|\^/| Maple 2016 (X86 64 LINUX)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2016
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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#BEGIN OUTFILE1
# before write maple top matter
# before write_ats library and user def block
#BEGIN ATS LIBRARY BLOCK
# Begin Function number 2
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s\n",str);
> fi;# end if 1;
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
# End Function number 2
# Begin Function number 3
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s",str);
> fi;# end if 1;
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
# End Function number 3
# Begin Function number 4
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> print(label,str);
> fi;# end if 1;
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
# End Function number 4
# Begin Function number 5
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 5
# Begin Function number 6
> omniout_complex := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> if vallen = 4 then
> printf("%-30s = %-20.4g %-20g %s \n",prelabel,Re(value), Im(value), postlabel);
> else
> printf("%-30s = %-20.12g %-20.12g %s \n",prelabel,Re(value),Im(value), postlabel);
> fi;# end if 0;
> fi;# end if -1;
> end;
omniout_complex := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then printf("%-30s = %-20.4g %-20g %s \n", prelabel,
Re(value), Im(value), postlabel)
else printf("%-30s = %-20.12g %-20.12g %s \n", prelabel, Re(value),
Im(value), postlabel)
end if
end if
end proc
# End Function number 6
# Begin Function number 7
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number -1
> if vallen = 5 then # if number 0
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;# end if 0;
> fi;# end if -1;
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 7
# Begin Function number 8
> logitem_time := proc(fd,secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> fprintf(fd,"
");
> if (secs_in >= 0) then # if number -1
> years_int := int_trunc(secs_in / glob_sec_in_year);
> sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
> days_int := int_trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := sec_temp mod int_trunc(glob_sec_in_day) ;
> hours_int := int_trunc(sec_temp / glob_sec_in_hour);
> sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
> minutes_int := int_trunc(sec_temp / glob_sec_in_minute);
> sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
> if (years_int > 0) then # if number 0
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 1
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 2
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 3
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 3
> else
> fprintf(fd," 0.0 Seconds");
> fi;# end if 2
> fprintf(fd," | \n");
> end;
logitem_time := proc(fd, secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
fprintf(fd, "");
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, " 0.0 Seconds")
end if;
fprintf(fd, " | \n")
end proc
# End Function number 8
# Begin Function number 9
> omniout_timestr := proc(secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> if (secs_in >= 0) then # if number 2
> years_int := int_trunc(secs_in / glob_sec_in_year);
> sec_temp := (int_trunc(secs_in) mod int_trunc(glob_sec_in_year));
> days_int := int_trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_day)) ;
> hours_int := int_trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_hour));
> minutes_int := int_trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod int_trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 3
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 4
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 5
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 6
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 6
> else
> printf(" 0.0 Seconds\n");
> fi;# end if 5
> end;
omniout_timestr := proc(secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" 0.0 Seconds\n")
end if
end proc
# End Function number 9
# Begin Function number 10
> zero_ats_ar := proc(arr_a)
> global ATS_MAX_TERMS;
> local iii;
> iii := 1;
> while (iii <= ATS_MAX_TERMS) do # do number 1
> arr_a [iii] := glob__0;
> iii := iii + 1;
> od;# end do number 1
> end;
zero_ats_ar := proc(arr_a)
local iii;
global ATS_MAX_TERMS;
iii := 1;
while iii <= ATS_MAX_TERMS do arr_a[iii] := glob__0; iii := iii + 1
end do
end proc
# End Function number 10
# Begin Function number 11
> ats := proc(mmm_ats,arr_a,arr_b,jjj_ats)
> global ATS_MAX_TERMS;
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := glob__0;
> if (jjj_ats <= mmm_ats) then # if number 5
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> if ((lll_ats <= ATS_MAX_TERMS and (iii_ats <= ATS_MAX_TERMS) )) then # if number 6
> ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]);
> fi;# end if 6;
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 5;
> ret_ats;
> end;
ats := proc(mmm_ats, arr_a, arr_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
global ATS_MAX_TERMS;
ret_ats := glob__0;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
if lll_ats <= ATS_MAX_TERMS and iii_ats <= ATS_MAX_TERMS then
ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats])
end if;
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
# End Function number 11
# Begin Function number 12
> att := proc(mmm_att,arr_aa,arr_bb,jjj_att)
> global ATS_MAX_TERMS;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := glob__0;
> if (jjj_att < mmm_att) then # if number 5
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while ((iii_att < mmm_att) and (iii_att <= ATS_MAX_TERMS) ) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if ((lll_att <= ATS_MAX_TERMS and (iii_att <= ATS_MAX_TERMS) )) then # if number 6
> ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att);
> fi;# end if 6;
> iii_att := iii_att + 1;
> od;# end do number 1;
> ret_att := ret_att / c(mmm_att) ;
> fi;# end if 5;
> ret_att;
> end;
att := proc(mmm_att, arr_aa, arr_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global ATS_MAX_TERMS;
ret_att := glob__0;
if jjj_att < mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att < mmm_att and iii_att <= ATS_MAX_TERMS do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= ATS_MAX_TERMS and iii_att <= ATS_MAX_TERMS then
ret_att :=
ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])*c(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/c(mmm_att)
end if;
ret_att
end proc
# End Function number 12
# Begin Function number 13
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
# End Function number 13
# Begin Function number 14
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
# End Function number 14
# Begin Function number 15
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
# End Function number 15
# Begin Function number 16
> logitem_good_digits := proc(file,rel_error)
> global glob_small_float,glob_prec;
> local good_digits;
> fprintf(file,"");
> fprintf(file,"%d",glob_min_good_digits);
> fprintf(file," | ");
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float, glob_prec;
fprintf(file, "");
fprintf(file, "%d", glob_min_good_digits);
fprintf(file, " | ")
end proc
# End Function number 16
# Begin Function number 17
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
# End Function number 17
# Begin Function number 18
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
# End Function number 18
# Begin Function number 19
> logitem_complex := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g + %g I",Re(x),Im(x));
> fprintf(file," | ");
> end;
logitem_complex := proc(file, x)
fprintf(file, "");
fprintf(file, "%g + %g I", Re(x), Im(x));
fprintf(file, " | ")
end proc
# End Function number 19
# Begin Function number 20
> logitem_h_reason := proc(file)
> global glob_h_reason;
> fprintf(file,"");
> if (glob_h_reason = 1) then # if number 5
> fprintf(file,"Max H");
> elif
> (glob_h_reason = 2) then # if number 6
> fprintf(file,"Display Interval");
> elif
> (glob_h_reason = 3) then # if number 7
> fprintf(file,"Optimal");
> elif
> (glob_h_reason = 4) then # if number 8
> fprintf(file,"Pole Accuracy");
> elif
> (glob_h_reason = 5) then # if number 9
> fprintf(file,"Min H (Pole)");
> elif
> (glob_h_reason = 6) then # if number 10
> fprintf(file,"Pole");
> elif
> (glob_h_reason = 7) then # if number 11
> fprintf(file,"Opt Iter");
> else
> fprintf(file,"Impossible");
> fi;# end if 11
> fprintf(file," | ");
> end;
logitem_h_reason := proc(file)
global glob_h_reason;
fprintf(file, "");
if glob_h_reason = 1 then fprintf(file, "Max H")
elif glob_h_reason = 2 then fprintf(file, "Display Interval")
elif glob_h_reason = 3 then fprintf(file, "Optimal")
elif glob_h_reason = 4 then fprintf(file, "Pole Accuracy")
elif glob_h_reason = 5 then fprintf(file, "Min H (Pole)")
elif glob_h_reason = 6 then fprintf(file, "Pole")
elif glob_h_reason = 7 then fprintf(file, "Opt Iter")
else fprintf(file, "Impossible")
end if;
fprintf(file, " | ")
end proc
# End Function number 20
# Begin Function number 21
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
# End Function number 21
# Begin Function number 22
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file) fprintf(file, "\n") end proc
# End Function number 22
# Begin Function number 23
> chk_data := proc()
> global glob_max_iter,ALWAYS, ATS_MAX_TERMS;
> local errflag;
> errflag := false;
> if (glob_max_iter < 2) then # if number 11
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 11;
> if (errflag) then # if number 11
> quit;
> fi;# end if 11
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, ATS_MAX_TERMS;
errflag := false;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
# End Function number 23
# Begin Function number 24
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := c(clock_sec2);
> sub1 := c(t_end2-t_start2);
> sub2 := c(t2-t_start2);
> if (sub1 = glob__0) then # if number 11
> sec_left := glob__0;
> else
> if (sub2 > glob__0) then # if number 12
> rrr := (sub1/sub2);
> sec_left := rrr * c(ms2) - c(ms2);
> else
> sec_left := glob__0;
> fi;# end if 12
> fi;# end if 11;
> sec_left;
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := c(clock_sec2);
sub1 := c(t_end2 - t_start2);
sub2 := c(t2 - t_start2);
if sub1 = glob__0 then sec_left := glob__0
else
if glob__0 < sub2 then
rrr := sub1/sub2; sec_left := rrr*c(ms2) - c(ms2)
else sec_left := glob__0
end if
end if;
sec_left
end proc
# End Function number 24
# Begin Function number 25
> comp_percent := proc(t_end2,t_start2, t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub2 > glob_small_float) then # if number 11
> rrr := (glob__100*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 11;
> rrr;
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < sub2 then rrr := glob__100*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
# End Function number 25
# Begin Function number 26
> comp_rad_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 11
> ret := float_abs(term1 * glob_h / term2);
> else
> ret := glob_larger_float;
> fi;# end if 11;
> ret;
> #BOTTOM TWO TERM RADIUS ANALYSIS
> end;
comp_rad_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := float_abs(term1*glob_h/term2)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 26
# Begin Function number 27
> comp_ord_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM ORDER ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 11
> ret := glob__1 + float_abs(term2) * c(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(c(last_no));
> else
> ret := glob_larger_float;
> fi;# end if 11;
> ret;
> #BOTTOM TWO TERM ORDER ANALYSIS
> end;
comp_ord_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := glob__1 + float_abs(term2)*
c(last_no)*ln(float_abs(term1*glob_h/term2))/ln(c(last_no))
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 27
# Begin Function number 28
> c := proc(in_val)
> #To Force Conversion when needed
> local ret;
> ret := evalc(in_val);
> ret;
> #End Conversion
> end;
c := proc(in_val) local ret; ret := evalc(in_val); ret end proc
# End Function number 28
# Begin Function number 29
> comp_rad_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret,temp;
> temp := float_abs(term2*term2*c(last_no)+glob__m2*term2*term2-term1*term3*c(last_no)+term1*term3);
> if (float_abs(temp) > glob__0) then # if number 11
> ret := float_abs((term2*glob_h*term1)/(temp));
> else
> ret := glob_larger_float;
> fi;# end if 11;
> ret;
> #BOTTOM THREE TERM RADIUS ANALYSIS
> end;
comp_rad_from_three_terms := proc(term1, term2, term3, last_no)
local ret, temp;
global glob_h, glob_larger_float;
temp := float_abs(term2*term2*c(last_no) + glob__m2*term2*term2
- term1*term3*c(last_no) + term1*term3);
if glob__0 < float_abs(temp) then
ret := float_abs(term2*glob_h*term1/temp)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 29
# Begin Function number 30
> comp_ord_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM ORDER ANALYSIS
> local ret;
> ret := float_abs((glob__4*term1*term3*c(last_no)-glob__3*term1*term3-glob__4*term2*term2*c(last_no)+glob__4*term2*term2+term2*term2*c(last_no*last_no)-term1*term3*c(last_no*last_no))/(term2*term2*c(last_no)-glob__2*term2*term2-term1*term3*c(last_no)+term1*term3));
> ret;
> #TOP THREE TERM ORDER ANALYSIS
> end;
comp_ord_from_three_terms := proc(term1, term2, term3, last_no)
local ret;
ret := float_abs((glob__4*term1*term3*c(last_no) - glob__3*term1*term3
- glob__4*term2*term2*c(last_no) + glob__4*term2*term2
+ term2*term2*c(last_no*last_no) - term1*term3*c(last_no*last_no))
/(term2*term2*c(last_no) - glob__2*term2*term2
- term1*term3*c(last_no) + term1*term3));
ret
end proc
# End Function number 30
# Begin Function number 31
> comp_rad_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> #TOP SIX TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float,glob_six_term_ord_save;
> local ret,rm0,rm1,rm2,rm3,rm4,nr1,nr2,dr1,dr2,ds2,rad_c,ord_no,ds1,rcs;
> if ((term5 <> glob__0) and (term4 <> glob__0) and (term3 <> glob__0) and (term2 <> glob__0) and (term1 <> glob__0)) then # if number 11
> rm0 := term6/term5;
> rm1 := term5/term4;
> rm2 := term4/term3;
> rm3 := term3/term2;
> rm4 := term2/term1;
> nr1 := c(last_no-1)*rm0 - glob__2*c(last_no-2)*rm1 + c(last_no-3)*rm2;
> nr2 := c(last_no-2)*rm1 - glob__2*c(last_no-3)*rm2 + c(last_no-4)*rm3;
> dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
> dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
> ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
> ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
> if ((float_abs(nr1 * dr2 - nr2 * dr1) = glob__0) or (float_abs(dr1) = glob__0)) then # if number 12
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> else
> if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0) then # if number 13
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) -c(last_no)/glob__2;
> if (float_abs(rcs) <> glob__0) then # if number 14
> if (rcs > glob__0) then # if number 15
> rad_c := float_abs( sqrt(rcs) * float_abs(glob_h));
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 15
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 14
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 13
> fi;# end if 12
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 11;
> glob_six_term_ord_save := ord_no;
> rad_c;
> #BOTTOM SIX TERM RADIUS ANALYSIS
> end;
comp_rad_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
local ret, rm0, rm1, rm2, rm3, rm4, nr1, nr2, dr1, dr2, ds2, rad_c, ord_no,
ds1, rcs;
global glob_h, glob_larger_float, glob_six_term_ord_save;
if term5 <> glob__0 and term4 <> glob__0 and term3 <> glob__0 and
term2 <> glob__0 and term1 <> glob__0 then
rm0 := term6/term5;
rm1 := term5/term4;
rm2 := term4/term3;
rm3 := term3/term2;
rm4 := term2/term1;
nr1 := c(last_no - 1)*rm0 - glob__2*c(last_no - 2)*rm1
+ c(last_no - 3)*rm2;
nr2 := c(last_no - 2)*rm1 - glob__2*c(last_no - 3)*rm2
+ c(last_no - 4)*rm3;
dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
if
float_abs(nr1*dr2 - nr2*dr1) = glob__0 or float_abs(dr1) = glob__0
then rad_c := glob_larger_float; ord_no := glob_larger_float
else
if glob__0 < float_abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no :=
(rcs*nr1 - ds1)/(glob__2*dr1) - c(last_no)/glob__2;
if float_abs(rcs) <> glob__0 then
if glob__0 < rcs then
rad_c := float_abs(sqrt(rcs)*float_abs(glob_h))
else
rad_c := glob_larger_float;
ord_no := glob_larger_float
end if
else
rad_c := glob_larger_float; ord_no := glob_larger_float
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if;
glob_six_term_ord_save := ord_no;
rad_c
end proc
# End Function number 31
# Begin Function number 32
> comp_ord_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> global glob_six_term_ord_save;
> #TOP SIX TERM ORDER ANALYSIS
> #TOP SAVED FROM SIX TERM RADIUS ANALYSIS
> glob_six_term_ord_save;
> #BOTTOM SIX TERM ORDER ANALYSIS
> end;
comp_ord_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
global glob_six_term_ord_save;
glob_six_term_ord_save
end proc
# End Function number 32
# Begin Function number 33
> factorial_2 := proc(nnn)
> ret := nnn!;
> ret;;
> end;
Warning, `ret` is implicitly declared local to procedure `factorial_2`
factorial_2 := proc(nnn) local ret; ret := nnn!; ret end proc
# End Function number 33
# Begin Function number 34
> factorial_1 := proc(nnn)
> global ATS_MAX_TERMS,array_fact_1;
> local ret;
> if (nnn <= ATS_MAX_TERMS) then # if number 11
> if (array_fact_1[nnn] = 0) then # if number 12
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 12;
> else
> ret := factorial_2(nnn);
> fi;# end if 11;
> ret;
> end;
factorial_1 := proc(nnn)
local ret;
global ATS_MAX_TERMS, array_fact_1;
if nnn <= ATS_MAX_TERMS then
if array_fact_1[nnn] = 0 then
ret := factorial_2(nnn); array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := factorial_2(nnn)
end if;
ret
end proc
# End Function number 34
# Begin Function number 35
> factorial_3 := proc(mmm,nnn)
> global ATS_MAX_TERMS,array_fact_2;
> local ret;
> if ((nnn <= ATS_MAX_TERMS) and (mmm <= ATS_MAX_TERMS)) then # if number 11
> if (array_fact_2[mmm,nnn] = 0) then # if number 12
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 12;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 11;
> ret;
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global ATS_MAX_TERMS, array_fact_2;
if nnn <= ATS_MAX_TERMS and mmm <= ATS_MAX_TERMS then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := factorial_2(mmm)/factorial_2(nnn)
end if;
ret
end proc
# End Function number 35
# Begin Function number 36
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
# End Function number 36
# Begin Function number 37
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
# End Function number 37
# Begin Function number 38
> float_abs := proc(x)
> abs(x);
> end;
float_abs := proc(x) abs(x) end proc
# End Function number 38
# Begin Function number 39
> expt := proc(x,y)
> x^y;
> end;
expt := proc(x, y) x^y end proc
# End Function number 39
# Begin Function number 40
> neg := proc(x)
> -x;
> end;
neg := proc(x) -x end proc
# End Function number 40
# Begin Function number 41
> int_trunc := proc(x)
> trunc(x);
> end;
int_trunc := proc(x) trunc(x) end proc
# End Function number 41
# Begin Function number 42
> estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer)
> local desired_abs_gbl_error,range,estimated_steps,step_error;
> global glob_desired_digits_correct,ALWAYS,ATS_MAX_TERMS;
> omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
> desired_abs_gbl_error := expt(glob__10,c( -glob_desired_digits_correct)) * c(float_abs(c(estimated_answer)));
> omniout_float(ALWAYS,"estimated_h",32,estimated_h,32,"");
> omniout_float(ALWAYS,"estimated_answer",32,estimated_answer,32,"");
> omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,"");
> range := (x_end - x_start);
> omniout_float(ALWAYS,"range",32,range,32,"");
> estimated_steps := range / estimated_h;
> omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,"");
> step_error := (c(float_abs(desired_abs_gbl_error) /sqrt(c( estimated_steps))/c(ATS_MAX_TERMS)));
> omniout_float(ALWAYS,"step_error",32,step_error,32,"");
> (step_error);;
> end;
estimated_needed_step_error := proc(
x_start, x_end, estimated_h, estimated_answer)
local desired_abs_gbl_error, range, estimated_steps, step_error;
global glob_desired_digits_correct, ALWAYS, ATS_MAX_TERMS;
omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, "");
desired_abs_gbl_error :=
expt(glob__10, c(-glob_desired_digits_correct))*
c(float_abs(c(estimated_answer)));
omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, "");
omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, "")
;
omniout_float(ALWAYS, "desired_abs_gbl_error", 32,
desired_abs_gbl_error, 32, "");
range := x_end - x_start;
omniout_float(ALWAYS, "range", 32, range, 32, "");
estimated_steps := range/estimated_h;
omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, "");
step_error := c(float_abs(desired_abs_gbl_error)/(
sqrt(c(estimated_steps))*c(ATS_MAX_TERMS)));
omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
step_error
end proc
# End Function number 42
#END ATS LIBRARY BLOCK
#BEGIN USER FUNCTION BLOCK
#BEGIN BLOCK 3
#BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return(c(10.0) * (c(0.1) * c(x) + c(0.2)) * arctan(sqrt ( c(0.1) * c(x) +
> c(0.2))) - c(10.0) * sqrt( c(0.1) * c(x) + c(0.2)) + c(10.0) * arctan(sqrt( c(0.1) * c(x) + c(0.2))));
> end;
exact_soln_y := proc(x)
return
c(10.0)*(c(0.1)*c(x) + c(0.2))*arctan(sqrt(c(0.1)*c(x) + c(0.2)))
- c(10.0)*sqrt(c(0.1)*c(x) + c(0.2))
+ c(10.0)*arctan(sqrt(c(0.1)*c(x) + c(0.2)))
end proc
> next_delta := proc()
> global glob_nxt, x_delta;
> x_delta := [ 0.001 + 0.00004 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.000 + 0.000 * I ];
> glob_nxt := glob_nxt + 1;
> it := x_delta[glob_nxt];
> return it;
> end;
Warning, `it` is implicitly declared local to procedure `next_delta`
next_delta := proc()
local it;
global glob_nxt, x_delta;
x_delta := [0.001 + 0.00004*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0. + 0.*I];
glob_nxt := glob_nxt + 1;
it := x_delta[glob_nxt];
return it
end proc
#END USER DEF BLOCK
#END BLOCK 3
#END USER FUNCTION BLOCK
# before write_aux functions
# Begin Function number 2
> display_poles := proc()
> local rad_given;
> global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ;
> if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1
> rad_given := float_abs(array_x[1] - (array_given_rad_poles[1,1] + array_given_rad_poles[1,2] * I ));
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," ");
> omniout_complex(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," ");
> if ((float_abs(rad_given) < float_abs(glob_least_given_sing)) and
> (float_abs(rad_given) > 0.0)) then # if number 2
> glob_least_given_sing := rad_given;
> fi;# end if 2;
> elif
> (glob_type_given_pole = 3) then # if number 2
> omniout_str(ALWAYS,"NO POLE (given) for Equation 1");
> elif
> (glob_type_given_pole = 5) then # if number 3
> omniout_str(ALWAYS,"SOME POLE (given) for Equation 1");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 1");
> fi;# end if 3;
> if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," ");
> if ((float_abs(array_rad_test_poles[1,1]) < glob_least_ratio_sing)) then # if number 4
> glob_least_ratio_sing := array_rad_test_poles[1,1];
> fi;# end if 4;
> omniout_complex(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," ");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," ");
> if ((float_abs(array_rad_test_poles[1,2]) < glob_least_3_sing)) then # if number 4
> glob_least_3_sing := array_rad_test_poles[1,2];
> fi;# end if 4;
> omniout_complex(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," ");
> if ((float_abs(array_rad_test_poles[1,3]) < glob_least_6_sing)) then # if number 4
> glob_least_6_sing := array_rad_test_poles[1,3];
> fi;# end if 4;
> omniout_complex(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1");
> fi;# end if 3
> ;
> end;
display_poles := proc()
local rad_given;
global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float,
glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord,
glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
glob_least_3_sing, glob_least_6_sing, glob_least_given_sing,
glob_least_ratio_sing, array_x;
if glob_type_given_pole = 1 or glob_type_given_pole = 2 then
rad_given := float_abs(array_x[1] - array_given_rad_poles[1, 1]
- array_given_rad_poles[1, 2]*I);
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 1 ", 4,
rad_given, 4, " ");
omniout_complex(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles[1, 1], 4, " ");
if float_abs(rad_given) < float_abs(glob_least_given_sing) and
0. < float_abs(rad_given) then glob_least_given_sing := rad_given
end if
elif glob_type_given_pole = 3 then
omniout_str(ALWAYS, "NO POLE (given) for Equation 1")
elif glob_type_given_pole = 5 then
omniout_str(ALWAYS, "SOME POLE (given) for Equation 1")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 1")
end if;
if array_rad_test_poles[1, 1] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (ratio test) for eq 1 ", 4,
array_rad_test_poles[1, 1], 4, " ");
if float_abs(array_rad_test_poles[1, 1]) < glob_least_ratio_sing
then glob_least_ratio_sing := array_rad_test_poles[1, 1]
end if;
omniout_complex(ALWAYS,
"Order of pole (ratio test) ", 4,
array_ord_test_poles[1, 1], 4, " ")
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 2] and
array_rad_test_poles[1, 2] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 1 ", 4,
array_rad_test_poles[1, 2], 4, " ");
if float_abs(array_rad_test_poles[1, 2]) < glob_least_3_sing then
glob_least_3_sing := array_rad_test_poles[1, 2]
end if;
omniout_complex(ALWAYS,
"Order of pole (three term test) ", 4,
array_ord_test_poles[1, 2], 4, " ")
else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 3] and
array_rad_test_poles[1, 3] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 1 ", 4,
array_rad_test_poles[1, 3], 4, " ");
if float_abs(array_rad_test_poles[1, 3]) < glob_least_6_sing then
glob_least_6_sing := array_rad_test_poles[1, 3]
end if;
omniout_complex(ALWAYS,
"Order of pole (six term test) ", 4,
array_ord_test_poles[1, 3], 4, " ")
else omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 1")
end if
end proc
# End Function number 2
# Begin Function number 3
> my_check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 3
> ret := glob__1;
> else
> ret := glob__m1;
> fi;# end if 3;
> ret;;
> end;
my_check_sign := proc(x0, xf)
local ret;
if x0 < xf then ret := glob__1 else ret := glob__m1 end if; ret
end proc
# End Function number 3
# Begin Function number 4
> est_size_answer := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
#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_a1,
> array_tmp4_a2,
> 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_0D1,
array_const_0D2, 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_a1, array_tmp4_a2,
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_0D1,
> array_const_0D2,
#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_a1,
> array_tmp4_a2,
> 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_0D1,
array_const_0D2, 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_a1, array_tmp4_a2,
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_0D1,
> array_const_0D2,
#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_a1,
> array_tmp4_a2,
> 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_0D1,
array_const_0D2, 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_a1, array_tmp4_a2,
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_0D1,
> array_const_0D2,
#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_a1,
> array_tmp4_a2,
> 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_0D1,
array_const_0D2, 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_a1, array_tmp4_a2,
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_0D1,
> array_const_0D2,
#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_a1,
> array_tmp4_a2,
> 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_0D1,
array_const_0D2, 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_a1, array_tmp4_a2,
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_0D1,
> array_const_0D2,
#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_a1,
> array_tmp4_a2,
> 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_0D1,
array_const_0D2, 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_a1, array_tmp4_a2,
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_0D1,
> array_const_0D2,
#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_a1,
> array_tmp4_a2,
> 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_0D1,
array_const_0D2, 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_a1, array_tmp4_a2,
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_0D1,
> array_const_0D2,
#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_a1,
> array_tmp4_a2,
> 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_0D1[1] * array_x[1];
> #emit pre add LINEAR - CONST $eq_no = 1 i = 1
> array_tmp2[1] := array_tmp1[1] + array_const_0D2[1];
> #emit pre sqrt 1 $eq_no = 1
> array_tmp3[1] := sqrt(array_tmp2[1]);
> #emit pre arctan $eq_no = 1
> array_tmp4[1] := arctan(array_tmp3[1]);
> array_tmp4_a1[1] := sin(array_tmp4[1]);
> array_tmp4_a2[1] := cos(array_tmp4[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_0D1[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 arctan $eq_no = 1
> array_tmp4[2] := (ats(2,array_tmp3,array_tmp4_a2,2) - array_tmp3[1] * att(1,array_tmp4_a1,array_tmp4,2) - att(1,array_tmp4_a2,array_tmp4,2)) / (array_tmp4_a2[1] + array_tmp3[1] * array_tmp4_a1[1]);
> array_tmp4_a1[2] := att(1,array_tmp4_a2,array_tmp4,1);
> array_tmp4_a2[2] := neg(att(1,array_tmp4_a1,array_tmp4,1));
> #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 arctan $eq_no = 1
> array_tmp4[3] := (ats(3,array_tmp3,array_tmp4_a2,2) - array_tmp3[1] * att(2,array_tmp4_a1,array_tmp4,2) - att(2,array_tmp4_a2,array_tmp4,2)) / (array_tmp4_a2[1] + array_tmp3[1] * array_tmp4_a1[1]);
> array_tmp4_a1[3] := att(2,array_tmp4_a2,array_tmp4,1);
> array_tmp4_a2[3] := neg(att(2,array_tmp4_a1,array_tmp4,1));
> #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 arctan $eq_no = 1
> array_tmp4[4] := (ats(4,array_tmp3,array_tmp4_a2,2) - array_tmp3[1] * att(3,array_tmp4_a1,array_tmp4,2) - att(3,array_tmp4_a2,array_tmp4,2)) / (array_tmp4_a2[1] + array_tmp3[1] * array_tmp4_a1[1]);
> array_tmp4_a1[4] := att(3,array_tmp4_a2,array_tmp4,1);
> array_tmp4_a2[4] := neg(att(3,array_tmp4_a1,array_tmp4,1));
> #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 arctan $eq_no = 1
> array_tmp4[5] := (ats(5,array_tmp3,array_tmp4_a2,2) - array_tmp3[1] * att(4,array_tmp4_a1,array_tmp4,2) - att(4,array_tmp4_a2,array_tmp4,2)) / (array_tmp4_a2[1] + array_tmp3[1] * array_tmp4_a1[1]);
> array_tmp4_a1[5] := att(4,array_tmp4_a2,array_tmp4,1);
> array_tmp4_a2[5] := neg(att(4,array_tmp4_a1,array_tmp4,1));
> #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 atan $eq_no = 1
> array_tmp4[kkk] := (ats(kkk,array_tmp3,array_tmp4_a2,2) - array_tmp3[1] * att(kkk-1,array_tmp4_a1,array_tmp4,2) - att(kkk-1,array_tmp4_a2,array_tmp4,2))/(array_tmp4_a2[1] + array_tmp3[1] * array_tmp4_a1[1]);
> array_tmp4_a1[kkk] := att(kkk-1,array_tmp4_a2,array_tmp4,1);
> array_tmp4_a2[kkk] := neg(att(kkk-1,array_tmp4_a1,array_tmp4,1));
> #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_0D1,
array_const_0D2, 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_a1, array_tmp4_a2,
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_0D1[1]*array_x[1];
array_tmp2[1] := array_tmp1[1] + array_const_0D2[1];
array_tmp3[1] := sqrt(array_tmp2[1]);
array_tmp4[1] := arctan(array_tmp3[1]);
array_tmp4_a1[1] := sin(array_tmp4[1]);
array_tmp4_a2[1] := cos(array_tmp4[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_0D1[1]*array_x[2];
array_tmp2[2] := array_tmp1[2];
array_tmp3[2] := array_tmp2[2]/(array_tmp3[1]*glob__2);
array_tmp4[2] := (ats(2, array_tmp3, array_tmp4_a2, 2)
- array_tmp3[1]*att(1, array_tmp4_a1, array_tmp4, 2)
- att(1, array_tmp4_a2, array_tmp4, 2))/(
array_tmp3[1]*array_tmp4_a1[1] + array_tmp4_a2[1]);
array_tmp4_a1[2] := att(1, array_tmp4_a2, array_tmp4, 1);
array_tmp4_a2[2] := neg(att(1, array_tmp4_a1, array_tmp4, 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[3] := (ats(3, array_tmp3, array_tmp4_a2, 2)
- array_tmp3[1]*att(2, array_tmp4_a1, array_tmp4, 2)
- att(2, array_tmp4_a2, array_tmp4, 2))/(
array_tmp3[1]*array_tmp4_a1[1] + array_tmp4_a2[1]);
array_tmp4_a1[3] := att(2, array_tmp4_a2, array_tmp4, 1);
array_tmp4_a2[3] := neg(att(2, array_tmp4_a1, array_tmp4, 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[4] := (ats(4, array_tmp3, array_tmp4_a2, 2)
- array_tmp3[1]*att(3, array_tmp4_a1, array_tmp4, 2)
- att(3, array_tmp4_a2, array_tmp4, 2))/(
array_tmp3[1]*array_tmp4_a1[1] + array_tmp4_a2[1]);
array_tmp4_a1[4] := att(3, array_tmp4_a2, array_tmp4, 1);
array_tmp4_a2[4] := neg(att(3, array_tmp4_a1, array_tmp4, 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[5] := (ats(5, array_tmp3, array_tmp4_a2, 2)
- array_tmp3[1]*att(4, array_tmp4_a1, array_tmp4, 2)
- att(4, array_tmp4_a2, array_tmp4, 2))/(
array_tmp3[1]*array_tmp4_a1[1] + array_tmp4_a2[1]);
array_tmp4_a1[5] := att(4, array_tmp4_a2, array_tmp4, 1);
array_tmp4_a2[5] := neg(att(4, array_tmp4_a1, array_tmp4, 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] := (ats(kkk, array_tmp3, array_tmp4_a2, 2)
- array_tmp3[1]*att(kkk - 1, array_tmp4_a1, array_tmp4, 2)
- att(kkk - 1, array_tmp4_a2, array_tmp4, 2))/(
array_tmp3[1]*array_tmp4_a1[1] + array_tmp4_a2[1]);
array_tmp4_a1[kkk] := att(kkk - 1, array_tmp4_a2, array_tmp4, 1);
array_tmp4_a2[kkk] :=
neg(att(kkk - 1, array_tmp4_a1, array_tmp4, 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_0D1,
> array_const_0D2,
> #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_a1,
> array_tmp4_a2,
> 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 := 40;
> # before first input block
> #BEGIN FIRST INPUT BLOCK
> #BEGIN BLOCK 1
> #BEGIN FIRST INPUT BLOCK
> Digits:=32;
> max_terms:=40;
> #END BLOCK 1
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> # before generate arrays
> array_y_init:= Array(0..(40),[]);
> array_norms:= Array(0..(40),[]);
> array_fact_1:= Array(0..(40),[]);
> array_1st_rel_error:= Array(0..(2),[]);
> array_last_rel_error:= Array(0..(2),[]);
> array_est_rel_error:= Array(0..(2),[]);
> array_max_est_error:= Array(0..(2),[]);
> array_type_pole:= Array(0..(2),[]);
> array_type_real_pole:= Array(0..(2),[]);
> array_type_complex_pole:= Array(0..(2),[]);
> array_est_digits:= Array(0..(2),[]);
> array_y:= Array(0..(40),[]);
> array_x:= Array(0..(40),[]);
> array_tmp0:= Array(0..(40),[]);
> array_tmp1:= Array(0..(40),[]);
> array_tmp2:= Array(0..(40),[]);
> array_tmp3:= Array(0..(40),[]);
> array_tmp4_a1:= Array(0..(40),[]);
> array_tmp4_a2:= Array(0..(40),[]);
> array_tmp4:= Array(0..(40),[]);
> array_tmp5:= Array(0..(40),[]);
> array_m1:= Array(0..(40),[]);
> array_y_higher := Array(0..(2) ,(0..40+ 1),[]);
> array_y_higher_work := Array(0..(2) ,(0..40+ 1),[]);
> array_y_higher_work2 := Array(0..(2) ,(0..40+ 1),[]);
> array_y_set_initial := Array(0..(2) ,(0..40+ 1),[]);
> array_given_rad_poles := Array(0..(2) ,(0..3+ 1),[]);
> array_given_ord_poles := Array(0..(2) ,(0..3+ 1),[]);
> array_rad_test_poles := Array(0..(2) ,(0..4+ 1),[]);
> array_ord_test_poles := Array(0..(2) ,(0..4+ 1),[]);
> array_fact_2 := Array(0..(40) ,(0..40+ 1),[]);
> # before generate constants
> # before generate globals definition
> #Top Generate Globals Definition
> #Bottom Generate Globals Deninition
> # before generate const definition
> # before arrays initialized
> term := 1;
> while (term <= 40) do # do number 1
> array_y_init[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_norms[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_fact_1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_1st_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_last_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_est_rel_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_max_est_error[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_real_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_type_complex_pole[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 2) do # do number 1
> array_est_digits[term] := 0;
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_y[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_x[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp0[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp3[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp4_a1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp4_a2[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp4[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_tmp5[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> term := 1;
> while (term <= 40) do # do number 1
> array_m1[term] := c(0.0);
> term := term + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_y_higher[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_y_higher_work[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_y_higher_work2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_y_set_initial[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_rad_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 3) do # do number 2
> array_given_ord_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_rad_test_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=2) do # do number 1
> term := 1;
> while (term <= 4) do # do number 2
> array_ord_test_poles[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> ord := 1;
> while (ord <=40) do # do number 1
> term := 1;
> while (term <= 40) do # do number 2
> array_fact_2[ord,term] := c(0.0);
> term := term + 1;
> od;# end do number 2;
> ord := ord + 1;
> od;# end do number 1;
> # before symbols initialized
> #BEGIN SYMBOLS INITIALIZATED
> zero_ats_ar(array_y);
> zero_ats_ar(array_x);
> zero_ats_ar(array_tmp0);
> zero_ats_ar(array_tmp1);
> zero_ats_ar(array_tmp2);
> zero_ats_ar(array_tmp3);
> zero_ats_ar(array_tmp4_a1);
> zero_ats_ar(array_tmp4_a2);
> 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_0D1);
> array_const_0D1[1] := c(0.1);
> zero_ats_ar(array_const_0D2);
> array_const_0D2[1] := c(0.2);
> zero_ats_ar(array_m1);
> array_m1[1] := glob__m1;
> #END SYMBOLS INITIALIZATED
> # before generate factorials init
> #Initing Factorial Tables
> iiif := 0;
> while (iiif <= ATS_MAX_TERMS) do # do number 1
> jjjf := 0;
> while (jjjf <= ATS_MAX_TERMS) do # do number 2
> array_fact_1[iiif] := 0;
> array_fact_2[iiif,jjjf] := 0;
> jjjf := jjjf + 1;
> od;# end do number 2;
> iiif := iiif + 1;
> od;# end do number 1;
> #Done Initing Factorial Table
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> glob_iolevel := 5;
> glob_yes_pole := 4;
> glob_no_pole := 3;
> glob_not_given := 0;
> glob_no_sing_tests := 4;
> glob_ratio_test := 1;
> glob_three_term_test := 2;
> glob_six_term_test := 3;
> glob_log_10 := log(c(10.0));
> MAX_UNCHANGED := 10;
> glob__small := c(0.1e-50);
> glob_small_float := c(0.1e-50);
> glob_smallish_float := c(0.1e-60);
> glob_large_float := c(1.0e100);
> glob_larger_float := c(1.1e100);
> glob__m2 := c(-2);
> glob__m1 := c(-1);
> glob__0 := c(0);
> glob__1 := c(1);
> glob__2 := c(2);
> glob__3 := c(3);
> glob__4 := c(4);
> glob__5 := c(5);
> glob__8 := c(8);
> glob__10 := c(10);
> glob__100 := c(100);
> glob__pi := c(0.0);
> glob__0_5 := c(0.5);
> glob__0_8 := c(0.8);
> glob__m0_8 := c(-0.8);
> glob__0_25 := c(0.25);
> glob__0_125 := c(0.125);
> glob_h := 0.1;
> glob_nxt := 1;
> glob_prec := c(1.0e-16);
> glob_check_sign := c(1.0);
> glob_desired_digits_correct := c(8.0);
> glob_max_estimated_step_error := c(0.0);
> glob_ratio_of_radius := c(0.1);
> glob_percent_done := c(0.0);
> glob_total_exp_sec := c(0.1);
> glob_optimal_expect_sec := c(0.1);
> glob_estimated_size_answer := c(100.0);
> glob_almost_1 := c(0.9990);
> glob_clock_sec := c(0.0);
> glob_clock_start_sec := c(0.0);
> glob_disp_incr := c(0.1);
> glob_diff_rc_fm := c(0.1);
> glob_diff_rc_fmm1 := c(0.1);
> glob_diff_rc_fmm2 := c(0.1);
> glob_diff_ord_fm := c(0.1);
> glob_diff_ord_fmm1 := c(0.1);
> glob_diff_ord_fmm2 := c(0.1);
> glob_six_term_ord_save := c(0.1);
> glob_guess_error_rc := c(0.1);
> glob_guess_error_ord := c(0.1);
> glob_least_given_sing := c(9.9e200);
> glob_least_ratio_sing := c(9.9e200);
> glob_least_3_sing := c(9.9e100);
> glob_least_6_sing := c(9.9e100);
> glob_last_good_h := c(0.1);
> glob_max_h := c(0.1);
> glob_min_h := c(0.000001);
> glob_display_interval := c(0.1);
> glob_abserr := c(0.1e-10);
> glob_relerr := c(0.1e-10);
> glob_min_pole_est := c(0.1e+10);
> glob_max_rel_trunc_err := c(0.1e-10);
> glob_max_trunc_err := c(0.1e-10);
> glob_max_hours := c(0.0);
> glob_optimal_clock_start_sec := c(0.0);
> glob_optimal_start := c(0.0);
> glob_upper_ratio_limit := c(1.0001);
> glob_lower_ratio_limit := c(0.9999);
> glob_max_sec := c(10000.0);
> glob_orig_start_sec := c(0.0);
> glob_normmax := c(0.0);
> glob_max_minutes := c(0.0);
> glob_next_display := c(0.0);
> glob_est_digits := 1;
> glob_subiter_method := 3;
> glob_html_log := true;
> glob_min_good_digits := 99999;
> glob_good_digits := 0;
> glob_min_apfp_est_good_digits := 99999;
> glob_apfp_est_good_digits := 0;
> glob_max_opt_iter := 10;
> glob_dump := false;
> glob_djd_debug := true;
> glob_display_flag := true;
> glob_djd_debug2 := true;
> glob_h_reason := 0;
> glob_sec_in_minute := 60 ;
> glob_min_in_hour := 60;
> glob_hours_in_day := 24;
> glob_days_in_year := 365;
> glob_sec_in_hour := 3600;
> glob_sec_in_day := 86400;
> glob_sec_in_year := 31536000;
> glob_not_yet_finished := true;
> glob_initial_pass := true;
> glob_not_yet_start_msg := true;
> glob_reached_optimal_h := false;
> glob_optimal_done := false;
> glob_type_given_pole := 0;
> glob_optimize := false;
> glob_look_poles := false;
> glob_dump_closed_form := false;
> glob_max_iter := 10000;
> glob_no_eqs := 0;
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_start := 0;
> glob_iter := 0;
> # before generate set diff initial
> array_y_set_initial[1,1] := true;
> array_y_set_initial[1,2] := false;
> array_y_set_initial[1,3] := false;
> array_y_set_initial[1,4] := false;
> array_y_set_initial[1,5] := false;
> array_y_set_initial[1,6] := false;
> array_y_set_initial[1,7] := false;
> array_y_set_initial[1,8] := false;
> array_y_set_initial[1,9] := false;
> array_y_set_initial[1,10] := false;
> array_y_set_initial[1,11] := false;
> array_y_set_initial[1,12] := false;
> array_y_set_initial[1,13] := false;
> array_y_set_initial[1,14] := false;
> array_y_set_initial[1,15] := false;
> array_y_set_initial[1,16] := false;
> array_y_set_initial[1,17] := false;
> array_y_set_initial[1,18] := false;
> array_y_set_initial[1,19] := false;
> array_y_set_initial[1,20] := false;
> array_y_set_initial[1,21] := false;
> array_y_set_initial[1,22] := false;
> array_y_set_initial[1,23] := false;
> array_y_set_initial[1,24] := false;
> array_y_set_initial[1,25] := false;
> array_y_set_initial[1,26] := false;
> array_y_set_initial[1,27] := false;
> array_y_set_initial[1,28] := false;
> array_y_set_initial[1,29] := false;
> array_y_set_initial[1,30] := false;
> array_y_set_initial[1,31] := false;
> array_y_set_initial[1,32] := false;
> array_y_set_initial[1,33] := false;
> array_y_set_initial[1,34] := false;
> array_y_set_initial[1,35] := false;
> array_y_set_initial[1,36] := false;
> array_y_set_initial[1,37] := false;
> array_y_set_initial[1,38] := false;
> array_y_set_initial[1,39] := false;
> array_y_set_initial[1,40] := false;
> # before generate init omniout const
> ALWAYS := 1;
> INFO := 2;
> DEBUGL := 3;
> DEBUGMASSIVE := 4;
> ATS_MAX_TERMS := 40;
> glob_iolevel := INFO;
> # set default block
> #Write Set Defaults
> glob_orig_start_sec := elapsed_time_seconds();
> glob_display_flag := true;
> glob_no_eqs := 1;
> glob_iter := -1;
> opt_iter := -1;
> glob_max_iter := 10000;
> glob_max_hours := (0.0);
> glob_max_minutes := (15.0);
> omniout_str(ALWAYS,"##############ECHO OF PROBLEM#################");
> omniout_str(ALWAYS,"##############temp/arctan_sqrtpostcpx.cpx#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = arctan ( sqrt ( 0.1 * x + 0.2 ) ) ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=40;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := -1.1 + 0.1 * I;");
> omniout_str(ALWAYS,"x_end := 99.0 + 99.0 * I;");
> omniout_str(ALWAYS,"array_y_init[0 + 1] := exact_soln_y(x_start);");
> omniout_str(ALWAYS,"glob_look_poles := true;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_max_h :=c(0.01);");
> 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(-2.0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_rad_poles[1,2] := c(0.0);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_ord_poles[1,1] := c(0.5);");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"array_given_ord_poles[1,2] := c(0.0);");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=8;");
> omniout_str(ALWAYS,"glob_max_minutes:=(3.0);");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"glob_max_iter:=10000;");
> omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);");
> omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);");
> omniout_str(ALWAYS,"glob_look_poles:=true;");
> omniout_str(ALWAYS,"glob_h:=c(0.001);");
> omniout_str(ALWAYS,"glob_display_interval:=c(0.01);");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"return(c(10.0) * (c(0.1) * c(x) + c(0.2)) * arctan(sqrt ( c(0.1) * c(x) +");
> omniout_str(ALWAYS,"c(0.2))) - c(10.0) * sqrt( c(0.1) * c(x) + c(0.2)) + c(10.0) * arctan(sqrt( c(0.1) * c(x) + c(0.2))));");
> 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 := -1.1 + 0.1 * I;
> x_end := 99.0 + 99.0 * I;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_max_h :=c(0.01);
> glob_type_given_pole := 1;
> array_given_rad_poles[1,1] := c(-2.0);
> 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 ) = arctan ( sqrt ( 0.1 * x + 0.2 ) ) ; ");
> 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,"2017-11-26T14:35:50-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"arctan_sqrt")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = arctan ( sqrt ( 0.1 * x + 0.2 ) ) ; ")
> ;
> 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,"arctan_sqrt diffeq.mxt")
> ;
> logitem_str(html_log_file,"arctan_sqrt maple results")
> ;
> logitem_str(html_log_file,"Good Accuracy - Wasn't for Real")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 15;
> if (glob_html_log) then # if number 15
> fclose(html_log_file);
> fi;# end if 15
> ;
> ;;
> end;
> # End Function number 12
> #END OUTFILEMAIN
> end;
Warning, `h_new` is implicitly declared local to procedure `main`
Warning, `ratio` is implicitly declared local to procedure `main`
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max,
term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order,
sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it,
last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err,
estimated_step_error, min_value, est_answer, found_h, repeat_it, h_new,
ratio;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_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_a1, array_tmp4_a2,
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 := 40;
Digits := 32;
max_terms := 40;
glob_html_log := true;
array_y_init := Array(0 .. 40, []);
array_norms := Array(0 .. 40, []);
array_fact_1 := Array(0 .. 40, []);
array_1st_rel_error := Array(0 .. 2, []);
array_last_rel_error := Array(0 .. 2, []);
array_est_rel_error := Array(0 .. 2, []);
array_max_est_error := Array(0 .. 2, []);
array_type_pole := Array(0 .. 2, []);
array_type_real_pole := Array(0 .. 2, []);
array_type_complex_pole := Array(0 .. 2, []);
array_est_digits := Array(0 .. 2, []);
array_y := Array(0 .. 40, []);
array_x := Array(0 .. 40, []);
array_tmp0 := Array(0 .. 40, []);
array_tmp1 := Array(0 .. 40, []);
array_tmp2 := Array(0 .. 40, []);
array_tmp3 := Array(0 .. 40, []);
array_tmp4_a1 := Array(0 .. 40, []);
array_tmp4_a2 := Array(0 .. 40, []);
array_tmp4 := Array(0 .. 40, []);
array_tmp5 := Array(0 .. 40, []);
array_m1 := Array(0 .. 40, []);
array_y_higher := Array(0 .. 2, 0 .. 41, []);
array_y_higher_work := Array(0 .. 2, 0 .. 41, []);
array_y_higher_work2 := Array(0 .. 2, 0 .. 41, []);
array_y_set_initial := Array(0 .. 2, 0 .. 41, []);
array_given_rad_poles := Array(0 .. 2, 0 .. 4, []);
array_given_ord_poles := Array(0 .. 2, 0 .. 4, []);
array_rad_test_poles := Array(0 .. 2, 0 .. 5, []);
array_ord_test_poles := Array(0 .. 2, 0 .. 5, []);
array_fact_2 := Array(0 .. 40, 0 .. 41, []);
term := 1;
while term <= 40 do array_y_init[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 40 do array_norms[term] := c(0.); term := term + 1 end do
;
term := 1;
while term <= 40 do array_fact_1[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_1st_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do
array_last_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_est_rel_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_max_est_error[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 2 do array_type_pole[term] := 0; term := term + 1 end do;
term := 1;
while term <= 2 do array_type_real_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 2 do array_type_complex_pole[term] := 0; term := term + 1
end do;
term := 1;
while term <= 2 do array_est_digits[term] := 0; term := term + 1 end do
;
term := 1;
while term <= 40 do array_y[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_x[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp0[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp1[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp2[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp3[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp4_a1[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 40 do array_tmp4_a2[term] := c(0.); term := term + 1
end do;
term := 1;
while term <= 40 do array_tmp4[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_tmp5[term] := c(0.); term := term + 1 end do;
term := 1;
while term <= 40 do array_m1[term] := c(0.); term := term + 1 end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 40 do
array_y_higher[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 40 do
array_y_higher_work[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 40 do
array_y_higher_work2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 40 do
array_y_set_initial[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_rad_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 3 do
array_given_ord_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 4 do
array_rad_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 2 do
term := 1;
while term <= 4 do
array_ord_test_poles[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
ord := 1;
while ord <= 40 do
term := 1;
while term <= 40 do
array_fact_2[ord, term] := c(0.); term := term + 1
end do;
ord := ord + 1
end do;
zero_ats_ar(array_y);
zero_ats_ar(array_x);
zero_ats_ar(array_tmp0);
zero_ats_ar(array_tmp1);
zero_ats_ar(array_tmp2);
zero_ats_ar(array_tmp3);
zero_ats_ar(array_tmp4_a1);
zero_ats_ar(array_tmp4_a2);
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_0D1);
array_const_0D1[1] := c(0.1);
zero_ats_ar(array_const_0D2);
array_const_0D2[1] := c(0.2);
zero_ats_ar(array_m1);
array_m1[1] := glob__m1;
iiif := 0;
while iiif <= ATS_MAX_TERMS do
jjjf := 0;
while jjjf <= ATS_MAX_TERMS do
array_fact_1[iiif] := 0;
array_fact_2[iiif, jjjf] := 0;
jjjf := jjjf + 1
end do;
iiif := iiif + 1
end do;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
glob_iolevel := 5;
glob_yes_pole := 4;
glob_no_pole := 3;
glob_not_given := 0;
glob_no_sing_tests := 4;
glob_ratio_test := 1;
glob_three_term_test := 2;
glob_six_term_test := 3;
glob_log_10 := log(c(10.0));
MAX_UNCHANGED := 10;
glob__small := c(0.1*10^(-50));
glob_small_float := c(0.1*10^(-50));
glob_smallish_float := c(0.1*10^(-60));
glob_large_float := c(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob__m2 := c(-2);
glob__m1 := c(-1);
glob__0 := c(0);
glob__1 := c(1);
glob__2 := c(2);
glob__3 := c(3);
glob__4 := c(4);
glob__5 := c(5);
glob__8 := c(8);
glob__10 := c(10);
glob__100 := c(100);
glob__pi := c(0.);
glob__0_5 := c(0.5);
glob__0_8 := c(0.8);
glob__m0_8 := c(-0.8);
glob__0_25 := c(0.25);
glob__0_125 := c(0.125);
glob_h := 0.1;
glob_nxt := 1;
glob_prec := c(0.10*10^(-15));
glob_check_sign := c(1.0);
glob_desired_digits_correct := c(8.0);
glob_max_estimated_step_error := c(0.);
glob_ratio_of_radius := c(0.1);
glob_percent_done := c(0.);
glob_total_exp_sec := c(0.1);
glob_optimal_expect_sec := c(0.1);
glob_estimated_size_answer := c(100.0);
glob_almost_1 := c(0.9990);
glob_clock_sec := c(0.);
glob_clock_start_sec := c(0.);
glob_disp_incr := c(0.1);
glob_diff_rc_fm := c(0.1);
glob_diff_rc_fmm1 := c(0.1);
glob_diff_rc_fmm2 := c(0.1);
glob_diff_ord_fm := c(0.1);
glob_diff_ord_fmm1 := c(0.1);
glob_diff_ord_fmm2 := c(0.1);
glob_six_term_ord_save := c(0.1);
glob_guess_error_rc := c(0.1);
glob_guess_error_ord := c(0.1);
glob_least_given_sing := c(0.99*10^201);
glob_least_ratio_sing := c(0.99*10^201);
glob_least_3_sing := c(0.99*10^101);
glob_least_6_sing := c(0.99*10^101);
glob_last_good_h := c(0.1);
glob_max_h := c(0.1);
glob_min_h := c(0.1*10^(-5));
glob_display_interval := c(0.1);
glob_abserr := c(0.1*10^(-10));
glob_relerr := c(0.1*10^(-10));
glob_min_pole_est := c(0.1*10^10);
glob_max_rel_trunc_err := c(0.1*10^(-10));
glob_max_trunc_err := c(0.1*10^(-10));
glob_max_hours := c(0.);
glob_optimal_clock_start_sec := c(0.);
glob_optimal_start := c(0.);
glob_upper_ratio_limit := c(1.0001);
glob_lower_ratio_limit := c(0.9999);
glob_max_sec := c(10000.0);
glob_orig_start_sec := c(0.);
glob_normmax := c(0.);
glob_max_minutes := c(0.);
glob_next_display := c(0.);
glob_est_digits := 1;
glob_subiter_method := 3;
glob_html_log := true;
glob_min_good_digits := 99999;
glob_good_digits := 0;
glob_min_apfp_est_good_digits := 99999;
glob_apfp_est_good_digits := 0;
glob_max_opt_iter := 10;
glob_dump := false;
glob_djd_debug := true;
glob_display_flag := true;
glob_djd_debug2 := true;
glob_h_reason := 0;
glob_sec_in_minute := 60;
glob_min_in_hour := 60;
glob_hours_in_day := 24;
glob_days_in_year := 365;
glob_sec_in_hour := 3600;
glob_sec_in_day := 86400;
glob_sec_in_year := 31536000;
glob_not_yet_finished := true;
glob_initial_pass := true;
glob_not_yet_start_msg := true;
glob_reached_optimal_h := false;
glob_optimal_done := false;
glob_type_given_pole := 0;
glob_optimize := false;
glob_look_poles := false;
glob_dump_closed_form := false;
glob_max_iter := 10000;
glob_no_eqs := 0;
glob_unchanged_h_cnt := 0;
glob_warned := false;
glob_warned2 := false;
glob_start := 0;
glob_iter := 0;
array_y_set_initial[1, 1] := true;
array_y_set_initial[1, 2] := false;
array_y_set_initial[1, 3] := false;
array_y_set_initial[1, 4] := false;
array_y_set_initial[1, 5] := false;
array_y_set_initial[1, 6] := false;
array_y_set_initial[1, 7] := false;
array_y_set_initial[1, 8] := false;
array_y_set_initial[1, 9] := false;
array_y_set_initial[1, 10] := false;
array_y_set_initial[1, 11] := false;
array_y_set_initial[1, 12] := false;
array_y_set_initial[1, 13] := false;
array_y_set_initial[1, 14] := false;
array_y_set_initial[1, 15] := false;
array_y_set_initial[1, 16] := false;
array_y_set_initial[1, 17] := false;
array_y_set_initial[1, 18] := false;
array_y_set_initial[1, 19] := false;
array_y_set_initial[1, 20] := false;
array_y_set_initial[1, 21] := false;
array_y_set_initial[1, 22] := false;
array_y_set_initial[1, 23] := false;
array_y_set_initial[1, 24] := false;
array_y_set_initial[1, 25] := false;
array_y_set_initial[1, 26] := false;
array_y_set_initial[1, 27] := false;
array_y_set_initial[1, 28] := false;
array_y_set_initial[1, 29] := false;
array_y_set_initial[1, 30] := false;
array_y_set_initial[1, 31] := false;
array_y_set_initial[1, 32] := false;
array_y_set_initial[1, 33] := false;
array_y_set_initial[1, 34] := false;
array_y_set_initial[1, 35] := false;
array_y_set_initial[1, 36] := false;
array_y_set_initial[1, 37] := false;
array_y_set_initial[1, 38] := false;
array_y_set_initial[1, 39] := false;
array_y_set_initial[1, 40] := false;
ALWAYS := 1;
INFO := 2;
DEBUGL := 3;
DEBUGMASSIVE := 4;
ATS_MAX_TERMS := 40;
glob_iolevel := INFO;
glob_orig_start_sec := elapsed_time_seconds();
glob_display_flag := true;
glob_no_eqs := 1;
glob_iter := -1;
opt_iter := -1;
glob_max_iter := 10000;
glob_max_hours := 0.;
glob_max_minutes := 15.0;
omniout_str(ALWAYS, "##############ECHO OF PROBLEM#################");
omniout_str(ALWAYS,
"##############temp/arctan_sqrtpostcpx.cpx#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = arctan ( sqrt ( 0\
.1 * x + 0.2 ) ) ; ");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=40;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := -1.1 + 0.1 * I;");
omniout_str(ALWAYS, "x_end := 99.0 + 99.0 * I;");
omniout_str(ALWAYS, "array_y_init[0 + 1] := exact_soln_y(x_start);");
omniout_str(ALWAYS, "glob_look_poles := true;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "glob_max_h :=c(0.01);");
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(-2.0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_rad_poles[1,2] := c(0.0);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_ord_poles[1,1] := c(0.5);");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "array_given_ord_poles[1,2] := c(0.0);");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=8;");
omniout_str(ALWAYS, "glob_max_minutes:=(3.0);");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "glob_max_iter:=10000;");
omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);");
omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);");
omniout_str(ALWAYS, "glob_look_poles:=true;");
omniout_str(ALWAYS, "glob_h:=c(0.001);");
omniout_str(ALWAYS, "glob_display_interval:=c(0.01);");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "return(c(10.0) * (c(0.1) * c(x) + c(0.2)) * arct\
an(sqrt ( c(0.1) * c(x) +");
omniout_str(ALWAYS, "c(0.2))) - c(10.0) * sqrt( c(0.1) * c(x) + c(0.2\
)) + c(10.0) * arctan(sqrt( c(0.1) * c(x) + c(0.2))));");
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,");
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omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 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(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob_almost_1 := c(0.99);
x_start := -1.1 + 0.1*I;
x_end := 99.0 + 99.0*I;
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_h := c(0.01);
glob_type_given_pole := 1;
array_given_rad_poles[1, 1] := c(-2.0);
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 ) = arctan ( sqrt (\
0.1 * x + 0.2 ) ) ; ");
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, "2017-11-26T14:35:50-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"arctan_sqrt");
logitem_str(html_log_file, "diff ( y , x , 1 ) = ar\
ctan ( sqrt ( 0.1 * x + 0.2 ) ) ; ");
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, "arctan_sqrt diffeq.mxt");
logitem_str(html_log_file, "arctan_sqrt maple results");
logitem_str(html_log_file, "Good Accuracy - Wasn't for Real");
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=3.8MB, alloc=40.3MB, time=0.08
##############ECHO OF PROBLEM#################
##############temp/arctan_sqrtpostcpx.cpx#################
diff ( y , x , 1 ) = arctan ( sqrt ( 0.1 * x + 0.2 ) ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=40;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := -1.1 + 0.1 * I;
x_end := 99.0 + 99.0 * I;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_max_h :=c(0.01);
glob_type_given_pole := 1;
array_given_rad_poles[1,1] := c(-2.0);
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(c(10.0) * (c(0.1) * c(x) + c(0.2)) * arctan(sqrt ( c(0.1) * c(x) +
c(0.2))) - c(10.0) * sqrt( c(0.1) * c(x) + c(0.2)) + c(10.0) * arctan(sqrt( c(0.1) * c(x) + c(0.2))));
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
memory used=34.7MB, alloc=40.3MB, time=0.45
x[1] = -1.1 0.1
h = 0.0001 0.005
y[1] (numeric) = 0.176115197062 0.029162139066
y[1] (closed_form) = 0.176115197062 0.029162139066
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 0.9055
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0999 0.105
h = 0.0001 0.003
y[1] (numeric) = 0.176066556187 0.0306235825185
y[1] (closed_form) = 0.176066176572 0.0306236155925
absolute error = 3.811e-07
relative error = 0.0002132 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.9062
Order of pole (given) = 0.5 0
NO 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=80.2MB, alloc=44.3MB, time=1.02
x[1] = -1.0998 0.108
h = 0.001 0.001
y[1] (numeric) = 0.176046552583 0.0315013701346
y[1] (closed_form) = 0.176046627856 0.0315013564935
absolute error = 7.650e-08
relative error = 4.277e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.9067
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0988 0.109
h = 0.001 0.003
y[1] (numeric) = 0.176321932456 0.0318101613941
y[1] (closed_form) = 0.176322222121 0.0318100486822
absolute error = 3.108e-07
relative error = 0.0001735 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.9078
Order of pole (given) = 0.5 0
NO 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=125.6MB, alloc=44.3MB, time=1.58
x[1] = -1.0978 0.112
h = 0.0001 0.004
y[1] (numeric) = 0.176564167781 0.0327037687936
y[1] (closed_form) = 0.17656401296 0.0327038402137
absolute error = 1.705e-07
relative error = 9.495e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.9091
Order of pole (given) = 0.5 0
NO 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=171.1MB, alloc=44.3MB, time=2.14
x[1] = -1.0977 0.116
h = 0.003 0.006
y[1] (numeric) = 0.17652427357 0.0338755016633
y[1] (closed_form) = 0.176523789201 0.033875330633
absolute error = 5.137e-07
relative error = 0.0002858 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.9097
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0947 0.122
h = 0.0001 0.005
y[1] (numeric) = 0.1772939366 0.0356844116489
y[1] (closed_form) = 0.177293338495 0.0356860321252
absolute error = 1.727e-06
relative error = 0.0009551 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9135
Order of pole (given) = 0.5 0
NO 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=216.6MB, alloc=44.3MB, time=2.70
x[1] = -1.0946 0.127
h = 0.0001 0.003
y[1] (numeric) = 0.177228368222 0.0371525837223
y[1] (closed_form) = 0.177228037447 0.0371530730699
absolute error = 5.907e-07
relative error = 0.0003262 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9143
Order of pole (given) = 0.5 0
NO 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=262.0MB, alloc=44.3MB, time=3.27
x[1] = -1.0945 0.13
h = 0.001 0.001
y[1] (numeric) = 0.177198653306 0.0380338704785
y[1] (closed_form) = 0.177198774491 0.0380343071867
absolute error = 4.532e-07
relative error = 0.0002501 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.9148
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0935 0.131
h = 0.001 0.003
y[1] (numeric) = 0.177471824073 0.0383469932792
y[1] (closed_form) = 0.177472157225 0.0383473285183
absolute error = 4.726e-07
relative error = 0.0002603 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.9159
Order of pole (given) = 0.5 0
NO 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=307.4MB, alloc=44.3MB, time=3.83
x[1] = -1.0925 0.134
h = 0.0001 0.004
y[1] (numeric) = 0.177705317013 0.0392470477831
y[1] (closed_form) = 0.177705210418 0.0392475722233
absolute error = 5.352e-07
relative error = 0.0002941 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.9173
Order of pole (given) = 0.5 0
NO 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=352.9MB, alloc=44.3MB, time=4.40
x[1] = -1.0924 0.138
h = 0.003 0.006
y[1] (numeric) = 0.177652482442 0.0404233745912
y[1] (closed_form) = 0.177652044718 0.0404236622585
absolute error = 5.238e-07
relative error = 0.0002875 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 0.918
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0894 0.144
h = 0.0001 0.005
y[1] (numeric) = 0.17840582439 0.0422485165225
y[1] (closed_form) = 0.178405297568 0.0422505879716
absolute error = 2.137e-06
relative error = 0.001166 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9219
Order of pole (given) = 0.5 0
NO 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=398.5MB, alloc=44.3MB, time=4.96
x[1] = -1.0893 0.149
h = 0.0001 0.003
y[1] (numeric) = 0.178324149916 0.0437224416433
y[1] (closed_form) = 0.178323873935 0.0437233842958
absolute error = 9.822e-07
relative error = 0.000535 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9228
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0892 0.152
h = 0.001 0.001
y[1] (numeric) = 0.178284820787 0.0446073399822
y[1] (closed_form) = 0.178284993683 0.0446082242487
absolute error = 9.010e-07
relative error = 0.0004903 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9234
Order of pole (given) = 0.5 0
NO 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=444.0MB, alloc=44.3MB, time=5.52
x[1] = -1.0882 0.153
h = 0.001 0.003
y[1] (numeric) = 0.178555852027 0.0449248015374
y[1] (closed_form) = 0.178556234419 0.0449255820495
absolute error = 8.692e-07
relative error = 0.0004721 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9245
Order of pole (given) = 0.5 0
NO 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=489.5MB, alloc=44.3MB, time=6.09
x[1] = -1.0872 0.156
h = 0.0001 0.004
y[1] (numeric) = 0.1787807342 0.0458313870048
y[1] (closed_form) = 0.178780681684 0.0458323615616
absolute error = 9.760e-07
relative error = 0.0005288 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.926
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] = -1.0871 0.16
h = 0.003 0.006
y[1] (numeric) = 0.178715088079 0.0470124567713
y[1] (closed_form) = 0.178714703061 0.0470132002048
absolute error = 8.372e-07
relative error = 0.0004531 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9268
Order of pole (given) = 0.5 0
NO 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=535.0MB, alloc=44.3MB, time=6.65
x[1] = -1.0841 0.166
h = 0.0001 0.005
y[1] (numeric) = 0.179452411351 0.0488539628905
y[1] (closed_form) = 0.179451961275 0.0488564816879
absolute error = 2.559e-06
relative error = 0.001376 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9308
Order of pole (given) = 0.5 0
NO 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=580.5MB, alloc=44.3MB, time=7.22
x[1] = -1.084 0.171
h = 0.0001 0.003
y[1] (numeric) = 0.17935479249 0.0503338236965
y[1] (closed_form) = 0.179354577075 0.0503352165292
absolute error = 1.409e-06
relative error = 0.0007566 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9318
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0839 0.174
h = 0.001 0.001
y[1] (numeric) = 0.179305948542 0.051222441313
y[1] (closed_form) = 0.17930617878 0.0512237701953
absolute error = 1.349e-06
relative error = 0.0007232 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9325
Order of pole (given) = 0.5 0
NO 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=626.0MB, alloc=44.3MB, time=7.78
x[1] = -1.0829 0.175
h = 0.001 0.003
y[1] (numeric) = 0.179574909086 0.0515442464695
y[1] (closed_form) = 0.17957534631 0.0515454694248
absolute error = 1.299e-06
relative error = 0.0006952 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9336
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0819 0.178
h = 0.0001 0.004
y[1] (numeric) = 0.179791312977 0.0524574412988
y[1] (closed_form) = 0.17979132022 0.0524588629169
absolute error = 1.422e-06
relative error = 0.0007591 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9352
Order of pole (given) = 0.5 0
NO 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=671.4MB, alloc=44.3MB, time=8.34
x[1] = -1.0818 0.182
h = 0.003 0.006
y[1] (numeric) = 0.179712987111 0.0536433967537
y[1] (closed_form) = 0.179712660678 0.0536445928601
absolute error = 1.240e-06
relative error = 0.0006611 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9361
Order of pole (given) = 0.5 0
NO 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=717.0MB, alloc=44.3MB, time=8.90
x[1] = -1.0788 0.188
h = 0.0001 0.005
y[1] (numeric) = 0.18043459404 0.0555013876371
y[1] (closed_form) = 0.180434225968 0.0555043500457
absolute error = 2.985e-06
relative error = 0.001581 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9402
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0787 0.193
h = 0.0001 0.003
y[1] (numeric) = 0.180321196 0.0569873589445
y[1] (closed_form) = 0.180321046737 0.056989198691
absolute error = 1.846e-06
relative error = 0.000976 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9413
Order of pole (given) = 0.5 0
NO 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=762.4MB, alloc=44.3MB, time=9.47
x[1] = -1.0786 0.196
h = 0.001 0.001
y[1] (numeric) = 0.180262938612 0.0578797987795
y[1] (closed_form) = 0.180263231651 0.0578815691964
absolute error = 1.795e-06
relative error = 0.0009478 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.942
Order of pole (given) = 0.5 0
NO 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=807.9MB, alloc=44.3MB, time=10.04
x[1] = -1.0776 0.197
h = 0.0001 0.004
y[1] (numeric) = 0.180529896431 0.0582059501177
y[1] (closed_form) = 0.180530393916 0.0582076125465
absolute error = 1.735e-06
relative error = 0.0009148 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9432
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0775 0.201
h = 0.003 0.006
y[1] (numeric) = 0.180441292822 0.0593959832509
y[1] (closed_form) = 0.180440866283 0.0593975133409
absolute error = 1.588e-06
relative error = 0.0008362 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9441
Order of pole (given) = 0.5 0
NO 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=853.3MB, alloc=44.3MB, time=10.60
x[1] = -1.0745 0.207
h = 0.0001 0.005
y[1] (numeric) = 0.181149415118 0.0612680692107
y[1] (closed_form) = 0.181148966705 0.0612713575941
absolute error = 3.319e-06
relative error = 0.001736 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9484
Order of pole (given) = 0.5 0
NO 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=898.8MB, alloc=44.3MB, time=11.16
x[1] = -1.0744 0.212
h = 0.0001 0.003
y[1] (numeric) = 0.181022494006 0.0627592490312
y[1] (closed_form) = 0.181022250988 0.0627614177662
absolute error = 2.182e-06
relative error = 0.001139 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9496
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0743 0.215
h = 0.001 0.001
y[1] (numeric) = 0.180956169203 0.0636549472611
y[1] (closed_form) = 0.18095636557 0.0636570421441
absolute error = 2.104e-06
relative error = 0.001097 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9503
Order of pole (given) = 0.5 0
NO 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=944.3MB, alloc=44.3MB, time=11.72
x[1] = -1.0733 0.216
h = 0.001 0.003
y[1] (numeric) = 0.181221405071 0.0639848172872
y[1] (closed_form) = 0.181221803701 0.0639868024658
absolute error = 2.025e-06
relative error = 0.001054 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9515
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0723 0.219
h = 0.0001 0.004
y[1] (numeric) = 0.181422306454 0.064910403693
y[1] (closed_form) = 0.1814222844 0.0649125955925
absolute error = 2.192e-06
relative error = 0.001138 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9532
Order of pole (given) = 0.5 0
NO 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=989.9MB, alloc=44.3MB, time=12.29
x[1] = -1.0722 0.223
h = 0.003 0.006
y[1] (numeric) = 0.181320683966 0.0661056614002
y[1] (closed_form) = 0.181320326499 0.0661076380873
absolute error = 2.009e-06
relative error = 0.001041 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9542
Order of pole (given) = 0.5 0
NO 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=1035.3MB, alloc=44.3MB, time=12.86
x[1] = -1.0692 0.229
h = 0.0001 0.005
y[1] (numeric) = 0.182013649063 0.0679944300634
y[1] (closed_form) = 0.182013291944 0.0679981549085
absolute error = 3.742e-06
relative error = 0.001926 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9586
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0691 0.234
h = 0.0001 0.003
y[1] (numeric) = 0.181871261926 0.0694920269778
y[1] (closed_form) = 0.181871095 0.0694946362783
absolute error = 2.615e-06
relative error = 0.001343 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9599
Order of pole (given) = 0.5 0
NO 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=44.3MB, time=13.44
x[1] = -1.069 0.237
h = 0.001 0.001
y[1] (numeric) = 0.181795715477 0.0703917276485
y[1] (closed_form) = 0.181795984379 0.0703942580652
absolute error = 2.545e-06
relative error = 0.001305 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9607
Order of pole (given) = 0.5 0
NO 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=1126.5MB, alloc=44.3MB, time=14.00
x[1] = -1.068 0.238
h = 0.001 0.003
y[1] (numeric) = 0.182059072515 0.0707259437652
y[1] (closed_form) = 0.182059541099 0.0707283626204
absolute error = 2.464e-06
relative error = 0.001261 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9619
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.067 0.241
h = 0.0001 0.004
y[1] (numeric) = 0.182251875938 0.0716583361263
y[1] (closed_form) = 0.182251928935 0.0716609656855
absolute error = 2.630e-06
relative error = 0.001343 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9636
Order of pole (given) = 0.5 0
NO 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=1171.9MB, alloc=44.3MB, time=14.56
x[1] = -1.0669 0.245
h = 0.003 0.006
y[1] (numeric) = 0.182137962209 0.0728588548596
y[1] (closed_form) = 0.182137679156 0.0728612746603
absolute error = 2.436e-06
relative error = 0.001242 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9647
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0639 0.251
h = 0.0001 0.005
y[1] (numeric) = 0.18281606906 0.0747643951778
y[1] (closed_form) = 0.182815807916 0.0747685524978
absolute error = 4.166e-06
relative error = 0.002109 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9692
Order of pole (given) = 0.5 0
NO 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=1217.6MB, alloc=44.3MB, time=15.12
x[1] = -1.0638 0.256
h = 0.0001 0.003
y[1] (numeric) = 0.182658388493 0.076268561848
y[1] (closed_form) = 0.182658302708 0.0762716081133
absolute error = 3.047e-06
relative error = 0.00154 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9706
Order of pole (given) = 0.5 0
NO 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=1263.2MB, alloc=44.3MB, time=15.69
x[1] = -1.0637 0.259
h = 0.001 0.001
y[1] (numeric) = 0.182573725873 0.0771723544827
y[1] (closed_form) = 0.182574072268 0.0771753170199
absolute error = 2.983e-06
relative error = 0.001505 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9715
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0627 0.26
h = 0.001 0.003
y[1] (numeric) = 0.182835269117 0.0775109133579
y[1] (closed_form) = 0.1828358126 0.0775137625835
absolute error = 2.901e-06
relative error = 0.001461 %
Correct digits = 5
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
memory used=1308.7MB, alloc=44.3MB, time=16.25
x[1] = -1.0617 0.263
h = 0.0001 0.004
y[1] (numeric) = 0.183020107671 0.0784501699962
y[1] (closed_form) = 0.183020240698 0.0784532336929
absolute error = 3.067e-06
relative error = 0.00154 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9745
Order of pole (given) = 0.5 0
NO 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=1354.4MB, alloc=44.3MB, time=16.82
x[1] = -1.0616 0.267
h = 0.003 0.006
y[1] (numeric) = 0.182894042397 0.0796560684534
y[1] (closed_form) = 0.182893838907 0.0796589277748
absolute error = 2.867e-06
relative error = 0.001437 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9756
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0586 0.273
h = 0.0001 0.005
y[1] (numeric) = 0.183557587719 0.0815784590393
y[1] (closed_form) = 0.183557427031 0.0815830447847
absolute error = 4.589e-06
relative error = 0.002284 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9802
Order of pole (given) = 0.5 0
NO 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=1399.9MB, alloc=44.3MB, time=17.39
x[1] = -1.0585 0.278
h = 0.0001 0.003
y[1] (numeric) = 0.183384787983 0.0830893405437
y[1] (closed_form) = 0.183384788198 0.0830928200814
absolute error = 3.480e-06
relative error = 0.001728 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9817
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0584 0.281
h = 0.001 0.001
y[1] (numeric) = 0.183291115552 0.0839973100878
y[1] (closed_form) = 0.183291544219 0.0840007012402
absolute error = 3.418e-06
relative error = 0.001695 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9826
Order of pole (given) = 0.5 0
NO 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=1445.5MB, alloc=44.3MB, time=17.95
x[1] = -1.0574 0.282
h = 0.001 0.003
y[1] (numeric) = 0.183550908862 0.0843402065385
y[1] (closed_form) = 0.183551532016 0.0843434827336
absolute error = 3.335e-06
relative error = 0.001651 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9839
Order of pole (given) = 0.5 0
NO 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=1491.1MB, alloc=44.3MB, time=18.52
x[1] = -1.0564 0.285
h = 0.0001 0.004
y[1] (numeric) = 0.183727915143 0.0852863809143
y[1] (closed_form) = 0.183728132996 0.0852898751361
absolute error = 3.501e-06
relative error = 0.001728 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9857
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0563 0.289
h = 0.003 0.006
y[1] (numeric) = 0.183589839159 0.0864977717488
y[1] (closed_form) = 0.18358972019 0.0865010669013
absolute error = 3.297e-06
relative error = 0.001625 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.987
Order of pole (given) = 0.5 0
NO 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=1536.6MB, alloc=44.3MB, time=19.08
x[1] = -1.0533 0.295
h = 0.0001 0.005
y[1] (numeric) = 0.184239116989 0.0884370812802
y[1] (closed_form) = 0.184239061043 0.0884420913507
absolute error = 5.010e-06
relative error = 0.002452 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9916
Order of pole (given) = 0.5 0
NO 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=1582.2MB, alloc=44.3MB, time=19.64
x[1] = -1.0532 0.3
h = 0.0001 0.003
y[1] (numeric) = 0.184051373594 0.0899548152487
y[1] (closed_form) = 0.184051464478 0.089958724287
absolute error = 3.910e-06
relative error = 0.001909 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9932
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0531 0.303
h = 0.001 0.001
y[1] (numeric) = 0.183948798347 0.0908670421595
y[1] (closed_form) = 0.183949313888 0.0908708583405
absolute error = 3.851e-06
relative error = 0.001877 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9942
Order of pole (given) = 0.5 0
NO 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=1627.7MB, alloc=44.3MB, time=20.21
x[1] = -1.0521 0.304
h = 0.0001 0.004
y[1] (numeric) = 0.184206904353 0.091214269262
y[1] (closed_form) = 0.184207611777 0.0912179689418
absolute error = 3.767e-06
relative error = 0.001832 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9955
Order of pole (given) = 0.5 0
NO 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=1673.3MB, alloc=44.3MB, time=20.78
x[1] = -1.052 0.308
h = 0.003 0.006
y[1] (numeric) = 0.184059102354 0.092430212901
y[1] (closed_form) = 0.184058906618 0.0924338377705
absolute error = 3.630e-06
relative error = 0.001763 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 0.9968
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.049 0.314
h = 0.0001 0.005
y[1] (numeric) = 0.184696129841 0.0943839681689
y[1] (closed_form) = 0.184696014138 0.0943892979871
absolute error = 5.331e-06
relative error = 0.00257 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.001
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
memory used=1718.8MB, alloc=44.3MB, time=21.34
x[1] = -1.0489 0.319
h = 0.0001 0.003
y[1] (numeric) = 0.18449558093 0.095907530001
y[1] (closed_form) = 0.184495600187 0.0959117633224
absolute error = 4.233e-06
relative error = 0.002036 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.003
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0488 0.322
h = 0.001 0.001
y[1] (numeric) = 0.184385376494 0.0968233782777
y[1] (closed_form) = 0.184385817145 0.0968275149933
absolute error = 4.160e-06
relative error = 0.001998 %
Correct digits = 5
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
memory used=1764.3MB, alloc=44.3MB, time=21.90
x[1] = -1.0478 0.323
h = 0.001 0.003
y[1] (numeric) = 0.184642027856 0.0971743071607
y[1] (closed_form) = 0.184642658168 0.0971783260944
absolute error = 4.068e-06
relative error = 0.00195 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.005
Order of pole (given) = 0.5 0
NO 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=1809.8MB, alloc=44.3MB, time=22.47
x[1] = -1.0468 0.326
h = 0.0001 0.004
y[1] (numeric) = 0.184804726724 0.0981333905499
y[1] (closed_form) = 0.184804961314 0.0981376336431
absolute error = 4.250e-06
relative error = 0.002031 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.007
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0467 0.33
h = 0.003 0.006
y[1] (numeric) = 0.184644610692 0.099355141976
y[1] (closed_form) = 0.18464450824 0.0993591956496
absolute error = 4.055e-06
relative error = 0.001934 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.009
Order of pole (given) = 0.5 0
NO 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=1855.4MB, alloc=44.3MB, time=23.03
x[1] = -1.0437 0.336
h = 0.0001 0.005
y[1] (numeric) = 0.185267908788 0.10132592239
y[1] (closed_form) = 0.185267905347 0.10133166885
absolute error = 5.746e-06
relative error = 0.002721 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.014
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=1901.0MB, alloc=44.3MB, time=23.60
x[1] = -1.0436 0.341
h = 0.0001 0.003
y[1] (numeric) = 0.185052743367 0.102856575623
y[1] (closed_form) = 0.185052861532 0.102861231304
absolute error = 4.657e-06
relative error = 0.0022 %
Correct digits = 5
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
x[1] = -1.0435 0.344
h = 0.001 0.001
y[1] (numeric) = 0.184933835286 0.10377682067
y[1] (closed_form) = 0.184934370949 0.103781375611
absolute error = 4.586e-06
relative error = 0.002163 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.016
Order of pole (given) = 0.5 0
NO 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=1946.6MB, alloc=44.3MB, time=24.16
x[1] = -1.0425 0.345
h = 0.001 0.003
y[1] (numeric) = 0.185188912576 0.104132063773
y[1] (closed_form) = 0.185189635304 0.10413649957
absolute error = 4.494e-06
relative error = 0.002115 %
Correct digits = 5
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] = -1.0415 0.348
h = 0.0001 0.004
y[1] (numeric) = 0.185344153412 0.105098194033
y[1] (closed_form) = 0.185344485584 0.105102856969
absolute error = 4.675e-06
relative error = 0.002194 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.02
Order of pole (given) = 0.5 0
NO 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=1992.1MB, alloc=44.3MB, time=24.72
x[1] = -1.0414 0.352
h = 0.003 0.006
y[1] (numeric) = 0.185172431927 0.106325729566
y[1] (closed_form) = 0.185172427174 0.106330208142
absolute error = 4.479e-06
relative error = 0.002097 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.021
Order of pole (given) = 0.5 0
NO 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=2037.5MB, alloc=44.3MB, time=25.28
x[1] = -1.0384 0.358
h = 0.0001 0.005
y[1] (numeric) = 0.185782285043 0.108313577676
y[1] (closed_form) = 0.185782397614 0.108319736585
absolute error = 6.160e-06
relative error = 0.002864 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.026
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0383 0.363
h = 0.0001 0.003
y[1] (numeric) = 0.185552680205 0.109851439567
y[1] (closed_form) = 0.185552901421 0.109856513667
absolute error = 5.079e-06
relative error = 0.002355 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.028
Order of pole (given) = 0.5 0
NO 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=2083.1MB, alloc=44.3MB, time=25.85
x[1] = -1.0382 0.366
h = 0.001 0.001
y[1] (numeric) = 0.185425176123 0.110776149598
y[1] (closed_form) = 0.185425810899 0.110781119001
absolute error = 5.010e-06
relative error = 0.002319 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.029
Order of pole (given) = 0.5 0
NO 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=2128.8MB, alloc=44.3MB, time=26.42
x[1] = -1.0372 0.367
h = 0.001 0.003
y[1] (numeric) = 0.185678738237 0.111135695601
y[1] (closed_form) = 0.185679557494 0.111140544592
absolute error = 4.918e-06
relative error = 0.002273 %
Correct digits = 5
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] = -1.0362 0.37
h = 0.0001 0.004
y[1] (numeric) = 0.185826649879 0.112108909011
y[1] (closed_form) = 0.18582708373 0.112113987931
absolute error = 5.097e-06
relative error = 0.002349 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.032
Order of pole (given) = 0.5 0
NO 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=2174.4MB, alloc=44.3MB, time=26.98
x[1] = -1.0361 0.374
h = 0.003 0.006
y[1] (numeric) = 0.185643465382 0.113342319227
y[1] (closed_form) = 0.185643562556 0.113347218752
absolute error = 4.900e-06
relative error = 0.002253 %
Correct digits = 5
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
x[1] = -1.0331 0.38
h = 0.0001 0.005
y[1] (numeric) = 0.186240153937 0.115347269296
y[1] (closed_form) = 0.186240386092 0.115353836449
absolute error = 6.571e-06
relative error = 0.003 %
Correct digits = 5
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
memory used=2220.0MB, alloc=44.3MB, time=27.54
x[1] = -1.033 0.385
h = 0.0001 0.003
y[1] (numeric) = 0.185996286661 0.116892450354
y[1] (closed_form) = 0.185996614888 0.116897938895
absolute error = 5.498e-06
relative error = 0.002503 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.041
Order of pole (given) = 0.5 0
NO 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=2265.6MB, alloc=44.3MB, time=28.11
x[1] = -1.0329 0.388
h = 0.001 0.001
y[1] (numeric) = 0.185860294049 0.117821689539
y[1] (closed_form) = 0.18586103187 0.117827069599
absolute error = 5.430e-06
relative error = 0.002468 %
Correct digits = 5
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] = -1.0319 0.389
h = 0.001 0.003
y[1] (numeric) = 0.18611239852 0.118185525795
y[1] (closed_form) = 0.186113318252 0.118190784263
absolute error = 5.338e-06
relative error = 0.002421 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.043
Order of pole (given) = 0.5 0
NO 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=2311.2MB, alloc=44.3MB, time=28.67
x[1] = -1.0309 0.392
h = 0.0001 0.004
y[1] (numeric) = 0.186253108415 0.119165854624
y[1] (closed_form) = 0.186253647871 0.119171345629
absolute error = 5.517e-06
relative error = 0.002495 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.045
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
memory used=2356.9MB, alloc=44.3MB, time=29.24
x[1] = -1.0308 0.396
h = 0.003 0.006
y[1] (numeric) = 0.18605860311 0.120405224769
y[1] (closed_form) = 0.186058806257 0.120410541246
absolute error = 5.320e-06
relative error = 0.002401 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.047
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0278 0.402
h = 0.0001 0.005
y[1] (numeric) = 0.186642403295 0.122427303204
y[1] (closed_form) = 0.186642758434 0.122434274389
absolute error = 6.980e-06
relative error = 0.003127 %
Correct digits = 5
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=2402.5MB, alloc=44.3MB, time=29.80
x[1] = -1.0277 0.407
h = 0.0001 0.003
y[1] (numeric) = 0.186384450153 0.123979907407
y[1] (closed_form) = 0.186384889178 0.12398580638
absolute error = 5.915e-06
relative error = 0.002642 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.054
Order of pole (given) = 0.5 0
NO 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=2448.1MB, alloc=44.3MB, time=30.37
x[1] = -1.0276 0.41
h = 0.001 0.001
y[1] (numeric) = 0.186240076145 0.124913736004
y[1] (closed_form) = 0.186240920777 0.124919522883
absolute error = 5.848e-06
relative error = 0.002608 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.055
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0266 0.411
h = 0.0001 0.004
y[1] (numeric) = 0.18649077913 0.125281848638
y[1] (closed_form) = 0.18649180312 0.12528751283
absolute error = 5.756e-06
relative error = 0.002562 %
Correct digits = 5
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
memory used=2493.6MB, alloc=44.3MB, time=30.93
x[1] = -1.0265 0.415
h = 0.003 0.006
y[1] (numeric) = 0.186287111467 0.126526135208
y[1] (closed_form) = 0.18628725853 0.126531774435
absolute error = 5.641e-06
relative error = 0.002505 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.058
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0235 0.421
h = 0.0001 0.005
y[1] (numeric) = 0.186859831236 0.128562823501
y[1] (closed_form) = 0.186860144582 0.128570106361
absolute error = 7.290e-06
relative error = 0.003214 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.063
Order of pole (given) = 0.5 0
NO 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=2539.2MB, alloc=44.3MB, time=31.50
x[1] = -1.0234 0.426
h = 0.0001 0.003
y[1] (numeric) = 0.18658980435 0.130121730796
y[1] (closed_form) = 0.18659019132 0.130127946959
absolute error = 6.228e-06
relative error = 0.002738 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.065
Order of pole (given) = 0.5 0
NO 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=2584.7MB, alloc=44.3MB, time=32.06
x[1] = -1.0233 0.429
h = 0.001 0.001
y[1] (numeric) = 0.186438245759 0.131059457064
y[1] (closed_form) = 0.186439034932 0.131065558107
absolute error = 6.152e-06
relative error = 0.002699 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.067
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] = -1.0223 0.43
h = 0.001 0.003
y[1] (numeric) = 0.186687735605 0.131431222874
y[1] (closed_form) = 0.186688701968 0.131437200325
absolute error = 6.055e-06
relative error = 0.002652 %
Correct digits = 5
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=2630.3MB, alloc=44.3MB, time=32.62
x[1] = -1.0213 0.433
h = 0.0001 0.004
y[1] (numeric) = 0.186815293164 0.132424782492
y[1] (closed_form) = 0.186815888685 0.132430996928
absolute error = 6.243e-06
relative error = 0.002726 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.07
Order of pole (given) = 0.5 0
NO 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=2675.9MB, alloc=44.3MB, time=33.19
x[1] = -1.0212 0.437
h = 0.003 0.006
y[1] (numeric) = 0.186600026075 0.133675321154
y[1] (closed_form) = 0.186600286218 0.133681369861
absolute error = 6.054e-06
relative error = 0.002638 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.072
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] = -1.0182 0.443
h = 0.0001 0.005
y[1] (numeric) = 0.187160359366 0.135729170666
y[1] (closed_form) = 0.187160801632 0.135736849767
absolute error = 7.692e-06
relative error = 0.003327 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.077
Order of pole (given) = 0.5 0
NO 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=2721.4MB, alloc=44.3MB, time=33.75
x[1] = -1.0181 0.448
h = 0.0001 0.003
y[1] (numeric) = 0.186876572149 0.137295680042
y[1] (closed_form) = 0.186877076561 0.137302299168
absolute error = 6.638e-06
relative error = 0.002863 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.079
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.018 0.451
h = 0.001 0.001
y[1] (numeric) = 0.186716829484 0.138238099177
y[1] (closed_form) = 0.186717732088 0.138244599872
absolute error = 6.563e-06
relative error = 0.002825 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.081
Order of pole (given) = 0.5 0
NO 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=2767.1MB, alloc=44.3MB, time=34.31
x[1] = -1.017 0.452
h = 0.001 0.003
y[1] (numeric) = 0.186965018841 0.138614113236
y[1] (closed_form) = 0.186966096122 0.138620489397
absolute error = 6.467e-06
relative error = 0.002778 %
Correct digits = 5
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
memory used=2812.6MB, alloc=44.3MB, time=34.88
x[1] = -1.016 0.455
h = 0.0001 0.004
y[1] (numeric) = 0.187085730257 0.139614861559
y[1] (closed_form) = 0.187086441727 0.139621476826
absolute error = 6.653e-06
relative error = 0.00285 %
Correct digits = 5
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] = -1.0159 0.459
h = 0.003 0.006
y[1] (numeric) = 0.186859545138 0.140871577843
y[1] (closed_form) = 0.186859921907 0.140878031962
absolute error = 6.465e-06
relative error = 0.002763 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.086
Order of pole (given) = 0.5 0
NO 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=2858.1MB, alloc=44.3MB, time=35.45
x[1] = -1.0129 0.465
h = 0.0001 0.005
y[1] (numeric) = 0.187407755121 0.142942594786
y[1] (closed_form) = 0.187408329243 0.142950665935
absolute error = 8.092e-06
relative error = 0.003433 %
Correct digits = 4
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=2903.7MB, alloc=44.3MB, time=36.01
x[1] = -1.0128 0.47
h = 0.0001 0.003
y[1] (numeric) = 0.187110381688 0.144516792763
y[1] (closed_form) = 0.187111006852 0.144523810801
absolute error = 7.046e-06
relative error = 0.00298 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.093
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0127 0.473
h = 0.001 0.001
y[1] (numeric) = 0.186942560357 0.145463954598
y[1] (closed_form) = 0.186943579701 0.14547085105
absolute error = 6.971e-06
relative error = 0.002943 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.095
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
memory used=2949.1MB, alloc=44.3MB, time=36.57
x[1] = -1.0117 0.474
h = 0.001 0.003
y[1] (numeric) = 0.187189501427 0.145844200021
y[1] (closed_form) = 0.187190692961 0.145850971073
absolute error = 6.875e-06
relative error = 0.002897 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.096
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -1.0107 0.477
h = 0.0001 0.004
y[1] (numeric) = 0.18730348776 0.146852155548
y[1] (closed_form) = 0.187304318467 0.14685916767
absolute error = 7.061e-06
relative error = 0.002967 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.098
Order of pole (given) = 0.5 0
NO 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=2994.8MB, alloc=44.3MB, time=37.13
x[1] = -1.0106 0.481
h = 0.003 0.006
y[1] (numeric) = 0.18706652405 0.148115115801
y[1] (closed_form) = 0.187067020827 0.148121971255
absolute error = 6.873e-06
relative error = 0.002881 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.1
Order of pole (given) = 0.5 0
NO 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=3040.4MB, alloc=44.3MB, time=37.70
x[1] = -1.0076 0.487
h = 0.0001 0.005
y[1] (numeric) = 0.187602869064 0.150203300137
y[1] (closed_form) = 0.187603577829 0.15021175916
absolute error = 8.489e-06
relative error = 0.003532 %
Correct digits = 4
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] = -1.0075 0.492
h = 0.0001 0.003
y[1] (numeric) = 0.187292082241 0.151785267581
y[1] (closed_form) = 0.187292831308 0.15179268048
absolute error = 7.451e-06
relative error = 0.003091 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.108
Order of pole (given) = 0.5 0
NO 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=3086.0MB, alloc=44.3MB, time=38.26
x[1] = -1.0074 0.495
h = 0.001 0.001
y[1] (numeric) = 0.187116286798 0.15273721858
y[1] (closed_form) = 0.187117426039 0.15274450689
absolute error = 7.377e-06
relative error = 0.003054 %
Correct digits = 5
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=3131.6MB, alloc=44.3MB, time=38.83
x[1] = -1.0064 0.496
h = 0.001 0.003
y[1] (numeric) = 0.187362030404 0.153121677605
y[1] (closed_form) = 0.187363339377 0.153128839722
absolute error = 7.281e-06
relative error = 0.003009 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.111
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] = -1.0054 0.499
h = 0.0001 0.004
y[1] (numeric) = 0.187469410844 0.154136855711
y[1] (closed_form) = 0.187470363923 0.154144260711
absolute error = 7.466e-06
relative error = 0.003076 %
Correct digits = 5
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
memory used=3177.0MB, alloc=44.3MB, time=39.39
x[1] = -1.0053 0.503
h = 0.003 0.006
y[1] (numeric) = 0.187221806852 0.155406121842
y[1] (closed_form) = 0.187222426857 0.15541337455
absolute error = 7.279e-06
relative error = 0.002992 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.115
Order of pole (given) = 0.5 0
NO 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=3222.6MB, alloc=44.3MB, time=39.95
x[1] = -1.0023 0.509
h = 0.0001 0.005
y[1] (numeric) = 0.18774654032 0.157511467665
y[1] (closed_form) = 0.187747386368 0.157520310412
absolute error = 8.883e-06
relative error = 0.003625 %
Correct digits = 4
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] = -1.0022 0.514
h = 0.0001 0.003
y[1] (numeric) = 0.187422511466 0.159101280021
y[1] (closed_form) = 0.187423387438 0.159109083736
absolute error = 7.853e-06
relative error = 0.003194 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.122
Order of pole (given) = 0.5 0
NO 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=3268.2MB, alloc=44.3MB, time=40.52
x[1] = -1.0021 0.517
h = 0.001 0.001
y[1] (numeric) = 0.187238845515 0.160058063424
y[1] (closed_form) = 0.187240107664 0.160065739691
absolute error = 7.779e-06
relative error = 0.003158 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.124
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] = -1.0011 0.518
h = 0.0001 0.004
y[1] (numeric) = 0.187483441113 0.160446717493
y[1] (closed_form) = 0.187484870564 0.160454266843
absolute error = 7.683e-06
relative error = 0.003114 %
Correct digits = 5
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
memory used=3313.7MB, alloc=44.3MB, time=41.08
x[1] = -1.001 0.522
h = 0.003 0.006
y[1] (numeric) = 0.187227227354 0.161721167318
y[1] (closed_form) = 0.187227809201 0.161728734064
absolute error = 7.589e-06
relative error = 0.003067 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 1.127
Order of pole (given) = 0.5 0
NO 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=3359.4MB, alloc=44.3MB, time=41.65
x[1] = -0.998 0.528
h = 0.0001 0.005
y[1] (numeric) = 0.187741960897 0.163841141948
y[1] (closed_form) = 0.187742780595 0.163850287206
absolute error = 9.182e-06
relative error = 0.003685 %
Correct digits = 4
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] = -0.9979 0.533
h = 0.0001 0.003
y[1] (numeric) = 0.187406575161 0.165437608398
y[1] (closed_form) = 0.187407416045 0.165445720682
absolute error = 8.156e-06
relative error = 0.003262 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.135
Order of pole (given) = 0.5 0
NO 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=3405.0MB, alloc=44.3MB, time=42.22
x[1] = -0.9978 0.536
h = 0.001 0.001
y[1] (numeric) = 0.187216158499 0.166398491542
y[1] (closed_form) = 0.187217382164 0.166406473984
absolute error = 8.076e-06
relative error = 0.003224 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.137
Order of pole (given) = 0.5 0
NO 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=3450.6MB, alloc=44.3MB, time=42.78
x[1] = -0.9968 0.537
h = 0.001 0.003
y[1] (numeric) = 0.187459754845 0.166790728256
y[1] (closed_form) = 0.187461143752 0.166798583183
absolute error = 7.977e-06
relative error = 0.003179 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.138
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9958 0.54
h = 0.0001 0.004
y[1] (numeric) = 0.187555067519 0.167819301391
y[1] (closed_form) = 0.18755610955 0.167827402257
absolute error = 8.168e-06
relative error = 0.003245 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.14
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
memory used=3496.3MB, alloc=44.3MB, time=43.34
x[1] = -0.9957 0.544
h = 0.003 0.006
y[1] (numeric) = 0.18728795149 0.169100328718
y[1] (closed_form) = 0.187288662197 0.169108285176
absolute error = 7.988e-06
relative error = 0.003166 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.142
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9927 0.55
h = 0.0001 0.005
y[1] (numeric) = 0.187791531996 0.171237442396
y[1] (closed_form) = 0.187792493574 0.171246963759
absolute error = 9.570e-06
relative error = 0.003765 %
Correct digits = 4
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=3541.9MB, alloc=44.3MB, time=43.91
x[1] = -0.9926 0.555
h = 0.0001 0.003
y[1] (numeric) = 0.187443217931 0.1728418825
y[1] (closed_form) = 0.187444190962 0.172850378137
absolute error = 8.551e-06
relative error = 0.003354 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.15
Order of pole (given) = 0.5 0
NO 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=3587.5MB, alloc=44.3MB, time=44.48
x[1] = -0.9925 0.558
h = 0.001 0.001
y[1] (numeric) = 0.187245120277 0.173807671602
y[1] (closed_form) = 0.187246472123 0.173816034796
absolute error = 8.472e-06
relative error = 0.003316 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.152
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] = -0.9915 0.559
h = 0.001 0.003
y[1] (numeric) = 0.187487657299 0.17420406752
y[1] (closed_form) = 0.187489172017 0.174212302596
absolute error = 8.373e-06
relative error = 0.003272 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.153
Order of pole (given) = 0.5 0
NO 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=3633.1MB, alloc=44.3MB, time=45.04
x[1] = -0.9905 0.562
h = 0.0001 0.004
y[1] (numeric) = 0.18757669419 0.175239892815
y[1] (closed_form) = 0.187577866803 0.175248375252
absolute error = 8.563e-06
relative error = 0.003336 %
Correct digits = 4
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
memory used=3678.9MB, alloc=44.3MB, time=45.61
x[1] = -0.9904 0.566
h = 0.003 0.006
y[1] (numeric) = 0.187299325622 0.176527381872
y[1] (closed_form) = 0.18730016798 0.176535723986
absolute error = 8.385e-06
relative error = 0.003258 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.157
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9874 0.572
h = 0.0001 0.005
y[1] (numeric) = 0.187791992256 0.178681613884
y[1] (closed_form) = 0.187793097971 0.178691507289
absolute error = 9.955e-06
relative error = 0.00384 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.163
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
memory used=3724.4MB, alloc=44.3MB, time=46.17
x[1] = -0.9873 0.577
h = 0.0001 0.003
y[1] (numeric) = 0.187430916307 0.180294088822
y[1] (closed_form) = 0.18743202408 0.18030296381
absolute error = 8.944e-06
relative error = 0.003439 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.166
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9872 0.58
h = 0.001 0.001
y[1] (numeric) = 0.18722523812 0.181264818645
y[1] (closed_form) = 0.187226720764 0.181273558722
absolute error = 8.865e-06
relative error = 0.003402 %
Correct digits = 4
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
memory used=3770.0MB, alloc=44.3MB, time=46.74
x[1] = -0.9862 0.581
h = 0.001 0.003
y[1] (numeric) = 0.187466761469 0.181665353326
y[1] (closed_form) = 0.187468404648 0.18167396474
absolute error = 8.767e-06
relative error = 0.003358 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.168
Order of pole (given) = 0.5 0
NO 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=3815.7MB, alloc=44.3MB, time=47.32
x[1] = -0.9852 0.584
h = 0.0001 0.004
y[1] (numeric) = 0.187549634138 0.182708435636
y[1] (closed_form) = 0.18755093992 0.182717295708
absolute error = 8.956e-06
relative error = 0.00342 %
Correct digits = 4
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] = -0.9851 0.588
h = 0.003 0.006
y[1] (numeric) = 0.187262145928 0.184002432909
y[1] (closed_form) = 0.187263122587 0.184011156644
absolute error = 8.778e-06
relative error = 0.003344 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.173
Order of pole (given) = 0.5 0
NO 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=3861.4MB, alloc=44.3MB, time=47.90
x[1] = -0.9821 0.594
h = 0.0001 0.005
y[1] (numeric) = 0.187744132821 0.186173758048
y[1] (closed_form) = 0.187745384809 0.186184019469
absolute error = 1.034e-05
relative error = 0.00391 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.179
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
memory used=3907.0MB, alloc=44.3MB, time=48.46
x[1] = -0.982 0.599
h = 0.0001 0.003
y[1] (numeric) = 0.187370459478 0.187794324451
y[1] (closed_form) = 0.187371704454 0.187803574811
absolute error = 9.334e-06
relative error = 0.003518 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.181
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9819 0.602
h = 0.001 0.001
y[1] (numeric) = 0.187157299982 0.188770027065
y[1] (closed_form) = 0.187158915913 0.188779140171
absolute error = 9.255e-06
relative error = 0.003482 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.183
Order of pole (given) = 0.5 0
NO 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=3952.5MB, alloc=44.3MB, time=49.03
x[1] = -0.9809 0.603
h = 0.001 0.003
y[1] (numeric) = 0.187397854016 0.18917467954
y[1] (closed_form) = 0.187399628178 0.189183663497
absolute error = 9.157e-06
relative error = 0.003439 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.184
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9799 0.606
h = 0.0001 0.004
y[1] (numeric) = 0.187474671973 0.190225021382
y[1] (closed_form) = 0.187476113381 0.190234255175
absolute error = 9.346e-06
relative error = 0.003499 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.187
Order of pole (given) = 0.5 0
NO 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=3998.1MB, alloc=44.3MB, time=49.59
x[1] = -0.9798 0.61
h = 0.003 0.006
y[1] (numeric) = 0.187177195392 0.191525569805
y[1] (closed_form) = 0.187178308865 0.191534671147
absolute error = 9.169e-06
relative error = 0.003424 %
Correct digits = 4
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=4043.7MB, alloc=44.3MB, time=50.16
x[1] = -0.9768 0.616
h = 0.0001 0.005
y[1] (numeric) = 0.187648731656 0.193713958685
y[1] (closed_form) = 0.187650131933 0.193724584138
absolute error = 1.072e-05
relative error = 0.003974 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.194
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9767 0.621
h = 0.0001 0.003
y[1] (numeric) = 0.187262623362 0.195342668853
y[1] (closed_form) = 0.187264007875 0.195352290635
absolute error = 9.721e-06
relative error = 0.003592 %
Correct digits = 4
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
memory used=4089.4MB, alloc=44.3MB, time=50.72
x[1] = -0.9766 0.624
h = 0.001 0.001
y[1] (numeric) = 0.187042080497 0.196323373758
y[1] (closed_form) = 0.18704383208 0.196332856064
absolute error = 9.643e-06
relative error = 0.003556 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.199
Order of pole (given) = 0.5 0
NO 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=4135.0MB, alloc=44.3MB, time=51.28
x[1] = -0.9756 0.625
h = 0.0001 0.004
y[1] (numeric) = 0.187281708307 0.196732122596
y[1] (closed_form) = 0.187283615852 0.196741475321
absolute error = 9.545e-06
relative error = 0.003514 %
Correct digits = 4
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] = -0.9755 0.629
h = 0.003 0.006
y[1] (numeric) = 0.186976149221 0.198038042809
y[1] (closed_form) = 0.186977239853 0.198047448492
absolute error = 9.469e-06
relative error = 0.003476 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.202
Order of pole (given) = 0.5 0
NO 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=4180.5MB, alloc=44.3MB, time=51.85
x[1] = -0.9725 0.635
h = 0.0001 0.005
y[1] (numeric) = 0.187438666874 0.200240972227
y[1] (closed_form) = 0.187440053964 0.200251890498
absolute error = 1.101e-05
relative error = 0.004013 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.208
Order of pole (given) = 0.5 0
NO 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=4226.3MB, alloc=44.3MB, time=52.42
x[1] = -0.9724 0.64
h = 0.0001 0.003
y[1] (numeric) = 0.187041885673 0.201876585469
y[1] (closed_form) = 0.187043249624 0.20188650635
absolute error = 1.001e-05
relative error = 0.003639 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.211
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9723 0.643
h = 0.001 0.001
y[1] (numeric) = 0.186815004848 0.202861531551
y[1] (closed_form) = 0.186816732575 0.202871311091
absolute error = 9.931e-06
relative error = 0.003601 %
Correct digits = 4
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
memory used=4271.9MB, alloc=44.3MB, time=52.98
x[1] = -0.9713 0.644
h = 0.001 0.003
y[1] (numeric) = 0.187053820513 0.203273778569
y[1] (closed_form) = 0.187055702282 0.20328342817
absolute error = 9.831e-06
relative error = 0.003559 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.214
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9703 0.647
h = 0.0001 0.004
y[1] (numeric) = 0.187119570029 0.204337558859
y[1] (closed_form) = 0.187121127496 0.204347460248
absolute error = 1.002e-05
relative error = 0.003617 %
Correct digits = 4
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
memory used=4317.5MB, alloc=44.3MB, time=53.55
x[1] = -0.9702 0.651
h = 0.003 0.006
y[1] (numeric) = 0.186803771876 0.205650284873
y[1] (closed_form) = 0.186805003707 0.205660060799
absolute error = 9.853e-06
relative error = 0.003546 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.218
Order of pole (given) = 0.5 0
NO 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=4363.2MB, alloc=44.3MB, time=54.12
x[1] = -0.9672 0.657
h = 0.0001 0.005
y[1] (numeric) = 0.187256252432 0.207870215856
y[1] (closed_form) = 0.187257791315 0.207881490878
absolute error = 1.138e-05
relative error = 0.004067 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.224
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
x[1] = -0.9671 0.662
h = 0.0001 0.003
y[1] (numeric) = 0.186847332351 0.209514061229
y[1] (closed_form) = 0.18684883991 0.20952434629
absolute error = 1.039e-05
relative error = 0.003703 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.227
Order of pole (given) = 0.5 0
NO 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=4408.8MB, alloc=44.3MB, time=54.68
x[1] = -0.967 0.665
h = 0.001 0.001
y[1] (numeric) = 0.186613246565 0.210504059228
y[1] (closed_form) = 0.186615114075 0.21051420094
absolute error = 1.031e-05
relative error = 0.003666 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.229
Order of pole (given) = 0.5 0
NO 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=4454.5MB, alloc=44.3MB, time=55.24
x[1] = -0.966 0.666
h = 0.001 0.003
y[1] (numeric) = 0.186851213177 0.210920362163
y[1] (closed_form) = 0.186853232527 0.210930373596
absolute error = 1.021e-05
relative error = 0.003624 %
Correct digits = 4
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] = -0.965 0.669
h = 0.0001 0.004
y[1] (numeric) = 0.186911209939 0.211991398772
y[1] (closed_form) = 0.186912909437 0.212001662865
absolute error = 1.040e-05
relative error = 0.003681 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.232
Order of pole (given) = 0.5 0
NO 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=4500.0MB, alloc=44.3MB, time=55.81
x[1] = -0.9649 0.673
h = 0.003 0.006
y[1] (numeric) = 0.186585789047 0.213310782127
y[1] (closed_form) = 0.186587164233 0.213320924368
absolute error = 1.024e-05
relative error = 0.003611 %
Correct digits = 4
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] = -0.9619 0.679
h = 0.0001 0.005
y[1] (numeric) = 0.187028447502 0.215547674905
y[1] (closed_form) = 0.187030139887 0.215559302818
absolute error = 1.175e-05
relative error = 0.004117 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.24
Order of pole (given) = 0.5 0
NO 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=4545.6MB, alloc=44.3MB, time=56.37
x[1] = -0.9618 0.684
h = 0.0001 0.003
y[1] (numeric) = 0.186607544814 0.217199793417
y[1] (closed_form) = 0.186609197979 0.217210438804
absolute error = 1.077e-05
relative error = 0.003762 %
Correct digits = 4
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=4591.2MB, alloc=44.3MB, time=56.94
x[1] = -0.9617 0.687
h = 0.001 0.001
y[1] (numeric) = 0.186366348161 0.218194866161
y[1] (closed_form) = 0.186368357492 0.218205366296
absolute error = 1.069e-05
relative error = 0.003725 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.245
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9607 0.688
h = 0.001 0.003
y[1] (numeric) = 0.186603505345 0.218615202536
y[1] (closed_form) = 0.186605664349 0.218625572099
absolute error = 1.059e-05
relative error = 0.003685 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.246
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
memory used=4636.7MB, alloc=44.3MB, time=57.50
x[1] = -0.9597 0.691
h = 0.0001 0.004
y[1] (numeric) = 0.186657850937 0.219693490239
y[1] (closed_form) = 0.18665969447 0.219704113236
absolute error = 1.078e-05
relative error = 0.00374 %
Correct digits = 4
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
memory used=4682.5MB, alloc=44.3MB, time=58.07
x[1] = -0.9596 0.695
h = 0.003 0.006
y[1] (numeric) = 0.18632293182 0.221019561679
y[1] (closed_form) = 0.186324452404 0.221030066344
absolute error = 1.061e-05
relative error = 0.003672 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.251
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9566 0.701
h = 0.0001 0.005
y[1] (numeric) = 0.186755978325 0.22327337339
y[1] (closed_form) = 0.186757825821 0.223285350382
absolute error = 1.212e-05
relative error = 0.004163 %
Correct digits = 4
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
memory used=4727.9MB, alloc=44.3MB, time=58.63
x[1] = -0.9565 0.706
h = 0.0001 0.003
y[1] (numeric) = 0.186323247037 0.224933802487
y[1] (closed_form) = 0.186325047699 0.224944804382
absolute error = 1.115e-05
relative error = 0.003817 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.26
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9564 0.709
h = 0.001 0.001
y[1] (numeric) = 0.186075032209 0.225933970702
y[1] (closed_form) = 0.186077185291 0.225944825545
absolute error = 1.107e-05
relative error = 0.003781 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.262
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
memory used=4773.6MB, alloc=44.3MB, time=59.20
x[1] = -0.9554 0.71
h = 0.001 0.003
y[1] (numeric) = 0.186311418432 0.226358317774
y[1] (closed_form) = 0.186313719056 0.226369041796
absolute error = 1.097e-05
relative error = 0.003741 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.263
Order of pole (given) = 0.5 0
NO 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=4819.3MB, alloc=44.3MB, time=59.76
x[1] = -0.9544 0.713
h = 0.0001 0.004
y[1] (numeric) = 0.186360212401 0.227443849652
y[1] (closed_form) = 0.186362201864 0.227454827793
absolute error = 1.116e-05
relative error = 0.003794 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.266
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] = -0.9543 0.717
h = 0.003 0.006
y[1] (numeric) = 0.186015917726 0.228776637149
y[1] (closed_form) = 0.186017585638 0.228787500384
absolute error = 1.099e-05
relative error = 0.003727 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.268
Order of pole (given) = 0.5 0
NO 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=4864.9MB, alloc=44.3MB, time=60.33
x[1] = -0.9513 0.723
h = 0.0001 0.005
y[1] (numeric) = 0.186439557652 0.231047322087
y[1] (closed_form) = 0.186441561776 0.231059644392
absolute error = 1.248e-05
relative error = 0.004205 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.274
Order of pole (given) = 0.5 0
NO 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=4910.6MB, alloc=44.3MB, time=60.89
x[1] = -0.9512 0.728
h = 0.0001 0.003
y[1] (numeric) = 0.185995149478 0.232716095833
y[1] (closed_form) = 0.185997099426 0.232727450461
absolute error = 1.152e-05
relative error = 0.003867 %
Correct digits = 4
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] = -0.9511 0.731
h = 0.001 0.001
y[1] (numeric) = 0.18574000775 0.233721378253
y[1] (closed_form) = 0.185742306411 0.233732584127
absolute error = 1.144e-05
relative error = 0.003832 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.278
Order of pole (given) = 0.5 0
NO 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=4956.3MB, alloc=44.3MB, time=61.46
x[1] = -0.9501 0.732
h = 0.0001 0.004
y[1] (numeric) = 0.185975660352 0.234149713054
y[1] (closed_form) = 0.185978104463 0.234160787896
absolute error = 1.134e-05
relative error = 0.003793 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.28
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.95 0.736
h = 0.003 0.006
y[1] (numeric) = 0.185623777597 0.235487997553
y[1] (closed_form) = 0.185625435657 0.235499155
absolute error = 1.128e-05
relative error = 0.003762 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.282
Order of pole (given) = 0.5 0
NO 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=5001.9MB, alloc=44.3MB, time=62.02
x[1] = -0.947 0.742
h = 0.0001 0.005
y[1] (numeric) = 0.186039281312 0.237773058989
y[1] (closed_form) = 0.186041283424 0.237785664276
absolute error = 1.276e-05
relative error = 0.004227 %
Correct digits = 4
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
memory used=5047.5MB, alloc=44.3MB, time=62.59
x[1] = -0.9469 0.747
h = 0.0001 0.003
y[1] (numeric) = 0.18558484189 0.239448903681
y[1] (closed_form) = 0.18558678363 0.239460547578
absolute error = 1.180e-05
relative error = 0.003896 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.291
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9468 0.75
h = 0.001 0.001
y[1] (numeric) = 0.185323748528 0.240458520737
y[1] (closed_form) = 0.185326035844 0.240470014447
absolute error = 1.172e-05
relative error = 0.00386 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.293
Order of pole (given) = 0.5 0
NO 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=5093.1MB, alloc=44.3MB, time=63.16
x[1] = -0.9458 0.751
h = 0.001 0.003
y[1] (numeric) = 0.185558751591 0.240890261352
y[1] (closed_form) = 0.185561182585 0.240901623857
absolute error = 1.162e-05
relative error = 0.003821 %
Correct digits = 4
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
memory used=5138.8MB, alloc=44.3MB, time=63.72
x[1] = -0.9448 0.754
h = 0.0001 0.004
y[1] (numeric) = 0.185597387295 0.241989185795
y[1] (closed_form) = 0.185599514955 0.242000803516
absolute error = 1.181e-05
relative error = 0.003873 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.297
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9447 0.758
h = 0.0001 0.004
y[1] (numeric) = 0.185235886314 0.243334427525
y[1] (closed_form) = 0.185237695065 0.243345936502
absolute error = 1.165e-05
relative error = 0.003809 %
Correct digits = 4
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
memory used=5184.3MB, alloc=44.3MB, time=64.29
x[1] = -0.9446 0.762
h = 0.003 0.006
y[1] (numeric) = 0.184872244633 0.244680395649
y[1] (closed_form) = 0.184874053444 0.244691904731
absolute error = 1.165e-05
relative error = 0.003799 %
Correct digits = 4
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=5230.0MB, alloc=44.3MB, time=64.86
x[1] = -0.9416 0.768
h = 0.0001 0.005
y[1] (numeric) = 0.185276547944 0.246984806651
y[1] (closed_form) = 0.1852787113 0.246997748558
absolute error = 1.312e-05
relative error = 0.00425 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.308
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9415 0.773
h = 0.0001 0.003
y[1] (numeric) = 0.184808438747 0.248670088406
y[1] (closed_form) = 0.184810533437 0.248682077328
absolute error = 1.217e-05
relative error = 0.003928 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.311
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
memory used=5275.6MB, alloc=44.3MB, time=65.42
x[1] = -0.9414 0.776
h = 0.001 0.001
y[1] (numeric) = 0.184539233075 0.249685492872
y[1] (closed_form) = 0.184541669146 0.249697329686
absolute error = 1.208e-05
relative error = 0.003892 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.313
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9404 0.777
h = 0.001 0.003
y[1] (numeric) = 0.184773311811 0.250121834193
y[1] (closed_form) = 0.184775889192 0.250133539568
absolute error = 1.199e-05
relative error = 0.003854 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.314
Order of pole (given) = 0.5 0
NO 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=5321.2MB, alloc=44.3MB, time=65.99
x[1] = -0.9394 0.78
h = 0.0001 0.004
y[1] (numeric) = 0.184805499134 0.251229028754
y[1] (closed_form) = 0.184807777978 0.251240990018
absolute error = 1.218e-05
relative error = 0.003904 %
Correct digits = 4
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
memory used=5367.0MB, alloc=44.3MB, time=66.56
x[1] = -0.9393 0.784
h = 0.003 0.006
y[1] (numeric) = 0.184433160458 0.252581896194
y[1] (closed_form) = 0.184435122013 0.25259375249
absolute error = 1.202e-05
relative error = 0.003842 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.319
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9363 0.79
h = 0.0001 0.005
y[1] (numeric) = 0.184828654434 0.254903035921
y[1] (closed_form) = 0.184830978665 0.254916312084
absolute error = 1.348e-05
relative error = 0.00428 %
Correct digits = 4
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
memory used=5412.5MB, alloc=44.3MB, time=67.12
x[1] = -0.9362 0.795
h = 0.0001 0.003
y[1] (numeric) = 0.184349313236 0.256596753797
y[1] (closed_form) = 0.18435156223 0.256609084327
absolute error = 1.253e-05
relative error = 0.003967 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.328
Order of pole (given) = 0.5 0
NO 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=5458.3MB, alloc=44.3MB, time=67.68
x[1] = -0.9361 0.798
h = 0.001 0.001
y[1] (numeric) = 0.184073448194 0.2576173224
y[1] (closed_form) = 0.184076034992 0.257629499395
absolute error = 1.245e-05
relative error = 0.003932 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.33
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9351 0.799
h = 0.001 0.003
y[1] (numeric) = 0.18430690116 0.258057582428
y[1] (closed_form) = 0.184309627282 0.258069627886
absolute error = 1.235e-05
relative error = 0.003894 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.331
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
memory used=5504.0MB, alloc=44.3MB, time=68.25
x[1] = -0.9341 0.802
h = 0.0001 0.004
y[1] (numeric) = 0.18433391876 0.259171982785
y[1] (closed_form) = 0.184336350375 0.259184284494
absolute error = 1.254e-05
relative error = 0.003943 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.334
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] = -0.934 0.806
h = 0.003 0.006
y[1] (numeric) = 0.18395267945 0.260531659396
y[1] (closed_form) = 0.183954795282 0.26054385922
absolute error = 1.238e-05
relative error = 0.003882 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.336
Order of pole (given) = 0.5 0
NO 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=5549.6MB, alloc=44.3MB, time=68.82
x[1] = -0.931 0.812
h = 0.0001 0.005
y[1] (numeric) = 0.184339551101 0.262869472648
y[1] (closed_form) = 0.184342037386 0.262883079501
absolute error = 1.383e-05
relative error = 0.004308 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.342
Order of pole (given) = 0.5 0
NO 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=5595.4MB, alloc=44.3MB, time=69.38
x[1] = -0.9309 0.817
h = 0.0001 0.003
y[1] (numeric) = 0.183849120354 0.264571648676
y[1] (closed_form) = 0.183851525067 0.264584317211
absolute error = 1.289e-05
relative error = 0.004002 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.346
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9308 0.82
h = 0.001 0.001
y[1] (numeric) = 0.183566681519 0.265597393072
y[1] (closed_form) = 0.183569420504 0.265609906724
absolute error = 1.281e-05
relative error = 0.003967 %
Correct digits = 4
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
memory used=5641.1MB, alloc=44.3MB, time=69.95
x[1] = -0.9298 0.821
h = 0.001 0.003
y[1] (numeric) = 0.183799541823 0.26604154825
y[1] (closed_form) = 0.183802418183 0.2660539303
absolute error = 1.271e-05
relative error = 0.003931 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.349
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
memory used=5686.7MB, alloc=44.3MB, time=70.52
x[1] = -0.9288 0.824
h = 0.0001 0.004
y[1] (numeric) = 0.183821479379 0.2671631405
y[1] (closed_form) = 0.18382406519 0.267175779095
absolute error = 1.290e-05
relative error = 0.003978 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.351
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9287 0.828
h = 0.003 0.006
y[1] (numeric) = 0.18343145274 0.268529642269
y[1] (closed_form) = 0.183433724293 0.268542181982
absolute error = 1.274e-05
relative error = 0.003919 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.354
Order of pole (given) = 0.5 0
NO 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=5732.4MB, alloc=44.3MB, time=71.08
x[1] = -0.9257 0.834
h = 0.0001 0.005
y[1] (numeric) = 0.183809884714 0.270884072036
y[1] (closed_form) = 0.18381253416 0.270898006063
absolute error = 1.418e-05
relative error = 0.004333 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.36
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] = -0.9256 0.839
h = 0.0001 0.003
y[1] (numeric) = 0.183308504535 0.272594725679
y[1] (closed_form) = 0.183311066301 0.272607728661
absolute error = 1.325e-05
relative error = 0.004034 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.363
Order of pole (given) = 0.5 0
NO 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=5778.1MB, alloc=44.3MB, time=71.65
x[1] = -0.9255 0.842
h = 0.001 0.001
y[1] (numeric) = 0.183019576055 0.273625656015
y[1] (closed_form) = 0.183022468606 0.273638502845
absolute error = 1.317e-05
relative error = 0.004 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.365
Order of pole (given) = 0.5 0
NO 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=5823.9MB, alloc=44.3MB, time=72.22
x[1] = -0.9245 0.843
h = 0.001 0.003
y[1] (numeric) = 0.183251875832 0.274073682733
y[1] (closed_form) = 0.183254903845 0.274086397925
absolute error = 1.307e-05
relative error = 0.003964 %
Correct digits = 4
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] = -0.9235 0.846
h = 0.0001 0.004
y[1] (numeric) = 0.183268821133 0.275202451888
y[1] (closed_form) = 0.183271562486 0.275215423857
absolute error = 1.326e-05
relative error = 0.00401 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.369
Order of pole (given) = 0.5 0
NO 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=5869.5MB, alloc=44.3MB, time=72.79
x[1] = -0.9234 0.85
h = 0.003 0.006
y[1] (numeric) = 0.182870118591 0.276575792813
y[1] (closed_form) = 0.182872547227 0.276588668822
absolute error = 1.310e-05
relative error = 0.003952 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.372
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
memory used=5915.1MB, alloc=44.3MB, time=73.35
x[1] = -0.9204 0.856
h = 0.0001 0.005
y[1] (numeric) = 0.183240289273 0.278946780436
y[1] (closed_form) = 0.183243102914 0.278961038173
absolute error = 1.453e-05
relative error = 0.004354 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.378
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9203 0.861
h = 0.0001 0.003
y[1] (numeric) = 0.182728097454 0.280665928733
y[1] (closed_form) = 0.182730817528 0.280679262651
absolute error = 1.361e-05
relative error = 0.004063 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.381
Order of pole (given) = 0.5 0
NO 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=5960.8MB, alloc=44.3MB, time=73.92
x[1] = -0.9202 0.864
h = 0.001 0.001
y[1] (numeric) = 0.182432762054 0.281702053735
y[1] (closed_form) = 0.182435809473 0.281715230306
absolute error = 1.352e-05
relative error = 0.00403 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.383
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] = -0.9192 0.865
h = 0.0001 0.004
y[1] (numeric) = 0.182664532496 0.282153928351
y[1] (closed_form) = 0.182667713498 0.282166973277
absolute error = 1.343e-05
relative error = 0.003995 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.384
Order of pole (given) = 0.5 0
NO 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=6006.4MB, alloc=44.3MB, time=74.48
x[1] = -0.9191 0.869
h = 0.003 0.006
y[1] (numeric) = 0.182258805536 0.283532858159
y[1] (closed_form) = 0.182261237752 0.283546015826
absolute error = 1.338e-05
relative error = 0.00397 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.387
Order of pole (given) = 0.5 0
NO 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=6052.1MB, alloc=44.3MB, time=75.05
x[1] = -0.9161 0.875
h = 0.0001 0.005
y[1] (numeric) = 0.182621808575 0.285917954526
y[1] (closed_form) = 0.182624631818 0.285932483272
absolute error = 1.480e-05
relative error = 0.004362 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.393
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.916 0.88
h = 0.0001 0.003
y[1] (numeric) = 0.182100317614 0.287644300029
y[1] (closed_form) = 0.182103042306 0.287657911069
absolute error = 1.388e-05
relative error = 0.004077 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.396
Order of pole (given) = 0.5 0
NO 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=6097.8MB, alloc=44.3MB, time=75.62
x[1] = -0.9159 0.883
h = 0.001 0.001
y[1] (numeric) = 0.181799470522 0.288684827384
y[1] (closed_form) = 0.181802519649 0.288698280064
absolute error = 1.379e-05
relative error = 0.004043 %
Correct digits = 4
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=6143.5MB, alloc=44.3MB, time=76.18
x[1] = -0.9149 0.884
h = 0.001 0.003
y[1] (numeric) = 0.182030764155 0.28913998939
y[1] (closed_form) = 0.182033945275 0.289153310418
absolute error = 1.370e-05
relative error = 0.004008 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.4
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9139 0.887
h = 0.0001 0.004
y[1] (numeric) = 0.182038562339 0.290282012737
y[1] (closed_form) = 0.182041463853 0.290295590857
absolute error = 1.388e-05
relative error = 0.004052 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.402
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
memory used=6189.1MB, alloc=44.3MB, time=76.75
x[1] = -0.9138 0.891
h = 0.003 0.006
y[1] (numeric) = 0.18162392436 0.291668010317
y[1] (closed_form) = 0.181626516024 0.291681497736
absolute error = 1.373e-05
relative error = 0.003997 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.405
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] = -0.9108 0.897
h = 0.0001 0.005
y[1] (numeric) = 0.181978987757 0.29406955355
y[1] (closed_form) = 0.181981976991 0.294084399707
absolute error = 1.514e-05
relative error = 0.004379 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.411
Order of pole (given) = 0.5 0
NO 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=6234.7MB, alloc=44.3MB, time=77.31
x[1] = -0.9107 0.902
h = 0.0001 0.003
y[1] (numeric) = 0.181446935288 0.295804420981
y[1] (closed_form) = 0.18144982047 0.295818356563
absolute error = 1.423e-05
relative error = 0.004101 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.414
Order of pole (given) = 0.5 0
NO 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=6280.5MB, alloc=44.3MB, time=77.88
x[1] = -0.9106 0.905
h = 0.001 0.001
y[1] (numeric) = 0.181139831401 0.296850156672
y[1] (closed_form) = 0.181143037664 0.296863932828
absolute error = 1.414e-05
relative error = 0.004067 %
Correct digits = 4
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
x[1] = -0.9096 0.906
h = 0.001 0.003
y[1] (numeric) = 0.181370651605 0.297309122932
y[1] (closed_form) = 0.181373988048 0.297322767478
absolute error = 1.405e-05
relative error = 0.004033 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.418
Order of pole (given) = 0.5 0
NO 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=6326.1MB, alloc=44.3MB, time=78.44
x[1] = -0.9086 0.909
h = 0.0001 0.004
y[1] (numeric) = 0.181373698776 0.298458275999
y[1] (closed_form) = 0.181376759306 0.298472177703
absolute error = 1.423e-05
relative error = 0.004076 %
Correct digits = 4
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
memory used=6371.8MB, alloc=44.3MB, time=79.01
x[1] = -0.9085 0.913
h = 0.003 0.006
y[1] (numeric) = 0.180950693288 0.299851143993
y[1] (closed_form) = 0.180953445543 0.299864957707
absolute error = 1.409e-05
relative error = 0.004022 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.423
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9055 0.919
h = 0.0001 0.005
y[1] (numeric) = 0.181297983778 0.302269071509
y[1] (closed_form) = 0.181301139859 0.302284231756
absolute error = 1.549e-05
relative error = 0.004393 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.429
Order of pole (given) = 0.5 0
NO 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=6417.4MB, alloc=44.3MB, time=79.58
x[1] = -0.9054 0.924
h = 0.0001 0.003
y[1] (numeric) = 0.180755501069 0.304012471653
y[1] (closed_form) = 0.180758547793 0.304026728401
absolute error = 1.458e-05
relative error = 0.004122 %
Correct digits = 4
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] = -0.9053 0.927
h = 0.001 0.001
y[1] (numeric) = 0.18044221913 0.305063420747
y[1] (closed_form) = 0.18044558363 0.305077517068
absolute error = 1.449e-05
relative error = 0.004089 %
Correct digits = 4
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
memory used=6463.1MB, alloc=44.3MB, time=80.14
x[1] = -0.9043 0.928
h = 0.001 0.003
y[1] (numeric) = 0.180672594557 0.305526167652
y[1] (closed_form) = 0.180676087453 0.305540132427
absolute error = 1.439e-05
relative error = 0.004055 %
Correct digits = 4
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=6508.8MB, alloc=44.3MB, time=80.70
x[1] = -0.9033 0.931
h = 0.0001 0.004
y[1] (numeric) = 0.180670971551 0.30668243196
y[1] (closed_form) = 0.180674192165 0.30669665391
absolute error = 1.458e-05
relative error = 0.004097 %
Correct digits = 4
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] = -0.9032 0.935
h = 0.003 0.006
y[1] (numeric) = 0.180239702871 0.30808217764
y[1] (closed_form) = 0.18024261679 0.30809631424
absolute error = 1.443e-05
relative error = 0.004044 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.441
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
memory used=6554.4MB, alloc=44.3MB, time=81.27
x[1] = -0.9002 0.941
h = 0.0001 0.005
y[1] (numeric) = 0.1805793833 0.310516425762
y[1] (closed_form) = 0.180582707026 0.31053189683
absolute error = 1.582e-05
relative error = 0.004405 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.447
Order of pole (given) = 0.5 0
NO 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=6600.0MB, alloc=44.3MB, time=81.83
x[1] = -0.9001 0.946
h = 0.0001 0.003
y[1] (numeric) = 0.180026599373 0.312268367457
y[1] (closed_form) = 0.180029808627 0.312282942044
absolute error = 1.492e-05
relative error = 0.00414 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.451
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.9 0.949
h = 0.001 0.001
y[1] (numeric) = 0.17970721676 0.313324533887
y[1] (closed_form) = 0.179710740529 0.313338947107
absolute error = 1.484e-05
relative error = 0.004108 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.453
Order of pole (given) = 0.5 0
NO 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=6645.7MB, alloc=44.3MB, time=82.41
x[1] = -0.899 0.95
h = 0.001 0.003
y[1] (numeric) = 0.179937175224 0.313791037875
y[1] (closed_form) = 0.179940825643 0.313805319636
absolute error = 1.474e-05
relative error = 0.004075 %
Correct digits = 4
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] = -0.898 0.953
h = 0.0001 0.004
y[1] (numeric) = 0.179930961166 0.314954394217
y[1] (closed_form) = 0.179934342864 0.31496893312
absolute error = 1.493e-05
relative error = 0.004115 %
Correct digits = 4
memory used=6691.4MB, alloc=44.3MB, time=82.98
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
x[1] = -0.8979 0.957
h = 0.003 0.006
y[1] (numeric) = 0.179491531812 0.316361023349
y[1] (closed_form) = 0.179494608403 0.316375479475
absolute error = 1.478e-05
relative error = 0.004063 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.46
Order of pole (given) = 0.5 0
NO 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=6737.1MB, alloc=52.3MB, time=83.56
x[1] = -0.8949 0.963
h = 0.0001 0.005
y[1] (numeric) = 0.179823761234 0.318811527423
y[1] (closed_form) = 0.179827253348 0.318827306093
absolute error = 1.616e-05
relative error = 0.004415 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.466
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] = -0.8948 0.968
h = 0.0001 0.003
y[1] (numeric) = 0.179260802894 0.320572017673
y[1] (closed_form) = 0.179264175602 0.320586906819
absolute error = 1.527e-05
relative error = 0.004156 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.469
Order of pole (given) = 0.5 0
NO 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=6782.8MB, alloc=52.3MB, time=84.12
x[1] = -0.8947 0.971
h = 0.001 0.001
y[1] (numeric) = 0.178935395635 0.321633404302
y[1] (closed_form) = 0.178939079646 0.321648131197
absolute error = 1.518e-05
relative error = 0.004124 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.471
Order of pole (given) = 0.5 0
NO 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=6828.5MB, alloc=52.3MB, time=84.67
x[1] = -0.8937 0.972
h = 0.0001 0.004
y[1] (numeric) = 0.179164964146 0.32210364188
y[1] (closed_form) = 0.179168773091 0.322118237425
absolute error = 1.508e-05
relative error = 0.004092 %
Correct digits = 4
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] = -0.8936 0.976
h = 0.003 0.006
y[1] (numeric) = 0.178718925129 0.323515891118
y[1] (closed_form) = 0.178722014208 0.323530618958
absolute error = 1.505e-05
relative error = 0.004071 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.475
Order of pole (given) = 0.5 0
NO 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=6874.0MB, alloc=52.3MB, time=85.23
x[1] = -0.8906 0.982
h = 0.0001 0.005
y[1] (numeric) = 0.17904467294 0.325980249093
y[1] (closed_form) = 0.1790481824 0.32599628939
absolute error = 1.642e-05
relative error = 0.004415 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.482
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
memory used=6919.7MB, alloc=52.3MB, time=85.79
x[1] = -0.8905 0.987
h = 0.0001 0.003
y[1] (numeric) = 0.178472954762 0.327747982755
y[1] (closed_form) = 0.17847634063 0.327763139409
absolute error = 1.553e-05
relative error = 0.004161 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.485
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] = -0.8904 0.99
h = 0.001 0.001
y[1] (numeric) = 0.178142359343 0.328813793717
y[1] (closed_form) = 0.178146053796 0.32882878737
absolute error = 1.544e-05
relative error = 0.004129 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.487
Order of pole (given) = 0.5 0
NO 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=6965.3MB, alloc=52.3MB, time=86.34
x[1] = -0.8894 0.991
h = 0.001 0.003
y[1] (numeric) = 0.178371569133 0.329287222074
y[1] (closed_form) = 0.178375387066 0.329302084465
absolute error = 1.534e-05
relative error = 0.004097 %
Correct digits = 4
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] = -0.8884 0.994
h = 0.0001 0.004
y[1] (numeric) = 0.17835693316 0.330463669102
y[1] (closed_form) = 0.178360488832 0.330478788499
absolute error = 1.553e-05
relative error = 0.004136 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.491
Order of pole (given) = 0.5 0
NO 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=7011.0MB, alloc=52.3MB, time=86.90
x[1] = -0.8883 0.998
h = 0.003 0.006
y[1] (numeric) = 0.177902503396 0.331883022871
y[1] (closed_form) = 0.177905756896 0.331898064122
absolute error = 1.539e-05
relative error = 0.004087 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.494
Order of pole (given) = 0.5 0
NO 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=7056.7MB, alloc=52.3MB, time=87.46
x[1] = -0.8853 1.004
h = 0.0001 0.005
y[1] (numeric) = 0.178221087199 0.334363516066
y[1] (closed_form) = 0.178224766333 0.334379858113
absolute error = 1.675e-05
relative error = 0.004421 %
Correct digits = 4
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] = -0.8852 1.009
h = 0.0001 0.003
y[1] (numeric) = 0.177639424726 0.336139808231
y[1] (closed_form) = 0.177642975655 0.336155273475
absolute error = 1.587e-05
relative error = 0.004173 %
Correct digits = 4
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
memory used=7102.3MB, alloc=52.3MB, time=88.02
x[1] = -0.8851 1.012
h = 0.001 0.001
y[1] (numeric) = 0.177302942601 0.337210842944
y[1] (closed_form) = 0.177306798988 0.337226144407
absolute error = 1.578e-05
relative error = 0.004142 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.506
Order of pole (given) = 0.5 0
NO 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=7148.1MB, alloc=52.3MB, time=88.58
x[1] = -0.8841 1.013
h = 0.001 0.003
y[1] (numeric) = 0.177531810915 0.337687961707
y[1] (closed_form) = 0.177535789126 0.337703132051
absolute error = 1.568e-05
relative error = 0.004111 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.507
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] = -0.8831 1.016
h = 0.0001 0.004
y[1] (numeric) = 0.177512801365 0.338871443163
y[1] (closed_form) = 0.177516520697 0.33888687036
absolute error = 1.587e-05
relative error = 0.004148 %
Correct digits = 4
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
memory used=7193.6MB, alloc=52.3MB, time=89.13
x[1] = -0.883 1.02
h = 0.003 0.006
y[1] (numeric) = 0.177050494475 0.340297690471
y[1] (closed_form) = 0.177053913229 0.340313041909
absolute error = 1.573e-05
relative error = 0.0041 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.513
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.88 1.026
h = 0.0001 0.005
y[1] (numeric) = 0.177362063021 0.342794251992
y[1] (closed_form) = 0.177365912429 0.342810892707
absolute error = 1.708e-05
relative error = 0.004425 %
Correct digits = 4
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
memory used=7239.3MB, alloc=52.3MB, time=89.69
x[1] = -0.8799 1.031
h = 0.0001 0.003
y[1] (numeric) = 0.1767705769 0.344579104942
y[1] (closed_form) = 0.176774293656 0.34459487563
absolute error = 1.620e-05
relative error = 0.004184 %
Correct digits = 4
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
memory used=7285.0MB, alloc=52.3MB, time=90.25
x[1] = -0.8798 1.034
h = 0.001 0.001
y[1] (numeric) = 0.176428280359 0.345655363519
y[1] (closed_form) = 0.176432299492 0.345670969696
absolute error = 1.612e-05
relative error = 0.004152 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.524
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8788 1.035
h = 0.001 0.003
y[1] (numeric) = 0.176656832042 0.346136149458
y[1] (closed_form) = 0.176660971373 0.346151624677
absolute error = 1.602e-05
relative error = 0.004122 %
Correct digits = 4
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
memory used=7330.7MB, alloc=52.3MB, time=90.80
x[1] = -0.8778 1.038
h = 0.0001 0.004
y[1] (numeric) = 0.176633521777 0.347326643815
y[1] (closed_form) = 0.17663740555 0.347342375696
absolute error = 1.620e-05
relative error = 0.004158 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.529
Order of pole (given) = 0.5 0
NO 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=7376.4MB, alloc=52.3MB, time=91.36
x[1] = -0.8777 1.042
h = 0.003 0.006
y[1] (numeric) = 0.176163433583 0.34875978536
y[1] (closed_form) = 0.176167018372 0.34877544381
absolute error = 1.606e-05
relative error = 0.004111 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.531
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
x[1] = -0.8747 1.048
h = 0.0001 0.005
y[1] (numeric) = 0.1764681322 0.351272347727
y[1] (closed_form) = 0.176472152441 0.351289284079
absolute error = 1.741e-05
relative error = 0.004428 %
Correct digits = 4
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
memory used=7422.1MB, alloc=52.3MB, time=91.92
x[1] = -0.8746 1.053
h = 0.0001 0.003
y[1] (numeric) = 0.175866940987 0.353065762283
y[1] (closed_form) = 0.175870824283 0.353081835315
absolute error = 1.654e-05
relative error = 0.004192 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.541
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] = -0.8745 1.056
h = 0.001 0.001
y[1] (numeric) = 0.175518901048 0.354147243987
y[1] (closed_form) = 0.175523083686 0.354163151828
absolute error = 1.645e-05
relative error = 0.004161 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.543
Order of pole (given) = 0.5 0
NO 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=7467.7MB, alloc=52.3MB, time=92.47
x[1] = -0.8735 1.057
h = 0.001 0.003
y[1] (numeric) = 0.175747160235 0.354631673989
y[1] (closed_form) = 0.175751461476 0.354647451047
absolute error = 1.635e-05
relative error = 0.004132 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.545
Order of pole (given) = 0.5 0
NO 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=7513.4MB, alloc=52.3MB, time=93.03
x[1] = -0.8725 1.06
h = 0.0001 0.004
y[1] (numeric) = 0.175719620589 0.355829159244
y[1] (closed_form) = 0.175723669531 0.355845192739
absolute error = 1.654e-05
relative error = 0.004167 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.548
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8724 1.064
h = 0.003 0.006
y[1] (numeric) = 0.175241845238 0.357269194599
y[1] (closed_form) = 0.175245596791 0.357285156931
absolute error = 1.640e-05
relative error = 0.00412 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.55
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=7559.1MB, alloc=52.3MB, time=93.59
x[1] = -0.8694 1.07
h = 0.0001 0.005
y[1] (numeric) = 0.175539815926 0.359797689831
y[1] (closed_form) = 0.175544007514 0.359814918834
absolute error = 1.773e-05
relative error = 0.004429 %
Correct digits = 4
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
memory used=7604.7MB, alloc=52.3MB, time=94.14
x[1] = -0.8693 1.075
h = 0.0001 0.003
y[1] (numeric) = 0.174929036115 0.361599665434
y[1] (closed_form) = 0.174933086617 0.361616037756
absolute error = 1.687e-05
relative error = 0.004199 %
Correct digits = 4
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] = -0.8692 1.078
h = 0.001 0.001
y[1] (numeric) = 0.17457532255 0.362686368729
y[1] (closed_form) = 0.174579669403 0.362702575227
absolute error = 1.678e-05
relative error = 0.004168 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.562
Order of pole (given) = 0.5 0
NO 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=7650.4MB, alloc=52.3MB, time=94.70
x[1] = -0.8682 1.079
h = 0.0001 0.004
y[1] (numeric) = 0.174803312691 0.363174419809
y[1] (closed_form) = 0.174807776582 0.363190495715
absolute error = 1.668e-05
relative error = 0.004139 %
Correct digits = 4
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] = -0.8681 1.083
h = 0.003 0.006
y[1] (numeric) = 0.174319308795 0.364620080109
y[1] (closed_form) = 0.174323080383 0.364636304565
absolute error = 1.666e-05
relative error = 0.004121 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.567
Order of pole (given) = 0.5 0
NO 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=7696.0MB, alloc=52.3MB, time=95.27
x[1] = -0.8651 1.089
h = 0.0001 0.005
y[1] (numeric) = 0.174611410857 0.367162157156
y[1] (closed_form) = 0.174615626392 0.367179638781
absolute error = 1.798e-05
relative error = 0.004423 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.573
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
memory used=7741.7MB, alloc=52.3MB, time=95.82
x[1] = -0.865 1.094
h = 0.0001 0.003
y[1] (numeric) = 0.173992367295 0.368971388013
y[1] (closed_form) = 0.173996438218 0.368988018571
absolute error = 1.712e-05
relative error = 0.004197 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.576
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] = -0.8649 1.097
h = 0.001 0.001
y[1] (numeric) = 0.173633762835 0.370062517598
y[1] (closed_form) = 0.173638127578 0.370078981786
absolute error = 1.703e-05
relative error = 0.004167 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.579
Order of pole (given) = 0.5 0
NO 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=7787.3MB, alloc=52.3MB, time=96.38
x[1] = -0.8639 1.098
h = 0.001 0.003
y[1] (numeric) = 0.173861496899 0.370553664443
y[1] (closed_form) = 0.173865977352 0.370569998197
absolute error = 1.694e-05
relative error = 0.004138 %
Correct digits = 4
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
memory used=7833.2MB, alloc=52.3MB, time=96.94
x[1] = -0.8629 1.101
h = 0.0001 0.004
y[1] (numeric) = 0.173826189485 0.371764049678
y[1] (closed_form) = 0.173830423552 0.371780639399
absolute error = 1.712e-05
relative error = 0.004172 %
Correct digits = 4
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] = -0.8628 1.105
h = 0.003 0.006
y[1] (numeric) = 0.173334273045 0.373216819073
y[1] (closed_form) = 0.173338212658 0.373233341719
absolute error = 1.699e-05
relative error = 0.004128 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.586
Order of pole (given) = 0.5 0
NO 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=7878.8MB, alloc=52.3MB, time=97.50
x[1] = -0.8598 1.111
h = 0.0001 0.005
y[1] (numeric) = 0.173619903674 0.375774703018
y[1] (closed_form) = 0.173624291442 0.375792471867
absolute error = 1.830e-05
relative error = 0.004421 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.592
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
x[1] = -0.8597 1.116
h = 0.0001 0.003
y[1] (numeric) = 0.172991482969 0.377592491816
y[1] (closed_form) = 0.172995722251 0.377609416111
absolute error = 1.745e-05
relative error = 0.004201 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.596
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
memory used=7924.5MB, alloc=52.3MB, time=98.06
x[1] = -0.8596 1.119
h = 0.001 0.001
y[1] (numeric) = 0.172627331504 0.378688838963
y[1] (closed_form) = 0.172631861697 0.378705596334
absolute error = 1.736e-05
relative error = 0.004171 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.598
Order of pole (given) = 0.5 0
NO 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=7970.3MB, alloc=52.3MB, time=98.62
x[1] = -0.8586 1.12
h = 0.001 0.003
y[1] (numeric) = 0.172854838683 0.379183564747
y[1] (closed_form) = 0.172859483074 0.3792001919
absolute error = 1.726e-05
relative error = 0.004143 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.599
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] = -0.8576 1.123
h = 0.0001 0.004
y[1] (numeric) = 0.172815498103 0.380400876483
y[1] (closed_form) = 0.172819899202 0.38041775929
absolute error = 1.745e-05
relative error = 0.004176 %
Correct digits = 4
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
memory used=8015.9MB, alloc=52.3MB, time=99.18
x[1] = -0.8575 1.127
h = 0.003 0.006
y[1] (numeric) = 0.172316154916 0.381860533861
y[1] (closed_form) = 0.172320263147 0.381877351702
absolute error = 1.731e-05
relative error = 0.004132 %
Correct digits = 4
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
memory used=8061.4MB, alloc=52.3MB, time=99.73
x[1] = -0.8545 1.133
h = 0.0001 0.005
y[1] (numeric) = 0.172595447084 0.384434155666
y[1] (closed_form) = 0.17260000749 0.384452208884
absolute error = 1.862e-05
relative error = 0.004418 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.611
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8544 1.138
h = 0.0001 0.003
y[1] (numeric) = 0.171957760055 0.386260498306
y[1] (closed_form) = 0.171962168234 0.386277713414
absolute error = 1.777e-05
relative error = 0.004203 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.615
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
memory used=8107.2MB, alloc=52.3MB, time=100.29
x[1] = -0.8543 1.141
h = 0.001 0.001
y[1] (numeric) = 0.171588127919 0.387362059428
y[1] (closed_form) = 0.171592824145 0.387379107098
absolute error = 1.768e-05
relative error = 0.004174 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.617
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] = -0.8533 1.142
h = 0.001 0.003
y[1] (numeric) = 0.171815429826 0.387860341571
y[1] (closed_form) = 0.171820238766 0.387877259252
absolute error = 1.759e-05
relative error = 0.004146 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.618
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
memory used=8152.9MB, alloc=52.3MB, time=100.85
x[1] = -0.8523 1.145
h = 0.0001 0.004
y[1] (numeric) = 0.171772121847 0.389084556341
y[1] (closed_form) = 0.171776690533 0.389101729334
absolute error = 1.777e-05
relative error = 0.004178 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.621
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
memory used=8198.6MB, alloc=52.3MB, time=101.41
x[1] = -0.8522 1.149
h = 0.003 0.006
y[1] (numeric) = 0.171265439892 0.390551097484
y[1] (closed_form) = 0.171269717292 0.390568207567
absolute error = 1.764e-05
relative error = 0.004135 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.624
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8492 1.155
h = 0.0001 0.005
y[1] (numeric) = 0.171538523584 0.393140387877
y[1] (closed_form) = 0.171543256996 0.393158722653
absolute error = 1.894e-05
relative error = 0.004414 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.63
Order of pole (given) = 0.5 0
NO 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=8244.3MB, alloc=52.3MB, time=101.97
x[1] = -0.8491 1.16
h = 0.0001 0.003
y[1] (numeric) = 0.170891679129 0.39497527917
y[1] (closed_form) = 0.170896256704 0.394992782209
absolute error = 1.809e-05
relative error = 0.004204 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.634
Order of pole (given) = 0.5 0
NO 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=8290.1MB, alloc=52.3MB, time=102.53
x[1] = -0.849 1.163
h = 0.001 0.001
y[1] (numeric) = 0.170516631497 0.396082050051
y[1] (closed_form) = 0.170521494297 0.396099385177
absolute error = 1.800e-05
relative error = 0.004175 %
Correct digits = 4
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] = -0.848 1.164
h = 0.001 0.003
y[1] (numeric) = 0.170743749145 0.396583866128
y[1] (closed_form) = 0.170748723202 0.396601071505
absolute error = 1.791e-05
relative error = 0.004148 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.638
Order of pole (given) = 0.5 0
NO 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=8335.7MB, alloc=52.3MB, time=103.08
x[1] = -0.847 1.167
h = 0.0001 0.004
y[1] (numeric) = 0.17069653818 0.397814960177
y[1] (closed_form) = 0.170701274967 0.397832420498
absolute error = 1.809e-05
relative error = 0.004179 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.641
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] = -0.8469 1.171
h = 0.003 0.006
y[1] (numeric) = 0.170182603907 0.399288380025
y[1] (closed_form) = 0.170187050984 0.399305779443
absolute error = 1.796e-05
relative error = 0.004137 %
Correct digits = 4
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
memory used=8381.4MB, alloc=52.3MB, time=103.64
x[1] = -0.8439 1.177
h = 0.0001 0.005
y[1] (numeric) = 0.170449606201 0.401893269565
y[1] (closed_form) = 0.170454512956 0.401911883132
absolute error = 1.925e-05
relative error = 0.004409 %
Correct digits = 4
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=8427.2MB, alloc=52.3MB, time=104.20
x[1] = -0.8438 1.182
h = 0.0001 0.003
y[1] (numeric) = 0.16979371134 0.403736703291
y[1] (closed_form) = 0.169798458772 0.403754491425
absolute error = 1.841e-05
relative error = 0.004203 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.653
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8437 1.185
h = 0.001 0.001
y[1] (numeric) = 0.169413312249 0.40484867912
y[1] (closed_form) = 0.169418342126 0.404866298903
absolute error = 1.832e-05
relative error = 0.004175 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.656
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
memory used=8472.9MB, alloc=52.3MB, time=104.76
x[1] = -0.8427 1.186
h = 0.0001 0.004
y[1] (numeric) = 0.169640266069 0.405354006871
y[1] (closed_form) = 0.169645405774 0.405371497155
absolute error = 1.823e-05
relative error = 0.004148 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.657
Order of pole (given) = 0.5 0
NO 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=8518.6MB, alloc=52.3MB, time=105.32
x[1] = -0.8426 1.19
h = 0.003 0.006
y[1] (numeric) = 0.169120453282 0.406833036724
y[1] (closed_form) = 0.169124926807 0.406850689094
absolute error = 1.821e-05
relative error = 0.004133 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.66
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] = -0.8396 1.196
h = 0.0001 0.005
y[1] (numeric) = 0.169382135824 0.409451227356
y[1] (closed_form) = 0.169387072172 0.409470084953
absolute error = 1.949e-05
relative error = 0.004399 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.666
Order of pole (given) = 0.5 0
NO 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=8564.2MB, alloc=52.3MB, time=105.88
x[1] = -0.8395 1.201
h = 0.0001 0.003
y[1] (numeric) = 0.168718433326 0.411301902296
y[1] (closed_form) = 0.168723207373 0.41131993979
absolute error = 1.866e-05
relative error = 0.004197 %
Correct digits = 4
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
x[1] = -0.8394 1.204
h = 0.001 0.001
y[1] (numeric) = 0.168333416392 0.412418291366
y[1] (closed_form) = 0.168338470531 0.412436160125
absolute error = 1.857e-05
relative error = 0.004169 %
Correct digits = 4
memory used=8609.8MB, alloc=52.3MB, time=106.44
Radius of convergence (given) for eq 1 = 1.672
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8384 1.205
h = 0.001 0.003
y[1] (numeric) = 0.168560203655 0.412926622518
y[1] (closed_form) = 0.168565366408 0.412944361986
absolute error = 1.848e-05
relative error = 0.004142 %
Correct digits = 4
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
memory used=8655.4MB, alloc=52.3MB, time=106.99
x[1] = -0.8374 1.208
h = 0.0001 0.004
y[1] (numeric) = 0.168505815814 0.414170408472
y[1] (closed_form) = 0.168510746712 0.414188402172
absolute error = 1.866e-05
relative error = 0.004172 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.677
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8373 1.212
h = 0.003 0.006
y[1] (numeric) = 0.167978529896 0.415656527823
y[1] (closed_form) = 0.167983173976 0.41567446424
absolute error = 1.853e-05
relative error = 0.004133 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.68
Order of pole (given) = 0.5 0
NO 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=8701.0MB, alloc=52.3MB, time=107.55
x[1] = -0.8343 1.218
h = 0.0001 0.005
y[1] (numeric) = 0.168234360877 0.418290189545
y[1] (closed_form) = 0.168239471141 0.418309320901
absolute error = 1.980e-05
relative error = 0.004392 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.686
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=8746.7MB, alloc=52.3MB, time=108.11
x[1] = -0.8342 1.223
h = 0.0001 0.003
y[1] (numeric) = 0.16756180233 0.420149394039
y[1] (closed_form) = 0.167566747029 0.420167711466
absolute error = 1.897e-05
relative error = 0.004194 %
Correct digits = 4
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
x[1] = -0.8341 1.226
h = 0.001 0.001
y[1] (numeric) = 0.167171550222 0.421270978383
y[1] (closed_form) = 0.16717677231 0.4212891267
absolute error = 1.888e-05
relative error = 0.004167 %
Correct digits = 4
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
memory used=8792.3MB, alloc=52.3MB, time=108.67
x[1] = -0.8331 1.227
h = 0.001 0.003
y[1] (numeric) = 0.16739821046 0.421782780462
y[1] (closed_form) = 0.167403539779 0.421800799758
absolute error = 1.879e-05
relative error = 0.004141 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.693
Order of pole (given) = 0.5 0
NO 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=8837.9MB, alloc=52.3MB, time=109.22
x[1] = -0.8321 1.23
h = 0.0001 0.004
y[1] (numeric) = 0.167340097013 0.423033377132
y[1] (closed_form) = 0.167345197313 0.423051650227
absolute error = 1.897e-05
relative error = 0.00417 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.696
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.832 1.234
h = 0.003 0.006
y[1] (numeric) = 0.166805798017 0.424526357482
y[1] (closed_form) = 0.166810613055 0.424544575164
absolute error = 1.884e-05
relative error = 0.004131 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.699
Order of pole (given) = 0.5 0
NO 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=8883.5MB, alloc=52.3MB, time=109.78
x[1] = -0.829 1.24
h = 0.0001 0.005
y[1] (numeric) = 0.167055896645 0.42717542061
y[1] (closed_form) = 0.167061181075 0.427194823078
absolute error = 2.011e-05
relative error = 0.004384 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.706
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
x[1] = -0.8289 1.245
h = 0.0001 0.003
y[1] (numeric) = 0.166374583906 0.429043145801
y[1] (closed_form) = 0.166379699617 0.429061740446
absolute error = 1.929e-05
relative error = 0.004191 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.709
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
memory used=8929.2MB, alloc=52.3MB, time=110.34
x[1] = -0.8288 1.248
h = 0.001 0.001
y[1] (numeric) = 0.165979157541 0.430169919092
y[1] (closed_form) = 0.165984547979 0.430188344284
absolute error = 1.920e-05
relative error = 0.004163 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.711
Order of pole (given) = 0.5 0
NO 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=8974.9MB, alloc=52.3MB, time=110.90
x[1] = -0.8278 1.249
h = 0.001 0.003
y[1] (numeric) = 0.166205709628 0.430685170321
y[1] (closed_form) = 0.166211205941 0.430703466768
absolute error = 1.910e-05
relative error = 0.004138 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.713
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] = -0.8268 1.252
h = 0.0001 0.004
y[1] (numeric) = 0.166143930077 0.4319425531
y[1] (closed_form) = 0.166149200154 0.431961102894
absolute error = 1.928e-05
relative error = 0.004167 %
Correct digits = 4
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
memory used=9020.5MB, alloc=52.3MB, time=111.45
x[1] = -0.8267 1.256
h = 0.003 0.006
y[1] (numeric) = 0.165602698844 0.433442386573
y[1] (closed_form) = 0.165607685209 0.433460882779
absolute error = 1.916e-05
relative error = 0.004128 %
Correct digits = 4
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
memory used=9066.2MB, alloc=52.3MB, time=112.01
x[1] = -0.8237 1.262
h = 0.0001 0.005
y[1] (numeric) = 0.165847181726 0.436106781436
y[1] (closed_form) = 0.165852640543 0.436126452411
absolute error = 2.041e-05
relative error = 0.004375 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.725
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8236 1.267
h = 0.0001 0.003
y[1] (numeric) = 0.16515721491 0.437983017658
y[1] (closed_form) = 0.165162501963 0.438001886845
absolute error = 1.960e-05
relative error = 0.004186 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.729
Order of pole (given) = 0.5 0
NO 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=9111.9MB, alloc=52.3MB, time=112.57
x[1] = -0.8235 1.27
h = 0.001 0.001
y[1] (numeric) = 0.164756674158 0.439114973104
y[1] (closed_form) = 0.164762233316 0.439133672523
absolute error = 1.951e-05
relative error = 0.004159 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.731
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] = -0.8225 1.271
h = 0.001 0.003
y[1] (numeric) = 0.164983136461 0.439633651883
y[1] (closed_form) = 0.164988800162 0.439652222844
absolute error = 1.942e-05
relative error = 0.004135 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.733
Order of pole (given) = 0.5 0
NO 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=9157.5MB, alloc=52.3MB, time=113.12
x[1] = -0.8215 1.274
h = 0.0001 0.004
y[1] (numeric) = 0.16491774911 0.440897796008
y[1] (closed_form) = 0.164923189309 0.440916619846
absolute error = 1.959e-05
relative error = 0.004162 %
Correct digits = 4
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
memory used=9203.1MB, alloc=52.3MB, time=113.68
x[1] = -0.8214 1.278
h = 0.003 0.006
y[1] (numeric) = 0.164369665102 0.442404474109
y[1] (closed_form) = 0.16437482313 0.442423246139
absolute error = 1.947e-05
relative error = 0.004125 %
Correct digits = 4
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] = -0.8184 1.284
h = 0.0001 0.005
y[1] (numeric) = 0.164608646315 0.445084131088
y[1] (closed_form) = 0.164614279716 0.445104068004
absolute error = 2.072e-05
relative error = 0.004366 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.745
Order of pole (given) = 0.5 0
NO 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=9248.8MB, alloc=52.3MB, time=114.24
x[1] = -0.8183 1.289
h = 0.0001 0.003
y[1] (numeric) = 0.163910123837 0.446968867912
y[1] (closed_form) = 0.163915582532 0.446988009006
absolute error = 1.990e-05
relative error = 0.004181 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.749
Order of pole (given) = 0.5 0
NO 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=9294.5MB, alloc=52.3MB, time=114.80
x[1] = -0.8182 1.292
h = 0.001 0.001
y[1] (numeric) = 0.163504527541 0.448105998285
y[1] (closed_form) = 0.163510255758 0.448124969325
absolute error = 1.982e-05
relative error = 0.004154 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.751
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] = -0.8172 1.293
h = 0.0001 0.004
y[1] (numeric) = 0.163730917935 0.448628083195
y[1] (closed_form) = 0.163736749385 0.44864692607
absolute error = 1.972e-05
relative error = 0.00413 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.752
Order of pole (given) = 0.5 0
NO 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=9340.2MB, alloc=52.3MB, time=115.36
x[1] = -0.8171 1.297
h = 0.003 0.006
y[1] (numeric) = 0.16317727713 0.45014034163
y[1] (closed_form) = 0.163182467077 0.450159357888
absolute error = 1.971e-05
relative error = 0.004117 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.755
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] = -0.8141 1.303
h = 0.0001 0.005
y[1] (numeric) = 0.163411431486 0.452833016316
y[1] (closed_form) = 0.163417099327 0.452853189092
absolute error = 2.095e-05
relative error = 0.004352 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.762
Order of pole (given) = 0.5 0
NO 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=9385.8MB, alloc=52.3MB, time=115.91
x[1] = -0.814 1.308
h = 0.0001 0.003
y[1] (numeric) = 0.162705521038 0.454724960925
y[1] (closed_form) = 0.162711011651 0.454744342925
absolute error = 2.014e-05
relative error = 0.004171 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.766
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=9431.5MB, alloc=52.3MB, time=116.47
x[1] = -0.8139 1.311
h = 0.001 0.001
y[1] (numeric) = 0.162295557933 0.455866480314
y[1] (closed_form) = 0.162301315879 0.455885692007
absolute error = 2.006e-05
relative error = 0.004145 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.768
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8129 1.312
h = 0.001 0.003
y[1] (numeric) = 0.162521860149 0.45639147952
y[1] (closed_form) = 0.162527720217 0.45641056329
absolute error = 1.996e-05
relative error = 0.004121 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.769
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
memory used=9477.2MB, alloc=52.3MB, time=117.03
x[1] = -0.8119 1.315
h = 0.0001 0.004
y[1] (numeric) = 0.162449830905 0.457668097201
y[1] (closed_form) = 0.16245547244 0.457687432961
absolute error = 2.014e-05
relative error = 0.004147 %
Correct digits = 4
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
memory used=9522.9MB, alloc=52.3MB, time=117.58
x[1] = -0.8118 1.319
h = 0.003 0.006
y[1] (numeric) = 0.16188912109 0.459187407511
y[1] (closed_form) = 0.161894483278 0.459206694682
absolute error = 2.002e-05
relative error = 0.004111 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.775
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8088 1.325
h = 0.0001 0.005
y[1] (numeric) = 0.162117980387 0.461895216321
y[1] (closed_form) = 0.162123823141 0.461915650368
absolute error = 2.125e-05
relative error = 0.004341 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.782
Order of pole (given) = 0.5 0
NO 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=9568.5MB, alloc=52.3MB, time=118.14
x[1] = -0.8087 1.33
h = 0.0001 0.003
y[1] (numeric) = 0.161403693143 0.463795641382
y[1] (closed_form) = 0.16140935591 0.463815290493
absolute error = 2.045e-05
relative error = 0.004164 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.786
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8086 1.333
h = 0.001 0.001
y[1] (numeric) = 0.160988781431 0.46494232185
y[1] (closed_form) = 0.160994709019 0.46496180042
absolute error = 2.036e-05
relative error = 0.004138 %
Correct digits = 4
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
memory used=9614.2MB, alloc=52.3MB, time=118.70
x[1] = -0.8076 1.334
h = 0.001 0.003
y[1] (numeric) = 0.161215043992 0.46547068802
y[1] (closed_form) = 0.161221072436 0.465490038972
absolute error = 2.027e-05
relative error = 0.004114 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.789
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
memory used=9659.9MB, alloc=52.3MB, time=119.26
x[1] = -0.8066 1.337
h = 0.0001 0.004
y[1] (numeric) = 0.161139567726 0.466753996199
y[1] (closed_form) = 0.161145380238 0.466773598623
absolute error = 2.045e-05
relative error = 0.00414 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.792
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] = -0.8065 1.341
h = 0.003 0.006
y[1] (numeric) = 0.160572225207 0.46828012462
y[1] (closed_form) = 0.160577759886 0.468299680119
absolute error = 2.032e-05
relative error = 0.004105 %
Correct digits = 4
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
memory used=9705.6MB, alloc=52.3MB, time=119.82
x[1] = -0.8035 1.347
h = 0.0001 0.005
y[1] (numeric) = 0.160795896671 0.471002998247
y[1] (closed_form) = 0.160801914466 0.471023691109
absolute error = 2.155e-05
relative error = 0.00433 %
Correct digits = 4
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=9751.3MB, alloc=52.3MB, time=120.38
x[1] = -0.8034 1.352
h = 0.0001 0.003
y[1] (numeric) = 0.160073326384 0.472911891379
y[1] (closed_form) = 0.160079161526 0.472931805076
absolute error = 2.075e-05
relative error = 0.004156 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.805
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8033 1.355
h = 0.001 0.001
y[1] (numeric) = 0.159653522099 0.474063724583
y[1] (closed_form) = 0.159659619587 0.474083467529
absolute error = 2.066e-05
relative error = 0.004131 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.808
Order of pole (given) = 0.5 0
NO 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=9796.9MB, alloc=52.3MB, time=120.93
x[1] = -0.8023 1.356
h = 0.001 0.003
y[1] (numeric) = 0.159879761558 0.474595436819
y[1] (closed_form) = 0.159885958659 0.474615052459
absolute error = 2.057e-05
relative error = 0.004108 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.809
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8013 1.359
h = 0.0001 0.004
y[1] (numeric) = 0.159800892252 0.475885410319
y[1] (closed_form) = 0.159806875976 0.475905276902
absolute error = 2.075e-05
relative error = 0.004133 %
Correct digits = 4
memory used=9842.7MB, alloc=52.3MB, time=121.49
Radius of convergence (given) for eq 1 = 1.812
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.8012 1.363
h = 0.003 0.006
y[1] (numeric) = 0.15922699143 0.477418346278
y[1] (closed_form) = 0.159232698827 0.477438167559
absolute error = 2.063e-05
relative error = 0.004098 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.815
Order of pole (given) = 0.5 0
NO 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=9888.4MB, alloc=52.3MB, time=122.04
x[1] = -0.7982 1.369
h = 0.0001 0.005
y[1] (numeric) = 0.159445580025 0.480156215591
y[1] (closed_form) = 0.159451772968 0.48017716485
absolute error = 2.185e-05
relative error = 0.004318 %
Correct digits = 4
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
x[1] = -0.7981 1.374
h = 0.0001 0.003
y[1] (numeric) = 0.158714818883 0.482073563816
y[1] (closed_form) = 0.158720826596 0.482093739615
absolute error = 2.105e-05
relative error = 0.004148 %
Correct digits = 4
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
memory used=9934.0MB, alloc=52.3MB, time=122.60
x[1] = -0.798 1.377
h = 0.001 0.001
y[1] (numeric) = 0.158290177116 0.483230541075
y[1] (closed_form) = 0.158296444737 0.483250545935
absolute error = 2.096e-05
relative error = 0.004123 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.828
Order of pole (given) = 0.5 0
NO 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=9979.8MB, alloc=52.3MB, time=123.16
x[1] = -0.797 1.378
h = 0.001 0.003
y[1] (numeric) = 0.158516409593 0.483765578667
y[1] (closed_form) = 0.158522775605 0.483785456538
absolute error = 2.087e-05
relative error = 0.0041 %
Correct digits = 4
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] = -0.796 1.381
h = 0.0001 0.004
y[1] (numeric) = 0.158434200178 0.485062192253
y[1] (closed_form) = 0.158440355325 0.485082320523
absolute error = 2.105e-05
relative error = 0.004125 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.832
Order of pole (given) = 0.5 0
NO 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=10025.5MB, alloc=52.3MB, time=123.72
x[1] = -0.7959 1.385
h = 0.003 0.006
y[1] (numeric) = 0.157853814213 0.486601924719
y[1] (closed_form) = 0.157859694529 0.486622009275
absolute error = 2.093e-05
relative error = 0.004091 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.835
Order of pole (given) = 0.5 0
NO 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=10071.2MB, alloc=52.3MB, time=124.28
x[1] = -0.7929 1.391
h = 0.0001 0.005
y[1] (numeric) = 0.158067422701 0.489354720789
y[1] (closed_form) = 0.158073790877 0.489375924062
absolute error = 2.214e-05
relative error = 0.004305 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.842
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7928 1.396
h = 0.0001 0.003
y[1] (numeric) = 0.157328561362 0.491280510572
y[1] (closed_form) = 0.157334741819 0.491300946021
absolute error = 2.135e-05
relative error = 0.004138 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.846
Order of pole (given) = 0.5 0
NO 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=10116.8MB, alloc=52.3MB, time=124.83
x[1] = -0.7927 1.399
h = 0.001 0.001
y[1] (numeric) = 0.156899136282 0.492442622883
y[1] (closed_form) = 0.156905574244 0.492462887231
absolute error = 2.126e-05
relative error = 0.004114 %
Correct digits = 4
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] = -0.7917 1.4
h = 0.003 0.006
y[1] (numeric) = 0.157125377479 0.49298096531
y[1] (closed_form) = 0.157131912633 0.493001102991
absolute error = 2.117e-05
relative error = 0.004092 %
Correct digits = 4
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
memory used=10162.4MB, alloc=52.3MB, time=125.39
x[1] = -0.7887 1.406
h = 0.0001 0.005
y[1] (numeric) = 0.157336801007 0.495743394214
y[1] (closed_form) = 0.157343017003 0.495765361913
absolute error = 2.283e-05
relative error = 0.004389 %
Correct digits = 4
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=10208.2MB, alloc=52.3MB, time=125.94
x[1] = -0.7886 1.411
h = 0.0001 0.003
y[1] (numeric) = 0.156592631701 0.49767518409
y[1] (closed_form) = 0.156598658451 0.497696387865
absolute error = 2.204e-05
relative error = 0.004225 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.86
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
x[1] = -0.7885 1.414
h = 0.001 0.001
y[1] (numeric) = 0.156160076282 0.498840942264
y[1] (closed_form) = 0.156166358902 0.498861974897
absolute error = 2.195e-05
relative error = 0.004199 %
Correct digits = 4
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
memory used=10253.9MB, alloc=52.3MB, time=126.50
x[1] = -0.7875 1.415
h = 0.001 0.003
y[1] (numeric) = 0.156386415021 0.499381545556
y[1] (closed_form) = 0.156392794027 0.499402451776
absolute error = 2.186e-05
relative error = 0.004177 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.863
Order of pole (given) = 0.5 0
NO 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=10299.6MB, alloc=52.3MB, time=127.06
x[1] = -0.7865 1.418
h = 0.0001 0.004
y[1] (numeric) = 0.156298850973 0.500689390811
y[1] (closed_form) = 0.156305023242 0.500710546425
absolute error = 2.204e-05
relative error = 0.004201 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.866
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7864 1.422
h = 0.003 0.006
y[1] (numeric) = 0.155707851941 0.502240728258
y[1] (closed_form) = 0.15571375192 0.502261842717
absolute error = 2.192e-05
relative error = 0.004169 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.869
Order of pole (given) = 0.5 0
NO 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=10345.2MB, alloc=52.3MB, time=127.61
x[1] = -0.7834 1.428
h = 0.0001 0.005
y[1] (numeric) = 0.15591365395 0.505018683282
y[1] (closed_form) = 0.155920045224 0.505040901052
absolute error = 2.312e-05
relative error = 0.004374 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.876
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] = -0.7833 1.433
h = 0.0001 0.003
y[1] (numeric) = 0.15516153372 0.50695888849
y[1] (closed_form) = 0.155167733394 0.506980347861
absolute error = 2.234e-05
relative error = 0.004213 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.88
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
memory used=10390.8MB, alloc=52.3MB, time=128.17
x[1] = -0.7832 1.436
h = 0.001 0.001
y[1] (numeric) = 0.154724284145 0.508129764547
y[1] (closed_form) = 0.154730737347 0.508151052647
absolute error = 2.224e-05
relative error = 0.004188 %
Correct digits = 4
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
memory used=10436.6MB, alloc=52.3MB, time=128.73
x[1] = -0.7822 1.437
h = 0.001 0.003
y[1] (numeric) = 0.15495065669 0.508673638086
y[1] (closed_form) = 0.154957205113 0.508694800102
absolute error = 2.215e-05
relative error = 0.004166 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.884
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7812 1.44
h = 0.0001 0.004
y[1] (numeric) = 0.154859889175 0.509988054161
y[1] (closed_form) = 0.154866233259 0.510009464999
absolute error = 2.233e-05
relative error = 0.00419 %
Correct digits = 4
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
memory used=10482.2MB, alloc=52.3MB, time=129.29
x[1] = -0.7811 1.444
h = 0.003 0.006
y[1] (numeric) = 0.154262595383 0.511546154679
y[1] (closed_form) = 0.154268668644 0.511567525854
absolute error = 2.222e-05
relative error = 0.004158 %
Correct digits = 4
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
memory used=10527.9MB, alloc=52.3MB, time=129.84
x[1] = -0.7781 1.45
h = 0.0001 0.005
y[1] (numeric) = 0.154463681345 0.514338849944
y[1] (closed_form) = 0.154470247933 0.514361315497
absolute error = 2.341e-05
relative error = 0.004358 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.896
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.778 1.455
h = 0.0001 0.003
y[1] (numeric) = 0.153703696887 0.516287455648
y[1] (closed_form) = 0.153710069601 0.516309168262
absolute error = 2.263e-05
relative error = 0.004201 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.9
Order of pole (given) = 0.5 0
NO 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=10573.6MB, alloc=52.3MB, time=130.40
x[1] = -0.7779 1.458
h = 0.001 0.001
y[1] (numeric) = 0.153261804944 0.517463439853
y[1] (closed_form) = 0.153268428876 0.517484981087
absolute error = 2.254e-05
relative error = 0.004176 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.902
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
x[1] = -0.7769 1.459
h = 0.001 0.003
y[1] (numeric) = 0.153488225943 0.518010563632
y[1] (closed_form) = 0.153494943952 0.518031979115
absolute error = 2.244e-05
relative error = 0.004154 %
Correct digits = 4
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
memory used=10619.2MB, alloc=52.3MB, time=130.96
x[1] = -0.7759 1.462
h = 0.0001 0.004
y[1] (numeric) = 0.153394304253 0.51933152522
y[1] (closed_form) = 0.15340082028 0.519353188943
absolute error = 2.262e-05
relative error = 0.004177 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.907
Order of pole (given) = 0.5 0
NO 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=10664.9MB, alloc=52.3MB, time=131.52
x[1] = -0.7758 1.466
h = 0.003 0.006
y[1] (numeric) = 0.152790784499 0.520896376363
y[1] (closed_form) = 0.15279703116 0.520918001881
absolute error = 2.251e-05
relative error = 0.004146 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.91
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] = -0.7728 1.472
h = 0.0001 0.005
y[1] (numeric) = 0.152987249583 0.523703743922
y[1] (closed_form) = 0.152993991507 0.523726455005
absolute error = 2.369e-05
relative error = 0.004342 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.916
Order of pole (given) = 0.5 0
NO 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=10710.5MB, alloc=52.3MB, time=132.08
x[1] = -0.7727 1.477
h = 0.0001 0.003
y[1] (numeric) = 0.152219486187 0.525660734844
y[1] (closed_form) = 0.152226032035 0.525682698383
absolute error = 2.292e-05
relative error = 0.004188 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.92
Order of pole (given) = 0.5 0
NO 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=10756.2MB, alloc=52.3MB, time=132.64
x[1] = -0.7726 1.48
h = 0.001 0.001
y[1] (numeric) = 0.151773002813 0.526841817215
y[1] (closed_form) = 0.151779797606 0.526863609284
absolute error = 2.283e-05
relative error = 0.004163 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.923
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7716 1.481
h = 0.0001 0.004
y[1] (numeric) = 0.151999486546 0.527392171414
y[1] (closed_form) = 0.152006374288 0.527413838069
absolute error = 2.274e-05
relative error = 0.004142 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.924
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
memory used=10801.9MB, alloc=52.3MB, time=133.19
x[1] = -0.7715 1.485
h = 0.003 0.006
y[1] (numeric) = 0.151390915003 0.528962524212
y[1] (closed_form) = 0.151397201329 0.528984379676
absolute error = 2.274e-05
relative error = 0.004133 %
Correct digits = 4
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] = -0.7685 1.491
h = 0.0001 0.005
y[1] (numeric) = 0.151583303649 0.531782413471
y[1] (closed_form) = 0.151590086929 0.531805347028
absolute error = 2.392e-05
relative error = 0.004325 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.934
Order of pole (given) = 0.5 0
NO 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=10847.7MB, alloc=52.3MB, time=133.75
x[1] = -0.7684 1.496
h = 0.0001 0.003
y[1] (numeric) = 0.150808812016 0.533746518253
y[1] (closed_form) = 0.150815397321 0.533768708834
absolute error = 2.315e-05
relative error = 0.004173 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.938
Order of pole (given) = 0.5 0
NO 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=10893.5MB, alloc=52.3MB, time=134.31
x[1] = -0.7683 1.499
h = 0.001 0.001
y[1] (numeric) = 0.150358356086 0.534931926901
y[1] (closed_form) = 0.150365188405 0.534953945924
absolute error = 2.305e-05
relative error = 0.004149 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.94
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7673 1.5
h = 0.001 0.003
y[1] (numeric) = 0.150584866814 0.535485046983
y[1] (closed_form) = 0.150591791125 0.53550694087
absolute error = 2.296e-05
relative error = 0.004128 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.942
Order of pole (given) = 0.5 0
NO 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=10939.2MB, alloc=52.3MB, time=134.87
x[1] = -0.7663 1.503
h = 0.0001 0.004
y[1] (numeric) = 0.150485126711 0.536818084676
y[1] (closed_form) = 0.150491853332 0.536840225723
absolute error = 2.314e-05
relative error = 0.00415 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.944
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
memory used=10984.8MB, alloc=52.3MB, time=135.42
x[1] = -0.7662 1.507
h = 0.003 0.006
y[1] (numeric) = 0.149870121143 0.538395390621
y[1] (closed_form) = 0.149876581064 0.538417496108
absolute error = 2.303e-05
relative error = 0.004121 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.948
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] = -0.7632 1.513
h = 0.0001 0.005
y[1] (numeric) = 0.150058061715 0.54122982762
y[1] (closed_form) = 0.150065020353 0.541253002598
absolute error = 2.420e-05
relative error = 0.004308 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.954
Order of pole (given) = 0.5 0
NO 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=11030.6MB, alloc=52.3MB, time=135.98
x[1] = -0.7631 1.518
h = 0.0001 0.003
y[1] (numeric) = 0.149275946395 0.543202289091
y[1] (closed_form) = 0.149282704989 0.543224726373
absolute error = 2.343e-05
relative error = 0.004159 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.958
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.763 1.521
h = 0.001 0.001
y[1] (numeric) = 0.148820991755 0.544392777309
y[1] (closed_form) = 0.148827995148 0.544415042976
absolute error = 2.334e-05
relative error = 0.004136 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.961
Order of pole (given) = 0.5 0
NO 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=11076.3MB, alloc=52.3MB, time=136.54
x[1] = -0.762 1.522
h = 0.001 0.003
y[1] (numeric) = 0.149047591069 0.544949091588
y[1] (closed_form) = 0.149054685365 0.544971232463
absolute error = 2.325e-05
relative error = 0.004115 %
Correct digits = 4
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
memory used=11122.1MB, alloc=52.3MB, time=137.10
x[1] = -0.761 1.525
h = 0.0001 0.004
y[1] (numeric) = 0.148944833062 0.546288603003
y[1] (closed_form) = 0.148951731914 0.54631099043
absolute error = 2.343e-05
relative error = 0.004137 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.965
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] = -0.7609 1.529
h = 0.003 0.006
y[1] (numeric) = 0.148323792417 0.547872622968
y[1] (closed_form) = 0.148330425996 0.547894976203
absolute error = 2.332e-05
relative error = 0.004108 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.968
Order of pole (given) = 0.5 0
NO 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=11167.7MB, alloc=52.3MB, time=137.66
x[1] = -0.7579 1.535
h = 0.0001 0.005
y[1] (numeric) = 0.14850737471 0.550721540621
y[1] (closed_form) = 0.148514508679 0.550744954859
absolute error = 2.448e-05
relative error = 0.004291 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.975
Order of pole (given) = 0.5 0
NO 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=11213.5MB, alloc=52.3MB, time=138.22
x[1] = -0.7578 1.54
h = 0.0001 0.003
y[1] (numeric) = 0.147717717132 0.552702342377
y[1] (closed_form) = 0.147724649059 0.552725024137
absolute error = 2.372e-05
relative error = 0.004145 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.979
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7577 1.543
h = 0.001 0.001
y[1] (numeric) = 0.147258312403 0.553897899552
y[1] (closed_form) = 0.147265486946 0.553920409656
absolute error = 2.363e-05
relative error = 0.004122 %
Correct digits = 4
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
memory used=11259.1MB, alloc=52.3MB, time=138.78
x[1] = -0.7567 1.544
h = 0.001 0.003
y[1] (numeric) = 0.147485013585 0.554457388739
y[1] (closed_form) = 0.147492277958 0.554479774397
absolute error = 2.353e-05
relative error = 0.004102 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.982
Order of pole (given) = 0.5 0
NO 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=11304.9MB, alloc=52.3MB, time=139.33
x[1] = -0.7557 1.547
h = 0.0001 0.004
y[1] (numeric) = 0.147379283513 0.555803348627
y[1] (closed_form) = 0.147386354654 0.555825980224
absolute error = 2.371e-05
relative error = 0.004123 %
Correct digits = 4
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] = -0.7556 1.551
h = 0.003 0.006
y[1] (numeric) = 0.146752272409 0.557394068979
y[1] (closed_form) = 0.146759079691 0.557416667721
absolute error = 2.360e-05
relative error = 0.004095 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.989
Order of pole (given) = 0.5 0
NO 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=11350.6MB, alloc=52.3MB, time=139.89
x[1] = -0.7526 1.557
h = 0.0001 0.005
y[1] (numeric) = 0.146931584438 0.560257400534
y[1] (closed_form) = 0.146938893701 0.560281051902
absolute error = 2.476e-05
relative error = 0.004274 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.995
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7525 1.562
h = 0.0001 0.003
y[1] (numeric) = 0.146134464743 0.562246525833
y[1] (closed_form) = 0.146141570029 0.562269449879
absolute error = 2.400e-05
relative error = 0.004131 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 1.999
Order of pole (given) = 0.5 0
NO 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=11396.3MB, alloc=52.3MB, time=140.45
x[1] = -0.7524 1.565
h = 0.001 0.001
y[1] (numeric) = 0.145670657768 0.563447141162
y[1] (closed_form) = 0.145678003518 0.563469893528
absolute error = 2.391e-05
relative error = 0.004108 %
Correct digits = 4
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
memory used=11442.1MB, alloc=52.3MB, time=141.01
x[1] = -0.7514 1.566
h = 0.001 0.003
y[1] (numeric) = 0.14589747377 0.564009786151
y[1] (closed_form) = 0.145904908296 0.56403241442
absolute error = 2.382e-05
relative error = 0.004088 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.003
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7504 1.569
h = 0.0001 0.004
y[1] (numeric) = 0.145788816636 0.565362169309
y[1] (closed_form) = 0.145796060105 0.565385042895
absolute error = 2.399e-05
relative error = 0.004109 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.006
Order of pole (given) = 0.5 0
NO 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=11487.7MB, alloc=52.3MB, time=141.57
x[1] = -0.7503 1.573
h = 0.003 0.006
y[1] (numeric) = 0.145155898666 0.566959576155
y[1] (closed_form) = 0.145162879681 0.566982418195
absolute error = 2.389e-05
relative error = 0.004081 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.009
Order of pole (given) = 0.5 0
NO 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=11533.5MB, alloc=52.3MB, time=142.13
x[1] = -0.7473 1.579
h = 0.0001 0.005
y[1] (numeric) = 0.145331026715 0.569837255209
y[1] (closed_form) = 0.14533851122 0.569861141606
absolute error = 2.503e-05
relative error = 0.004256 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.016
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7472 1.584
h = 0.0001 0.003
y[1] (numeric) = 0.144526523778 0.571834686991
y[1] (closed_form) = 0.144533802434 0.571857851162
absolute error = 2.428e-05
relative error = 0.004117 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.02
Order of pole (given) = 0.5 0
NO 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=11579.2MB, alloc=52.3MB, time=142.68
x[1] = -0.7471 1.587
h = 0.001 0.001
y[1] (numeric) = 0.144058361641 0.573040349495
y[1] (closed_form) = 0.144065878641 0.573063341978
absolute error = 2.419e-05
relative error = 0.004094 %
Correct digits = 4
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] = -0.7461 1.588
h = 0.0001 0.004
y[1] (numeric) = 0.1442853051 0.573606131365
y[1] (closed_form) = 0.144292909838 0.573629000101
absolute error = 2.410e-05
relative error = 0.004074 %
Correct digits = 4
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
memory used=11624.8MB, alloc=52.3MB, time=143.24
x[1] = -0.746 1.592
h = 0.003 0.006
y[1] (numeric) = 0.143647592617 0.5752089869
y[1] (closed_form) = 0.143654616903 0.575232051377
absolute error = 2.411e-05
relative error = 0.004067 %
Correct digits = 4
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
memory used=11670.6MB, alloc=52.3MB, time=143.80
x[1] = -0.743 1.598
h = 0.0001 0.005
y[1] (numeric) = 0.143819017205 0.578098914425
y[1] (closed_form) = 0.143826546315 0.578123016245
absolute error = 2.525e-05
relative error = 0.004238 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.033
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7429 1.603
h = 0.0001 0.003
y[1] (numeric) = 0.143008122572 0.580103395571
y[1] (closed_form) = 0.143015444211 0.580126779483
absolute error = 2.450e-05
relative error = 0.004101 %
Correct digits = 4
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
memory used=11716.3MB, alloc=52.3MB, time=144.36
x[1] = -0.7428 1.606
h = 0.001 0.001
y[1] (numeric) = 0.142536188854 0.58131334247
y[1] (closed_form) = 0.142543747035 0.581336554673
absolute error = 2.441e-05
relative error = 0.004078 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.04
Order of pole (given) = 0.5 0
NO 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=11762.1MB, alloc=52.3MB, time=144.92
x[1] = -0.7418 1.607
h = 0.001 0.003
y[1] (numeric) = 0.142763214844 0.581881811169
y[1] (closed_form) = 0.14277085988 0.581904899914
absolute error = 2.432e-05
relative error = 0.004059 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.041
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7408 1.61
h = 0.0001 0.004
y[1] (numeric) = 0.142649152315 0.583246045984
y[1] (closed_form) = 0.142656610255 0.583269378902
absolute error = 2.450e-05
relative error = 0.00408 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.044
Order of pole (given) = 0.5 0
NO 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=11807.8MB, alloc=52.3MB, time=145.48
x[1] = -0.7407 1.614
h = 0.003 0.006
y[1] (numeric) = 0.142005329634 0.584855788438
y[1] (closed_form) = 0.14201252769 0.584879092188
absolute error = 2.439e-05
relative error = 0.004052 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.047
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7377 1.62
h = 0.0001 0.005
y[1] (numeric) = 0.14217272713 0.587759941834
y[1] (closed_form) = 0.142180431376 0.587784274854
absolute error = 2.552e-05
relative error = 0.004221 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.054
Order of pole (given) = 0.5 0
NO 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=11853.6MB, alloc=52.3MB, time=146.04
x[1] = -0.7376 1.625
h = 0.0001 0.003
y[1] (numeric) = 0.141354592967 0.589772697855
y[1] (closed_form) = 0.141362087983 0.589796317954
absolute error = 2.478e-05
relative error = 0.004086 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.058
Order of pole (given) = 0.5 0
NO 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=11899.3MB, alloc=52.3MB, time=146.60
x[1] = -0.7375 1.628
h = 0.001 0.001
y[1] (numeric) = 0.140878389873 0.590987671616
y[1] (closed_form) = 0.140886119365 0.591011120023
absolute error = 2.469e-05
relative error = 0.004064 %
Correct digits = 4
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] = -0.7365 1.629
h = 0.001 0.003
y[1] (numeric) = 0.141105566243 0.591559242615
y[1] (closed_form) = 0.141113381584 0.591582567919
absolute error = 2.460e-05
relative error = 0.004045 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.062
Order of pole (given) = 0.5 0
NO 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=11944.9MB, alloc=52.3MB, time=147.16
x[1] = -0.7355 1.632
h = 0.0001 0.004
y[1] (numeric) = 0.14098870125 0.592929829397
y[1] (closed_form) = 0.140996331571 0.592953398237
absolute error = 2.477e-05
relative error = 0.004065 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.065
Order of pole (given) = 0.5 0
NO 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=11990.7MB, alloc=52.3MB, time=147.72
x[1] = -0.7354 1.636
h = 0.003 0.006
y[1] (numeric) = 0.140339148339 0.594546218062
y[1] (closed_form) = 0.14034652015 0.594569758964
absolute error = 2.467e-05
relative error = 0.004038 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.068
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
x[1] = -0.7324 1.642
h = 0.0001 0.005
y[1] (numeric) = 0.140502600325 0.597464531946
y[1] (closed_form) = 0.14051047962 0.59748909415
absolute error = 2.580e-05
relative error = 0.004203 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.074
Order of pole (given) = 0.5 0
NO 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=12036.4MB, alloc=52.3MB, time=148.28
x[1] = -0.7323 1.647
h = 0.0001 0.003
y[1] (numeric) = 0.139677302048 0.599485544977
y[1] (closed_form) = 0.139684970411 0.599509399189
absolute error = 2.506e-05
relative error = 0.00407 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.078
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7322 1.65
h = 0.001 0.001
y[1] (numeric) = 0.139196874585 0.600705534176
y[1] (closed_form) = 0.139204775387 0.600729216728
absolute error = 2.497e-05
relative error = 0.004049 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.081
Order of pole (given) = 0.5 0
NO 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=12082.0MB, alloc=52.3MB, time=148.83
x[1] = -0.7312 1.651
h = 0.001 0.003
y[1] (numeric) = 0.139424213116 0.601280189071
y[1] (closed_form) = 0.139432198777 0.601303748875
absolute error = 2.488e-05
relative error = 0.00403 %
Correct digits = 4
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
memory used=12127.8MB, alloc=52.3MB, time=149.39
x[1] = -0.7302 1.654
h = 0.0001 0.004
y[1] (numeric) = 0.139304587618 0.602657102838
y[1] (closed_form) = 0.139312390303 0.602680905537
absolute error = 2.505e-05
relative error = 0.004049 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.085
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7301 1.658
h = 0.003 0.006
y[1] (numeric) = 0.138649364323 0.604280122977
y[1] (closed_form) = 0.138656909859 0.604303898942
absolute error = 2.494e-05
relative error = 0.004023 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.088
Order of pole (given) = 0.5 0
NO 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=12173.6MB, alloc=52.3MB, time=149.95
x[1] = -0.7271 1.664
h = 0.0001 0.005
y[1] (numeric) = 0.138808950823 0.607212532347
y[1] (closed_form) = 0.138817005069 0.607237321748
absolute error = 2.607e-05
relative error = 0.004184 %
Correct digits = 4
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
memory used=12219.2MB, alloc=52.3MB, time=150.50
x[1] = -0.727 1.669
h = 0.0001 0.003
y[1] (numeric) = 0.137976562688 0.609241784284
y[1] (closed_form) = 0.137984404355 0.609265870565
absolute error = 2.533e-05
relative error = 0.004055 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.099
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7269 1.672
h = 0.001 0.001
y[1] (numeric) = 0.137491955168 0.610466777368
y[1] (closed_form) = 0.137500027264 0.610490692031
absolute error = 2.524e-05
relative error = 0.004033 %
Correct digits = 4
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
memory used=12264.9MB, alloc=52.3MB, time=151.06
x[1] = -0.7259 1.673
h = 0.001 0.003
y[1] (numeric) = 0.137719467359 0.611044497931
y[1] (closed_form) = 0.137727623341 0.611068290204
absolute error = 2.515e-05
relative error = 0.004015 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.103
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7249 1.676
h = 0.0001 0.004
y[1] (numeric) = 0.137597122577 0.612427713778
y[1] (closed_form) = 0.137605097594 0.6124517483
absolute error = 2.532e-05
relative error = 0.004034 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.106
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
memory used=12310.7MB, alloc=52.3MB, time=151.62
x[1] = -0.7248 1.68
h = 0.003 0.006
y[1] (numeric) = 0.136936287823 0.614057350475
y[1] (closed_form) = 0.136944007042 0.614081359442
absolute error = 2.522e-05
relative error = 0.004008 %
Correct digits = 4
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=12356.5MB, alloc=52.3MB, time=152.18
x[1] = -0.7218 1.686
h = 0.0001 0.005
y[1] (numeric) = 0.137092087344 0.617003790714
y[1] (closed_form) = 0.137100316432 0.617028805351
absolute error = 2.633e-05
relative error = 0.004166 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.116
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7217 1.691
h = 0.0001 0.003
y[1] (numeric) = 0.136252682475 0.619041263231
y[1] (closed_form) = 0.136260697389 0.619065579564
absolute error = 2.560e-05
relative error = 0.004039 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.12
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
memory used=12402.0MB, alloc=52.3MB, time=152.74
x[1] = -0.7216 1.694
h = 0.001 0.001
y[1] (numeric) = 0.135763938526 0.620271248524
y[1] (closed_form) = 0.135772181889 0.620295393294
absolute error = 2.551e-05
relative error = 0.004018 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.122
Order of pole (given) = 0.5 0
NO 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=12447.7MB, alloc=52.3MB, time=153.30
x[1] = -0.7206 1.695
h = 0.0001 0.004
y[1] (numeric) = 0.135991635606 0.620852016706
y[1] (closed_form) = 0.135999961896 0.620876039445
absolute error = 2.542e-05
relative error = 0.004 %
Correct digits = 4
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] = -0.7205 1.699
h = 0.003 0.006
y[1] (numeric) = 0.135326244641 0.622487044637
y[1] (closed_form) = 0.135334010255 0.622511268936
absolute error = 2.544e-05
relative error = 0.003993 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.127
Order of pole (given) = 0.5 0
NO 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=12493.3MB, alloc=52.3MB, time=153.85
x[1] = -0.7175 1.705
h = 0.0001 0.005
y[1] (numeric) = 0.135478680101 0.625445466872
y[1] (closed_form) = 0.135486956622 0.625470690247
absolute error = 2.655e-05
relative error = 0.004148 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.134
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7174 1.71
h = 0.0001 0.003
y[1] (numeric) = 0.134633195546 0.627489918138
y[1] (closed_form) = 0.134641256505 0.627514447291
absolute error = 2.582e-05
relative error = 0.004023 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.138
Order of pole (given) = 0.5 0
NO 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=12538.9MB, alloc=52.3MB, time=154.41
x[1] = -0.7173 1.713
h = 0.001 0.001
y[1] (numeric) = 0.134140866252 0.628724142545
y[1] (closed_form) = 0.134149153975 0.628748500169
absolute error = 2.573e-05
relative error = 0.004002 %
Correct digits = 4
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
memory used=12584.6MB, alloc=52.3MB, time=154.97
x[1] = -0.7163 1.714
h = 0.001 0.003
y[1] (numeric) = 0.134368695252 0.629307522077
y[1] (closed_form) = 0.134377065086 0.629331757968
absolute error = 2.564e-05
relative error = 0.003984 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.141
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7153 1.717
h = 0.0001 0.004
y[1] (numeric) = 0.134241323393 0.630702367348
y[1] (closed_form) = 0.134249515929 0.6307268443
absolute error = 2.581e-05
relative error = 0.004003 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.144
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
memory used=12630.3MB, alloc=52.3MB, time=155.52
x[1] = -0.7152 1.721
h = 0.003 0.006
y[1] (numeric) = 0.1335701224 0.63234421043
y[1] (closed_form) = 0.133578061609 0.632368663972
absolute error = 2.571e-05
relative error = 0.003978 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.148
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=12675.9MB, alloc=52.3MB, time=156.08
x[1] = -0.7122 1.727
h = 0.0001 0.005
y[1] (numeric) = 0.133718913825 0.635316545239
y[1] (closed_form) = 0.133727364983 0.635341990273
absolute error = 2.681e-05
relative error = 0.00413 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.154
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7121 1.732
h = 0.0001 0.003
y[1] (numeric) = 0.132866545891 0.637369183285
y[1] (closed_form) = 0.132874779987 0.637393938811
absolute error = 2.609e-05
relative error = 0.004007 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.158
Order of pole (given) = 0.5 0
NO 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=12721.7MB, alloc=52.3MB, time=156.64
x[1] = -0.712 1.735
h = 0.001 0.001
y[1] (numeric) = 0.132370159738 0.638608378388
y[1] (closed_form) = 0.132378618667 0.638632962461
absolute error = 2.600e-05
relative error = 0.003986 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.161
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.711 1.736
h = 0.001 0.003
y[1] (numeric) = 0.13259819403 0.639194772547
y[1] (closed_form) = 0.132606734139 0.639219235247
absolute error = 2.591e-05
relative error = 0.003969 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.162
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
memory used=12767.5MB, alloc=52.3MB, time=157.20
x[1] = -0.71 1.739
h = 0.0001 0.004
y[1] (numeric) = 0.132468217178 0.640595849574
y[1] (closed_form) = 0.132476581912 0.640620552679
absolute error = 2.608e-05
relative error = 0.003987 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.165
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
memory used=12813.3MB, alloc=52.3MB, time=157.76
x[1] = -0.7099 1.743
h = 0.003 0.006
y[1] (numeric) = 0.131791568582 0.642244266335
y[1] (closed_form) = 0.13179968131 0.642268947142
absolute error = 2.598e-05
relative error = 0.003962 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.169
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.7069 1.749
h = 0.0001 0.005
y[1] (numeric) = 0.131936790355 0.645230450218
y[1] (closed_form) = 0.131945416013 0.645256115026
absolute error = 2.708e-05
relative error = 0.004111 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.175
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=12859.0MB, alloc=52.3MB, time=158.32
x[1] = -0.7068 1.754
h = 0.0001 0.003
y[1] (numeric) = 0.13107760906 0.647291256156
y[1] (closed_form) = 0.131086016205 0.647316236117
absolute error = 2.636e-05
relative error = 0.003991 %
Correct digits = 4
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
memory used=12904.6MB, alloc=52.3MB, time=158.88
x[1] = -0.7067 1.757
h = 0.001 0.001
y[1] (numeric) = 0.130577207814 0.648535409975
y[1] (closed_form) = 0.130585837886 0.648560218569
absolute error = 2.627e-05
relative error = 0.00397 %
Correct digits = 4
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] = -0.7057 1.758
h = 0.001 0.003
y[1] (numeric) = 0.13080545789 0.649124801207
y[1] (closed_form) = 0.130814168226 0.649149488789
absolute error = 2.618e-05
relative error = 0.003953 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.183
Order of pole (given) = 0.5 0
NO 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=12950.3MB, alloc=52.3MB, time=159.43
x[1] = -0.7047 1.761
h = 0.0001 0.004
y[1] (numeric) = 0.130672914575 0.650532085416
y[1] (closed_form) = 0.130681451431 0.650557012745
absolute error = 2.635e-05
relative error = 0.003971 %
Correct digits = 4
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=12996.0MB, alloc=52.3MB, time=159.99
x[1] = -0.7046 1.765
h = 0.003 0.006
y[1] (numeric) = 0.129990873939 0.652187060356
y[1] (closed_form) = 0.129999160097 0.652211966475
absolute error = 2.625e-05
relative error = 0.003947 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.189
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
x[1] = -0.7016 1.771
h = 0.0001 0.005
y[1] (numeric) = 0.130132599073 0.655187030216
y[1] (closed_form) = 0.130141399086 0.655212912939
absolute error = 2.734e-05
relative error = 0.004092 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.196
Order of pole (given) = 0.5 0
NO 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=13041.6MB, alloc=52.3MB, time=160.55
x[1] = -0.7015 1.776
h = 0.0001 0.003
y[1] (numeric) = 0.129266673393 0.657255984993
y[1] (closed_form) = 0.129275253487 0.657281187476
absolute error = 2.662e-05
relative error = 0.003974 %
Correct digits = 4
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] = -0.7014 1.779
h = 0.001 0.001
y[1] (numeric) = 0.128762298196 0.658505085461
y[1] (closed_form) = 0.128771099339 0.658530116675
absolute error = 2.653e-05
relative error = 0.003954 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.203
Order of pole (given) = 0.5 0
NO 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=13087.3MB, alloc=52.3MB, time=161.10
x[1] = -0.7004 1.78
h = 0.001 0.003
y[1] (numeric) = 0.128990774303 0.659097456384
y[1] (closed_form) = 0.128999654809 0.659122366948
absolute error = 2.645e-05
relative error = 0.003938 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.204
Order of pole (given) = 0.5 0
NO 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=13133.0MB, alloc=52.3MB, time=161.67
x[1] = -0.6994 1.783
h = 0.0001 0.004
y[1] (numeric) = 0.128855702402 0.660510923298
y[1] (closed_form) = 0.128864411291 0.660536072948
absolute error = 2.661e-05
relative error = 0.003955 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.207
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
x[1] = -0.6993 1.787
h = 0.003 0.006
y[1] (numeric) = 0.128168324462 0.662172440796
y[1] (closed_form) = 0.128176783952 0.662197570302
absolute error = 2.652e-05
relative error = 0.003931 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.21
Order of pole (given) = 0.5 0
NO 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=13178.6MB, alloc=52.3MB, time=162.22
x[1] = -0.6963 1.793
h = 0.0001 0.005
y[1] (numeric) = 0.128306624638 0.665186133943
y[1] (closed_form) = 0.128315598853 0.665212232748
absolute error = 2.760e-05
relative error = 0.004074 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.217
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
memory used=13224.4MB, alloc=52.3MB, time=162.78
x[1] = -0.6962 1.798
h = 0.0001 0.003
y[1] (numeric) = 0.12743402253 0.667263218356
y[1] (closed_form) = 0.127442775467 0.667288641475
absolute error = 2.689e-05
relative error = 0.003958 %
Correct digits = 4
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] = -0.6961 1.801
h = 0.001 0.001
y[1] (numeric) = 0.126925713915 0.668517253328
y[1] (closed_form) = 0.126934686045 0.668542505285
absolute error = 2.680e-05
relative error = 0.003938 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.223
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=13270.0MB, alloc=52.3MB, time=163.34
x[1] = -0.6951 1.802
h = 0.0001 0.004
y[1] (numeric) = 0.127154426067 0.669112586727
y[1] (closed_form) = 0.127163476671 0.669137718396
absolute error = 2.671e-05
relative error = 0.003922 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.225
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.695 1.806
h = 0.003 0.006
y[1] (numeric) = 0.126462713192 0.670779434872
y[1] (closed_form) = 0.12647122179 0.670804772981
absolute error = 2.673e-05
relative error = 0.003916 %
Correct digits = 4
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
memory used=13315.7MB, alloc=52.3MB, time=163.90
x[1] = -0.692 1.812
h = 0.0001 0.005
y[1] (numeric) = 0.126597959222 0.673804851019
y[1] (closed_form) = 0.126606983337 0.673831152221
absolute error = 2.781e-05
relative error = 0.004056 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.235
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
memory used=13361.4MB, alloc=52.3MB, time=164.45
x[1] = -0.6919 1.817
h = 0.0001 0.003
y[1] (numeric) = 0.1257195674 0.67588883922
y[1] (closed_form) = 0.125728369047 0.6759144686
absolute error = 2.710e-05
relative error = 0.003942 %
Correct digits = 4
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] = -0.6918 1.82
h = 0.001 0.001
y[1] (numeric) = 0.125207846447 0.677147065658
y[1] (closed_form) = 0.12521686571 0.677172523953
absolute error = 2.701e-05
relative error = 0.003922 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.241
Order of pole (given) = 0.5 0
NO 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=13407.0MB, alloc=52.3MB, time=165.01
x[1] = -0.6908 1.821
h = 0.001 0.003
y[1] (numeric) = 0.125436734608 0.677744938372
y[1] (closed_form) = 0.125445831589 0.67777027668
absolute error = 2.692e-05
relative error = 0.003906 %
Correct digits = 4
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=13452.7MB, alloc=52.3MB, time=165.56
x[1] = -0.6898 1.824
h = 0.0001 0.004
y[1] (numeric) = 0.125296983264 0.679169815983
y[1] (closed_form) = 0.125305912032 0.679195392163
absolute error = 2.709e-05
relative error = 0.003922 %
Correct digits = 4
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] = -0.6897 1.828
h = 0.003 0.006
y[1] (numeric) = 0.124599739287 0.680843403626
y[1] (closed_form) = 0.12460842103 0.680868961606
absolute error = 2.699e-05
relative error = 0.0039 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.249
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=13498.4MB, alloc=52.3MB, time=166.12
x[1] = -0.6867 1.834
h = 0.0001 0.005
y[1] (numeric) = 0.124731691045 0.683882428315
y[1] (closed_form) = 0.124740889076 0.68390894225
absolute error = 2.806e-05
relative error = 0.004037 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.256
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6866 1.839
h = 0.0001 0.003
y[1] (numeric) = 0.123846746845 0.685974510839
y[1] (closed_form) = 0.123855721129 0.686000357413
absolute error = 2.736e-05
relative error = 0.003925 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.26
Order of pole (given) = 0.5 0
NO 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=13544.1MB, alloc=52.3MB, time=166.68
x[1] = -0.6865 1.842
h = 0.001 0.001
y[1] (numeric) = 0.12333116646 0.687237649459
y[1] (closed_form) = 0.12334035655 0.687263325069
absolute error = 2.727e-05
relative error = 0.003906 %
Correct digits = 4
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
memory used=13589.8MB, alloc=52.3MB, time=167.25
x[1] = -0.6855 1.843
h = 0.001 0.003
y[1] (numeric) = 0.123560308895 0.687838453175
y[1] (closed_form) = 0.12356957584 0.687864009162
absolute error = 2.718e-05
relative error = 0.00389 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.264
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6845 1.846
h = 0.0001 0.004
y[1] (numeric) = 0.123418134129 0.689269444473
y[1] (closed_form) = 0.123427234649 0.689295237666
absolute error = 2.735e-05
relative error = 0.003906 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.267
Order of pole (given) = 0.5 0
NO 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=13635.5MB, alloc=52.3MB, time=167.82
x[1] = -0.6844 1.85
h = 0.003 0.006
y[1] (numeric) = 0.122715705228 0.690949530023
y[1] (closed_form) = 0.122724559988 0.690975306023
absolute error = 2.725e-05
relative error = 0.003884 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.27
Order of pole (given) = 0.5 0
NO 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=13681.3MB, alloc=52.3MB, time=168.39
x[1] = -0.6814 1.856
h = 0.0001 0.005
y[1] (numeric) = 0.12284443076 0.694002101725
y[1] (closed_form) = 0.122853802532 0.694028826627
absolute error = 2.832e-05
relative error = 0.004018 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.277
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] = -0.6813 1.861
h = 0.0001 0.003
y[1] (numeric) = 0.121952999348 0.696102258992
y[1] (closed_form) = 0.121962146134 0.696128320943
absolute error = 2.762e-05
relative error = 0.003908 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.281
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=13727.0MB, alloc=52.3MB, time=168.95
x[1] = -0.6812 1.864
h = 0.001 0.001
y[1] (numeric) = 0.121433598388 0.697370297449
y[1] (closed_form) = 0.121442959195 0.697396188569
absolute error = 2.753e-05
relative error = 0.003889 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.283
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6802 1.865
h = 0.001 0.003
y[1] (numeric) = 0.121663004472 0.697974015425
y[1] (closed_form) = 0.121672441284 0.697999787284
absolute error = 2.745e-05
relative error = 0.003874 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.285
Order of pole (given) = 0.5 0
NO 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=13772.7MB, alloc=52.3MB, time=169.51
x[1] = -0.6792 1.868
h = 0.0001 0.004
y[1] (numeric) = 0.121518441777 0.699411096339
y[1] (closed_form) = 0.121527713923 0.699437104736
absolute error = 2.761e-05
relative error = 0.003889 %
Correct digits = 4
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
memory used=13818.4MB, alloc=52.3MB, time=170.07
x[1] = -0.6791 1.872
h = 0.003 0.006
y[1] (numeric) = 0.120810879664 0.701097663787
y[1] (closed_form) = 0.120819907308 0.701123655978
absolute error = 2.752e-05
relative error = 0.003867 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.291
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6761 1.878
h = 0.0001 0.005
y[1] (numeric) = 0.120936445812 0.704163721385
y[1] (closed_form) = 0.120945991142 0.704190655513
absolute error = 2.858e-05
relative error = 0.003999 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.298
Order of pole (given) = 0.5 0
NO 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=13864.2MB, alloc=52.3MB, time=170.63
x[1] = -0.676 1.883
h = 0.0001 0.003
y[1] (numeric) = 0.120038591418 0.706271933705
y[1] (closed_form) = 0.120047910563 0.706298209244
absolute error = 2.788e-05
relative error = 0.003891 %
Correct digits = 4
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=13910.0MB, alloc=52.3MB, time=171.20
x[1] = -0.6759 1.886
h = 0.001 0.001
y[1] (numeric) = 0.119515408177 0.707544859604
y[1] (closed_form) = 0.119524939581 0.707570964451
absolute error = 2.779e-05
relative error = 0.003873 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.304
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6749 1.887
h = 0.001 0.003
y[1] (numeric) = 0.119745087077 0.708151475259
y[1] (closed_form) = 0.119754693649 0.708177461207
absolute error = 2.770e-05
relative error = 0.003857 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.306
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
memory used=13955.6MB, alloc=52.3MB, time=171.93
x[1] = -0.6739 1.89
h = 0.0001 0.004
y[1] (numeric) = 0.119598171362 0.709594621829
y[1] (closed_form) = 0.119607615002 0.709620843648
absolute error = 2.787e-05
relative error = 0.003873 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.309
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6738 1.894
h = 0.003 0.006
y[1] (numeric) = 0.11888552701 0.711287655089
y[1] (closed_form) = 0.118894727393 0.711313861669
absolute error = 2.777e-05
relative error = 0.003851 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.312
Order of pole (given) = 0.5 0
NO 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=14001.4MB, alloc=52.3MB, time=172.51
x[1] = -0.6708 1.9
h = 0.0001 0.005
y[1] (numeric) = 0.119007999438 0.714367137881
y[1] (closed_form) = 0.119017718137 0.714394279516
absolute error = 2.883e-05
relative error = 0.003981 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.319
Order of pole (given) = 0.5 0
NO 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=14047.2MB, alloc=52.3MB, time=173.10
x[1] = -0.6707 1.905
h = 0.0001 0.003
y[1] (numeric) = 0.118103785373 0.716483385471
y[1] (closed_form) = 0.118113276726 0.716509872829
absolute error = 2.814e-05
relative error = 0.003875 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.323
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6706 1.908
h = 0.001 0.001
y[1] (numeric) = 0.117576857599 0.717761186366
y[1] (closed_form) = 0.117586559472 0.717787503179
absolute error = 2.805e-05
relative error = 0.003856 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.325
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
memory used=14092.8MB, alloc=52.3MB, time=173.69
x[1] = -0.6696 1.909
h = 0.0001 0.004
y[1] (numeric) = 0.117806818274 0.718370683279
y[1] (closed_form) = 0.117816594491 0.718396881556
absolute error = 2.796e-05
relative error = 0.003841 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.327
Order of pole (given) = 0.5 0
NO 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=14138.5MB, alloc=52.3MB, time=174.28
x[1] = -0.6695 1.913
h = 0.003 0.006
y[1] (numeric) = 0.117090044959 0.720068984497
y[1] (closed_form) = 0.117099296816 0.720095393305
absolute error = 2.798e-05
relative error = 0.003836 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.33
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6665 1.919
h = 0.0001 0.005
y[1] (numeric) = 0.117209747178 0.723159939145
y[1] (closed_form) = 0.117219517936 0.723187277157
absolute error = 2.903e-05
relative error = 0.003963 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.337
Order of pole (given) = 0.5 0
NO 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=14184.2MB, alloc=52.3MB, time=174.87
x[1] = -0.6664 1.924
h = 0.0001 0.003
y[1] (numeric) = 0.11630001354 0.725283012571
y[1] (closed_form) = 0.116309555933 0.725309699966
absolute error = 2.834e-05
relative error = 0.003858 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.341
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6663 1.927
h = 0.001 0.001
y[1] (numeric) = 0.115769834544 0.726564955698
y[1] (closed_form) = 0.115779585976 0.726591472661
absolute error = 2.825e-05
relative error = 0.00384 %
Correct digits = 4
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
memory used=14229.9MB, alloc=52.3MB, time=175.46
x[1] = -0.6653 1.928
h = 0.001 0.003
y[1] (numeric) = 0.116000010729 0.727176923171
y[1] (closed_form) = 0.1160098358 0.727203321901
absolute error = 2.817e-05
relative error = 0.003825 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.345
Order of pole (given) = 0.5 0
NO 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=14275.7MB, alloc=52.3MB, time=176.06
x[1] = -0.6643 1.931
h = 0.0001 0.004
y[1] (numeric) = 0.115848735988 0.728631266068
y[1] (closed_form) = 0.115858401295 0.728657899442
absolute error = 2.833e-05
relative error = 0.00384 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.348
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] = -0.6642 1.935
h = 0.003 0.006
y[1] (numeric) = 0.115126691393 0.730336228511
y[1] (closed_form) = 0.115136115723 0.730362848412
absolute error = 2.824e-05
relative error = 0.003819 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.351
Order of pole (given) = 0.5 0
NO 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=14321.5MB, alloc=52.3MB, time=176.64
x[1] = -0.6612 1.941
h = 0.0001 0.005
y[1] (numeric) = 0.115243419758 0.733440497251
y[1] (closed_form) = 0.115253363538 0.733468039627
absolute error = 2.928e-05
relative error = 0.003944 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.358
Order of pole (given) = 0.5 0
NO 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=14367.2MB, alloc=52.3MB, time=177.24
x[1] = -0.6611 1.946
h = 0.0001 0.003
y[1] (numeric) = 0.114327442123 0.735571569634
y[1] (closed_form) = 0.114337156445 0.73559846562
absolute error = 2.860e-05
relative error = 0.003841 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.362
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.661 1.949
h = 0.001 0.001
y[1] (numeric) = 0.113793587559 0.736858364923
y[1] (closed_form) = 0.113803509223 0.736885090636
absolute error = 2.851e-05
relative error = 0.003823 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.365
Order of pole (given) = 0.5 0
NO 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=14413.0MB, alloc=52.3MB, time=177.84
x[1] = -0.66 1.95
h = 0.001 0.003
y[1] (numeric) = 0.114024061863 0.73747318362
y[1] (closed_form) = 0.114034056363 0.737499791462
absolute error = 2.842e-05
relative error = 0.003809 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.366
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.659 1.953
h = 0.0001 0.004
y[1] (numeric) = 0.113870531163 0.738933524669
y[1] (closed_form) = 0.113880367561 0.738960366485
absolute error = 2.859e-05
relative error = 0.003823 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.369
Order of pole (given) = 0.5 0
NO 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=14458.9MB, alloc=52.3MB, time=178.45
x[1] = -0.6589 1.957
h = 0.003 0.006
y[1] (numeric) = 0.113143546378 0.740644907127
y[1] (closed_form) = 0.113153143017 0.740671736386
absolute error = 2.849e-05
relative error = 0.003803 %
Correct digits = 4
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
memory used=14504.4MB, alloc=52.3MB, time=179.04
x[1] = -0.6559 1.963
h = 0.0001 0.005
y[1] (numeric) = 0.113257363342 0.743762430427
y[1] (closed_form) = 0.113267479937 0.743790175511
absolute error = 2.953e-05
relative error = 0.003925 %
Correct digits = 4
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] = -0.6558 1.968
h = 0.0001 0.003
y[1] (numeric) = 0.112335202507 0.745901481747
y[1] (closed_form) = 0.112345088586 0.74592858462
absolute error = 2.885e-05
relative error = 0.003824 %
Correct digits = 4
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
memory used=14550.1MB, alloc=52.3MB, time=179.64
x[1] = -0.6557 1.971
h = 0.001 0.001
y[1] (numeric) = 0.111797708613 0.747193116636
y[1] (closed_form) = 0.111807800358 0.747220049403
absolute error = 2.876e-05
relative error = 0.003807 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.386
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
memory used=14595.9MB, alloc=52.3MB, time=180.25
x[1] = -0.6547 1.972
h = 0.001 0.003
y[1] (numeric) = 0.112028489443 0.747810770581
y[1] (closed_form) = 0.112038653234 0.747837585839
absolute error = 2.868e-05
relative error = 0.003792 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.387
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6537 1.975
h = 0.0001 0.004
y[1] (numeric) = 0.111872735571 0.749277086273
y[1] (closed_form) = 0.1118827429 0.749304134833
absolute error = 2.884e-05
relative error = 0.003807 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.39
Order of pole (given) = 0.5 0
NO 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=14641.6MB, alloc=52.3MB, time=180.85
x[1] = -0.6536 1.979
h = 0.003 0.006
y[1] (numeric) = 0.111140858847 0.750994872422
y[1] (closed_form) = 0.111150627622 0.751021909324
absolute error = 2.875e-05
relative error = 0.003787 %
Correct digits = 4
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] = -0.6506 1.985
h = 0.0001 0.005
y[1] (numeric) = 0.111251825795 0.754125591163
y[1] (closed_form) = 0.111262114992 0.75415353732
absolute error = 2.978e-05
relative error = 0.003907 %
Correct digits = 4
memory used=14687.3MB, alloc=52.3MB, time=181.45
Radius of convergence (given) for eq 1 = 2.4
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6505 1.99
h = 0.0001 0.003
y[1] (numeric) = 0.110323541712 0.756272601336
y[1] (closed_form) = 0.11033359937 0.756299909414
absolute error = 2.910e-05
relative error = 0.003808 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.404
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
memory used=14733.0MB, alloc=52.3MB, time=182.05
x[1] = -0.6504 1.993
h = 0.001 0.001
y[1] (numeric) = 0.109782444222 0.757569063234
y[1] (closed_form) = 0.109792705891 0.757596201381
absolute error = 2.901e-05
relative error = 0.00379 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.407
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6494 1.994
h = 0.001 0.003
y[1] (numeric) = 0.1100135398 0.758189536604
y[1] (closed_form) = 0.110023872736 0.758216557602
absolute error = 2.893e-05
relative error = 0.003776 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.408
Order of pole (given) = 0.5 0
NO 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=14778.7MB, alloc=52.3MB, time=182.66
x[1] = -0.6484 1.997
h = 0.0001 0.004
y[1] (numeric) = 0.109855595028 0.759661803549
y[1] (closed_form) = 0.109865773118 0.75968905718
absolute error = 2.909e-05
relative error = 0.00379 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.411
Order of pole (given) = 0.5 0
NO 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=14824.4MB, alloc=52.3MB, time=183.26
x[1] = -0.6483 2.001
h = 0.003 0.006
y[1] (numeric) = 0.109118873944 0.761385977024
y[1] (closed_form) = 0.109128814676 0.761413219877
absolute error = 2.900e-05
relative error = 0.00377 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.415
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] = -0.6453 2.007
h = 0.0001 0.005
y[1] (numeric) = 0.109227051217 0.7645298325
y[1] (closed_form) = 0.1092375128 0.764557978115
absolute error = 3.003e-05
relative error = 0.003888 %
Correct digits = 4
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
memory used=14869.9MB, alloc=52.3MB, time=183.84
x[1] = -0.6452 2.012
h = 0.0001 0.003
y[1] (numeric) = 0.108292703011 0.766684781386
y[1] (closed_form) = 0.108302932065 0.766712293009
absolute error = 2.935e-05
relative error = 0.003791 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.426
Order of pole (given) = 0.5 0
NO 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=14915.7MB, alloc=52.3MB, time=184.42
x[1] = -0.6451 2.015
h = 0.001 0.001
y[1] (numeric) = 0.107748037163 0.767986057677
y[1] (closed_form) = 0.107758468594 0.768013399549
absolute error = 2.926e-05
relative error = 0.003773 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.428
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6441 2.016
h = 0.0001 0.004
y[1] (numeric) = 0.107979455536 0.768609334799
y[1] (closed_form) = 0.107989957465 0.768636559884
absolute error = 2.918e-05
relative error = 0.003759 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.43
Order of pole (given) = 0.5 0
NO 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=14961.4MB, alloc=52.3MB, time=185.00
x[1] = -0.644 2.02
h = 0.003 0.006
y[1] (numeric) = 0.107238797682 0.770338712222
y[1] (closed_form) = 0.107248791952 0.770366151256
absolute error = 2.920e-05
relative error = 0.003755 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.433
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.641 2.026
h = 0.0001 0.005
y[1] (numeric) = 0.107344465698 0.773493796395
y[1] (closed_form) = 0.107354981235 0.773522132665
absolute error = 3.022e-05
relative error = 0.00387 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.44
Order of pole (given) = 0.5 0
NO 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=15007.0MB, alloc=52.3MB, time=185.59
x[1] = -0.6409 2.031
h = 0.0001 0.003
y[1] (numeric) = 0.106404850186 0.775655491202
y[1] (closed_form) = 0.106415132318 0.775683196954
absolute error = 2.955e-05
relative error = 0.003774 %
Correct digits = 4
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
memory used=15052.8MB, alloc=52.3MB, time=186.17
x[1] = -0.6408 2.034
h = 0.001 0.001
y[1] (numeric) = 0.105857083517 0.7769608595
y[1] (closed_form) = 0.105867566633 0.776988395641
absolute error = 2.946e-05
relative error = 0.003757 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.446
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6398 2.035
h = 0.001 0.003
y[1] (numeric) = 0.106088752904 0.777586541535
y[1] (closed_form) = 0.106099305863 0.77761396119
absolute error = 2.938e-05
relative error = 0.003744 %
Correct digits = 4
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
memory used=15098.4MB, alloc=52.3MB, time=186.76
x[1] = -0.6388 2.038
h = 0.0001 0.004
y[1] (numeric) = 0.105926745302 0.779069795333
y[1] (closed_form) = 0.105937146369 0.779097446391
absolute error = 2.954e-05
relative error = 0.003757 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.451
Order of pole (given) = 0.5 0
NO 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=15144.1MB, alloc=52.3MB, time=187.35
x[1] = -0.6387 2.042
h = 0.003 0.006
y[1] (numeric) = 0.105181058771 0.780805754046
y[1] (closed_form) = 0.105191224669 0.780833395937
absolute error = 2.945e-05
relative error = 0.003738 %
Correct digits = 4
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] = -0.6357 2.048
h = 0.0001 0.005
y[1] (numeric) = 0.105284047394 0.783973867497
y[1] (closed_form) = 0.105294734919 0.784002400271
absolute error = 3.047e-05
relative error = 0.003852 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.461
Order of pole (given) = 0.5 0
NO 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=15189.8MB, alloc=52.3MB, time=187.92
x[1] = -0.6356 2.053
h = 0.0001 0.003
y[1] (numeric) = 0.104338475876 0.786143464099
y[1] (closed_form) = 0.104348929064 0.786171370362
absolute error = 2.980e-05
relative error = 0.003758 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.465
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] = -0.6355 2.056
h = 0.001 0.001
y[1] (numeric) = 0.103787205287 0.78745362367
y[1] (closed_form) = 0.103797857862 0.787481360512
absolute error = 2.971e-05
relative error = 0.003741 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.468
Order of pole (given) = 0.5 0
NO 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=15235.6MB, alloc=52.3MB, time=188.50
x[1] = -0.6345 2.057
h = 0.001 0.003
y[1] (numeric) = 0.104019212165 0.788082080781
y[1] (closed_form) = 0.104029933835 0.788109701497
absolute error = 2.963e-05
relative error = 0.003727 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.469
Order of pole (given) = 0.5 0
NO 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=15281.5MB, alloc=52.3MB, time=189.07
x[1] = -0.6335 2.06
h = 0.0001 0.004
y[1] (numeric) = 0.103855103497 0.78957121997
y[1] (closed_form) = 0.103865674827 0.789599071418
absolute error = 2.979e-05
relative error = 0.003741 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.472
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6334 2.064
h = 0.003 0.006
y[1] (numeric) = 0.103104705344 0.791313519538
y[1] (closed_form) = 0.103115042673 0.791341362655
absolute error = 2.970e-05
relative error = 0.003722 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.475
Order of pole (given) = 0.5 0
NO 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=15327.1MB, alloc=52.3MB, time=189.67
x[1] = -0.6304 2.07
h = 0.0001 0.005
y[1] (numeric) = 0.103205072064 0.794494604723
y[1] (closed_form) = 0.103215931345 0.794523332442
absolute error = 3.071e-05
relative error = 0.003833 %
Correct digits = 4
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
memory used=15372.8MB, alloc=52.3MB, time=190.24
x[1] = -0.6303 2.075
h = 0.0001 0.003
y[1] (numeric) = 0.102253601393 0.796672082849
y[1] (closed_form) = 0.102264225436 0.796700188021
absolute error = 3.005e-05
relative error = 0.003741 %
Correct digits = 4
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] = -0.6302 2.078
h = 0.001 0.001
y[1] (numeric) = 0.10169886076 0.797987021022
y[1] (closed_form) = 0.101709682614 0.798014956969
absolute error = 2.996e-05
relative error = 0.003724 %
Correct digits = 4
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
memory used=15418.4MB, alloc=52.3MB, time=190.89
x[1] = -0.6292 2.079
h = 0.001 0.003
y[1] (numeric) = 0.101931212691 0.798618237955
y[1] (closed_form) = 0.101942102902 0.798646058136
absolute error = 2.988e-05
relative error = 0.003711 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.49
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6282 2.082
h = 0.0001 0.004
y[1] (numeric) = 0.101765033334 0.80011323962
y[1] (closed_form) = 0.101775774736 0.800141289864
absolute error = 3.004e-05
relative error = 0.003724 %
Correct digits = 4
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=15464.1MB, alloc=52.3MB, time=191.46
x[1] = -0.6281 2.086
h = 0.003 0.006
y[1] (numeric) = 0.10100996868 0.801861863554
y[1] (closed_form) = 0.101020477239 0.801889906286
absolute error = 2.995e-05
relative error = 0.003705 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.497
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
memory used=15509.7MB, alloc=52.3MB, time=192.04
x[1] = -0.6251 2.092
h = 0.0001 0.005
y[1] (numeric) = 0.101107770039 0.805055863332
y[1] (closed_form) = 0.101118800842 0.805084784458
absolute error = 3.095e-05
relative error = 0.003815 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.503
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.625 2.097
h = 0.0001 0.003
y[1] (numeric) = 0.100150456305 0.807241202682
y[1] (closed_form) = 0.100161250997 0.807269505183
absolute error = 3.029e-05
relative error = 0.003724 %
Correct digits = 4
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
memory used=15555.5MB, alloc=52.3MB, time=192.61
x[1] = -0.6249 2.1
h = 0.001 0.001
y[1] (numeric) = 0.0995922790484 0.808560906776
y[1] (closed_form) = 0.0996032699943 0.808589040253
absolute error = 3.020e-05
relative error = 0.003707 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.51
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
memory used=15601.3MB, alloc=52.3MB, time=193.18
x[1] = -0.6239 2.101
h = 0.001 0.003
y[1] (numeric) = 0.0998249834329 0.809194868422
y[1] (closed_form) = 0.0998360420093 0.80922288649
absolute error = 3.012e-05
relative error = 0.003694 %
Correct digits = 4
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
x[1] = -0.6229 2.104
h = 0.0001 0.004
y[1] (numeric) = 0.0996567632995 0.810695709774
y[1] (closed_form) = 0.0996676745761 0.810723957236
absolute error = 3.028e-05
relative error = 0.003707 %
Correct digits = 4
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
memory used=15646.9MB, alloc=52.3MB, time=193.75
x[1] = -0.6228 2.108
h = 0.003 0.006
y[1] (numeric) = 0.098897076662 0.812450641565
y[1] (closed_form) = 0.0989077562439 0.81247888232
absolute error = 3.019e-05
relative error = 0.003689 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.518
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] = -0.6198 2.114
h = 0.0001 0.005
y[1] (numeric) = 0.0989923682753 0.815657499201
y[1] (closed_form) = 0.0990035703612 0.815686612213
absolute error = 3.119e-05
relative error = 0.003796 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.525
Order of pole (given) = 0.5 0
NO 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=15692.6MB, alloc=52.3MB, time=194.32
x[1] = -0.6197 2.119
h = 0.0001 0.003
y[1] (numeric) = 0.0980292668201 0.81785067945
y[1] (closed_form) = 0.0980402319504 0.817879177718
absolute error = 3.053e-05
relative error = 0.003707 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.529
Order of pole (given) = 0.5 0
NO 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=15738.3MB, alloc=52.3MB, time=194.90
x[1] = -0.6196 2.122
h = 0.001 0.001
y[1] (numeric) = 0.0974676859123 0.819175136778
y[1] (closed_form) = 0.0974788457581 0.819203466227
absolute error = 3.045e-05
relative error = 0.003691 %
Correct digits = 4
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
x[1] = -0.6186 2.123
h = 0.0001 0.004
y[1] (numeric) = 0.0977007499954 0.819811828167
y[1] (closed_form) = 0.0977119767546 0.819840042566
absolute error = 3.037e-05
relative error = 0.003678 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.533
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=15784.0MB, alloc=52.3MB, time=195.48
x[1] = -0.6185 2.127
h = 0.003 0.006
y[1] (numeric) = 0.0969373063412 0.821571899168
y[1] (closed_form) = 0.0969480412683 0.821600330361
absolute error = 3.039e-05
relative error = 0.003673 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.536
Order of pole (given) = 0.5 0
NO 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=15829.7MB, alloc=52.3MB, time=196.05
x[1] = -0.6155 2.133
h = 0.0001 0.005
y[1] (numeric) = 0.0970303292402 0.824789750284
y[1] (closed_form) = 0.0970415869423 0.824819048508
absolute error = 3.139e-05
relative error = 0.003779 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.543
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6154 2.138
h = 0.0001 0.003
y[1] (numeric) = 0.0960621965931 0.826989595368
y[1] (closed_form) = 0.0960732165892 0.827018282147
absolute error = 3.073e-05
relative error = 0.003691 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.547
Order of pole (given) = 0.5 0
NO 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=15875.5MB, alloc=52.3MB, time=196.64
x[1] = -0.6153 2.141
h = 0.001 0.001
y[1] (numeric) = 0.0954976555899 0.828318093939
y[1] (closed_form) = 0.0955088689896 0.828346612061
absolute error = 3.064e-05
relative error = 0.003675 %
Correct digits = 4
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
x[1] = -0.6143 2.142
h = 0.001 0.003
y[1] (numeric) = 0.0957310026985 0.82895712752
y[1] (closed_form) = 0.0957422823982 0.828985530891
absolute error = 3.056e-05
relative error = 0.003662 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.551
Order of pole (given) = 0.5 0
NO 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=15921.1MB, alloc=52.3MB, time=197.21
x[1] = -0.6133 2.145
h = 0.0001 0.004
y[1] (numeric) = 0.0955589942991 0.83046875146
y[1] (closed_form) = 0.0955701294618 0.830497383
absolute error = 3.072e-05
relative error = 0.003675 %
Correct digits = 4
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
memory used=15966.9MB, alloc=52.3MB, time=197.80
x[1] = -0.6132 2.149
h = 0.003 0.006
y[1] (numeric) = 0.0947907490165 0.832235322887
y[1] (closed_form) = 0.0948016545864 0.832263949192
absolute error = 3.063e-05
relative error = 0.003657 %
Correct digits = 4
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] = -0.6102 2.155
h = 0.0001 0.005
y[1] (numeric) = 0.0948813639239 0.835465927996
y[1] (closed_form) = 0.0948927924712 0.835495415324
absolute error = 3.162e-05
relative error = 0.003761 %
Correct digits = 4
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
memory used=16012.6MB, alloc=52.3MB, time=198.38
x[1] = -0.6101 2.16
h = 0.0001 0.003
y[1] (numeric) = 0.0939075448375 0.837673576752
y[1] (closed_form) = 0.093918734885 0.837702456441
absolute error = 3.097e-05
relative error = 0.003674 %
Correct digits = 4
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
memory used=16058.4MB, alloc=52.3MB, time=198.96
x[1] = -0.61 2.163
h = 0.001 0.001
y[1] (numeric) = 0.0933396605281 0.839006805319
y[1] (closed_form) = 0.0933510424751 0.839035516565
absolute error = 3.089e-05
relative error = 0.003658 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.571
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.609 2.164
h = 0.001 0.003
y[1] (numeric) = 0.0935733805899 0.839648541244
y[1] (closed_form) = 0.0935848281382 0.839677138095
absolute error = 3.080e-05
relative error = 0.003646 %
Correct digits = 4
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
memory used=16104.0MB, alloc=52.3MB, time=199.53
x[1] = -0.608 2.167
h = 0.0001 0.004
y[1] (numeric) = 0.0933994147861 0.841165940718
y[1] (closed_form) = 0.0934107192493 0.841194765071
absolute error = 3.096e-05
relative error = 0.003658 %
Correct digits = 4
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] = -0.6079 2.171
h = 0.003 0.006
y[1] (numeric) = 0.0926266718359 0.84293877322
y[1] (closed_form) = 0.0926377478276 0.842967593102
absolute error = 3.087e-05
relative error = 0.003641 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.579
Order of pole (given) = 0.5 0
NO 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=16149.7MB, alloc=52.3MB, time=200.11
x[1] = -0.6049 2.177
h = 0.0001 0.005
y[1] (numeric) = 0.0927149318255 0.846182076721
y[1] (closed_form) = 0.0927265309679 0.846211751685
absolute error = 3.186e-05
relative error = 0.003743 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.586
Order of pole (given) = 0.5 0
NO 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=16195.5MB, alloc=52.3MB, time=200.69
x[1] = -0.6048 2.182
h = 0.0001 0.003
y[1] (numeric) = 0.0917354795841 0.848397508777
y[1] (closed_form) = 0.091746839459 0.848426579866
absolute error = 3.121e-05
relative error = 0.003657 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.59
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.6047 2.185
h = 0.001 0.001
y[1] (numeric) = 0.0911642837094 0.849735454643
y[1] (closed_form) = 0.0911758339977 0.849764357508
absolute error = 3.113e-05
relative error = 0.003642 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.593
Order of pole (given) = 0.5 0
NO 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=16241.1MB, alloc=52.3MB, time=201.27
x[1] = -0.6037 2.186
h = 0.001 0.003
y[1] (numeric) = 0.0913983835441 0.850379878336
y[1] (closed_form) = 0.0914099987444 0.850408667161
absolute error = 3.104e-05
relative error = 0.00363 %
Correct digits = 4
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
memory used=16286.8MB, alloc=52.3MB, time=201.84
x[1] = -0.6027 2.189
h = 0.0001 0.004
y[1] (numeric) = 0.0912224885518 0.851903031041
y[1] (closed_form) = 0.0912339620996 0.851932046702
absolute error = 3.120e-05
relative error = 0.003642 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.597
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] = -0.6026 2.193
h = 0.003 0.006
y[1] (numeric) = 0.0904452902265 0.853682108071
y[1] (closed_form) = 0.0904565364148 0.853711120014
absolute error = 3.112e-05
relative error = 0.003624 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.6
Order of pole (given) = 0.5 0
NO 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=16332.6MB, alloc=52.3MB, time=202.42
x[1] = -0.5996 2.199
h = 0.0001 0.005
y[1] (numeric) = 0.0905312475244 0.85693805476
y[1] (closed_form) = 0.0905430170087 0.856967915908
absolute error = 3.210e-05
relative error = 0.003725 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.607
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5995 2.204
h = 0.0001 0.003
y[1] (numeric) = 0.0895462147208 0.859161249737
y[1] (closed_form) = 0.0895577441948 0.859190510737
absolute error = 3.145e-05
relative error = 0.003641 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.611
Order of pole (given) = 0.5 0
NO 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=16378.4MB, alloc=52.3MB, time=202.99
x[1] = -0.5994 2.207
h = 0.001 0.001
y[1] (numeric) = 0.0889717386077 0.860503900208
y[1] (closed_form) = 0.0889834570267 0.860532993207
absolute error = 3.136e-05
relative error = 0.003625 %
Correct digits = 4
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
memory used=16424.1MB, alloc=52.3MB, time=203.59
x[1] = -0.5984 2.208
h = 0.001 0.003
y[1] (numeric) = 0.0892062248938 0.861150997229
y[1] (closed_form) = 0.0892180075448 0.861179976542
absolute error = 3.128e-05
relative error = 0.003613 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.615
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] = -0.5974 2.211
h = 0.0001 0.004
y[1] (numeric) = 0.0890284285131 0.862679880988
y[1] (closed_form) = 0.0890400709252 0.862709086474
absolute error = 3.144e-05
relative error = 0.003625 %
Correct digits = 4
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
memory used=16469.7MB, alloc=52.3MB, time=204.17
x[1] = -0.5973 2.215
h = 0.003 0.006
y[1] (numeric) = 0.0882468165565 0.864465186003
y[1] (closed_form) = 0.0882582327118 0.864494388506
absolute error = 3.135e-05
relative error = 0.003608 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.622
Order of pole (given) = 0.5 0
NO 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=16515.5MB, alloc=52.3MB, time=204.76
x[1] = -0.5943 2.221
h = 0.0001 0.005
y[1] (numeric) = 0.0883305225606 0.867733721066
y[1] (closed_form) = 0.0883424621302 0.867763766965
absolute error = 3.233e-05
relative error = 0.003707 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.628
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] = -0.5942 2.226
h = 0.0001 0.003
y[1] (numeric) = 0.087339961109 0.869964658584
y[1] (closed_form) = 0.08735165995 0.869994108024
absolute error = 3.169e-05
relative error = 0.003624 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.633
Order of pole (given) = 0.5 0
NO 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=16561.2MB, alloc=52.3MB, time=205.32
x[1] = -0.5941 2.229
h = 0.001 0.001
y[1] (numeric) = 0.0867622356786 0.871312000975
y[1] (closed_form) = 0.0867741220135 0.871341282639
absolute error = 3.160e-05
relative error = 0.003609 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.635
Order of pole (given) = 0.5 0
NO 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=16606.9MB, alloc=52.3MB, time=205.89
x[1] = -0.5931 2.23
h = 0.0001 0.004
y[1] (numeric) = 0.0869971149576 0.871961757015
y[1] (closed_form) = 0.0870090648535 0.871990925347
absolute error = 3.152e-05
relative error = 0.003597 %
Correct digits = 4
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] = -0.593 2.234
h = 0.003 0.006
y[1] (numeric) = 0.0862119144786 0.873752136224
y[1] (closed_form) = 0.0862233875636 0.873781523703
absolute error = 3.155e-05
relative error = 0.003593 %
Correct digits = 4
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
memory used=16652.4MB, alloc=52.3MB, time=206.45
x[1] = -0.59 2.24
h = 0.0001 0.005
y[1] (numeric) = 0.0862935741123 0.877031437347
y[1] (closed_form) = 0.0863055707605 0.877061663273
absolute error = 3.252e-05
relative error = 0.00369 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.647
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] = -0.5899 2.245
h = 0.0001 0.003
y[1] (numeric) = 0.0852982029498 0.879268958042
y[1] (closed_form) = 0.0853099582267 0.879298590646
absolute error = 3.188e-05
relative error = 0.003609 %
Correct digits = 4
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
memory used=16698.0MB, alloc=52.3MB, time=207.02
x[1] = -0.5898 2.248
h = 0.001 0.001
y[1] (numeric) = 0.0847176493876 0.880620290715
y[1] (closed_form) = 0.0847295909203 0.880649755725
absolute error = 3.179e-05
relative error = 0.003594 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.654
Order of pole (given) = 0.5 0
NO 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=16743.8MB, alloc=52.3MB, time=207.60
x[1] = -0.5888 2.249
h = 0.001 0.003
y[1] (numeric) = 0.0849528406329 0.881272328978
y[1] (closed_form) = 0.0849648451522 0.88130168095
absolute error = 3.171e-05
relative error = 0.003582 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.655
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] = -0.5878 2.252
h = 0.0001 0.004
y[1] (numeric) = 0.0847715111642 0.882811796423
y[1] (closed_form) = 0.0847833780337 0.882841373351
absolute error = 3.187e-05
relative error = 0.003593 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.658
Order of pole (given) = 0.5 0
NO 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=16789.4MB, alloc=52.3MB, time=208.17
x[1] = -0.5877 2.256
h = 0.003 0.006
y[1] (numeric) = 0.0839817220152 0.884608594819
y[1] (closed_form) = 0.0839933646472 0.884638170115
absolute error = 3.178e-05
relative error = 0.003577 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.662
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
memory used=16835.0MB, alloc=52.3MB, time=208.75
x[1] = -0.5847 2.262
h = 0.0001 0.005
y[1] (numeric) = 0.0840612244958 0.88790038395
y[1] (closed_form) = 0.0840733907605 0.887930792
absolute error = 3.275e-05
relative error = 0.003672 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.668
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5846 2.267
h = 0.0001 0.003
y[1] (numeric) = 0.0830604197684 0.890145609878
y[1] (closed_form) = 0.0830723439876 0.890175428225
absolute error = 3.211e-05
relative error = 0.003592 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.673
Order of pole (given) = 0.5 0
NO 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=16880.7MB, alloc=52.3MB, time=209.33
x[1] = -0.5845 2.27
h = 0.001 0.001
y[1] (numeric) = 0.0824766735236 0.891501611245
y[1] (closed_form) = 0.0824887825788 0.891531262231
absolute error = 3.203e-05
relative error = 0.003577 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.675
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5835 2.271
h = 0.001 0.003
y[1] (numeric) = 0.0827122697471 0.892156282324
y[1] (closed_form) = 0.0827244411344 0.892185820623
absolute error = 3.195e-05
relative error = 0.003566 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.677
Order of pole (given) = 0.5 0
NO 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=16926.4MB, alloc=52.3MB, time=209.90
x[1] = -0.5825 2.274
h = 0.0001 0.004
y[1] (numeric) = 0.0825291164597 0.893701418405
y[1] (closed_form) = 0.0825411515585 0.893731181
absolute error = 3.210e-05
relative error = 0.003577 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.68
Order of pole (given) = 0.5 0
NO 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=16972.0MB, alloc=52.3MB, time=210.48
x[1] = -0.5824 2.278
h = 0.003 0.006
y[1] (numeric) = 0.0817350303609 0.895504397963
y[1] (closed_form) = 0.0817468422995 0.895534159627
absolute error = 3.202e-05
relative error = 0.003561 %
Correct digits = 4
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] = -0.5794 2.284
h = 0.0001 0.005
y[1] (numeric) = 0.0818124248133 0.898808621389
y[1] (closed_form) = 0.0818247604294 0.898839210177
absolute error = 3.298e-05
relative error = 0.003654 %
Correct digits = 4
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
memory used=17017.8MB, alloc=52.3MB, time=211.06
x[1] = -0.5793 2.289
h = 0.0001 0.003
y[1] (numeric) = 0.0808062365673 0.901061532183
y[1] (closed_form) = 0.080818329486 0.90109153485
absolute error = 3.235e-05
relative error = 0.003576 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.694
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
memory used=17063.5MB, alloc=52.3MB, time=211.64
x[1] = -0.5792 2.292
h = 0.001 0.001
y[1] (numeric) = 0.080219327443 0.902422189584
y[1] (closed_form) = 0.0802316037944 0.902452025126
absolute error = 3.226e-05
relative error = 0.003561 %
Correct digits = 4
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] = -0.5782 2.293
h = 0.001 0.003
y[1] (numeric) = 0.0804553348105 0.903079479539
y[1] (closed_form) = 0.0804676728483 0.903109202745
absolute error = 3.218e-05
relative error = 0.003549 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.698
Order of pole (given) = 0.5 0
NO 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=17109.2MB, alloc=52.3MB, time=212.22
x[1] = -0.5772 2.296
h = 0.0001 0.004
y[1] (numeric) = 0.0802703839785 0.904630262568
y[1] (closed_form) = 0.0802825870716 0.90466020941
absolute error = 3.234e-05
relative error = 0.003561 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.701
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] = -0.5771 2.3
h = 0.003 0.006
y[1] (numeric) = 0.0794720406542 0.906439406771
y[1] (closed_form) = 0.0794840216552 0.906469353372
absolute error = 3.225e-05
relative error = 0.003545 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.705
Order of pole (given) = 0.5 0
NO 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=17154.9MB, alloc=52.3MB, time=212.80
x[1] = -0.5741 2.306
h = 0.0001 0.005
y[1] (numeric) = 0.079547375444 0.909756011161
y[1] (closed_form) = 0.0795598801439 0.909786779316
absolute error = 3.321e-05
relative error = 0.003637 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.711
Order of pole (given) = 0.5 0
NO 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=17200.6MB, alloc=52.3MB, time=213.37
x[1] = -0.574 2.311
h = 0.0001 0.003
y[1] (numeric) = 0.0785358530965 0.912016586469
y[1] (closed_form) = 0.0785481144689 0.912046772049
absolute error = 3.258e-05
relative error = 0.003559 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.716
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] = -0.5739 2.314
h = 0.001 0.001
y[1] (numeric) = 0.0779458105197 0.913381887256
y[1] (closed_form) = 0.0779582539378 0.913411905951
absolute error = 3.250e-05
relative error = 0.003545 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.718
Order of pole (given) = 0.5 0
NO 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=17246.2MB, alloc=52.3MB, time=213.95
x[1] = -0.5729 2.315
h = 0.001 0.003
y[1] (numeric) = 0.0781822350729 0.914041782274
y[1] (closed_form) = 0.0781947395399 0.914071688982
absolute error = 3.242e-05
relative error = 0.003533 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.72
Order of pole (given) = 0.5 0
NO 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=17291.9MB, alloc=52.3MB, time=214.53
x[1] = -0.5719 2.318
h = 0.0001 0.004
y[1] (numeric) = 0.0779955125954 0.915598190689
y[1] (closed_form) = 0.0780078834442 0.915628320376
absolute error = 3.257e-05
relative error = 0.003544 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.723
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
x[1] = -0.5718 2.322
h = 0.003 0.006
y[1] (numeric) = 0.077192951271 0.917413483035
y[1] (closed_form) = 0.0772051010874 0.917443613158
absolute error = 3.249e-05
relative error = 0.003529 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.726
Order of pole (given) = 0.5 0
NO 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=17337.5MB, alloc=52.3MB, time=215.11
x[1] = -0.5688 2.328
h = 0.0001 0.005
y[1] (numeric) = 0.0772662740214 0.920742415437
y[1] (closed_form) = 0.0772789475347 0.920773361605
absolute error = 3.344e-05
relative error = 0.003619 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.733
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5687 2.333
h = 0.0001 0.003
y[1] (numeric) = 0.0762494663727 0.923010634922
y[1] (closed_form) = 0.0762618959498 0.923041002026
absolute error = 3.281e-05
relative error = 0.003543 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.737
Order of pole (given) = 0.5 0
NO 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=17383.2MB, alloc=52.3MB, time=215.70
x[1] = -0.5686 2.336
h = 0.001 0.001
y[1] (numeric) = 0.0756563194016 0.924380566466
y[1] (closed_form) = 0.0756689296531 0.924410766927
absolute error = 3.273e-05
relative error = 0.003529 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.74
Order of pole (given) = 0.5 0
NO 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=17428.8MB, alloc=52.3MB, time=216.28
x[1] = -0.5676 2.337
h = 0.0001 0.004
y[1] (numeric) = 0.0758931670605 0.925043052857
y[1] (closed_form) = 0.0759058377318 0.925073141679
absolute error = 3.265e-05
relative error = 0.003517 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.741
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5675 2.341
h = 0.003 0.006
y[1] (numeric) = 0.0750871754897 0.926863354443
y[1] (closed_form) = 0.0750993836261 0.926893664344
absolute error = 3.268e-05
relative error = 0.003514 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.745
Order of pole (given) = 0.5 0
NO 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=17474.5MB, alloc=52.3MB, time=216.86
x[1] = -0.5645 2.347
h = 0.0001 0.005
y[1] (numeric) = 0.0751586579239 0.930202833063
y[1] (closed_form) = 0.0751713898027 0.930233954313
absolute error = 3.362e-05
relative error = 0.003603 %
Correct digits = 4
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
memory used=17520.2MB, alloc=52.3MB, time=217.44
x[1] = -0.5644 2.352
h = 0.0001 0.003
y[1] (numeric) = 0.074137248752 0.932477553954
y[1] (closed_form) = 0.0741497361457 0.932508099127
absolute error = 3.300e-05
relative error = 0.003528 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.756
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5643 2.355
h = 0.001 0.001
y[1] (numeric) = 0.073541397657 0.933851424883
y[1] (closed_form) = 0.0735540645543 0.933881803609
absolute error = 3.291e-05
relative error = 0.003514 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.758
Order of pole (given) = 0.5 0
NO 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=17565.9MB, alloc=52.3MB, time=218.02
x[1] = -0.5633 2.356
h = 0.001 0.003
y[1] (numeric) = 0.0737785835126 0.934516136108
y[1] (closed_form) = 0.0737913102906 0.934546403486
absolute error = 3.283e-05
relative error = 0.003502 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.76
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] = -0.5623 2.359
h = 0.0001 0.004
y[1] (numeric) = 0.0735885656875 0.93608293471
y[1] (closed_form) = 0.0736011612787 0.936113423864
absolute error = 3.299e-05
relative error = 0.003513 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.763
Order of pole (given) = 0.5 0
NO 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=17611.6MB, alloc=52.3MB, time=218.60
x[1] = -0.5622 2.363
h = 0.003 0.006
y[1] (numeric) = 0.0727781856075 0.937909574292
y[1] (closed_form) = 0.0727905621073 0.937940065123
absolute error = 3.291e-05
relative error = 0.003498 %
Correct digits = 4
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=17657.2MB, alloc=52.3MB, time=219.18
x[1] = -0.5592 2.369
h = 0.0001 0.005
y[1] (numeric) = 0.072847743316 0.941261283939
y[1] (closed_form) = 0.072860643515 0.941292580718
absolute error = 3.385e-05
relative error = 0.003586 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.773
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5591 2.374
h = 0.0001 0.003
y[1] (numeric) = 0.071821138289 0.943543611788
y[1] (closed_form) = 0.0718337934324 0.943574335937
absolute error = 3.323e-05
relative error = 0.003511 %
Correct digits = 4
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
memory used=17702.7MB, alloc=52.3MB, time=219.76
x[1] = -0.559 2.377
h = 0.001 0.001
y[1] (numeric) = 0.0712222360616 0.944922090357
y[1] (closed_form) = 0.0712350693662 0.944952648307
absolute error = 3.314e-05
relative error = 0.003497 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.78
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
memory used=17748.5MB, alloc=52.3MB, time=220.34
x[1] = -0.558 2.378
h = 0.001 0.003
y[1] (numeric) = 0.0714598558855 0.945589367875
y[1] (closed_form) = 0.0714727484566 0.945619814822
absolute error = 3.306e-05
relative error = 0.003487 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.781
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
x[1] = -0.557 2.381
h = 0.0001 0.004
y[1] (numeric) = 0.0712681387576 0.947161731175
y[1] (closed_form) = 0.0712809014209 0.947192399245
absolute error = 3.322e-05
relative error = 0.003497 %
Correct digits = 4
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=17794.1MB, alloc=52.3MB, time=220.92
x[1] = -0.5569 2.385
h = 0.003 0.006
y[1] (numeric) = 0.0704536504184 0.948994472245
y[1] (closed_form) = 0.0704661950256 0.949025142637
absolute error = 3.314e-05
relative error = 0.003482 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.788
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
memory used=17839.8MB, alloc=52.3MB, time=221.50
x[1] = -0.5539 2.391
h = 0.0001 0.005
y[1] (numeric) = 0.0705213289827 0.952358361025
y[1] (closed_form) = 0.0705343972251 0.952389832022
absolute error = 3.408e-05
relative error = 0.003568 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.794
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5538 2.396
h = 0.0001 0.003
y[1] (numeric) = 0.0694895751997 0.954648275557
y[1] (closed_form) = 0.0695023978356 0.954679177335
absolute error = 3.346e-05
relative error = 0.003495 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.799
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
memory used=17885.5MB, alloc=52.3MB, time=222.08
x[1] = -0.5537 2.399
h = 0.001 0.001
y[1] (numeric) = 0.0688876498805 0.956031349188
y[1] (closed_form) = 0.0689006493501 0.956062085018
absolute error = 3.337e-05
relative error = 0.003482 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.801
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5527 2.4
h = 0.001 0.003
y[1] (numeric) = 0.0691257092602 0.956701179653
y[1] (closed_form) = 0.06913876739 0.956731804825
absolute error = 3.329e-05
relative error = 0.003471 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.803
Order of pole (given) = 0.5 0
NO 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=17931.2MB, alloc=52.3MB, time=222.66
x[1] = -0.5517 2.403
h = 0.0001 0.004
y[1] (numeric) = 0.0689323173515 0.958279086573
y[1] (closed_form) = 0.0689452468364 0.958309932217
absolute error = 3.345e-05
relative error = 0.003481 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.806
Order of pole (given) = 0.5 0
NO 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=17976.9MB, alloc=52.3MB, time=223.24
x[1] = -0.5516 2.407
h = 0.003 0.006
y[1] (numeric) = 0.06811375814 0.960117912705
y[1] (closed_form) = 0.0681264705959 0.960148761305
absolute error = 3.337e-05
relative error = 0.003466 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.809
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5486 2.413
h = 0.0001 0.005
y[1] (numeric) = 0.0681796024588 0.963493929092
y[1] (closed_form) = 0.0681928384658 0.96352557301
absolute error = 3.430e-05
relative error = 0.003551 %
Correct digits = 4
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
memory used=18022.5MB, alloc=52.3MB, time=223.82
x[1] = -0.5485 2.418
h = 0.0001 0.003
y[1] (numeric) = 0.0671427464458 0.965791410057
y[1] (closed_form) = 0.0671557363142 0.965822488134
absolute error = 3.368e-05
relative error = 0.003479 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.82
Order of pole (given) = 0.5 0
NO 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=18068.2MB, alloc=52.3MB, time=224.40
x[1] = -0.5484 2.421
h = 0.001 0.001
y[1] (numeric) = 0.0665378257325 0.967179066194
y[1] (closed_form) = 0.0665509911222 0.967209978576
absolute error = 3.360e-05
relative error = 0.003466 %
Correct digits = 4
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] = -0.5474 2.422
h = 0.001 0.003
y[1] (numeric) = 0.066776330145 0.96785143638
y[1] (closed_form) = 0.0667895535961 0.967882238449
absolute error = 3.352e-05
relative error = 0.003455 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.824
Order of pole (given) = 0.5 0
NO 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=18113.9MB, alloc=52.3MB, time=224.98
x[1] = -0.5464 2.425
h = 0.0001 0.004
y[1] (numeric) = 0.0665812876387 0.969434865966
y[1] (closed_form) = 0.0665943836923 0.969465887858
absolute error = 3.367e-05
relative error = 0.003465 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.827
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5463 2.429
h = 0.003 0.006
y[1] (numeric) = 0.0657586944874 0.97127976076
y[1] (closed_form) = 0.0657715745307 0.971310786231
absolute error = 3.359e-05
relative error = 0.003451 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.831
Order of pole (given) = 0.5 0
NO 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=18159.7MB, alloc=52.3MB, time=225.56
x[1] = -0.5433 2.435
h = 0.0001 0.005
y[1] (numeric) = 0.0658227487908 0.974667853593
y[1] (closed_form) = 0.0658361522815 0.974699669149
absolute error = 3.452e-05
relative error = 0.003534 %
Correct digits = 4
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
memory used=18205.4MB, alloc=52.3MB, time=226.15
x[1] = -0.5432 2.44
h = 0.0001 0.003
y[1] (numeric) = 0.0647808365111 0.976972880773
y[1] (closed_form) = 0.0647939933499 0.977004133834
absolute error = 3.391e-05
relative error = 0.003463 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.842
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5431 2.443
h = 0.001 0.001
y[1] (numeric) = 0.0641729477651 0.978365106883
y[1] (closed_form) = 0.064186278827 0.978396194506
absolute error = 3.383e-05
relative error = 0.00345 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.844
Order of pole (given) = 0.5 0
NO 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=18251.1MB, alloc=52.3MB, time=226.73
x[1] = -0.5421 2.444
h = 0.0001 0.004
y[1] (numeric) = 0.0644119025795 0.979040003681
y[1] (closed_form) = 0.0644252911117 0.979070981332
absolute error = 3.375e-05
relative error = 0.003439 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.846
Order of pole (given) = 0.5 0
NO 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=18296.7MB, alloc=52.3MB, time=227.32
x[1] = -0.542 2.448
h = 0.003 0.006
y[1] (numeric) = 0.0635860281573 0.98088984308
y[1] (closed_form) = 0.0635989677413 0.980921043373
absolute error = 3.378e-05
relative error = 0.003436 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.849
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] = -0.539 2.454
h = 0.0001 0.005
y[1] (numeric) = 0.0636484335617 0.984288269603
y[1] (closed_form) = 0.0636618965502 0.98432025552
absolute error = 3.470e-05
relative error = 0.003518 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.856
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=18342.4MB, alloc=52.3MB, time=227.90
x[1] = -0.5389 2.459
h = 0.0001 0.003
y[1] (numeric) = 0.0626021158374 0.986599716653
y[1] (closed_form) = 0.062615331707 0.986631142923
absolute error = 3.409e-05
relative error = 0.003448 %
Correct digits = 4
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
x[1] = -0.5388 2.462
h = 0.001 0.001
y[1] (numeric) = 0.0619916397309 0.98799583151
y[1] (closed_form) = 0.0620050287148 0.988027092549
absolute error = 3.401e-05
relative error = 0.003435 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.863
Order of pole (given) = 0.5 0
NO 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=18388.0MB, alloc=52.3MB, time=228.48
x[1] = -0.5378 2.463
h = 0.001 0.003
y[1] (numeric) = 0.0622309565687 0.988672898171
y[1] (closed_form) = 0.0622444025159 0.988704049524
absolute error = 3.393e-05
relative error = 0.003425 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.864
Order of pole (given) = 0.5 0
NO 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=18433.7MB, alloc=52.3MB, time=229.06
x[1] = -0.5368 2.466
h = 0.0001 0.004
y[1] (numeric) = 0.0620328407157 0.99026652981
y[1] (closed_form) = 0.0620461615534 0.990297899799
absolute error = 3.408e-05
relative error = 0.003435 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.867
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] = -0.5367 2.47
h = 0.003 0.006
y[1] (numeric) = 0.0612027662883 0.992122626381
y[1] (closed_form) = 0.0612158729826 0.992154001092
absolute error = 3.400e-05
relative error = 0.003421 %
Correct digits = 4
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
memory used=18479.4MB, alloc=52.3MB, time=229.64
x[1] = -0.5337 2.476
h = 0.0001 0.005
y[1] (numeric) = 0.0612634628473 0.995533035614
y[1] (closed_form) = 0.0612770928071 0.995565190818
absolute error = 3.492e-05
relative error = 0.003501 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.878
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
memory used=18525.3MB, alloc=52.3MB, time=230.22
x[1] = -0.5336 2.481
h = 0.0001 0.003
y[1] (numeric) = 0.0602121731613 0.99785199188
y[1] (closed_form) = 0.0602255555224 0.997883590723
absolute error = 3.432e-05
relative error = 0.003433 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.882
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] = -0.5335 2.484
h = 0.001 0.001
y[1] (numeric) = 0.0595987792095 0.999252653776
y[1] (closed_form) = 0.0596123334133 0.999284087647
absolute error = 3.423e-05
relative error = 0.00342 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.885
Order of pole (given) = 0.5 0
NO 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=18571.0MB, alloc=52.3MB, time=230.80
x[1] = -0.5325 2.485
h = 0.001 0.003
y[1] (numeric) = 0.0598385563145 0.999932223019
y[1] (closed_form) = 0.059852166904 0.999963547544
absolute error = 3.415e-05
relative error = 0.003409 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.886
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5315 2.488
h = 0.0001 0.004
y[1] (numeric) = 0.0596388574806 1.00153131834
y[1] (closed_form) = 0.0596523441647 1.00156286086
absolute error = 3.430e-05
relative error = 0.003419 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.889
Order of pole (given) = 0.5 0
NO 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=18616.7MB, alloc=52.3MB, time=231.38
x[1] = -0.5314 2.492
h = 0.003 0.006
y[1] (numeric) = 0.0588048525263 1.00339343724
y[1] (closed_form) = 0.0588181260627 1.00342498507
absolute error = 3.423e-05
relative error = 0.003405 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.893
Order of pole (given) = 0.5 0
NO 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=18662.4MB, alloc=52.3MB, time=231.96
x[1] = -0.5284 2.498
h = 0.0001 0.005
y[1] (numeric) = 0.0588638826295 1.00681577904
y[1] (closed_form) = 0.0588776792748 1.00684810229
absolute error = 3.514e-05
relative error = 0.003485 %
Correct digits = 4
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] = -0.5283 2.503
h = 0.0001 0.003
y[1] (numeric) = 0.0578076653917 1.00914222439
y[1] (closed_form) = 0.0578212139754 1.00917399454
absolute error = 3.454e-05
relative error = 0.003417 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.904
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
memory used=18708.0MB, alloc=52.3MB, time=232.54
x[1] = -0.5282 2.506
h = 0.001 0.001
y[1] (numeric) = 0.0571913800271 1.01054742087
y[1] (closed_form) = 0.0572050991958 1.0105790263
absolute error = 3.445e-05
relative error = 0.003404 %
Correct digits = 4
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
memory used=18753.9MB, alloc=52.3MB, time=233.12
x[1] = -0.5272 2.507
h = 0.001 0.003
y[1] (numeric) = 0.0574316224724 1.0112294799
y[1] (closed_form) = 0.0574453974563 1.01126097633
absolute error = 3.438e-05
relative error = 0.003394 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.908
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5262 2.51
h = 0.0001 0.004
y[1] (numeric) = 0.0572303635939 1.01283401843
y[1] (closed_form) = 0.0572440158618 1.01286573221
absolute error = 3.453e-05
relative error = 0.003403 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.911
Order of pole (given) = 0.5 0
NO 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=18799.4MB, alloc=52.3MB, time=233.70
x[1] = -0.5261 2.514
h = 0.003 0.006
y[1] (numeric) = 0.0563924633664 1.01470214337
y[1] (closed_form) = 0.0564059034747 1.01473386305
absolute error = 3.445e-05
relative error = 0.00339 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.914
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5231 2.52
h = 0.0001 0.005
y[1] (numeric) = 0.0564498687871 1.01813636794
y[1] (closed_form) = 0.0564638318304 1.018168858
absolute error = 3.536e-05
relative error = 0.003468 %
Correct digits = 4
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=18845.2MB, alloc=52.3MB, time=234.29
x[1] = -0.523 2.525
h = 0.0001 0.003
y[1] (numeric) = 0.0553887678835 1.0204702823
y[1] (closed_form) = 0.055402482419 1.02050222248
absolute error = 3.476e-05
relative error = 0.003401 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.925
Order of pole (given) = 0.5 0
NO 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=18891.0MB, alloc=52.3MB, time=234.86
x[1] = -0.5229 2.528
h = 0.001 0.001
y[1] (numeric) = 0.0547696172252 1.02188000092
y[1] (closed_form) = 0.0547835011017 1.02191177665
absolute error = 3.468e-05
relative error = 0.003388 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.928
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5219 2.529
h = 0.001 0.003
y[1] (numeric) = 0.0550103299855 1.02256453707
y[1] (closed_form) = 0.0550242691137 1.02259620413
absolute error = 3.460e-05
relative error = 0.003379 %
Correct digits = 4
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
memory used=18936.5MB, alloc=52.3MB, time=235.42
x[1] = -0.5209 2.532
h = 0.0001 0.004
y[1] (numeric) = 0.0548075336912 1.02417449845
y[1] (closed_form) = 0.0548213512786 1.02420638222
absolute error = 3.475e-05
relative error = 0.003388 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.932
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
memory used=18982.4MB, alloc=52.3MB, time=236.00
x[1] = -0.5208 2.536
h = 0.003 0.006
y[1] (numeric) = 0.0539657730289 1.02604861317
y[1] (closed_form) = 0.0539793794367 1.02608050342
absolute error = 3.467e-05
relative error = 0.003374 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.936
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
x[1] = -0.5178 2.542
h = 0.0001 0.005
y[1] (numeric) = 0.0540215949364 1.02949467106
y[1] (closed_form) = 0.0540357240888 1.02952732672
absolute error = 3.558e-05
relative error = 0.003451 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.943
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
memory used=19028.0MB, alloc=52.3MB, time=236.57
x[1] = -0.5177 2.547
h = 0.0001 0.003
y[1] (numeric) = 0.0529556537383 1.03183603438
y[1] (closed_form) = 0.052969533953 1.03186814335
absolute error = 3.498e-05
relative error = 0.003386 %
Correct digits = 4
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] = -0.5176 2.55
h = 0.001 0.001
y[1] (numeric) = 0.0523336635981 1.03325026274
y[1] (closed_form) = 0.052347711923 1.03328220753
absolute error = 3.490e-05
relative error = 0.003373 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.95
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
memory used=19073.8MB, alloc=52.3MB, time=237.15
x[1] = -0.5166 2.551
h = 0.0001 0.004
y[1] (numeric) = 0.0525748515518 1.03393726344
y[1] (closed_form) = 0.0525889545718 1.0339690999
absolute error = 3.482e-05
relative error = 0.003363 %
Correct digits = 4
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
memory used=19119.5MB, alloc=52.3MB, time=237.74
x[1] = -0.5165 2.555
h = 0.003 0.006
y[1] (numeric) = 0.0517299501054 1.03581625865
y[1] (closed_form) = 0.0517436171254 1.035848319
absolute error = 3.485e-05
relative error = 0.00336 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.954
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5135 2.561
h = 0.0001 0.005
y[1] (numeric) = 0.0517843013297 1.03927244473
y[1] (closed_form) = 0.0517984909758 1.03930526624
absolute error = 3.576e-05
relative error = 0.003436 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.961
Order of pole (given) = 0.5 0
NO 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=19165.2MB, alloc=52.3MB, time=238.29
x[1] = -0.5134 2.566
h = 0.0001 0.003
y[1] (numeric) = 0.0507141397044 1.04162014688
y[1] (closed_form) = 0.0507280800178 1.04165242442
absolute error = 3.516e-05
relative error = 0.003371 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.966
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
memory used=19210.9MB, alloc=52.3MB, time=238.85
x[1] = -0.5133 2.569
h = 0.001 0.001
y[1] (numeric) = 0.0500896723518 1.04303821376
y[1] (closed_form) = 0.0501037797235 1.04307032733
absolute error = 3.508e-05
relative error = 0.003359 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.968
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5123 2.57
h = 0.001 0.003
y[1] (numeric) = 0.0503312440148 1.04372733162
y[1] (closed_form) = 0.0503454056039 1.04375933714
absolute error = 3.500e-05
relative error = 0.003349 %
Correct digits = 4
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
memory used=19256.6MB, alloc=52.3MB, time=239.42
x[1] = -0.5113 2.573
h = 0.0001 0.004
y[1] (numeric) = 0.0501255821185 1.04534731218
y[1] (closed_form) = 0.0501396243238 1.04537953325
absolute error = 3.515e-05
relative error = 0.003358 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.973
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5112 2.577
h = 0.003 0.006
y[1] (numeric) = 0.0492766585238 1.04723248435
y[1] (closed_form) = 0.0492904913464 1.04726471294
absolute error = 3.507e-05
relative error = 0.003345 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.976
Order of pole (given) = 0.5 0
NO 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=19302.3MB, alloc=52.3MB, time=239.98
x[1] = -0.5082 2.583
h = 0.0001 0.005
y[1] (numeric) = 0.0493295018553 1.05070041312
y[1] (closed_form) = 0.0493438570833 1.050733398
absolute error = 3.597e-05
relative error = 0.00342 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.983
Order of pole (given) = 0.5 0
NO 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=19348.0MB, alloc=52.3MB, time=240.53
x[1] = -0.5081 2.588
h = 0.0001 0.003
y[1] (numeric) = 0.0482545795389 1.05305552756
y[1] (closed_form) = 0.0482686850338 1.0530879716
absolute error = 3.538e-05
relative error = 0.003356 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.987
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.508 2.591
h = 0.001 0.001
y[1] (numeric) = 0.0476273200808 1.05447808147
y[1] (closed_form) = 0.0476415914276 1.05451036181
absolute error = 3.529e-05
relative error = 0.003344 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.99
Order of pole (given) = 0.5 0
NO 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=19393.6MB, alloc=52.3MB, time=241.09
x[1] = -0.507 2.592
h = 0.001 0.003
y[1] (numeric) = 0.0478693759129 1.05516964084
y[1] (closed_form) = 0.0478837009329 1.05520181346
absolute error = 3.522e-05
relative error = 0.003334 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.991
Order of pole (given) = 0.5 0
NO 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=19439.3MB, alloc=52.3MB, time=241.65
x[1] = -0.506 2.595
h = 0.0001 0.004
y[1] (numeric) = 0.0476622399304 1.05679498693
y[1] (closed_form) = 0.0476764467022 1.05682737447
absolute error = 3.537e-05
relative error = 0.003343 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.994
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5059 2.599
h = 0.003 0.006
y[1] (numeric) = 0.046809553528 1.05868610299
y[1] (closed_form) = 0.0468235518756 1.0587184986
absolute error = 3.529e-05
relative error = 0.00333 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 2.998
Order of pole (given) = 0.5 0
NO 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=19485.0MB, alloc=52.3MB, time=242.21
x[1] = -0.5029 2.605
h = 0.0001 0.005
y[1] (numeric) = 0.0468609284707 1.06216572599
y[1] (closed_form) = 0.0468754489878 1.06219887305
absolute error = 3.619e-05
relative error = 0.003404 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.005
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5028 2.61
h = 0.0001 0.003
y[1] (numeric) = 0.0457812874122 1.06452823277
y[1] (closed_form) = 0.0457955578107 1.06456084211
absolute error = 3.560e-05
relative error = 0.003341 %
Correct digits = 4
memory used=19530.8MB, alloc=52.3MB, time=242.77
Radius of convergence (given) for eq 1 = 3.009
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5027 2.613
h = 0.001 0.001
y[1] (numeric) = 0.04515126081 1.0659552614
y[1] (closed_form) = 0.0451656958669 1.06598770732
absolute error = 3.551e-05
relative error = 0.003328 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.012
Order of pole (given) = 0.5 0
NO 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=19576.6MB, alloc=52.3MB, time=243.33
x[1] = -0.5017 2.614
h = 0.001 0.003
y[1] (numeric) = 0.045393805425 1.06664925001
y[1] (closed_form) = 0.0454082936174 1.06668158854
absolute error = 3.544e-05
relative error = 0.003319 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.013
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.5007 2.617
h = 0.0001 0.004
y[1] (numeric) = 0.0451852168521 1.06827994175
y[1] (closed_form) = 0.0451995879184 1.06831249455
absolute error = 3.558e-05
relative error = 0.003328 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.016
Order of pole (given) = 0.5 0
NO 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=19622.3MB, alloc=52.3MB, time=243.89
x[1] = -0.5006 2.621
h = 0.003 0.006
y[1] (numeric) = 0.0443288009437 1.07017698558
y[1] (closed_form) = 0.0443429645369 1.070209547
absolute error = 3.551e-05
relative error = 0.003315 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.02
Order of pole (given) = 0.5 0
NO 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=19668.1MB, alloc=52.3MB, time=244.44
x[1] = -0.4976 2.627
h = 0.0001 0.005
y[1] (numeric) = 0.0443787464433 1.07366825466
y[1] (closed_form) = 0.0443934319555 1.07370156274
absolute error = 3.640e-05
relative error = 0.003387 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.026
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4975 2.632
h = 0.0001 0.003
y[1] (numeric) = 0.0432944281111 1.07603813392
y[1] (closed_form) = 0.043308863134 1.07607090735
absolute error = 3.581e-05
relative error = 0.003325 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.031
Order of pole (given) = 0.5 0
NO 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=19713.7MB, alloc=52.3MB, time=245.00
x[1] = -0.4974 2.635
h = 0.001 0.001
y[1] (numeric) = 0.0426616590392 1.07746962498
y[1] (closed_form) = 0.0426762575393 1.07750223527
absolute error = 3.573e-05
relative error = 0.003313 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.033
Order of pole (given) = 0.5 0
NO 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=19759.5MB, alloc=52.3MB, time=245.56
x[1] = -0.4964 2.636
h = 0.001 0.003
y[1] (numeric) = 0.0429046969627 1.07816603067
y[1] (closed_form) = 0.0429193480671 1.0781985339
absolute error = 3.565e-05
relative error = 0.003304 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.035
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4954 2.639
h = 0.0001 0.004
y[1] (numeric) = 0.0426946770155 1.07980204826
y[1] (closed_form) = 0.0427092121029 1.07983476514
absolute error = 3.580e-05
relative error = 0.003313 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.038
Order of pole (given) = 0.5 0
NO 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=19805.1MB, alloc=52.3MB, time=246.12
x[1] = -0.4953 2.643
h = 0.003 0.006
y[1] (numeric) = 0.0418345645217 1.08170500379
y[1] (closed_form) = 0.0418488930798 1.08173772982
absolute error = 3.573e-05
relative error = 0.0033 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.041
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4923 2.649
h = 0.0001 0.005
y[1] (numeric) = 0.0418831189764 1.08520787115
y[1] (closed_form) = 0.0418979691887 1.0852413391
absolute error = 3.661e-05
relative error = 0.003371 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.048
Order of pole (given) = 0.5 0
NO 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=19850.8MB, alloc=52.3MB, time=246.68
x[1] = -0.4922 2.654
h = 0.0001 0.003
y[1] (numeric) = 0.0407941643674 1.08758510305
y[1] (closed_form) = 0.0408087637337 1.0876180394
absolute error = 3.603e-05
relative error = 0.00331 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.052
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=19896.6MB, alloc=52.3MB, time=247.24
x[1] = -0.4921 2.657
h = 0.001 0.001
y[1] (numeric) = 0.0401586772179 1.08902104429
y[1] (closed_form) = 0.0401734388929 1.08905381777
absolute error = 3.594e-05
relative error = 0.003298 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.055
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4911 2.658
h = 0.0001 0.004
y[1] (numeric) = 0.0404022128896 1.089719855
y[1] (closed_form) = 0.0404170266438 1.08975252175
absolute error = 3.587e-05
relative error = 0.003289 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.056
Order of pole (given) = 0.5 0
NO 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=19942.4MB, alloc=52.3MB, time=247.80
x[1] = -0.491 2.662
h = 0.003 0.006
y[1] (numeric) = 0.0395390923291 1.09162762754
y[1] (closed_form) = 0.0395534824392 1.09166051915
absolute error = 3.590e-05
relative error = 0.003287 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.06
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
memory used=19988.0MB, alloc=52.3MB, time=248.36
x[1] = -0.488 2.668
h = 0.0001 0.005
y[1] (numeric) = 0.0395863423672 1.09514042432
y[1] (closed_form) = 0.0396012539482 1.0951740538
absolute error = 3.679e-05
relative error = 0.003357 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.067
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] = -0.4879 2.673
h = 0.0001 0.003
y[1] (numeric) = 0.0384933422164 1.09752391471
y[1] (closed_form) = 0.03850800262 1.09755701519
absolute error = 3.620e-05
relative error = 0.003296 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.071
Order of pole (given) = 0.5 0
NO 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=20033.7MB, alloc=52.3MB, time=248.92
x[1] = -0.4878 2.676
h = 0.001 0.001
y[1] (numeric) = 0.037855481945 1.09896364475
y[1] (closed_form) = 0.0378703036576 1.09899658258
absolute error = 3.612e-05
relative error = 0.003285 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.074
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4868 2.677
h = 0.001 0.003
y[1] (numeric) = 0.0380994210974 1.09966452204
y[1] (closed_form) = 0.0381142944384 1.09969735341
absolute error = 3.604e-05
relative error = 0.003276 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.075
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
memory used=20079.4MB, alloc=52.3MB, time=249.48
x[1] = -0.4858 2.68
h = 0.0001 0.004
y[1] (numeric) = 0.0378867303374 1.1013103811
y[1] (closed_form) = 0.0379014896986 1.10134342497
absolute error = 3.619e-05
relative error = 0.003284 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.078
Order of pole (given) = 0.5 0
NO 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=20125.2MB, alloc=52.3MB, time=250.04
x[1] = -0.4857 2.684
h = 0.003 0.006
y[1] (numeric) = 0.037019755733 1.10322425117
y[1] (closed_form) = 0.0370343102954 1.10325730517
absolute error = 3.612e-05
relative error = 0.003272 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.082
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] = -0.4827 2.69
h = 0.0001 0.005
y[1] (numeric) = 0.0370656853158 1.10674855857
y[1] (closed_form) = 0.0370807610586 1.10678234579
absolute error = 3.700e-05
relative error = 0.003341 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.088
Order of pole (given) = 0.5 0
NO 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=20170.9MB, alloc=52.3MB, time=250.60
x[1] = -0.4826 2.695
h = 0.0001 0.003
y[1] (numeric) = 0.0359681241801 1.10913936531
y[1] (closed_form) = 0.0359829484148 1.10917262653
absolute error = 3.642e-05
relative error = 0.003281 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.093
Order of pole (given) = 0.5 0
NO 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=20216.7MB, alloc=52.3MB, time=251.16
x[1] = -0.4825 2.698
h = 0.001 0.001
y[1] (numeric) = 0.0353275906306 1.1105835231
y[1] (closed_form) = 0.0353425750282 1.11061662195
absolute error = 3.633e-05
relative error = 0.00327 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.095
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] = -0.4815 2.699
h = 0.001 0.003
y[1] (numeric) = 0.03557203571 1.11128678329
y[1] (closed_form) = 0.0355870712224 1.11131977601
absolute error = 3.626e-05
relative error = 0.003261 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.097
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
memory used=20262.3MB, alloc=52.3MB, time=251.72
x[1] = -0.4805 2.702
h = 0.0001 0.004
y[1] (numeric) = 0.0353579730032 1.11293791252
y[1] (closed_form) = 0.0353728956085 1.11297111711
absolute error = 3.640e-05
relative error = 0.003269 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.1
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4804 2.706
h = 0.003 0.006
y[1] (numeric) = 0.0344873941363 1.11485764891
y[1] (closed_form) = 0.0345021128661 1.11489086414
absolute error = 3.633e-05
relative error = 0.003257 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.103
Order of pole (given) = 0.5 0
NO 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=20308.1MB, alloc=52.3MB, time=252.28
x[1] = -0.4774 2.712
h = 0.0001 0.005
y[1] (numeric) = 0.03453204015 1.11839342005
y[1] (closed_form) = 0.0345472797565 1.1184273639
absolute error = 3.721e-05
relative error = 0.003325 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.11
Order of pole (given) = 0.5 0
NO 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=20353.8MB, alloc=52.3MB, time=252.83
x[1] = -0.4773 2.717
h = 0.0001 0.003
y[1] (numeric) = 0.0334299577199 1.12079152345
y[1] (closed_form) = 0.033444945501 1.12082494427
absolute error = 3.663e-05
relative error = 0.003266 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.115
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4772 2.72
h = 0.001 0.001
y[1] (numeric) = 0.0327867745042 1.12224009684
y[1] (closed_form) = 0.0328019213137 1.12227335556
absolute error = 3.655e-05
relative error = 0.003255 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.117
Order of pole (given) = 0.5 0
NO 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=20399.5MB, alloc=52.3MB, time=253.39
x[1] = -0.4762 2.721
h = 0.001 0.003
y[1] (numeric) = 0.0330317297127 1.12294572815
y[1] (closed_form) = 0.0330469271294 1.12297888107
absolute error = 3.647e-05
relative error = 0.003246 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.119
Order of pole (given) = 0.5 0
NO 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=20445.4MB, alloc=52.3MB, time=253.95
x[1] = -0.4752 2.724
h = 0.0001 0.004
y[1] (numeric) = 0.0328163152424 1.12460210821
y[1] (closed_form) = 0.0328314008126 1.12463547239
absolute error = 3.662e-05
relative error = 0.003254 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.122
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4751 2.728
h = 0.003 0.006
y[1] (numeric) = 0.0319421636228 1.12652769501
y[1] (closed_form) = 0.0319570462338 1.12656107033
absolute error = 3.654e-05
relative error = 0.003242 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.125
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
memory used=20491.0MB, alloc=52.3MB, time=254.51
x[1] = -0.4721 2.734
h = 0.0001 0.005
y[1] (numeric) = 0.031985562446 1.13007488334
y[1] (closed_form) = 0.0320009656174 1.13010898271
absolute error = 3.742e-05
relative error = 0.00331 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.132
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] = -0.472 2.739
h = 0.0001 0.003
y[1] (numeric) = 0.0308789979706 1.13248026374
y[1] (closed_form) = 0.0308941490123 1.13251384302
absolute error = 3.684e-05
relative error = 0.003252 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.136
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
memory used=20536.7MB, alloc=52.3MB, time=255.06
x[1] = -0.4719 2.742
h = 0.001 0.001
y[1] (numeric) = 0.0302331884366 1.13393324061
y[1] (closed_form) = 0.0302484973839 1.13396665807
absolute error = 3.676e-05
relative error = 0.00324 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.139
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
memory used=20582.5MB, alloc=52.3MB, time=255.62
x[1] = -0.4709 2.743
h = 0.001 0.003
y[1] (numeric) = 0.0304786578972 1.13464123136
y[1] (closed_form) = 0.0304940169499 1.13467454335
absolute error = 3.668e-05
relative error = 0.003232 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.14
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] = -0.4699 2.746
h = 0.0001 0.004
y[1] (numeric) = 0.0302619115913 1.13630284304
y[1] (closed_form) = 0.030277159846 1.13633636566
absolute error = 3.683e-05
relative error = 0.00324 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.144
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
memory used=20628.1MB, alloc=52.3MB, time=256.18
x[1] = -0.4698 2.75
h = 0.003 0.006
y[1] (numeric) = 0.0293842183789 1.13823426438
y[1] (closed_form) = 0.0293992645837 1.13826779864
absolute error = 3.676e-05
relative error = 0.003228 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.147
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=20673.9MB, alloc=52.3MB, time=256.74
x[1] = -0.4668 2.756
h = 0.0001 0.005
y[1] (numeric) = 0.0294264058922 1.14179282365
y[1] (closed_form) = 0.0294419723288 1.14182707743
absolute error = 3.762e-05
relative error = 0.003294 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.154
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4667 2.761
h = 0.0001 0.003
y[1] (numeric) = 0.0283153981866 1.14420546148
y[1] (closed_form) = 0.0283307122019 1.14423919809
absolute error = 3.705e-05
relative error = 0.003237 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.158
Order of pole (given) = 0.5 0
NO 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=20719.8MB, alloc=52.3MB, time=257.30
x[1] = -0.4666 2.764
h = 0.001 0.001
y[1] (numeric) = 0.0276669854231 1.14566282973
y[1] (closed_form) = 0.0276824562325 1.14569640481
absolute error = 3.697e-05
relative error = 0.003226 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.161
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4656 2.765
h = 0.0001 0.004
y[1] (numeric) = 0.0279129731814 1.14637316834
y[1] (closed_form) = 0.0279284936001 1.14640663827
absolute error = 3.689e-05
relative error = 0.003217 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.162
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
memory used=20765.4MB, alloc=52.3MB, time=257.86
x[1] = -0.4655 2.769
h = 0.003 0.006
y[1] (numeric) = 0.0270323974886 1.14830934399
y[1] (closed_form) = 0.0270475060687 1.14834303949
absolute error = 3.693e-05
relative error = 0.003215 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.166
Order of pole (given) = 0.5 0
NO 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=20811.1MB, alloc=52.3MB, time=258.41
x[1] = -0.4625 2.775
h = 0.0001 0.005
y[1] (numeric) = 0.027073435999 1.15187764032
y[1] (closed_form) = 0.0270890645717 1.15191205149
absolute error = 3.779e-05
relative error = 0.00328 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.172
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4624 2.78
h = 0.0001 0.003
y[1] (numeric) = 0.0259585483314 1.15429645715
y[1] (closed_form) = 0.0259739242073 1.15433035364
absolute error = 3.722e-05
relative error = 0.003224 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.177
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
memory used=20856.8MB, alloc=52.3MB, time=258.97
x[1] = -0.4623 2.783
h = 0.001 0.001
y[1] (numeric) = 0.025307860974 1.15575756508
y[1] (closed_form) = 0.025323392693 1.15579130026
absolute error = 3.714e-05
relative error = 0.003213 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.18
Order of pole (given) = 0.5 0
NO 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=20902.6MB, alloc=52.3MB, time=259.53
x[1] = -0.4613 2.784
h = 0.001 0.003
y[1] (numeric) = 0.0255542702654 1.15646992168
y[1] (closed_form) = 0.0255698511675 1.15650355198
absolute error = 3.706e-05
relative error = 0.003204 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.181
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4603 2.787
h = 0.0001 0.004
y[1] (numeric) = 0.0253350361243 1.1581412021
y[1] (closed_form) = 0.0253505081554 1.15817504191
absolute error = 3.721e-05
relative error = 0.003212 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.184
Order of pole (given) = 0.5 0
NO 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=20948.3MB, alloc=52.3MB, time=260.09
x[1] = -0.4602 2.791
h = 0.003 0.006
y[1] (numeric) = 0.0244507655353 1.16008339675
y[1] (closed_form) = 0.0244660371848 1.16011724909
absolute error = 3.714e-05
relative error = 0.0032 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.188
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4572 2.797
h = 0.0001 0.005
y[1] (numeric) = 0.0244906587496 1.16366297922
y[1] (closed_form) = 0.024506450041 1.16369754279
absolute error = 3.800e-05
relative error = 0.003265 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.194
Order of pole (given) = 0.5 0
NO 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=20993.9MB, alloc=52.3MB, time=260.64
x[1] = -0.4571 2.802
h = 0.0001 0.003
y[1] (numeric) = 0.0233713991795 1.16608901762
y[1] (closed_form) = 0.0233869375053 1.16612306938
absolute error = 3.743e-05
relative error = 0.003209 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.199
Order of pole (given) = 0.5 0
NO 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=21039.7MB, alloc=52.3MB, time=261.20
x[1] = -0.457 2.805
h = 0.001 0.001
y[1] (numeric) = 0.022718151023 1.16755449481
y[1] (closed_form) = 0.0227338441012 1.16758838554
absolute error = 3.735e-05
relative error = 0.003198 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.201
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] = -0.456 2.806
h = 0.001 0.003
y[1] (numeric) = 0.0229650860745 1.16826917801
y[1] (closed_form) = 0.0229808278503 1.16830296419
absolute error = 3.727e-05
relative error = 0.00319 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.203
Order of pole (given) = 0.5 0
NO 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=21085.3MB, alloc=52.3MB, time=261.76
x[1] = -0.455 2.809
h = 0.0001 0.004
y[1] (numeric) = 0.0227445759625 1.16994563593
y[1] (closed_form) = 0.0227602098825 1.169979631
absolute error = 3.742e-05
relative error = 0.003198 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.206
Order of pole (given) = 0.5 0
NO 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=21131.0MB, alloc=52.3MB, time=262.32
x[1] = -0.4549 2.813
h = 0.003 0.006
y[1] (numeric) = 0.0218568512271 1.17189362033
y[1] (closed_form) = 0.0218722856555 1.1719276284
absolute error = 3.735e-05
relative error = 0.003186 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.209
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4519 2.819
h = 0.0001 0.005
y[1] (numeric) = 0.0218956336486 1.17548444355
y[1] (closed_form) = 0.021911587357 1.17551915846
absolute error = 3.821e-05
relative error = 0.00325 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.216
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
memory used=21176.9MB, alloc=52.3MB, time=262.88
x[1] = -0.4518 2.824
h = 0.0001 0.003
y[1] (numeric) = 0.0207720397886 1.17791768409
y[1] (closed_form) = 0.0207877402744 1.17795189003
absolute error = 3.764e-05
relative error = 0.003195 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.221
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] = -0.4517 2.827
h = 0.001 0.001
y[1] (numeric) = 0.0201162532034 1.17938751856
y[1] (closed_form) = 0.0201321073618 1.17942156375
absolute error = 3.756e-05
relative error = 0.003184 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.223
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=21222.6MB, alloc=52.3MB, time=263.44
x[1] = -0.4507 2.828
h = 0.001 0.003
y[1] (numeric) = 0.0203637178466 1.18010451705
y[1] (closed_form) = 0.0203796202225 1.18013845801
absolute error = 3.748e-05
relative error = 0.003176 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.225
Order of pole (given) = 0.5 0
NO 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=21268.3MB, alloc=52.3MB, time=263.99
x[1] = -0.4497 2.831
h = 0.0001 0.004
y[1] (numeric) = 0.0201419507472 1.18178613368
y[1] (closed_form) = 0.0201577462713 1.18182028291
absolute error = 3.763e-05
relative error = 0.003183 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.228
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] = -0.4496 2.835
h = 0.003 0.006
y[1] (numeric) = 0.0192508017267 1.18373989212
y[1] (closed_form) = 0.0192663986426 1.18377405483
absolute error = 3.755e-05
relative error = 0.003172 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.231
Order of pole (given) = 0.5 0
NO 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=21314.0MB, alloc=52.3MB, time=264.55
x[1] = -0.4466 2.841
h = 0.0001 0.005
y[1] (numeric) = 0.0192885073957 1.18734191106
y[1] (closed_form) = 0.0193046232187 1.18737677624
absolute error = 3.841e-05
relative error = 0.003234 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.238
Order of pole (given) = 0.5 0
NO 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=21359.8MB, alloc=52.3MB, time=265.11
x[1] = -0.4465 2.846
h = 0.0001 0.003
y[1] (numeric) = 0.0181606164517 1.18978233435
y[1] (closed_form) = 0.0181764788067 1.18981669338
absolute error = 3.784e-05
relative error = 0.00318 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.242
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] = -0.4464 2.849
h = 0.001 0.001
y[1] (numeric) = 0.017502313565 1.19125651415
y[1] (closed_form) = 0.0175183285236 1.19129071272
absolute error = 3.776e-05
relative error = 0.00317 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.245
Order of pole (given) = 0.5 0
NO 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=21405.7MB, alloc=52.3MB, time=265.67
x[1] = -0.4454 2.85
h = 0.001 0.003
y[1] (numeric) = 0.0177503115603 1.19197581671
y[1] (closed_form) = 0.0177663742617 1.19200991135
absolute error = 3.769e-05
relative error = 0.003161 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.246
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] = -0.4444 2.853
h = 0.0001 0.004
y[1] (numeric) = 0.0175273062233 1.19366257336
y[1] (closed_form) = 0.0175432630656 1.19369687569
absolute error = 3.783e-05
relative error = 0.003169 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.25
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
memory used=21451.3MB, alloc=52.3MB, time=266.23
x[1] = -0.4443 2.857
h = 0.003 0.006
y[1] (numeric) = 0.0166327624562 1.19562209021
y[1] (closed_form) = 0.0166485215672 1.19565640646
absolute error = 3.776e-05
relative error = 0.003158 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.253
Order of pole (given) = 0.5 0
NO 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=21497.0MB, alloc=52.3MB, time=266.79
x[1] = -0.4413 2.863
h = 0.0001 0.005
y[1] (numeric) = 0.0166694249584 1.19923526009
y[1] (closed_form) = 0.0166857025932 1.1992702745
absolute error = 3.861e-05
relative error = 0.003219 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.26
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = -0.4412 2.868
h = 0.0001 0.003
y[1] (numeric) = 0.0155372737361 1.20168284681
y[1] (closed_form) = 0.0155532976687 1.20171735787
absolute error = 3.805e-05
relative error = 0.003166 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 3.264
Order of pole (given) = 0.5 0
NO 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=21542.7MB, alloc=52.3MB, time=267.34
x[1] = -0.4411 2.871
h = 0.001 0.001
y[1] (numeric) = 0.0148764764364 1.20316136004
y[1] (closed_form) = 0.0148926519141 1.20319571092
absolute error = 3.797e-05
relative error = 0.003155 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.267
Order of pole (given) = 0.5 0
NO 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=21588.4MB, alloc=52.3MB, time=267.90
x[1] = -0.4401 2.872
h = 0.001 0.003
y[1] (numeric) = 0.015125011474 1.20388295552
y[1] (closed_form) = 0.0151412342252 1.20391720279
absolute error = 3.790e-05
relative error = 0.003147 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 3.268
Order of pole (given) = 0.5 0
NO 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!
Maximum Time Reached before Solution Completed!
diff ( y , x , 1 ) = arctan ( sqrt ( 0.1 * x + 0.2 ) ) ;
Iterations = 754
Total Elapsed Time = 4 Minutes 28 Seconds
Expected Time Remaining = 0 Seconds
Optimized Time Remaining = 0 Seconds
Expected Total Time = 4 Minutes 28 Seconds
> quit
memory used=21621.0MB, alloc=52.3MB, time=268.28