1] (closed_form) = 0.515325483499 0.637881690134
absolute error = 8.881e-06
relative error = 0.001083 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.084
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.493
Order of pole (three term test) = 2.778e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.32 1.026
h = 0.0001 0.005
y[1] (numeric) = 0.517496039227 0.641340238087
y[1] (closed_form) = 0.517491245186 0.641332021107
absolute error = 9.513e-06
relative error = 0.001154 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.089
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.558
Order of pole (three term test) = 4.369e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3201 1.031
h = 0.0001 0.003
y[1] (numeric) = 0.517850329023 0.644354586822
y[1] (closed_form) = 0.517845822971 0.644346700084
absolute error = 9.083e-06
relative error = 0.001099 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.092
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.256
Order of pole (three term test) = 3.584e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3202 1.034
h = 0.001 0.001
y[1] (numeric) = 0.51808764133 0.646160282821
y[1] (closed_form) = 0.518083052489 0.646152546013
absolute error = 8.995e-06
relative error = 0.001086 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.093
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9863
Order of pole (three term test) = 2.576e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3212 1.035
h = 0.001 0.003
y[1] (numeric) = 0.518750433706 0.646705017617
y[1] (closed_form) = 0.518745829555 0.646697367861
absolute error = 8.928e-06
relative error = 0.001077 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.095
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.684
Order of pole (three term test) = 5.824e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3222 1.038
h = 0.0001 0.004
y[1] (numeric) = 0.519531028511 0.648457223857
y[1] (closed_form) = 0.519526462695 0.648449398279
absolute error = 9.060e-06
relative error = 0.00109 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.097
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.653
Order of pole (three term test) = 3.290e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3223 1.042
h = 0.003 0.006
y[1] (numeric) = 0.519827478108 0.650865308386
y[1] (closed_form) = 0.51982305686 0.650857433364
absolute error = 9.031e-06
relative error = 0.001084 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.099
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.519
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3253 1.048
h = 0.0001 0.005
y[1] (numeric) = 0.52199236839 0.654307514624
y[1] (closed_form) = 0.521987422886 0.65429922445
absolute error = 9.653e-06
relative error = 0.001153 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.105
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.569
Order of pole (three term test) = 1.016e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3254 1.053
h = 0.0001 0.003
y[1] (numeric) = 0.522348419748 0.657315693107
y[1] (closed_form) = 0.522343763084 0.657307723838
absolute error = 9.230e-06
relative error = 0.001099 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.107
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.265
Order of pole (three term test) = 1.275e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3255 1.056
h = 0.001 0.001
y[1] (numeric) = 0.522586722715 0.659117671285
y[1] (closed_form) = 0.522581986801 0.659109851006
absolute error = 9.143e-06
relative error = 0.001087 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.109
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 0.9936
Order of pole (three term test) = 1.619e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3265 1.057
h = 0.001 0.003
y[1] (numeric) = 0.523248657626 0.659660811079
y[1] (closed_form) = 0.523243907969 0.659653076799
absolute error = 9.076e-06
relative error = 0.001078 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.11
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.719
Order of pole (three term test) = 2.269e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3275 1.06
h = 0.0001 0.004
y[1] (numeric) = 0.524029135417 0.661408974607
y[1] (closed_form) = 0.524024420821 0.661401066514
absolute error = 9.207e-06
relative error = 0.001091 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.113
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.673
Order of pole (three term test) = 3.541e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3276 1.064
h = 0.003 0.006
y[1] (numeric) = 0.524326921661 0.663812133759
y[1] (closed_form) = 0.524322348735 0.663804174734
absolute error = 9.179e-06
relative error = 0.001085 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.115
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.545
Order of pole (three term test) = 5.659e-29 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=423.2MB, alloc=52.3MB, time=4.92
x[1] = 0.3306 1.07
h = 0.0001 0.005
y[1] (numeric) = 0.52649030379 0.667245933803
y[1] (closed_form) = 0.526485208013 0.667237573798
absolute error = 9.791e-06
relative error = 0.001152 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.12
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.581
Order of pole (three term test) = 2.018e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3307 1.075
h = 0.0001 0.003
y[1] (numeric) = 0.526847995902 0.67024800618
y[1] (closed_form) = 0.526843189583 0.670239957932
absolute error = 9.374e-06
relative error = 0.0011 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.123
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.274
Order of pole (three term test) = 2.095e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3308 1.078
h = 0.001 0.001
y[1] (numeric) = 0.527087217906 0.67204630641
y[1] (closed_form) = 0.527082335776 0.672038406149
absolute error = 9.287e-06
relative error = 0.001087 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.125
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.001
Order of pole (three term test) = 2.320e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3318 1.079
h = 0.0001 0.004
y[1] (numeric) = 0.527748283646 0.672587887945
y[1] (closed_form) = 0.527743389284 0.672580072618
absolute error = 9.221e-06
relative error = 0.001079 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.126
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.015
Order of pole (three term test) = 3.984e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3319 1.083
h = 0.003 0.006
y[1] (numeric) = 0.528047099962 0.674987059925
y[1] (closed_form) = 0.528042446974 0.674978996391
absolute error = 9.310e-06
relative error = 0.001086 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.128
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.568
Order of pole (three term test) = 2.486e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3349 1.089
h = 0.0001 0.005
y[1] (numeric) = 0.530209196943 0.678413722651
y[1] (closed_form) = 0.530204022383 0.67840527008
absolute error = 9.911e-06
relative error = 0.001151 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.134
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.591
Order of pole (three term test) = 2.694e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.335 1.094
h = 0.0001 0.003
y[1] (numeric) = 0.530568279452 0.681410609139
y[1] (closed_form) = 0.530563394812 0.681402460604
absolute error = 9.500e-06
relative error = 0.0011 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.136
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.282
Order of pole (three term test) = 3.241e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3351 1.097
h = 0.001 0.001
y[1] (numeric) = 0.530808280236 0.683205785838
y[1] (closed_form) = 0.530803322678 0.683197784424
absolute error = 9.413e-06
relative error = 0.001088 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.138
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.007
Order of pole (three term test) = 1.718e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3361 1.098
h = 0.001 0.003
y[1] (numeric) = 0.531468607263 0.683746044553
y[1] (closed_form) = 0.53146363874 0.683738127164
absolute error = 9.347e-06
relative error = 0.001079 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.139
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.784
Order of pole (three term test) = 2.409e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3371 1.101
h = 0.0001 0.004
y[1] (numeric) = 0.532248755854 0.685486846471
y[1] (closed_form) = 0.532243816586 0.685478759052
absolute error = 9.476e-06
relative error = 0.001092 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.142
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.71
Order of pole (three term test) = 1.661e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3372 1.105
h = 0.003 0.006
y[1] (numeric) = 0.53254883636 0.687880994422
y[1] (closed_form) = 0.532544033465 0.687872853527
absolute error = 9.452e-06
relative error = 0.001087 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.144
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.594
Order of pole (three term test) = 2.789e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3402 1.111
h = 0.0001 0.005
y[1] (numeric) = 0.534709231603 0.691299523462
y[1] (closed_form) = 0.534703909069 0.691291007061
absolute error = 1.004e-05
relative error = 0.001149 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.15
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.603
Order of pole (three term test) = 5.590e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3403 1.116
h = 0.0001 0.003
y[1] (numeric) = 0.535069740214 0.69429042527
y[1] (closed_form) = 0.535064707817 0.694282204107
absolute error = 9.639e-06
relative error = 0.0011 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.152
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.292
Order of pole (three term test) = 3.222e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3404 1.119
h = 0.001 0.001
y[1] (numeric) = 0.535310532865 0.696081999311
y[1] (closed_form) = 0.535305430807 0.696073924167
absolute error = 9.552e-06
relative error = 0.001088 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.154
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.015
Order of pole (three term test) = 1.910e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3414 1.12
h = 0.001 0.003
y[1] (numeric) = 0.53596997139 0.696620766545
y[1] (closed_form) = 0.535964859769 0.696612774343
absolute error = 9.487e-06
relative error = 0.001079 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.155
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.819
Order of pole (three term test) = 5.167e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3424 1.123
h = 0.0001 0.004
y[1] (numeric) = 0.536749837482 0.69835770127
y[1] (closed_form) = 0.536744752174 0.698349541125
absolute error = 9.615e-06
relative error = 0.001092 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.158
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.73
Order of pole (three term test) = 1.219e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3425 1.127
h = 0.003 0.006
y[1] (numeric) = 0.537050991162 0.700747075475
y[1] (closed_form) = 0.537046039421 0.700738860637
absolute error = 9.592e-06
relative error = 0.001086 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.16
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.621
Order of pole (three term test) = 4.384e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3455 1.133
h = 0.0001 0.005
y[1] (numeric) = 0.53920958952 0.704157616558
y[1] (closed_form) = 0.539204120327 0.704149039404
absolute error = 1.017e-05
relative error = 0.001147 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.166
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.614
Order of pole (three term test) = 1.881e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3456 1.138
h = 0.0001 0.003
y[1] (numeric) = 0.539571415023 0.70714260123
y[1] (closed_form) = 0.539566235985 0.707134310705
absolute error = 9.775e-06
relative error = 0.001099 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.168
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.301
Order of pole (three term test) = 3.170e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3457 1.141
h = 0.001 0.001
y[1] (numeric) = 0.539812934907 0.708930614367
y[1] (closed_form) = 0.539807689369 0.708922468713
absolute error = 9.689e-06
relative error = 0.001087 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.17
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.022
Order of pole (three term test) = 1.201e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3467 1.142
h = 0.001 0.003
y[1] (numeric) = 0.540471476224 0.709467925253
y[1] (closed_form) = 0.540466222472 0.709459861451
absolute error = 9.624e-06
relative error = 0.001079 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.171
Order of pole (given) = 1 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) = 4.291e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3477 1.145
h = 0.0001 0.004
y[1] (numeric) = 0.541251007301 0.711201054189
y[1] (closed_form) = 0.54124577703 0.711192824548
absolute error = 9.751e-06
relative error = 0.001091 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.174
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.75
Order of pole (three term test) = 1.641e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3478 1.149
h = 0.003 0.006
y[1] (numeric) = 0.541553148463 0.713585709635
y[1] (closed_form) = 0.541548048987 0.713577424173
absolute error = 9.729e-06
relative error = 0.001086 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.176
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.648
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3508 1.155
h = 0.0001 0.005
y[1] (numeric) = 0.543709860091 0.716988407334
y[1] (closed_form) = 0.543704245588 0.716979772403
absolute error = 1.030e-05
relative error = 0.001145 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.182
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.626
Order of pole (three term test) = 5.622e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3509 1.16
h = 0.0001 0.003
y[1] (numeric) = 0.544072897165 0.719967543291
y[1] (closed_form) = 0.544067572651 0.719959186572
absolute error = 9.909e-06
relative error = 0.001098 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.184
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.311
Order of pole (three term test) = 3.867e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.351 1.163
h = 0.001 0.001
y[1] (numeric) = 0.544315081991 0.72175203775
y[1] (closed_form) = 0.544309694042 0.721743824712
absolute error = 9.823e-06
relative error = 0.001087 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.186
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.03
Order of pole (three term test) = 2.388e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.352 1.164
h = 0.001 0.003
y[1] (numeric) = 0.544972718351 0.72228792683
y[1] (closed_form) = 0.544967323484 0.72227979455
absolute error = 9.759e-06
relative error = 0.001079 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.187
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.891
Order of pole (three term test) = 4.732e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.353 1.167
h = 0.0001 0.004
y[1] (numeric) = 0.545751864393 0.724017311155
y[1] (closed_form) = 0.545746490281 0.724009015153
absolute error = 9.885e-06
relative error = 0.00109 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.19
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.771
Order of pole (three term test) = 3.263e-29 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=467.3MB, alloc=52.3MB, time=5.42
x[1] = 0.3531 1.171
h = 0.003 0.006
y[1] (numeric) = 0.546054910435 0.72639730346
y[1] (closed_form) = 0.546049664385 0.726388950595
absolute error = 9.864e-06
relative error = 0.001085 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.192
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.675
Order of pole (three term test) = 2.741e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3561 1.177
h = 0.0001 0.005
y[1] (numeric) = 0.548209650598 0.729792301071
y[1] (closed_form) = 0.548203892167 0.729783611247
absolute error = 1.042e-05
relative error = 0.001142 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.198
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.638
Order of pole (three term test) = 4.986e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3562 1.182
h = 0.0001 0.003
y[1] (numeric) = 0.548573797729 0.732765657475
y[1] (closed_form) = 0.548568328945 0.732757237636
absolute error = 1.004e-05
relative error = 0.001097 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.201
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.321
Order of pole (three term test) = 4.564e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3563 1.185
h = 0.001 0.001
y[1] (numeric) = 0.548816587492 0.734546675879
y[1] (closed_form) = 0.548811058244 0.73453839849
absolute error = 9.954e-06
relative error = 0.001086 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.202
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.038
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3573 1.186
h = 0.0001 0.004
y[1] (numeric) = 0.549473312054 0.735081177093
y[1] (closed_form) = 0.549467777132 0.735072979366
absolute error = 9.891e-06
relative error = 0.001078 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.204
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.235
Order of pole (three term test) = 1.469e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3574 1.19
h = 0.003 0.006
y[1] (numeric) = 0.549777046049 0.737457398778
y[1] (closed_form) = 0.549771718613 0.737448954505
absolute error = 9.984e-06
relative error = 0.001085 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.206
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.698
Order of pole (three term test) = 3.691e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3604 1.196
h = 0.0001 0.005
y[1] (numeric) = 0.551930114581 0.740845857336
y[1] (closed_form) = 0.551924277061 0.740837086641
absolute error = 1.054e-05
relative error = 0.00114 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.212
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.649
Order of pole (three term test) = 1.985e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3605 1.201
h = 0.0001 0.003
y[1] (numeric) = 0.552295206471 0.743814306393
y[1] (closed_form) = 0.552289658265 0.743805798746
absolute error = 1.016e-05
relative error = 0.001096 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.214
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.329
Order of pole (three term test) = 2.390e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3606 1.204
h = 0.001 0.001
y[1] (numeric) = 0.552538511306 0.745592373374
y[1] (closed_form) = 0.552532905137 0.745584007126
absolute error = 1.007e-05
relative error = 0.001085 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.216
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.044
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3616 1.205
h = 0.001 0.003
y[1] (numeric) = 0.553194462203 0.746125695717
y[1] (closed_form) = 0.553188851403 0.746117408197
absolute error = 1.001e-05
relative error = 0.001078 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.218
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.959
Order of pole (three term test) = 2.220e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3626 1.208
h = 0.0001 0.004
y[1] (numeric) = 0.55397280977 0.7478482681
y[1] (closed_form) = 0.553967214909 0.747839820795
absolute error = 1.013e-05
relative error = 0.001089 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.22
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.809
Order of pole (three term test) = 1.299e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3627 1.212
h = 0.003 0.006
y[1] (numeric) = 0.554277383976 0.75021974174
y[1] (closed_form) = 0.554271912204 0.750211235813
absolute error = 1.011e-05
relative error = 0.001084 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.222
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.726
Order of pole (three term test) = 5.144e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3657 1.218
h = 0.0001 0.005
y[1] (numeric) = 0.556428334674 0.753600762219
y[1] (closed_form) = 0.556422355837 0.753591941766
absolute error = 1.066e-05
relative error = 0.001138 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.228
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.661
Order of pole (three term test) = 5.577e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3658 1.223
h = 0.0001 0.003
y[1] (numeric) = 0.556794356692 0.756563560846
y[1] (closed_form) = 0.556788666526 0.756554995563
absolute error = 1.028e-05
relative error = 0.001095 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.231
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.339
Order of pole (three term test) = 5.311e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3659 1.226
h = 0.001 0.001
y[1] (numeric) = 0.557038160185 0.75833823122
y[1] (closed_form) = 0.557032414858 0.758329806043
absolute error = 1.020e-05
relative error = 0.001084 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.233
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.052
Order of pole (three term test) = 4.751e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3669 1.227
h = 0.001 0.003
y[1] (numeric) = 0.557693188442 0.758870227166
y[1] (closed_form) = 0.557687439635 0.758861879619
absolute error = 1.014e-05
relative error = 0.001076 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.234
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.995
Order of pole (three term test) = 3.120e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3679 1.23
h = 0.0001 0.004
y[1] (numeric) = 0.558471020235 0.760589227649
y[1] (closed_form) = 0.558465284936 0.760580722457
absolute error = 1.026e-05
relative error = 0.001087 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.237
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.83
Order of pole (three term test) = 3.041e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.368 1.234
h = 0.003 0.006
y[1] (numeric) = 0.558776278746 0.762956198954
y[1] (closed_form) = 0.558770663914 0.762947634319
absolute error = 1.024e-05
relative error = 0.001083 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.239
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.753
Order of pole (three term test) = 1.022e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.371 1.24
h = 0.0001 0.005
y[1] (numeric) = 0.560925040494 0.766329920497
y[1] (closed_form) = 0.560918921794 0.766321052907
absolute error = 1.077e-05
relative error = 0.001134 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.245
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.673
Order of pole (three term test) = 4.896e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3711 1.245
h = 0.0001 0.003
y[1] (numeric) = 0.561291901491 0.76928713933
y[1] (closed_form) = 0.561286070672 0.769278519221
absolute error = 1.041e-05
relative error = 0.001093 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.247
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.349
Order of pole (three term test) = 2.359e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3712 1.248
h = 0.001 0.001
y[1] (numeric) = 0.56153614986 0.771058456468
y[1] (closed_form) = 0.561530266595 0.771049975144
absolute error = 1.032e-05
relative error = 0.001082 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.249
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.06
Order of pole (three term test) = 1.980e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3722 1.249
h = 0.001 0.003
y[1] (numeric) = 0.562190251012 0.77158915821
y[1] (closed_form) = 0.562184365369 0.771580753415
absolute error = 1.026e-05
relative error = 0.001075 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.251
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.032
Order of pole (three term test) = 3.099e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3732 1.252
h = 0.0001 0.004
y[1] (numeric) = 0.562967525908 0.773304646565
y[1] (closed_form) = 0.562961651441 0.773296086271
absolute error = 1.038e-05
relative error = 0.001085 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.253
Order of pole (given) = 1 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) = 1.208e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3733 1.256
h = 0.003 0.006
y[1] (numeric) = 0.563273397355 0.775667172682
y[1] (closed_form) = 0.563267640775 0.775658552195
absolute error = 1.037e-05
relative error = 0.001081 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.255
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.781
Order of pole (three term test) = 2.031e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3763 1.262
h = 0.0001 0.005
y[1] (numeric) = 0.565419903447 0.779033732797
y[1] (closed_form) = 0.565413646356 0.779024820604
absolute error = 1.089e-05
relative error = 0.001131 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.261
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.686
Order of pole (three term test) = 2.750e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3764 1.267
h = 0.0001 0.003
y[1] (numeric) = 0.56578751572 0.781985442757
y[1] (closed_form) = 0.565781545582 0.781976770542
absolute error = 1.053e-05
relative error = 0.001091 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.264
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.359
Order of pole (three term test) = 3.489e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3765 1.27
h = 0.001 0.001
y[1] (numeric) = 0.566032157252 0.783753450156
y[1] (closed_form) = 0.566026137296 0.78374491538
absolute error = 1.044e-05
relative error = 0.00108 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.266
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.068
Order of pole (three term test) = 2.638e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3775 1.271
h = 0.001 0.003
y[1] (numeric) = 0.566685327578 0.784282889261
y[1] (closed_form) = 0.566679306303 0.784274429918
absolute error = 1.038e-05
relative error = 0.001073 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.267
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.07
Order of pole (three term test) = 4.687e-29 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=511.4MB, alloc=52.3MB, time=5.93
x[1] = 0.3785 1.274
h = 0.0001 0.004
y[1] (numeric) = 0.567462006571 0.78599492477
y[1] (closed_form) = 0.567455994232 0.785986312069
absolute error = 1.050e-05
relative error = 0.001083 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.27
Order of pole (given) = 1 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) = 2.399e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3786 1.278
h = 0.003 0.006
y[1] (numeric) = 0.567768422313 0.788353063018
y[1] (closed_form) = 0.567762525323 0.788344389443
absolute error = 1.049e-05
relative error = 0.00108 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.272
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.809
Order of pole (three term test) = 2.852e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3816 1.284
h = 0.0001 0.005
y[1] (numeric) = 0.569912610276 0.791712597506
y[1] (closed_form) = 0.569906216282 0.79170364316
absolute error = 1.100e-05
relative error = 0.001128 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.278
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.698
Order of pole (three term test) = 3.860e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3817 1.289
h = 0.0001 0.003
y[1] (numeric) = 0.570280889473 0.794658869698
y[1] (closed_form) = 0.570274781378 0.79465014801
absolute error = 1.065e-05
relative error = 0.001089 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.281
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.369
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3818 1.292
h = 0.001 0.001
y[1] (numeric) = 0.570525874462 0.796423610923
y[1] (closed_form) = 0.570519719093 0.796415025305
absolute error = 1.056e-05
relative error = 0.001078 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.283
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.075
Order of pole (three term test) = 1.745e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3828 1.293
h = 0.0001 0.004
y[1] (numeric) = 0.571178110955 0.796951818336
y[1] (closed_form) = 0.571171955277 0.796943307058
absolute error = 1.050e-05
relative error = 0.001071 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.284
Order of pole (given) = 1 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) = 3.815e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3829 1.297
h = 0.003 0.006
y[1] (numeric) = 0.571484929441 0.799306411506
y[1] (closed_form) = 0.571478951135 0.799297658329
absolute error = 1.060e-05
relative error = 0.001079 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.286
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.833
Order of pole (three term test) = 1.712e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3859 1.303
h = 0.0001 0.005
y[1] (numeric) = 0.573627156637 0.80265997742
y[1] (closed_form) = 0.573620684331 0.802650952678
absolute error = 1.111e-05
relative error = 0.001126 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.292
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.709
Order of pole (three term test) = 6.283e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.386 1.308
h = 0.0001 0.003
y[1] (numeric) = 0.573996008464 0.80560163261
y[1] (closed_form) = 0.573989821137 0.805592834358
absolute error = 1.076e-05
relative error = 0.001087 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.295
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.378
Order of pole (three term test) = 8.773e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3861 1.311
h = 0.001 0.001
y[1] (numeric) = 0.57424128898 0.807363600639
y[1] (closed_form) = 0.574235056518 0.807354937293
absolute error = 1.067e-05
relative error = 0.001077 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.297
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.082
Order of pole (three term test) = 3.292e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3871 1.312
h = 0.001 0.003
y[1] (numeric) = 0.574892733947 0.807890760995
y[1] (closed_form) = 0.574886502025 0.807882171062
absolute error = 1.061e-05
relative error = 0.00107 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.298
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.139
Order of pole (three term test) = 3.258e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3881 1.315
h = 0.0001 0.004
y[1] (numeric) = 0.575668246704 0.809596519382
y[1] (closed_form) = 0.57566201977 0.809587780044
absolute error = 1.073e-05
relative error = 0.00108 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.301
Order of pole (given) = 1 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) = 4.579e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3882 1.319
h = 0.003 0.006
y[1] (numeric) = 0.575975552244 0.811946650329
y[1] (closed_form) = 0.575969436056 0.811937848991
absolute error = 1.072e-05
relative error = 0.001077 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.303
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.861
Order of pole (three term test) = 3.470e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3912 1.325
h = 0.0001 0.005
y[1] (numeric) = 0.578115354186 0.815293437938
y[1] (closed_form) = 0.578108747754 0.8152843754
absolute error = 1.121e-05
relative error = 0.001122 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.309
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.721
Order of pole (three term test) = 1.021e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3913 1.33
h = 0.0001 0.003
y[1] (numeric) = 0.578484723731 0.818229786931
y[1] (closed_form) = 0.578478401005 0.818220943897
absolute error = 1.087e-05
relative error = 0.001085 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.312
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.388
Order of pole (three term test) = 1.230e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3914 1.333
h = 0.001 0.001
y[1] (numeric) = 0.578730259848 0.819988569307
y[1] (closed_form) = 0.578723894378 0.819979859776
absolute error = 1.079e-05
relative error = 0.001075 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.314
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.09
Order of pole (three term test) = 2.355e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3924 1.334
h = 0.001 0.003
y[1] (numeric) = 0.579380766792 0.820514553873
y[1] (closed_form) = 0.579374402794 0.82050591667
absolute error = 1.073e-05
relative error = 0.001068 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.315
Order of pole (given) = 1 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) = 2.554e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3934 1.337
h = 0.0001 0.004
y[1] (numeric) = 0.580155582386 0.822217025538
y[1] (closed_form) = 0.580149221391 0.822208241059
absolute error = 1.085e-05
relative error = 0.001078 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.318
Order of pole (given) = 1 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) = 3.671e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3935 1.341
h = 0.003 0.006
y[1] (numeric) = 0.580463249558 0.824562932154
y[1] (closed_form) = 0.580456996895 0.824554085172
absolute error = 1.083e-05
relative error = 0.001074 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.32
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.89
Order of pole (three term test) = 1.871e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3965 1.347
h = 0.0001 0.005
y[1] (numeric) = 0.582600574984 0.827903072116
y[1] (closed_form) = 0.582593835948 0.827893973998
absolute error = 1.132e-05
relative error = 0.001118 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.326
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.734
Order of pole (three term test) = 6.092e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3966 1.352
h = 0.0001 0.003
y[1] (numeric) = 0.582970386972 0.830834186086
y[1] (closed_form) = 0.582963930264 0.830825300665
absolute error = 1.098e-05
relative error = 0.001082 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.329
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.398
Order of pole (three term test) = 3.857e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3967 1.355
h = 0.001 0.001
y[1] (numeric) = 0.583216134417 0.8325898263
y[1] (closed_form) = 0.583209637278 0.832581072965
absolute error = 1.090e-05
relative error = 0.001072 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.331
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.098
Order of pole (three term test) = 3.486e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3977 1.356
h = 0.001 0.003
y[1] (numeric) = 0.583865702167 0.833114664244
y[1] (closed_form) = 0.58385920739 0.833105982159
absolute error = 1.084e-05
relative error = 0.001066 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.332
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.215
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3987 1.359
h = 0.0001 0.004
y[1] (numeric) = 0.584639789068 0.834813906233
y[1] (closed_form) = 0.584633295395 0.83480507899
absolute error = 1.096e-05
relative error = 0.001075 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.335
Order of pole (given) = 1 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) = 4.751e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.3988 1.363
h = 0.003 0.006
y[1] (numeric) = 0.584947759058 0.837155645849
y[1] (closed_form) = 0.584941371344 0.837146755658
absolute error = 1.095e-05
relative error = 0.001072 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.337
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.919
Order of pole (three term test) = 2.674e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4018 1.369
h = 0.0001 0.005
y[1] (numeric) = 0.587082560311 0.840489266919
y[1] (closed_form) = 0.587075690199 0.840480135361
absolute error = 1.143e-05
relative error = 0.001115 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.343
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.747
Order of pole (three term test) = 5.110e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4019 1.374
h = 0.0001 0.003
y[1] (numeric) = 0.587452742457 0.843415216897
y[1] (closed_form) = 0.587446153199 0.843406291405
absolute error = 1.109e-05
relative error = 0.001079 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.346
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.408
Order of pole (three term test) = 5.227e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.402 1.377
h = 0.001 0.001
y[1] (numeric) = 0.587698658749 0.845167758318
y[1] (closed_form) = 0.587692031294 0.845158963483
absolute error = 1.101e-05
relative error = 0.00107 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.348
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.106
Order of pole (three term test) = 4.535e-29 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=555.4MB, alloc=52.3MB, time=6.44
x[1] = 0.403 1.378
h = 0.001 0.003
y[1] (numeric) = 0.588347286705 0.845691478192
y[1] (closed_form) = 0.588340662464 0.845682753535
absolute error = 1.095e-05
relative error = 0.001063 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.35
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.254
Order of pole (three term test) = 4.485e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.404 1.381
h = 0.0001 0.004
y[1] (numeric) = 0.589120615151 0.847387546887
y[1] (closed_form) = 0.589113990194 0.847378679181
absolute error = 1.107e-05
relative error = 0.001073 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.352
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.976
Order of pole (three term test) = 4.369e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4041 1.385
h = 0.003 0.006
y[1] (numeric) = 0.589428831506 0.849725176681
y[1] (closed_form) = 0.58942231018 0.849716245633
absolute error = 1.106e-05
relative error = 0.001069 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.355
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.947
Order of pole (three term test) = 2.323e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4071 1.391
h = 0.0001 0.005
y[1] (numeric) = 0.591561064377 0.853052405675
y[1] (closed_form) = 0.591554064722 0.853043242743
absolute error = 1.153e-05
relative error = 0.001111 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.36
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.76
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4072 1.396
h = 0.0001 0.003
y[1] (numeric) = 0.591931547303 0.855973262481
y[1] (closed_form) = 0.591924826937 0.855964299156
absolute error = 1.120e-05
relative error = 0.001076 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.364
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.419
Order of pole (three term test) = 2.870e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4073 1.399
h = 0.001 0.001
y[1] (numeric) = 0.592177591694 0.857722748314
y[1] (closed_form) = 0.592170835291 0.857713914206
absolute error = 1.112e-05
relative error = 0.001067 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.365
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.114
Order of pole (three term test) = 2.539e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4083 1.4
h = 0.003 0.006
y[1] (numeric) = 0.5928252798 0.858245378053
y[1] (closed_form) = 0.592818527423 0.858236613059
absolute error = 1.106e-05
relative error = 0.001061 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.367
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 11.23
Order of pole (three term test) = 6.976e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4113 1.406
h = 0.0001 0.005
y[1] (numeric) = 0.594955503165 0.861568812791
y[1] (closed_form) = 0.594948337069 0.861559357879
absolute error = 1.186e-05
relative error = 0.001133 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.373
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.769
Order of pole (three term test) = 7.121e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4114 1.411
h = 0.0001 0.003
y[1] (numeric) = 0.595326028013 0.86448620143
y[1] (closed_form) = 0.595319139923 0.864476941822
absolute error = 1.154e-05
relative error = 0.001099 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.376
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.426
Order of pole (three term test) = 2.732e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4115 1.414
h = 0.001 0.001
y[1] (numeric) = 0.595572062069 0.866233608268
y[1] (closed_form) = 0.595565139349 0.866224476831
absolute error = 1.146e-05
relative error = 0.00109 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.378
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.12
Order of pole (three term test) = 2.279e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4125 1.415
h = 0.001 0.003
y[1] (numeric) = 0.596219077252 0.86675552767
y[1] (closed_form) = 0.596212159069 0.8667464646
absolute error = 1.140e-05
relative error = 0.001084 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.379
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.32
Order of pole (three term test) = 2.390e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4135 1.418
h = 0.0001 0.004
y[1] (numeric) = 0.596990985805 0.868446386774
y[1] (closed_form) = 0.596984064065 0.868437184226
absolute error = 1.152e-05
relative error = 0.001093 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.382
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.014
Order of pole (three term test) = 1.097e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4136 1.422
h = 0.003 0.006
y[1] (numeric) = 0.597299395912 0.87077720543
y[1] (closed_form) = 0.597292573965 0.870767939049
absolute error = 1.151e-05
relative error = 0.00109 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.384
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.997
Order of pole (three term test) = 1.549e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4166 1.428
h = 0.0001 0.005
y[1] (numeric) = 0.599427048308 0.874093994328
y[1] (closed_form) = 0.59941975531 0.874084511326
absolute error = 1.196e-05
relative error = 0.001129 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.39
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.782
Order of pole (three term test) = 3.590e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4167 1.433
h = 0.0001 0.003
y[1] (numeric) = 0.599797764934 0.877006410265
y[1] (closed_form) = 0.599790748244 0.876997116394
absolute error = 1.165e-05
relative error = 0.001096 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.393
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.436
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4168 1.436
h = 0.001 0.001
y[1] (numeric) = 0.600043863172 0.878750834901
y[1] (closed_form) = 0.600036813889 0.878741667751
absolute error = 1.156e-05
relative error = 0.001087 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.395
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.128
Order of pole (three term test) = 2.519e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4178 1.437
h = 0.001 0.003
y[1] (numeric) = 0.600689940221 0.879271709914
y[1] (closed_form) = 0.600682896226 0.879262610083
absolute error = 1.151e-05
relative error = 0.001081 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.396
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.359
Order of pole (three term test) = 4.015e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4188 1.44
h = 0.0001 0.004
y[1] (numeric) = 0.601461019898 0.880959544448
y[1] (closed_form) = 0.601453970732 0.880950307208
absolute error = 1.162e-05
relative error = 0.001089 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.399
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.036
Order of pole (three term test) = 2.168e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4189 1.444
h = 0.003 0.006
y[1] (numeric) = 0.601769537209 0.883286407028
y[1] (closed_form) = 0.601762585626 0.883277105694
absolute error = 1.161e-05
relative error = 0.001086 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.402
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.026
Order of pole (three term test) = 1.859e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4219 1.45
h = 0.0001 0.005
y[1] (numeric) = 0.603894521398 0.886597135788
y[1] (closed_form) = 0.603887103032 0.88658762657
absolute error = 1.206e-05
relative error = 0.001124 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.408
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.795
Order of pole (three term test) = 4.918e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.422 1.455
h = 0.0001 0.003
y[1] (numeric) = 0.604265367773 0.889504648899
y[1] (closed_form) = 0.604258223946 0.889495322803
absolute error = 1.175e-05
relative error = 0.001092 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.411
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.447
Order of pole (three term test) = 1.326e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4221 1.458
h = 0.001 0.001
y[1] (numeric) = 0.604511493836 0.891246133881
y[1] (closed_form) = 0.604504319382 0.891236933053
absolute error = 1.167e-05
relative error = 0.001083 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.413
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.137
Order of pole (three term test) = 2.226e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4231 1.459
h = 0.001 0.003
y[1] (numeric) = 0.605156633984 0.891765990801
y[1] (closed_form) = 0.605149465535 0.891756856253
absolute error = 1.161e-05
relative error = 0.001077 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.414
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.398
Order of pole (three term test) = 1.555e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4241 1.462
h = 0.0001 0.004
y[1] (numeric) = 0.605926860931 0.893450854491
y[1] (closed_form) = 0.605919685769 0.893441584586
absolute error = 1.172e-05
relative error = 0.001086 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.417
Order of pole (given) = 1 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) = 2.141e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4242 1.466
h = 0.003 0.006
y[1] (numeric) = 0.606235437083 0.89577381711
y[1] (closed_form) = 0.606228357337 0.895764482894
absolute error = 1.172e-05
relative error = 0.001083 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.419
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.056
Order of pole (three term test) = 2.546e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4272 1.472
h = 0.0001 0.005
y[1] (numeric) = 0.608357720284 0.899078605134
y[1] (closed_form) = 0.608350178082 0.899069071507
absolute error = 1.216e-05
relative error = 0.00112 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.425
Order of pole (given) = 1 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) = 1.535e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4273 1.477
h = 0.0001 0.003
y[1] (numeric) = 0.608728636959 0.901981284869
y[1] (closed_form) = 0.60872136746 0.901971928517
absolute error = 1.185e-05
relative error = 0.001089 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.428
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.457
Order of pole (three term test) = 8.277e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4274 1.48
h = 0.001 0.001
y[1] (numeric) = 0.608974756024 0.90371987246
y[1] (closed_form) = 0.608967457798 0.903710639918
absolute error = 1.177e-05
relative error = 0.00108 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.43
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.145
Order of pole (three term test) = 2.240e-29 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=599.5MB, alloc=52.3MB, time=6.94
x[1] = 0.4284 1.481
h = 0.0001 0.004
y[1] (numeric) = 0.609618960941 0.904238736991
y[1] (closed_form) = 0.609611669401 0.904229569702
absolute error = 1.171e-05
relative error = 0.001074 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.431
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.879
Order of pole (three term test) = 6.780e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4285 1.485
h = 0.003 0.006
y[1] (numeric) = 0.609927556695 0.90655855161
y[1] (closed_form) = 0.609920398168 0.906549155482
absolute error = 1.181e-05
relative error = 0.001081 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.434
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.081
Order of pole (three term test) = 3.382e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4315 1.491
h = 0.0001 0.005
y[1] (numeric) = 0.61204755973 0.909858287465
y[1] (closed_form) = 0.612039942418 0.909848699065
absolute error = 1.225e-05
relative error = 0.001117 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.44
Order of pole (given) = 1 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) = 1.289e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4316 1.496
h = 0.0001 0.003
y[1] (numeric) = 0.612418547676 0.912756861966
y[1] (closed_form) = 0.612411201504 0.912747445912
absolute error = 1.194e-05
relative error = 0.001087 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.443
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.466
Order of pole (three term test) = 4.820e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4317 1.499
h = 0.001 0.001
y[1] (numeric) = 0.612664667805 0.914492988562
y[1] (closed_form) = 0.612657294505 0.914483695086
absolute error = 1.186e-05
relative error = 0.001078 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.445
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.152
Order of pole (three term test) = 2.916e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4327 1.5
h = 0.001 0.003
y[1] (numeric) = 0.613308080769 0.915011007909
y[1] (closed_form) = 0.613300714729 0.915001778815
absolute error = 1.181e-05
relative error = 0.001072 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.446
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.471
Order of pole (three term test) = 1.441e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4337 1.503
h = 0.0001 0.004
y[1] (numeric) = 0.61407669637 0.916690473206
y[1] (closed_form) = 0.614069320905 0.91668111251
absolute error = 1.192e-05
relative error = 0.00108 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.449
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.099
Order of pole (three term test) = 4.045e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4338 1.507
h = 0.003 0.006
y[1] (numeric) = 0.614385305093 0.919006326392
y[1] (closed_form) = 0.61437802113 0.918996901067
absolute error = 1.191e-05
relative error = 0.001078 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.452
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.11
Order of pole (three term test) = 9.433e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4368 1.513
h = 0.0001 0.005
y[1] (numeric) = 0.616502552115 0.922300337997
y[1] (closed_form) = 0.616494813791 0.922290728397
absolute error = 1.234e-05
relative error = 0.001112 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.458
Order of pole (given) = 1 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) = 1.270e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4369 1.518
h = 0.0001 0.003
y[1] (numeric) = 0.616873505499 0.925194206424
y[1] (closed_form) = 0.616866036367 0.925184763613
absolute error = 1.204e-05
relative error = 0.001083 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.461
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.477
Order of pole (three term test) = 1.539e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.437 1.521
h = 0.001 0.001
y[1] (numeric) = 0.61711955726 0.926927513042
y[1] (closed_form) = 0.617112062778 0.926918191351
absolute error = 1.196e-05
relative error = 0.001074 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.463
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.16
Order of pole (three term test) = 8.130e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.438 1.522
h = 0.001 0.003
y[1] (numeric) = 0.617762038874 0.927444586307
y[1] (closed_form) = 0.617754552275 0.92743532799
absolute error = 1.191e-05
relative error = 0.001068 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.464
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.51
Order of pole (three term test) = 4.193e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.439 1.525
h = 0.0001 0.004
y[1] (numeric) = 0.618529740759 0.929121230053
y[1] (closed_form) = 0.618522243385 0.929111842133
absolute error = 1.201e-05
relative error = 0.001076 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.467
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.121
Order of pole (three term test) = 3.222e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4391 1.529
h = 0.003 0.006
y[1] (numeric) = 0.618838280302 0.931433341136
y[1] (closed_form) = 0.618830872386 0.931423888486
absolute error = 1.201e-05
relative error = 0.001074 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.469
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.14
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4421 1.535
h = 0.0001 0.005
y[1] (numeric) = 0.620952746213 0.934721742131
y[1] (closed_form) = 0.620944888399 0.934712112957
absolute error = 1.243e-05
relative error = 0.001108 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.475
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.845
Order of pole (three term test) = 2.502e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4422 1.54
h = 0.0001 0.003
y[1] (numeric) = 0.621323612507 0.937610972498
y[1] (closed_form) = 0.621316021886 0.93760150471
absolute error = 1.213e-05
relative error = 0.001079 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.479
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.488
Order of pole (three term test) = 3.017e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4423 1.543
h = 0.001 0.001
y[1] (numeric) = 0.621569565203 0.939341500456
y[1] (closed_form) = 0.621561950946 0.939332152331
absolute error = 1.206e-05
relative error = 0.00107 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.481
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.169
Order of pole (three term test) = 8.006e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4433 1.544
h = 0.001 0.003
y[1] (numeric) = 0.622211118244 0.939857651693
y[1] (closed_form) = 0.622203512463 0.939848365943
absolute error = 1.200e-05
relative error = 0.001065 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.482
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.55
Order of pole (three term test) = 2.919e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4443 1.547
h = 0.0001 0.004
y[1] (numeric) = 0.622977887886 0.941531524679
y[1] (closed_form) = 0.622970270041 0.941522111306
absolute error = 1.211e-05
relative error = 0.001073 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.485
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.144
Order of pole (three term test) = 1.720e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4444 1.551
h = 0.003 0.006
y[1] (numeric) = 0.623286317367 0.94383994817
y[1] (closed_form) = 0.623278786978 0.943830470002
absolute error = 1.211e-05
relative error = 0.00107 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.487
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.17
Order of pole (three term test) = 2.276e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4474 1.557
h = 0.0001 0.005
y[1] (numeric) = 0.625397979512 0.947122850169
y[1] (closed_form) = 0.625390003721 0.947113202987
absolute error = 1.252e-05
relative error = 0.001103 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.493
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.859
Order of pole (three term test) = 2.871e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4475 1.562
h = 0.0001 0.003
y[1] (numeric) = 0.625768708449 0.950007509905
y[1] (closed_form) = 0.625760997806 0.949998018853
absolute error = 1.223e-05
relative error = 0.001075 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.497
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.498
Order of pole (three term test) = 2.968e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4476 1.565
h = 0.001 0.001
y[1] (numeric) = 0.62601453273 0.951735300142
y[1] (closed_form) = 0.626006800104 0.951725927299
absolute error = 1.215e-05
relative error = 0.001067 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.498
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.177
Order of pole (three term test) = 4.982e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4486 1.566
h = 0.001 0.003
y[1] (numeric) = 0.626655160314 0.952250552838
y[1] (closed_form) = 0.626647436729 0.952241241386
absolute error = 1.210e-05
relative error = 0.001061 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.5
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.59
Order of pole (three term test) = 4.061e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4496 1.569
h = 0.0001 0.004
y[1] (numeric) = 0.627420980424 0.953921705072
y[1] (closed_form) = 0.627413243547 0.953912267955
absolute error = 1.220e-05
relative error = 0.001069 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.503
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.166
Order of pole (three term test) = 4.281e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4497 1.573
h = 0.003 0.006
y[1] (numeric) = 0.627729260741 0.95622649499
y[1] (closed_form) = 0.627721609361 0.956216993047
absolute error = 1.220e-05
relative error = 0.001067 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.505
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.2
Order of pole (three term test) = 2.845e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4527 1.579
h = 0.0001 0.005
y[1] (numeric) = 0.629838098793 0.959504007581
y[1] (closed_form) = 0.629830006532 0.959494343899
absolute error = 1.260e-05
relative error = 0.001098 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.511
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.872
Order of pole (three term test) = 6.878e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4528 1.584
h = 0.0001 0.003
y[1] (numeric) = 0.630208642291 0.962384163494
y[1] (closed_form) = 0.630200813091 0.962374650833
absolute error = 1.232e-05
relative error = 0.001071 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.514
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.509
Order of pole (three term test) = 4.146e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4529 1.587
h = 0.001 0.001
y[1] (numeric) = 0.630454310106 0.964109256552
memory used=643.6MB, alloc=52.3MB, time=7.45
y[1] (closed_form) = 0.630446460518 0.964099860652
absolute error = 1.224e-05
relative error = 0.001063 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.516
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.186
Order of pole (three term test) = 2.192e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4539 1.588
h = 0.0001 0.004
y[1] (numeric) = 0.631094015668 0.964623633644
y[1] (closed_form) = 0.631086175656 0.964614298159
absolute error = 1.219e-05
relative error = 0.001058 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.518
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.124
Order of pole (three term test) = 1.351e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.454 1.592
h = 0.003 0.006
y[1] (numeric) = 0.631402151729 0.966925491448
y[1] (closed_form) = 0.63139442384 0.966915936052
absolute error = 1.229e-05
relative error = 0.001064 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.52
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.226
Order of pole (three term test) = 3.368e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.457 1.598
h = 0.0001 0.005
y[1] (numeric) = 0.633508606773 0.970198417304
y[1] (closed_form) = 0.63350044183 0.970188706301
absolute error = 1.269e-05
relative error = 0.001095 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.527
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.884
Order of pole (three term test) = 4.616e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4571 1.603
h = 0.0001 0.003
y[1] (numeric) = 0.633879006341 0.97307474653
y[1] (closed_form) = 0.63387110269 0.97306518224
absolute error = 1.241e-05
relative error = 0.001068 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.53
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.518
Order of pole (three term test) = 5.177e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4572 1.606
h = 0.001 0.001
y[1] (numeric) = 0.634124549451 0.9747975478
y[1] (closed_form) = 0.634116626757 0.974788099045
absolute error = 1.233e-05
relative error = 0.00106 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.532
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.193
Order of pole (three term test) = 3.069e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4582 1.607
h = 0.001 0.003
y[1] (numeric) = 0.63476347441 0.975311178227
y[1] (closed_form) = 0.634755561743 0.975301789066
absolute error = 1.228e-05
relative error = 0.001055 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.533
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.664
Order of pole (three term test) = 2.578e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4592 1.61
h = 0.0001 0.004
y[1] (numeric) = 0.635527516725 0.976977386426
y[1] (closed_form) = 0.635519588611 0.976967875171
absolute error = 1.238e-05
relative error = 0.001062 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.536
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.209
Order of pole (three term test) = 4.166e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4593 1.614
h = 0.003 0.006
y[1] (numeric) = 0.635835463044 0.979275554292
y[1] (closed_form) = 0.635827616889 0.979265978216
absolute error = 1.238e-05
relative error = 0.00106 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.538
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.256
Order of pole (three term test) = 5.227e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4623 1.62
h = 0.0001 0.005
y[1] (numeric) = 0.637939060742 0.982543289117
y[1] (closed_form) = 0.637930782091 0.982533564291
absolute error = 1.277e-05
relative error = 0.00109 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.545
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.897
Order of pole (three term test) = 3.382e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4624 1.625
h = 0.0001 0.003
y[1] (numeric) = 0.638309190183 0.985415236573
y[1] (closed_form) = 0.638301170669 0.985405653612
absolute error = 1.250e-05
relative error = 0.001064 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.548
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.529
Order of pole (three term test) = 2.142e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4625 1.628
h = 0.001 0.001
y[1] (numeric) = 0.638554527464 0.987135414691
y[1] (closed_form) = 0.638546490397 0.987125945826
absolute error = 1.242e-05
relative error = 0.001056 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.55
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.201
Order of pole (three term test) = 2.019e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4635 1.629
h = 0.001 0.003
y[1] (numeric) = 0.639192537306 0.987648210792
y[1] (closed_form) = 0.639184510751 0.98763880057
absolute error = 1.237e-05
relative error = 0.001051 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.551
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.705
Order of pole (three term test) = 4.435e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4645 1.632
h = 0.0001 0.004
y[1] (numeric) = 0.639955586459 0.989311836772
y[1] (closed_form) = 0.63994754339 0.98930230635
absolute error = 1.247e-05
relative error = 0.001058 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.554
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.232
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4646 1.636
h = 0.003 0.006
y[1] (numeric) = 0.640263280417 0.991606522258
y[1] (closed_form) = 0.640255317464 0.991596927073
absolute error = 1.247e-05
relative error = 0.001056 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.557
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.286
Order of pole (three term test) = 3.242e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4676 1.642
h = 0.0001 0.005
y[1] (numeric) = 0.642364006529 0.994869169925
y[1] (closed_form) = 0.642355615651 0.994859432627
absolute error = 1.285e-05
relative error = 0.001085 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.563
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.911
Order of pole (three term test) = 8.707e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4677 1.647
h = 0.0001 0.003
y[1] (numeric) = 0.642733823609 0.997736800517
y[1] (closed_form) = 0.642725689682 0.997727200375
absolute error = 1.258e-05
relative error = 0.00106 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.566
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.54
Order of pole (three term test) = 2.302e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4678 1.65
h = 0.001 0.001
y[1] (numeric) = 0.642978930487 0.999454394815
y[1] (closed_form) = 0.642970780442 0.999444907337
absolute error = 1.251e-05
relative error = 0.001052 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.568
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.21
Order of pole (three term test) = 3.939e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4688 1.651
h = 0.001 0.003
y[1] (numeric) = 0.643616029446 0.999966377993
y[1] (closed_form) = 0.643607890374 0.999956948218
absolute error = 1.246e-05
relative error = 0.001047 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.569
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.745
Order of pole (three term test) = 2.749e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4698 1.654
h = 0.0001 0.004
y[1] (numeric) = 0.644378072472 1.00162746872
y[1] (closed_form) = 0.644369915871 1.00161792061
absolute error = 1.256e-05
relative error = 0.001054 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.572
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.255
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4699 1.658
h = 0.003 0.006
y[1] (numeric) = 0.644685481283 1.00391872374
y[1] (closed_form) = 0.644677402995 1.00390911096
absolute error = 1.256e-05
relative error = 0.001052 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.575
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.317
Order of pole (three term test) = 4.492e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4729 1.664
h = 0.0001 0.005
y[1] (numeric) = 0.646783323495 1.00717638614
y[1] (closed_form) = 0.646774821857 1.00716663767
absolute error = 1.293e-05
relative error = 0.001081 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.581
Order of pole (given) = 1 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) = 1.206e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.473 1.669
h = 0.0001 0.003
y[1] (numeric) = 0.647152787883 1.01003976405
y[1] (closed_form) = 0.647144540984 1.01003014817
absolute error = 1.267e-05
relative error = 0.001056 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.584
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.551
Order of pole (three term test) = 2.907e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4731 1.672
h = 0.001 0.001
y[1] (numeric) = 0.647397640913 1.01175481341
y[1] (closed_form) = 0.64738937928 1.01174530877
absolute error = 1.259e-05
relative error = 0.001048 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.586
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.218
Order of pole (three term test) = 3.856e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4741 1.673
h = 0.001 0.003
y[1] (numeric) = 0.648033833465 1.01226600455
y[1] (closed_form) = 0.648025583241 1.01225655668
absolute error = 1.254e-05
relative error = 0.001044 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.588
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.786
Order of pole (three term test) = 2.573e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4751 1.676
h = 0.0001 0.004
y[1] (numeric) = 0.648794858402 1.01392460618
y[1] (closed_form) = 0.648786589684 1.01391504183
absolute error = 1.264e-05
relative error = 0.00105 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.59
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.278
Order of pole (three term test) = 1.569e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4752 1.68
h = 0.003 0.006
y[1] (numeric) = 0.649101950775 1.01621248207
y[1] (closed_form) = 0.649093758606 1.01620285315
absolute error = 1.264e-05
relative error = 0.001048 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.593
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.347
Order of pole (three term test) = 1.243e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4782 1.686
h = 0.0001 0.005
y[1] (numeric) = 0.6511968986 1.01946525913
y[1] (closed_form) = 0.651188287659 1.01945550074
absolute error = 1.301e-05
relative error = 0.001076 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.599
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.938
Order of pole (three term test) = 4.717e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4783 1.691
h = 0.0001 0.003
y[1] (numeric) = 0.6515659718 1.02232444782
memory used=687.6MB, alloc=52.3MB, time=7.96
y[1] (closed_form) = 0.651557613364 1.02231481756
absolute error = 1.275e-05
relative error = 0.001052 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.603
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.562
Order of pole (three term test) = 2.010e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4784 1.694
h = 0.001 0.001
y[1] (numeric) = 0.651810548628 1.02403699066
y[1] (closed_form) = 0.651802176789 1.02402747023
absolute error = 1.268e-05
relative error = 0.001044 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.605
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.227
Order of pole (three term test) = 1.193e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4794 1.695
h = 0.0001 0.004
y[1] (numeric) = 0.652445839475 1.02454741012
y[1] (closed_form) = 0.652437479459 1.02453794556
absolute error = 1.263e-05
relative error = 0.00104 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.606
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.373
Order of pole (three term test) = 3.675e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4795 1.699
h = 0.003 0.006
y[1] (numeric) = 0.652752656009 1.02683255967
y[1] (closed_form) = 0.65274438999 1.02682288472
absolute error = 1.273e-05
relative error = 0.001046 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.609
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.373
Order of pole (three term test) = 2.131e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4825 1.705
h = 0.0001 0.005
y[1] (numeric) = 0.654845161986 1.03008117549
y[1] (closed_form) = 0.654836481061 1.03007137632
absolute error = 1.309e-05
relative error = 0.001073 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.615
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.949
Order of pole (three term test) = 4.819e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4826 1.71
h = 0.0001 0.003
y[1] (numeric) = 0.655213917879 1.03293680323
y[1] (closed_form) = 0.65520548757 1.03292712843
absolute error = 1.283e-05
relative error = 0.001049 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.618
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.571
Order of pole (three term test) = 3.745e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4827 1.713
h = 0.001 0.001
y[1] (numeric) = 0.655458269105 1.03464721531
y[1] (closed_form) = 0.655449826518 1.03463764914
absolute error = 1.276e-05
relative error = 0.001042 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.62
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.234
Order of pole (three term test) = 1.405e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4837 1.714
h = 0.001 0.003
y[1] (numeric) = 0.656092796588 1.03515697582
y[1] (closed_form) = 0.656084366173 1.03514746475
absolute error = 1.271e-05
relative error = 0.001037 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.622
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.862
Order of pole (three term test) = 3.733e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4847 1.717
h = 0.0001 0.004
y[1] (numeric) = 0.65685192689 1.03681105359
y[1] (closed_form) = 0.656843476291 1.0368014294
absolute error = 1.281e-05
relative error = 0.001044 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.624
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.321
Order of pole (three term test) = 4.875e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4848 1.721
h = 0.003 0.006
y[1] (numeric) = 0.6571583909 1.03909277163
y[1] (closed_form) = 0.657150013669 1.03908308313
absolute error = 1.281e-05
relative error = 0.001042 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.627
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.404
Order of pole (three term test) = 4.528e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4878 1.727
h = 0.0001 0.005
y[1] (numeric) = 0.659247986401 1.0423366828
y[1] (closed_form) = 0.659239198836 1.04232687593
absolute error = 1.317e-05
relative error = 0.001068 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.633
Order of pole (given) = 1 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) = 1.820e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4879 1.732
h = 0.0001 0.003
y[1] (numeric) = 0.6596162834 1.04518823695
y[1] (closed_form) = 0.659607744181 1.04517855025
absolute error = 1.291e-05
relative error = 0.001045 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.637
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.583
Order of pole (three term test) = 4.087e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.488 1.735
h = 0.001 0.001
y[1] (numeric) = 0.659860319146 1.0468962125
y[1] (closed_form) = 0.659851768889 1.04688663303
absolute error = 1.284e-05
relative error = 0.001038 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.639
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.243
Order of pole (three term test) = 3.976e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.489 1.736
h = 0.001 0.003
y[1] (numeric) = 0.660493953983 1.04740523799
y[1] (closed_form) = 0.660485416271 1.04739571272
absolute error = 1.279e-05
relative error = 0.001033 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.64
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.903
Order of pole (three term test) = 4.783e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.49 1.739
h = 0.0001 0.004
y[1] (numeric) = 0.661252036591 1.04905695428
y[1] (closed_form) = 0.661243477864 1.04904731768
absolute error = 1.289e-05
relative error = 0.001039 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.643
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.344
Order of pole (three term test) = 2.628e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4901 1.743
h = 0.003 0.006
y[1] (numeric) = 0.661558101842 1.05133543632
y[1] (closed_form) = 0.661549614829 1.05132573557
absolute error = 1.289e-05
relative error = 0.001038 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.645
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.435
Order of pole (three term test) = 3.124e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4931 1.749
h = 0.0001 0.005
y[1] (numeric) = 0.663644781146 1.05457473724
y[1] (closed_form) = 0.66363588836 1.0545649238
absolute error = 1.324e-05
relative error = 0.001063 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.652
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.977
Order of pole (three term test) = 4.505e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4932 1.754
h = 0.0001 0.003
y[1] (numeric) = 0.664012585655 1.0574222791
y[1] (closed_form) = 0.66400393893 1.05741258172
absolute error = 1.299e-05
relative error = 0.001041 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.655
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.594
Order of pole (three term test) = 1.013e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4933 1.757
h = 0.001 0.001
y[1] (numeric) = 0.664256286471 1.05912785517
y[1] (closed_form) = 0.664247629905 1.05911826365
absolute error = 1.292e-05
relative error = 0.001033 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.657
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.252
Order of pole (three term test) = 2.089e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4943 1.758
h = 0.001 0.003
y[1] (numeric) = 0.664889033922 1.05963616462
y[1] (closed_form) = 0.664880390251 1.05962662642
absolute error = 1.287e-05
relative error = 0.001029 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.659
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.945
Order of pole (three term test) = 7.009e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4953 1.761
h = 0.0001 0.004
y[1] (numeric) = 0.665646060347 1.06128556257
y[1] (closed_form) = 0.665637394874 1.06127591479
absolute error = 1.297e-05
relative error = 0.001035 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.661
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.367
Order of pole (three term test) = 1.811e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4954 1.765
h = 0.003 0.006
y[1] (numeric) = 0.665951700835 1.06356085755
y[1] (closed_form) = 0.665943105458 1.06355114582
absolute error = 1.297e-05
relative error = 0.001034 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.664
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.466
Order of pole (three term test) = 2.153e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4984 1.771
h = 0.0001 0.005
y[1] (numeric) = 0.668035459716 1.06679564077
y[1] (closed_form) = 0.668026463116 1.06678582182
absolute error = 1.332e-05
relative error = 0.001058 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.67
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.991
Order of pole (three term test) = 5.218e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4985 1.776
h = 0.0001 0.003
y[1] (numeric) = 0.668402739731 1.06963923081
y[1] (closed_form) = 0.668393986894 1.06962952396
absolute error = 1.307e-05
relative error = 0.001036 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.674
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.605
Order of pole (three term test) = 2.196e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4986 1.779
h = 0.001 0.001
y[1] (numeric) = 0.668646087109 1.07134244398
y[1] (closed_form) = 0.668637325582 1.07133284161
absolute error = 1.300e-05
relative error = 0.001029 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.676
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.261
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.4996 1.78
h = 0.001 0.003
y[1] (numeric) = 0.669277952598 1.07185005588
y[1] (closed_form) = 0.669269204299 1.07184050597
absolute error = 1.295e-05
relative error = 0.001025 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.677
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.986
Order of pole (three term test) = 1.284e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5006 1.783
h = 0.0001 0.004
y[1] (numeric) = 0.670033915152 1.07349717787
y[1] (closed_form) = 0.670025144303 1.0734875201
absolute error = 1.305e-05
relative error = 0.001031 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.68
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.391
Order of pole (three term test) = 3.526e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5007 1.787
h = 0.003 0.006
y[1] (numeric) = 0.67033910612 1.07576933407
y[1] (closed_form) = 0.670330403787 1.07575961258
absolute error = 1.305e-05
relative error = 0.001029 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.683
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.497
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=731.6MB, alloc=52.3MB, time=8.46
x[1] = 0.5037 1.793
h = 0.0001 0.005
y[1] (numeric) = 0.672419941772 1.07899969026
y[1] (closed_form) = 0.672410842748 1.07898986684
absolute error = 1.339e-05
relative error = 0.001053 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.689
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.005
Order of pole (three term test) = 2.859e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5038 1.798
h = 0.0001 0.003
y[1] (numeric) = 0.672786666817 1.0818393882
y[1] (closed_form) = 0.672777809251 1.08182967302
absolute error = 1.315e-05
relative error = 0.001032 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.692
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.616
Order of pole (three term test) = 1.910e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5039 1.801
h = 0.001 0.001
y[1] (numeric) = 0.673029643157 1.08354027454
y[1] (closed_form) = 0.673020778009 1.08353066247
absolute error = 1.308e-05
relative error = 0.001025 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.694
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.269
Order of pole (three term test) = 2.534e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5049 1.802
h = 0.0001 0.004
y[1] (numeric) = 0.673660632259 1.08404720693
y[1] (closed_form) = 0.673651780651 1.08403764648
absolute error = 1.303e-05
relative error = 0.001021 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.696
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.627
Order of pole (three term test) = 2.206e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.505 1.806
h = 0.003 0.006
y[1] (numeric) = 0.673965442868 1.08631683089
y[1] (closed_form) = 0.673956669581 1.08630706984
absolute error = 1.312e-05
relative error = 0.001027 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.698
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.524
Order of pole (three term test) = 7.776e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.508 1.812
h = 0.0001 0.005
y[1] (numeric) = 0.676043812383 1.08954341279
y[1] (closed_form) = 0.67603464623 1.0895335543
absolute error = 1.346e-05
relative error = 0.00105 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.705
Order of pole (given) = 1 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) = 2.325e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5081 1.817
h = 0.0001 0.003
y[1] (numeric) = 0.676410081861 1.09237980064
y[1] (closed_form) = 0.676401155221 1.09237004713
absolute error = 1.322e-05
relative error = 0.001029 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.708
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.625
Order of pole (three term test) = 2.505e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5082 1.82
h = 0.001 0.001
y[1] (numeric) = 0.676652752538 1.09407870794
y[1] (closed_form) = 0.676643819252 1.0940690564
absolute error = 1.315e-05
relative error = 0.001022 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.71
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.277
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5092 1.821
h = 0.001 0.003
y[1] (numeric) = 0.677282999657 1.09458505919
y[1] (closed_form) = 0.677274080175 1.09457545855
absolute error = 1.310e-05
relative error = 0.001018 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.712
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.063
Order of pole (three term test) = 2.952e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5102 1.824
h = 0.0001 0.004
y[1] (numeric) = 0.678036990676 1.09622804341
y[1] (closed_form) = 0.678028047341 1.09621833804
absolute error = 1.320e-05
relative error = 0.001024 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.714
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.435
Order of pole (three term test) = 4.693e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5103 1.828
h = 0.003 0.006
y[1] (numeric) = 0.678341319443 1.09849447942
y[1] (closed_form) = 0.678332441773 1.09848471076
absolute error = 1.320e-05
relative error = 0.001022 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.717
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.555
Order of pole (three term test) = 2.671e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5133 1.834
h = 0.0001 0.005
y[1] (numeric) = 0.680416763001 1.10171679813
y[1] (closed_form) = 0.680407496963 1.101706937
absolute error = 1.353e-05
relative error = 0.001045 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.723
Order of pole (given) = 1 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) = 4.515e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5134 1.839
h = 0.0001 0.003
y[1] (numeric) = 0.680782423993 1.10454940247
y[1] (closed_form) = 0.680773395151 1.10453964268
absolute error = 1.330e-05
relative error = 0.001025 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.727
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.637
Order of pole (three term test) = 5.438e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5135 1.842
h = 0.001 0.001
y[1] (numeric) = 0.681024692763 1.10624604856
y[1] (closed_form) = 0.681015658305 1.10623638939
absolute error = 1.323e-05
relative error = 0.001018 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.729
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.286
Order of pole (three term test) = 9.122e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5145 1.843
h = 0.001 0.003
y[1] (numeric) = 0.681654074026 1.10675175274
y[1] (closed_form) = 0.681645053652 1.10674214365
absolute error = 1.318e-05
relative error = 0.001014 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.73
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.105
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5155 1.846
h = 0.0001 0.004
y[1] (numeric) = 0.682406982801 1.1083925779
y[1] (closed_form) = 0.682397937936 1.10838286574
absolute error = 1.327e-05
relative error = 0.00102 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.733
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.458
Order of pole (three term test) = 3.490e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5156 1.85
h = 0.003 0.006
y[1] (numeric) = 0.682710797153 1.11065600947
y[1] (closed_form) = 0.682701816473 1.11064623428
absolute error = 1.327e-05
relative error = 0.001018 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.736
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.587
Order of pole (three term test) = 1.607e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5186 1.856
h = 0.0001 0.005
y[1] (numeric) = 0.684783315627 1.11387415047
y[1] (closed_form) = 0.684773951051 1.11386428764
absolute error = 1.360e-05
relative error = 0.00104 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.742
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.044
Order of pole (three term test) = 3.916e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5187 1.861
h = 0.0001 0.003
y[1] (numeric) = 0.685148341737 1.11670302871
y[1] (closed_form) = 0.685139212038 1.11669326366
absolute error = 1.337e-05
relative error = 0.00102 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.746
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.648
Order of pole (three term test) = 5.273e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5188 1.864
h = 0.001 0.001
y[1] (numeric) = 0.685390193411 1.11839744823
y[1] (closed_form) = 0.685381059088 1.11838778248
absolute error = 1.330e-05
relative error = 0.001014 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.748
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.295
Order of pole (three term test) = 8.844e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5198 1.865
h = 0.001 0.003
y[1] (numeric) = 0.686018714764 1.11890252213
y[1] (closed_form) = 0.686009594786 1.11889290564
absolute error = 1.325e-05
relative error = 0.00101 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.749
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.147
Order of pole (three term test) = 3.081e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5208 1.868
h = 0.0001 0.004
y[1] (numeric) = 0.686770536372 1.12054122767
y[1] (closed_form) = 0.686761391303 1.12053150974
absolute error = 1.334e-05
relative error = 0.001015 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.752
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.482
Order of pole (three term test) = 8.455e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5209 1.872
h = 0.003 0.006
y[1] (numeric) = 0.68707381595 1.12280170058
y[1] (closed_form) = 0.687064733619 1.1227919199
absolute error = 1.335e-05
relative error = 0.001014 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.755
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.618
Order of pole (three term test) = 2.246e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5239 1.878
h = 0.0001 0.005
y[1] (numeric) = 0.689143411362 1.1260157476
y[1] (closed_form) = 0.689133949582 1.12600588394
absolute error = 1.367e-05
relative error = 0.001035 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.761
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.058
Order of pole (three term test) = 3.274e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.524 1.883
h = 0.0001 0.003
y[1] (numeric) = 0.689507777514 1.12884095632
y[1] (closed_form) = 0.689498548291 1.128831187
absolute error = 1.344e-05
relative error = 0.001016 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.764
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.659
Order of pole (three term test) = 3.230e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5241 1.886
h = 0.001 0.001
y[1] (numeric) = 0.689749197685 1.13053318342
y[1] (closed_form) = 0.689739964791 1.13052351209
absolute error = 1.337e-05
relative error = 0.00101 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.767
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.303
Order of pole (three term test) = 1.915e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5251 1.887
h = 0.001 0.003
y[1] (numeric) = 0.690376865178 1.13103764339
y[1] (closed_form) = 0.690367646875 1.13102802052
absolute error = 1.333e-05
relative error = 0.001006 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.768
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.189
Order of pole (three term test) = 4.240e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5261 1.89
h = 0.0001 0.004
y[1] (numeric) = 0.69112759533 1.13267426802
y[1] (closed_form) = 0.69111835137 1.13266454531
absolute error = 1.342e-05
relative error = 0.001011 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.771
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.506
Order of pole (three term test) = 2.894e-29 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=775.7MB, alloc=52.3MB, time=8.97
x[1] = 0.5262 1.894
h = 0.003 0.006
y[1] (numeric) = 0.691430320809 1.13493182739
y[1] (closed_form) = 0.691421138174 1.13492204222
absolute error = 1.342e-05
relative error = 0.00101 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.774
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.65
Order of pole (three term test) = 1.375e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5292 1.9
h = 0.0001 0.005
y[1] (numeric) = 0.693496996264 1.13814186241
y[1] (closed_form) = 0.693487438597 1.13813199877
absolute error = 1.373e-05
relative error = 0.001031 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.78
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.072
Order of pole (three term test) = 3.831e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5293 1.905
h = 0.0001 0.003
y[1] (numeric) = 0.693860678651 1.14096345737
y[1] (closed_form) = 0.693851351223 1.14095368473
absolute error = 1.351e-05
relative error = 0.001012 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.783
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.671
Order of pole (three term test) = 4.505e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5294 1.908
h = 0.001 0.001
y[1] (numeric) = 0.694101653663 1.1426535257
y[1] (closed_form) = 0.69409232348 1.14264384975
absolute error = 1.344e-05
relative error = 0.001005 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.785
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.312
Order of pole (three term test) = 2.415e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5304 1.909
h = 0.0001 0.004
y[1] (numeric) = 0.694728473439 1.14315738766
y[1] (closed_form) = 0.694719158078 1.14314775939
absolute error = 1.340e-05
relative error = 0.001002 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.787
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.885
Order of pole (three term test) = 7.208e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5305 1.913
h = 0.003 0.006
y[1] (numeric) = 0.695030736578 1.14541259647
y[1] (closed_form) = 0.69502148601 1.1454027774
absolute error = 1.349e-05
relative error = 0.001007 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.79
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.677
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5335 1.919
h = 0.0001 0.005
y[1] (numeric) = 0.697094948396 1.14861920773
y[1] (closed_form) = 0.697085326524 1.148609314
absolute error = 1.380e-05
relative error = 0.001027 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.796
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.084
Order of pole (three term test) = 4.813e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5336 1.924
h = 0.0001 0.003
y[1] (numeric) = 0.697458066248 1.1514377276
y[1] (closed_form) = 0.69744867266 1.15142792205
absolute error = 1.358e-05
relative error = 0.001009 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.8
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.68
Order of pole (three term test) = 1.289e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5337 1.927
h = 0.001 0.001
y[1] (numeric) = 0.697698672875 1.15312595878
y[1] (closed_form) = 0.697689277308 1.15311624883
absolute error = 1.351e-05
relative error = 0.001003 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.802
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.32
Order of pole (three term test) = 1.559e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5347 1.928
h = 0.001 0.003
y[1] (numeric) = 0.698324774824 1.15362930847
y[1] (closed_form) = 0.698315394274 1.15361964552
absolute error = 1.347e-05
relative error = 0.0009987 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.803
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.268
Order of pole (three term test) = 1.506e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5357 1.931
h = 0.0001 0.004
y[1] (numeric) = 0.699073488399 1.15526214843
y[1] (closed_form) = 0.699064081205 1.15525238856
absolute error = 1.356e-05
relative error = 0.001004 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.806
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.55
Order of pole (three term test) = 2.920e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5358 1.935
h = 0.003 0.006
y[1] (numeric) = 0.69937516824 1.15751439711
y[1] (closed_form) = 0.699365819823 1.15750457535
absolute error = 1.356e-05
relative error = 0.001003 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.809
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.709
Order of pole (three term test) = 2.452e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5388 1.941
h = 0.0001 0.005
y[1] (numeric) = 0.701436467634 1.16071714446
y[1] (closed_form) = 0.701426752275 1.16070725226
absolute error = 1.387e-05
relative error = 0.001022 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.815
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.099
Order of pole (three term test) = 1.462e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5389 1.946
h = 0.0001 0.003
y[1] (numeric) = 0.701798859993 1.16353215192
y[1] (closed_form) = 0.701789370606 1.16352234473
absolute error = 1.365e-05
relative error = 0.001004 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.819
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.692
Order of pole (three term test) = 7.311e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.539 1.949
h = 0.001 0.001
y[1] (numeric) = 0.702038997558 1.16521828545
y[1] (closed_form) = 0.702029507042 1.16520857259
absolute error = 1.358e-05
relative error = 0.0009983 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.821
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.329
Order of pole (three term test) = 2.087e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.54 1.95
h = 0.001 0.003
y[1] (numeric) = 0.702664263265 1.1657210658
y[1] (closed_form) = 0.702654787968 1.16571139919
absolute error = 1.354e-05
relative error = 0.0009945 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.822
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.31
Order of pole (three term test) = 5.812e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.541 1.953
h = 0.0001 0.004
y[1] (numeric) = 0.703411875919 1.16735193153
y[1] (closed_form) = 0.703402373503 1.16734216953
absolute error = 1.362e-05
relative error = 0.0009996 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.825
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.574
Order of pole (three term test) = 3.984e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5411 1.957
h = 0.003 0.006
y[1] (numeric) = 0.703712951225 1.16960139192
y[1] (closed_form) = 0.703703506264 1.16959156835
absolute error = 1.363e-05
relative error = 0.0009984 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.828
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.741
Order of pole (three term test) = 1.673e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5441 1.963
h = 0.0001 0.005
y[1] (numeric) = 0.705771344101 1.17280035254
y[1] (closed_form) = 0.705761536526 1.17279046263
absolute error = 1.393e-05
relative error = 0.001018 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.834
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.113
Order of pole (three term test) = 3.214e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5442 1.968
h = 0.0001 0.003
y[1] (numeric) = 0.706132990537 1.17561190102
y[1] (closed_form) = 0.706123406627 1.17560209305
absolute error = 1.371e-05
relative error = 0.001 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.838
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.703
Order of pole (three term test) = 4.552e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5443 1.971
h = 0.001 0.001
y[1] (numeric) = 0.706372647375 1.17729596912
y[1] (closed_form) = 0.706363063155 1.17728625422
absolute error = 1.365e-05
relative error = 0.000994 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.84
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.338
Order of pole (three term test) = 5.688e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5453 1.972
h = 0.001 0.003
y[1] (numeric) = 0.706997083208 1.17779819493
y[1] (closed_form) = 0.706987514397 1.17778852554
absolute error = 1.360e-05
relative error = 0.0009903 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.841
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.353
Order of pole (three term test) = 3.081e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5463 1.975
h = 0.0001 0.004
y[1] (numeric) = 0.707743592836 1.17942712238
y[1] (closed_form) = 0.707733996458 1.1794173591
absolute error = 1.369e-05
relative error = 0.0009953 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.844
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.598
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5464 1.979
h = 0.003 0.006
y[1] (numeric) = 0.70804404792 1.18167383705
y[1] (closed_form) = 0.708034507705 1.18166401255
absolute error = 1.369e-05
relative error = 0.0009941 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.847
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.773
Order of pole (three term test) = 4.558e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5494 1.985
h = 0.0001 0.005
y[1] (numeric) = 0.71009954105 1.1848690865
y[1] (closed_form) = 0.710089642514 1.1848591996
absolute error = 1.399e-05
relative error = 0.001013 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.853
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.127
Order of pole (three term test) = 3.433e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5495 1.99
h = 0.0001 0.003
y[1] (numeric) = 0.710460422222 1.18767722863
y[1] (closed_form) = 0.710450745053 1.18766742069
absolute error = 1.378e-05
relative error = 0.0009956 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.857
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.715
Order of pole (three term test) = 1.461e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5496 1.993
h = 0.001 0.001
y[1] (numeric) = 0.710699587313 1.18935926301
y[1] (closed_form) = 0.710689910618 1.1893495469
absolute error = 1.371e-05
relative error = 0.0009897 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.859
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.347
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5506 1.994
h = 0.001 0.003
y[1] (numeric) = 0.7113231997 1.18986094872
y[1] (closed_form) = 0.71131353859 1.18985127738
absolute error = 1.367e-05
relative error = 0.0009861 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.86
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.396
Order of pole (three term test) = 1.987e-29 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=819.7MB, alloc=52.3MB, time=9.48
x[1] = 0.5516 1.997
h = 0.0001 0.004
y[1] (numeric) = 0.712068604693 1.19148797312
y[1] (closed_form) = 0.712058915597 1.19147820939
absolute error = 1.376e-05
relative error = 0.000991 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.863
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.623
Order of pole (three term test) = 2.090e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5517 2.001
h = 0.003 0.006
y[1] (numeric) = 0.712368424718 1.19373198401
y[1] (closed_form) = 0.712358790525 1.19372215939
absolute error = 1.376e-05
relative error = 0.0009899 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.866
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.805
Order of pole (three term test) = 3.617e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5547 2.007
h = 0.0001 0.005
y[1] (numeric) = 0.71442102569 1.19692359623
y[1] (closed_form) = 0.714411037433 1.19691371304
absolute error = 1.405e-05
relative error = 0.001008 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.872
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.141
Order of pole (three term test) = 3.692e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5548 2.012
h = 0.0001 0.003
y[1] (numeric) = 0.714781123306 1.19972838383
y[1] (closed_form) = 0.714771354125 1.1997185767
absolute error = 1.384e-05
relative error = 0.0009912 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.876
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.726
Order of pole (three term test) = 4.442e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5549 2.015
h = 0.001 0.001
y[1] (numeric) = 0.715019786246 1.20140841571
y[1] (closed_form) = 0.715010018294 1.2013986992
absolute error = 1.378e-05
relative error = 0.0009855 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.878
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.356
Order of pole (three term test) = 1.898e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5559 2.016
h = 0.0001 0.004
y[1] (numeric) = 0.715642581666 1.20190957538
y[1] (closed_form) = 0.715632829462 1.2018999029
absolute error = 1.374e-05
relative error = 0.0009819 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.879
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.147
Order of pole (three term test) = 4.578e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.556 2.02
h = 0.003 0.006
y[1] (numeric) = 0.715941876033 1.20415140475
y[1] (closed_form) = 0.715932176974 1.20414155116
absolute error = 1.383e-05
relative error = 0.000987 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.882
Order of pole (given) = 1 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) = 3.472e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.559 2.026
h = 0.0001 0.005
y[1] (numeric) = 0.717992036353 1.20733990988
y[1] (closed_form) = 0.71798198682 1.20733000094
absolute error = 1.411e-05
relative error = 0.001005 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.889
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.153
Order of pole (three term test) = 1.501e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5591 2.031
h = 0.0001 0.003
y[1] (numeric) = 0.718351484764 1.21014184127
y[1] (closed_form) = 0.718341652377 1.21013200595
absolute error = 1.391e-05
relative error = 0.0009882 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.892
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.736
Order of pole (three term test) = 2.580e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5592 2.034
h = 0.001 0.001
y[1] (numeric) = 0.718589730948 1.21182016795
y[1] (closed_form) = 0.71857990043 1.21181042221
absolute error = 1.384e-05
relative error = 0.0009826 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.894
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.364
Order of pole (three term test) = 9.669e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5602 2.035
h = 0.001 0.003
y[1] (numeric) = 0.719211834418 1.21232087618
y[1] (closed_form) = 0.719202019786 1.21231117386
absolute error = 1.380e-05
relative error = 0.0009791 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.896
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.475
Order of pole (three term test) = 2.019e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5612 2.038
h = 0.0001 0.004
y[1] (numeric) = 0.719955202971 1.21394443774
y[1] (closed_form) = 0.719945359628 1.21393464573
absolute error = 1.388e-05
relative error = 0.0009838 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.899
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.668
Order of pole (three term test) = 1.844e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5613 2.042
h = 0.003 0.006
y[1] (numeric) = 0.720253835659 1.21618351894
y[1] (closed_form) = 0.720244044945 1.21617366669
absolute error = 1.389e-05
relative error = 0.0009827 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.902
Order of pole (given) = 1 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) = 3.460e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5643 2.048
h = 0.0001 0.005
y[1] (numeric) = 0.722301119111 1.21936852039
y[1] (closed_form) = 0.72229098211 1.21935861639
absolute error = 1.417e-05
relative error = 0.001 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.908
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.168
Order of pole (three term test) = 1.746e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5644 2.053
h = 0.0001 0.003
y[1] (numeric) = 0.722659751979 1.22216719134
y[1] (closed_form) = 0.722649829853 1.22215735823
absolute error = 1.397e-05
relative error = 0.0009839 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.911
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.747
Order of pole (three term test) = 7.000e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5645 2.056
h = 0.001 0.001
y[1] (numeric) = 0.722897477855 1.2238435722
y[1] (closed_form) = 0.722887558296 1.22383382747
absolute error = 1.391e-05
relative error = 0.0009783 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.914
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.373
Order of pole (three term test) = 9.276e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5655 2.057
h = 0.001 0.003
y[1] (numeric) = 0.723518776369 1.22434377967
y[1] (closed_form) = 0.723508872838 1.22433407766
absolute error = 1.386e-05
relative error = 0.0009749 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.915
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.518
Order of pole (three term test) = 5.103e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5665 2.06
h = 0.0001 0.004
y[1] (numeric) = 0.724261037821 1.22596553527
y[1] (closed_form) = 0.724251105233 1.22595574498
absolute error = 1.395e-05
relative error = 0.0009795 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.918
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.692
Order of pole (three term test) = 1.452e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5666 2.064
h = 0.003 0.006
y[1] (numeric) = 0.724558996951 1.22820202889
y[1] (closed_form) = 0.724549115814 1.22819217874
absolute error = 1.395e-05
relative error = 0.0009784 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.921
Order of pole (given) = 1 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) = 3.318e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5696 2.07
h = 0.0001 0.005
y[1] (numeric) = 0.726603413217 1.23138359622
y[1] (closed_form) = 0.72659318994 1.23137369777
absolute error = 1.423e-05
relative error = 0.0009953 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.927
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.182
Order of pole (three term test) = 7.887e-31 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5697 2.075
h = 0.0001 0.003
y[1] (numeric) = 0.726961215031 1.23417905626
y[1] (closed_form) = 0.72695120437 1.23416922606
absolute error = 1.403e-05
relative error = 0.0009795 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.931
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.759
Order of pole (three term test) = 1.022e-28 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5698 2.078
h = 0.001 0.001
y[1] (numeric) = 0.727198411833 1.23585352113
y[1] (closed_form) = 0.727188404411 1.23584377811
absolute error = 1.397e-05
relative error = 0.000974 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.933
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.382
Order of pole (three term test) = 1.383e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5708 2.079
h = 0.001 0.003
y[1] (numeric) = 0.727818911983 1.2363532409
y[1] (closed_form) = 0.727808920718 1.23634353992
absolute error = 1.393e-05
relative error = 0.0009707 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.934
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.561
Order of pole (three term test) = 2.549e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5718 2.082
h = 0.0001 0.004
y[1] (numeric) = 0.728560066429 1.2379732232
y[1] (closed_form) = 0.728550045786 1.23796343533
absolute error = 1.401e-05
relative error = 0.0009752 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.937
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.716
Order of pole (three term test) = 1.893e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5719 2.086
h = 0.003 0.006
y[1] (numeric) = 0.728857340161 1.24020716869
y[1] (closed_form) = 0.728847369817 1.24019732134
absolute error = 1.401e-05
relative error = 0.0009742 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.94
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.929
Order of pole (three term test) = 2.009e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5749 2.092
h = 0.0001 0.005
y[1] (numeric) = 0.730898899563 1.24338536995
y[1] (closed_form) = 0.730888591187 1.24337547764
absolute error = 1.429e-05
relative error = 0.0009906 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.946
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.197
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.575 2.097
h = 0.0001 0.003
y[1] (numeric) = 0.73125585571 1.24617766783
y[1] (closed_form) = 0.731245757702 1.24616784119
absolute error = 1.409e-05
relative error = 0.0009752 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.95
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.771
Order of pole (three term test) = 3.743e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5751 2.1
h = 0.001 0.001
y[1] (numeric) = 0.731492515199 1.24785024604
y[1] (closed_form) = 0.731482421075 1.24784050542
absolute error = 1.403e-05
relative error = 0.0009698 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.952
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.391
Order of pole (three term test) = 1.709e-29 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=863.7MB, alloc=52.3MB, time=9.98
x[1] = 0.5761 2.101
h = 0.001 0.003
y[1] (numeric) = 0.732112223603 1.24834949082
y[1] (closed_form) = 0.732102145755 1.24833979157
absolute error = 1.399e-05
relative error = 0.0009665 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.954
Order of pole (given) = 1 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) = 2.646e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5771 2.104
h = 0.0001 0.004
y[1] (numeric) = 0.732852271524 1.24996773184
y[1] (closed_form) = 0.732842164 1.24995794706
absolute error = 1.407e-05
relative error = 0.0009709 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.957
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.741
Order of pole (three term test) = 2.291e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5772 2.108
h = 0.003 0.006
y[1] (numeric) = 0.733148848717 1.25219916801
y[1] (closed_form) = 0.733138790367 1.25218932413
absolute error = 1.407e-05
relative error = 0.0009699 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.959
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.962
Order of pole (three term test) = 2.718e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5802 2.114
h = 0.0001 0.005
y[1] (numeric) = 0.735187562179 1.25537406979
y[1] (closed_form) = 0.735177169862 1.25536418419
absolute error = 1.434e-05
relative error = 0.0009859 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.966
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.211
Order of pole (three term test) = 2.165e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5803 2.119
h = 0.0001 0.003
y[1] (numeric) = 0.735543658903 1.25816325347
y[1] (closed_form) = 0.735533474723 1.25815343105
absolute error = 1.415e-05
relative error = 0.0009709 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.969
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.782
Order of pole (three term test) = 5.059e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5804 2.122
h = 0.001 0.001
y[1] (numeric) = 0.735779773349 1.25983397389
y[1] (closed_form) = 0.73576959367 1.25982423634
absolute error = 1.409e-05
relative error = 0.0009656 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.972
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.4
Order of pole (three term test) = 4.649e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5814 2.123
h = 0.0001 0.004
y[1] (numeric) = 0.736398696642 1.26033275608
y[1] (closed_form) = 0.736388533348 1.26032305922
absolute error = 1.405e-05
relative error = 0.0009623 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.973
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.412
Order of pole (three term test) = 3.995e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5815 2.127
h = 0.003 0.006
y[1] (numeric) = 0.73669470024 1.26256216738
y[1] (closed_form) = 0.736684580073 1.2625522988
absolute error = 1.414e-05
relative error = 0.000967 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.976
Order of pole (given) = 1 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) = 3.514e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5845 2.133
h = 0.0001 0.005
y[1] (numeric) = 0.738731011439 1.2657342476
y[1] (closed_form) = 0.738720560734 1.26572434003
absolute error = 1.440e-05
relative error = 0.0009826 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.982
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.223
Order of pole (three term test) = 3.362e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5846 2.138
h = 0.0001 0.003
y[1] (numeric) = 0.739086394352 1.26852077806
y[1] (closed_form) = 0.739076149903 1.26851093155
absolute error = 1.421e-05
relative error = 0.0009679 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.986
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.792
Order of pole (three term test) = 1.345e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5847 2.141
h = 0.001 0.001
y[1] (numeric) = 0.739322055493 1.27018991549
y[1] (closed_form) = 0.739311816069 1.27018015288
absolute error = 1.415e-05
relative error = 0.0009626 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.988
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.408
Order of pole (three term test) = 5.939e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5857 2.142
h = 0.001 0.003
y[1] (numeric) = 0.739940313629 1.27068829993
y[1] (closed_form) = 0.739930090684 1.27067857746
absolute error = 1.411e-05
relative error = 0.0009595 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.99
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.685
Order of pole (three term test) = 2.065e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5867 2.145
h = 0.0001 0.004
y[1] (numeric) = 0.740678324958 1.27230337075
y[1] (closed_form) = 0.740668071822 1.27229356523
absolute error = 1.419e-05
relative error = 0.0009637 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.993
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.786
Order of pole (three term test) = 5.942e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5868 2.149
h = 0.003 0.006
y[1] (numeric) = 0.740973607513 1.2745302302
y[1] (closed_form) = 0.740963401525 1.2745203663
absolute error = 1.419e-05
relative error = 0.0009628 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 2.995
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.022
Order of pole (three term test) = 4.765e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5898 2.155
h = 0.0001 0.005
y[1] (numeric) = 0.743007093813 1.27769913123
y[1] (closed_form) = 0.742996561276 1.27768923137
absolute error = 1.445e-05
relative error = 0.000978 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.002
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.238
Order of pole (three term test) = 3.977e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5899 2.16
h = 0.0001 0.003
y[1] (numeric) = 0.743361593333 1.28048263453
y[1] (closed_form) = 0.743351264846 1.28047279338
absolute error = 1.427e-05
relative error = 0.0009635 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.006
Order of pole (given) = 1 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) = 3.039e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.59 2.163
h = 0.001 0.001
y[1] (numeric) = 0.743596695988 1.28214996654
y[1] (closed_form) = 0.743586373098 1.28214020816
absolute error = 1.421e-05
relative error = 0.0009584 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.008
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.417
Order of pole (three term test) = 4.181e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.591 2.164
h = 0.001 0.003
y[1] (numeric) = 0.744214181256 1.28264791069
y[1] (closed_form) = 0.744203874934 1.28263819179
absolute error = 1.417e-05
relative error = 0.0009553 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.009
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.729
Order of pole (three term test) = 3.938e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.592 2.167
h = 0.0001 0.004
y[1] (numeric) = 0.744951089035 1.28426132839
y[1] (closed_form) = 0.744940752285 1.28425152775
absolute error = 1.424e-05
relative error = 0.0009594 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.012
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.811
Order of pole (three term test) = 1.524e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5921 2.171
h = 0.003 0.006
y[1] (numeric) = 0.745245646361 1.28648578597
y[1] (closed_form) = 0.745235355709 1.28647592735
absolute error = 1.425e-05
relative error = 0.0009585 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.015
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.055
Order of pole (three term test) = 1.278e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5951 2.177
h = 0.0001 0.005
y[1] (numeric) = 0.747276320215 1.28965157038
y[1] (closed_form) = 0.74726570696 1.28964167872
absolute error = 1.451e-05
relative error = 0.0009734 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.021
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.252
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5952 2.182
h = 0.0001 0.003
y[1] (numeric) = 0.747629924872 1.29243209231
y[1] (closed_form) = 0.747619513477 1.29242225707
absolute error = 1.432e-05
relative error = 0.0009592 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.025
Order of pole (given) = 1 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) = 4.252e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5953 2.185
h = 0.001 0.001
y[1] (numeric) = 0.74786446265 1.29409764642
y[1] (closed_form) = 0.747854057398 1.29408789284
absolute error = 1.426e-05
relative error = 0.0009542 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.027
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.426
Order of pole (three term test) = 2.288e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5963 2.186
h = 0.001 0.003
y[1] (numeric) = 0.748481181715 1.29459516176
y[1] (closed_form) = 0.748470793114 1.29458544705
absolute error = 1.422e-05
relative error = 0.0009511 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.029
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.772
Order of pole (three term test) = 5.332e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5973 2.189
h = 0.0001 0.004
y[1] (numeric) = 0.749216987743 1.29620695599
y[1] (closed_form) = 0.749206568494 1.29619716081
absolute error = 1.430e-05
relative error = 0.0009552 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.032
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.836
Order of pole (three term test) = 2.991e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.5974 2.193
h = 0.003 0.006
y[1] (numeric) = 0.749510811153 1.29842904812
y[1] (closed_form) = 0.749500436977 1.29841919536
absolute error = 1.431e-05
relative error = 0.0009543 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.035
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.087
Order of pole (three term test) = 4.332e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6004 2.199
h = 0.0001 0.005
y[1] (numeric) = 0.751538685477 1.30159177715
y[1] (closed_form) = 0.751527992599 1.30158189417
absolute error = 1.456e-05
relative error = 0.0009688 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.041
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.267
Order of pole (three term test) = 2.279e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6005 2.204
h = 0.0001 0.003
y[1] (numeric) = 0.751891384532 1.30436936271
y[1] (closed_form) = 0.751880891342 1.30435953394
absolute error = 1.438e-05
relative error = 0.000955 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.045
Order of pole (given) = 1 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) = 2.739e-29 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=907.9MB, alloc=52.3MB, time=10.49
x[1] = 0.6006 2.207
h = 0.001 0.001
y[1] (numeric) = 0.752125351472 1.30603316599
y[1] (closed_form) = 0.752114864951 1.30602341778
absolute error = 1.432e-05
relative error = 0.00095 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.047
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.436
Order of pole (three term test) = 1.026e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6016 2.208
h = 0.001 0.003
y[1] (numeric) = 0.752741310999 1.30653026375
y[1] (closed_form) = 0.752730841203 1.30652055377
absolute error = 1.428e-05
relative error = 0.000947 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.048
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.816
Order of pole (three term test) = 3.636e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6026 2.211
h = 0.0001 0.004
y[1] (numeric) = 0.753476017369 1.30814046355
y[1] (closed_form) = 0.753465516723 1.30813067437
absolute error = 1.436e-05
relative error = 0.000951 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.051
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.861
Order of pole (three term test) = 9.753e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6027 2.215
h = 0.003 0.006
y[1] (numeric) = 0.75376909875 1.31036022604
y[1] (closed_form) = 0.753758642176 1.31035037969
absolute error = 1.436e-05
relative error = 0.0009501 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.054
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.12
Order of pole (three term test) = 2.586e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6057 2.221
h = 0.0001 0.005
y[1] (numeric) = 0.755794186888 1.31351995959
y[1] (closed_form) = 0.75578341547 1.31351008575
absolute error = 1.461e-05
relative error = 0.0009642 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.061
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.282
Order of pole (three term test) = 1.225e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6058 2.226
h = 0.0001 0.003
y[1] (numeric) = 0.756145970309 1.31629465307
y[1] (closed_form) = 0.756135396423 1.31628483127
absolute error = 1.443e-05
relative error = 0.0009507 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.064
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.839
Order of pole (three term test) = 4.950e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6059 2.229
h = 0.001 0.001
y[1] (numeric) = 0.756379360864 1.31795673212
y[1] (closed_form) = 0.756368794149 1.31794698982
absolute error = 1.437e-05
relative error = 0.0009458 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.066
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.445
Order of pole (three term test) = 2.179e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6069 2.23
h = 0.0001 0.004
y[1] (numeric) = 0.756994567514 1.3184534232
y[1] (closed_form) = 0.756984017589 1.31844371852
absolute error = 1.433e-05
relative error = 0.0009429 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.068
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.68
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.607 2.234
h = 0.003 0.006
y[1] (numeric) = 0.757287039985 1.32067130551
y[1] (closed_form) = 0.757276524582 1.32066143817
absolute error = 1.442e-05
relative error = 0.0009472 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.071
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.148
Order of pole (three term test) = 2.211e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.61 2.24
h = 0.0001 0.005
y[1] (numeric) = 0.759309775596 1.32382847468
y[1] (closed_form) = 0.759298948604 1.32381858217
absolute error = 1.467e-05
relative error = 0.000961 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.077
Order of pole (given) = 1 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) = 2.362e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6101 2.245
h = 0.0001 0.003
y[1] (numeric) = 0.759660797096 1.32660070257
y[1] (closed_form) = 0.75965016582 1.32659086028
absolute error = 1.449e-05
relative error = 0.0009477 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.081
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.849
Order of pole (three term test) = 2.676e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6102 2.248
h = 0.001 0.001
y[1] (numeric) = 0.759893707493 1.32826131149
y[1] (closed_form) = 0.759883083817 1.32825154778
absolute error = 1.443e-05
relative error = 0.0009429 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.083
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.453
Order of pole (three term test) = 3.757e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6112 2.249
h = 0.001 0.003
y[1] (numeric) = 0.760508276092 1.32875765219
y[1] (closed_form) = 0.760497669262 1.32874792559
absolute error = 1.439e-05
relative error = 0.00094 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.085
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.898
Order of pole (three term test) = 7.017e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6122 2.252
h = 0.0001 0.004
y[1] (numeric) = 0.761240960973 1.33036494743
y[1] (closed_form) = 0.761230322952 1.33035514391
absolute error = 1.447e-05
relative error = 0.0009438 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.088
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.907
Order of pole (three term test) = 5.360e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6123 2.256
h = 0.003 0.006
y[1] (numeric) = 0.761532668649 1.33258045925
y[1] (closed_form) = 0.761522072894 1.3325705993
absolute error = 1.447e-05
relative error = 0.000943 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.091
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.181
Order of pole (three term test) = 1.995e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6153 2.262
h = 0.0001 0.005
y[1] (numeric) = 0.763552643272 1.33573474118
y[1] (closed_form) = 0.763541739704 1.33572485861
absolute error = 1.472e-05
relative error = 0.0009565 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.097
Order of pole (given) = 1 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) = 5.285e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6154 2.267
h = 0.0001 0.003
y[1] (numeric) = 0.763902731735 1.3385041573
y[1] (closed_form) = 0.763892021761 1.33849432291
absolute error = 1.454e-05
relative error = 0.0009435 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.101
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.861
Order of pole (three term test) = 6.339e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6155 2.27
h = 0.001 0.001
y[1] (numeric) = 0.76413505616 1.34016309026
y[1] (closed_form) = 0.764124354249 1.34015333341
absolute error = 1.448e-05
relative error = 0.0009387 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.103
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.462
Order of pole (three term test) = 5.046e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6165 2.271
h = 0.001 0.003
y[1] (numeric) = 0.764748884126 1.34065904394
y[1] (closed_form) = 0.764738199112 1.3406493236
absolute error = 1.444e-05
relative error = 0.0009359 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.104
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.942
Order of pole (three term test) = 4.205e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6175 2.274
h = 0.0001 0.004
y[1] (numeric) = 0.765480476504 1.34226482472
y[1] (closed_form) = 0.765469760147 1.34225502866
absolute error = 1.452e-05
relative error = 0.0009396 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.107
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.932
Order of pole (three term test) = 4.447e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6176 2.278
h = 0.003 0.006
y[1] (numeric) = 0.76577142149 1.344478106
y[1] (closed_form) = 0.765760746462 1.34446825393
absolute error = 1.453e-05
relative error = 0.0009389 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.11
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.214
Order of pole (three term test) = 2.672e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6206 2.284
h = 0.0001 0.005
y[1] (numeric) = 0.767788649555 1.34762955697
y[1] (closed_form) = 0.767777670447 1.34761968474
absolute error = 1.476e-05
relative error = 0.000952 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.117
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.323
Order of pole (three term test) = 3.160e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6207 2.289
h = 0.0001 0.003
y[1] (numeric) = 0.768137796813 1.35039620351
y[1] (closed_form) = 0.768127009195 1.3503863775
absolute error = 1.459e-05
relative error = 0.0009393 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.12
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.873
Order of pole (three term test) = 2.400e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6208 2.292
h = 0.001 0.001
y[1] (numeric) = 0.76836953081 1.35205348587
y[1] (closed_form) = 0.768358751699 1.35204373636
absolute error = 1.453e-05
relative error = 0.0009346 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.123
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.471
Order of pole (three term test) = 2.620e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6218 2.293
h = 0.001 0.003
y[1] (numeric) = 0.768982624773 1.35254906266
y[1] (closed_form) = 0.768971862602 1.35253934907
absolute error = 1.450e-05
relative error = 0.0009318 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.124
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.986
Order of pole (three term test) = 6.713e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6228 2.296
h = 0.0001 0.004
y[1] (numeric) = 0.769713127743 1.35415335585
y[1] (closed_form) = 0.769702334092 1.35414356772
absolute error = 1.457e-05
relative error = 0.0009355 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.127
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.957
Order of pole (three term test) = 3.863e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6229 2.3
h = 0.003 0.006
y[1] (numeric) = 0.770003303928 1.35636444014
y[1] (closed_form) = 0.769992550693 1.35635459641
absolute error = 1.458e-05
relative error = 0.0009347 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.13
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.247
Order of pole (three term test) = 3.575e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6259 2.306
h = 0.0001 0.005
y[1] (numeric) = 0.772017800185 1.35951311522
y[1] (closed_form) = 0.772006746557 1.35950325371
absolute error = 1.481e-05
relative error = 0.0009475 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.136
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.338
Order of pole (three term test) = 3.896e-29 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=951.9MB, alloc=52.3MB, time=10.99
x[1] = 0.626 2.311
h = 0.0001 0.003
y[1] (numeric) = 0.772365998668 1.36227703366
y[1] (closed_form) = 0.772355134446 1.36226721646
absolute error = 1.464e-05
relative error = 0.000935 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.14
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.885
Order of pole (three term test) = 3.588e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6261 2.314
h = 0.001 0.001
y[1] (numeric) = 0.772597138133 1.36393269034
y[1] (closed_form) = 0.772586282842 1.36392294861
absolute error = 1.459e-05
relative error = 0.0009305 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.142
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.481
Order of pole (three term test) = 6.363e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6271 2.315
h = 0.001 0.003
y[1] (numeric) = 0.773209504703 1.3644279001
y[1] (closed_form) = 0.773198666389 1.36441819374
absolute error = 1.455e-05
relative error = 0.0009277 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.144
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.03
Order of pole (three term test) = 3.299e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6281 2.318
h = 0.0001 0.004
y[1] (numeric) = 0.773938921583 1.36603073203
y[1] (closed_form) = 0.773928051666 1.36602095227
absolute error = 1.462e-05
relative error = 0.0009313 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.147
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 3.982
Order of pole (three term test) = 4.507e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6282 2.322
h = 0.003 0.006
y[1] (numeric) = 0.774228323322 1.36823965232
y[1] (closed_form) = 0.774217492931 1.36822981738
absolute error = 1.463e-05
relative error = 0.0009306 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.15
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.281
Order of pole (three term test) = 1.433e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6312 2.328
h = 0.0001 0.005
y[1] (numeric) = 0.776240102816 1.37138560537
y[1] (closed_form) = 0.776228975675 1.37137575496
absolute error = 1.486e-05
relative error = 0.0009431 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.156
Order of pole (given) = 1 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) = 3.991e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6313 2.333
h = 0.0001 0.003
y[1] (numeric) = 0.776587345529 1.37414683651
y[1] (closed_form) = 0.776576405728 1.37413702853
absolute error = 1.469e-05
relative error = 0.0009309 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.16
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.897
Order of pole (three term test) = 3.064e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6314 2.336
h = 0.001 0.001
y[1] (numeric) = 0.776817886693 1.37580089198
y[1] (closed_form) = 0.776806956229 1.37579115848
absolute error = 1.464e-05
relative error = 0.0009264 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.162
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.49
Order of pole (three term test) = 4.089e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6324 2.337
h = 0.0001 0.004
y[1] (numeric) = 0.777429532456 1.37629574434
y[1] (closed_form) = 0.777418618999 1.37628604564
absolute error = 1.460e-05
relative error = 0.0009237 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.164
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.951
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6325 2.341
h = 0.003 0.006
y[1] (numeric) = 0.777718300285 1.37850291777
y[1] (closed_form) = 0.777707413966 1.37849306508
absolute error = 1.468e-05
relative error = 0.0009277 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.167
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.309
Order of pole (three term test) = 2.204e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6355 2.347
h = 0.0001 0.005
y[1] (numeric) = 0.77972778511 1.38164653794
y[1] (closed_form) = 0.779716605115 1.38163667172
absolute error = 1.491e-05
relative error = 0.0009399 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.173
Order of pole (given) = 1 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) = 3.609e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6356 2.352
h = 0.0001 0.003
y[1] (numeric) = 0.780074231309 1.38440547656
y[1] (closed_form) = 0.780063236912 1.3843956512
absolute error = 1.474e-05
relative error = 0.0009279 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.177
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.907
Order of pole (three term test) = 4.029e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6357 2.355
h = 0.001 0.001
y[1] (numeric) = 0.780304273386 1.38605816588
y[1] (closed_form) = 0.780293288674 1.38604841415
absolute error = 1.469e-05
relative error = 0.0009235 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.179
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.498
Order of pole (three term test) = 3.904e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6367 2.356
h = 0.001 0.003
y[1] (numeric) = 0.780915308065 1.38655270962
y[1] (closed_form) = 0.780904340387 1.38654299223
absolute error = 1.465e-05
relative error = 0.0009208 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.181
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.112
Order of pole (three term test) = 2.629e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6377 2.359
h = 0.0001 0.004
y[1] (numeric) = 0.781642730218 1.38815287793
y[1] (closed_form) = 0.781631730735 1.38814308923
absolute error = 1.472e-05
relative error = 0.0009243 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.183
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.028
Order of pole (three term test) = 2.751e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6378 2.363
h = 0.003 0.006
y[1] (numeric) = 0.781930702265 1.39035784802
y[1] (closed_form) = 0.781919740697 1.39034800491
absolute error = 1.473e-05
relative error = 0.0009236 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.187
Order of pole (given) = 1 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) = 1.630e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6408 2.369
h = 0.0001 0.005
y[1] (numeric) = 0.783937498421 1.39349884351
y[1] (closed_form) = 0.783926246738 1.39348898903
absolute error = 1.496e-05
relative error = 0.0009355 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.193
Order of pole (given) = 1 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) = 3.041e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6409 2.374
h = 0.0001 0.003
y[1] (numeric) = 0.784282976809 1.3962551688
y[1] (closed_form) = 0.784271908696 1.39624535342
absolute error = 1.479e-05
relative error = 0.0009238 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.197
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.919
Order of pole (three term test) = 2.885e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.641 2.377
h = 0.001 0.001
y[1] (numeric) = 0.784512414135 1.39790630135
y[1] (closed_form) = 0.78450135608 1.39789655861
absolute error = 1.474e-05
relative error = 0.0009194 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.199
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.507
Order of pole (three term test) = 6.829e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.642 2.378
h = 0.001 0.003
y[1] (numeric) = 0.785122740089 1.398400505
y[1] (closed_form) = 0.785111699086 1.39839079606
absolute error = 1.470e-05
relative error = 0.0009168 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.2
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.156
Order of pole (three term test) = 3.353e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.643 2.381
h = 0.0001 0.004
y[1] (numeric) = 0.78584908647 1.39999928453
y[1] (closed_form) = 0.785838013579 1.39998950538
absolute error = 1.477e-05
relative error = 0.0009202 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.203
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.053
Order of pole (three term test) = 9.159e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6431 2.385
h = 0.003 0.006
y[1] (numeric) = 0.786136269956 1.40220218185
y[1] (closed_form) = 0.786125234147 1.40219234872
absolute error = 1.478e-05
relative error = 0.0009195 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.206
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.376
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6461 2.391
h = 0.0001 0.005
y[1] (numeric) = 0.788140393222 1.40534060328
y[1] (closed_form) = 0.788129070814 1.40533076085
absolute error = 1.500e-05
relative error = 0.0009311 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.213
Order of pole (given) = 1 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) = 2.862e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6462 2.396
h = 0.0001 0.003
y[1] (numeric) = 0.788484898323 1.40809435407
y[1] (closed_form) = 0.788473757475 1.40808454903
absolute error = 1.484e-05
relative error = 0.0009196 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.217
Order of pole (given) = 1 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) = 4.004e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6463 2.399
h = 0.001 0.001
y[1] (numeric) = 0.788713728015 1.40974395314
y[1] (closed_form) = 0.788702597582 1.40973421979
absolute error = 1.479e-05
relative error = 0.0009153 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.219
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.517
Order of pole (three term test) = 1.285e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6473 2.4
h = 0.001 0.003
y[1] (numeric) = 0.789323351755 1.41023782564
y[1] (closed_form) = 0.789312238388 1.41022812555
absolute error = 1.475e-05
relative error = 0.0009128 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.22
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.201
Order of pole (three term test) = 4.517e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6483 2.403
h = 0.0001 0.004
y[1] (numeric) = 0.790048626432 1.41183524074
y[1] (closed_form) = 0.790037481106 1.41182547152
absolute error = 1.482e-05
relative error = 0.0009161 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.223
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.078
Order of pole (three term test) = 1.218e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6484 2.407
h = 0.003 0.006
y[1] (numeric) = 0.790335017341 1.41403609615
y[1] (closed_form) = 0.790323908284 1.41402627337
absolute error = 1.483e-05
relative error = 0.0009154 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.226
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.409
Order of pole (three term test) = 1.613e-29 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=995.9MB, alloc=52.3MB, time=11.50
x[1] = 0.6514 2.413
h = 0.0001 0.005
y[1] (numeric) = 0.792336483706 1.41717199303
y[1] (closed_form) = 0.792325091521 1.41716216295
absolute error = 1.505e-05
relative error = 0.0009268 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.233
Order of pole (given) = 1 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) = 4.097e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6515 2.418
h = 0.0001 0.003
y[1] (numeric) = 0.792680010528 1.41992320748
y[1] (closed_form) = 0.792668797915 1.41991341315
absolute error = 1.489e-05
relative error = 0.0009155 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.237
Order of pole (given) = 1 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) = 4.653e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6516 2.421
h = 0.001 0.001
y[1] (numeric) = 0.792908229989 1.42157129599
y[1] (closed_form) = 0.79289702813 1.42156157239
absolute error = 1.483e-05
relative error = 0.0009113 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.239
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.526
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6526 2.422
h = 0.001 0.003
y[1] (numeric) = 0.793517157993 1.42206484602
y[1] (closed_form) = 0.793505973208 1.42205515516
absolute error = 1.480e-05
relative error = 0.0009088 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.24
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.246
Order of pole (three term test) = 5.926e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6536 2.425
h = 0.0001 0.004
y[1] (numeric) = 0.7942413652 1.42366092054
y[1] (closed_form) = 0.794230148397 1.42365116161
absolute error = 1.487e-05
relative error = 0.000912 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.243
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.104
Order of pole (three term test) = 1.618e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6537 2.429
h = 0.003 0.006
y[1] (numeric) = 0.794526959895 1.42585976439
y[1] (closed_form) = 0.794515778567 1.42584995232
absolute error = 1.488e-05
relative error = 0.0009114 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.246
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.443
Order of pole (three term test) = 5.798e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6567 2.435
h = 0.0001 0.005
y[1] (numeric) = 0.796525785538 1.42899318516
y[1] (closed_form) = 0.796514324508 1.42898336772
absolute error = 1.509e-05
relative error = 0.0009224 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.253
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.425
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6568 2.44
h = 0.0001 0.003
y[1] (numeric) = 0.796868329554 1.43174190079
y[1] (closed_form) = 0.796857046129 1.4317321175
absolute error = 1.493e-05
relative error = 0.0009114 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.257
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.955
Order of pole (three term test) = 1.817e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6569 2.443
h = 0.001 0.001
y[1] (numeric) = 0.797095936456 1.43338850124
y[1] (closed_form) = 0.79708466411 1.43337878774
absolute error = 1.488e-05
relative error = 0.0009073 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.259
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.535
Order of pole (three term test) = 1.602e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6579 2.444
h = 0.0001 0.004
y[1] (numeric) = 0.79770417517 1.43388173728
y[1] (closed_form) = 0.7976929199 1.43387205602
absolute error = 1.485e-05
relative error = 0.0009048 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.26
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.224
Order of pole (three term test) = 2.456e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.658 2.448
h = 0.003 0.006
y[1] (numeric) = 0.797989119351 1.43607895696
y[1] (closed_form) = 0.797977884885 1.43606912994
absolute error = 1.493e-05
relative error = 0.0009085 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.263
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.471
Order of pole (three term test) = 3.626e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.661 2.454
h = 0.0001 0.005
y[1] (numeric) = 0.799985713764 1.43921025319
y[1] (closed_form) = 0.79997420249 1.43920042243
absolute error = 1.514e-05
relative error = 0.0009193 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.27
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.438
Order of pole (three term test) = 3.908e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6611 2.459
h = 0.0001 0.003
y[1] (numeric) = 0.800327437701 1.44195683569
y[1] (closed_form) = 0.800316102371 1.44194703773
absolute error = 1.498e-05
relative error = 0.0009085 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.274
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.965
Order of pole (three term test) = 2.436e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6612 2.462
h = 0.001 0.001
y[1] (numeric) = 0.800554533034 1.44360216566
y[1] (closed_form) = 0.800543209064 1.44359243671
absolute error = 1.493e-05
relative error = 0.0009044 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.276
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.543
Order of pole (three term test) = 1.223e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6622 2.463
h = 0.001 0.003
y[1] (numeric) = 0.80116218717 1.44409512995
y[1] (closed_form) = 0.801150880278 1.44408543279
absolute error = 1.490e-05
relative error = 0.000902 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.277
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.329
Order of pole (three term test) = 6.084e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6632 2.466
h = 0.0001 0.004
y[1] (numeric) = 0.801884435171 1.44568875924
y[1] (closed_form) = 0.801873096171 1.44567899592
absolute error = 1.496e-05
relative error = 0.0009051 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.28
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.151
Order of pole (three term test) = 3.183e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6633 2.47
h = 0.003 0.006
y[1] (numeric) = 0.802168562978 1.4478839294
y[1] (closed_form) = 0.802157258018 1.44787411373
absolute error = 1.497e-05
relative error = 0.0009045 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.283
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.505
Order of pole (three term test) = 2.585e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6663 2.476
h = 0.0001 0.005
y[1] (numeric) = 0.804162546672 1.45101283709
y[1] (closed_form) = 0.804150968249 1.45100301948
absolute error = 1.518e-05
relative error = 0.0009151 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.29
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.453
Order of pole (three term test) = 1.803e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6664 2.481
h = 0.0001 0.003
y[1] (numeric) = 0.804503280123 1.45375698883
y[1] (closed_form) = 0.804491875714 1.45374720251
absolute error = 1.503e-05
relative error = 0.0009045 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.294
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.977
Order of pole (three term test) = 1.020e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6665 2.484
h = 0.001 0.001
y[1] (numeric) = 0.804729758991 1.45540087157
y[1] (closed_form) = 0.804718366239 1.45539115334
absolute error = 1.497e-05
relative error = 0.0009004 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.296
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.553
Order of pole (three term test) = 2.711e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6675 2.485
h = 0.001 0.003
y[1] (numeric) = 0.805336735633 1.45589353713
y[1] (closed_form) = 0.805325359953 1.45588385021
absolute error = 1.494e-05
relative error = 0.000898 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.297
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.373
Order of pole (three term test) = 4.187e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6685 2.488
h = 0.0001 0.004
y[1] (numeric) = 0.806057928829 1.45748589153
y[1] (closed_form) = 0.806046521013 1.45747613945
absolute error = 1.501e-05
relative error = 0.0009011 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.3
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.176
Order of pole (three term test) = 1.445e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6686 2.492
h = 0.003 0.006
y[1] (numeric) = 0.80634125162 1.45967913402
y[1] (closed_form) = 0.806329877102 1.45966933
absolute error = 1.502e-05
relative error = 0.0009005 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.303
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.538
Order of pole (three term test) = 1.711e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6716 2.498
h = 0.0001 0.005
y[1] (numeric) = 0.808332641231 1.46280569867
y[1] (closed_form) = 0.808320996552 1.46279589447
absolute error = 1.522e-05
relative error = 0.0009108 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.31
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.468
Order of pole (three term test) = 1.131e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6717 2.503
h = 0.0001 0.003
y[1] (numeric) = 0.808672380903 1.46554745536
y[1] (closed_form) = 0.808660908328 1.46553768097
absolute error = 1.507e-05
relative error = 0.0009004 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.314
Order of pole (given) = 1 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) = 1.908e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6718 2.506
h = 0.001 0.001
y[1] (numeric) = 0.808898241695 1.46718991228
y[1] (closed_form) = 0.80888678106 1.46718020509
absolute error = 1.502e-05
relative error = 0.0008965 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.316
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.562
Order of pole (three term test) = 3.804e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6728 2.507
h = 0.001 0.003
y[1] (numeric) = 0.809504547181 1.46768228699
y[1] (closed_form) = 0.809493103607 1.46767261062
absolute error = 1.499e-05
relative error = 0.0008941 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.318
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.418
Order of pole (three term test) = 2.476e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6738 2.51
h = 0.0001 0.004
y[1] (numeric) = 0.810224690352 1.46927338855
y[1] (closed_form) = 0.810213214625 1.46926364801
absolute error = 1.505e-05
relative error = 0.0008971 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.32
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.201
Order of pole (three term test) = 9.552e-30 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1040.0MB, alloc=52.3MB, time=12.00
x[1] = 0.6739 2.514
h = 0.003 0.006
y[1] (numeric) = 0.810507205808 1.47146473173
y[1] (closed_form) = 0.810495762654 1.47145493967
absolute error = 1.506e-05
relative error = 0.0008965 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.324
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.572
Order of pole (three term test) = 5.652e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6769 2.52
h = 0.0001 0.005
y[1] (numeric) = 0.812496018099 1.47458899788
y[1] (closed_form) = 0.812484308041 1.47457920731
absolute error = 1.526e-05
relative error = 0.0009066 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.33
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.483
Order of pole (three term test) = 1.662e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.677 2.525
h = 0.0001 0.003
y[1] (numeric) = 0.812834761088 1.4773283946
y[1] (closed_form) = 0.812823221247 1.47731863242
absolute error = 1.512e-05
relative error = 0.0008964 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.334
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.001
Order of pole (three term test) = 2.520e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6771 2.528
h = 0.001 0.001
y[1] (numeric) = 0.813060002422 1.47896944674
y[1] (closed_form) = 0.813048474791 1.47895975088
absolute error = 1.506e-05
relative error = 0.0008925 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.336
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.572
Order of pole (three term test) = 9.423e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6781 2.529
h = 0.001 0.003
y[1] (numeric) = 0.813665643048 1.47946153826
y[1] (closed_form) = 0.813654132463 1.47945187275
absolute error = 1.503e-05
relative error = 0.0008902 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.338
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.463
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6791 2.532
h = 0.0001 0.004
y[1] (numeric) = 0.814384741095 1.48105140859
y[1] (closed_form) = 0.814373198348 1.48104167988
absolute error = 1.510e-05
relative error = 0.0008931 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.341
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.227
Order of pole (three term test) = 1.261e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6792 2.536
h = 0.003 0.006
y[1] (numeric) = 0.814666447203 1.48324088034
y[1] (closed_form) = 0.814654936321 1.48323110053
absolute error = 1.510e-05
relative error = 0.0008926 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.344
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.606
Order of pole (three term test) = 5.005e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6822 2.542
h = 0.0001 0.005
y[1] (numeric) = 0.816652699043 1.48636289157
y[1] (closed_form) = 0.816640924473 1.48635311486
absolute error = 1.530e-05
relative error = 0.0009024 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.35
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.498
Order of pole (three term test) = 2.774e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6823 2.547
h = 0.0001 0.003
y[1] (numeric) = 0.816990442824 1.4890999628
y[1] (closed_form) = 0.816978836603 1.4890902131
absolute error = 1.516e-05
relative error = 0.0008924 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.354
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.013
Order of pole (three term test) = 2.397e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6824 2.55
h = 0.001 0.001
y[1] (numeric) = 0.817215063536 1.49073963083
y[1] (closed_form) = 0.817203469782 1.49072994658
absolute error = 1.511e-05
relative error = 0.0008886 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.356
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.581
Order of pole (three term test) = 2.563e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6834 2.551
h = 0.0001 0.004
y[1] (numeric) = 0.817820045555 1.49123144663
y[1] (closed_form) = 0.817808468827 1.49122179226
absolute error = 1.507e-05
relative error = 0.0008863 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.358
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.5
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6835 2.555
h = 0.003 0.006
y[1] (numeric) = 0.818101091349 1.49341940701
y[1] (closed_form) = 0.818089529999 1.49340961467
absolute error = 1.515e-05
relative error = 0.0008898 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.361
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.635
Order of pole (three term test) = 2.113e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6865 2.561
h = 0.0001 0.005
y[1] (numeric) = 0.820085178992 1.49653948121
y[1] (closed_form) = 0.820073356668 1.49652969336
absolute error = 1.535e-05
relative error = 0.0008994 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.367
Order of pole (given) = 1 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) = 2.484e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6866 2.566
h = 0.0001 0.003
y[1] (numeric) = 0.820422088093 1.49927456596
y[1] (closed_form) = 0.820410432543 1.49926480395
absolute error = 1.520e-05
relative error = 0.0008896 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.371
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.023
Order of pole (three term test) = 2.083e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6867 2.569
h = 0.001 0.001
y[1] (numeric) = 0.820646189981 1.50091305147
y[1] (closed_form) = 0.82063454712 1.50090335416
absolute error = 1.515e-05
relative error = 0.0008858 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.374
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.589
Order of pole (three term test) = 1.759e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6877 2.57
h = 0.001 0.003
y[1] (numeric) = 0.821250613232 1.50140462803
y[1] (closed_form) = 0.821238987383 1.50139496021
absolute error = 1.512e-05
relative error = 0.0008836 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.375
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.547
Order of pole (three term test) = 4.710e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6887 2.573
h = 0.0001 0.004
y[1] (numeric) = 0.821967794039 1.50299225107
y[1] (closed_form) = 0.821956136025 1.50298252182
absolute error = 1.518e-05
relative error = 0.0008864 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.378
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.274
Order of pole (three term test) = 7.058e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6888 2.577
h = 0.003 0.006
y[1] (numeric) = 0.822248011299 1.50517830339
y[1] (closed_form) = 0.822236383871 1.5051685238
absolute error = 1.519e-05
relative error = 0.0008859 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.381
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.668
Order of pole (three term test) = 1.760e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6918 2.583
h = 0.0001 0.005
y[1] (numeric) = 0.824229569632 1.50829620145
y[1] (closed_form) = 0.824217684367 1.50828642786
absolute error = 1.539e-05
relative error = 0.0008953 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.388
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.525
Order of pole (three term test) = 4.625e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6919 2.588
h = 0.0001 0.003
y[1] (numeric) = 0.824565475375 1.51102902328
y[1] (closed_form) = 0.824553755054 1.51101927422
absolute error = 1.525e-05
relative error = 0.0008856 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.391
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.036
Order of pole (three term test) = 4.701e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.692 2.591
h = 0.001 0.001
y[1] (numeric) = 0.824788954786 1.51266616218
y[1] (closed_form) = 0.82477724739 1.51265647699
absolute error = 1.519e-05
relative error = 0.0008819 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.394
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.599
Order of pole (three term test) = 1.464e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.693 2.592
h = 0.001 0.003
y[1] (numeric) = 0.825392730862 1.5131574765
y[1] (closed_form) = 0.82538104045 1.51314782034
absolute error = 1.516e-05
relative error = 0.0008797 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.395
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.592
Order of pole (three term test) = 5.078e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.694 2.595
h = 0.0001 0.004
y[1] (numeric) = 0.826108880904 1.51474392784
y[1] (closed_form) = 0.826097158345 1.51473421117
absolute error = 1.523e-05
relative error = 0.0008825 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.398
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.3
Order of pole (three term test) = 1.958e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6941 2.599
h = 0.003 0.006
y[1] (numeric) = 0.826388284309 1.51692818581
y[1] (closed_form) = 0.826376591673 1.51691841922
absolute error = 1.523e-05
relative error = 0.000882 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.401
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.702
Order of pole (three term test) = 3.275e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6971 2.605
h = 0.0001 0.005
y[1] (numeric) = 0.828367330448 1.52004394869
y[1] (closed_form) = 0.828355383069 1.52003418955
absolute error = 1.543e-05
relative error = 0.0008912 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.408
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.541
Order of pole (three term test) = 8.599e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6972 2.61
h = 0.0001 0.003
y[1] (numeric) = 0.8287022313 1.5227745404
y[1] (closed_form) = 0.828690447057 1.52276480453
absolute error = 1.529e-05
relative error = 0.0008817 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.412
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.048
Order of pole (three term test) = 5.175e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6973 2.613
h = 0.001 0.001
y[1] (numeric) = 0.828925087648 1.52441035236
y[1] (closed_form) = 0.828913316551 1.52440067952
absolute error = 1.524e-05
relative error = 0.000878 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.414
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.609
Order of pole (three term test) = 1.361e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6983 2.614
h = 0.001 0.003
y[1] (numeric) = 0.829528222673 1.52490141136
y[1] (closed_form) = 0.829516468531 1.52489176711
absolute error = 1.520e-05
relative error = 0.0008759 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.415
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.637
Order of pole (three term test) = 1.414e-29 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1083.9MB, alloc=52.3MB, time=12.51
x[1] = 0.6993 2.617
h = 0.0001 0.004
y[1] (numeric) = 0.830243347238 1.52648671099
y[1] (closed_form) = 0.830231560973 1.52647700714
absolute error = 1.527e-05
relative error = 0.0008786 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.418
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.325
Order of pole (three term test) = 5.145e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.6994 2.621
h = 0.003 0.006
y[1] (numeric) = 0.830521935836 1.52866920068
y[1] (closed_form) = 0.830510178848 1.52865944732
absolute error = 1.528e-05
relative error = 0.0008781 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.422
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.736
Order of pole (three term test) = 2.162e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7024 2.627
h = 0.0001 0.005
y[1] (numeric) = 0.832498486956 1.53178286843
y[1] (closed_form) = 0.832486478275 1.53177312392
absolute error = 1.546e-05
relative error = 0.0008871 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.428
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.556
Order of pole (three term test) = 2.525e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7025 2.632
h = 0.0001 0.003
y[1] (numeric) = 0.832832381699 1.53451126227
y[1] (closed_form) = 0.832820534368 1.5345015398
absolute error = 1.533e-05
relative error = 0.0008778 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.432
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.06
Order of pole (three term test) = 4.276e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7026 2.635
h = 0.001 0.001
y[1] (numeric) = 0.833054614579 1.5361457666
y[1] (closed_form) = 0.833042780606 1.53613610635
absolute error = 1.528e-05
relative error = 0.0008742 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.434
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.618
Order of pole (three term test) = 2.527e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7036 2.636
h = 0.001 0.003
y[1] (numeric) = 0.83365711463 1.53663657705
y[1] (closed_form) = 0.833645297578 1.53662694495
absolute error = 1.525e-05
relative error = 0.0008721 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.436
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.683
Order of pole (three term test) = 1.761e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7046 2.639
h = 0.0001 0.004
y[1] (numeric) = 0.834371219089 1.53822074455
y[1] (closed_form) = 0.834359369946 1.53821105374
absolute error = 1.531e-05
relative error = 0.0008747 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.439
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.351
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7047 2.643
h = 0.003 0.006
y[1] (numeric) = 0.834648992172 1.54040149156
y[1] (closed_form) = 0.834637171676 1.54039175165
absolute error = 1.532e-05
relative error = 0.0008742 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.442
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.77
Order of pole (three term test) = 2.837e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7077 2.649
h = 0.0001 0.005
y[1] (numeric) = 0.836623065493 1.54351310339
y[1] (closed_form) = 0.836610996313 1.54350337369
absolute error = 1.550e-05
relative error = 0.000883 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.448
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.571
Order of pole (three term test) = 1.047e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7078 2.654
h = 0.0001 0.003
y[1] (numeric) = 0.836955953214 1.54623933104
y[1] (closed_form) = 0.836944043617 1.54622962219
absolute error = 1.537e-05
relative error = 0.0008739 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.452
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.072
Order of pole (three term test) = 6.270e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7079 2.657
h = 0.001 0.001
y[1] (numeric) = 0.837177562395 1.54787254672
y[1] (closed_form) = 0.837165666358 1.54786289928
absolute error = 1.532e-05
relative error = 0.0008704 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.455
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.628
Order of pole (three term test) = 2.343e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7089 2.658
h = 0.0001 0.004
y[1] (numeric) = 0.8377794335 1.54836311521
y[1] (closed_form) = 0.837767554347 1.54835349549
absolute error = 1.529e-05
relative error = 0.0008683 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.456
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 9.778
Order of pole (three term test) = 3.864e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.709 2.662
h = 0.003 0.006
y[1] (numeric) = 0.838056541962 1.55054245447
y[1] (closed_form) = 0.838044673539 1.55053270416
absolute error = 1.536e-05
relative error = 0.0008715 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.459
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.799
Order of pole (three term test) = 3.659e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.712 2.668
h = 0.0001 0.005
y[1] (numeric) = 0.840028520161 1.55365229816
y[1] (closed_form) = 0.840016405597 1.55364255921
absolute error = 1.554e-05
relative error = 0.0008801 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.466
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.584
Order of pole (three term test) = 3.364e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7121 2.673
h = 0.0001 0.003
y[1] (numeric) = 0.840360565859 1.55637667417
y[1] (closed_form) = 0.840348609387 1.55636695505
absolute error = 1.541e-05
relative error = 0.0008711 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.47
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.083
Order of pole (three term test) = 6.513e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7122 2.676
h = 0.001 0.001
y[1] (numeric) = 0.840581653174 1.55800878814
y[1] (closed_form) = 0.840569710436 1.55799912975
absolute error = 1.536e-05
relative error = 0.0008676 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.472
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.636
Order of pole (three term test) = 2.951e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7132 2.677
h = 0.001 0.003
y[1] (numeric) = 0.841182990472 1.5584991461
y[1] (closed_form) = 0.841171064588 1.55848951508
absolute error = 1.533e-05
relative error = 0.0008656 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.473
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.767
Order of pole (three term test) = 4.340e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7142 2.68
h = 0.0001 0.004
y[1] (numeric) = 0.841895224249 1.56008124579
y[1] (closed_form) = 0.841883266342 1.56007155766
absolute error = 1.539e-05
relative error = 0.0008681 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.476
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.399
Order of pole (three term test) = 4.406e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7143 2.684
h = 0.003 0.006
y[1] (numeric) = 0.842171498823 1.56225880698
y[1] (closed_form) = 0.842159568422 1.56224907052
absolute error = 1.540e-05
relative error = 0.0008677 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.48
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.833
Order of pole (three term test) = 5.018e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7173 2.69
h = 0.0001 0.005
y[1] (numeric) = 0.844141030906 1.5653666657
y[1] (closed_form) = 0.844128857298 1.56535694185
absolute error = 1.558e-05
relative error = 0.0008761 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.486
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.599
Order of pole (three term test) = 5.462e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7174 2.695
h = 0.0001 0.003
y[1] (numeric) = 0.844472068275 1.56808893301
y[1] (closed_form) = 0.844460051032 1.56807922788
absolute error = 1.545e-05
relative error = 0.0008673 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.49
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.095
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7175 2.698
h = 0.001 0.001
y[1] (numeric) = 0.844692531686 1.56971979277
y[1] (closed_form) = 0.844680528357 1.56971014759
absolute error = 1.540e-05
relative error = 0.0008638 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.492
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.645
Order of pole (three term test) = 2.317e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7185 2.699
h = 0.001 0.003
y[1] (numeric) = 0.845293251049 1.57020992066
y[1] (closed_form) = 0.845281264533 1.57020030243
absolute error = 1.537e-05
relative error = 0.0008618 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.494
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.812
Order of pole (three term test) = 1.893e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7195 2.702
h = 0.0001 0.004
y[1] (numeric) = 0.846004480256 1.57179094219
y[1] (closed_form) = 0.845992461769 1.57178126769
absolute error = 1.543e-05
relative error = 0.0008643 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.497
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.424
Order of pole (three term test) = 5.181e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7196 2.706
h = 0.003 0.006
y[1] (numeric) = 0.846279938264 1.57396683152
y[1] (closed_form) = 0.846267946692 1.5739571091
absolute error = 1.544e-05
relative error = 0.0008639 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.5
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.868
Order of pole (three term test) = 2.437e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7226 2.712
h = 0.0001 0.005
y[1] (numeric) = 0.848247041533 1.57707274213
y[1] (closed_form) = 0.848234809647 1.57706303353
absolute error = 1.562e-05
relative error = 0.0008721 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.506
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.614
Order of pole (three term test) = 3.858e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7227 2.717
h = 0.0001 0.003
y[1] (numeric) = 0.848577070456 1.57979293089
y[1] (closed_form) = 0.848564993227 1.57978323992
absolute error = 1.548e-05
relative error = 0.0008635 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.51
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.107
Order of pole (three term test) = 1.910e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7228 2.72
h = 0.001 0.001
y[1] (numeric) = 0.848796910193 1.58142255449
y[1] (closed_form) = 0.84878484705 1.5814129227
absolute error = 1.544e-05
relative error = 0.0008601 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.513
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.655
Order of pole (three term test) = 1.069e-28 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1127.9MB, alloc=52.3MB, time=13.01
x[1] = 0.7238 2.721
h = 0.001 0.003
y[1] (numeric) = 0.849397017508 1.58191245843
y[1] (closed_form) = 0.849384971133 1.58190285318
absolute error = 1.541e-05
relative error = 0.0008581 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.514
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.858
Order of pole (three term test) = 5.530e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7248 2.724
h = 0.0001 0.004
y[1] (numeric) = 0.850107247777 1.58349241991
y[1] (closed_form) = 0.850095169488 1.58348275923
absolute error = 1.547e-05
relative error = 0.0008606 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.517
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.45
Order of pole (three term test) = 1.477e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7249 2.728
h = 0.003 0.006
y[1] (numeric) = 0.850381889363 1.58566666132
y[1] (closed_form) = 0.850369837412 1.58565695312
absolute error = 1.548e-05
relative error = 0.0008601 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.52
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.902
Order of pole (three term test) = 1.592e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7279 2.734
h = 0.0001 0.005
y[1] (numeric) = 0.852346581127 1.58877065988
y[1] (closed_form) = 0.852334291716 1.58876096668
absolute error = 1.565e-05
relative error = 0.0008681 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.527
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.629
Order of pole (three term test) = 2.501e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.728 2.739
h = 0.0001 0.003
y[1] (numeric) = 0.852675601738 1.59148879971
y[1] (closed_form) = 0.852663465298 1.59147912308
absolute error = 1.552e-05
relative error = 0.0008597 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.531
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.119
Order of pole (three term test) = 2.494e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7281 2.742
h = 0.001 0.001
y[1] (numeric) = 0.852894818178 1.59311720489
y[1] (closed_form) = 0.852882695987 1.59310758667
absolute error = 1.547e-05
relative error = 0.0008563 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.533
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.665
Order of pole (three term test) = 3.807e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7291 2.743
h = 0.001 0.003
y[1] (numeric) = 0.853494319281 1.59360689084
y[1] (closed_form) = 0.85348221381 1.59359729877
absolute error = 1.545e-05
relative error = 0.0008544 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.535
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.903
Order of pole (three term test) = 3.228e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7301 2.746
h = 0.0001 0.004
y[1] (numeric) = 0.854203556295 1.59518581005
y[1] (closed_form) = 0.854191418973 1.59517616335
absolute error = 1.550e-05
relative error = 0.0008568 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.537
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.476
Order of pole (three term test) = 1.373e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7302 2.75
h = 0.003 0.006
y[1] (numeric) = 0.854477381798 1.59735842705
y[1] (closed_form) = 0.854465270251 1.59734873323
absolute error = 1.551e-05
relative error = 0.0008564 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.541
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.936
Order of pole (three term test) = 5.192e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7332 2.756
h = 0.0001 0.005
y[1] (numeric) = 0.856439679364 1.60046054888
y[1] (closed_form) = 0.85642733317 1.60045087119
absolute error = 1.569e-05
relative error = 0.0008642 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.547
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.644
Order of pole (three term test) = 5.597e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7333 2.761
h = 0.0001 0.003
y[1] (numeric) = 0.856767692041 1.60317666888
y[1] (closed_form) = 0.856755497151 1.60316700674
absolute error = 1.556e-05
relative error = 0.0008559 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.551
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.131
Order of pole (three term test) = 1.626e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7334 2.764
h = 0.001 0.001
y[1] (numeric) = 0.856986285698 1.60480387306
y[1] (closed_form) = 0.856974105212 1.60479426859
absolute error = 1.551e-05
relative error = 0.0008526 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.554
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.674
Order of pole (three term test) = 4.345e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7344 2.765
h = 0.0001 0.004
y[1] (numeric) = 0.857585186373 1.60529334684
y[1] (closed_form) = 0.857573022557 1.60528376812
absolute error = 1.548e-05
relative error = 0.0008507 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.555
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 10.06
Order of pole (three term test) = 2.641e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7345 2.769
h = 0.003 0.006
y[1] (numeric) = 0.857858347352 1.60746465129
y[1] (closed_form) = 0.85784619029 1.60745494891
absolute error = 1.555e-05
relative error = 0.0008537 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.558
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 5.965
Order of pole (three term test) = 2.912e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7375 2.775
h = 0.0001 0.005
y[1] (numeric) = 0.859818619721 1.61056515716
y[1] (closed_form) = 0.859806230389 1.61055547187
absolute error = 1.573e-05
relative error = 0.0008614 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.565
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.657
Order of pole (three term test) = 3.425e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7376 2.78
h = 0.0001 0.003
y[1] (numeric) = 0.860145788878 1.61327954948
y[1] (closed_form) = 0.860133549443 1.61326987887
absolute error = 1.560e-05
relative error = 0.0008532 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.569
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.142
Order of pole (three term test) = 8.939e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7377 2.783
h = 0.001 0.001
y[1] (numeric) = 0.860363861007 1.6149057262
y[1] (closed_form) = 0.86035163611 1.61489611262
absolute error = 1.555e-05
relative error = 0.0008499 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.571
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.682
Order of pole (three term test) = 1.082e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7387 2.784
h = 0.001 0.003
y[1] (numeric) = 0.860962251881 1.61539501483
y[1] (closed_form) = 0.860950043613 1.61538542667
absolute error = 1.552e-05
relative error = 0.000848 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.572
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 7.988
Order of pole (three term test) = 4.016e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7397 2.787
h = 0.0001 0.004
y[1] (numeric) = 0.861669667897 1.616972029
y[1] (closed_form) = 0.861657427901 1.61696238769
absolute error = 1.558e-05
relative error = 0.0008504 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.575
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.524
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7398 2.791
h = 0.003 0.006
y[1] (numeric) = 0.861941995104 1.61914167484
y[1] (closed_form) = 0.861929779865 1.61913198716
absolute error = 1.559e-05
relative error = 0.00085 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.579
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6
Order of pole (three term test) = 1.695e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7428 2.797
h = 0.0001 0.005
y[1] (numeric) = 0.863899905046 1.6222403679
y[1] (closed_form) = 0.863887460279 1.62223069836
absolute error = 1.576e-05
relative error = 0.0008575 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.585
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.673
Order of pole (three term test) = 8.914e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7429 2.802
h = 0.0001 0.003
y[1] (numeric) = 0.86422606724 1.62495279324
y[1] (closed_form) = 0.864213770741 1.6249431374
absolute error = 1.563e-05
relative error = 0.0008495 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.589
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.154
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.743 2.805
h = 0.001 0.001
y[1] (numeric) = 0.864443517695 1.62657780059
y[1] (closed_form) = 0.864431235871 1.62656820106
absolute error = 1.559e-05
relative error = 0.0008463 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.592
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.692
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.744 2.806
h = 0.001 0.003
y[1] (numeric) = 0.865041318698 1.62706688755
y[1] (closed_form) = 0.865029053449 1.62705731306
absolute error = 1.556e-05
relative error = 0.0008444 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.593
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.034
Order of pole (three term test) = 1.940e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.745 2.809
h = 0.0001 0.004
y[1] (numeric) = 0.865747757764 1.62864290839
y[1] (closed_form) = 0.865735460867 1.62863328153
absolute error = 1.562e-05
relative error = 0.0008467 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.596
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.55
Order of pole (three term test) = 2.640e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7451 2.813
h = 0.003 0.006
y[1] (numeric) = 0.866019270597 1.63081099489
y[1] (closed_form) = 0.866006997928 1.63080132204
absolute error = 1.563e-05
relative error = 0.0008463 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.599
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.034
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7481 2.819
h = 0.0001 0.005
y[1] (numeric) = 0.867974835377 1.63390790835
y[1] (closed_form) = 0.867962335884 1.63389825465
absolute error = 1.579e-05
relative error = 0.0008536 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.606
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.688
Order of pole (three term test) = 5.438e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7482 2.824
h = 0.0001 0.003
y[1] (numeric) = 0.868299991621 1.6366183944
y[1] (closed_form) = 0.868287638787 1.63660875347
absolute error = 1.567e-05
relative error = 0.0008458 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.61
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.167
Order of pole (three term test) = 3.082e-29 0
NO COMPLEX POLE (six term test) for Equation 1
memory used=1172.1MB, alloc=52.3MB, time=13.52
x[1] = 0.7483 2.827
h = 0.001 0.001
y[1] (numeric) = 0.868516821281 1.63824224895
y[1] (closed_form) = 0.868504483251 1.63823266361
absolute error = 1.562e-05
relative error = 0.0008426 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.612
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.702
Order of pole (three term test) = 0 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7493 2.828
h = 0.001 0.003
y[1] (numeric) = 0.869114038048 1.63873113965
y[1] (closed_form) = 0.869101716538 1.63872157898
absolute error = 1.560e-05
relative error = 0.0008408 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.613
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.08
Order of pole (three term test) = 5.041e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7503 2.831
h = 0.0001 0.004
y[1] (numeric) = 0.86981950601 1.6403061836
y[1] (closed_form) = 0.869807152934 1.64029657132
absolute error = 1.565e-05
relative error = 0.000843 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.616
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.576
Order of pole (three term test) = 2.425e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7504 2.835
h = 0.003 0.006
y[1] (numeric) = 0.870090205484 1.64247273273
y[1] (closed_form) = 0.870077876122 1.64246307486
absolute error = 1.566e-05
relative error = 0.0008426 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.62
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.068
Order of pole (three term test) = 2.863e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7534 2.841
h = 0.0001 0.005
y[1] (numeric) = 0.872043442337 1.6455678991
y[1] (closed_form) = 0.872030888815 1.64555826135
absolute error = 1.583e-05
relative error = 0.0008498 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.626
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.703
Order of pole (three term test) = 1.673e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7535 2.846
h = 0.0001 0.003
y[1] (numeric) = 0.872367593844 1.64827647307
y[1] (closed_form) = 0.872355185392 1.64826684718
absolute error = 1.570e-05
relative error = 0.0008421 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.63
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.179
Order of pole (three term test) = 4.753e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7536 2.849
h = 0.001 0.001
y[1] (numeric) = 0.872583803705 1.64989919112
y[1] (closed_form) = 0.872571410179 1.64988962011
absolute error = 1.566e-05
relative error = 0.000839 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.633
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.711
Order of pole (three term test) = 3.339e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7546 2.85
h = 0.001 0.003
y[1] (numeric) = 0.873180441818 1.65038789081
y[1] (closed_form) = 0.873168064753 1.65037834412
absolute error = 1.563e-05
relative error = 0.0008372 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.634
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.126
Order of pole (three term test) = 1.156e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7556 2.853
h = 0.0001 0.004
y[1] (numeric) = 0.873884944548 1.65196197399
y[1] (closed_form) = 0.873872536006 1.65195237643
absolute error = 1.569e-05
relative error = 0.0008394 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.637
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 4.602
Order of pole (three term test) = 3.146e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7557 2.857
h = 0.003 0.006
y[1] (numeric) = 0.874154831837 1.65412700736
y[1] (closed_form) = 0.874142446505 1.6541173646
absolute error = 1.570e-05
relative error = 0.000839 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.64
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 6.103
Order of pole (three term test) = 7.429e-30 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7587 2.863
h = 0.0001 0.005
y[1] (numeric) = 0.876105757957 1.65722045847
y[1] (closed_form) = 0.876093151092 1.65721083676
absolute error = 1.586e-05
relative error = 0.000846 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.647
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.719
Order of pole (three term test) = 2.170e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7588 2.868
h = 0.0001 0.003
y[1] (numeric) = 0.876428906131 1.65992714711
y[1] (closed_form) = 0.876416442767 1.65991753637
absolute error = 1.574e-05
relative error = 0.0008385 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.651
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 2.191
Order of pole (three term test) = 3.573e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7589 2.871
h = 0.001 0.001
y[1] (numeric) = 0.876644497298 1.66154874464
y[1] (closed_form) = 0.876632048976 1.6615391881
absolute error = 1.569e-05
relative error = 0.0008354 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.653
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 1.721
Order of pole (three term test) = 3.061e-29 0
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 0.7599 2.872
h = 0.001 0.003
y[1] (numeric) = 0.877240562285 1.66203725848
y[1] (closed_form) = 0.877228130363 1.6620277259
absolute error = 1.567e-05
relative error = 0.0008336 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.655
Order of pole (given) = 1 0
NO POLE (ratio test) for Equation 1
Radius of convergence (three term test) for eq 1 = 8.172
Order of pole (three term test) = 2.459e-29 0
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff ( y , x , 1 ) = ( 0.1 * x + 0.2 ) / ( 0.2 * x + 0.3 ) ;
Iterations = 754
Total Elapsed Time = 13 Seconds
Expected Time Remaining = 0 Seconds
Optimized Time Remaining = 0 Seconds
Expected Total Time = 13 Seconds
> quit
memory used=1195.6MB, alloc=52.3MB, time=13.78