|\^/| 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(cos(sqrt(c(2.0)*c(x)+c(3.0)))+sqrt(c(2.0)*c(x)+c(3.0))*sin(sqrt(c(2.0)*c(x)+c(3.0))));
> end;
exact_soln_y := proc(x)
return cos(sqrt(c(2.0)*c(x) + c(3.0)))
+ sqrt(c(2.0)*c(x) + c(3.0))*sin(sqrt(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_2D0,
> array_const_3D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local min_size;
> min_size := glob_estimated_size_answer;
> if (float_abs(array_y[1]) < min_size) then # if number 3
> min_size := float_abs(array_y[1]);
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> if (min_size < glob__1) then # if number 3
> min_size := glob__1;
> omniout_float(ALWAYS,"min_size",32,min_size,32,"");
> fi;# end if 3;
> min_size;
> end;
est_size_answer := proc()
local min_size;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_3D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
min_size := glob_estimated_size_answer;
if float_abs(array_y[1]) < min_size then
min_size := float_abs(array_y[1]);
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
if min_size < glob__1 then
min_size := glob__1;
omniout_float(ALWAYS, "min_size", 32, min_size, 32, "")
end if;
min_size
end proc
# End Function number 4
# Begin Function number 5
> test_suggested_h := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_3D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local max_estimated_step_error,hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> max_estimated_step_error := glob__small;
> no_terms := ATS_MAX_TERMS;
> hn_div_ho := glob__0_5;
> hn_div_ho_2 := glob__0_25;
> hn_div_ho_3 := glob__0_125;
> omniout_float(ALWAYS,"hn_div_ho",32,hn_div_ho,32,"");
> omniout_float(ALWAYS,"hn_div_ho_2",32,hn_div_ho_2,32,"");
> omniout_float(ALWAYS,"hn_div_ho_3",32,hn_div_ho_3,32,"");
> est_tmp := float_abs(array_y[no_terms-3] + array_y[no_terms - 2] * hn_div_ho + array_y[no_terms - 1] * hn_div_ho_2 + array_y[no_terms] * hn_div_ho_3);
> if (est_tmp >= max_estimated_step_error) then # if number 3
> max_estimated_step_error := est_tmp;
> fi;# end if 3;
> omniout_float(ALWAYS,"max_estimated_step_error",32,max_estimated_step_error,32,"");
> max_estimated_step_error;
> end;
test_suggested_h := proc()
local max_estimated_step_error, hn_div_ho, hn_div_ho_2, hn_div_ho_3,
no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_3D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
max_estimated_step_error := glob__small;
no_terms := ATS_MAX_TERMS;
hn_div_ho := glob__0_5;
hn_div_ho_2 := glob__0_25;
hn_div_ho_3 := glob__0_125;
omniout_float(ALWAYS, "hn_div_ho", 32, hn_div_ho, 32, "");
omniout_float(ALWAYS, "hn_div_ho_2", 32, hn_div_ho_2, 32, "");
omniout_float(ALWAYS, "hn_div_ho_3", 32, hn_div_ho_3, 32, "");
est_tmp := float_abs(array_y[no_terms - 3]
+ array_y[no_terms - 2]*hn_div_ho
+ array_y[no_terms - 1]*hn_div_ho_2
+ array_y[no_terms]*hn_div_ho_3);
if max_estimated_step_error <= est_tmp then
max_estimated_step_error := est_tmp
end if;
omniout_float(ALWAYS, "max_estimated_step_error", 32,
max_estimated_step_error, 32, "");
max_estimated_step_error
end proc
# End Function number 5
# Begin Function number 6
> track_estimated_error := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_3D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local hn_div_ho,hn_div_ho_2,hn_div_ho_3,no_terms,est_tmp;
> no_terms := ATS_MAX_TERMS;
> hn_div_ho := glob__0_5;
> hn_div_ho_2 := glob__0_25;
> hn_div_ho_3 := glob__0_125;
> est_tmp := c(float_abs(array_y[no_terms-3])) + c(float_abs(array_y[no_terms - 2])) * c(hn_div_ho) + c(float_abs(array_y[no_terms - 1])) * c(hn_div_ho_2) + c(float_abs(array_y[no_terms])) * c(hn_div_ho_3);
> if (glob_prec * c(float_abs(array_y[1])) > c(est_tmp)) then # if number 3
> est_tmp := c(glob_prec) * c(float_abs(array_y[1]));
> fi;# end if 3;
> if (c(est_tmp) >= c(array_max_est_error[1])) then # if number 3
> array_max_est_error[1] := c(est_tmp);
> fi;# end if 3
> ;
> end;
track_estimated_error := proc()
local hn_div_ho, hn_div_ho_2, hn_div_ho_3, no_terms, est_tmp;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_3D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
no_terms := ATS_MAX_TERMS;
hn_div_ho := glob__0_5;
hn_div_ho_2 := glob__0_25;
hn_div_ho_3 := glob__0_125;
est_tmp := c(float_abs(array_y[no_terms - 3]))
+ c(float_abs(array_y[no_terms - 2]))*c(hn_div_ho)
+ c(float_abs(array_y[no_terms - 1]))*c(hn_div_ho_2)
+ c(float_abs(array_y[no_terms]))*c(hn_div_ho_3);
if c(est_tmp) < glob_prec*c(float_abs(array_y[1])) then
est_tmp := c(glob_prec)*c(float_abs(array_y[1]))
end if;
if c(array_max_est_error[1]) <= c(est_tmp) then
array_max_est_error[1] := c(est_tmp)
end if
end proc
# End Function number 6
# Begin Function number 7
> reached_interval := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_3D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local ret;
> if ((glob_check_sign * array_x[1]) >= (glob_check_sign * glob_next_display - glob_h/glob__10)) then # if number 3
> ret := true;
> else
> ret := false;
> fi;# end if 3;
> return(ret);
> end;
reached_interval := proc()
local ret;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_3D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
if glob_check_sign*glob_next_display - glob_h/glob__10 <=
glob_check_sign*array_x[1] then ret := true
else ret := false
end if;
return ret
end proc
# End Function number 7
# Begin Function number 8
> display_alot := proc(iter)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_3D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no, est_rel_err;
> #TOP DISPLAY ALOT
> ind_var := array_x[1];
> omniout_complex(ALWAYS,"x[1] ",33,ind_var,20," ");
> term_no := 1;
> numeric_val := array_y[term_no];
> omniout_complex(ALWAYS,"h ",33,glob_h,20," ");
> omniout_complex(ALWAYS,"y[1] (numeric) ",33,numeric_val,20," ");
> closed_form_val_y := evalf(exact_soln_y(ind_var));
> omniout_complex(ALWAYS,"y[1] (closed_form) ",33,closed_form_val_y,20," ");
> abserr := float_abs(numeric_val - closed_form_val_y);
> if (float_abs(closed_form_val_y) > 0.0) then # if number 3
> relerr := abserr/float_abs(closed_form_val_y);
> if (float_abs(c(relerr)) > 0.0) then # if number 4
> glob_good_digits := round(-log10(relerr));
> else
> relerr := 0.0 ;
> glob_good_digits := Digits - 2;
> fi;# end if 4;
> else
> ;
> relerr := glob__m1 ;
> glob_good_digits := -16;
> fi;# end if 3;
> if (glob_good_digits < glob_min_good_digits) then # if number 3
> glob_min_good_digits := glob_good_digits;
> fi;# end if 3;
> omniout_float(ALWAYS,"absolute error ",4,abserr,4," ");
> omniout_float(ALWAYS,"relative error ",4,relerr * glob__100 ,4,"%");
> omniout_int(INFO,"Correct digits ",32,glob_good_digits,4," ")
> ;
> #BOTTOM DISPLAY ALOT
> end;
display_alot := proc(iter)
local abserr, closed_form_val_y, ind_var, numeric_val, relerr, term_no,
est_rel_err;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_3D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
ind_var := array_x[1];
omniout_complex(ALWAYS, "x[1] ", 33,
ind_var, 20, " ");
term_no := 1;
numeric_val := array_y[term_no];
omniout_complex(ALWAYS, "h ", 33, glob_h,
20, " ");
omniout_complex(ALWAYS, "y[1] (numeric) ", 33,
numeric_val, 20, " ");
closed_form_val_y := evalf(exact_soln_y(ind_var));
omniout_complex(ALWAYS, "y[1] (closed_form) ", 33,
closed_form_val_y, 20, " ");
abserr := float_abs(numeric_val - closed_form_val_y);
if 0. < float_abs(closed_form_val_y) then
relerr := abserr/float_abs(closed_form_val_y);
if 0. < float_abs(c(relerr)) then
glob_good_digits := round(-log10(relerr))
else relerr := 0.; glob_good_digits := Digits - 2
end if
else relerr := glob__m1; glob_good_digits := -16
end if;
if glob_good_digits < glob_min_good_digits then
glob_min_good_digits := glob_good_digits
end if;
omniout_float(ALWAYS, "absolute error ", 4, abserr, 4,
" ");
omniout_float(ALWAYS, "relative error ", 4,
relerr*glob__100, 4, "%");
omniout_int(INFO, "Correct digits ", 32,
glob_good_digits, 4, " ")
end proc
# End Function number 8
# Begin Function number 9
> prog_report := proc(x_start,x_end)
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_3D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec, percent_done, total_clock_sec;
> #TOP PROGRESS REPORT
> clock_sec1 := elapsed_time_seconds();
> total_clock_sec := (clock_sec1) - (glob_orig_start_sec);
> glob_clock_sec := (clock_sec1) - (glob_clock_start_sec);
> left_sec := (glob_max_sec) + (glob_orig_start_sec) - (clock_sec1);
> expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) + (glob_h) ,( clock_sec1) - (glob_orig_start_sec));
> opt_clock_sec := ( clock_sec1) - (glob_optimal_clock_start_sec);
> glob_optimal_expect_sec := comp_expect_sec((x_end),(x_start),(array_x[1]) +( glob_h) ,( opt_clock_sec));
> glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
> percent_done := comp_percent((x_end),(x_start),(array_x[1]) + (glob_h));
> glob_percent_done := percent_done;
> omniout_str_noeol(INFO,"Total Elapsed Time ");
> omniout_timestr((total_clock_sec));
> if (c(percent_done) < glob__100) then # if number 3
> omniout_str_noeol(INFO,"Expected Time Remaining ");
> omniout_timestr((expect_sec));
> omniout_str_noeol(INFO,"Optimized Time Remaining ");
> omniout_timestr((glob_optimal_expect_sec));
> omniout_str_noeol(INFO,"Expected Total Time ");
> omniout_timestr((glob_total_exp_sec));
> fi;# end if 3;
> #BOTTOM PROGRESS REPORT
> end;
prog_report := proc(x_start, x_end)
local clock_sec, opt_clock_sec, clock_sec1, expect_sec, left_sec,
percent_done, total_clock_sec;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_3D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
clock_sec1 := elapsed_time_seconds();
total_clock_sec := clock_sec1 - glob_orig_start_sec;
glob_clock_sec := clock_sec1 - glob_clock_start_sec;
left_sec := glob_max_sec + glob_orig_start_sec - clock_sec1;
expect_sec := comp_expect_sec(x_end, x_start, array_x[1] + glob_h,
clock_sec1 - glob_orig_start_sec);
opt_clock_sec := clock_sec1 - glob_optimal_clock_start_sec;
glob_optimal_expect_sec :=
comp_expect_sec(x_end, x_start, array_x[1] + glob_h, opt_clock_sec)
;
glob_total_exp_sec := glob_optimal_expect_sec + c(total_clock_sec);
percent_done := comp_percent(x_end, x_start, array_x[1] + glob_h);
glob_percent_done := percent_done;
omniout_str_noeol(INFO, "Total Elapsed Time ");
omniout_timestr(total_clock_sec);
if c(percent_done) < glob__100 then
omniout_str_noeol(INFO, "Expected Time Remaining ");
omniout_timestr(expect_sec);
omniout_str_noeol(INFO, "Optimized Time Remaining ");
omniout_timestr(glob_optimal_expect_sec);
omniout_str_noeol(INFO, "Expected Total Time ");
omniout_timestr(glob_total_exp_sec)
end if
end proc
# End Function number 9
# Begin Function number 10
> check_for_pole := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_3D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_tmp5,
> array_m1,
> array_y_higher,
> array_y_higher_work,
> array_y_higher_work2,
> array_y_set_initial,
> array_given_rad_poles,
> array_given_ord_poles,
> array_rad_test_poles,
> array_ord_test_poles,
> array_fact_2,
> ATS_MAX_TERMS,
> glob_last;
> local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2, term3, part1, part2, part3, part4, part5, part6, part7, part8, part9, part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4, found_sing, h_new, ratio, term, local_test, tmp_rad,tmp_ord, tmp_ratio, prev_tmp_rad, last_no;
> #TOP CHECK FOR POLE
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,1] := glob_larger_float;
> array_ord_test_poles[1,1] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-3 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 3
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 3;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 3
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 4
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 5
> found_sing := 0;
> fi;# end if 5;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 5
> if (rad_c < array_rad_test_poles[1,1]) then # if number 6
> array_rad_test_poles[1,1] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_ratio(array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,1] := rad_c;
> array_ord_test_poles[1,1] := tmp_ord;
> fi;# end if 6;
> fi;# end if 5;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,2] := glob_larger_float;
> array_ord_test_poles[1,2] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-4 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 5
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 5;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 5
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 6
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 7
> found_sing := 0;
> fi;# end if 7;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 7
> if (rad_c < array_rad_test_poles[1,2]) then # if number 8
> array_rad_test_poles[1,2] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_three_terms(array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,2] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 9
> glob_min_pole_est := rad_c;
> fi;# end if 9;
> array_ord_test_poles[1,2] := tmp_ord;
> fi;# end if 8;
> fi;# end if 7;
> #BOTTOM general radius test1
> tmp_rad := glob_larger_float;
> prev_tmp_rad := glob_larger_float;
> tmp_ratio := glob_larger_float;
> rad_c := glob_larger_float;
> array_rad_test_poles[1,3] := glob_larger_float;
> array_ord_test_poles[1,3] := glob_larger_float;
> found_sing := 1;
> last_no := ATS_MAX_TERMS - 1 - 10;
> cnt := 0;
> while (last_no < ATS_MAX_TERMS-7 and found_sing = 1) do # do number 1
> tmp_rad := comp_rad_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> if (float_abs(prev_tmp_rad) > glob__0) then # if number 7
> tmp_ratio := tmp_rad / prev_tmp_rad;
> else
> tmp_ratio := glob_large_float;
> fi;# end if 7;
> if ((cnt > 0 ) and (tmp_ratio < glob_upper_ratio_limit) and (tmp_ratio > glob_lower_ratio_limit)) then # if number 7
> rad_c := tmp_rad;
> elif
> (cnt = 0) then # if number 8
> rad_c := tmp_rad;
> elif
> (cnt > 0) then # if number 9
> found_sing := 0;
> fi;# end if 9;
> prev_tmp_rad := tmp_rad;;
> cnt := cnt + 1;
> last_no := last_no + 1;
> od;# end do number 1;
> if (found_sing = 1) then # if number 9
> if (rad_c < array_rad_test_poles[1,3]) then # if number 10
> array_rad_test_poles[1,3] := rad_c;
> last_no := last_no - 1;
> tmp_ord := comp_ord_from_six_terms(array_y_higher[1,last_no-5],array_y_higher[1,last_no-4],array_y_higher[1,last_no-3],array_y_higher[1,last_no-2],array_y_higher[1,last_no-1],array_y_higher[1,last_no],last_no);
> array_rad_test_poles[1,3] := rad_c;
> if (rad_c < glob_min_pole_est) then # if number 11
> glob_min_pole_est := rad_c;
> fi;# end if 11;
> array_ord_test_poles[1,3] := tmp_ord;
> fi;# end if 10;
> fi;# end if 9;
> #BOTTOM general radius test1
> ;
> if (true) then # if number 9
> display_poles();
> fi;# end if 9
> end;
check_for_pole := proc()
local cnt, dr1, dr2, ds1, ds2, hdrc, m, n, nr1, nr2, ord_no, term1, term2,
term3, part1, part2, part3, part4, part5, part6, part7, part8, part9,
part10, part11, part12, part13, part14, rad_c, rcs, rm0, rm1, rm2, rm3, rm4,
found_sing, h_new, ratio, term, local_test, tmp_rad, tmp_ord, tmp_ratio,
prev_tmp_rad, last_no;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_3D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5,
array_m1, array_y_higher, array_y_higher_work, array_y_higher_work2,
array_y_set_initial, array_given_rad_poles, array_given_ord_poles,
array_rad_test_poles, array_ord_test_poles, array_fact_2, ATS_MAX_TERMS,
glob_last;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 1] := glob_larger_float;
array_ord_test_poles[1, 1] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 3 and found_sing = 1 do
tmp_rad := comp_rad_from_ratio(array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 1] then
array_rad_test_poles[1, 1] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_ratio(array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
array_rad_test_poles[1, 1] := rad_c;
array_ord_test_poles[1, 1] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 2] := glob_larger_float;
array_ord_test_poles[1, 2] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 4 and found_sing = 1 do
tmp_rad := comp_rad_from_three_terms(
array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 2] then
array_rad_test_poles[1, 2] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_three_terms(
array_y_higher[1, last_no - 2],
array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
last_no);
array_rad_test_poles[1, 2] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 2] := tmp_ord
end if
end if;
tmp_rad := glob_larger_float;
prev_tmp_rad := glob_larger_float;
tmp_ratio := glob_larger_float;
rad_c := glob_larger_float;
array_rad_test_poles[1, 3] := glob_larger_float;
array_ord_test_poles[1, 3] := glob_larger_float;
found_sing := 1;
last_no := ATS_MAX_TERMS - 11;
cnt := 0;
while last_no < ATS_MAX_TERMS - 7 and found_sing = 1 do
tmp_rad := comp_rad_from_six_terms(array_y_higher[1, last_no - 5],
array_y_higher[1, last_no - 4], array_y_higher[1, last_no - 3],
array_y_higher[1, last_no - 2], array_y_higher[1, last_no - 1],
array_y_higher[1, last_no], last_no);
if glob__0 < float_abs(prev_tmp_rad) then
tmp_ratio := tmp_rad/prev_tmp_rad
else tmp_ratio := glob_large_float
end if;
if 0 < cnt and tmp_ratio < glob_upper_ratio_limit and
glob_lower_ratio_limit < tmp_ratio then rad_c := tmp_rad
elif cnt = 0 then rad_c := tmp_rad
elif 0 < cnt then found_sing := 0
end if;
prev_tmp_rad := tmp_rad;
cnt := cnt + 1;
last_no := last_no + 1
end do;
if found_sing = 1 then
if rad_c < array_rad_test_poles[1, 3] then
array_rad_test_poles[1, 3] := rad_c;
last_no := last_no - 1;
tmp_ord := comp_ord_from_six_terms(
array_y_higher[1, last_no - 5],
array_y_higher[1, last_no - 4],
array_y_higher[1, last_no - 3],
array_y_higher[1, last_no - 2],
array_y_higher[1, last_no - 1], array_y_higher[1, last_no],
last_no);
array_rad_test_poles[1, 3] := rad_c;
if rad_c < glob_min_pole_est then glob_min_pole_est := rad_c
end if;
array_ord_test_poles[1, 3] := tmp_ord
end if
end if;
display_poles()
end proc
# End Function number 10
# Begin Function number 11
> atomall := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_3D0,
#END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_tmp5,
> 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_2D0[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp2[1] := array_tmp1[1] + array_const_3D0[1];
> #emit pre sqrt 1 $eq_no = 1
> array_tmp3[1] := sqrt(array_tmp2[1]);
> array_tmp4_g[1] := sin(array_tmp3[1]);
> array_tmp4[1] := cos(array_tmp3[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp5[1] := array_const_0D0[1] + array_tmp4[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_tmp5[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_2D0[1] * array_x[2];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 2
> array_tmp2[2] := array_tmp1[2];
> #emit pre sqrt 2 $eq_no = 1
> array_tmp3[2] := array_tmp2[2] / array_tmp3[1]/glob__2;
> #emit pre cos FULL $eq_no = 1
> array_tmp4_g[2] := (att(1,array_tmp4,array_tmp3,1));
> array_tmp4[2] := (neg(att(1,array_tmp4_g,array_tmp3,1)));
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp5[2] := array_tmp4[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_tmp5[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 sqrt ID_LINEAR iii = 3 $eq_no = 1
> array_tmp3[3] := 0;
> array_tmp3[3] := neg(ats(3,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2;
> #emit pre cos FULL $eq_no = 1
> array_tmp4_g[3] := (att(2,array_tmp4,array_tmp3,1));
> array_tmp4[3] := (neg(att(2,array_tmp4_g,array_tmp3,1)));
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp5[3] := array_tmp4[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_tmp5[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 sqrt ID_LINEAR iii = 4 $eq_no = 1
> array_tmp3[4] := 0;
> array_tmp3[4] := neg(ats(4,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2;
> #emit pre cos FULL $eq_no = 1
> array_tmp4_g[4] := (att(3,array_tmp4,array_tmp3,1));
> array_tmp4[4] := (neg(att(3,array_tmp4_g,array_tmp3,1)));
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp5[4] := array_tmp4[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_tmp5[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 sqrt ID_LINEAR iii = 5 $eq_no = 1
> array_tmp3[5] := 0;
> array_tmp3[5] := neg(ats(5,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2;
> #emit pre cos FULL $eq_no = 1
> array_tmp4_g[5] := (att(4,array_tmp4,array_tmp3,1));
> array_tmp4[5] := (neg(att(4,array_tmp4_g,array_tmp3,1)));
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp5[5] := array_tmp4[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_tmp5[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 sqrt LINEAR $eq_no = 1
> array_tmp3[kkk] := 0;
> array_tmp3[kkk] := neg(ats(kkk,array_tmp3,array_tmp3,2)) /array_tmp3[1] / glob__2;
> #emit cos FULL $eq_no = 1
> array_tmp4[kkk] := neg(att(kkk-1,array_tmp4_g,array_tmp3,1));
> array_tmp4_g[kkk] := att(kkk-1,array_tmp4,array_tmp3,1);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp5[kkk] := array_tmp4[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_tmp5[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
> array_y[kkk + order_d] := c(temporary);
> array_y_higher[1,kkk + order_d] := c(temporary);
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := c(temporary) / c(glob_h) * c(adj2);
> else
> temporary := c(temporary);
> fi;# end if 4;
> array_y_higher[adj3,term] := c(temporary);
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 1
> fi;# end if 2
> fi;# end if 1;
> kkk := kkk + 1;
> od;# end do number 1;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_3D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5,
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_2D0[1]*array_x[1];
array_tmp2[1] := array_tmp1[1] + array_const_3D0[1];
array_tmp3[1] := sqrt(array_tmp2[1]);
array_tmp4_g[1] := sin(array_tmp3[1]);
array_tmp4[1] := cos(array_tmp3[1]);
array_tmp5[1] := array_const_0D0[1] + array_tmp4[1];
if not array_y_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[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_2D0[1]*array_x[2];
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := array_tmp2[2]/(array_tmp3[1]*glob__2);
array_tmp4_g[2] := att(1, array_tmp4, array_tmp3, 1);
array_tmp4[2] := neg(att(1, array_tmp4_g, array_tmp3, 1));
array_tmp5[2] := array_tmp4[2];
if not array_y_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
if 3 <= ATS_MAX_TERMS then
array_y[3] := temporary; array_y_higher[1, 3] := temporary
end if;
temporary := c(temporary)*c(2)/c(glob_h);
array_y_higher[2, 2] := c(temporary)
end if
end if;
kkk := 3;
array_tmp3[3] := 0;
array_tmp3[3] :=
neg(ats(3, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2);
array_tmp4_g[3] := att(2, array_tmp4, array_tmp3, 1);
array_tmp4[3] := neg(att(2, array_tmp4_g, array_tmp3, 1));
array_tmp5[3] := array_tmp4[3];
if not array_y_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[3])*expt(glob_h, c(1))*c(factorial_3(2, 3));
if 4 <= ATS_MAX_TERMS then
array_y[4] := temporary; array_y_higher[1, 4] := temporary
end if;
temporary := c(temporary)*c(3)/c(glob_h);
array_y_higher[2, 3] := c(temporary)
end if
end if;
kkk := 4;
array_tmp3[4] := 0;
array_tmp3[4] :=
neg(ats(4, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2);
array_tmp4_g[4] := att(3, array_tmp4, array_tmp3, 1);
array_tmp4[4] := neg(att(3, array_tmp4_g, array_tmp3, 1));
array_tmp5[4] := array_tmp4[4];
if not array_y_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[4])*expt(glob_h, c(1))*c(factorial_3(3, 4));
if 5 <= ATS_MAX_TERMS then
array_y[5] := temporary; array_y_higher[1, 5] := temporary
end if;
temporary := c(temporary)*c(4)/c(glob_h);
array_y_higher[2, 4] := c(temporary)
end if
end if;
kkk := 5;
array_tmp3[5] := 0;
array_tmp3[5] :=
neg(ats(5, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2);
array_tmp4_g[5] := att(4, array_tmp4, array_tmp3, 1);
array_tmp4[5] := neg(att(4, array_tmp4_g, array_tmp3, 1));
array_tmp5[5] := array_tmp4[5];
if not array_y_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[5])*expt(glob_h, c(1))*c(factorial_3(4, 5));
if 6 <= ATS_MAX_TERMS then
array_y[6] := temporary; array_y_higher[1, 6] := temporary
end if;
temporary := c(temporary)*c(5)/c(glob_h);
array_y_higher[2, 5] := c(temporary)
end if
end if;
kkk := 6;
while kkk <= ATS_MAX_TERMS do
array_tmp3[kkk] := 0;
array_tmp3[kkk] := neg(ats(kkk, array_tmp3, array_tmp3, 2))/(
array_tmp3[1]*glob__2);
array_tmp4[kkk] := neg(att(kkk - 1, array_tmp4_g, array_tmp3, 1));
array_tmp4_g[kkk] := att(kkk - 1, array_tmp4, array_tmp3, 1);
array_tmp5[kkk] := array_tmp4[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_tmp5[kkk])*expt(glob_h, c(order_d))*
c(factorial_3(kkk - 1, kkk + order_d - 1));
array_y[kkk + order_d] := c(temporary);
array_y_higher[1, kkk + order_d] := c(temporary);
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while
1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1
do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := c(temporary)*c(adj2)/c(glob_h)
else temporary := c(temporary)
end if;
array_y_higher[adj3, term] := c(temporary)
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
# End Function number 12
#END OUTFILE5
# Begin Function number 12
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it;
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_2D0,
> array_const_3D0,
> #END CONST
> array_y_init,
> array_norms,
> array_fact_1,
> array_1st_rel_error,
> array_last_rel_error,
> array_est_rel_error,
> array_max_est_error,
> array_type_pole,
> array_type_real_pole,
> array_type_complex_pole,
> array_est_digits,
> array_y,
> array_x,
> array_tmp0,
> array_tmp1,
> array_tmp2,
> array_tmp3,
> array_tmp4_g,
> array_tmp4,
> array_tmp5,
> 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_g:= Array(0..(30),[]);
> array_tmp4:= Array(0..(30),[]);
> array_tmp5:= 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_g[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_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_g);
> zero_ats_ar(array_tmp4);
> zero_ats_ar(array_tmp5);
> zero_ats_ar(array_m1);
> zero_ats_ar(array_const_1);
> array_const_1[1] := c(1);
> zero_ats_ar(array_const_0D0);
> array_const_0D0[1] := c(0.0);
> zero_ats_ar(array_const_2D0);
> array_const_2D0[1] := c(2.0);
> zero_ats_ar(array_const_3D0);
> array_const_3D0[1] := c(3.0);
> zero_ats_ar(array_m1);
> array_m1[1] := glob__m1;
> #END SYMBOLS INITIALIZATED
> # before generate factorials init
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= ATS_MAX_TERMS) do # do number 1
> jjjf := 0;
> while (jjjf <= ATS_MAX_TERMS) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Table
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> glob_yes_pole := 4;
> glob_no_pole := 3;
> glob_not_given := 0;
> glob_no_sing_tests := 4;
> glob_ratio_test := 1;
> glob_three_term_test := 2;
> glob_six_term_test := 3;
> glob_log_10 := log(c(10.0));
> MAX_UNCHANGED := 10;
> glob__small := c(0.1e-50);
> glob_small_float := c(0.1e-50);
> glob_smallish_float := c(0.1e-60);
> glob_large_float := c(1.0e100);
> glob_larger_float := c(1.1e100);
> glob__m2 := c(-2);
> glob__m1 := c(-1);
> glob__0 := c(0);
> glob__1 := c(1);
> glob__2 := c(2);
> glob__3 := c(3);
> glob__4 := c(4);
> glob__5 := c(5);
> glob__8 := c(8);
> glob__10 := c(10);
> glob__100 := c(100);
> glob__pi := c(0.0);
> glob__0_5 := c(0.5);
> glob__0_8 := c(0.8);
> glob__m0_8 := c(-0.8);
> glob__0_25 := c(0.25);
> glob__0_125 := c(0.125);
> glob_h := 0.1;
> glob_nxt := 1;
> glob_prec := c(1.0e-16);
> glob_check_sign := c(1.0);
> glob_desired_digits_correct := c(8.0);
> glob_max_estimated_step_error := c(0.0);
> glob_ratio_of_radius := c(0.1);
> glob_percent_done := c(0.0);
> glob_total_exp_sec := c(0.1);
> glob_optimal_expect_sec := c(0.1);
> glob_estimated_size_answer := c(100.0);
> glob_almost_1 := c(0.9990);
> glob_clock_sec := c(0.0);
> glob_clock_start_sec := c(0.0);
> glob_disp_incr := c(0.1);
> glob_diff_rc_fm := c(0.1);
> glob_diff_rc_fmm1 := c(0.1);
> glob_diff_rc_fmm2 := c(0.1);
> glob_diff_ord_fm := c(0.1);
> glob_diff_ord_fmm1 := c(0.1);
> glob_diff_ord_fmm2 := c(0.1);
> glob_six_term_ord_save := c(0.1);
> glob_guess_error_rc := c(0.1);
> glob_guess_error_ord := c(0.1);
> glob_least_given_sing := c(9.9e200);
> glob_least_ratio_sing := c(9.9e200);
> glob_least_3_sing := c(9.9e100);
> glob_least_6_sing := c(9.9e100);
> glob_last_good_h := c(0.1);
> glob_max_h := c(0.1);
> glob_min_h := c(0.000001);
> glob_display_interval := c(0.1);
> glob_abserr := c(0.1e-10);
> glob_relerr := c(0.1e-10);
> glob_min_pole_est := c(0.1e+10);
> glob_max_rel_trunc_err := c(0.1e-10);
> glob_max_trunc_err := c(0.1e-10);
> glob_max_hours := c(0.0);
> glob_optimal_clock_start_sec := c(0.0);
> glob_optimal_start := c(0.0);
> glob_upper_ratio_limit := c(1.0001);
> glob_lower_ratio_limit := c(0.9999);
> glob_max_sec := c(10000.0);
> glob_orig_start_sec := c(0.0);
> glob_normmax := c(0.0);
> glob_max_minutes := c(0.0);
> glob_next_display := c(0.0);
> glob_est_digits := 1;
> glob_subiter_method := 3;
> glob_html_log := true;
> glob_min_good_digits := 99999;
> glob_good_digits := 0;
> glob_min_apfp_est_good_digits := 99999;
> glob_apfp_est_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> glob_h_reason := 0;
> glob_sec_in_minute := 60 ;
> glob_min_in_hour := 60;
> glob_hours_in_day := 24;
> glob_days_in_year := 365;
> glob_sec_in_hour := 3600;
> glob_sec_in_day := 86400;
> glob_sec_in_year := 31536000;
> glob_not_yet_finished := true;
> glob_initial_pass := true;
> glob_not_yet_start_msg := true;
> glob_reached_optimal_h := false;
> glob_optimal_done := false;
> glob_type_given_pole := 0;
> glob_optimize := false;
> glob_look_poles := false;
> glob_dump_closed_form := false;
> glob_max_iter := 10000;
> glob_no_eqs := 0;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_start := 0;
> glob_iter := 0;
> # before generate set diff initial
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> 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/cos_sqrt_linpostcpx.cpx#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = cos ( sqrt ( 2.0 * x + 3.0 ) ) ; ");
> 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 := -1.4 + 0.1 * I;");
> omniout_str(ALWAYS,"x_end := 99.0 + 99.0 * I;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"glob_max_h := 0.0001;");
> omniout_str(ALWAYS,"glob_upper_ratio_limit := c(1.001);");
> omniout_str(ALWAYS,"glob_lower_ratio_limit := c(0.999);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_type_given_pole := 1;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_rad_poles[1,1] := c(-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(0.5);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_ord_poles[1,2] := c(0.0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=8;");
> omniout_str(ALWAYS,"glob_max_minutes:=(3.0);");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"glob_max_iter:=10000;");
> omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);");
> omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);");
> omniout_str(ALWAYS,"glob_look_poles:=true;");
> omniout_str(ALWAYS,"glob_h:=c(0.001);");
> omniout_str(ALWAYS,"glob_display_interval:=c(0.01);");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"return(cos(sqrt(c(2.0)*c(x)+c(3.0)))+sqrt(c(2.0)*c(x)+c(3.0))*sin(sqrt(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 := -1.4 + 0.1 * I;
> x_end := 99.0 + 99.0 * I;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_max_h := 0.0001;
> glob_upper_ratio_limit := c(1.001);
> glob_lower_ratio_limit := c(0.999);
> 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(0.5);
> 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 ) = cos ( sqrt ( 2.0 * x + 3.0 ) ) ; ");
> omniout_int(INFO,"Iterations ",32,glob_iter,4," ")
> ;
> prog_report(x_start,x_end);
> if (glob_html_log) then # if number 10
> logstart(html_log_file);
> logitem_str(html_log_file,"2017-11-26T14:42:02-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"cos_sqrt_lin")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = cos ( sqrt ( 2.0 * x + 3.0 ) ) ; ")
> ;
> logitem_complex(html_log_file,x_start)
> ;
> logitem_complex(html_log_file,x_end)
> ;
> logitem_complex(html_log_file,array_x[1])
> ;
> logitem_complex(html_log_file,glob_h)
> ;
> logitem_h_reason(html_log_file)
> ;
> logitem_integer(html_log_file,Digits)
> ;
> ;
> glob_desired_digits_correct := 0.0;
> logitem_float(html_log_file,glob_desired_digits_correct)
> ;
> if (array_est_digits[1] <> -16) then # if number 11
> logitem_integer(html_log_file,array_est_digits[1])
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_min_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_min_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> if (glob_good_digits <> -16) then # if number 11
> logitem_integer(html_log_file,glob_good_digits)
> ;
> else
> logitem_str(html_log_file,"Unknown")
> ;
> fi;# end if 11;
> logitem_str(html_log_file,"NA")
> ;
> logitem_str(html_log_file,"NA")
> ;
> logitem_integer(html_log_file,ATS_MAX_TERMS)
> ;
> if (glob_type_given_pole = 0) then # if number 11
> logitem_str(html_log_file,"Not Given")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 4) then # if number 12
> logitem_str(html_log_file,"No Solution")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 5) then # if number 13
> logitem_str(html_log_file,"Some Pole")
> ;
> logitem_str(html_log_file,"????")
> ;
> elif
> (glob_type_given_pole = 3) then # if number 14
> logitem_str(html_log_file,"No Pole")
> ;
> logitem_str(html_log_file,"NA")
> ;
> elif
> (glob_type_given_pole = 1) then # if number 15
> logitem_str(html_log_file,"Real Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> elif
> (glob_type_given_pole = 2) then # if number 16
> logitem_str(html_log_file,"Complex Sing")
> ;
> logitem_float(html_log_file,glob_least_given_sing)
> ;
> fi;# end if 16;
> if (glob_least_ratio_sing < glob_large_float) then # if number 16
> glob_least_ratio_sing := 0;
> logitem_float(html_log_file,glob_least_ratio_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_3_sing < glob_large_float) then # if number 16
> logitem_float(html_log_file,glob_least_3_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> if (glob_least_6_sing < glob_large_float) then # if number 16
> glob_least_6_sing := 0.0;
> logitem_float(html_log_file,glob_least_6_sing)
> ;
> else
> logitem_str(html_log_file,"NONE")
> ;
> fi;# end if 16;
> logitem_integer(html_log_file,glob_iter)
> ;
> logitem_time(html_log_file,(glob_clock_sec))
> ;
> if (c(glob_percent_done) < glob__100) then # if number 16
> logitem_time(html_log_file,(glob_total_exp_sec))
> ;
> 0;
> else
> logitem_str(html_log_file,"Done")
> ;
> 0;
> fi;# end if 16;
> log_revs(html_log_file," 309 | ")
> ;
> logitem_str(html_log_file,"cos_sqrt_lin diffeq.mxt")
> ;
> logitem_str(html_log_file,"cos_sqrt_lin maple results")
> ;
> logitem_str(html_log_file,"Poor Accuracy")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 15;
> if (glob_html_log) then # if number 15
> fclose(html_log_file);
> fi;# end if 15
> ;
> ;;
> end;
> # End Function number 12
> #END OUTFILEMAIN
> end;
Warning, `h_new` is implicitly declared local to procedure `main`
Warning, `ratio` is implicitly declared local to procedure `main`
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max,
term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order,
sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it,
last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err,
estimated_step_error, min_value, est_answer, found_h, repeat_it, h_new,
ratio;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_2D0,
array_const_3D0, array_y_init, array_norms, array_fact_1,
array_1st_rel_error, array_last_rel_error, array_est_rel_error,
array_max_est_error, array_type_pole, array_type_real_pole,
array_type_complex_pole, array_est_digits, array_y, array_x, array_tmp0,
array_tmp1, array_tmp2, array_tmp3, array_tmp4_g, array_tmp4, array_tmp5,
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_g := Array(0 .. 30, []);
array_tmp4 := Array(0 .. 30, []);
array_tmp5 := 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_g[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_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_g);
zero_ats_ar(array_tmp4);
zero_ats_ar(array_tmp5);
zero_ats_ar(array_m1);
zero_ats_ar(array_const_1);
array_const_1[1] := c(1);
zero_ats_ar(array_const_0D0);
array_const_0D0[1] := c(0.);
zero_ats_ar(array_const_2D0);
array_const_2D0[1] := c(2.0);
zero_ats_ar(array_const_3D0);
array_const_3D0[1] := c(3.0);
zero_ats_ar(array_m1);
array_m1[1] := glob__m1;
iiif := 0;
while iiif <= ATS_MAX_TERMS do
jjjf := 0;
while jjjf <= ATS_MAX_TERMS do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
glob_yes_pole := 4;
glob_no_pole := 3;
glob_not_given := 0;
glob_no_sing_tests := 4;
glob_ratio_test := 1;
glob_three_term_test := 2;
glob_six_term_test := 3;
glob_log_10 := log(c(10.0));
MAX_UNCHANGED := 10;
glob__small := c(0.1*10^(-50));
glob_small_float := c(0.1*10^(-50));
glob_smallish_float := c(0.1*10^(-60));
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob__m2 := c(-2);
glob__m1 := c(-1);
glob__0 := c(0);
glob__1 := c(1);
glob__2 := c(2);
glob__3 := c(3);
glob__4 := c(4);
glob__5 := c(5);
glob__8 := c(8);
glob__10 := c(10);
glob__100 := c(100);
glob__pi := c(0.);
glob__0_5 := c(0.5);
glob__0_8 := c(0.8);
glob__m0_8 := c(-0.8);
glob__0_25 := c(0.25);
glob__0_125 := c(0.125);
glob_h := 0.1;
glob_nxt := 1;
glob_prec := c(0.10*10^(-15));
glob_check_sign := c(1.0);
glob_desired_digits_correct := c(8.0);
glob_max_estimated_step_error := c(0.);
glob_ratio_of_radius := c(0.1);
glob_percent_done := c(0.);
glob_total_exp_sec := c(0.1);
glob_optimal_expect_sec := c(0.1);
glob_estimated_size_answer := c(100.0);
glob_almost_1 := c(0.9990);
glob_clock_sec := c(0.);
glob_clock_start_sec := c(0.);
glob_disp_incr := c(0.1);
glob_diff_rc_fm := c(0.1);
glob_diff_rc_fmm1 := c(0.1);
glob_diff_rc_fmm2 := c(0.1);
glob_diff_ord_fm := c(0.1);
glob_diff_ord_fmm1 := c(0.1);
glob_diff_ord_fmm2 := c(0.1);
glob_six_term_ord_save := c(0.1);
glob_guess_error_rc := c(0.1);
glob_guess_error_ord := c(0.1);
glob_least_given_sing := c(0.99*10^201);
glob_least_ratio_sing := c(0.99*10^201);
glob_least_3_sing := c(0.99*10^101);
glob_least_6_sing := c(0.99*10^101);
glob_last_good_h := c(0.1);
glob_max_h := c(0.1);
glob_min_h := c(0.1*10^(-5));
glob_display_interval := c(0.1);
glob_abserr := c(0.1*10^(-10));
glob_relerr := c(0.1*10^(-10));
glob_min_pole_est := c(0.1*10^10);
glob_max_rel_trunc_err := c(0.1*10^(-10));
glob_max_trunc_err := c(0.1*10^(-10));
glob_max_hours := c(0.);
glob_optimal_clock_start_sec := c(0.);
glob_optimal_start := c(0.);
glob_upper_ratio_limit := c(1.0001);
glob_lower_ratio_limit := c(0.9999);
glob_max_sec := c(10000.0);
glob_orig_start_sec := c(0.);
glob_normmax := c(0.);
glob_max_minutes := c(0.);
glob_next_display := c(0.);
glob_est_digits := 1;
glob_subiter_method := 3;
glob_html_log := true;
glob_min_good_digits := 99999;
glob_good_digits := 0;
glob_min_apfp_est_good_digits := 99999;
glob_apfp_est_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
glob_h_reason := 0;
glob_sec_in_minute := 60;
glob_min_in_hour := 60;
glob_hours_in_day := 24;
glob_days_in_year := 365;
glob_sec_in_hour := 3600;
glob_sec_in_day := 86400;
glob_sec_in_year := 31536000;
glob_not_yet_finished := true;
glob_initial_pass := true;
glob_not_yet_start_msg := true;
glob_reached_optimal_h := false;
glob_optimal_done := false;
glob_type_given_pole := 0;
glob_optimize := false;
glob_look_poles := false;
glob_dump_closed_form := false;
glob_max_iter := 10000;
glob_no_eqs := 0;
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_start := 0;
glob_iter := 0;
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
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/cos_sqrt_linpostcpx.cpx#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = cos ( sqrt ( 2.0 \
* x + 3.0 ) ) ; ");
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 := -1.4 + 0.1 * I;");
omniout_str(ALWAYS, "x_end := 99.0 + 99.0 * I;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "glob_max_h := 0.0001;");
omniout_str(ALWAYS, "glob_upper_ratio_limit := c(1.001);");
omniout_str(ALWAYS, "glob_lower_ratio_limit := c(0.999);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_type_given_pole := 1;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_rad_poles[1,1] := c(-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(0.5);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_ord_poles[1,2] := c(0.0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=8;");
omniout_str(ALWAYS, "glob_max_minutes:=(3.0);");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "glob_max_iter:=10000;");
omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);");
omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);");
omniout_str(ALWAYS, "glob_look_poles:=true;");
omniout_str(ALWAYS, "glob_h:=c(0.001);");
omniout_str(ALWAYS, "glob_display_interval:=c(0.01);");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "return(cos(sqrt(c(2.0)*c(x)+c(3.0)))+sqrt(c(2.0)\
*c(x)+c(3.0))*sin(sqrt(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,");
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omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.000 + 0.000 * I ];");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_nxt := glob_nxt + 1;");
omniout_str(ALWAYS, "it := x_delta[glob_nxt];");
omniout_str(ALWAYS, "return it;");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "#END USER DEF BLOCK");
omniout_str(ALWAYS, "#######END OF ECHO OF PROBLEM#################");
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_small_float := glob__0;
glob_smallish_float := glob__0;
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob_almost_1 := c(0.99);
x_start := -1.4 + 0.1*I;
x_end := 99.0 + 99.0*I;
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_h := 0.0001;
glob_upper_ratio_limit := c(1.001);
glob_lower_ratio_limit := c(0.999);
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(0.5);
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 ) = cos ( sqrt ( 2.\
0 * x + 3.0 ) ) ; ");
omniout_int(INFO, "Iterations ", 32, glob_iter,
4, " ");
prog_report(x_start, x_end);
if glob_html_log then
logstart(html_log_file);
logitem_str(html_log_file, "2017-11-26T14:42:02-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"cos_sqrt_lin");
logitem_str(html_log_file, "diff ( y , x , 1 ) = co\
s ( sqrt ( 2.0 * x + 3.0 ) ) ; ");
logitem_complex(html_log_file, x_start);
logitem_complex(html_log_file, x_end);
logitem_complex(html_log_file, array_x[1]);
logitem_complex(html_log_file, glob_h);
logitem_h_reason(html_log_file);
logitem_integer(html_log_file, Digits);
glob_desired_digits_correct := 0.;
logitem_float(html_log_file, glob_desired_digits_correct);
if array_est_digits[1] <> -16 then
logitem_integer(html_log_file, array_est_digits[1])
else logitem_str(html_log_file, "Unknown")
end if;
if glob_min_good_digits <> -16 then
logitem_integer(html_log_file, glob_min_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
if glob_good_digits <> -16 then
logitem_integer(html_log_file, glob_good_digits)
else logitem_str(html_log_file, "Unknown")
end if;
logitem_str(html_log_file, "NA");
logitem_str(html_log_file, "NA");
logitem_integer(html_log_file, ATS_MAX_TERMS);
if glob_type_given_pole = 0 then
logitem_str(html_log_file, "Not Given");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 4 then
logitem_str(html_log_file, "No Solution");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 5 then
logitem_str(html_log_file, "Some Pole");
logitem_str(html_log_file, "????")
elif glob_type_given_pole = 3 then
logitem_str(html_log_file, "No Pole");
logitem_str(html_log_file, "NA")
elif glob_type_given_pole = 1 then
logitem_str(html_log_file, "Real Sing");
logitem_float(html_log_file, glob_least_given_sing)
elif glob_type_given_pole = 2 then
logitem_str(html_log_file, "Complex Sing");
logitem_float(html_log_file, glob_least_given_sing)
end if;
if glob_least_ratio_sing < glob_large_float then
glob_least_ratio_sing := 0;
logitem_float(html_log_file, glob_least_ratio_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_3_sing < glob_large_float then
logitem_float(html_log_file, glob_least_3_sing)
else logitem_str(html_log_file, "NONE")
end if;
if glob_least_6_sing < glob_large_float then
glob_least_6_sing := 0.;
logitem_float(html_log_file, glob_least_6_sing)
else logitem_str(html_log_file, "NONE")
end if;
logitem_integer(html_log_file, glob_iter);
logitem_time(html_log_file, glob_clock_sec);
if c(glob_percent_done) < glob__100 then
logitem_time(html_log_file, glob_total_exp_sec); 0
else logitem_str(html_log_file, "Done"); 0
end if;
log_revs(html_log_file, " 309 | ");
logitem_str(html_log_file, "cos_sqrt_lin diffeq.mxt");
logitem_str(html_log_file, "cos_sqrt_lin maple results");
logitem_str(html_log_file, "Poor Accuracy");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end if
end proc
# End Function number 12
> main();
memory used=3.9MB, alloc=40.3MB, time=0.08
##############ECHO OF PROBLEM#################
##############temp/cos_sqrt_linpostcpx.cpx#################
diff ( y , x , 1 ) = cos ( sqrt ( 2.0 * x + 3.0 ) ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=30;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := -1.4 + 0.1 * I;
x_end := 99.0 + 99.0 * I;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_h := 0.0001;
glob_upper_ratio_limit := c(1.001);
glob_lower_ratio_limit := c(0.999);
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(0.5);
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(cos(sqrt(c(2.0)*c(x)+c(3.0)))+sqrt(c(2.0)*c(x)+c(3.0))*sin(sqrt(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,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.000 + 0.000 * I ];
glob_nxt := glob_nxt + 1;
it := x_delta[glob_nxt];
return it;
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = -1.4 0.1
h = 0.0001 0.005
y[1] (numeric) = 1.09988999683 0.0901111079483
y[1] (closed_form) = 1.09988999683 0.0901111079483
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 0.1414
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3999 0.105
h = 0.0001 0.003
y[1] (numeric) = 1.1004634081 0.094601521103
y[1] (closed_form) = 1.10047550513 0.094600651045
absolute error = 1.213e-05
relative error = 0.001098 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.1451
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=30.8MB, alloc=40.3MB, time=0.44
x[1] = -1.3998 0.108
h = 0.001 0.001
y[1] (numeric) = 1.10085790704 0.0972906183304
y[1] (closed_form) = 1.10087437151 0.0972893274481
absolute error = 1.652e-05
relative error = 0.001494 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.1473
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3988 0.109
h = 0.001 0.003
y[1] (numeric) = 1.10186187209 0.0980857612963
y[1] (closed_form) = 1.10187830804 0.0980835029701
absolute error = 1.659e-05
relative error = 0.0015 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.1487
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3978 0.112
h = 0.0001 0.004
y[1] (numeric) = 1.10307646365 0.100676083871
y[1] (closed_form) = 1.10309665752 0.100670780385
absolute error = 2.088e-05
relative error = 0.001885 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.1516
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3977 0.116
h = 0.003 0.006
y[1] (numeric) = 1.10359902245 0.104255185665
y[1] (closed_form) = 1.10362694456 0.104249200593
absolute error = 2.856e-05
relative error = 0.002576 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.1547
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3947 0.122
h = 0.0001 0.005
y[1] (numeric) = 1.1069630791 0.109302385791
y[1] (closed_form) = 1.10700339631 0.109278511355
absolute error = 4.686e-05
relative error = 0.004212 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.1612
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=76.4MB, alloc=52.3MB, time=1.05
x[1] = -1.3946 0.127
h = 0.0001 0.003
y[1] (numeric) = 1.10764109733 0.11376117394
y[1] (closed_form) = 1.10769355533 0.113736282244
absolute error = 5.806e-05
relative error = 0.005214 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.165
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3945 0.13
h = 0.001 0.001
y[1] (numeric) = 1.10809813477 0.116430318362
y[1] (closed_form) = 1.10815494707 0.116404969063
absolute error = 6.221e-05
relative error = 0.005583 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.1674
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3935 0.131
h = 0.001 0.003
y[1] (numeric) = 1.10911716558 0.117198451878
y[1] (closed_form) = 1.10917394129 0.117172136724
absolute error = 6.258e-05
relative error = 0.005611 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.1688
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3925 0.134
h = 0.0001 0.004
y[1] (numeric) = 1.11038886458 0.119749812795
y[1] (closed_form) = 1.11044936882 0.119720429947
absolute error = 6.726e-05
relative error = 0.006022 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.1718
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3924 0.138
h = 0.003 0.006
y[1] (numeric) = 1.1109948878 0.123302825609
y[1] (closed_form) = 1.11106309966 0.123272703505
absolute error = 7.457e-05
relative error = 0.00667 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.175
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=121.9MB, alloc=52.3MB, time=1.64
x[1] = -1.3894 0.144
h = 0.0001 0.005
y[1] (numeric) = 1.11446691609 0.128250855544
y[1] (closed_form) = 1.11454736281 0.128202777957
absolute error = 9.372e-05
relative error = 0.008354 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.1816
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3893 0.149
h = 0.0001 0.003
y[1] (numeric) = 1.11524921273 0.132677235782
y[1] (closed_form) = 1.11534175878 0.132628050361
absolute error = 0.0001048
relative error = 0.009331 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.1856
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3892 0.152
h = 0.001 0.001
y[1] (numeric) = 1.11576853427 0.135325993553
y[1] (closed_form) = 1.11586542138 0.135276315233
absolute error = 0.0001089
relative error = 0.009687 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.1881
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3882 0.153
h = 0.001 0.003
y[1] (numeric) = 1.11680240392 0.136067050685
y[1] (closed_form) = 1.11689924658 0.13601640828
absolute error = 0.0001093
relative error = 0.009713 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.1895
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3872 0.156
h = 0.0001 0.004
y[1] (numeric) = 1.11813082357 0.138579089825
y[1] (closed_form) = 1.11823136541 0.13852535731
absolute error = 0.000114
relative error = 0.01012 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.1925
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=167.4MB, alloc=52.3MB, time=2.22
x[1] = -1.3871 0.16
h = 0.003 0.006
y[1] (numeric) = 1.11881997585 0.142105434595
y[1] (closed_form) = 1.11892820487 0.142050905814
absolute error = 0.0001212
relative error = 0.01074 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.1958
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3841 0.166
h = 0.0001 0.005
y[1] (numeric) = 1.12239905406 0.146953654034
y[1] (closed_form) = 1.12251935851 0.146881105825
absolute error = 0.0001405
relative error = 0.01241 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.2025
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.384 0.171
h = 0.0001 0.003
y[1] (numeric) = 1.12328521026 0.151346900834
y[1] (closed_form) = 1.12341757487 0.151273156054
absolute error = 0.0001515
relative error = 0.01337 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.2066
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3839 0.174
h = 0.001 0.001
y[1] (numeric) = 1.12386655969 0.153974840121
y[1] (closed_form) = 1.1240032522 0.153900568192
absolute error = 0.0001556
relative error = 0.01371 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.2092
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3829 0.175
h = 0.001 0.003
y[1] (numeric) = 1.12491504124 0.154688755073
y[1] (closed_form) = 1.1250516816 0.154613520947
absolute error = 0.000156
relative error = 0.01374 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.2106
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=213.0MB, alloc=52.3MB, time=2.80
x[1] = -1.3819 0.178
h = 0.0001 0.004
y[1] (numeric) = 1.12629979358 0.157161114407
y[1] (closed_form) = 1.12644010375 0.157082767873
absolute error = 0.0001607
relative error = 0.01413 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.2136
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3818 0.182
h = 0.003 0.006
y[1] (numeric) = 1.12707173744 0.160660214353
y[1] (closed_form) = 1.12721971448 0.160581015003
absolute error = 0.0001678
relative error = 0.01474 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.217
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3788 0.188
h = 0.0001 0.005
y[1] (numeric) = 1.13075694208 0.16540798825
y[1] (closed_form) = 1.13091683581 0.165310707184
absolute error = 0.0001872
relative error = 0.01638 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.2237
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3787 0.193
h = 0.0001 0.003
y[1] (numeric) = 1.13174653681 0.169767379402
y[1] (closed_form) = 1.13191845322 0.169668814145
absolute error = 0.0001982
relative error = 0.01731 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.228
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3786 0.196
h = 0.001 0.001
y[1] (numeric) = 1.13238965624 0.172374070241
y[1] (closed_form) = 1.1325658875 0.172274944344
absolute error = 0.0002022
relative error = 0.01765 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.2306
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=258.6MB, alloc=52.3MB, time=3.38
x[1] = -1.3776 0.197
h = 0.0001 0.004
y[1] (numeric) = 1.13345252273 0.17306077833
y[1] (closed_form) = 1.13362869425 0.172960692204
absolute error = 0.0002026
relative error = 0.01767 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.2319
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3775 0.201
h = 0.003 0.006
y[1] (numeric) = 1.13429580505 0.176536947356
y[1] (closed_form) = 1.1344796144 0.176435959777
absolute error = 0.0002097
relative error = 0.01827 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.2354
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3745 0.207
h = 0.0001 0.005
y[1] (numeric) = 1.13807282569 0.181199005591
y[1] (closed_form) = 1.13826841624 0.181079881885
absolute error = 0.000229
relative error = 0.01987 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.2421
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3744 0.212
h = 0.0001 0.003
y[1] (numeric) = 1.13915153287 0.185529904194
y[1] (closed_form) = 1.13935911588 0.18540942103
absolute error = 0.00024
relative error = 0.02079 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.2464
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3743 0.215
h = 0.001 0.001
y[1] (numeric) = 1.13984787415 0.188118693729
y[1] (closed_form) = 1.14005976125 0.187997621399
absolute error = 0.000244
relative error = 0.02112 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.249
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=304.2MB, alloc=52.3MB, time=3.96
x[1] = -1.3733 0.216
h = 0.001 0.003
y[1] (numeric) = 1.14092326607 0.188782099767
y[1] (closed_form) = 1.14113508696 0.18866006886
absolute error = 0.0002445
relative error = 0.02114 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.2504
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3723 0.219
h = 0.0001 0.004
y[1] (numeric) = 1.14241228649 0.191180338551
y[1] (closed_form) = 1.14262772276 0.191055153717
absolute error = 0.0002492
relative error = 0.02151 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.2535
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3722 0.223
h = 0.003 0.006
y[1] (numeric) = 1.14333772122 0.194628191273
y[1] (closed_form) = 1.14356078733 0.19450204901
absolute error = 0.0002563
relative error = 0.02209 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.257
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3692 0.229
h = 0.0001 0.005
y[1] (numeric) = 1.14721915275 0.19918862462
y[1] (closed_form) = 1.14745384225 0.199044286291
absolute error = 0.0002755
relative error = 0.02366 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.2637
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3691 0.234
h = 0.0001 0.003
y[1] (numeric) = 1.14840051731 0.203484326504
y[1] (closed_form) = 1.1486471638 0.203338542244
absolute error = 0.0002865
relative error = 0.02456 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.2681
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.369 0.237
h = 0.001 0.001
y[1] (numeric) = 1.14915814947 0.206051069103
y[1] (closed_form) = 1.14940908717 0.205904663129
absolute error = 0.0002905
relative error = 0.02488 %
Correct digits = 4
memory used=349.8MB, alloc=52.3MB, time=4.54
Radius of convergence (given) for eq 1 = 0.2708
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.368 0.238
h = 0.001 0.003
y[1] (numeric) = 1.15024750467 0.206687148115
y[1] (closed_form) = 1.15049836873 0.206539785631
absolute error = 0.0002909
relative error = 0.02489 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.2722
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.367 0.241
h = 0.0001 0.004
y[1] (numeric) = 1.15179174567 0.209044689717
y[1] (closed_form) = 1.15204619567 0.208894151363
absolute error = 0.0002956
relative error = 0.02525 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.2753
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3669 0.245
h = 0.003 0.006
y[1] (numeric) = 1.15279900144 0.212463655552
y[1] (closed_form) = 1.15306106099 0.212312104029
absolute error = 0.0003027
relative error = 0.02582 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.2788
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3639 0.251
h = 0.0001 0.005
y[1] (numeric) = 1.15678391542 0.216921843149
y[1] (closed_form) = 1.15705744085 0.216752036658
absolute error = 0.0003219
relative error = 0.02735 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.2855
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3638 0.256
h = 0.0001 0.003
y[1] (numeric) = 1.15806750944 0.221181634294
y[1] (closed_form) = 1.15835295706 0.221010295757
absolute error = 0.0003329
relative error = 0.02823 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.29
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=395.4MB, alloc=52.3MB, time=5.12
x[1] = -1.3637 0.259
h = 0.001 0.001
y[1] (numeric) = 1.15888616995 0.223725904924
y[1] (closed_form) = 1.15917589595 0.22355391248
absolute error = 0.0003369
relative error = 0.02854 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.2927
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3627 0.26
h = 0.001 0.003
y[1] (numeric) = 1.15998926136 0.224334595331
y[1] (closed_form) = 1.16027890638 0.224161648486
absolute error = 0.0003373
relative error = 0.02855 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.294
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3617 0.263
h = 0.0001 0.004
y[1] (numeric) = 1.16158833048 0.226651089775
y[1] (closed_form) = 1.16188153193 0.226474945249
absolute error = 0.000342
relative error = 0.02889 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.2971
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3616 0.267
h = 0.003 0.006
y[1] (numeric) = 1.1626770615 0.230040600281
y[1] (closed_form) = 1.16297785212 0.229863387046
absolute error = 0.0003491
relative error = 0.02945 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.3007
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3586 0.273
h = 0.0001 0.005
y[1] (numeric) = 1.16676452771 0.234395926107
y[1] (closed_form) = 1.16707662699 0.234200399949
absolute error = 0.0003683
relative error = 0.03094 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 0.3074
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=441.0MB, alloc=52.3MB, time=5.70
x[1] = -1.3585 0.278
h = 0.0001 0.003
y[1] (numeric) = 1.16814992075 0.238619095196
y[1] (closed_form) = 1.16847390787 0.238421951157
absolute error = 0.0003793
relative error = 0.0318 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3119
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3584 0.281
h = 0.001 0.001
y[1] (numeric) = 1.1690293455 0.241140470487
y[1] (closed_form) = 1.1693575982 0.240942640637
absolute error = 0.0003833
relative error = 0.0321 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3147
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3574 0.282
h = 0.001 0.003
y[1] (numeric) = 1.17014594602 0.24172171179
y[1] (closed_form) = 1.17047411045 0.241522929679
absolute error = 0.0003837
relative error = 0.0321 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.316
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3564 0.285
h = 0.0001 0.004
y[1] (numeric) = 1.17179944964 0.243996811193
y[1] (closed_form) = 1.17213114094 0.243794809729
absolute error = 0.0003884
relative error = 0.03244 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3191
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3563 0.289
h = 0.003 0.006
y[1] (numeric) = 1.17296930796 0.247356300059
y[1] (closed_form) = 1.17330856795 0.247153174528
absolute error = 0.0003954
relative error = 0.03298 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3228
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=486.6MB, alloc=52.3MB, time=6.28
x[1] = -1.3533 0.295
h = 0.0001 0.005
y[1] (numeric) = 1.17715839448 0.251608152907
y[1] (closed_form) = 1.17750880612 0.251386657389
absolute error = 0.0004145
relative error = 0.03443 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3295
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3532 0.3
h = 0.0001 0.003
y[1] (numeric) = 1.17864515352 0.255793991301
y[1] (closed_form) = 1.17900741893 0.255570792296
absolute error = 0.0004255
relative error = 0.03527 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.334
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3531 0.303
h = 0.001 0.001
y[1] (numeric) = 1.17958507679 0.258292049532
y[1] (closed_form) = 1.17995159499 0.258068133052
absolute error = 0.0004295
relative error = 0.03556 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3367
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3521 0.304
h = 0.0001 0.004
y[1] (numeric) = 1.18071495929 0.258845782301
y[1] (closed_form) = 1.18108138199 0.258620915733
absolute error = 0.0004299
relative error = 0.03556 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3381
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.352 0.308
h = 0.003 0.006
y[1] (numeric) = 1.18195474407 0.262179937223
y[1] (closed_form) = 1.1823287101 0.261953899991
absolute error = 0.000437
relative error = 0.03608 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3417
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=532.2MB, alloc=52.3MB, time=6.87
x[1] = -1.349 0.314
h = 0.0001 0.005
y[1] (numeric) = 1.18623179677 0.266343433565
y[1] (closed_form) = 1.18661678008 0.266098976042
absolute error = 0.000456
relative error = 0.0375 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3484
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3489 0.319
h = 0.0001 0.003
y[1] (numeric) = 1.18780591568 0.270497773919
y[1] (closed_form) = 1.1882027246 0.270251538983
absolute error = 0.000467
relative error = 0.03832 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.353
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3488 0.322
h = 0.001 0.001
y[1] (numeric) = 1.18879798462 0.272976141469
y[1] (closed_form) = 1.1891990357 0.272729161817
absolute error = 0.000471
relative error = 0.0386 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3557
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3478 0.323
h = 0.001 0.003
y[1] (numeric) = 1.18993944653 0.273506303572
y[1] (closed_form) = 1.19034039589 0.273258375641
absolute error = 0.0004714
relative error = 0.0386 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3571
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3468 0.326
h = 0.0001 0.004
y[1] (numeric) = 1.19169369127 0.275704095052
y[1] (closed_form) = 1.19209811259 0.275452907459
absolute error = 0.0004761
relative error = 0.03891 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3602
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=577.8MB, alloc=52.3MB, time=7.44
x[1] = -1.3467 0.33
h = 0.003 0.006
y[1] (numeric) = 1.1930139486 0.279007177189
y[1] (closed_form) = 1.19342590081 0.278754762718
absolute error = 0.0004831
relative error = 0.03942 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3639
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3437 0.336
h = 0.0001 0.005
y[1] (numeric) = 1.19739089006 0.283066064848
y[1] (closed_form) = 1.19781370277 0.282795174582
absolute error = 0.0005021
relative error = 0.0408 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3706
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3436 0.341
h = 0.0001 0.003
y[1] (numeric) = 1.19906557068 0.287181757747
y[1] (closed_form) = 1.19950017518 0.28690900483
absolute error = 0.0005131
relative error = 0.0416 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3752
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3435 0.344
h = 0.001 0.001
y[1] (numeric) = 1.20011764445 0.28963602466
y[1] (closed_form) = 1.20055647829 0.289362495726
absolute error = 0.0005171
relative error = 0.04187 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3779
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3425 0.345
h = 0.001 0.003
y[1] (numeric) = 1.2012719663 0.290138567793
y[1] (closed_form) = 1.20171069127 0.289864092808
absolute error = 0.0005175
relative error = 0.04186 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3793
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=623.5MB, alloc=52.3MB, time=8.02
x[1] = -1.3415 0.348
h = 0.0001 0.004
y[1] (numeric) = 1.20307951723 0.292293975885
y[1] (closed_form) = 1.20352168443 0.292016219968
absolute error = 0.0005222
relative error = 0.04216 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3824
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3414 0.352
h = 0.003 0.006
y[1] (numeric) = 1.20447990129 0.295565423833
y[1] (closed_form) = 1.2049295785 0.295286386146
absolute error = 0.0005292
relative error = 0.04266 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3861
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3384 0.358
h = 0.0001 0.005
y[1] (numeric) = 1.20895579461 0.299519105282
y[1] (closed_form) = 1.20941617563 0.299221537102
absolute error = 0.0005482
relative error = 0.044 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3928
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3383 0.363
h = 0.0001 0.003
y[1] (numeric) = 1.21073059643 0.303595449664
y[1] (closed_form) = 1.21120273543 0.303295933774
absolute error = 0.0005591
relative error = 0.04478 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.3974
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3382 0.366
h = 0.001 0.001
y[1] (numeric) = 1.21184240476 0.306025198876
y[1] (closed_form) = 1.21231876024 0.305724875832
absolute error = 0.0005631
relative error = 0.04504 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4002
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=669.1MB, alloc=52.3MB, time=8.60
x[1] = -1.3372 0.367
h = 0.001 0.003
y[1] (numeric) = 1.21300935933 0.306500066672
y[1] (closed_form) = 1.21348559881 0.306198799834
absolute error = 0.0005635
relative error = 0.04503 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4015
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3362 0.37
h = 0.0001 0.004
y[1] (numeric) = 1.21486981841 0.308612751595
y[1] (closed_form) = 1.21534947033 0.308308182701
absolute error = 0.0005682
relative error = 0.04531 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4046
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3361 0.374
h = 0.003 0.006
y[1] (numeric) = 1.21634997298 0.311852007252
y[1] (closed_form) = 1.21683711387 0.311546101847
absolute error = 0.0005752
relative error = 0.0458 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4083
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3331 0.38
h = 0.0001 0.005
y[1] (numeric) = 1.22092387952 0.315699889742
y[1] (closed_form) = 1.2214215676 0.315375399935
absolute error = 0.0005941
relative error = 0.0471 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.415
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.333 0.385
h = 0.0001 0.003
y[1] (numeric) = 1.2227983594 0.319736187202
y[1] (closed_form) = 1.22330777161 0.319409664805
absolute error = 0.0006051
relative error = 0.04786 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4197
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=715.0MB, alloc=52.3MB, time=9.18
x[1] = -1.3329 0.388
h = 0.001 0.001
y[1] (numeric) = 1.22396963044 0.322141003279
y[1] (closed_form) = 1.22448324623 0.321813642742
absolute error = 0.0006091
relative error = 0.04811 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4225
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3319 0.389
h = 0.001 0.003
y[1] (numeric) = 1.22514899048 0.32258814044
y[1] (closed_form) = 1.22566248319 0.322259838394
absolute error = 0.0006095
relative error = 0.04809 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4238
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3309 0.392
h = 0.0001 0.004
y[1] (numeric) = 1.22706195855 0.324657764522
y[1] (closed_form) = 1.22757883385 0.32432613944
absolute error = 0.0006141
relative error = 0.04837 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4269
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3308 0.396
h = 0.003 0.006
y[1] (numeric) = 1.22862152527 0.327864271923
y[1] (closed_form) = 1.22914586831 0.327531255742
absolute error = 0.0006212
relative error = 0.04883 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4306
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3278 0.402
h = 0.0001 0.005
y[1] (numeric) = 1.23329250474 0.331605767482
y[1] (closed_form) = 1.23382723838 0.331254113768
absolute error = 0.00064
relative error = 0.0501 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4373
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=760.7MB, alloc=52.3MB, time=9.76
x[1] = -1.3277 0.407
h = 0.0001 0.003
y[1] (numeric) = 1.2352662169 0.335601322276
y[1] (closed_form) = 1.23581264073 0.33524755127
absolute error = 0.0006509
relative error = 0.05084 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.442
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3276 0.41
h = 0.001 0.001
y[1] (numeric) = 1.23649667723 0.337980791418
y[1] (closed_form) = 1.23704729167 0.337626151424
absolute error = 0.0006549
relative error = 0.05108 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4448
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3266 0.411
h = 0.0001 0.004
y[1] (numeric) = 1.23768821546 0.338400143714
y[1] (closed_form) = 1.23823869978 0.338044564521
absolute error = 0.0006553
relative error = 0.05106 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4461
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3265 0.415
h = 0.003 0.006
y[1] (numeric) = 1.23931625415 0.341578957617
y[1] (closed_form) = 1.2398741823 0.341221941638
absolute error = 0.0006624
relative error = 0.05151 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4498
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3235 0.421
h = 0.0001 0.005
y[1] (numeric) = 1.24407131321 0.345229552724
y[1] (closed_form) = 1.24463949783 0.34485385223
absolute error = 0.0006812
relative error = 0.05274 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4565
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=806.4MB, alloc=52.3MB, time=10.35
x[1] = -1.3234 0.426
h = 0.0001 0.003
y[1] (numeric) = 1.2461305788 0.349190657271
y[1] (closed_form) = 1.24671042529 0.348812766314
absolute error = 0.0006921
relative error = 0.05346 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4612
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3233 0.429
h = 0.001 0.001
y[1] (numeric) = 1.24741207574 0.351548679101
y[1] (closed_form) = 1.24799610201 0.35116989255
absolute error = 0.0006961
relative error = 0.05369 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.464
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3223 0.43
h = 0.001 0.003
y[1] (numeric) = 1.2486142464 0.351944213881
y[1] (closed_form) = 1.24919813645 0.35156449006
absolute error = 0.0006965
relative error = 0.05367 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4653
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3213 0.433
h = 0.0001 0.004
y[1] (numeric) = 1.25062437761 0.35393343449
y[1] (closed_form) = 1.25121159479 0.353550348631
absolute error = 0.0007011
relative error = 0.05392 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4684
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3212 0.437
h = 0.003 0.006
y[1] (numeric) = 1.25233115641 0.357078468439
y[1] (closed_form) = 1.25292580201 0.356693890044
absolute error = 0.0007082
relative error = 0.05436 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4722
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3182 0.443
h = 0.0001 0.005
y[1] (numeric) = 1.25718154109 0.360621583997
y[1] (closed_form) = 1.2577862866 0.360218269386
absolute error = 0.0007269
relative error = 0.05556 %
Correct digits = 3
memory used=852.2MB, alloc=52.3MB, time=10.93
Radius of convergence (given) for eq 1 = 0.4789
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3181 0.448
h = 0.0001 0.003
y[1] (numeric) = 1.25933921071 0.364540652981
y[1] (closed_form) = 1.25995558389 0.364135063538
absolute error = 0.0007378
relative error = 0.05626 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4835
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.318 0.451
h = 0.001 0.001
y[1] (numeric) = 1.26067938886 0.366872558932
y[1] (closed_form) = 1.26129992872 0.366466043281
absolute error = 0.0007418
relative error = 0.05648 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4863
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.317 0.452
h = 0.001 0.003
y[1] (numeric) = 1.26189331539 0.367240208068
y[1] (closed_form) = 1.26251371204 0.366832757508
absolute error = 0.0007422
relative error = 0.05646 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4876
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.316 0.455
h = 0.0001 0.004
y[1] (numeric) = 1.26395481152 0.369185408688
y[1] (closed_form) = 1.26457850525 0.368774575534
absolute error = 0.0007468
relative error = 0.0567 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4908
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3159 0.459
h = 0.003 0.006
y[1] (numeric) = 1.26573997214 0.372296111406
y[1] (closed_form) = 1.26637107255 0.371883731552
absolute error = 0.0007539
relative error = 0.05712 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.4945
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=897.9MB, alloc=52.3MB, time=11.51
x[1] = -1.3129 0.465
h = 0.0001 0.005
y[1] (numeric) = 1.2706847373 0.375731173088
y[1] (closed_form) = 1.27132578107 0.375300006073
absolute error = 0.0007726
relative error = 0.05828 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5012
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3128 0.47
h = 0.0001 0.003
y[1] (numeric) = 1.27294035764 0.379607518377
y[1] (closed_form) = 1.27359299469 0.379173992347
absolute error = 0.0007835
relative error = 0.05896 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5059
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3127 0.473
h = 0.001 0.001
y[1] (numeric) = 1.27433893907 0.381912899305
y[1] (closed_form) = 1.27499572964 0.381478416571
absolute error = 0.0007875
relative error = 0.05917 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5087
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3117 0.474
h = 0.001 0.003
y[1] (numeric) = 1.27556439416 0.382252611614
y[1] (closed_form) = 1.27622103453 0.381817196359
absolute error = 0.0007879
relative error = 0.05915 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.51
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3107 0.477
h = 0.0001 0.004
y[1] (numeric) = 1.27767685175 0.384153462717
y[1] (closed_form) = 1.27833675913 0.383714644462
absolute error = 0.0007925
relative error = 0.05938 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5132
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=943.6MB, alloc=52.3MB, time=12.08
x[1] = -1.3106 0.481
h = 0.003 0.006
y[1] (numeric) = 1.27954002767 0.387229286522
y[1] (closed_form) = 1.28020731978 0.38678886755
absolute error = 0.0007995
relative error = 0.05978 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5169
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3076 0.487
h = 0.0001 0.005
y[1] (numeric) = 1.28457822652 0.390555724773
y[1] (closed_form) = 1.28525530543 0.390096468453
absolute error = 0.0008181
relative error = 0.06091 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5236
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3075 0.492
h = 0.0001 0.003
y[1] (numeric) = 1.28693134165 0.39438866092
y[1] (closed_form) = 1.28761997925 0.393926961589
absolute error = 0.0008291
relative error = 0.06157 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5283
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3074 0.495
h = 0.001 0.001
y[1] (numeric) = 1.28838804689 0.39666710932
y[1] (closed_form) = 1.28908082475 0.3962044229
absolute error = 0.0008331
relative error = 0.06177 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5311
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3064 0.496
h = 0.001 0.003
y[1] (numeric) = 1.28962480319 0.396978834685
y[1] (closed_form) = 1.29031742391 0.396515218161
absolute error = 0.0008335
relative error = 0.06174 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5324
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=989.4MB, alloc=52.3MB, time=12.67
x[1] = -1.3054 0.499
h = 0.0001 0.004
y[1] (numeric) = 1.29178781773 0.39883500886
y[1] (closed_form) = 1.2924836753 0.398367969078
absolute error = 0.0008381
relative error = 0.06196 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5356
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3053 0.503
h = 0.003 0.006
y[1] (numeric) = 1.29372864033 0.401875408231
y[1] (closed_form) = 1.2944318605 0.401406713864
absolute error = 0.0008451
relative error = 0.06236 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5394
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3023 0.509
h = 0.0001 0.005
y[1] (numeric) = 1.29885932445 0.405092658276
y[1] (closed_form) = 1.29957217486 0.404605077129
absolute error = 0.0008636
relative error = 0.06345 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.546
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3022 0.514
h = 0.0001 0.003
y[1] (numeric) = 1.30130947583 0.408881502524
y[1] (closed_form) = 1.30203385011 0.40839139456
absolute error = 0.0008746
relative error = 0.06409 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5507
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.3021 0.517
h = 0.001 0.001
y[1] (numeric) = 1.30282402385 0.411132612532
y[1] (closed_form) = 1.30355252506 0.410641487203
absolute error = 0.0008786
relative error = 0.06429 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5536
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1035.2MB, alloc=52.3MB, time=13.26
x[1] = -1.3011 0.518
h = 0.0001 0.004
y[1] (numeric) = 1.30407185402 0.411416301901
y[1] (closed_form) = 1.30480019116 0.41092424891
absolute error = 0.000879
relative error = 0.06425 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5549
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.301 0.522
h = 0.003 0.006
y[1] (numeric) = 1.30607965113 0.414426691344
y[1] (closed_form) = 1.30681532747 0.413932938738
absolute error = 0.000886
relative error = 0.06463 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5586
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.298 0.528
h = 0.0001 0.005
y[1] (numeric) = 1.31129049249 0.417550593494
y[1] (closed_form) = 1.31203566488 0.417037910291
absolute error = 0.0009045
relative error = 0.0657 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5653
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2979 0.533
h = 0.0001 0.003
y[1] (numeric) = 1.31382433651 0.421302088642
y[1] (closed_form) = 1.31458100361 0.420786806223
absolute error = 0.0009155
relative error = 0.06632 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.57
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2978 0.536
h = 0.001 0.001
y[1] (numeric) = 1.31538877964 0.423530027363
y[1] (closed_form) = 1.31614956248 0.423013701444
absolute error = 0.0009194
relative error = 0.06651 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5729
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1080.9MB, alloc=52.3MB, time=13.84
x[1] = -1.2968 0.537
h = 0.001 0.003
y[1] (numeric) = 1.31664629453 0.423789674038
y[1] (closed_form) = 1.31740690733 0.423272422499
absolute error = 0.0009198
relative error = 0.06647 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5742
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2958 0.54
h = 0.0001 0.004
y[1] (numeric) = 1.31890284471 0.425562441523
y[1] (closed_form) = 1.31966663832 0.425041729074
absolute error = 0.0009244
relative error = 0.06668 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5773
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2957 0.544
h = 0.003 0.006
y[1] (numeric) = 1.32098759866 0.428536394258
y[1] (closed_form) = 1.32175871378 0.428013927115
absolute error = 0.0009314
relative error = 0.06704 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5811
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2927 0.55
h = 0.0001 0.005
y[1] (numeric) = 1.32628916282 0.431550058665
y[1] (closed_form) = 1.32706961737 0.431008612887
absolute error = 0.0009499
relative error = 0.06808 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5878
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2926 0.555
h = 0.0001 0.003
y[1] (numeric) = 1.328919191 0.435256193108
y[1] (closed_form) = 1.32971110501 0.43471206467
absolute error = 0.0009608
relative error = 0.06868 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5925
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1126.6MB, alloc=52.3MB, time=14.42
x[1] = -1.2925 0.558
h = 0.001 0.001
y[1] (numeric) = 1.33054095466 0.437456039209
y[1] (closed_form) = 1.3313369709 0.43691083719
absolute error = 0.0009648
relative error = 0.06886 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5953
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2915 0.559
h = 0.001 0.003
y[1] (numeric) = 1.33180912094 0.437687558731
y[1] (closed_form) = 1.33260496026 0.437141433585
absolute error = 0.0009652
relative error = 0.06882 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5966
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2905 0.562
h = 0.0001 0.004
y[1] (numeric) = 1.33411506871 0.439414719491
y[1] (closed_form) = 1.33491405852 0.438865113611
absolute error = 0.0009698
relative error = 0.06901 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.5998
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2904 0.566
h = 0.003 0.006
y[1] (numeric) = 1.33627640973 0.442351694704
y[1] (closed_form) = 1.33708269834 0.441800280683
absolute error = 0.0009768
relative error = 0.06937 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6036
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2874 0.572
h = 0.0001 0.005
y[1] (numeric) = 1.34166774364 0.44525457025
y[1] (closed_form) = 1.34248321505 0.444684130303
absolute error = 0.0009952
relative error = 0.07037 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6102
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1172.4MB, alloc=52.3MB, time=15.01
x[1] = -1.2873 0.577
h = 0.0001 0.003
y[1] (numeric) = 1.34439348999 0.448914668928
y[1] (closed_form) = 1.34522038534 0.44834146308
absolute error = 0.001006
relative error = 0.07096 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.615
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2872 0.58
h = 0.001 0.001
y[1] (numeric) = 1.34607228873 0.451086021243
y[1] (closed_form) = 1.34690327271 0.450511711833
absolute error = 0.00101
relative error = 0.07112 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6178
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2862 0.581
h = 0.001 0.003
y[1] (numeric) = 1.34735087906 0.451289367598
y[1] (closed_form) = 1.34818167925 0.450714137581
absolute error = 0.001011
relative error = 0.07109 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6191
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2852 0.584
h = 0.0001 0.004
y[1] (numeric) = 1.34970581576 0.452970602404
y[1] (closed_form) = 1.35053973604 0.452391871979
absolute error = 0.001015
relative error = 0.07127 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6222
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2851 0.588
h = 0.003 0.006
y[1] (numeric) = 1.3519433672 0.455870062947
y[1] (closed_form) = 1.35278456338 0.455289471087
absolute error = 0.001022
relative error = 0.07161 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.626
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1218.1MB, alloc=52.3MB, time=15.59
x[1] = -1.2821 0.594
h = 0.0001 0.005
y[1] (numeric) = 1.35742351623 0.458661603295
y[1] (closed_form) = 1.35827373855 0.458061938964
absolute error = 0.00104
relative error = 0.07258 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6327
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.282 0.599
h = 0.0001 0.003
y[1] (numeric) = 1.36024451218 0.462274993868
y[1] (closed_form) = 1.36110612267 0.461672480596
absolute error = 0.001051
relative error = 0.07315 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6374
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2819 0.602
h = 0.001 0.001
y[1] (numeric) = 1.36198005903 0.464417452883
y[1] (closed_form) = 1.36284574445 0.463813806171
absolute error = 0.001055
relative error = 0.07331 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6403
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2809 0.603
h = 0.001 0.003
y[1] (numeric) = 1.36326884606 0.464592581117
y[1] (closed_form) = 1.36413434085 0.463988016344
absolute error = 0.001056
relative error = 0.07327 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6416
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2799 0.606
h = 0.0001 0.004
y[1] (numeric) = 1.36567236196 0.466227572867
y[1] (closed_form) = 1.3665409464 0.465619488166
absolute error = 0.00106
relative error = 0.07344 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6447
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1263.8MB, alloc=52.3MB, time=16.18
x[1] = -1.2798 0.61
h = 0.003 0.006
y[1] (numeric) = 1.36798574514 0.469088983781
y[1] (closed_form) = 1.36886158234 0.468478984499
absolute error = 0.001067
relative error = 0.07377 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6485
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2768 0.616
h = 0.0001 0.005
y[1] (numeric) = 1.37355375311 0.471768647381
y[1] (closed_form) = 1.37443845979 0.471139529827
absolute error = 0.001086
relative error = 0.07472 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6552
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2767 0.621
h = 0.0001 0.003
y[1] (numeric) = 1.37646952753 0.475334660225
y[1] (closed_form) = 1.37736558632 0.474702610898
absolute error = 0.001097
relative error = 0.07527 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6599
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2766 0.624
h = 0.001 0.001
y[1] (numeric) = 1.37826153399 0.477447828085
y[1] (closed_form) = 1.3791616539 0.476814615539
absolute error = 0.001101
relative error = 0.07542 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6628
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2756 0.625
h = 0.0001 0.004
y[1] (numeric) = 1.37956029038 0.477594694305
y[1] (closed_form) = 1.38046021285 0.476960566272
absolute error = 0.001101
relative error = 0.07538 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6641
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2755 0.629
h = 0.003 0.006
y[1] (numeric) = 1.38193910797 0.480423822319
y[1] (closed_form) = 1.38284625985 0.479787735269
absolute error = 0.001108
relative error = 0.07569 %
Correct digits = 3
memory used=1309.6MB, alloc=52.3MB, time=16.76
Radius of convergence (given) for eq 1 = 0.6679
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2725 0.635
h = 0.0001 0.005
y[1] (numeric) = 1.3875833165 0.483007787183
y[1] (closed_form) = 1.3884992035 0.482352541167
absolute error = 0.001126
relative error = 0.07661 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6745
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2724 0.64
h = 0.0001 0.003
y[1] (numeric) = 1.39058086901 0.486533606041
y[1] (closed_form) = 1.39150807785 0.485875356686
absolute error = 0.001137
relative error = 0.07715 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6793
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2723 0.643
h = 0.001 0.001
y[1] (numeric) = 1.39242159717 0.488621911568
y[1] (closed_form) = 1.39335285553 0.487962473274
absolute error = 0.001141
relative error = 0.07729 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6821
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2713 0.644
h = 0.001 0.003
y[1] (numeric) = 1.39372909017 0.488744531519
y[1] (closed_form) = 1.3946601452 0.488084179893
absolute error = 0.001141
relative error = 0.07725 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6834
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2703 0.647
h = 0.0001 0.004
y[1] (numeric) = 1.39622246626 0.490293206153
y[1] (closed_form) = 1.39715655436 0.489629298317
absolute error = 0.001146
relative error = 0.07741 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6866
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1355.3MB, alloc=52.3MB, time=17.33
x[1] = -1.2702 0.651
h = 0.003 0.006
y[1] (numeric) = 1.39867640785 0.493083291841
y[1] (closed_form) = 1.39961770578 0.492417370653
absolute error = 0.001153
relative error = 0.07771 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.6904
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2672 0.657
h = 0.0001 0.005
y[1] (numeric) = 1.40440669835 0.49555437356
y[1] (closed_form) = 1.40535657465 0.494869248989
absolute error = 0.001171
relative error = 0.07861 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.697
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2671 0.662
h = 0.0001 0.003
y[1] (numeric) = 1.40749815375 0.499031570262
y[1] (closed_form) = 1.40845931532 0.498343359908
absolute error = 0.001182
relative error = 0.07912 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7018
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.267 0.665
h = 0.001 0.001
y[1] (numeric) = 1.40939480535 0.501089845263
y[1] (closed_form) = 1.41036000245 0.50040041637
absolute error = 0.001186
relative error = 0.07926 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7046
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.266 0.666
h = 0.001 0.003
y[1] (numeric) = 1.41071184522 0.501184121635
y[1] (closed_form) = 1.41167683222 0.500493782035
absolute error = 0.001186
relative error = 0.07922 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7059
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1401.2MB, alloc=52.3MB, time=17.91
x[1] = -1.265 0.669
h = 0.0001 0.004
y[1] (numeric) = 1.41325262639 0.502685652903
y[1] (closed_form) = 1.41422061583 0.501991738009
absolute error = 0.001191
relative error = 0.07937 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7091
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2649 0.673
h = 0.003 0.006
y[1] (numeric) = 1.41578131135 0.505436166096
y[1] (closed_form) = 1.41675648693 0.504740185135
absolute error = 0.001198
relative error = 0.07966 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7129
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2619 0.679
h = 0.0001 0.005
y[1] (numeric) = 1.42159672322 0.507793836796
y[1] (closed_form) = 1.4225803204 0.507078608777
absolute error = 0.001216
relative error = 0.08053 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7195
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2618 0.684
h = 0.0001 0.003
y[1] (numeric) = 1.42478160305 0.511221749509
y[1] (closed_form) = 1.42577644862 0.510503353478
absolute error = 0.001227
relative error = 0.08103 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7243
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2617 0.687
h = 0.001 0.001
y[1] (numeric) = 1.42673388526 0.513249600873
y[1] (closed_form) = 1.42773275228 0.5125299568
absolute error = 0.001231
relative error = 0.08116 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7272
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1447.0MB, alloc=52.3MB, time=18.49
x[1] = -1.2607 0.688
h = 0.001 0.003
y[1] (numeric) = 1.4280602447 0.513315492801
y[1] (closed_form) = 1.42905889485 0.512594940673
absolute error = 0.001231
relative error = 0.08111 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7284
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2597 0.691
h = 0.0001 0.004
y[1] (numeric) = 1.43064801723 0.51476957182
y[1] (closed_form) = 1.43164963915 0.514045425465
absolute error = 0.001236
relative error = 0.08125 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7316
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2596 0.695
h = 0.003 0.006
y[1] (numeric) = 1.43325105899 0.517479986026
y[1] (closed_form) = 1.43425984313 0.516753721041
absolute error = 0.001243
relative error = 0.08154 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7354
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2566 0.701
h = 0.0001 0.005
y[1] (numeric) = 1.43915063014 0.519723722622
y[1] (closed_form) = 1.44016767908 0.518978167646
absolute error = 0.001261
relative error = 0.08238 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7421
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2565 0.706
h = 0.0001 0.003
y[1] (numeric) = 1.44242845341 0.523101692261
y[1] (closed_form) = 1.44345671359 0.52235288726
absolute error = 0.001272
relative error = 0.08286 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7468
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1492.9MB, alloc=52.3MB, time=19.08
x[1] = -1.2564 0.709
h = 0.001 0.001
y[1] (numeric) = 1.44443607189 0.525098728546
y[1] (closed_form) = 1.44546833932 0.524348646098
absolute error = 0.001276
relative error = 0.08299 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7497
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2554 0.71
h = 0.001 0.003
y[1] (numeric) = 1.44577152362 0.525136196223
y[1] (closed_form) = 1.44680356744 0.524385208397
absolute error = 0.001276
relative error = 0.08294 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.751
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2544 0.713
h = 0.0001 0.004
y[1] (numeric) = 1.44840587278 0.526542516246
y[1] (closed_form) = 1.44944085763 0.525787915416
absolute error = 0.001281
relative error = 0.08307 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7541
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2543 0.717
h = 0.003 0.006
y[1] (numeric) = 1.45108288274 0.529212307182
y[1] (closed_form) = 1.45212500571 0.528455535311
absolute error = 0.001288
relative error = 0.08334 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7579
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2513 0.723
h = 0.0001 0.005
y[1] (numeric) = 1.45706564962 0.53134159138
y[1] (closed_form) = 1.45811588055 0.530565487326
absolute error = 0.001306
relative error = 0.08416 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7646
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1538.7MB, alloc=52.3MB, time=19.66
x[1] = -1.2512 0.728
h = 0.0001 0.003
y[1] (numeric) = 1.46043593281 0.534668961611
y[1] (closed_form) = 1.46149733753 0.533889525739
absolute error = 0.001317
relative error = 0.08463 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7693
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2511 0.731
h = 0.001 0.001
y[1] (numeric) = 1.46249859174 0.536634793052
y[1] (closed_form) = 1.46356398941 0.535854050422
absolute error = 0.001321
relative error = 0.08475 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7722
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2501 0.732
h = 0.0001 0.004
y[1] (numeric) = 1.4638429085 0.536643797727
y[1] (closed_form) = 1.46490807585 0.535862152423
absolute error = 0.001321
relative error = 0.0847 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7735
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.25 0.736
h = 0.003 0.006
y[1] (numeric) = 1.46658377078 0.539279076709
y[1] (closed_form) = 1.46765605264 0.538495216514
absolute error = 0.001328
relative error = 0.08496 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7773
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.247 0.742
h = 0.0001 0.005
y[1] (numeric) = 1.47263874872 0.5413104081
y[1] (closed_form) = 1.47371900403 0.54050717813
absolute error = 0.001346
relative error = 0.08576 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7839
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1584.6MB, alloc=52.3MB, time=20.25
x[1] = -1.2469 0.747
h = 0.0001 0.003
y[1] (numeric) = 1.47608884254 0.544594794076
y[1] (closed_form) = 1.47718024013 0.543788161608
absolute error = 0.001357
relative error = 0.08622 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7887
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2468 0.75
h = 0.001 0.001
y[1] (numeric) = 1.47819901844 0.546534105412
y[1] (closed_form) = 1.47929439692 0.545726140861
absolute error = 0.001361
relative error = 0.08632 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7916
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2458 0.751
h = 0.001 0.003
y[1] (numeric) = 1.47955112363 0.546518681774
y[1] (closed_form) = 1.480646266 0.54570981682
absolute error = 0.001361
relative error = 0.08628 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7929
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2448 0.754
h = 0.0001 0.004
y[1] (numeric) = 1.48227161119 0.547835867465
y[1] (closed_form) = 1.48336963748 0.547023354607
absolute error = 0.001366
relative error = 0.0864 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.796
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2447 0.758
h = 0.0001 0.004
y[1] (numeric) = 1.48508571617 0.550429550258
y[1] (closed_form) = 1.48619083575 0.549614768952
absolute error = 0.001373
relative error = 0.08665 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.7998
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1630.4MB, alloc=52.3MB, time=20.83
x[1] = -1.2446 0.762
h = 0.003 0.006
y[1] (numeric) = 1.48791399758 0.553018695118
y[1] (closed_form) = 1.48902621114 0.552201637583
absolute error = 0.00138
relative error = 0.0869 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.8037
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2416 0.768
h = 0.0001 0.005
y[1] (numeric) = 1.49406865116 0.554917603162
y[1] (closed_form) = 1.49518865565 0.554081122236
absolute error = 0.001398
relative error = 0.08767 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.8103
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2415 0.773
h = 0.0001 0.003
y[1] (numeric) = 1.49762802485 0.558144531049
y[1] (closed_form) = 1.49875913003 0.557304550776
absolute error = 0.001409
relative error = 0.08811 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.8151
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2414 0.776
h = 0.001 0.001
y[1] (numeric) = 1.49980327582 0.560048368731
y[1] (closed_form) = 1.50093834595 0.559207021671
absolute error = 0.001413
relative error = 0.08821 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.818
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2404 0.777
h = 0.001 0.003
y[1] (numeric) = 1.50116632002 0.559999780907
y[1] (closed_form) = 1.50230114609 0.55915753643
absolute error = 0.001413
relative error = 0.08816 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.8192
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1676.1MB, alloc=52.3MB, time=21.42
x[1] = -1.2394 0.78
h = 0.0001 0.004
y[1] (numeric) = 1.50394181215 0.561261573284
y[1] (closed_form) = 1.50507948657 0.560415658262
absolute error = 0.001418
relative error = 0.08827 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.8224
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2393 0.784
h = 0.003 0.006
y[1] (numeric) = 1.50684289901 0.563808500702
y[1] (closed_form) = 1.50798763966 0.562960255368
absolute error = 0.001425
relative error = 0.08851 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.8262
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2363 0.79
h = 0.0001 0.005
y[1] (numeric) = 1.51307784092 0.56559136587
y[1] (closed_form) = 1.51423021554 0.564723657199
absolute error = 0.001443
relative error = 0.08926 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.8328
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2362 0.795
h = 0.0001 0.003
y[1] (numeric) = 1.51672822408 0.568765696034
y[1] (closed_form) = 1.51789166101 0.567894406883
absolute error = 0.001454
relative error = 0.08969 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.8376
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2361 0.798
h = 0.001 0.001
y[1] (numeric) = 1.51895762782 0.570637141983
y[1] (closed_form) = 1.52012501508 0.569764457018
absolute error = 0.001458
relative error = 0.08978 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.8405
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1721.9MB, alloc=52.3MB, time=22.00
x[1] = -1.2351 0.799
h = 0.001 0.003
y[1] (numeric) = 1.52032884956 0.570559968918
y[1] (closed_form) = 1.5214959861 0.569686389323
absolute error = 0.001458
relative error = 0.08973 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.8418
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2341 0.802
h = 0.0001 0.004
y[1] (numeric) = 1.52314924987 0.571772766163
y[1] (closed_form) = 1.52431920381 0.570895497863
absolute error = 0.001462
relative error = 0.08984 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.8449
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.234 0.806
h = 0.003 0.006
y[1] (numeric) = 1.52612274246 0.574276958597
y[1] (closed_form) = 1.52729973765 0.573397308189
absolute error = 0.001469
relative error = 0.09007 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.8488
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.231 0.812
h = 0.0001 0.005
y[1] (numeric) = 1.53243700309 0.575943281867
y[1] (closed_form) = 1.53362147528 0.575044128912
absolute error = 0.001487
relative error = 0.09079 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.8554
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2309 0.817
h = 0.0001 0.003
y[1] (numeric) = 1.53617790201 0.579064369016
y[1] (closed_form) = 1.53737339783 0.578161554677
absolute error = 0.001498
relative error = 0.09121 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.8602
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2308 0.82
h = 0.001 0.001
y[1] (numeric) = 1.53846115666 0.580903040185
y[1] (closed_form) = 1.53966058808 0.579998801099
absolute error = 0.001502
relative error = 0.0913 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.8631
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1767.8MB, alloc=52.3MB, time=22.58
x[1] = -1.2298 0.821
h = 0.001 0.003
y[1] (numeric) = 1.53984032876 0.580797247382
y[1] (closed_form) = 1.54103950283 0.579892116479
absolute error = 0.001502
relative error = 0.09125 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.8643
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2288 0.824
h = 0.0001 0.004
y[1] (numeric) = 1.54270521745 0.58196075348
y[1] (closed_form) = 1.54390717789 0.581051915868
absolute error = 0.001507
relative error = 0.09135 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.8675
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2287 0.828
h = 0.003 0.006
y[1] (numeric) = 1.54575071705 0.584421697756
y[1] (closed_form) = 1.54695969358 0.583510426393
absolute error = 0.001514
relative error = 0.09157 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.8713
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2257 0.834
h = 0.0001 0.005
y[1] (numeric) = 1.55214332542 0.585970984902
y[1] (closed_form) = 1.55335962194 0.585040172524
absolute error = 0.001532
relative error = 0.09227 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.878
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2256 0.839
h = 0.0001 0.003
y[1] (numeric) = 1.5559742439 0.589038186528
y[1] (closed_form) = 1.55720152508 0.588103632091
absolute error = 0.001543
relative error = 0.09267 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.8827
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1813.5MB, alloc=52.3MB, time=23.17
x[1] = -1.2255 0.842
h = 0.001 0.001
y[1] (numeric) = 1.55831104615 0.590843701563
y[1] (closed_form) = 1.55954224807 0.589907693539
absolute error = 0.001547
relative error = 0.09276 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.8856
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2245 0.843
h = 0.001 0.003
y[1] (numeric) = 1.55969794149 0.590709255576
y[1] (closed_form) = 1.56092887944 0.589772358576
absolute error = 0.001547
relative error = 0.09271 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.8869
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2235 0.846
h = 0.0001 0.004
y[1] (numeric) = 1.56260689777 0.59182317666
y[1] (closed_form) = 1.56384059102 0.590882555099
absolute error = 0.001551
relative error = 0.0928 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.89
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2234 0.85
h = 0.003 0.006
y[1] (numeric) = 1.56572400371 0.594240361843
y[1] (closed_form) = 1.56696468769 0.593297255047
absolute error = 0.001558
relative error = 0.09301 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.8939
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2204 0.856
h = 0.0001 0.005
y[1] (numeric) = 1.57219398745 0.595672123438
y[1] (closed_form) = 1.57344183439 0.594709437897
absolute error = 0.001576
relative error = 0.0937 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.9005
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1859.2MB, alloc=52.3MB, time=23.76
x[1] = -1.2203 0.861
h = 0.0001 0.003
y[1] (numeric) = 1.57611442684 0.598684799825
y[1] (closed_form) = 1.57737321915 0.59771829178
absolute error = 0.001587
relative error = 0.09408 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.9053
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2202 0.864
h = 0.001 0.001
y[1] (numeric) = 1.57850447191 0.600456779067
y[1] (closed_form) = 1.57976717001 0.59948878869
absolute error = 0.001591
relative error = 0.09416 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.9082
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2192 0.865
h = 0.0001 0.004
y[1] (numeric) = 1.57989886341 0.600293647502
y[1] (closed_form) = 1.58116129095 0.599324771017
absolute error = 0.001591
relative error = 0.09411 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.9094
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2191 0.869
h = 0.003 0.006
y[1] (numeric) = 1.58307781557 0.602673603951
y[1] (closed_form) = 1.58434720974 0.601702199115
absolute error = 0.001598
relative error = 0.09432 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.9133
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2161 0.875
h = 0.0001 0.005
y[1] (numeric) = 1.58961502957 0.604004721125
y[1] (closed_form) = 1.59089145196 0.603013703785
absolute error = 0.001616
relative error = 0.09498 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.9199
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1905.0MB, alloc=52.3MB, time=24.35
x[1] = -1.216 0.88
h = 0.0001 0.003
y[1] (numeric) = 1.59361278421 0.606971012112
y[1] (closed_form) = 1.59490011886 0.605976102737
absolute error = 0.001627
relative error = 0.09536 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.9247
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2159 0.883
h = 0.001 0.001
y[1] (numeric) = 1.59604881937 0.608714451397
y[1] (closed_form) = 1.59734004719 0.607718034845
absolute error = 0.001631
relative error = 0.09543 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.9276
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2149 0.884
h = 0.001 0.003
y[1] (numeric) = 1.59744982373 0.608526688721
y[1] (closed_form) = 1.59874077528 0.607529388471
absolute error = 0.001631
relative error = 0.09538 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.9288
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2139 0.887
h = 0.0001 0.004
y[1] (numeric) = 1.60044025511 0.609548081935
y[1] (closed_form) = 1.60173390421 0.608547023947
absolute error = 0.001636
relative error = 0.09547 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.932
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2138 0.891
h = 0.003 0.006
y[1] (numeric) = 1.6036900662 0.611883331092
y[1] (closed_form) = 1.60499065888 0.61087969218
absolute error = 0.001643
relative error = 0.09566 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.9358
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1950.7MB, alloc=52.3MB, time=24.93
x[1] = -1.2108 0.897
h = 0.0001 0.005
y[1] (numeric) = 1.61030284829 0.613096013165
y[1] (closed_form) = 1.61161031211 0.612072725391
absolute error = 0.00166
relative error = 0.09631 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.9425
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2107 0.902
h = 0.0001 0.003
y[1] (numeric) = 1.61438919699 0.616006589985
y[1] (closed_form) = 1.61570753322 0.614979330161
absolute error = 0.001671
relative error = 0.09668 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.9473
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2106 0.905
h = 0.001 0.001
y[1] (numeric) = 1.61687790849 0.617715787873
y[1] (closed_form) = 1.61820012272 0.616686992302
absolute error = 0.001675
relative error = 0.09674 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.9501
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2096 0.906
h = 0.001 0.003
y[1] (numeric) = 1.61828598696 0.617499279435
y[1] (closed_form) = 1.61960791836 0.616469603083
absolute error = 0.001676
relative error = 0.09669 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.9514
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2086 0.909
h = 0.0001 0.004
y[1] (numeric) = 1.62131928031 0.618470253767
y[1] (closed_form) = 1.62264387803 0.617436802268
absolute error = 0.00168
relative error = 0.09677 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.9546
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1996.2MB, alloc=52.3MB, time=25.52
x[1] = -1.2085 0.913
h = 0.003 0.006
y[1] (numeric) = 1.62463954676 0.620760289731
y[1] (closed_form) = 1.6259710621 0.619724206272
absolute error = 0.001687
relative error = 0.09696 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.9584
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2055 0.919
h = 0.0001 0.005
y[1] (numeric) = 1.63132692065 0.621854060998
y[1] (closed_form) = 1.63266515004 0.620798293057
absolute error = 0.001705
relative error = 0.09759 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.965
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2054 0.924
h = 0.0001 0.003
y[1] (numeric) = 1.63550135776 0.624708291919
y[1] (closed_form) = 1.63685041938 0.623648472147
absolute error = 0.001716
relative error = 0.09794 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.9698
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2053 0.927
h = 0.001 0.001
y[1] (numeric) = 1.63804243667 0.626382873605
y[1] (closed_form) = 1.63939536103 0.625321489611
absolute error = 0.00172
relative error = 0.098 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.9727
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2043 0.928
h = 0.001 0.003
y[1] (numeric) = 1.6394573623 0.626137590015
y[1] (closed_form) = 1.6408099973 0.625075328184
absolute error = 0.00172
relative error = 0.09795 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.974
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2041.8MB, alloc=52.3MB, time=26.10
x[1] = -1.2033 0.931
h = 0.0001 0.004
y[1] (numeric) = 1.64253309315 0.627057859889
y[1] (closed_form) = 1.64388836318 0.625991805655
absolute error = 0.001724
relative error = 0.09803 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.9771
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2032 0.935
h = 0.003 0.006
y[1] (numeric) = 1.64592340677 0.629302180397
y[1] (closed_form) = 1.64728556826 0.628233443326
absolute error = 0.001731
relative error = 0.09821 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.981
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2002 0.941
h = 0.0001 0.005
y[1] (numeric) = 1.65268439487 0.630276569956
y[1] (closed_form) = 1.6540531133 0.62918811352
absolute error = 0.001749
relative error = 0.09882 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.9876
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2001 0.946
h = 0.0001 0.003
y[1] (numeric) = 1.65694641228 0.633073826057
y[1] (closed_form) = 1.65832592246 0.631981238248
absolute error = 0.00176
relative error = 0.09916 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.9924
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.2 0.949
h = 0.001 0.001
y[1] (numeric) = 1.65953954827 0.634713418444
y[1] (closed_form) = 1.66092290581 0.633619238032
absolute error = 0.001764
relative error = 0.09922 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.9953
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2087.4MB, alloc=52.3MB, time=26.68
x[1] = -1.199 0.95
h = 0.001 0.003
y[1] (numeric) = 1.66096109419 0.634439331361
y[1] (closed_form) = 1.66234415584 0.633344276081
absolute error = 0.001764
relative error = 0.09917 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.9965
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.198 0.953
h = 0.0001 0.004
y[1] (numeric) = 1.66407883713 0.635308613355
y[1] (closed_form) = 1.66546450249 0.634209748574
absolute error = 0.001768
relative error = 0.09923 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 0.9997
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1979 0.957
h = 0.003 0.006
y[1] (numeric) = 1.66753878781 0.637506718408
y[1] (closed_form) = 1.66893131826 0.636405120072
absolute error = 0.001776
relative error = 0.09941 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.004
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1949 0.963
h = 0.0001 0.005
y[1] (numeric) = 1.6743724112 0.638361260161
y[1] (closed_form) = 1.67577134146 0.637239908313
absolute error = 0.001793
relative error = 0.1 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.01
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1948 0.968
h = 0.0001 0.003
y[1] (numeric) = 1.67872149843 0.641100915343
y[1] (closed_form) = 1.68013117965 0.639975352816
absolute error = 0.001804
relative error = 0.1003 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.015
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2132.8MB, alloc=52.3MB, time=27.26
x[1] = -1.1947 0.971
h = 0.001 0.001
y[1] (numeric) = 1.68136637971 0.642705147047
y[1] (closed_form) = 1.68277989281 0.641577963632
absolute error = 0.001808
relative error = 0.1004 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.018
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1937 0.972
h = 0.0001 0.004
y[1] (numeric) = 1.6827943191 0.642402229176
y[1] (closed_form) = 1.6842075298 0.64127417389
absolute error = 0.001808
relative error = 0.1003 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.019
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1936 0.976
h = 0.003 0.006
y[1] (numeric) = 1.68631444209 0.644560976347
y[1] (closed_form) = 1.68773449328 0.643430144996
absolute error = 0.001815
relative error = 0.1005 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.023
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1906 0.982
h = 0.0001 0.005
y[1] (numeric) = 1.69321123775 0.645312836876
y[1] (closed_form) = 1.69463755388 0.644162221336
absolute error = 0.001833
relative error = 0.1011 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.03
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1905 0.987
h = 0.0001 0.003
y[1] (numeric) = 1.69763555738 0.648003440751
y[1] (closed_form) = 1.69907259006 0.646848545971
absolute error = 0.001844
relative error = 0.1014 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.034
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2178.3MB, alloc=52.3MB, time=27.85
x[1] = -1.1904 0.99
h = 0.001 0.001
y[1] (numeric) = 1.70032515576 0.649577550383
y[1] (closed_form) = 1.70176600724 0.648421010257
absolute error = 0.001848
relative error = 0.1015 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.037
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1894 0.991
h = 0.001 0.003
y[1] (numeric) = 1.7017587607 0.649249867357
y[1] (closed_form) = 1.70319930416 0.648092457882
absolute error = 0.001848
relative error = 0.1014 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.039
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1884 0.994
h = 0.0001 0.004
y[1] (numeric) = 1.7049541582 0.650024014295
y[1] (closed_form) = 1.70639724713 0.648862763539
absolute error = 0.001852
relative error = 0.1015 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.042
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1883 0.998
h = 0.003 0.006
y[1] (numeric) = 1.70854315358 0.652135618063
y[1] (closed_form) = 1.7099930586 0.650971539487
absolute error = 0.001859
relative error = 0.1016 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.046
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1853 1.004
h = 0.0001 0.005
y[1] (numeric) = 1.71551076504 0.652766764583
y[1] (closed_form) = 1.71696677782 0.65158286904
absolute error = 0.001877
relative error = 0.1022 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.052
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2223.8MB, alloc=52.3MB, time=28.42
x[1] = -1.1852 1.009
h = 0.0001 0.003
y[1] (numeric) = 1.72002120557 0.655398603884
y[1] (closed_form) = 1.72148789354 0.65421035024
absolute error = 0.001888
relative error = 0.1025 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.057
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1851 1.012
h = 0.001 0.001
y[1] (numeric) = 1.72276196972 0.65693666259
y[1] (closed_form) = 1.7242324608 0.655746735489
absolute error = 0.001892
relative error = 0.1025 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.06
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1841 1.013
h = 0.001 0.003
y[1] (numeric) = 1.72420154654 0.656580098072
y[1] (closed_form) = 1.72567172314 0.655389304667
absolute error = 0.001892
relative error = 0.1025 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.061
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1831 1.016
h = 0.0001 0.004
y[1] (numeric) = 1.72743773738 0.657302453137
y[1] (closed_form) = 1.72891042796 0.656107801795
absolute error = 0.001896
relative error = 0.1025 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.064
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.183 1.02
h = 0.003 0.006
y[1] (numeric) = 1.7310951919 0.659366418645
y[1] (closed_form) = 1.73257467163 0.658168889224
absolute error = 0.001903
relative error = 0.1027 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.068
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2269.4MB, alloc=52.3MB, time=28.98
x[1] = -1.18 1.026
h = 0.0001 0.005
y[1] (numeric) = 1.73813263655 0.659876398794
y[1] (closed_form) = 1.73961806686 0.658659020362
absolute error = 0.001921
relative error = 0.1032 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.075
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1799 1.031
h = 0.0001 0.003
y[1] (numeric) = 1.74272868061 0.662448855488
y[1] (closed_form) = 1.74422474443 0.661227040335
absolute error = 0.001932
relative error = 0.1036 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.08
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1798 1.034
h = 0.001 0.001
y[1] (numeric) = 1.74552029472 0.663950496785
y[1] (closed_form) = 1.74702014585 0.66272698016
absolute error = 0.001936
relative error = 0.1036 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.082
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1788 1.035
h = 0.001 0.003
y[1] (numeric) = 1.74696561677 0.663565026472
y[1] (closed_form) = 1.74846514698 0.662340646615
absolute error = 0.001936
relative error = 0.1035 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.084
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1778 1.038
h = 0.0001 0.004
y[1] (numeric) = 1.75024217199 0.664235314565
y[1] (closed_form) = 1.75174418466 0.663007060271
absolute error = 0.00194
relative error = 0.1036 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.087
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1777 1.042
h = 0.003 0.006
y[1] (numeric) = 1.75396766819 0.666251150573
y[1] (closed_form) = 1.75547644284 0.6650199681
absolute error = 0.001947
relative error = 0.1037 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.091
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2315.0MB, alloc=52.3MB, time=29.55
x[1] = -1.1747 1.048
h = 0.0001 0.005
y[1] (numeric) = 1.76107396218 0.666639516798
y[1] (closed_form) = 1.76258853024 0.665388454006
absolute error = 0.001964
relative error = 0.1043 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.097
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1746 1.053
h = 0.0001 0.003
y[1] (numeric) = 1.76575509004 0.669151975692
y[1] (closed_form) = 1.76728024962 0.667896397803
absolute error = 0.001975
relative error = 0.1046 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.102
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1745 1.056
h = 0.001 0.001
y[1] (numeric) = 1.76859723688 0.670616834822
y[1] (closed_form) = 1.77012616786 0.669359527542
absolute error = 0.00198
relative error = 0.1046 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.105
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1735 1.057
h = 0.001 0.003
y[1] (numeric) = 1.7700480776 0.670202435455
y[1] (closed_form) = 1.77157668123 0.668944268041
absolute error = 0.00198
relative error = 0.1045 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.106
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1725 1.06
h = 0.0001 0.004
y[1] (numeric) = 1.77336456737 0.670820383639
y[1] (closed_form) = 1.77489562189 0.669558325442
absolute error = 0.001984
relative error = 0.1046 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.109
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2360.5MB, alloc=52.3MB, time=30.12
x[1] = -1.1724 1.064
h = 0.003 0.006
y[1] (numeric) = 1.77715768587 0.672787601191
y[1] (closed_form) = 1.77869547501 0.67152256488
absolute error = 0.001991
relative error = 0.1047 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.113
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1694 1.07
h = 0.0001 0.005
y[1] (numeric) = 1.78433184415 0.673053910746
y[1] (closed_form) = 1.7858752695 0.671768963542
absolute error = 0.002008
relative error = 0.1053 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.12
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1693 1.075
h = 0.0001 0.003
y[1] (numeric) = 1.78909753372 0.675505759495
y[1] (closed_form) = 1.7906515083 0.674216219063
absolute error = 0.002019
relative error = 0.1055 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.125
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1692 1.078
h = 0.001 0.001
y[1] (numeric) = 1.79198989467 0.676933473431
y[1] (closed_form) = 1.79354762464 0.675642175782
absolute error = 0.002023
relative error = 0.1056 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.128
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1682 1.079
h = 0.0001 0.004
y[1] (numeric) = 1.79344602757 0.676490122793
y[1] (closed_form) = 1.79500342378 0.675197968135
absolute error = 0.002024
relative error = 0.1055 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.129
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2405.9MB, alloc=52.3MB, time=30.84
x[1] = -1.1681 1.083
h = 0.003 0.006
y[1] (numeric) = 1.79729760493 0.678415898794
y[1] (closed_form) = 1.7988617106 0.677120724134
absolute error = 0.002031
relative error = 0.1057 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.133
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1651 1.089
h = 0.0001 0.005
y[1] (numeric) = 1.80453084983 0.67857758758
y[1] (closed_form) = 1.80610045674 0.677262474424
absolute error = 0.002048
relative error = 0.1062 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.139
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.165 1.094
h = 0.0001 0.003
y[1] (numeric) = 1.80936963927 0.680977775755
y[1] (closed_form) = 1.81094975969 0.679658001807
absolute error = 0.002059
relative error = 0.1064 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.144
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1649 1.097
h = 0.001 0.001
y[1] (numeric) = 1.81230541498 0.682373819923
y[1] (closed_form) = 1.81388927725 0.681052264693
absolute error = 0.002063
relative error = 0.1065 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.147
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1639 1.098
h = 0.001 0.003
y[1] (numeric) = 1.81376626713 0.681905591373
y[1] (closed_form) = 1.8153497901 0.680583181767
absolute error = 0.002063
relative error = 0.1064 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.148
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2451.5MB, alloc=52.3MB, time=31.45
x[1] = -1.1629 1.101
h = 0.0001 0.004
y[1] (numeric) = 1.81715654973 0.682425891747
y[1] (closed_form) = 1.81874246489 0.68109956098
absolute error = 0.002067
relative error = 0.1065 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.151
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1628 1.105
h = 0.003 0.006
y[1] (numeric) = 1.8210749678 0.684302141806
y[1] (closed_form) = 1.82266756674 0.682972740108
absolute error = 0.002075
relative error = 0.1066 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.155
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1598 1.111
h = 0.0001 0.005
y[1] (numeric) = 1.82837424595 0.684340951111
y[1] (closed_form) = 1.82997218892 0.68299158171
absolute error = 0.002091
relative error = 0.1071 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.162
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1597 1.116
h = 0.0001 0.003
y[1] (numeric) = 1.83329662657 0.686679391021
y[1] (closed_form) = 1.83490504018 0.685325283151
absolute error = 0.002103
relative error = 0.1073 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.167
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1596 1.119
h = 0.001 0.001
y[1] (numeric) = 1.83628202412 0.688037615261
y[1] (closed_form) = 1.83789416335 0.686681698461
absolute error = 0.002107
relative error = 0.1074 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.17
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2497.2MB, alloc=52.3MB, time=32.22
x[1] = -1.1586 1.12
h = 0.001 0.003
y[1] (numeric) = 1.83774774747 0.687540394178
y[1] (closed_form) = 1.83935954104 0.686183626174
absolute error = 0.002107
relative error = 0.1073 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.171
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1576 1.123
h = 0.0001 0.004
y[1] (numeric) = 1.84117673323 0.688007580629
y[1] (closed_form) = 1.84279088727 0.686646875564
absolute error = 0.002111
relative error = 0.1074 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.174
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1575 1.127
h = 0.003 0.006
y[1] (numeric) = 1.84516156933 0.689833821038
y[1] (closed_form) = 1.84678237922 0.688469995572
absolute error = 0.002118
relative error = 0.1075 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.178
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1545 1.133
h = 0.0001 0.005
y[1] (numeric) = 1.85252589221 0.689749321865
y[1] (closed_form) = 1.85415188892 0.68836550022
absolute error = 0.002135
relative error = 0.108 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.185
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1544 1.138
h = 0.0001 0.003
y[1] (numeric) = 1.85753133519 0.692025409313
y[1] (closed_form) = 1.85916775935 0.69063677177
absolute error = 0.002146
relative error = 0.1082 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.189
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2542.7MB, alloc=52.3MB, time=32.82
x[1] = -1.1543 1.141
h = 0.001 0.001
y[1] (numeric) = 1.860566032 0.693345455544
y[1] (closed_form) = 1.86220616546 0.69195498152
absolute error = 0.00215
relative error = 0.1082 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.192
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1533 1.142
h = 0.001 0.003
y[1] (numeric) = 1.86203640029 0.69281922269
y[1] (closed_form) = 1.86367618173 0.691427900662
absolute error = 0.002151
relative error = 0.1082 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.193
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1523 1.145
h = 0.0001 0.004
y[1] (numeric) = 1.86550365595 0.693233030632
y[1] (closed_form) = 1.86714576611 0.691837755797
absolute error = 0.002155
relative error = 0.1082 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.197
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1522 1.149
h = 0.003 0.006
y[1] (numeric) = 1.86955448352 0.69500878128
y[1] (closed_form) = 1.87120322139 0.693610336738
absolute error = 0.002162
relative error = 0.1083 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.2
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1492 1.155
h = 0.0001 0.005
y[1] (numeric) = 1.87698286144 0.694800549442
y[1] (closed_form) = 1.87863662891 0.693382080979
absolute error = 0.002179
relative error = 0.1088 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.207
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2588.2MB, alloc=52.3MB, time=33.40
x[1] = -1.1491 1.16
h = 0.0001 0.003
y[1] (numeric) = 1.88207083565 0.697013683099
y[1] (closed_form) = 1.88373498709 0.695590321559
absolute error = 0.00219
relative error = 0.1091 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.212
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.149 1.163
h = 0.001 0.001
y[1] (numeric) = 1.88515450776 0.698295194981
y[1] (closed_form) = 1.88682235206 0.696869969505
absolute error = 0.002194
relative error = 0.1091 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.215
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.148 1.164
h = 0.001 0.003
y[1] (numeric) = 1.88662929483 0.69773993216
y[1] (closed_form) = 1.88829678078 0.696313861904
absolute error = 0.002194
relative error = 0.109 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.216
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.147 1.167
h = 0.0001 0.004
y[1] (numeric) = 1.89013438629 0.698100099173
y[1] (closed_form) = 1.89180416914 0.696670060521
absolute error = 0.002198
relative error = 0.109 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.219
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1469 1.171
h = 0.003 0.006
y[1] (numeric) = 1.89425077692 0.699824882256
y[1] (closed_form) = 1.89592715916 0.698391624757
absolute error = 0.002206
relative error = 0.1092 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.223
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2633.8MB, alloc=52.3MB, time=33.99
x[1] = -1.1439 1.177
h = 0.0001 0.005
y[1] (numeric) = 1.90174221903 0.699492498381
y[1] (closed_form) = 1.90342347366 0.69803918995
absolute error = 0.002222
relative error = 0.1096 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.23
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1438 1.182
h = 0.0001 0.003
y[1] (numeric) = 1.90691219103 0.701642079793
y[1] (closed_form) = 1.90860378583 0.700183801356
absolute error = 0.002233
relative error = 0.1099 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.235
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1437 1.185
h = 0.001 0.001
y[1] (numeric) = 1.91004451313 0.702884702732
y[1] (closed_form) = 1.91173978425 0.701424533
absolute error = 0.002237
relative error = 0.1099 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.237
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1427 1.186
h = 0.0001 0.004
y[1] (numeric) = 1.91152349291 0.702300392782
y[1] (closed_form) = 1.91321839937 0.700839381522
absolute error = 0.002238
relative error = 0.1098 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.239
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1426 1.19
h = 0.003 0.006
y[1] (numeric) = 1.91569659022 0.70398169659
y[1] (closed_form) = 1.91739807029 0.702517425231
absolute error = 0.002245
relative error = 0.1099 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.243
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2679.3MB, alloc=52.3MB, time=34.58
x[1] = -1.1396 1.196
h = 0.0001 0.005
y[1] (numeric) = 1.9232430072 0.703542849769
y[1] (closed_form) = 1.92494922465 0.702058502942
absolute error = 0.002262
relative error = 0.1104 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.249
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1395 1.201
h = 0.0001 0.003
y[1] (numeric) = 1.92848389791 0.705638218566
y[1] (closed_form) = 1.9302004185 0.704148835191
absolute error = 0.002273
relative error = 0.1106 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.254
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1394 1.204
h = 0.001 0.001
y[1] (numeric) = 1.93165830374 0.706847658803
y[1] (closed_form) = 1.93337848664 0.705356360462
absolute error = 0.002277
relative error = 0.1106 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.257
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1384 1.205
h = 0.001 0.003
y[1] (numeric) = 1.93314105776 0.706238379386
y[1] (closed_form) = 1.93486087055 0.70474624226
absolute error = 0.002277
relative error = 0.1106 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.258
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1374 1.208
h = 0.0001 0.004
y[1] (numeric) = 1.93671604074 0.706498480594
y[1] (closed_form) = 1.93843809131 0.705002346099
absolute error = 0.002281
relative error = 0.1106 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.261
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2724.9MB, alloc=52.3MB, time=35.15
x[1] = -1.1373 1.212
h = 0.003 0.006
y[1] (numeric) = 1.9409539029 0.708127930014
y[1] (closed_form) = 1.94268250019 0.70662848533
absolute error = 0.002288
relative error = 0.1107 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.265
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1343 1.218
h = 0.0001 0.005
y[1] (numeric) = 1.94856154224 0.707564151775
y[1] (closed_form) = 1.95029471968 0.706044605974
absolute error = 0.002305
relative error = 0.1111 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.272
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1342 1.223
h = 0.0001 0.003
y[1] (numeric) = 1.95388343906 0.709594855993
y[1] (closed_form) = 1.95562687529 0.708070197181
absolute error = 0.002316
relative error = 0.1114 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.277
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1341 1.226
h = 0.001 0.001
y[1] (numeric) = 1.95710589013 0.71076474821
y[1] (closed_form) = 1.95885297192 0.709238147253
absolute error = 0.00232
relative error = 0.1114 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.279
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1331 1.227
h = 0.001 0.003
y[1] (numeric) = 1.95859241663 0.710126389805
y[1] (closed_form) = 1.96033912203 0.708598953362
absolute error = 0.00232
relative error = 0.1113 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.281
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2770.3MB, alloc=52.3MB, time=35.72
x[1] = -1.1321 1.23
h = 0.0001 0.004
y[1] (numeric) = 1.96220399189 0.71033210615
y[1] (closed_form) = 1.96395290313 0.708800657193
absolute error = 0.002325
relative error = 0.1113 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.284
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.132 1.234
h = 0.003 0.006
y[1] (numeric) = 1.96650618706 0.711909228726
y[1] (closed_form) = 1.96826161612 0.710374420913
absolute error = 0.002332
relative error = 0.1114 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.288
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.129 1.24
h = 0.0001 0.005
y[1] (numeric) = 1.97417405467 0.711220113452
y[1] (closed_form) = 1.97593390668 0.709665179604
absolute error = 0.002348
relative error = 0.1119 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.294
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1289 1.245
h = 0.0001 0.003
y[1] (numeric) = 1.97957641759 0.713185562862
y[1] (closed_form) = 1.9813464837 0.711625439794
absolute error = 0.002359
relative error = 0.1121 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.299
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1288 1.248
h = 0.001 0.001
y[1] (numeric) = 1.98284658471 0.71431555746
y[1] (closed_form) = 1.98462027953 0.712753465163
absolute error = 0.002363
relative error = 0.1121 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.302
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2815.8MB, alloc=52.3MB, time=36.30
x[1] = -1.1278 1.249
h = 0.001 0.003
y[1] (numeric) = 1.98433665788 0.713648105872
y[1] (closed_form) = 1.98610997007 0.712085181414
absolute error = 0.002364
relative error = 0.112 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.303
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1268 1.252
h = 0.0001 0.004
y[1] (numeric) = 1.98798438805 0.713799183309
y[1] (closed_form) = 1.98975987409 0.71223223135
absolute error = 0.002368
relative error = 0.1121 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.306
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1267 1.256
h = 0.003 0.006
y[1] (numeric) = 1.99235048078 0.715323510167
y[1] (closed_form) = 1.99413245553 0.713753150851
absolute error = 0.002375
relative error = 0.1121 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.31
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1237 1.262
h = 0.0001 0.005
y[1] (numeric) = 2.00007758149 0.714508657055
y[1] (closed_form) = 2.00186382201 0.712918147517
absolute error = 0.002392
relative error = 0.1126 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.317
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1236 1.267
h = 0.0001 0.003
y[1] (numeric) = 2.00555986822 0.716408264326
y[1] (closed_form) = 2.00735627786 0.714812489613
absolute error = 0.002403
relative error = 0.1128 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.322
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2861.3MB, alloc=52.3MB, time=36.88
x[1] = -1.1235 1.27
h = 0.001 0.001
y[1] (numeric) = 2.00887742087 0.717498013458
y[1] (closed_form) = 2.01067744226 0.715900242531
absolute error = 0.002407
relative error = 0.1128 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.325
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1225 1.271
h = 0.001 0.003
y[1] (numeric) = 2.01037081503 0.71680145553
y[1] (closed_form) = 2.01217044755 0.715202855791
absolute error = 0.002407
relative error = 0.1127 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.326
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1215 1.274
h = 0.0001 0.004
y[1] (numeric) = 2.0140542619 0.716897642192
y[1] (closed_form) = 2.01585603625 0.715295000121
absolute error = 0.002411
relative error = 0.1127 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.329
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1214 1.278
h = 0.003 0.006
y[1] (numeric) = 2.01848381494 0.718368706783
y[1] (closed_form) = 2.0202920487 0.716762609022
absolute error = 0.002419
relative error = 0.1128 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.333
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1184 1.284
h = 0.0001 0.005
y[1] (numeric) = 2.02626915253 0.717427719845
y[1] (closed_form) = 2.02808149487 0.715801448406
absolute error = 0.002435
relative error = 0.1132 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.34
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2906.8MB, alloc=52.3MB, time=37.47
x[1] = -1.1183 1.289
h = 0.0001 0.003
y[1] (numeric) = 2.03183081853 0.719260900546
y[1] (closed_form) = 2.03365328472 0.717629288233
absolute error = 0.002446
relative error = 0.1134 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.344
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1182 1.292
h = 0.001 0.001
y[1] (numeric) = 2.03519542486 0.720310058129
y[1] (closed_form) = 2.03702148573 0.718676422714
absolute error = 0.00245
relative error = 0.1134 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.347
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1172 1.293
h = 0.0001 0.004
y[1] (numeric) = 2.03669191441 0.719584381733
y[1] (closed_form) = 2.0385175802 0.717949920882
absolute error = 0.00245
relative error = 0.1134 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.348
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1171 1.297
h = 0.003 0.006
y[1] (numeric) = 2.04117638405 0.721009975721
y[1] (closed_form) = 2.04300848285 0.719372018579
absolute error = 0.002458
relative error = 0.1135 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.352
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1141 1.303
h = 0.0001 0.005
y[1] (numeric) = 2.04901256028 0.71996078112
y[1] (closed_form) = 2.05084863263 0.71830262882
absolute error = 0.002474
relative error = 0.1139 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.359
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.114 1.308
h = 0.0001 0.003
y[1] (numeric) = 2.05464291624 0.721737254961
y[1] (closed_form) = 2.05648907411 0.720073696289
absolute error = 0.002485
relative error = 0.1141 %
Correct digits = 3
memory used=2952.3MB, alloc=52.3MB, time=38.06
Radius of convergence (given) for eq 1 = 1.364
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1139 1.311
h = 0.001 0.001
y[1] (numeric) = 2.05804824716 0.722751752002
y[1] (closed_form) = 2.05989798525 0.721086146958
absolute error = 0.002489
relative error = 0.1141 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.367
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1129 1.312
h = 0.001 0.003
y[1] (numeric) = 2.0595475676 0.722001035697
y[1] (closed_form) = 2.06139690525 0.720334608068
absolute error = 0.002489
relative error = 0.114 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.368
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1119 1.315
h = 0.0001 0.004
y[1] (numeric) = 2.06329696672 0.721994833629
y[1] (closed_form) = 2.06514838664 0.720324336103
absolute error = 0.002494
relative error = 0.114 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.371
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1118 1.319
h = 0.003 0.006
y[1] (numeric) = 2.06784408217 0.723366299387
y[1] (closed_form) = 2.06970190705 0.72169225633
absolute error = 0.002501
relative error = 0.1141 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.375
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1088 1.325
h = 0.0001 0.005
y[1] (numeric) = 2.07573664332 0.722190235039
y[1] (closed_form) = 2.07759828459 0.720495974725
absolute error = 0.002517
relative error = 0.1145 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.382
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2997.9MB, alloc=52.3MB, time=38.64
x[1] = -1.1087 1.33
h = 0.0001 0.003
y[1] (numeric) = 2.0814453662 0.72389919601
y[1] (closed_form) = 2.08331704714 0.722199454099
absolute error = 0.002528
relative error = 0.1147 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.386
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1086 1.333
h = 0.001 0.001
y[1] (numeric) = 2.08489713385 0.724872458226
y[1] (closed_form) = 2.08677237774 0.723170643236
absolute error = 0.002532
relative error = 0.1147 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.389
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1076 1.334
h = 0.001 0.003
y[1] (numeric) = 2.08639913036 0.724092600953
y[1] (closed_form) = 2.08827396763 0.722389966802
absolute error = 0.002533
relative error = 0.1146 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.391
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1066 1.337
h = 0.0001 0.004
y[1] (numeric) = 2.09018299104 0.724030794345
y[1] (closed_form) = 2.09205987844 0.722324075911
absolute error = 0.002537
relative error = 0.1146 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.394
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1065 1.341
h = 0.003 0.006
y[1] (numeric) = 2.09479231155 0.725347670772
y[1] (closed_form) = 2.09667557404 0.723637358955
absolute error = 0.002544
relative error = 0.1147 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.398
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3043.4MB, alloc=52.3MB, time=39.23
x[1] = -1.1035 1.347
h = 0.0001 0.005
y[1] (numeric) = 2.10274025837 0.724044354452
y[1] (closed_form) = 2.10462718011 0.722313804008
absolute error = 0.00256
relative error = 0.1151 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.404
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1034 1.352
h = 0.0001 0.003
y[1] (numeric) = 2.10852679721 0.725685226424
y[1] (closed_form) = 2.11042371246 0.723949119417
absolute error = 0.002571
relative error = 0.1153 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.409
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1033 1.355
h = 0.001 0.001
y[1] (numeric) = 2.11202466595 0.726616912769
y[1] (closed_form) = 2.11392512679 0.724878706074
absolute error = 0.002575
relative error = 0.1152 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.412
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1023 1.356
h = 0.001 0.003
y[1] (numeric) = 2.11352911326 0.725807905355
y[1] (closed_form) = 2.11542916131 0.724068882948
absolute error = 0.002576
relative error = 0.1152 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.413
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.1013 1.359
h = 0.0001 0.004
y[1] (numeric) = 2.11734699419 0.725690250739
y[1] (closed_form) = 2.11924906017 0.72394712982
absolute error = 0.00258
relative error = 0.1152 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.416
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3089.0MB, alloc=52.3MB, time=39.81
x[1] = -1.1012 1.363
h = 0.003 0.006
y[1] (numeric) = 2.12201807561 0.726952080295
y[1] (closed_form) = 2.12392648665 0.725205318312
absolute error = 0.002587
relative error = 0.1153 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.42
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0982 1.369
h = 0.0001 0.005
y[1] (numeric) = 2.13002040784 0.725521134595
y[1] (closed_form) = 2.131932321 0.723754113341
absolute error = 0.002603
relative error = 0.1156 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.427
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0981 1.374
h = 0.0001 0.003
y[1] (numeric) = 2.13588420945 0.727093344361
y[1] (closed_form) = 2.13780606967 0.725320691839
absolute error = 0.002615
relative error = 0.1158 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.432
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.098 1.377
h = 0.001 0.001
y[1] (numeric) = 2.13942784235 0.72798311556
y[1] (closed_form) = 2.14135323066 0.72620833684
absolute error = 0.002619
relative error = 0.1158 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.434
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.097 1.378
h = 0.001 0.003
y[1] (numeric) = 2.14093451531 0.727144949862
y[1] (closed_form) = 2.14285948471 0.725369358903
absolute error = 0.002619
relative error = 0.1158 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.436
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3134.6MB, alloc=52.3MB, time=40.41
x[1] = -1.096 1.381
h = 0.0001 0.004
y[1] (numeric) = 2.14478597438 0.72697120595
y[1] (closed_form) = 2.14671292948 0.725191502406
absolute error = 0.002623
relative error = 0.1158 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.439
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0959 1.385
h = 0.003 0.006
y[1] (numeric) = 2.14951837083 0.728177533447
y[1] (closed_form) = 2.15145164073 0.726394141328
absolute error = 0.00263
relative error = 0.1158 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.443
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0929 1.391
h = 0.0001 0.005
y[1] (numeric) = 2.15757408723 0.726618585775
y[1] (closed_form) = 2.15951070215 0.72481491447
absolute error = 0.002646
relative error = 0.1162 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.449
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0928 1.396
h = 0.0001 0.003
y[1] (numeric) = 2.16351459623 0.728121563055
y[1] (closed_form) = 2.16546111145 0.726312186036
absolute error = 0.002658
relative error = 0.1164 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.454
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0927 1.399
h = 0.001 0.001
y[1] (numeric) = 2.16710365503 0.728969081609
y[1] (closed_form) = 2.16905368076 0.727157551982
absolute error = 0.002662
relative error = 0.1163 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.457
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3180.1MB, alloc=52.3MB, time=41.00
x[1] = -1.0917 1.4
h = 0.003 0.006
y[1] (numeric) = 2.16861232863 0.728101750511
y[1] (closed_form) = 2.17056192933 0.726289412143
absolute error = 0.002662
relative error = 0.1163 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.458
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0887 1.406
h = 0.0001 0.005
y[1] (numeric) = 2.17670095503 0.726453220355
y[1] (closed_form) = 2.17865378756 0.7246205966
absolute error = 0.002678
relative error = 0.1166 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.465
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0886 1.411
h = 0.0001 0.003
y[1] (numeric) = 2.18269214565 0.727906328512
y[1] (closed_form) = 2.18465484428 0.726067949173
absolute error = 0.002689
relative error = 0.1168 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.47
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0885 1.414
h = 0.001 0.001
y[1] (numeric) = 2.18631118098 0.728723452971
y[1] (closed_form) = 2.1882773773 0.726882903358
absolute error = 0.002693
relative error = 0.1168 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.473
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0875 1.415
h = 0.001 0.003
y[1] (numeric) = 2.18782036542 0.727836012112
y[1] (closed_form) = 2.18978613261 0.725994656334
absolute error = 0.002693
relative error = 0.1168 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.474
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3225.7MB, alloc=52.3MB, time=41.58
x[1] = -1.0865 1.418
h = 0.0001 0.004
y[1] (numeric) = 2.19172606964 0.727566233203
y[1] (closed_form) = 2.19369376767 0.725720742256
absolute error = 0.002698
relative error = 0.1168 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.477
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0864 1.422
h = 0.003 0.006
y[1] (numeric) = 2.19655951969 0.728676333793
y[1] (closed_form) = 2.19853347985 0.726827075237
absolute error = 0.002705
relative error = 0.1168 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.481
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0834 1.428
h = 0.0001 0.005
y[1] (numeric) = 2.2046998243 0.726899212089
y[1] (closed_form) = 2.2066768639 0.725029646339
absolute error = 0.002721
relative error = 0.1171 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.488
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0833 1.433
h = 0.0001 0.003
y[1] (numeric) = 2.21076676571 0.728282145957
y[1] (closed_form) = 2.21275362415 0.726406750626
absolute error = 0.002732
relative error = 0.1173 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.492
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0832 1.436
h = 0.001 0.001
y[1] (numeric) = 2.2144306447 0.729056460739
y[1] (closed_form) = 2.21642098307 0.727178868893
absolute error = 0.002736
relative error = 0.1173 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.495
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3271.2MB, alloc=52.3MB, time=42.17
x[1] = -1.0822 1.437
h = 0.001 0.003
y[1] (numeric) = 2.21594145015 0.728139850461
y[1] (closed_form) = 2.21793135331 0.726261455991
absolute error = 0.002736
relative error = 0.1173 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.497
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0812 1.44
h = 0.0001 0.004
y[1] (numeric) = 2.21987953443 0.72781335572
y[1] (closed_form) = 2.2218713361 0.725930812431
absolute error = 0.002741
relative error = 0.1173 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.5
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0811 1.444
h = 0.003 0.006
y[1] (numeric) = 2.22477308109 0.7288667538
y[1] (closed_form) = 2.22677111412 0.726980395855
absolute error = 0.002748
relative error = 0.1173 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.504
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0781 1.45
h = 0.0001 0.005
y[1] (numeric) = 2.23296406486 0.726960677807
y[1] (closed_form) = 2.23496502032 0.725053994707
absolute error = 0.002764
relative error = 0.1176 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.51
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.078 1.455
h = 0.0001 0.003
y[1] (numeric) = 2.23910619588 0.728272875054
y[1] (closed_form) = 2.24111692262 0.72636028864
absolute error = 0.002775
relative error = 0.1178 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.515
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3316.7MB, alloc=52.3MB, time=42.75
x[1] = -1.0779 1.458
h = 0.001 0.001
y[1] (numeric) = 2.24281457688 0.729004047479
y[1] (closed_form) = 2.24482876568 0.727089238409
absolute error = 0.002779
relative error = 0.1178 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.518
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0769 1.459
h = 0.001 0.003
y[1] (numeric) = 2.24432677869 0.728058263423
y[1] (closed_form) = 2.24634052624 0.726142655293
absolute error = 0.002779
relative error = 0.1177 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.519
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0759 1.462
h = 0.0001 0.004
y[1] (numeric) = 2.24829679817 0.727674819636
y[1] (closed_form) = 2.25031241183 0.725755049193
absolute error = 0.002784
relative error = 0.1177 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.522
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0758 1.466
h = 0.003 0.006
y[1] (numeric) = 2.2532499892 0.728671068758
y[1] (closed_form) = 2.25527180329 0.726747436787
absolute error = 0.002791
relative error = 0.1178 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.526
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0728 1.472
h = 0.0001 0.005
y[1] (numeric) = 2.2614906475 0.72663568367
y[1] (closed_form) = 2.26351522703 0.724691709306
absolute error = 0.002807
relative error = 0.1181 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.533
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3362.2MB, alloc=52.3MB, time=43.34
x[1] = -1.0727 1.477
h = 0.0001 0.003
y[1] (numeric) = 2.26770740478 0.72787658491
y[1] (closed_form) = 2.26974170775 0.725926633764
absolute error = 0.002818
relative error = 0.1183 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.538
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0726 1.48
h = 0.001 0.001
y[1] (numeric) = 2.27145994486 0.728564284086
y[1] (closed_form) = 2.27349769191 0.726612084241
absolute error = 0.002822
relative error = 0.1182 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.54
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0716 1.481
h = 0.0001 0.004
y[1] (numeric) = 2.27297331855 0.727589322916
y[1] (closed_form) = 2.2750106183 0.725636327602
absolute error = 0.002822
relative error = 0.1182 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.542
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0715 1.485
h = 0.003 0.006
y[1] (numeric) = 2.27797817531 0.728536726384
y[1] (closed_form) = 2.28002164791 0.726579830124
absolute error = 0.002829
relative error = 0.1182 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.546
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0685 1.491
h = 0.0001 0.005
y[1] (numeric) = 2.28626233259 0.726390331315
y[1] (closed_form) = 2.28830843574 0.724413076538
absolute error = 0.002845
relative error = 0.1185 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.552
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3407.7MB, alloc=52.3MB, time=43.92
x[1] = -1.0684 1.496
h = 0.0001 0.003
y[1] (numeric) = 2.29254373121 0.727570297416
y[1] (closed_form) = 2.29459951723 0.725587002255
absolute error = 0.002857
relative error = 0.1187 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.557
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0683 1.499
h = 0.001 0.001
y[1] (numeric) = 2.29633452956 0.728220833104
y[1] (closed_form) = 2.29839374443 0.726235266693
absolute error = 0.002861
relative error = 0.1187 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.56
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0673 1.5
h = 0.001 0.003
y[1] (numeric) = 2.29784907988 0.727220765681
y[1] (closed_form) = 2.29990784223 0.72523440684
absolute error = 0.002861
relative error = 0.1186 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.561
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0663 1.503
h = 0.0001 0.004
y[1] (numeric) = 2.30187802148 0.726731107651
y[1] (closed_form) = 2.30393858975 0.724740561415
absolute error = 0.002865
relative error = 0.1186 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.564
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0662 1.507
h = 0.003 0.006
y[1] (numeric) = 2.30694168049 0.727620533462
y[1] (closed_form) = 2.30900839163 0.725626038564
absolute error = 0.002872
relative error = 0.1187 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.568
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3453.3MB, alloc=52.3MB, time=44.50
x[1] = -1.0632 1.513
h = 0.0001 0.005
y[1] (numeric) = 2.31527364458 0.725344169911
y[1] (closed_form) = 2.31734282934 0.723329300609
absolute error = 0.002888
relative error = 0.119 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.575
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0631 1.518
h = 0.0001 0.003
y[1] (numeric) = 2.32162862208 0.726451800205
y[1] (closed_form) = 2.3237074413 0.724430817541
absolute error = 0.002899
relative error = 0.1191 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.58
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.063 1.521
h = 0.001 0.001
y[1] (numeric) = 2.32546294192 0.727058247574
y[1] (closed_form) = 2.32754517182 0.725034967803
absolute error = 0.002903
relative error = 0.1191 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.583
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.062 1.522
h = 0.001 0.003
y[1] (numeric) = 2.32697824676 0.726028996885
y[1] (closed_form) = 2.32906001814 0.72400492832
absolute error = 0.002904
relative error = 0.119 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.584
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.061 1.525
h = 0.0001 0.004
y[1] (numeric) = 2.33103784942 0.725481729382
y[1] (closed_form) = 2.33312139422 0.723453460376
absolute error = 0.002908
relative error = 0.119 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.587
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3498.9MB, alloc=52.3MB, time=45.08
x[1] = -1.0609 1.529
h = 0.003 0.006
y[1] (numeric) = 2.33615985486 0.726312736693
y[1] (closed_form) = 2.33824951104 0.724280472645
absolute error = 0.002915
relative error = 0.1191 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.591
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0579 1.535
h = 0.0001 0.005
y[1] (numeric) = 2.34453861851 0.723906063619
y[1] (closed_form) = 2.34663059141 0.721853410005
absolute error = 0.002931
relative error = 0.1194 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.597
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0578 1.54
h = 0.0001 0.003
y[1] (numeric) = 2.35096660537 0.724940807153
y[1] (closed_form) = 2.35306816404 0.722881967465
absolute error = 0.002942
relative error = 0.1195 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.602
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0577 1.543
h = 0.001 0.001
y[1] (numeric) = 2.35484410015 0.725502840422
y[1] (closed_form) = 2.35694905123 0.72344167787
absolute error = 0.002946
relative error = 0.1195 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.605
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0567 1.544
h = 0.001 0.003
y[1] (numeric) = 2.35635993541 0.724444406058
y[1] (closed_form) = 2.35846442198 0.722382458374
absolute error = 0.002946
relative error = 0.1194 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.606
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3544.4MB, alloc=52.3MB, time=45.67
x[1] = -1.0557 1.547
h = 0.0001 0.004
y[1] (numeric) = 2.36044975136 0.723839304304
y[1] (closed_form) = 2.36255597882 0.721773143287
absolute error = 0.00295
relative error = 0.1194 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.61
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0556 1.551
h = 0.003 0.006
y[1] (numeric) = 2.36562964439 0.724611455812
y[1] (closed_form) = 2.36774195155 0.722541253549
absolute error = 0.002958
relative error = 0.1195 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.613
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0526 1.557
h = 0.0001 0.005
y[1] (numeric) = 2.37405419948 0.722074136993
y[1] (closed_form) = 2.37616866651 0.719983530725
absolute error = 0.002973
relative error = 0.1198 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.62
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0525 1.562
h = 0.0001 0.003
y[1] (numeric) = 2.38055462407 0.723035445776
y[1] (closed_form) = 2.38267862786 0.720938580991
absolute error = 0.002985
relative error = 0.1199 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.625
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0524 1.565
h = 0.001 0.001
y[1] (numeric) = 2.38447494599 0.723552740962
y[1] (closed_form) = 2.38660232381 0.721453527657
absolute error = 0.002989
relative error = 0.1199 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.628
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0514 1.566
h = 0.001 0.003
y[1] (numeric) = 2.3859910877 0.722465123536
y[1] (closed_form) = 2.38811799507 0.720365128784
absolute error = 0.002989
relative error = 0.1198 %
Correct digits = 3
memory used=3590.0MB, alloc=52.3MB, time=46.26
Radius of convergence (given) for eq 1 = 1.629
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0504 1.569
h = 0.0001 0.004
y[1] (numeric) = 2.39011066846 0.721801964943
y[1] (closed_form) = 2.39223928416 0.719697744125
absolute error = 0.002993
relative error = 0.1198 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.632
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0503 1.573
h = 0.003 0.006
y[1] (numeric) = 2.39534798858 0.722514825732
y[1] (closed_form) = 2.3974826521 0.720406517637
absolute error = 0.003
relative error = 0.1198 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.636
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0473 1.579
h = 0.0001 0.005
y[1] (numeric) = 2.40381732611 0.71984652976
y[1] (closed_form) = 2.40595399269 0.717717803944
absolute error = 0.003016
relative error = 0.1201 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.643
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0472 1.584
h = 0.0001 0.003
y[1] (numeric) = 2.41038961471 0.720733858773
y[1] (closed_form) = 2.41253576875 0.718598802265
absolute error = 0.003027
relative error = 0.1203 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.647
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0471 1.587
h = 0.001 0.001
y[1] (numeric) = 2.4143524147 0.721206093693
y[1] (closed_form) = 2.41650192431 0.719068663111
absolute error = 0.003031
relative error = 0.1202 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.65
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3635.5MB, alloc=52.3MB, time=46.85
x[1] = -1.0461 1.588
h = 0.0001 0.004
y[1] (numeric) = 2.41586863908 0.720089294837
y[1] (closed_form) = 2.41801767229 0.717951086518
absolute error = 0.003032
relative error = 0.1202 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.652
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.046 1.592
h = 0.003 0.006
y[1] (numeric) = 2.42115573495 0.720751449143
y[1] (closed_form) = 2.42331078774 0.718609114817
absolute error = 0.003039
relative error = 0.1202 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.655
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.043 1.598
h = 0.0001 0.005
y[1] (numeric) = 2.4296643766 0.717970667776
y[1] (closed_form) = 2.43182129766 0.715807902636
absolute error = 0.003054
relative error = 0.1205 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.662
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0429 1.603
h = 0.0001 0.003
y[1] (numeric) = 2.4362989523 0.718794730009
y[1] (closed_form) = 2.43846531902 0.716625571674
absolute error = 0.003066
relative error = 0.1206 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.667
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0428 1.606
h = 0.001 0.001
y[1] (numeric) = 2.44029857751 0.719228422254
y[1] (closed_form) = 2.44246828411 0.717056867707
absolute error = 0.00307
relative error = 0.1206 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.67
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3681.1MB, alloc=52.3MB, time=47.44
x[1] = -1.0418 1.607
h = 0.001 0.003
y[1] (numeric) = 2.44181504151 0.718086504439
y[1] (closed_form) = 2.44398426658 0.715914175299
absolute error = 0.00307
relative error = 0.1205 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.671
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0408 1.61
h = 0.0001 0.004
y[1] (numeric) = 2.44598950927 0.717315072608
y[1] (closed_form) = 2.44816038212 0.715138493735
absolute error = 0.003074
relative error = 0.1205 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.674
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0407 1.614
h = 0.003 0.006
y[1] (numeric) = 2.45133317479 0.717917128872
y[1] (closed_form) = 2.45351003619 0.715736377152
absolute error = 0.003081
relative error = 0.1206 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.678
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0377 1.62
h = 0.0001 0.005
y[1] (numeric) = 2.45988472301 0.715004754455
y[1] (closed_form) = 2.46206329594 0.71280355955
absolute error = 0.003097
relative error = 0.1208 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.685
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0376 1.625
h = 0.0001 0.003
y[1] (numeric) = 2.46659009594 0.715753823796
y[1] (closed_form) = 2.46877806469 0.71354616402
absolute error = 0.003108
relative error = 0.121 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.69
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3726.6MB, alloc=52.3MB, time=48.01
x[1] = -1.0375 1.628
h = 0.001 0.001
y[1] (numeric) = 2.47063155024 0.71614185688
y[1] (closed_form) = 2.4728228402 0.713931775524
absolute error = 0.003112
relative error = 0.1209 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.692
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0365 1.629
h = 0.001 0.003
y[1] (numeric) = 2.47214768084 0.714970760718
y[1] (closed_form) = 2.47433848336 0.712759908525
absolute error = 0.003112
relative error = 0.1209 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.694
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0355 1.632
h = 0.0001 0.004
y[1] (numeric) = 2.47635062905 0.71414064201
y[1] (closed_form) = 2.47854304668 0.711925527797
absolute error = 0.003117
relative error = 0.1209 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.697
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0354 1.636
h = 0.003 0.006
y[1] (numeric) = 2.48175040011 0.714682171002
y[1] (closed_form) = 2.48394877388 0.712462838414
absolute error = 0.003124
relative error = 0.1209 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.701
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0324 1.642
h = 0.0001 0.005
y[1] (numeric) = 2.49034384352 0.711637885894
y[1] (closed_form) = 2.49254377214 0.709398098472
absolute error = 0.003139
relative error = 0.1211 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.707
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3772.2MB, alloc=52.3MB, time=48.60
x[1] = -1.0323 1.647
h = 0.0001 0.003
y[1] (numeric) = 2.49711943391 0.712311425826
y[1] (closed_form) = 2.49932870821 0.710065102126
absolute error = 0.003151
relative error = 0.1213 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.712
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0322 1.65
h = 0.001 0.001
y[1] (numeric) = 2.50120236472 0.71265348272
y[1] (closed_form) = 2.50341494146 0.710404712174
absolute error = 0.003155
relative error = 0.1212 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.715
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0312 1.651
h = 0.001 0.003
y[1] (numeric) = 2.50271793855 0.711453212754
y[1] (closed_form) = 2.50493002198 0.709203675152
absolute error = 0.003155
relative error = 0.1212 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.716
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0302 1.654
h = 0.0001 0.004
y[1] (numeric) = 2.50694891599 0.710564193037
y[1] (closed_form) = 2.50916258182 0.708310381286
absolute error = 0.003159
relative error = 0.1212 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.719
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0301 1.658
h = 0.003 0.006
y[1] (numeric) = 2.51240432564 0.711044769059
y[1] (closed_form) = 2.51462391502 0.70878669358
absolute error = 0.003166
relative error = 0.1212 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.723
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3817.7MB, alloc=52.3MB, time=49.16
x[1] = -1.0271 1.664
h = 0.0001 0.005
y[1] (numeric) = 2.52103865206 0.707868260434
y[1] (closed_form) = 2.52325963965 0.705589719193
absolute error = 0.003182
relative error = 0.1214 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.73
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.027 1.669
h = 0.0001 0.003
y[1] (numeric) = 2.5278838781 0.708465737429
y[1] (closed_form) = 2.53011416094 0.706180588777
absolute error = 0.003193
relative error = 0.1216 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.735
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0269 1.672
h = 0.001 0.001
y[1] (numeric) = 2.53200793161 0.708761502916
y[1] (closed_form) = 2.53424149802 0.706473882254
absolute error = 0.003197
relative error = 0.1215 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.738
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0259 1.673
h = 0.001 0.003
y[1] (numeric) = 2.53352272548 0.707532064704
y[1] (closed_form) = 2.53575579273 0.705243680791
absolute error = 0.003197
relative error = 0.1215 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.739
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0249 1.676
h = 0.0001 0.004
y[1] (numeric) = 2.53778128024 0.706583932041
y[1] (closed_form) = 2.54001589715 0.704291262007
absolute error = 0.003202
relative error = 0.1215 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.742
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3863.3MB, alloc=52.3MB, time=49.73
x[1] = -1.0248 1.68
h = 0.003 0.006
y[1] (numeric) = 2.54329185989 0.7070031318
y[1] (closed_form) = 2.54553236756 0.704706152862
absolute error = 0.003209
relative error = 0.1215 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.746
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0218 1.686
h = 0.0001 0.005
y[1] (numeric) = 2.55196605638 0.703694091647
y[1] (closed_form) = 2.55420780567 0.701376636739
absolute error = 0.003224
relative error = 0.1217 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.753
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0217 1.691
h = 0.0001 0.003
y[1] (numeric) = 2.55888033416 0.704214975172
y[1] (closed_form) = 2.561131328 0.701890841992
absolute error = 0.003236
relative error = 0.1218 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.757
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0216 1.694
h = 0.001 0.001
y[1] (numeric) = 2.56304515537 0.704464135849
y[1] (closed_form) = 2.56529941379 0.702137505598
absolute error = 0.00324
relative error = 0.1218 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.76
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0206 1.695
h = 0.0001 0.004
y[1] (numeric) = 2.56455894626 0.703205535964
y[1] (closed_form) = 2.56681269969 0.70087814629
absolute error = 0.00324
relative error = 0.1218 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.761
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3908.9MB, alloc=52.3MB, time=50.30
x[1] = -1.0205 1.699
h = 0.003 0.006
y[1] (numeric) = 2.57011737693 0.703572216405
y[1] (closed_form) = 2.57237699221 0.701240479799
absolute error = 0.003247
relative error = 0.1218 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.765
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0175 1.705
h = 0.0001 0.005
y[1] (numeric) = 2.57882666413 0.700149313059
y[1] (closed_form) = 2.5810873864 0.697797090408
absolute error = 0.003262
relative error = 0.122 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.772
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0174 1.71
h = 0.0001 0.003
y[1] (numeric) = 2.58580083116 0.700604657972
y[1] (closed_form) = 2.58807075494 0.698245695665
absolute error = 0.003274
relative error = 0.1221 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.777
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0173 1.713
h = 0.001 0.001
y[1] (numeric) = 2.59000101884 0.700813933053
y[1] (closed_form) = 2.59227419108 0.698452451956
absolute error = 0.003278
relative error = 0.1221 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.78
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0163 1.714
h = 0.001 0.003
y[1] (numeric) = 2.59151411518 0.699530222248
y[1] (closed_form) = 2.59378677738 0.697167984975
absolute error = 0.003278
relative error = 0.122 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.781
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3954.4MB, alloc=52.3MB, time=50.88
x[1] = -1.0153 1.717
h = 0.0001 0.004
y[1] (numeric) = 2.59582348982 0.698471853391
y[1] (closed_form) = 2.59809764082 0.696105307745
absolute error = 0.003282
relative error = 0.122 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.784
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0152 1.721
h = 0.003 0.006
y[1] (numeric) = 2.60143621812 0.698776371804
y[1] (closed_form) = 2.60371619892 0.696405433272
absolute error = 0.003289
relative error = 0.122 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.788
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0122 1.727
h = 0.0001 0.005
y[1] (numeric) = 2.61018349205 0.695220364518
y[1] (closed_form) = 2.61246442334 0.692828931075
absolute error = 0.003305
relative error = 0.1223 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.795
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0121 1.732
h = 0.0001 0.003
y[1] (numeric) = 2.61722562516 0.695598129738
y[1] (closed_form) = 2.6195157067 0.693199886284
absolute error = 0.003316
relative error = 0.1224 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.799
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.012 1.735
h = 0.001 0.001
y[1] (numeric) = 2.62146592041 0.695760217418
y[1] (closed_form) = 2.62375923126 0.693359430301
absolute error = 0.00332
relative error = 0.1223 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.802
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4000.0MB, alloc=52.3MB, time=51.45
x[1] = -1.011 1.736
h = 0.001 0.003
y[1] (numeric) = 2.62297759913 0.694447357212
y[1] (closed_form) = 2.62527039413 0.692045817792
absolute error = 0.00332
relative error = 0.1223 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.804
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.01 1.739
h = 0.0001 0.004
y[1] (numeric) = 2.62731325701 0.693329275827
y[1] (closed_form) = 2.62960750798 0.69092341651
absolute error = 0.003324
relative error = 0.1223 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.807
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0099 1.743
h = 0.003 0.006
y[1] (numeric) = 2.63297981075 0.693571214685
y[1] (closed_form) = 2.6352798582 0.691160917816
absolute error = 0.003332
relative error = 0.1223 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.811
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0069 1.749
h = 0.0001 0.005
y[1] (numeric) = 2.64176405627 0.689881809212
y[1] (closed_form) = 2.64406489778 0.687451009282
absolute error = 0.003347
relative error = 0.1225 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.817
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0068 1.754
h = 0.0001 0.003
y[1] (numeric) = 2.64887356571 0.690181472776
y[1] (closed_form) = 2.65118350593 0.687743792756
absolute error = 0.003358
relative error = 0.1226 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.822
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4045.6MB, alloc=52.3MB, time=52.04
x[1] = -1.0067 1.757
h = 0.001 0.001
y[1] (numeric) = 2.65315361008 0.690296064845
y[1] (closed_form) = 2.65546676035 0.687855816393
absolute error = 0.003362
relative error = 0.1226 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.825
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0057 1.758
h = 0.001 0.003
y[1] (numeric) = 2.65466364863 0.688954064706
y[1] (closed_form) = 2.65697627728 0.686513067849
absolute error = 0.003363
relative error = 0.1225 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.826
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0047 1.761
h = 0.0001 0.004
y[1] (numeric) = 2.65902513525 0.687776067331
y[1] (closed_form) = 2.66133918699 0.685330739208
absolute error = 0.003367
relative error = 0.1225 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.829
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0046 1.765
h = 0.003 0.006
y[1] (numeric) = 2.66474503956 0.687955012633
y[1] (closed_form) = 2.6670648543 0.68550520247
absolute error = 0.003374
relative error = 0.1225 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.833
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0016 1.771
h = 0.0001 0.005
y[1] (numeric) = 2.67356524083 0.684131919538
y[1] (closed_form) = 2.67588569325 0.681661598884
absolute error = 0.003389
relative error = 0.1227 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.84
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4091.1MB, alloc=52.3MB, time=52.67
x[1] = -1.0015 1.776
h = 0.0001 0.003
y[1] (numeric) = 2.68074153483 0.684352962496
y[1] (closed_form) = 2.68307103414 0.681875691949
absolute error = 0.003401
relative error = 0.1228 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.845
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0014 1.779
h = 0.001 0.001
y[1] (numeric) = 2.68506096867 0.68441975257
y[1] (closed_form) = 2.68739365866 0.681939888926
absolute error = 0.003405
relative error = 0.1228 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.848
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0004 1.78
h = 0.001 0.003
y[1] (numeric) = 2.6865691447 0.683048622977
y[1] (closed_form) = 2.68890130732 0.680568014848
absolute error = 0.003405
relative error = 0.1228 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.849
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9994 1.783
h = 0.0001 0.004
y[1] (numeric) = 2.6909560049 0.681810508347
y[1] (closed_form) = 2.69328955771 0.679325557743
absolute error = 0.003409
relative error = 0.1227 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.852
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9993 1.787
h = 0.003 0.006
y[1] (numeric) = 2.69672878332 0.681926048513
y[1] (closed_form) = 2.69906806545 0.679436571561
absolute error = 0.003416
relative error = 0.1227 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.856
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4136.6MB, alloc=52.3MB, time=53.24
x[1] = -0.9963 1.793
h = 0.0001 0.005
y[1] (numeric) = 2.70558392379 0.677968983175
y[1] (closed_form) = 2.70792368729 0.675458989018
absolute error = 0.003431
relative error = 0.123 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.862
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9962 1.798
h = 0.0001 0.003
y[1] (numeric) = 2.71282640858 0.678110889595
y[1] (closed_form) = 2.71517516686 0.675593876018
absolute error = 0.003443
relative error = 0.123 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.867
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9961 1.801
h = 0.001 0.001
y[1] (numeric) = 2.71718487107 0.67812957312
y[1] (closed_form) = 2.71953680056 0.675609941883
absolute error = 0.003447
relative error = 0.123 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.87
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9951 1.802
h = 0.0001 0.004
y[1] (numeric) = 2.7186909624 0.676729325557
y[1] (closed_form) = 2.7210423588 0.674208953781
absolute error = 0.003447
relative error = 0.123 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.871
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.995 1.806
h = 0.003 0.006
y[1] (numeric) = 2.72450963322 0.676790581966
y[1] (closed_form) = 2.72686672936 0.674265646526
absolute error = 0.003454
relative error = 0.123 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.875
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4182.1MB, alloc=52.3MB, time=53.81
x[1] = -0.992 1.812
h = 0.0001 0.005
y[1] (numeric) = 2.73339563404 0.672718373248
y[1] (closed_form) = 2.73575307713 0.670172913538
absolute error = 0.003469
relative error = 0.1232 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.882
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9919 1.817
h = 0.0001 0.003
y[1] (numeric) = 2.74069556763 0.67279252954
y[1] (closed_form) = 2.74306196124 0.670239990161
absolute error = 0.003481
relative error = 0.1233 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.887
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9918 1.82
h = 0.001 0.001
y[1] (numeric) = 2.7450879128 0.672770021106
y[1] (closed_form) = 2.74745746108 0.670214842774
absolute error = 0.003485
relative error = 0.1232 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.89
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9908 1.821
h = 0.001 0.003
y[1] (numeric) = 2.74659237857 0.671344691303
y[1] (closed_form) = 2.7489613888 0.668788775779
absolute error = 0.003485
relative error = 0.1232 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.891
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9898 1.824
h = 0.0001 0.004
y[1] (numeric) = 2.75102596115 0.669994473776
y[1] (closed_form) = 2.75339630039 0.66743419494
absolute error = 0.003489
relative error = 0.1232 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.894
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9897 1.828
h = 0.003 0.006
y[1] (numeric) = 2.75689661914 0.669991561014
y[1] (closed_form) = 2.75927262507 0.667426673457
absolute error = 0.003496
relative error = 0.1232 %
Correct digits = 3
memory used=4227.8MB, alloc=52.3MB, time=54.38
Radius of convergence (given) for eq 1 = 1.898
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9867 1.834
h = 0.0001 0.005
y[1] (numeric) = 2.76581566907 0.665784851115
y[1] (closed_form) = 2.76819186575 0.66319943391
absolute error = 0.003512
relative error = 0.1234 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.904
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9866 1.839
h = 0.0001 0.003
y[1] (numeric) = 2.77318068933 0.665778911762
y[1] (closed_form) = 2.7755657839 0.663186345876
absolute error = 0.003523
relative error = 0.1234 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.909
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9865 1.842
h = 0.001 0.001
y[1] (numeric) = 2.77761139221 0.665707730616
y[1] (closed_form) = 2.77999962179 0.663112501406
absolute error = 0.003527
relative error = 0.1234 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.912
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9855 1.843
h = 0.001 0.003
y[1] (numeric) = 2.7791133602 0.664253304255
y[1] (closed_form) = 2.78150104604 0.661657341843
absolute error = 0.003527
relative error = 0.1234 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.913
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9845 1.846
h = 0.0001 0.004
y[1] (numeric) = 2.78357101307 0.66284240041
y[1] (closed_form) = 2.78595999492 0.660242063924
absolute error = 0.003531
relative error = 0.1233 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.917
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4273.3MB, alloc=52.3MB, time=54.94
x[1] = -0.9844 1.85
h = 0.003 0.006
y[1] (numeric) = 2.78949317817 0.662774912744
y[1] (closed_form) = 2.79188779253 0.660169923743
absolute error = 0.003538
relative error = 0.1233 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.921
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9814 1.856
h = 0.0001 0.005
y[1] (numeric) = 2.7984442587 0.6584334308
y[1] (closed_form) = 2.80083890769 0.655807907489
absolute error = 0.003554
relative error = 0.1235 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.927
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9813 1.861
h = 0.0001 0.003
y[1] (numeric) = 2.80587376616 0.658346888507
y[1] (closed_form) = 2.8082772601 0.655714147781
absolute error = 0.003565
relative error = 0.1236 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.932
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9812 1.864
h = 0.001 0.001
y[1] (numeric) = 2.81034246256 0.658226735325
y[1] (closed_form) = 2.81274907177 0.655591307009
absolute error = 0.003569
relative error = 0.1236 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.935
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9802 1.865
h = 0.001 0.003
y[1] (numeric) = 2.81184171113 0.656743226773
y[1] (closed_form) = 2.81424777093 0.654107069268
absolute error = 0.003569
relative error = 0.1235 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.936
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4318.8MB, alloc=52.3MB, time=55.52
x[1] = -0.9792 1.868
h = 0.0001 0.004
y[1] (numeric) = 2.81632297667 0.655271443835
y[1] (closed_form) = 2.81873029946 0.652630901651
absolute error = 0.003573
relative error = 0.1235 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.939
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9791 1.872
h = 0.003 0.006
y[1] (numeric) = 2.82229616632 0.655138979049
y[1] (closed_form) = 2.82470908724 0.65249374074
absolute error = 0.00358
relative error = 0.1235 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.943
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9761 1.878
h = 0.0001 0.005
y[1] (numeric) = 2.83127825831 0.650662459006
y[1] (closed_form) = 2.8336910578 0.647996682438
absolute error = 0.003596
relative error = 0.1237 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.95
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.976 1.883
h = 0.0001 0.003
y[1] (numeric) = 2.83877165151 0.650494809514
y[1] (closed_form) = 2.84119324275 0.647821747077
absolute error = 0.003607
relative error = 0.1238 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.955
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9759 1.886
h = 0.001 0.001
y[1] (numeric) = 2.8432779761 0.650325386811
y[1] (closed_form) = 2.84570266276 0.647649612623
absolute error = 0.003611
relative error = 0.1237 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.957
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4364.3MB, alloc=52.3MB, time=56.08
x[1] = -0.9749 1.887
h = 0.001 0.003
y[1] (numeric) = 2.8447742838 0.648812811438
y[1] (closed_form) = 2.84719841541 0.646136312097
absolute error = 0.003611
relative error = 0.1237 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.959
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9739 1.89
h = 0.0001 0.004
y[1] (numeric) = 2.84927870377 0.647279958838
y[1] (closed_form) = 2.85170406532 0.644599064369
absolute error = 0.003615
relative error = 0.1237 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.962
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9738 1.894
h = 0.003 0.006
y[1] (numeric) = 2.85530243384 0.647082117156
y[1] (closed_form) = 2.85773335897 0.644396483133
absolute error = 0.003622
relative error = 0.1237 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.966
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9708 1.9
h = 0.0001 0.005
y[1] (numeric) = 2.86431451753 0.642470297768
y[1] (closed_form) = 2.86674516524 0.639764122253
absolute error = 0.003638
relative error = 0.1238 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.972
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9707 1.905
h = 0.0001 0.003
y[1] (numeric) = 2.87187119307 0.642221039858
y[1] (closed_form) = 2.87431057905 0.639507510303
absolute error = 0.003649
relative error = 0.1239 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.977
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4409.9MB, alloc=52.3MB, time=56.66
x[1] = -0.9706 1.908
h = 0.001 0.001
y[1] (numeric) = 2.87641477936 0.642002051992
y[1] (closed_form) = 2.87885724082 0.639285786627
absolute error = 0.003653
relative error = 0.1239 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.98
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9696 1.909
h = 0.0001 0.004
y[1] (numeric) = 2.87790792495 0.64046042617
y[1] (closed_form) = 2.88034982573 0.637743439712
absolute error = 0.003653
relative error = 0.1238 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.981
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9695 1.913
h = 0.003 0.006
y[1] (numeric) = 2.88397555574 0.640206585074
y[1] (closed_form) = 2.88642298984 0.637484822468
absolute error = 0.00366
relative error = 0.1238 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.985
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9665 1.919
h = 0.0001 0.005
y[1] (numeric) = 2.89301425405 0.635478439714
y[1] (closed_form) = 2.89546127656 0.632736131549
absolute error = 0.003675
relative error = 0.124 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.992
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9664 1.924
h = 0.0001 0.003
y[1] (numeric) = 2.90062589643 0.635159280963
y[1] (closed_form) = 2.90308161176 0.632409559661
absolute error = 0.003687
relative error = 0.1241 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 1.997
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4455.5MB, alloc=52.3MB, time=57.23
x[1] = -0.9663 1.927
h = 0.001 0.001
y[1] (numeric) = 2.9052018572 0.634897831619
y[1] (closed_form) = 2.90766063105 0.632145353645
absolute error = 0.003691
relative error = 0.124 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9653 1.928
h = 0.001 0.003
y[1] (numeric) = 2.90669244969 0.633331172766
y[1] (closed_form) = 2.90915065798 0.630577977145
absolute error = 0.003691
relative error = 0.124 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.001
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9643 1.931
h = 0.0001 0.004
y[1] (numeric) = 2.91123946574 0.63168444701
y[1] (closed_form) = 2.91369884252 0.628926836843
absolute error = 0.003695
relative error = 0.124 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.004
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9642 1.935
h = 0.003 0.006
y[1] (numeric) = 2.9173567358 0.63136448688
y[1] (closed_form) = 2.9198216119 0.628602056416
absolute error = 0.003702
relative error = 0.124 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.008
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9612 1.941
h = 0.0001 0.005
y[1] (numeric) = 2.92642352965 0.626500556694
y[1] (closed_form) = 2.92888783831 0.623717578767
absolute error = 0.003717
relative error = 0.1241 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.014
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4501.1MB, alloc=52.3MB, time=57.80
x[1] = -0.9611 1.946
h = 0.0001 0.003
y[1] (numeric) = 2.93409733231 0.626098857743
y[1] (closed_form) = 2.93657027978 0.623308399028
absolute error = 0.003729
relative error = 0.1242 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.019
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.961 1.949
h = 0.001 0.001
y[1] (numeric) = 2.9387098733 0.625787293625
y[1] (closed_form) = 2.94118585915 0.622994054374
absolute error = 0.003733
relative error = 0.1242 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.022
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.96 1.95
h = 0.001 0.003
y[1] (numeric) = 2.94019689229 0.624191614822
y[1] (closed_form) = 2.94267230701 0.621397662028
absolute error = 0.003733
relative error = 0.1241 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.023
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.959 1.953
h = 0.0001 0.004
y[1] (numeric) = 2.94476575077 0.622483280914
y[1] (closed_form) = 2.94724230084 0.619684903574
absolute error = 0.003737
relative error = 0.1241 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.027
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9589 1.957
h = 0.003 0.006
y[1] (numeric) = 2.95093217242 0.622096807896
y[1] (closed_form) = 2.95341418674 0.619293567351
absolute error = 0.003744
relative error = 0.1241 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.03
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4546.7MB, alloc=52.3MB, time=58.38
x[1] = -0.9559 1.963
h = 0.0001 0.005
y[1] (numeric) = 2.9600260403 0.617096845387
y[1] (closed_form) = 2.96250733142 0.614273056188
absolute error = 0.003759
relative error = 0.1242 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.037
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9558 1.968
h = 0.0001 0.003
y[1] (numeric) = 2.96776139427 0.616612113719
y[1] (closed_form) = 2.97025126992 0.613780776364
absolute error = 0.00377
relative error = 0.1243 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.042
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9557 1.971
h = 0.001 0.001
y[1] (numeric) = 2.97241014573 0.616250144452
y[1] (closed_form) = 2.97490303954 0.613416002803
absolute error = 0.003775
relative error = 0.1243 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.045
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9547 1.972
h = 0.001 0.003
y[1] (numeric) = 2.97389337055 0.614625464936
y[1] (closed_form) = 2.97638568766 0.611790613872
absolute error = 0.003775
relative error = 0.1242 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.046
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9537 1.975
h = 0.0001 0.004
y[1] (numeric) = 2.97848361091 0.612855340809
y[1] (closed_form) = 2.98097703021 0.610016055355
absolute error = 0.003779
relative error = 0.1242 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.049
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4592.1MB, alloc=52.3MB, time=58.94
x[1] = -0.9536 1.979
h = 0.003 0.006
y[1] (numeric) = 2.98469869407 0.61240196456
y[1] (closed_form) = 2.98719754239 0.609557773178
absolute error = 0.003786
relative error = 0.1242 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.053
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9506 1.985
h = 0.0001 0.005
y[1] (numeric) = 2.99381861393 0.607265727039
y[1] (closed_form) = 2.99631658336 0.604400986523
absolute error = 0.003801
relative error = 0.1243 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.06
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9505 1.99
h = 0.0001 0.003
y[1] (numeric) = 3.00161490833 0.606697473195
y[1] (closed_form) = 3.00412140773 0.603825117439
absolute error = 0.003812
relative error = 0.1244 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.064
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9504 1.993
h = 0.001 0.001
y[1] (numeric) = 3.0062994994 0.606284810256
y[1] (closed_form) = 3.00880899663 0.603409626555
absolute error = 0.003816
relative error = 0.1244 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.067
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9494 1.994
h = 0.001 0.003
y[1] (numeric) = 3.00777870958 0.604631150262
y[1] (closed_form) = 3.01028762457 0.601755261295
absolute error = 0.003816
relative error = 0.1243 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.069
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4637.6MB, alloc=52.3MB, time=59.52
x[1] = -0.9484 1.997
h = 0.0001 0.004
y[1] (numeric) = 3.0123898707 0.602799056055
y[1] (closed_form) = 3.0148998547 0.599918723012
absolute error = 0.003821
relative error = 0.1243 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.072
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9483 2.001
h = 0.003 0.006
y[1] (numeric) = 3.01865312378 0.602278388689
y[1] (closed_form) = 3.02116850138 0.599393107179
absolute error = 0.003828
relative error = 0.1243 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.076
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9453 2.007
h = 0.0001 0.005
y[1] (numeric) = 3.027798073 0.597005638271
y[1] (closed_form) = 3.03031241612 0.59409980786
absolute error = 0.003843
relative error = 0.1244 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.082
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9452 2.012
h = 0.0001 0.003
y[1] (numeric) = 3.03565469507 0.596353375855
y[1] (closed_form) = 3.03817751331 0.593439863405
absolute error = 0.003854
relative error = 0.1245 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.087
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9451 2.015
h = 0.001 0.001
y[1] (numeric) = 3.04037475376 0.595889732577
y[1] (closed_form) = 3.04290054942 0.592973368634
absolute error = 0.003858
relative error = 0.1244 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.09
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4683.3MB, alloc=52.3MB, time=60.09
x[1] = -0.9441 2.016
h = 0.0001 0.004
y[1] (numeric) = 3.04184972905 0.594207113336
y[1] (closed_form) = 3.04437493696 0.591290048299
absolute error = 0.003858
relative error = 0.1244 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.091
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.944 2.02
h = 0.003 0.006
y[1] (numeric) = 3.048154859 0.593628780056
y[1] (closed_form) = 3.05068542959 0.590706730694
absolute error = 0.003866
relative error = 0.1244 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.095
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.941 2.026
h = 0.0001 0.005
y[1] (numeric) = 3.05732216329 0.588238618629
y[1] (closed_form) = 3.05985156552 0.585296019283
absolute error = 0.00388
relative error = 0.1246 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.102
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9409 2.031
h = 0.0001 0.003
y[1] (numeric) = 3.06523122979 0.587514365938
y[1] (closed_form) = 3.06776906052 0.584564026626
absolute error = 0.003892
relative error = 0.1246 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.107
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9408 2.034
h = 0.001 0.001
y[1] (numeric) = 3.06998213101 0.587007028784
y[1] (closed_form) = 3.07252292178 0.584053817551
absolute error = 0.003896
relative error = 0.1246 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.109
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4728.8MB, alloc=52.3MB, time=60.66
x[1] = -0.9398 2.035
h = 0.001 0.003
y[1] (numeric) = 3.07145362944 0.585299446137
y[1] (closed_form) = 3.07399382767 0.582345537355
absolute error = 0.003896
relative error = 0.1245 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.111
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9388 2.038
h = 0.0001 0.004
y[1] (numeric) = 3.07610323312 0.583351805137
y[1] (closed_form) = 3.07864443864 0.580393434278
absolute error = 0.0039
relative error = 0.1245 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.114
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9387 2.042
h = 0.003 0.006
y[1] (numeric) = 3.08245561801 0.582705460662
y[1] (closed_form) = 3.08500215128 0.579742062246
absolute error = 0.003907
relative error = 0.1245 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.118
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9357 2.048
h = 0.0001 0.005
y[1] (numeric) = 3.09164605015 0.577178344283
y[1] (closed_form) = 3.0941912596 0.574194397439
absolute error = 0.003922
relative error = 0.1246 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.124
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9356 2.053
h = 0.0001 0.003
y[1] (numeric) = 3.09961430477 0.576369178766
y[1] (closed_form) = 3.10216788737 0.573377425684
absolute error = 0.003933
relative error = 0.1247 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.129
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4774.4MB, alloc=52.3MB, time=61.23
x[1] = -0.9355 2.056
h = 0.001 0.001
y[1] (numeric) = 3.10439998186 0.575810328331
y[1] (closed_form) = 3.10695650391 0.572815679979
absolute error = 0.003937
relative error = 0.1246 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.132
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9345 2.057
h = 0.001 0.003
y[1] (numeric) = 3.10586683587 0.574073825972
y[1] (closed_form) = 3.1084227599 0.571078484286
absolute error = 0.003938
relative error = 0.1246 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.133
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9335 2.06
h = 0.0001 0.004
y[1] (numeric) = 3.11053604008 0.572063707026
y[1] (closed_form) = 3.11309293815 0.569063894027
absolute error = 0.003942
relative error = 0.1246 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.136
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9334 2.064
h = 0.003 0.006
y[1] (numeric) = 3.11693518482 0.571348969464
y[1] (closed_form) = 3.11949737471 0.568344086896
absolute error = 0.003949
relative error = 0.1245 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.14
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9304 2.07
h = 0.0001 0.005
y[1] (numeric) = 3.12614772067 0.565684673986
y[1] (closed_form) = 3.1287084314 0.562659245255
absolute error = 0.003964
relative error = 0.1247 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.147
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4819.9MB, alloc=52.3MB, time=61.80
x[1] = -0.9303 2.075
h = 0.0001 0.003
y[1] (numeric) = 3.13417454522 0.564790118011
y[1] (closed_form) = 3.13674357347 0.561756817058
absolute error = 0.003975
relative error = 0.1247 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.152
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9302 2.078
h = 0.001 0.001
y[1] (numeric) = 3.13899462303 0.564179472932
y[1] (closed_form) = 3.14156657004 0.561143253466
absolute error = 0.003979
relative error = 0.1247 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.155
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9292 2.079
h = 0.001 0.003
y[1] (numeric) = 3.14045661298 0.562414074938
y[1] (closed_form) = 3.14302795652 0.559377166377
absolute error = 0.003979
relative error = 0.1246 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.156
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9282 2.082
h = 0.0001 0.004
y[1] (numeric) = 3.14514495443 0.560341306702
y[1] (closed_form) = 3.14771723871 0.557299917747
absolute error = 0.003983
relative error = 0.1246 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.159
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9281 2.086
h = 0.003 0.006
y[1] (numeric) = 3.15159036163 0.559557797667
y[1] (closed_form) = 3.15416790165 0.556511297318
absolute error = 0.003991
relative error = 0.1246 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.163
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9251 2.092
h = 0.0001 0.005
y[1] (numeric) = 3.1608239766 0.553756103744
y[1] (closed_form) = 3.16339988219 0.550689060207
absolute error = 0.004005
relative error = 0.1247 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.17
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4865.4MB, alloc=52.3MB, time=62.37
x[1] = -0.925 2.097
h = 0.0001 0.003
y[1] (numeric) = 3.16890875103 0.552775682759
y[1] (closed_form) = 3.17149291826 0.549700701303
absolute error = 0.004017
relative error = 0.1248 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.174
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9249 2.1
h = 0.001 0.001
y[1] (numeric) = 3.17376285332 0.552112963538
y[1] (closed_form) = 3.17634991852 0.549035040433
absolute error = 0.004021
relative error = 0.1247 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.177
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9239 2.101
h = 0.001 0.003
y[1] (numeric) = 3.1752197598 0.550318694979
y[1] (closed_form) = 3.17780621609 0.547240087039
absolute error = 0.004021
relative error = 0.1247 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.179
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9229 2.104
h = 0.0001 0.004
y[1] (numeric) = 3.17992677464 0.548183108318
y[1] (closed_form) = 3.18251413837 0.545100011061
absolute error = 0.004025
relative error = 0.1247 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.182
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9228 2.108
h = 0.003 0.006
y[1] (numeric) = 3.18641794547 0.547330451896
y[1] (closed_form) = 3.18901052867 0.544242201607
absolute error = 0.004032
relative error = 0.1246 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.186
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4911.1MB, alloc=52.3MB, time=62.93
x[1] = -0.9198 2.114
h = 0.0001 0.005
y[1] (numeric) = 3.19567161447 0.541391144985
y[1] (closed_form) = 3.19826240807 0.53828235519
absolute error = 0.004047
relative error = 0.1248 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.192
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9197 2.119
h = 0.0001 0.003
y[1] (numeric) = 3.20381371689 0.540324387521
y[1] (closed_form) = 3.20641271597 0.537207594399
absolute error = 0.004058
relative error = 0.1248 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.197
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9196 2.122
h = 0.001 0.001
y[1] (numeric) = 3.20870146634 0.539609316525
y[1] (closed_form) = 3.2113033425 0.536489558725
absolute error = 0.004062
relative error = 0.1248 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.2
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9186 2.123
h = 0.0001 0.004
y[1] (numeric) = 3.21015307017 0.53778620346
y[1] (closed_form) = 3.21275433202 0.534665765108
absolute error = 0.004062
relative error = 0.1247 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.201
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9185 2.127
h = 0.003 0.006
y[1] (numeric) = 3.21668406267 0.536874264151
y[1] (closed_form) = 3.21929051243 0.533748637655
absolute error = 0.00407
relative error = 0.1247 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.205
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4956.6MB, alloc=52.3MB, time=63.51
x[1] = -0.9155 2.133
h = 0.0001 0.005
y[1] (numeric) = 3.22595581495 0.53081655869
y[1] (closed_form) = 3.22856034156 0.527670394579
absolute error = 0.004084
relative error = 0.1249 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.212
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9154 2.138
h = 0.0001 0.003
y[1] (numeric) = 3.23414780003 0.529675783258
y[1] (closed_form) = 3.23676048434 0.526521559077
absolute error = 0.004096
relative error = 0.1249 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.216
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9153 2.141
h = 0.001 0.001
y[1] (numeric) = 3.23906483693 0.528915823374
y[1] (closed_form) = 3.24168038055 0.525758614527
absolute error = 0.0041
relative error = 0.1248 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.219
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9143 2.142
h = 0.001 0.003
y[1] (numeric) = 3.24051204424 0.52706783683
y[1] (closed_form) = 3.24312696885 0.523909951072
absolute error = 0.0041
relative error = 0.1248 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.221
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9133 2.145
h = 0.0001 0.004
y[1] (numeric) = 3.24525332248 0.524815126515
y[1] (closed_form) = 3.24786909259 0.521652734856
absolute error = 0.004104
relative error = 0.1248 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.224
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5002.2MB, alloc=52.3MB, time=64.07
x[1] = -0.9132 2.149
h = 0.003 0.006
y[1] (numeric) = 3.25182915019 0.523833341958
y[1] (closed_form) = 3.25445007233 0.52066571985
absolute error = 0.004111
relative error = 0.1247 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.228
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9102 2.155
h = 0.0001 0.005
y[1] (numeric) = 3.26111905031 0.517637624844
y[1] (closed_form) = 3.26373789432 0.51444947012
absolute error = 0.004126
relative error = 0.1249 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.234
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9101 2.16
h = 0.0001 0.003
y[1] (numeric) = 3.26936720684 0.516409636404
y[1] (closed_form) = 3.27199415188 0.513213356737
absolute error = 0.004137
relative error = 0.1249 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.239
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.91 2.163
h = 0.001 0.001
y[1] (numeric) = 3.27431718917 0.515596808588
y[1] (closed_form) = 3.27694697247 0.512397521425
absolute error = 0.004141
relative error = 0.1249 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.242
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.909 2.164
h = 0.001 0.003
y[1] (numeric) = 3.27575868628 0.513720026057
y[1] (closed_form) = 3.27838784519 0.510520066308
absolute error = 0.004142
relative error = 0.1248 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.243
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5047.8MB, alloc=52.3MB, time=64.64
x[1] = -0.908 2.167
h = 0.0001 0.004
y[1] (numeric) = 3.28051730998 0.511404020118
y[1] (closed_form) = 3.28314728102 0.508199545994
absolute error = 0.004146
relative error = 0.1248 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.246
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9079 2.171
h = 0.003 0.006
y[1] (numeric) = 3.28713747058 0.510352020465
y[1] (closed_form) = 3.28977255689 0.507142274788
absolute error = 0.004153
relative error = 0.1248 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.25
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9049 2.177
h = 0.0001 0.005
y[1] (numeric) = 3.29644449216 0.504018090875
y[1] (closed_form) = 3.29907734545 0.500787818288
absolute error = 0.004167
relative error = 0.1249 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.257
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9048 2.182
h = 0.0001 0.003
y[1] (numeric) = 3.30474819299 0.502702426784
y[1] (closed_form) = 3.30738909039 0.499463964672
absolute error = 0.004179
relative error = 0.1249 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.262
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9047 2.185
h = 0.001 0.001
y[1] (numeric) = 3.30973074036 0.501836458745
y[1] (closed_form) = 3.31237445485 0.498594966414
absolute error = 0.004183
relative error = 0.1249 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.265
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5093.3MB, alloc=52.3MB, time=65.21
x[1] = -0.9037 2.186
h = 0.001 0.003
y[1] (numeric) = 3.31116630873 0.499930909114
y[1] (closed_form) = 3.3138093935 0.496688748546
absolute error = 0.004183
relative error = 0.1248 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.266
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9027 2.189
h = 0.0001 0.004
y[1] (numeric) = 3.31594181201 0.497551446944
y[1] (closed_form) = 3.3185856755 0.494304763682
absolute error = 0.004187
relative error = 0.1248 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.269
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9026 2.193
h = 0.003 0.006
y[1] (numeric) = 3.32260580103 0.496428865845
y[1] (closed_form) = 3.32525474288 0.493176870116
absolute error = 0.004194
relative error = 0.1248 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.273
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8996 2.199
h = 0.0001 0.005
y[1] (numeric) = 3.33192891729 0.489956527756
y[1] (closed_form) = 3.33457547133 0.486684011528
absolute error = 0.004209
relative error = 0.1249 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.279
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8995 2.204
h = 0.0001 0.003
y[1] (numeric) = 3.34028753348 0.488552728471
y[1] (closed_form) = 3.34294207442 0.485271958426
absolute error = 0.00422
relative error = 0.1249 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.284
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5138.7MB, alloc=52.3MB, time=65.77
x[1] = -0.8994 2.207
h = 0.001 0.001
y[1] (numeric) = 3.34530226441 0.487633349792
y[1] (closed_form) = 3.3479596012 0.484349526914
absolute error = 0.004224
relative error = 0.1249 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.287
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8984 2.208
h = 0.001 0.003
y[1] (numeric) = 3.34673168578 0.485699062938
y[1] (closed_form) = 3.34938838752 0.482414576192
absolute error = 0.004224
relative error = 0.1248 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.288
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8974 2.211
h = 0.0001 0.004
y[1] (numeric) = 3.35152360224 0.48325598614
y[1] (closed_form) = 3.35418104928 0.47996696854
absolute error = 0.004228
relative error = 0.1248 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.292
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8973 2.215
h = 0.003 0.006
y[1] (numeric) = 3.3582309138 0.482062459736
y[1] (closed_form) = 3.36089340211 0.478768088943
absolute error = 0.004236
relative error = 0.1248 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.296
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8943 2.221
h = 0.0001 0.005
y[1] (numeric) = 3.36756909756 0.475451521919
y[1] (closed_form) = 3.37022904339 0.472136637742
absolute error = 0.00425
relative error = 0.1249 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.302
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5184.4MB, alloc=52.3MB, time=66.34
x[1] = -0.8942 2.226
h = 0.0001 0.003
y[1] (numeric) = 3.37598199836 0.473959131
y[1] (closed_form) = 3.37864987362 0.470635929008
absolute error = 0.004262
relative error = 0.1249 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.307
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8941 2.229
h = 0.001 0.001
y[1] (numeric) = 3.38102853034 0.472986073145
y[1] (closed_form) = 3.38369918012 0.469659795814
absolute error = 0.004266
relative error = 0.1249 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.31
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8931 2.23
h = 0.0001 0.004
y[1] (numeric) = 3.38245158666 0.471023079924
y[1] (closed_form) = 3.38512159609 0.467696143117
absolute error = 0.004266
relative error = 0.1248 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.311
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.893 2.234
h = 0.003 0.006
y[1] (numeric) = 3.38919663423 0.46976870354
y[1] (closed_form) = 3.3918716527 0.466436379184
absolute error = 0.004273
relative error = 0.1248 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.315
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.89 2.24
h = 0.0001 0.005
y[1] (numeric) = 3.39854861878 0.463038477052
y[1] (closed_form) = 3.40122096162 0.459685644163
absolute error = 0.004288
relative error = 0.1249 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.322
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5229.9MB, alloc=52.3MB, time=66.91
x[1] = -0.8899 2.245
h = 0.0001 0.003
y[1] (numeric) = 3.40700880215 0.461470102658
y[1] (closed_form) = 3.40968902551 0.458108896411
absolute error = 0.004299
relative error = 0.125 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.326
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8898 2.248
h = 0.001 0.001
y[1] (numeric) = 3.41208304406 0.46045099855
y[1] (closed_form) = 3.41476602375 0.457086697422
absolute error = 0.004303
relative error = 0.1249 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.329
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8888 2.249
h = 0.001 0.003
y[1] (numeric) = 3.41350078858 0.458463241958
y[1] (closed_form) = 3.41618312334 0.45509828509
absolute error = 0.004303
relative error = 0.1249 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.331
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8878 2.252
h = 0.0001 0.004
y[1] (numeric) = 3.41832276528 0.455901561555
y[1] (closed_form) = 3.42100578318 0.452532058665
absolute error = 0.004307
relative error = 0.1248 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.334
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8877 2.256
h = 0.003 0.006
y[1] (numeric) = 3.42511019389 0.454575564376
y[1] (closed_form) = 3.42779818407 0.451200632568
absolute error = 0.004315
relative error = 0.1248 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.338
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5275.6MB, alloc=52.3MB, time=67.48
x[1] = -0.8847 2.262
h = 0.0001 0.005
y[1] (numeric) = 3.43447533579 0.447706382838
y[1] (closed_form) = 3.43716049584 0.444310950924
absolute error = 0.004329
relative error = 0.1249 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.344
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8846 2.267
h = 0.0001 0.003
y[1] (numeric) = 3.44298863071 0.446048568198
y[1] (closed_form) = 3.44568161332 0.442644699469
absolute error = 0.00434
relative error = 0.1249 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.349
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8845 2.27
h = 0.001 0.001
y[1] (numeric) = 3.44809396227 0.444975285651
y[1] (closed_form) = 3.45078967971 0.441568299736
absolute error = 0.004344
relative error = 0.1249 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.352
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8835 2.271
h = 0.001 0.003
y[1] (numeric) = 3.4495049363 0.442958880138
y[1] (closed_form) = 3.45220000354 0.439551242916
absolute error = 0.004345
relative error = 0.1248 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.353
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8825 2.274
h = 0.0001 0.004
y[1] (numeric) = 3.45434199104 0.440333138613
y[1] (closed_form) = 3.45703770794 0.436920947658
absolute error = 0.004349
relative error = 0.1248 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.356
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5321.1MB, alloc=52.3MB, time=68.04
x[1] = -0.8824 2.278
h = 0.003 0.006
y[1] (numeric) = 3.46117129139 0.43893516291
y[1] (closed_form) = 3.463871943 0.435517502852
absolute error = 0.004356
relative error = 0.1248 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.36
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8794 2.284
h = 0.0001 0.005
y[1] (numeric) = 3.47054856237 0.431926848799
y[1] (closed_form) = 3.47324622948 0.428488697765
absolute error = 0.00437
relative error = 0.1249 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.367
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8793 2.289
h = 0.0001 0.003
y[1] (numeric) = 3.47911433298 0.430179146358
y[1] (closed_form) = 3.48181976442 0.426732495346
absolute error = 0.004382
relative error = 0.1249 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.372
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8792 2.292
h = 0.001 0.001
y[1] (numeric) = 3.48425036869 0.429051422209
y[1] (closed_form) = 3.48695851337 0.425601631814
absolute error = 0.004386
relative error = 0.1249 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.375
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8782 2.293
h = 0.001 0.003
y[1] (numeric) = 3.4856543549 0.427006401445
y[1] (closed_form) = 3.48836184414 0.423555964199
absolute error = 0.004386
relative error = 0.1248 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.376
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5366.7MB, alloc=52.3MB, time=68.61
x[1] = -0.8772 2.296
h = 0.0001 0.004
y[1] (numeric) = 3.4905060194 0.424316448938
y[1] (closed_form) = 3.49321412479 0.420861450404
absolute error = 0.00439
relative error = 0.1248 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.379
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8771 2.3
h = 0.003 0.006
y[1] (numeric) = 3.49737668014 0.42284614048
y[1] (closed_form) = 3.50008968251 0.419385632847
absolute error = 0.004397
relative error = 0.1247 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.383
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8741 2.306
h = 0.0001 0.005
y[1] (numeric) = 3.5067650516 0.415698521062
y[1] (closed_form) = 3.50947491522 0.412217532286
absolute error = 0.004411
relative error = 0.1248 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.389
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.874 2.311
h = 0.0001 0.003
y[1] (numeric) = 3.51538266031 0.413860486385
y[1] (closed_form) = 3.51810022977 0.410370934763
absolute error = 0.004423
relative error = 0.1249 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.394
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8739 2.314
h = 0.001 0.001
y[1] (numeric) = 3.52054901364 0.41267805936
y[1] (closed_form) = 3.52326927465 0.409185346267
absolute error = 0.004427
relative error = 0.1248 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.397
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8729 2.315
h = 0.001 0.003
y[1] (numeric) = 3.52194579495 0.410604457994
y[1] (closed_form) = 3.5246653953 0.407111102527
absolute error = 0.004427
relative error = 0.1248 %
Correct digits = 3
memory used=5412.4MB, alloc=52.3MB, time=69.18
Radius of convergence (given) for eq 1 = 2.398
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8719 2.318
h = 0.0001 0.004
y[1] (numeric) = 3.52681160045 0.407850146858
y[1] (closed_form) = 3.52953178343 0.404352222705
absolute error = 0.004431
relative error = 0.1247 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.402
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8718 2.322
h = 0.003 0.006
y[1] (numeric) = 3.53372310885 0.406307153917
y[1] (closed_form) = 3.53644815091 0.402803680862
absolute error = 0.004438
relative error = 0.1247 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.405
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8688 2.328
h = 0.0001 0.005
y[1] (numeric) = 3.54312155191 0.399020061249
y[1] (closed_form) = 3.54584330107 0.395496117584
absolute error = 0.004453
relative error = 0.1248 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.412
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8687 2.333
h = 0.0001 0.003
y[1] (numeric) = 3.55179035936 0.397091253025
y[1] (closed_form) = 3.55451975563 0.393558683941
absolute error = 0.004464
relative error = 0.1248 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.417
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8686 2.336
h = 0.001 0.001
y[1] (numeric) = 3.55698664277 0.395853863738
y[1] (closed_form) = 3.5597187088 0.392318111206
absolute error = 0.004468
relative error = 0.1248 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.42
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5457.9MB, alloc=52.3MB, time=69.75
x[1] = -0.8676 2.337
h = 0.0001 0.004
y[1] (numeric) = 3.55837600236 0.393751717396
y[1] (closed_form) = 3.56110740254 0.390215326989
absolute error = 0.004468
relative error = 0.1247 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.421
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8675 2.341
h = 0.003 0.006
y[1] (numeric) = 3.56532313149 0.392146357603
y[1] (closed_form) = 3.56805935789 0.388604384707
absolute error = 0.004476
relative error = 0.1247 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.425
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8645 2.347
h = 0.0001 0.005
y[1] (numeric) = 3.57473108373 0.38473918347
y[1] (closed_form) = 3.5774638845 0.381176747757
absolute error = 0.00449
relative error = 0.1248 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.432
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8644 2.352
h = 0.0001 0.003
y[1] (numeric) = 3.58344453645 0.382732488884
y[1] (closed_form) = 3.58618493431 0.379161373426
absolute error = 0.004501
relative error = 0.1248 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.436
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8643 2.355
h = 0.001 0.001
y[1] (numeric) = 3.58866693045 0.381447933877
y[1] (closed_form) = 3.5914099795 0.377873615879
absolute error = 0.004506
relative error = 0.1248 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.439
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5503.5MB, alloc=52.3MB, time=70.31
x[1] = -0.8633 2.356
h = 0.001 0.003
y[1] (numeric) = 3.59005006767 0.37932115433
y[1] (closed_form) = 3.59279244637 0.375746202285
absolute error = 0.004506
relative error = 0.1247 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.441
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8623 2.359
h = 0.0001 0.004
y[1] (numeric) = 3.59494170777 0.376446856663
y[1] (closed_form) = 3.59768460676 0.372867322182
absolute error = 0.00451
relative error = 0.1247 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.444
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8622 2.363
h = 0.003 0.006
y[1] (numeric) = 3.60192873039 0.374768159413
y[1] (closed_form) = 3.60467641796 0.371183002019
absolute error = 0.004517
relative error = 0.1246 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.448
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8592 2.369
h = 0.0001 0.005
y[1] (numeric) = 3.61134484077 0.3672212
y[1] (closed_form) = 3.61408894879 0.363615591628
absolute error = 0.004531
relative error = 0.1247 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.454
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8591 2.374
h = 0.0001 0.003
y[1] (numeric) = 3.62010830314 0.365122911355
y[1] (closed_form) = 3.62285994901 0.361508561215
absolute error = 0.004543
relative error = 0.1248 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.459
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5549.0MB, alloc=52.3MB, time=70.88
x[1] = -0.859 2.377
h = 0.001 0.001
y[1] (numeric) = 3.62535990644 0.363782911824
y[1] (closed_form) = 3.62811418155 0.360165337369
absolute error = 0.004547
relative error = 0.1247 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.462
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.858 2.378
h = 0.001 0.003
y[1] (numeric) = 3.62673521873 0.361627653617
y[1] (closed_form) = 3.62948881835 0.358009449655
absolute error = 0.004547
relative error = 0.1247 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.463
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.857 2.381
h = 0.0001 0.004
y[1] (numeric) = 3.63163965798 0.358688581564
y[1] (closed_form) = 3.63439374432 0.355065788214
absolute error = 0.004551
relative error = 0.1246 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.466
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8569 2.385
h = 0.003 0.006
y[1] (numeric) = 3.638666058 0.356936201325
y[1] (closed_form) = 3.64142489453 0.353307745807
absolute error = 0.004558
relative error = 0.1246 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.47
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8539 2.391
h = 0.0001 0.005
y[1] (numeric) = 3.64808929675 0.349249302374
y[1] (closed_form) = 3.65084439992 0.345600408415
absolute error = 0.004572
relative error = 0.1247 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.477
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5594.7MB, alloc=52.3MB, time=71.44
x[1] = -0.8538 2.396
h = 0.0001 0.003
y[1] (numeric) = 3.65690212447 0.347058987301
y[1] (closed_form) = 3.65966470602 0.343401289847
absolute error = 0.004584
relative error = 0.1247 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.482
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8537 2.399
h = 0.001 0.001
y[1] (numeric) = 3.66218254662 0.345663289269
y[1] (closed_form) = 3.66494773537 0.342002345835
absolute error = 0.004588
relative error = 0.1246 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.485
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8527 2.4
h = 0.001 0.003
y[1] (numeric) = 3.66354981791 0.34347959082
y[1] (closed_form) = 3.66631432605 0.339818022441
absolute error = 0.004588
relative error = 0.1246 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.486
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8517 2.403
h = 0.0001 0.004
y[1] (numeric) = 3.6684665858 0.340475605277
y[1] (closed_form) = 3.67123154705 0.336809440718
absolute error = 0.004592
relative error = 0.1246 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.489
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8516 2.407
h = 0.003 0.006
y[1] (numeric) = 3.67553184519 0.33864920001
y[1] (closed_form) = 3.6783015181 0.334977334218
absolute error = 0.004599
relative error = 0.1245 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.493
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5640.1MB, alloc=52.3MB, time=72.01
x[1] = -0.8486 2.413
h = 0.0001 0.005
y[1] (numeric) = 3.68496118229 0.330822212047
y[1] (closed_form) = 3.68772696817 0.32712992105
absolute error = 0.004613
relative error = 0.1246 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.499
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8485 2.418
h = 0.0001 0.003
y[1] (numeric) = 3.69382272938 0.328539441314
y[1] (closed_form) = 3.69659593389 0.324838285393
absolute error = 0.004625
relative error = 0.1246 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.504
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8484 2.421
h = 0.001 0.001
y[1] (numeric) = 3.69913157894 0.327087792701
y[1] (closed_form) = 3.70190736852 0.323383369247
absolute error = 0.004629
relative error = 0.1246 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.507
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8474 2.422
h = 0.001 0.003
y[1] (numeric) = 3.70049059343 0.324875693404
y[1] (closed_form) = 3.70326569729 0.321170649586
absolute error = 0.004629
relative error = 0.1245 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.508
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8464 2.425
h = 0.0001 0.004
y[1] (numeric) = 3.705419219 0.321806657484
y[1] (closed_form) = 3.70819474237 0.318097010848
absolute error = 0.004633
relative error = 0.1245 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.512
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5685.6MB, alloc=52.3MB, time=72.58
x[1] = -0.8463 2.429
h = 0.003 0.006
y[1] (numeric) = 3.71252281841 0.319905887669
y[1] (closed_form) = 3.71530301474 0.316190500931
absolute error = 0.00464
relative error = 0.1245 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.515
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8433 2.435
h = 0.0001 0.005
y[1] (numeric) = 3.7219572236 0.311938665999
y[1] (closed_form) = 3.72473337935 0.30820286799
absolute error = 0.004654
relative error = 0.1245 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.522
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8432 2.44
h = 0.0001 0.003
y[1] (numeric) = 3.73086684237 0.309563013519
y[1] (closed_form) = 3.73365035676 0.305818289457
absolute error = 0.004666
relative error = 0.1246 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.527
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8431 2.443
h = 0.001 0.001
y[1] (numeric) = 3.73620372693 0.308055164148
y[1] (closed_form) = 3.73898980416 0.304307151109
absolute error = 0.00467
relative error = 0.1245 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.53
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8421 2.444
h = 0.0001 0.004
y[1] (numeric) = 3.73755426908 0.305814704365
y[1] (closed_form) = 3.74033965552 0.302066075566
absolute error = 0.00467
relative error = 0.1245 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.531
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5731.1MB, alloc=52.3MB, time=73.14
x[1] = -0.842 2.448
h = 0.003 0.006
y[1] (numeric) = 3.74469134521 0.303850101383
y[1] (closed_form) = 3.7474813711 0.300095699669
absolute error = 0.004678
relative error = 0.1244 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.535
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.839 2.454
h = 0.0001 0.005
y[1] (numeric) = 3.75413096039 0.295762102665
y[1] (closed_form) = 3.75691681345 0.291987300404
absolute error = 0.004691
relative error = 0.1245 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.541
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8389 2.459
h = 0.0001 0.003
y[1] (numeric) = 3.763082551 0.293306723975
y[1] (closed_form) = 3.76587571157 0.289522942565
absolute error = 0.004703
relative error = 0.1245 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.546
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8388 2.462
h = 0.001 0.001
y[1] (numeric) = 3.76844392564 0.291750627556
y[1] (closed_form) = 3.77123963011 0.287963538533
absolute error = 0.004707
relative error = 0.1245 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.549
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8378 2.463
h = 0.001 0.003
y[1] (numeric) = 3.76978733986 0.289485684664
y[1] (closed_form) = 3.77258234914 0.285697983801
absolute error = 0.004707
relative error = 0.1244 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.55
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5776.8MB, alloc=52.3MB, time=73.71
x[1] = -0.8368 2.466
h = 0.0001 0.004
y[1] (numeric) = 3.77473755353 0.286295376409
y[1] (closed_form) = 3.77753291981 0.282503060395
absolute error = 0.004711
relative error = 0.1244 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.554
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8367 2.47
h = 0.003 0.006
y[1] (numeric) = 3.78191200318 0.284255778563
y[1] (closed_form) = 3.78471197044 0.280457650168
absolute error = 0.004719
relative error = 0.1243 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.558
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8337 2.476
h = 0.0001 0.005
y[1] (numeric) = 3.7913547704 0.276027277338
y[1] (closed_form) = 3.79415041151 0.272208763628
absolute error = 0.004733
relative error = 0.1244 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.564
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8336 2.481
h = 0.0001 0.003
y[1] (numeric) = 3.80035322804 0.273478224669
y[1] (closed_form) = 3.80315611619 0.269650671236
absolute error = 0.004744
relative error = 0.1244 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.569
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8335 2.484
h = 0.001 0.001
y[1] (numeric) = 3.8057419078 0.271865462334
y[1] (closed_form) = 3.80854731747 0.268034580049
absolute error = 0.004748
relative error = 0.1244 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.572
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5822.3MB, alloc=52.3MB, time=74.27
x[1] = -0.8325 2.485
h = 0.001 0.003
y[1] (numeric) = 3.80707644886 0.269572234084
y[1] (closed_form) = 3.8098811583 0.265740744602
absolute error = 0.004748
relative error = 0.1243 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.573
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8315 2.488
h = 0.0001 0.004
y[1] (numeric) = 3.81203717215 0.266316490453
y[1] (closed_form) = 3.81484220493 0.262480379632
absolute error = 0.004752
relative error = 0.1243 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.576
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8314 2.492
h = 0.003 0.006
y[1] (numeric) = 3.81924847268 0.264201564482
y[1] (closed_form) = 3.82205806728 0.260359602963
absolute error = 0.00476
relative error = 0.1242 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.58
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8284 2.498
h = 0.0001 0.005
y[1] (numeric) = 3.82869336104 0.255832429723
y[1] (closed_form) = 3.8314984763 0.251970098815
absolute error = 0.004773
relative error = 0.1243 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.587
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8283 2.503
h = 0.0001 0.003
y[1] (numeric) = 3.83773803323 0.253189285982
y[1] (closed_form) = 3.84055033481 0.249317855078
absolute error = 0.004785
relative error = 0.1243 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.592
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5867.9MB, alloc=52.3MB, time=74.84
x[1] = -0.8282 2.506
h = 0.001 0.001
y[1] (numeric) = 3.84315362288 0.251519612993
y[1] (closed_form) = 3.84596842351 0.247644832109
absolute error = 0.004789
relative error = 0.1243 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.594
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8272 2.507
h = 0.001 0.003
y[1] (numeric) = 3.84447907604 0.249198142521
y[1] (closed_form) = 3.84729317142 0.245322759105
absolute error = 0.004789
relative error = 0.1242 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.596
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8262 2.51
h = 0.0001 0.004
y[1] (numeric) = 3.84944983638 0.245876835176
y[1] (closed_form) = 3.85226422144 0.241996824389
absolute error = 0.004793
relative error = 0.1242 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.599
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8261 2.514
h = 0.003 0.006
y[1] (numeric) = 3.8566974633 0.243686251305
y[1] (closed_form) = 3.85951637086 0.239800351697
absolute error = 0.004801
relative error = 0.1241 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.603
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8231 2.52
h = 0.0001 0.005
y[1] (numeric) = 3.86614344171 0.235176356758
y[1] (closed_form) = 3.86895771687 0.231270104383
absolute error = 0.004814
relative error = 0.1242 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.609
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5913.5MB, alloc=52.3MB, time=75.41
x[1] = -0.823 2.525
h = 0.0001 0.003
y[1] (numeric) = 3.87523367433 0.232438708011
y[1] (closed_form) = 3.87805507485 0.228523295667
absolute error = 0.004826
relative error = 0.1242 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.614
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8229 2.528
h = 0.001 0.001
y[1] (numeric) = 3.88067577768 0.230711881537
y[1] (closed_form) = 3.88349965468 0.226793098198
absolute error = 0.00483
relative error = 0.1242 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.617
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8219 2.529
h = 0.001 0.003
y[1] (numeric) = 3.88199192848 0.228362212945
y[1] (closed_form) = 3.88481509525 0.224442831761
absolute error = 0.00483
relative error = 0.1241 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.618
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8209 2.532
h = 0.0001 0.004
y[1] (numeric) = 3.8869722529 0.224975215764
y[1] (closed_form) = 3.88979567566 0.221051201333
absolute error = 0.004834
relative error = 0.1241 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.621
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8208 2.536
h = 0.003 0.006
y[1] (numeric) = 3.89425568044 0.222708646755
y[1] (closed_form) = 3.89708358621 0.218778705575
absolute error = 0.004842
relative error = 0.124 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.625
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5959.0MB, alloc=52.3MB, time=75.98
x[1] = -0.8178 2.542
h = 0.0001 0.005
y[1] (numeric) = 3.90370171765 0.214057870938
y[1] (closed_form) = 3.90652483812 0.210107594307
absolute error = 0.004855
relative error = 0.1241 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.632
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8177 2.547
h = 0.0001 0.003
y[1] (numeric) = 3.91283685494 0.211225306411
y[1] (closed_form) = 3.91566703955 0.207265810143
absolute error = 0.004867
relative error = 0.1241 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.637
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8176 2.55
h = 0.001 0.001
y[1] (numeric) = 3.91830507486 0.209441085535
y[1] (closed_form) = 3.9211377133 0.205478197367
absolute error = 0.004871
relative error = 0.1241 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.64
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8166 2.551
h = 0.0001 0.004
y[1] (numeric) = 3.91961170912 0.207063263892
y[1] (closed_form) = 3.92244363236 0.203099782585
absolute error = 0.004871
relative error = 0.124 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.641
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8165 2.555
h = 0.003 0.006
y[1] (numeric) = 3.92692644148 0.204731446275
y[1] (closed_form) = 3.92976281361 0.200762006194
absolute error = 0.004879
relative error = 0.124 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.645
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8135 2.561
h = 0.0001 0.005
y[1] (numeric) = 3.93637338346 0.195959294903
memory used=6004.6MB, alloc=52.3MB, time=76.54
y[1] (closed_form) = 3.93920483856 0.191969533012
absolute error = 0.004892
relative error = 0.124 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.651
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8134 2.566
h = 0.0001 0.003
y[1] (numeric) = 3.94554778409 0.193045227764
y[1] (closed_form) = 3.94838625113 0.189046194384
absolute error = 0.004904
relative error = 0.1241 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.656
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8133 2.569
h = 0.001 0.001
y[1] (numeric) = 3.95103885308 0.191211716885
y[1] (closed_form) = 3.95387975464 0.187209273429
absolute error = 0.004908
relative error = 0.124 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.659
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8123 2.57
h = 0.001 0.003
y[1] (numeric) = 3.95233745916 0.188809582031
y[1] (closed_form) = 3.9551776412 0.184806549446
absolute error = 0.004908
relative error = 0.124 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.66
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8113 2.573
h = 0.0001 0.004
y[1] (numeric) = 3.95733510588 0.18530012391
y[1] (closed_form) = 3.96017548127 0.18129244716
absolute error = 0.004912
relative error = 0.1239 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.664
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8112 2.577
h = 0.003 0.006
y[1] (numeric) = 3.96468466043 0.182891713635
y[1] (closed_form) = 3.96752944541 0.178878039608
absolute error = 0.00492
relative error = 0.1239 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.667
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6050.4MB, alloc=52.3MB, time=77.11
x[1] = -0.8082 2.583
h = 0.0001 0.005
y[1] (numeric) = 3.97412974324 0.173978455353
y[1] (closed_form) = 3.97696945853 0.169944478122
absolute error = 0.004933
relative error = 0.1239 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.674
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8081 2.588
h = 0.0001 0.003
y[1] (numeric) = 3.98334782883 0.170968708655
y[1] (closed_form) = 3.98619449437 0.166925400827
absolute error = 0.004945
relative error = 0.1239 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.679
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.808 2.591
h = 0.001 0.001
y[1] (numeric) = 3.9888642757 0.169077355419
y[1] (closed_form) = 3.99171335295 0.165030616819
absolute error = 0.004949
relative error = 0.1239 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.682
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.807 2.592
h = 0.001 0.003
y[1] (numeric) = 3.99015296694 0.166647151392
y[1] (closed_form) = 3.99300131975 0.162599828408
absolute error = 0.004949
relative error = 0.1238 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.683
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.806 2.595
h = 0.0001 0.004
y[1] (numeric) = 3.99515882397 0.163071649217
y[1] (closed_form) = 3.99800733641 0.15901967664
absolute error = 0.004953
relative error = 0.1238 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.686
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6096.0MB, alloc=52.3MB, time=77.68
x[1] = -0.8059 2.599
h = 0.003 0.006
y[1] (numeric) = 4.00254267172 0.160586325361
y[1] (closed_form) = 4.00539555381 0.15652831814
absolute error = 0.00496
relative error = 0.1238 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.69
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8029 2.605
h = 0.0001 0.005
y[1] (numeric) = 4.01198486369 0.151531852328
y[1] (closed_form) = 4.01483252358 0.147453561202
absolute error = 0.004974
relative error = 0.1238 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.697
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8028 2.61
h = 0.0001 0.003
y[1] (numeric) = 4.02124597383 0.148426024347
y[1] (closed_form) = 4.02410052204 0.14433834382
absolute error = 0.004986
relative error = 0.1238 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.702
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8027 2.613
h = 0.001 0.001
y[1] (numeric) = 4.02678739873 0.146476593305
y[1] (closed_form) = 4.02964433576 0.14238546142
absolute error = 0.00499
relative error = 0.1238 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.704
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8017 2.614
h = 0.001 0.003
y[1] (numeric) = 4.02806596178 0.144018367928
y[1] (closed_form) = 4.03092216947 0.139926656426
absolute error = 0.00499
relative error = 0.1237 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.706
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6141.6MB, alloc=52.3MB, time=78.25
x[1] = -0.8007 2.617
h = 0.0001 0.004
y[1] (numeric) = 4.03307955467 0.140376704129
y[1] (closed_form) = 4.03593588824 0.136280337762
absolute error = 0.004994
relative error = 0.1237 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.709
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8006 2.621
h = 0.003 0.006
y[1] (numeric) = 4.04049716488 0.137814149253
y[1] (closed_form) = 4.04335782801 0.133711711071
absolute error = 0.005001
relative error = 0.1236 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.713
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7976 2.627
h = 0.0001 0.005
y[1] (numeric) = 4.04993543422 0.128618358395
y[1] (closed_form) = 4.0527907228 0.124495656297
absolute error = 0.005015
relative error = 0.1237 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.719
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7975 2.632
h = 0.0001 0.003
y[1] (numeric) = 4.05923890693 0.125416050582
y[1] (closed_form) = 4.06210102164 0.121283900583
absolute error = 0.005027
relative error = 0.1237 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.724
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7974 2.635
h = 0.001 0.001
y[1] (numeric) = 4.06480490908 0.123408308205
y[1] (closed_form) = 4.06766938962 0.119272686377
absolute error = 0.005031
relative error = 0.1236 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.727
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6187.2MB, alloc=52.3MB, time=78.81
x[1] = -0.7964 2.636
h = 0.001 0.003
y[1] (numeric) = 4.06607313089 0.120922110257
y[1] (closed_form) = 4.06893687723 0.116785913599
absolute error = 0.005031
relative error = 0.1236 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.728
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7954 2.639
h = 0.0001 0.004
y[1] (numeric) = 4.07109398482 0.117214169481
y[1] (closed_form) = 4.0739578233 0.113073312843
absolute error = 0.005035
relative error = 0.1235 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.731
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7953 2.643
h = 0.003 0.006
y[1] (numeric) = 4.0785448255 0.114574068698
y[1] (closed_form) = 4.08141295329 0.110427103271
absolute error = 0.005042
relative error = 0.1235 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.735
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7923 2.649
h = 0.0001 0.005
y[1] (numeric) = 4.08797814036 0.105236861702
y[1] (closed_form) = 4.09084074137 0.101069653037
absolute error = 0.005056
relative error = 0.1235 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.742
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7922 2.654
h = 0.0001 0.003
y[1] (numeric) = 4.09732331205 0.101937678687
y[1] (closed_form) = 4.10019267678 0.0977609639293
absolute error = 0.005067
relative error = 0.1236 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.747
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6232.8MB, alloc=52.3MB, time=79.38
x[1] = -0.7921 2.657
h = 0.001 0.001
y[1] (numeric) = 4.10291348975 0.0998713933682
y[1] (closed_form) = 4.10578519725 0.0956911864217
absolute error = 0.005072
relative error = 0.1235 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.75
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7911 2.658
h = 0.0001 0.004
y[1] (numeric) = 4.10417115758 0.0973572725888
y[1] (closed_form) = 4.10704212602 0.0931764956193
absolute error = 0.005072
relative error = 0.1235 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.751
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.791 2.662
h = 0.003 0.006
y[1] (numeric) = 4.11165110418 0.0946505589421
y[1] (closed_form) = 4.1145263272 0.0904636419534
absolute error = 0.005079
relative error = 0.1234 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.755
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.788 2.668
h = 0.0001 0.005
y[1] (numeric) = 4.12108101409 0.0851914748142
y[1] (closed_form) = 4.12395057916 0.0809843311297
absolute error = 0.005093
relative error = 0.1235 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.761
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7879 2.673
h = 0.0001 0.003
y[1] (numeric) = 4.13046270664 0.0818090766175
y[1] (closed_form) = 4.13333898219 0.0775923762464
absolute error = 0.005104
relative error = 0.1235 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.766
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6278.3MB, alloc=52.3MB, time=79.95
x[1] = -0.7878 2.676
h = 0.001 0.001
y[1] (numeric) = 4.13607407256 0.0796924969403
y[1] (closed_form) = 4.13895267119 0.07547228667
absolute error = 0.005108
relative error = 0.1234 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.769
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7868 2.677
h = 0.001 0.003
y[1] (numeric) = 4.13732281755 0.0771542525158
y[1] (closed_form) = 4.14020067291 0.0729334763197
absolute error = 0.005109
relative error = 0.1234 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.77
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7858 2.68
h = 0.0001 0.004
y[1] (numeric) = 4.14235671027 0.0733227594519
y[1] (closed_form) = 4.145234595 0.0690973137717
absolute error = 0.005112
relative error = 0.1233 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.774
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7857 2.684
h = 0.003 0.006
y[1] (numeric) = 4.14986889738 0.0705379153053
y[1] (closed_form) = 4.15275099657 0.0663062920784
absolute error = 0.00512
relative error = 0.1233 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.777
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7827 2.69
h = 0.0001 0.005
y[1] (numeric) = 4.1592919336 0.0609372324809
y[1] (closed_form) = 4.1621682229 0.0566854045213
absolute error = 0.005133
relative error = 0.1233 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.784
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6323.9MB, alloc=52.3MB, time=80.52
x[1] = -0.7826 2.695
h = 0.0001 0.003
y[1] (numeric) = 4.16871409085 0.0574572239206
y[1] (closed_form) = 4.17159702774 0.0531957816486
absolute error = 0.005145
relative error = 0.1233 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.789
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7825 2.698
h = 0.001 0.001
y[1] (numeric) = 4.17434888512 0.0552816706459
y[1] (closed_form) = 4.17723412188 0.0510166983245
absolute error = 0.005149
relative error = 0.1233 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.792
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7815 2.699
h = 0.001 0.003
y[1] (numeric) = 4.17558668046 0.0527155959587
y[1] (closed_form) = 4.17847116915 0.0484500625572
absolute error = 0.005149
relative error = 0.1232 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.793
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7805 2.702
h = 0.0001 0.004
y[1] (numeric) = 4.18062647525 0.0488175024928
y[1] (closed_form) = 4.18351095952 0.0445472949392
absolute error = 0.005153
relative error = 0.1232 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.796
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7804 2.706
h = 0.003 0.006
y[1] (numeric) = 4.18817036772 0.0459542193319
y[1] (closed_form) = 4.19105902577 0.0416777978225
absolute error = 0.005161
relative error = 0.1231 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.8
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6369.5MB, alloc=52.3MB, time=81.08
x[1] = -0.7774 2.712
h = 0.0001 0.005
y[1] (numeric) = 4.19758549817 0.0362118531132
y[1] (closed_form) = 4.20046819454 0.0319152495217
absolute error = 0.005174
relative error = 0.1232 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.807
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7773 2.717
h = 0.0001 0.003
y[1] (numeric) = 4.20704745205 0.0326338479184
y[1] (closed_form) = 4.20993673289 0.0283275726961
absolute error = 0.005186
relative error = 0.1232 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.811
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7772 2.72
h = 0.001 0.001
y[1] (numeric) = 4.21270527035 0.0303990949376
y[1] (closed_form) = 4.21559682775 0.0260892696289
absolute error = 0.00519
relative error = 0.1231 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.814
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7762 2.721
h = 0.001 0.003
y[1] (numeric) = 4.21393190418 0.0278052424606
y[1] (closed_form) = 4.21682270872 0.023494860938
absolute error = 0.00519
relative error = 0.1231 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.816
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7752 2.724
h = 0.0001 0.004
y[1] (numeric) = 4.21897712488 0.023840441795
y[1] (closed_form) = 4.22186789121 0.0195253816087
absolute error = 0.005194
relative error = 0.123 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.819
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6415.2MB, alloc=52.3MB, time=81.66
x[1] = -0.7751 2.728
h = 0.003 0.006
y[1] (numeric) = 4.22655218593 0.0208984145854
y[1] (closed_form) = 4.2294470852 0.0165771042328
absolute error = 0.005201
relative error = 0.123 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.823
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7721 2.734
h = 0.0001 0.005
y[1] (numeric) = 4.2359583785 0.0110142850296
y[1] (closed_form) = 4.23884716446 0.00667281593264
absolute error = 0.005215
relative error = 0.123 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.829
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.772 2.739
h = 0.0001 0.003
y[1] (numeric) = 4.2454594594 0.00733790012302
y[1] (closed_form) = 4.24835476648 0.00298670238474
absolute error = 0.005226
relative error = 0.123 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.834
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7719 2.742
h = 0.001 0.001
y[1] (numeric) = 4.25113989653 0.0050437232568
y[1] (closed_form) = 4.25403745677 0.000688955508971
absolute error = 0.005231
relative error = 0.123 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.837
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7709 2.743
h = 0.001 0.003
y[1] (numeric) = 4.25235515728 0.00242214641505
y[1] (closed_form) = 4.2552519599 -0.00193317266055
absolute error = 0.005231
relative error = 0.1229 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.838
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6460.8MB, alloc=52.3MB, time=82.23
x[1] = -0.7699 2.746
h = 0.0001 0.004
y[1] (numeric) = 4.25740532739 -0.00160946603077
y[1] (closed_form) = 4.26030205801 -0.00596946812552
absolute error = 0.005235
relative error = 0.1229 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.841
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7698 2.75
h = 0.003 0.006
y[1] (numeric) = 4.26501101903 -0.00463053976074
y[1] (closed_form) = 4.2679118416 -0.00899682803288
absolute error = 0.005242
relative error = 0.1228 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.845
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7668 2.756
h = 0.0001 0.005
y[1] (numeric) = 4.27440724161 -0.0146565078434
y[1] (closed_form) = 4.27730179939 -0.0190429308362
absolute error = 0.005255
relative error = 0.1229 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.852
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7667 2.761
h = 0.0001 0.003
y[1] (numeric) = 4.28394677841 -0.0184316523423
y[1] (closed_form) = 4.2868477937 -0.022827860678
absolute error = 0.005267
relative error = 0.1229 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.857
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7666 2.764
h = 0.001 0.001
y[1] (numeric) = 4.28964942825 -0.0207854753413
y[1] (closed_form) = 4.29255267323 -0.0251852734961
absolute error = 0.005271
relative error = 0.1228 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.86
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6506.3MB, alloc=52.3MB, time=82.79
x[1] = -0.7656 2.765
h = 0.0001 0.004
y[1] (numeric) = 4.29085310468 -0.0234347221726
y[1] (closed_form) = 4.29375558732 -0.0278350667488
absolute error = 0.005271
relative error = 0.1228 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.861
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7655 2.769
h = 0.003 0.006
y[1] (numeric) = 4.29848567721 -0.0265237215389
y[1] (closed_form) = 4.30139221645 -0.0309303827178
absolute error = 0.005279
relative error = 0.1227 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.865
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7625 2.775
h = 0.0001 0.005
y[1] (numeric) = 4.30787418216 -0.0366719715719
y[1] (closed_form) = 4.31077432605 -0.0410987480456
absolute error = 0.005292
relative error = 0.1228 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.871
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7624 2.78
h = 0.0001 0.003
y[1] (numeric) = 4.31744746446 -0.0405319796106
y[1] (closed_form) = 4.3203540116 -0.044968590748
absolute error = 0.005304
relative error = 0.1228 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.876
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7623 2.783
h = 0.001 0.001
y[1] (numeric) = 4.32316962247 -0.0429370625074
y[1] (closed_form) = 4.32607837926 -0.0473772807048
absolute error = 0.005308
relative error = 0.1227 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.879
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7613 2.784
h = 0.001 0.003
y[1] (numeric) = 4.32436348729 -0.0456102238867
y[1] (closed_form) = 4.32727147762 -0.0500509843223
absolute error = 0.005308
relative error = 0.1227 %
Correct digits = 3
memory used=6551.9MB, alloc=52.3MB, time=83.36
Radius of convergence (given) for eq 1 = 2.88
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7603 2.787
h = 0.0001 0.004
y[1] (numeric) = 4.32942239654 -0.0497663826744
y[1] (closed_form) = 4.332330252 -0.0542118342208
absolute error = 0.005312
relative error = 0.1226 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.883
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7602 2.791
h = 0.003 0.006
y[1] (numeric) = 4.33708459855 -0.0529349900987
y[1] (closed_form) = 4.33999646971 -0.0573867947917
absolute error = 0.00532
relative error = 0.1226 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.887
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7572 2.797
h = 0.0001 0.005
y[1] (numeric) = 4.34646121375 -0.0632252182217
y[1] (closed_form) = 4.34936653838 -0.0676971129094
absolute error = 0.005333
relative error = 0.1226 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.894
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7571 2.802
h = 0.0001 0.003
y[1] (numeric) = 4.35607170356 -0.0671846922376
y[1] (closed_form) = 4.35898336739 -0.0716664777173
absolute error = 0.005345
relative error = 0.1226 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.899
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.757 2.805
h = 0.001 0.001
y[1] (numeric) = 4.36181531886 -0.0696498345322
y[1] (closed_form) = 4.36472916872 -0.0741352466701
absolute error = 0.005349
relative error = 0.1225 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.902
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6597.5MB, alloc=52.3MB, time=83.92
x[1] = -0.756 2.806
h = 0.001 0.003
y[1] (numeric) = 4.36299720648 -0.0723505647042
y[1] (closed_form) = 4.36591028518 -0.0768365141365
absolute error = 0.005349
relative error = 0.1225 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.903
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.755 2.809
h = 0.0001 0.004
y[1] (numeric) = 4.36805970145 -0.0765738278979
y[1] (closed_form) = 4.37097261147 -0.0810644723498
absolute error = 0.005353
relative error = 0.1224 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.906
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7549 2.813
h = 0.003 0.006
y[1] (numeric) = 4.37575099186 -0.0798223394218
y[1] (closed_form) = 4.37866787616 -0.0843193724611
absolute error = 0.00536
relative error = 0.1224 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.91
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7519 2.819
h = 0.0001 0.005
y[1] (numeric) = 4.38511468519 -0.09025460724
y[1] (closed_form) = 4.38802487194 -0.0947717042902
absolute error = 0.005373
relative error = 0.1224 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.917
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7518 2.824
h = 0.0001 0.003
y[1] (numeric) = 4.39476170704 -0.0943139179667
y[1] (closed_form) = 4.39767816871 -0.0988409616267
absolute error = 0.005385
relative error = 0.1224 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.921
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6643.0MB, alloc=52.3MB, time=84.48
x[1] = -0.7517 2.827
h = 0.001 0.001
y[1] (numeric) = 4.40052637102 -0.0968393363802
y[1] (closed_form) = 4.403444995 -0.101370026182
absolute error = 0.005389
relative error = 0.1224 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.924
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7507 2.828
h = 0.001 0.003
y[1] (numeric) = 4.40169607109 -0.0995675782552
y[1] (closed_form) = 4.40461391926 -0.104098800388
absolute error = 0.005389
relative error = 0.1223 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.926
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7497 2.831
h = 0.0001 0.004
y[1] (numeric) = 4.40676167409 -0.10385804188
y[1] (closed_form) = 4.40967931974 -0.108393962785
absolute error = 0.005393
relative error = 0.1223 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.929
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7496 2.835
h = 0.003 0.006
y[1] (numeric) = 4.4144815103 -0.107186750069
y[1] (closed_form) = 4.41740308865 -0.111729094801
absolute error = 0.005401
relative error = 0.1222 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.933
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7466 2.841
h = 0.0001 0.005
y[1] (numeric) = 4.42383124968 -0.117761114443
y[1] (closed_form) = 4.42674597964 -0.12232349652
absolute error = 0.005414
relative error = 0.1223 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.939
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6688.6MB, alloc=52.3MB, time=85.04
x[1] = -0.7465 2.846
h = 0.0001 0.003
y[1] (numeric) = 4.43351412662 -0.121920629404
y[1] (closed_form) = 4.43643506698 -0.126493013597
absolute error = 0.005426
relative error = 0.1222 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.944
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7464 2.849
h = 0.001 0.001
y[1] (numeric) = 4.43929942978 -0.124506538719
y[1] (closed_form) = 4.44222250866 -0.129082588423
absolute error = 0.00543
relative error = 0.1222 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.947
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7454 2.85
h = 0.001 0.003
y[1] (numeric) = 4.4404567323 -0.127262234262
y[1] (closed_form) = 4.44337903072 -0.131838811314
absolute error = 0.00543
relative error = 0.1222 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.948
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7444 2.853
h = 0.0001 0.004
y[1] (numeric) = 4.44552496535 -0.131619992125
y[1] (closed_form) = 4.44844702741 -0.136201271546
absolute error = 0.005434
relative error = 0.1221 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.951
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7443 2.857
h = 0.003 0.006
y[1] (numeric) = 4.45327280356 -0.135029186969
y[1] (closed_form) = 4.45619875661 -0.139616925256
absolute error = 0.005441
relative error = 0.122 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.955
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6734.2MB, alloc=52.3MB, time=85.61
x[1] = -0.7413 2.863
h = 0.0001 0.005
y[1] (numeric) = 4.46260755699 -0.145745700019
y[1] (closed_form) = 4.46552651096 -0.150353448302
absolute error = 0.005455
relative error = 0.1221 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.962
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7412 2.868
h = 0.0001 0.003
y[1] (numeric) = 4.4723256106 -0.150005783524
y[1] (closed_form) = 4.47525071023 -0.154623589118
absolute error = 0.005466
relative error = 0.1221 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.967
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7411 2.871
h = 0.001 0.001
y[1] (numeric) = 4.47813114259 -0.152652396581
y[1] (closed_form) = 4.48105835687 -0.15727388694
absolute error = 0.005471
relative error = 0.122 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.97
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7401 2.872
h = 0.001 0.003
y[1] (numeric) = 4.47927583789 -0.155435486815
y[1] (closed_form) = 4.48220226709 -0.160057499519
absolute error = 0.005471
relative error = 0.122 %
Correct digits = 3
Radius of convergence (given) for eq 1 = 2.971
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff ( y , x , 1 ) = cos ( sqrt ( 2.0 * x + 3.0 ) ) ;
Iterations = 754
Total Elapsed Time = 1 Minutes 26 Seconds
Expected Time Remaining = 0 Seconds
Optimized Time Remaining = 0 Seconds
Expected Total Time = 1 Minutes 26 Seconds
> quit
memory used=6776.4MB, alloc=52.3MB, time=86.10