|\^/| 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.
| Type ? for help.
#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(20.0) * exp(sqrt(c(0.1) * x + c(0.2))) * sqrt( c(0.1) * x + c(0.2)) - c(20.0) * exp(sqrt(c(0.1) * x + c(0.2))));
> end;
exact_soln_y := proc(x)
return c(20.0)*exp(sqrt(c(0.1)*x + c(0.2)))*sqrt(c(0.1)*x + c(0.2))
- c(20.0)*exp(sqrt(c(0.1)*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,
> 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, 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,
> 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, 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,
> 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, 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,
> 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, 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,
> 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, 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,
> 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, 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,
> 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, 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,
> 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 exp 1 $eq_no = 1
> array_tmp4[1] := exp(array_tmp3[1]);
> #emit pre add CONST FULL $eq_no = 1 i = 1
> array_tmp5[1] := array_const_0D0[1] + array_tmp4[1];
> #emit pre assign xxx $eq_no = 1 i = 1 $min_hdrs = 5
> if ( not array_y_set_initial[1,2]) then # if number 1
> if (1 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp5[1]) * (expt((glob_h) , c(1))) * c(factorial_3(0,1));
> if (2 <= ATS_MAX_TERMS) then # if number 3
> array_y[2] := temporary;
> array_y_higher[1,2] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(1);
> array_y_higher[2,1] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 2;
> #END ATOMHDR1
> #BEGIN ATOMHDR2
> #emit pre mult CONST - LINEAR $eq_no = 1 i = 2
> array_tmp1[2] := array_const_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 exp ID_FULL iii = 2 $eq_no = 1
> #emit pre exp 2 $eq_no = 1
> array_tmp4[2] := att(1,array_tmp4,array_tmp3,1);
> #emit pre add CONST FULL $eq_no = 1 i = 2
> array_tmp5[2] := array_tmp4[2];
> #emit pre assign xxx $eq_no = 1 i = 2 $min_hdrs = 5
> if ( not array_y_set_initial[1,3]) then # if number 1
> if (2 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp5[2]) * (expt((glob_h) , c(1))) * c(factorial_3(1,2));
> if (3 <= ATS_MAX_TERMS) then # if number 3
> array_y[3] := temporary;
> array_y_higher[1,3] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(2);
> array_y_higher[2,2] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 3;
> #END ATOMHDR2
> #BEGIN ATOMHDR3
> #emit pre sqrt ID_LINEAR iii = 3 $eq_no = 1
> array_tmp3[3] := 0;
> array_tmp3[3] := neg(ats(3,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2;
> #emit pre exp ID_FULL iii = 3 $eq_no = 1
> #emit pre exp 3 $eq_no = 1
> array_tmp4[3] := att(2,array_tmp4,array_tmp3,1);
> #emit pre add CONST FULL $eq_no = 1 i = 3
> array_tmp5[3] := array_tmp4[3];
> #emit pre assign xxx $eq_no = 1 i = 3 $min_hdrs = 5
> if ( not array_y_set_initial[1,4]) then # if number 1
> if (3 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp5[3]) * (expt((glob_h) , c(1))) * c(factorial_3(2,3));
> if (4 <= ATS_MAX_TERMS) then # if number 3
> array_y[4] := temporary;
> array_y_higher[1,4] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(3);
> array_y_higher[2,3] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 4;
> #END ATOMHDR3
> #BEGIN ATOMHDR4
> #emit pre sqrt ID_LINEAR iii = 4 $eq_no = 1
> array_tmp3[4] := 0;
> array_tmp3[4] := neg(ats(4,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2;
> #emit pre exp ID_FULL iii = 4 $eq_no = 1
> #emit pre exp 4 $eq_no = 1
> array_tmp4[4] := att(3,array_tmp4,array_tmp3,1);
> #emit pre add CONST FULL $eq_no = 1 i = 4
> array_tmp5[4] := array_tmp4[4];
> #emit pre assign xxx $eq_no = 1 i = 4 $min_hdrs = 5
> if ( not array_y_set_initial[1,5]) then # if number 1
> if (4 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp5[4]) * (expt((glob_h) , c(1))) * c(factorial_3(3,4));
> if (5 <= ATS_MAX_TERMS) then # if number 3
> array_y[5] := temporary;
> array_y_higher[1,5] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(4);
> array_y_higher[2,4] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 5;
> #END ATOMHDR4
> #BEGIN ATOMHDR5
> #emit pre sqrt ID_LINEAR iii = 5 $eq_no = 1
> array_tmp3[5] := 0;
> array_tmp3[5] := neg(ats(5,array_tmp3,array_tmp3,2)) / array_tmp3[1] /glob__2;
> #emit pre exp ID_FULL iii = 5 $eq_no = 1
> #emit pre exp 5 $eq_no = 1
> array_tmp4[5] := att(4,array_tmp4,array_tmp3,1);
> #emit pre add CONST FULL $eq_no = 1 i = 5
> array_tmp5[5] := array_tmp4[5];
> #emit pre assign xxx $eq_no = 1 i = 5 $min_hdrs = 5
> if ( not array_y_set_initial[1,6]) then # if number 1
> if (5 <= ATS_MAX_TERMS) then # if number 2
> temporary := c(array_tmp5[5]) * (expt((glob_h) , c(1))) * c(factorial_3(4,5));
> if (6 <= ATS_MAX_TERMS) then # if number 3
> array_y[6] := temporary;
> array_y_higher[1,6] := temporary;
> fi;# end if 3;
> temporary := c(temporary) / c(glob_h) * c(5);
> array_y_higher[2,5] := c(temporary);
> fi;# end if 2;
> fi;# end if 1;
> kkk := 6;
> #END ATOMHDR5
> #BEGIN OUTFILE3
> #Top Atomall While Loop-- outfile3
> while (kkk <= ATS_MAX_TERMS) do # do number 1
> #END OUTFILE3
> #BEGIN OUTFILE4
> #emit sqrt LINEAR $eq_no = 1
> array_tmp3[kkk] := 0;
> array_tmp3[kkk] := neg(ats(kkk,array_tmp3,array_tmp3,2)) /array_tmp3[1] / glob__2;
> #emit exp FULL $eq_no = 1
> array_tmp4[kkk] := att(kkk-1,array_tmp4,array_tmp3,1);
> #emit NOT FULL - FULL add $eq_no = 1
> array_tmp5[kkk] := array_tmp4[kkk];
> #emit assign $eq_no = 1
> order_d := 1;
> if (kkk + order_d <= ATS_MAX_TERMS) then # if number 1
> if ( not array_y_set_initial[1,kkk + order_d]) then # if number 2
> temporary := c(array_tmp5[kkk]) * expt((glob_h) , c(order_d)) * c(factorial_3((kkk - 1),(kkk + order_d - 1)));
> array_y[kkk + order_d] := c(temporary);
> array_y_higher[1,kkk + order_d] := c(temporary);
> term := kkk + order_d - 1;
> adj2 := kkk + order_d - 1;
> adj3 := 2;
> while ((term >= 1) and (term <= ATS_MAX_TERMS) and (adj3 < order_d + 1)) do # do number 1
> if (adj3 <= order_d + 1) then # if number 3
> if (adj2 > 0) then # if number 4
> temporary := c(temporary) / c(glob_h) * c(adj2);
> else
> temporary := c(temporary);
> fi;# end if 4;
> array_y_higher[adj3,term] := c(temporary);
> fi;# end if 3;
> term := term - 1;
> adj2 := adj2 - 1;
> adj3 := adj3 + 1;
> od;# end do number 1
> fi;# end if 2
> fi;# end if 1;
> kkk := kkk + 1;
> od;# end do number 1;
> #BOTTOM ATOMALL
> #END OUTFILE4
> #BEGIN OUTFILE5
> #BOTTOM ATOMALL ???
> end;
atomall := proc()
local kkk, order_d, adj2, adj3, temporary, term;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_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, 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] := exp(array_tmp3[1]);
array_tmp5[1] := array_const_0D0[1] + array_tmp4[1];
if not array_y_set_initial[1, 2] then
if 1 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[1])*expt(glob_h, c(1))*c(factorial_3(0, 1));
if 2 <= ATS_MAX_TERMS then
array_y[2] := temporary; array_y_higher[1, 2] := temporary
end if;
temporary := c(temporary)*c(1)/c(glob_h);
array_y_higher[2, 1] := c(temporary)
end if
end if;
kkk := 2;
array_tmp1[2] := array_const_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] := att(1, array_tmp4, array_tmp3, 1);
array_tmp5[2] := array_tmp4[2];
if not array_y_set_initial[1, 3] then
if 2 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[2])*expt(glob_h, c(1))*c(factorial_3(1, 2));
if 3 <= ATS_MAX_TERMS then
array_y[3] := temporary; array_y_higher[1, 3] := temporary
end if;
temporary := c(temporary)*c(2)/c(glob_h);
array_y_higher[2, 2] := c(temporary)
end if
end if;
kkk := 3;
array_tmp3[3] := 0;
array_tmp3[3] :=
neg(ats(3, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2);
array_tmp4[3] := att(2, array_tmp4, array_tmp3, 1);
array_tmp5[3] := array_tmp4[3];
if not array_y_set_initial[1, 4] then
if 3 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[3])*expt(glob_h, c(1))*c(factorial_3(2, 3));
if 4 <= ATS_MAX_TERMS then
array_y[4] := temporary; array_y_higher[1, 4] := temporary
end if;
temporary := c(temporary)*c(3)/c(glob_h);
array_y_higher[2, 3] := c(temporary)
end if
end if;
kkk := 4;
array_tmp3[4] := 0;
array_tmp3[4] :=
neg(ats(4, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2);
array_tmp4[4] := att(3, array_tmp4, array_tmp3, 1);
array_tmp5[4] := array_tmp4[4];
if not array_y_set_initial[1, 5] then
if 4 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[4])*expt(glob_h, c(1))*c(factorial_3(3, 4));
if 5 <= ATS_MAX_TERMS then
array_y[5] := temporary; array_y_higher[1, 5] := temporary
end if;
temporary := c(temporary)*c(4)/c(glob_h);
array_y_higher[2, 4] := c(temporary)
end if
end if;
kkk := 5;
array_tmp3[5] := 0;
array_tmp3[5] :=
neg(ats(5, array_tmp3, array_tmp3, 2))/(array_tmp3[1]*glob__2);
array_tmp4[5] := att(4, array_tmp4, array_tmp3, 1);
array_tmp5[5] := array_tmp4[5];
if not array_y_set_initial[1, 6] then
if 5 <= ATS_MAX_TERMS then
temporary :=
c(array_tmp5[5])*expt(glob_h, c(1))*c(factorial_3(4, 5));
if 6 <= ATS_MAX_TERMS then
array_y[6] := temporary; array_y_higher[1, 6] := temporary
end if;
temporary := c(temporary)*c(5)/c(glob_h);
array_y_higher[2, 5] := c(temporary)
end if
end if;
kkk := 6;
while kkk <= ATS_MAX_TERMS do
array_tmp3[kkk] := 0;
array_tmp3[kkk] := neg(ats(kkk, array_tmp3, array_tmp3, 2))/(
array_tmp3[1]*glob__2);
array_tmp4[kkk] := att(kkk - 1, array_tmp4, array_tmp3, 1);
array_tmp5[kkk] := array_tmp4[kkk];
order_d := 1;
if kkk + order_d <= ATS_MAX_TERMS then
if not array_y_set_initial[1, kkk + order_d] then
temporary := c(array_tmp5[kkk])*expt(glob_h, c(order_d))*
c(factorial_3(kkk - 1, kkk + order_d - 1));
array_y[kkk + order_d] := c(temporary);
array_y_higher[1, kkk + order_d] := c(temporary);
term := kkk + order_d - 1;
adj2 := kkk + order_d - 1;
adj3 := 2;
while
1 <= term and term <= ATS_MAX_TERMS and adj3 < order_d + 1
do
if adj3 <= order_d + 1 then
if 0 < adj2 then
temporary := c(temporary)*c(adj2)/c(glob_h)
else temporary := c(temporary)
end if;
array_y_higher[adj3, term] := c(temporary)
end if;
term := term - 1;
adj2 := adj2 - 1;
adj3 := adj3 + 1
end do
end if
end if;
kkk := kkk + 1
end do
end proc
# End Function number 12
#END OUTFILE5
# Begin Function number 12
> main := proc()
> #BEGIN OUTFIEMAIN
> local d1,d2,d3,d4,est_err_2,niii,done_once,max_terms,display_max,
> term,ord,order_diff,term_no,html_log_file,iiif,jjjf,
> rows,r_order,sub_iter,calc_term,iii,temp_sum,current_iter,
> x_start,x_end
> ,it,last_min_pole_est, opt_iter, tmp,subiter, est_needed_step_err,estimated_step_error,min_value,est_answer,found_h,repeat_it;
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
> #Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
> #Bottom Generate Globals Decl
> #BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_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,
> 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:=16;
> 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:= 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[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);
> 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/exp_sqrtpostcpx.cpx#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = exp ( sqrt ( 0.1 * x + 0.2 ) ) ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=16;");
> 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 := 2.1 + 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,"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,"");
> omniout_str(ALWAYS,"#END SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN OVERRIDE BLOCK");
> omniout_str(ALWAYS,"glob_desired_digits_correct:=8;");
> omniout_str(ALWAYS,"glob_max_minutes:=(3.0);");
> omniout_str(ALWAYS,"glob_subiter_method:=3;");
> omniout_str(ALWAYS,"glob_max_iter:=10000;");
> omniout_str(ALWAYS,"glob_upper_ratio_limit:=c(1.000001);");
> omniout_str(ALWAYS,"glob_lower_ratio_limit:=c(0.999999);");
> omniout_str(ALWAYS,"glob_look_poles:=true;");
> omniout_str(ALWAYS,"glob_h:=c(0.001);");
> omniout_str(ALWAYS,"glob_display_interval:=c(0.01);");
> omniout_str(ALWAYS,"#END OVERRIDE BLOCK");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN USER DEF BLOCK");
> omniout_str(ALWAYS,"exact_soln_y := proc(x)");
> omniout_str(ALWAYS,"return(c(20.0) * exp(sqrt(c(0.1) * x + c(0.2))) * sqrt( c(0.1) * x + c(0.2)) - c(20.0) * exp(sqrt(c(0.1) * 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 := 2.1 + 0.1 * I;
> x_end := 99.0 + 99.0 * I;
> array_y_init[0 + 1] := exact_soln_y(x_start);
> glob_look_poles := true;
> glob_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 ) = exp ( 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,"2017-11-26T14:48:20-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"exp_sqrt")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = exp ( 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,"exp_sqrt diffeq.mxt")
> ;
> logitem_str(html_log_file,"exp_sqrt maple results")
> ;
> logitem_str(html_log_file,"OK - 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, 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 := 16;
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 := 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[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);
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/exp_sqrtpostcpx.cpx#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = exp ( sqrt ( 0.1 \
* x + 0.2 ) ) ; ");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=16;");
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 := 2.1 + 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, "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, "");
omniout_str(ALWAYS, "#END SECOND INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN OVERRIDE BLOCK");
omniout_str(ALWAYS, "glob_desired_digits_correct:=8;");
omniout_str(ALWAYS, "glob_max_minutes:=(3.0);");
omniout_str(ALWAYS, "glob_subiter_method:=3;");
omniout_str(ALWAYS, "glob_max_iter:=10000;");
omniout_str(ALWAYS, "glob_upper_ratio_limit:=c(1.000001);");
omniout_str(ALWAYS, "glob_lower_ratio_limit:=c(0.999999);");
omniout_str(ALWAYS, "glob_look_poles:=true;");
omniout_str(ALWAYS, "glob_h:=c(0.001);");
omniout_str(ALWAYS, "glob_display_interval:=c(0.01);");
omniout_str(ALWAYS, "#END OVERRIDE BLOCK");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN USER DEF BLOCK");
omniout_str(ALWAYS, "exact_soln_y := proc(x)");
omniout_str(ALWAYS, "return(c(20.0) * exp(sqrt(c(0.1) * x + c(0.2))) \
* sqrt( c(0.1) * x + c(0.2)) - c(20.0) * exp(sqrt(c(0.1) * 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(0.10*10^101);
glob_larger_float := c(0.11*10^101);
glob_almost_1 := c(0.99);
x_start := 2.1 + 0.1*I;
x_end := 99.0 + 99.0*I;
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_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 ) = exp ( 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, "2017-11-26T14:48:20-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"exp_sqrt");
logitem_str(html_log_file, "diff ( y , x , 1 ) = ex\
p ( 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, "exp_sqrt diffeq.mxt");
logitem_str(html_log_file, "exp_sqrt maple results");
logitem_str(html_log_file, "OK - 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=3.9MB, alloc=40.3MB, time=0.08
##############ECHO OF PROBLEM#################
##############temp/exp_sqrtpostcpx.cpx#################
diff ( y , x , 1 ) = exp ( sqrt ( 0.1 * x + 0.2 ) ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=16;
max_terms:=40;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 2.1 + 0.1 * I;
x_end := 99.0 + 99.0 * I;
array_y_init[0 + 1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_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(20.0) * exp(sqrt(c(0.1) * x + c(0.2))) * sqrt( c(0.1) * x + c(0.2)) - c(20.0) * exp(sqrt(c(0.1) * 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
x[1] = 2.1 0.1
h = 0.0001 0.005
y[1] (numeric) = -13.6478158913 0.189708430568
y[1] (closed_form) = -13.6478158913 0.189708430568
absolute error = 0
relative error = 0 %
Correct digits = 14
Radius of convergence (given) for eq 1 = 4.101
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1001 0.105
h = 0.0001 0.003
y[1] (numeric) = -13.6477002463 0.199195441912
y[1] (closed_form) = -13.6477020967 0.199195523981
absolute error = 1.852e-06
relative error = 1.357e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 4.101
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=32.6MB, alloc=40.3MB, time=0.44
x[1] = 2.1002 0.108
h = 0.001 0.001
y[1] (numeric) = -13.6475571947 0.204888369796
y[1] (closed_form) = -13.6475597108 0.20488849917
absolute error = 2.519e-06
relative error = 1.846e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 4.102
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1012 0.109
h = 0.001 0.003
y[1] (numeric) = -13.6456760516 0.206801508724
y[1] (closed_form) = -13.645678567 0.206801786188
absolute error = 2.531e-06
relative error = 1.854e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 4.103
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] = 2.1022 0.112
h = 0.0001 0.004
y[1] (numeric) = -13.6438271978 0.212509523451
y[1] (closed_form) = -13.6438303035 0.212510248097
absolute error = 3.189e-06
relative error = 2.337e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 4.104
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1023 0.116
h = 0.003 0.006
y[1] (numeric) = -13.6437038094 0.22010094267
y[1] (closed_form) = -13.643708099 0.220101732342
absolute error = 4.362e-06
relative error = 3.196e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.104
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1053 0.122
h = 0.0001 0.005
y[1] (numeric) = -13.6381145233 0.23153723367
y[1] (closed_form) = -13.6381207985 0.231540699054
absolute error = 7.168e-06
relative error = 5.255e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.107
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=79.0MB, alloc=44.3MB, time=1.05
x[1] = 2.1054 0.127
h = 0.0001 0.003
y[1] (numeric) = -13.6380150694 0.24102857439
y[1] (closed_form) = -13.638023195 0.241032123444
absolute error = 8.867e-06
relative error = 6.501e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.107
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1055 0.13
h = 0.001 0.001
y[1] (numeric) = -13.6378817002 0.246724232066
y[1] (closed_form) = -13.6378904911 0.246727829043
absolute error = 9.498e-06
relative error = 6.964e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.108
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
x[1] = 2.1065 0.131
h = 0.001 0.003
y[1] (numeric) = -13.6360030092 0.248641426867
y[1] (closed_form) = -13.6360117993 0.248645171891
absolute error = 9.555e-06
relative error = 7.006e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.109
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
x[1] = 2.1075 0.134
h = 0.0001 0.004
y[1] (numeric) = -13.6341631148 0.254355101328
y[1] (closed_form) = -13.6341724947 0.254359293966
absolute error = 1.027e-05
relative error = 7.534e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.11
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
x[1] = 2.1076 0.138
h = 0.003 0.006
y[1] (numeric) = -13.6340526604 0.261950055306
y[1] (closed_form) = -13.6340632237 0.261954314073
absolute error = 1.139e-05
relative error = 8.352e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.11
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=125.2MB, alloc=44.3MB, time=1.65
x[1] = 2.1106 0.144
h = 0.0001 0.005
y[1] (numeric) = -13.6284804857 0.273400923819
y[1] (closed_form) = -13.6284930315 0.273407859406
absolute error = 1.434e-05
relative error = 0.0001052 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.113
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1107 0.149
h = 0.0001 0.003
y[1] (numeric) = -13.6283972149 0.282896607882
y[1] (closed_form) = -13.6284116105 0.282903628865
absolute error = 1.602e-05
relative error = 0.0001175 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.113
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1108 0.152
h = 0.001 0.001
y[1] (numeric) = -13.6282735225 0.28859500373
y[1] (closed_form) = -13.6282885832 0.288602073251
absolute error = 1.664e-05
relative error = 0.0001221 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.114
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1118 0.153
h = 0.001 0.003
y[1] (numeric) = -13.6263972791 0.290516255551
y[1] (closed_form) = -13.6264123389 0.290523473075
absolute error = 1.670e-05
relative error = 0.0001225 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.115
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] = 2.1128 0.156
h = 0.0001 0.004
y[1] (numeric) = -13.6245663363 0.296235596581
y[1] (closed_form) = -13.6245819851 0.296243262143
absolute error = 1.743e-05
relative error = 0.0001279 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.116
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
memory used=171.6MB, alloc=44.3MB, time=2.26
x[1] = 2.1129 0.16
h = 0.003 0.006
y[1] (numeric) = -13.6244688087 0.303834096511
y[1] (closed_form) = -13.6244856406 0.303841829299
absolute error = 1.852e-05
relative error = 0.0001359 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.116
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] = 2.1159 0.166
h = 0.0001 0.005
y[1] (numeric) = -13.6189137266 0.315299554433
y[1] (closed_form) = -13.618932538 0.31530996511
absolute error = 2.150e-05
relative error = 0.0001578 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.119
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
x[1] = 2.116 0.171
h = 0.0001 0.003
y[1] (numeric) = -13.6188466299 0.324799595806
y[1] (closed_form) = -13.6188672904 0.324810093595
absolute error = 2.317e-05
relative error = 0.0001701 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.12
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] = 2.1161 0.174
h = 0.001 0.001
y[1] (numeric) = -13.618732609 0.330500738123
y[1] (closed_form) = -13.6187539344 0.330511285061
absolute error = 2.379e-05
relative error = 0.0001746 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.12
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] = 2.1171 0.175
h = 0.001 0.003
y[1] (numeric) = -13.6168588086 0.332426048057
y[1] (closed_form) = -13.6168801329 0.332436742952
absolute error = 2.386e-05
relative error = 0.0001751 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.121
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=218.0MB, alloc=44.3MB, time=2.86
x[1] = 2.1181 0.178
h = 0.0001 0.004
y[1] (numeric) = -13.6150368093 0.338151062383
y[1] (closed_form) = -13.6150587221 0.338162205733
absolute error = 2.458e-05
relative error = 0.0001805 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.122
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] = 2.1182 0.182
h = 0.003 0.006
y[1] (numeric) = -13.6149522013 0.345753119349
y[1] (closed_form) = -13.6149752968 0.345764331012
absolute error = 2.567e-05
relative error = 0.0001885 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.122
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] = 2.1212 0.188
h = 0.0001 0.005
y[1] (numeric) = -13.6094141931 0.357233178332
y[1] (closed_form) = -13.6094392648 0.357247068918
absolute error = 2.866e-05
relative error = 0.0002105 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.125
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1213 0.193
h = 0.0001 0.003
y[1] (numeric) = -13.6093632616 0.366737590844
y[1] (closed_form) = -13.6093901818 0.366751570245
absolute error = 3.033e-05
relative error = 0.0002228 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.126
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1214 0.196
h = 0.001 0.001
y[1] (numeric) = -13.6092589066 0.372441487845
y[1] (closed_form) = -13.6092864914 0.372455516999
absolute error = 3.095e-05
relative error = 0.0002273 %
Correct digits = 6
memory used=264.4MB, alloc=44.3MB, time=3.46
Radius of convergence (given) for eq 1 = 4.126
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1224 0.197
h = 0.0001 0.004
y[1] (numeric) = -13.6073875447 0.374370856932
y[1] (closed_form) = -13.6074151283 0.374385033997
absolute error = 3.101e-05
relative error = 0.0002278 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.127
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
x[1] = 2.1225 0.201
h = 0.003 0.006
y[1] (numeric) = -13.6073140943 0.381975830595
y[1] (closed_form) = -13.6073428601 0.381990077
absolute error = 3.210e-05
relative error = 0.0002358 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.127
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
x[1] = 2.1255 0.207
h = 0.0001 0.005
y[1] (numeric) = -13.6017909415 0.393468263757
y[1] (closed_form) = -13.601821681 0.39348518998
absolute error = 3.509e-05
relative error = 0.0002579 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.131
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1256 0.212
h = 0.0001 0.003
y[1] (numeric) = -13.6017539694 0.402976257357
y[1] (closed_form) = -13.6017865569 0.40299327386
absolute error = 3.676e-05
relative error = 0.0002702 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.131
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=310.8MB, alloc=44.3MB, time=4.07
x[1] = 2.1257 0.215
h = 0.001 0.001
y[1] (numeric) = -13.601657963 0.40868241696
y[1] (closed_form) = -13.6016912149 0.408699483738
absolute error = 3.738e-05
relative error = 0.0002747 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.131
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1267 0.216
h = 0.001 0.003
y[1] (numeric) = -13.5997887448 0.41061525185
y[1] (closed_form) = -13.5998219953 0.410632466498
absolute error = 3.744e-05
relative error = 0.0002752 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.132
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] = 2.1277 0.219
h = 0.0001 0.004
y[1] (numeric) = -13.5979834336 0.416350734083
y[1] (closed_form) = -13.5980172715 0.416368397948
absolute error = 3.817e-05
relative error = 0.0002806 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.134
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] = 2.1278 0.223
h = 0.003 0.006
y[1] (numeric) = -13.5979228892 0.423959285287
y[1] (closed_form) = -13.5979579089 0.423977019474
absolute error = 3.925e-05
relative error = 0.0002885 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.134
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] = 2.1308 0.229
h = 0.0001 0.005
y[1] (numeric) = -13.5924167751 0.435466340778
y[1] (closed_form) = -13.5924537654 0.435486755747
absolute error = 4.225e-05
relative error = 0.0003107 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 4.137
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=357.2MB, alloc=44.3MB, time=4.68
x[1] = 2.1309 0.234
h = 0.0001 0.003
y[1] (numeric) = -13.5923959513 0.444978730989
y[1] (closed_form) = -13.5924347888 0.444999237918
absolute error = 4.392e-05
relative error = 0.0003229 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.138
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] = 2.131 0.237
h = 0.001 0.001
y[1] (numeric) = -13.5923096004 0.4506876604
y[1] (closed_form) = -13.5923491021 0.450708218201
absolute error = 4.453e-05
relative error = 0.0003274 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.138
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] = 2.132 0.238
h = 0.001 0.003
y[1] (numeric) = -13.5904428123 0.452624556292
y[1] (closed_form) = -13.5904823124 0.452645261915
absolute error = 4.460e-05
relative error = 0.000328 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.139
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.133 0.241
h = 0.0001 0.004
y[1] (numeric) = -13.5886464215 0.458365730567
y[1] (closed_form) = -13.5886865084 0.4583868858
absolute error = 4.533e-05
relative error = 0.0003334 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.14
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] = 2.1331 0.245
h = 0.003 0.006
y[1] (numeric) = -13.5885987757 0.465977869983
y[1] (closed_form) = -13.588640044 0.465999096604
absolute error = 4.641e-05
relative error = 0.0003413 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.14
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=403.6MB, alloc=44.3MB, time=5.29
x[1] = 2.1361 0.251
h = 0.0001 0.005
y[1] (numeric) = -13.5831096812 0.477499558766
y[1] (closed_form) = -13.583152917 0.477523467096
absolute error = 4.941e-05
relative error = 0.0003635 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.144
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1362 0.256
h = 0.0001 0.003
y[1] (numeric) = -13.5831049963 0.487016359018
y[1] (closed_form) = -13.5831500786 0.487040360976
absolute error = 5.107e-05
relative error = 0.0003758 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.144
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1363 0.259
h = 0.001 0.001
y[1] (numeric) = -13.5830282953 0.492728066205
y[1] (closed_form) = -13.5830740414 0.492752119628
absolute error = 5.168e-05
relative error = 0.0003803 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.144
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1373 0.26
h = 0.001 0.003
y[1] (numeric) = -13.5811639326 0.49466902399
y[1] (closed_form) = -13.5812096771 0.494693225183
absolute error = 5.175e-05
relative error = 0.0003808 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.145
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1383 0.263
h = 0.0001 0.004
y[1] (numeric) = -13.579376454 0.500415896618
y[1] (closed_form) = -13.5794227848 0.500440547807
absolute error = 5.248e-05
relative error = 0.0003862 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.147
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=450.0MB, alloc=44.3MB, time=5.90
x[1] = 2.1384 0.267
h = 0.003 0.006
y[1] (numeric) = -13.5793416993 0.508031634893
y[1] (closed_form) = -13.5793892109 0.508056358528
absolute error = 5.356e-05
relative error = 0.0003941 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.147
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1414 0.273
h = 0.0001 0.005
y[1] (numeric) = -13.5738696053 0.519567967691
y[1] (closed_form) = -13.5739190813 0.519595373925
absolute error = 5.656e-05
relative error = 0.0004164 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.15
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
x[1] = 2.1415 0.278
h = 0.0001 0.003
y[1] (numeric) = -13.5738810499 0.52908919127
y[1] (closed_form) = -13.5739323717 0.529116692787
absolute error = 5.823e-05
relative error = 0.0004286 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.151
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1416 0.281
h = 0.001 0.001
y[1] (numeric) = -13.5738139928 0.534803684117
y[1] (closed_form) = -13.5738659782 0.534831237687
absolute error = 5.884e-05
relative error = 0.0004331 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.151
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1426 0.282
h = 0.001 0.003
y[1] (numeric) = -13.5719520511 0.536748704631
y[1] (closed_form) = -13.5720040348 0.536776405919
absolute error = 5.890e-05
relative error = 0.0004337 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.152
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
memory used=496.4MB, alloc=44.3MB, time=6.50
x[1] = 2.1436 0.285
h = 0.0001 0.004
y[1] (numeric) = -13.5701734765 0.542501281813
y[1] (closed_form) = -13.5702260458 0.542529433476
absolute error = 5.963e-05
relative error = 0.0004391 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.153
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
x[1] = 2.1437 0.289
h = 0.003 0.006
y[1] (numeric) = -13.5701516051 0.550120629482
y[1] (closed_form) = -13.5702053548 0.550148854639
absolute error = 6.071e-05
relative error = 0.000447 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.154
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] = 2.1467 0.295
h = 0.0001 0.005
y[1] (numeric) = -13.5646964925 0.561671616775
y[1] (closed_form) = -13.5647522034 0.561702525385
absolute error = 6.371e-05
relative error = 0.0004693 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.157
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] = 2.1468 0.3
h = 0.0001 0.003
y[1] (numeric) = -13.564724057 0.571197276823
y[1] (closed_form) = -13.5647816129 0.571228282359
absolute error = 6.538e-05
relative error = 0.0004815 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.158
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
x[1] = 2.1469 0.303
h = 0.001 0.001
y[1] (numeric) = -13.564666638 0.576914563126
y[1] (closed_form) = -13.5647248573 0.576945621297
absolute error = 6.599e-05
relative error = 0.000486 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.158
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=542.8MB, alloc=44.3MB, time=7.10
x[1] = 2.1479 0.304
h = 0.0001 0.004
y[1] (numeric) = -13.5628071127 0.578863647153
y[1] (closed_form) = -13.5628653301 0.57889485299
absolute error = 6.605e-05
relative error = 0.0004866 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.159
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.148 0.308
h = 0.003 0.006
y[1] (numeric) = -13.5627963679 0.586485956585
y[1] (closed_form) = -13.5628557653 0.586517236907
absolute error = 6.713e-05
relative error = 0.0004945 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.159
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.151 0.314
h = 0.0001 0.005
y[1] (numeric) = -13.5573560316 0.59804936422
y[1] (closed_form) = -13.5574173875 0.598083328736
absolute error = 7.013e-05
relative error = 0.0005168 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.163
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1511 0.319
h = 0.0001 0.003
y[1] (numeric) = -13.5573975168 0.607578661585
y[1] (closed_form) = -13.5574607172 0.60761272444
absolute error = 7.180e-05
relative error = 0.000529 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.163
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1512 0.322
h = 0.001 0.001
y[1] (numeric) = -13.5573484226 0.613298243863
y[1] (closed_form) = -13.5574122861 0.613332359855
absolute error = 7.240e-05
relative error = 0.0005335 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.164
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=589.2MB, alloc=44.3MB, time=7.71
x[1] = 2.1522 0.323
h = 0.001 0.003
y[1] (numeric) = -13.5554910221 0.615250797507
y[1] (closed_form) = -13.5555548836 0.615285061118
absolute error = 7.247e-05
relative error = 0.0005341 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.165
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1532 0.326
h = 0.0001 0.004
y[1] (numeric) = -13.553729062 0.621013899838
y[1] (closed_form) = -13.5537935079 0.621048614515
absolute error = 7.320e-05
relative error = 0.0005395 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.166
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] = 2.1533 0.33
h = 0.003 0.006
y[1] (numeric) = -13.553731186 0.628639838137
y[1] (closed_form) = -13.5537968114 0.628674628244
absolute error = 7.428e-05
relative error = 0.0005474 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.166
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] = 2.1563 0.336
h = 0.0001 0.005
y[1] (numeric) = -13.5483077953 0.640217919359
y[1] (closed_form) = -13.5483753762 0.640255394446
absolute error = 7.728e-05
relative error = 0.0005697 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.17
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1564 0.341
h = 0.0001 0.003
y[1] (numeric) = -13.5483653824 0.649751677381
y[1] (closed_form) = -13.548434807 0.649789252426
absolute error = 7.894e-05
relative error = 0.000582 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.17
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=635.6MB, alloc=44.3MB, time=8.31
x[1] = 2.1565 0.344
h = 0.001 0.001
y[1] (numeric) = -13.5483259154 0.655474067458
y[1] (closed_form) = -13.5483960028 0.655511696213
absolute error = 7.955e-05
relative error = 0.0005865 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.171
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] = 2.1575 0.345
h = 0.001 0.003
y[1] (numeric) = -13.5464709229 0.657430685993
y[1] (closed_form) = -13.5465410082 0.657468462312
absolute error = 7.962e-05
relative error = 0.000587 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.172
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] = 2.1585 0.348
h = 0.0001 0.004
y[1] (numeric) = -13.544717843 0.663199510121
y[1] (closed_form) = -13.5447885121 0.663237737862
absolute error = 8.035e-05
relative error = 0.0005925 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.173
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
x[1] = 2.1586 0.352
h = 0.003 0.006
y[1] (numeric) = -13.5447328281 0.670829087399
y[1] (closed_form) = -13.5448046762 0.670867391595
absolute error = 8.142e-05
relative error = 0.0006004 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.173
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
x[1] = 2.1616 0.358
h = 0.0001 0.005
y[1] (numeric) = -13.5393263637 0.682421852003
y[1] (closed_form) = -13.5394001641 0.682462841927
absolute error = 8.442e-05
relative error = 0.0006227 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.177
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=682.0MB, alloc=44.3MB, time=8.91
x[1] = 2.1617 0.363
h = 0.0001 0.003
y[1] (numeric) = -13.5394000428 0.69196008341
y[1] (closed_form) = -13.5394756862 0.692001174898
absolute error = 8.608e-05
relative error = 0.000635 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.178
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1618 0.366
h = 0.001 0.001
y[1] (numeric) = -13.5393701969 0.69768528883
y[1] (closed_form) = -13.5394465027 0.697726434598
absolute error = 8.669e-05
relative error = 0.0006394 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.178
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1628 0.367
h = 0.001 0.003
y[1] (numeric) = -13.5375176079 0.699645972894
y[1] (closed_form) = -13.5375939115 0.699687266169
absolute error = 8.676e-05
relative error = 0.00064 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.179
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1638 0.37
h = 0.0001 0.004
y[1] (numeric) = -13.5357733999 0.705420524602
y[1] (closed_form) = -13.5358502867 0.705462269647
absolute error = 8.749e-05
relative error = 0.0006455 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.18
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
x[1] = 2.1639 0.374
h = 0.003 0.006
y[1] (numeric) = -13.5358012379 0.713053750942
y[1] (closed_form) = -13.5358793032 0.713095573459
absolute error = 8.856e-05
relative error = 0.0006534 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.181
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
memory used=728.4MB, alloc=52.3MB, time=9.53
x[1] = 2.1669 0.38
h = 0.0001 0.005
y[1] (numeric) = -13.5304116805 0.72466120848
y[1] (closed_form) = -13.530491695 0.724705717438
absolute error = 9.156e-05
relative error = 0.0006757 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.184
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] = 2.167 0.385
h = 0.0001 0.003
y[1] (numeric) = -13.5305014416 0.734203925855
y[1] (closed_form) = -13.5305832983 0.734248537969
absolute error = 9.322e-05
relative error = 0.000688 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.185
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1671 0.388
h = 0.001 0.001
y[1] (numeric) = -13.5304812106 0.739931954072
y[1] (closed_form) = -13.5305637294 0.739976621029
absolute error = 9.383e-05
relative error = 0.0006924 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.185
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1681 0.389
h = 0.001 0.003
y[1] (numeric) = -13.5286310206 0.741896704253
y[1] (closed_form) = -13.5287135371 0.741941518658
absolute error = 9.390e-05
relative error = 0.000693 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.186
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
x[1] = 2.1691 0.392
h = 0.0001 0.004
y[1] (numeric) = -13.5268956762 0.747676989213
y[1] (closed_form) = -13.5269787752 0.747722255731
absolute error = 9.463e-05
relative error = 0.0006985 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.187
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=774.8MB, alloc=52.3MB, time=10.12
x[1] = 2.1692 0.396
h = 0.003 0.006
y[1] (numeric) = -13.526936359 0.755313874581
y[1] (closed_form) = -13.5270206361 0.755359219577
absolute error = 9.570e-05
relative error = 0.0007064 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.188
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] = 2.1722 0.402
h = 0.0001 0.005
y[1] (numeric) = -13.5215636891 0.766936034368
y[1] (closed_form) = -13.5216499122 0.766984066483
absolute error = 9.870e-05
relative error = 0.0007288 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.192
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1723 0.407
h = 0.0001 0.003
y[1] (numeric) = -13.5216695222 0.776483250145
y[1] (closed_form) = -13.5217575866 0.776531386993
absolute error = 0.0001004
relative error = 0.000741 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.192
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1724 0.41
h = 0.001 0.001
y[1] (numeric) = -13.5216588999 0.782214108523
y[1] (closed_form) = -13.5217476262 0.782262300775
absolute error = 0.000101
relative error = 0.0007455 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.192
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1734 0.411
h = 0.0001 0.004
y[1] (numeric) = -13.5198111044 0.784182925357
y[1] (closed_form) = -13.5198998283 0.784231264997
absolute error = 0.000101
relative error = 0.0007461 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.194
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=821.3MB, alloc=52.3MB, time=10.72
x[1] = 2.1735 0.415
h = 0.003 0.006
y[1] (numeric) = -13.519862881 0.791822815222
y[1] (closed_form) = -13.5199527823 0.791871234294
absolute error = 0.0001021
relative error = 0.000754 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.194
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] = 2.1765 0.421
h = 0.0001 0.005
y[1] (numeric) = -13.514504907 0.803457436641
y[1] (closed_form) = -13.5145967518 0.803508543423
absolute error = 0.0001051
relative error = 0.0007764 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.198
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1766 0.426
h = 0.0001 0.003
y[1] (numeric) = -13.5146246198 0.813008343053
y[1] (closed_form) = -13.5147183052 0.813059555926
absolute error = 0.0001068
relative error = 0.0007886 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.198
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1767 0.429
h = 0.001 0.001
y[1] (numeric) = -13.5146222972 0.818741529013
y[1] (closed_form) = -13.5147166443 0.81879279777
absolute error = 0.0001074
relative error = 0.0007931 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.199
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
x[1] = 2.1777 0.43
h = 0.001 0.003
y[1] (numeric) = -13.5127766077 0.820713818226
y[1] (closed_form) = -13.5128709521 0.820765234322
absolute error = 0.0001074
relative error = 0.0007937 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.2
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
memory used=867.7MB, alloc=52.3MB, time=11.32
x[1] = 2.1787 0.433
h = 0.0001 0.004
y[1] (numeric) = -13.511057802 0.826504680819
y[1] (closed_form) = -13.5111527279 0.826556549647
absolute error = 0.0001082
relative error = 0.0007991 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.201
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] = 2.1788 0.437
h = 0.003 0.006
y[1] (numeric) = -13.5111224082 0.834148248122
y[1] (closed_form) = -13.5112185111 0.834200197286
absolute error = 0.0001092
relative error = 0.000807 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.202
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
x[1] = 2.1818 0.443
h = 0.0001 0.005
y[1] (numeric) = -13.5057812857 0.845797588718
y[1] (closed_form) = -13.5058793288 0.845852226203
absolute error = 0.0001122
relative error = 0.0008294 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.205
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1819 0.448
h = 0.0001 0.003
y[1] (numeric) = -13.5059170514 0.855353016396
y[1] (closed_form) = -13.5060169344 0.855407761525
absolute error = 0.0001139
relative error = 0.0008417 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.206
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
x[1] = 2.182 0.451
h = 0.001 0.001
y[1] (numeric) = -13.505924326 0.861089046057
y[1] (closed_form) = -13.5060248703 0.861143847621
absolute error = 0.0001145
relative error = 0.0008461 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.206
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=914.2MB, alloc=52.3MB, time=11.92
x[1] = 2.183 0.452
h = 0.001 0.003
y[1] (numeric) = -13.5040810227 0.863065402842
y[1] (closed_form) = -13.5041815642 0.863120351682
absolute error = 0.0001146
relative error = 0.0008467 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.207
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] = 2.184 0.455
h = 0.0001 0.004
y[1] (numeric) = -13.5023710563 0.86886201442
y[1] (closed_form) = -13.5024721786 0.868917416311
absolute error = 0.0001153
relative error = 0.0008522 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.209
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] = 2.1841 0.459
h = 0.003 0.006
y[1] (numeric) = -13.5024484838 0.876509268699
y[1] (closed_form) = -13.5025507827 0.876564751909
absolute error = 0.0001164
relative error = 0.0008601 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.209
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] = 2.1871 0.465
h = 0.0001 0.005
y[1] (numeric) = -13.4971241931 0.888173337105
y[1] (closed_form) = -13.4972284292 0.888231509211
absolute error = 0.0001194
relative error = 0.0008825 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.213
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=960.7MB, alloc=52.3MB, time=12.52
x[1] = 2.1872 0.47
h = 0.0001 0.003
y[1] (numeric) = -13.4972760014 0.897733298058
y[1] (closed_form) = -13.4973820765 0.897791579347
absolute error = 0.000121
relative error = 0.0008947 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.213
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1873 0.473
h = 0.001 0.001
y[1] (numeric) = -13.4972928668 0.903472178529
y[1] (closed_form) = -13.4973996029 0.903530516796
absolute error = 0.0001216
relative error = 0.0008992 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.214
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] = 2.1883 0.474
h = 0.001 0.003
y[1] (numeric) = -13.4954519452 0.905452603279
y[1] (closed_form) = -13.4955586783 0.90551108876
absolute error = 0.0001217
relative error = 0.0008998 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.215
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1893 0.477
h = 0.0001 0.004
y[1] (numeric) = -13.4937508095 0.911254969097
y[1] (closed_form) = -13.4938581228 0.91131390794
absolute error = 0.0001224
relative error = 0.0009053 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.216
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1894 0.481
h = 0.003 0.006
y[1] (numeric) = -13.49384105 0.918905919856
y[1] (closed_form) = -13.4939495392 0.918964940992
absolute error = 0.0001235
relative error = 0.0009131 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.217
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=1007.3MB, alloc=52.3MB, time=13.12
x[1] = 2.1924 0.487
h = 0.0001 0.005
y[1] (numeric) = -13.4885335716 0.930584724466
y[1] (closed_form) = -13.488643995 0.930646435038
absolute error = 0.0001265
relative error = 0.0009356 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.221
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] = 2.1925 0.492
h = 0.0001 0.003
y[1] (numeric) = -13.488701412 0.940149230553
y[1] (closed_form) = -13.4888136735 0.940211051833
absolute error = 0.0001282
relative error = 0.0009478 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.221
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] = 2.1926 0.495
h = 0.001 0.001
y[1] (numeric) = -13.4887278618 0.94589096885
y[1] (closed_form) = -13.4888407839 0.945952847648
absolute error = 0.0001288
relative error = 0.0009523 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.222
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.1936 0.496
h = 0.001 0.003
y[1] (numeric) = -13.4868893174 0.947875461909
y[1] (closed_form) = -13.4870022365 0.947937487857
absolute error = 0.0001288
relative error = 0.0009529 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.223
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
x[1] = 2.1946 0.499
h = 0.0001 0.004
y[1] (numeric) = -13.4851970038 0.953683587113
y[1] (closed_form) = -13.4853105025 0.953746066725
absolute error = 0.0001296
relative error = 0.0009584 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.224
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1053.7MB, alloc=52.3MB, time=13.72
x[1] = 2.1947 0.503
h = 0.003 0.006
y[1] (numeric) = -13.4853000488 0.961338243736
y[1] (closed_form) = -13.4854147228 0.961400806605
absolute error = 0.0001306
relative error = 0.0009662 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.225
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] = 2.1977 0.509
h = 0.0001 0.005
y[1] (numeric) = -13.4800093632 0.973031792709
y[1] (closed_form) = -13.4801259682 0.97309704552
absolute error = 0.0001336
relative error = 0.0009887 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.228
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] = 2.1978 0.514
h = 0.0001 0.003
y[1] (numeric) = -13.480193225 0.982600855638
y[1] (closed_form) = -13.4803116673 0.982666220669
absolute error = 0.0001353
relative error = 0.001001 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.229
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
x[1] = 2.1979 0.517
h = 0.001 0.001
y[1] (numeric) = -13.4802292527 0.988345458685
y[1] (closed_form) = -13.4803483554 0.988410881768
absolute error = 0.0001359
relative error = 0.001005 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.23
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] = 2.1989 0.518
h = 0.0001 0.004
y[1] (numeric) = -13.4783930811 0.99033402035
y[1] (closed_form) = -13.4785121806 0.990399590518
absolute error = 0.000136
relative error = 0.001006 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.231
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=1100.2MB, alloc=52.3MB, time=14.32
x[1] = 2.199 0.522
h = 0.003 0.006
y[1] (numeric) = -13.4785071852 0.997991721807
y[1] (closed_form) = -13.4786274596 0.998057376145
absolute error = 0.000137
relative error = 0.001014 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.231
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
x[1] = 2.202 0.528
h = 0.0001 0.005
y[1] (numeric) = -13.4732311143 1.00969776887
y[1] (closed_form) = -13.473353317 1.0097661136
absolute error = 0.00014
relative error = 0.001036 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.235
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] = 2.2021 0.533
h = 0.0001 0.003
y[1] (numeric) = -13.4734288129 1.01927057277
y[1] (closed_form) = -13.4735528521 1.01933903101
absolute error = 0.0001417
relative error = 0.001049 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.236
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2022 0.536
h = 0.001 0.001
y[1] (numeric) = -13.4734731139 1.02501753318
y[1] (closed_form) = -13.4735978132 1.02508604994
absolute error = 0.0001423
relative error = 0.001053 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.236
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2032 0.537
h = 0.001 0.003
y[1] (numeric) = -13.4716390296 1.02700956898
y[1] (closed_form) = -13.4717637257 1.02707823276
absolute error = 0.0001424
relative error = 0.001054 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.237
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1146.6MB, alloc=52.3MB, time=14.91
x[1] = 2.2042 0.54
h = 0.0001 0.004
y[1] (numeric) = -13.4699631778 1.03282831953
y[1] (closed_form) = -13.4700884522 1.03289743753
absolute error = 0.0001431
relative error = 0.001059 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.239
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] = 2.2043 0.544
h = 0.003 0.006
y[1] (numeric) = -13.4700900705 1.04048974418
y[1] (closed_form) = -13.4702165192 1.04055894721
absolute error = 0.0001441
relative error = 0.001067 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.239
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] = 2.2073 0.55
h = 0.0001 0.005
y[1] (numeric) = -13.464830756 1.05221055039
y[1] (closed_form) = -13.4649591299 1.05228244425
absolute error = 0.0001471
relative error = 0.001089 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.243
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
x[1] = 2.2074 0.555
h = 0.0001 0.003
y[1] (numeric) = -13.4650444561 1.06178793264
y[1] (closed_form) = -13.4651746657 1.06185994151
absolute error = 0.0001488
relative error = 0.001102 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.244
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2075 0.558
h = 0.001 0.001
y[1] (numeric) = -13.4650983231 1.06753777053
y[1] (closed_form) = -13.4652291924 1.06760983843
absolute error = 0.0001494
relative error = 0.001106 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.244
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1193.1MB, alloc=52.3MB, time=15.51
x[1] = 2.2085 0.559
h = 0.001 0.003
y[1] (numeric) = -13.4632666033 1.0695338754
y[1] (closed_form) = -13.4633974692 1.06960609027
absolute error = 0.0001495
relative error = 0.001107 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.245
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] = 2.2095 0.562
h = 0.0001 0.004
y[1] (numeric) = -13.461599549 1.07535839957
y[1] (closed_form) = -13.4617309927 1.07543106893
absolute error = 0.0001502
relative error = 0.001112 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.247
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2096 0.566
h = 0.003 0.006
y[1] (numeric) = -13.4617392215 1.08302355635
y[1] (closed_form) = -13.4618718389 1.08309631168
absolute error = 0.0001513
relative error = 0.00112 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.247
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2126 0.572
h = 0.0001 0.005
y[1] (numeric) = -13.4564966437 1.09475912921
y[1] (closed_form) = -13.4566311833 1.09483457578
absolute error = 0.0001543
relative error = 0.001143 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.251
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] = 2.2127 0.577
h = 0.0001 0.003
y[1] (numeric) = -13.4567263347 1.10434110109
y[1] (closed_form) = -13.456862709 1.10441666413
absolute error = 0.0001559
relative error = 0.001155 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.252
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1239.7MB, alloc=52.3MB, time=16.10
x[1] = 2.2128 0.58
h = 0.001 0.001
y[1] (numeric) = -13.4567897609 1.11009382311
y[1] (closed_form) = -13.4569267946 1.11016944571
absolute error = 0.0001565
relative error = 0.001159 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.253
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
x[1] = 2.2138 0.581
h = 0.001 0.003
y[1] (numeric) = -13.4549604012 1.11209399722
y[1] (closed_form) = -13.4550974314 1.11216976671
absolute error = 0.0001566
relative error = 0.00116 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.254
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2148 0.584
h = 0.0001 0.004
y[1] (numeric) = -13.4533021357 1.11792429973
y[1] (closed_form) = -13.4534397431 1.11800052399
absolute error = 0.0001573
relative error = 0.001165 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.255
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2149 0.588
h = 0.003 0.006
y[1] (numeric) = -13.4534545794 1.12559319757
y[1] (closed_form) = -13.4535933598 1.12566950873
absolute error = 0.0001584
relative error = 0.001173 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.256
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] = 2.2179 0.594
h = 0.0001 0.005
y[1] (numeric) = -13.4482287187 1.13734354432
y[1] (closed_form) = -13.4483694182 1.13742254708
absolute error = 0.0001614
relative error = 0.001196 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.26
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=1286.2MB, alloc=52.3MB, time=16.70
x[1] = 2.218 0.599
h = 0.0001 0.003
y[1] (numeric) = -13.4484743896 1.14693011695
y[1] (closed_form) = -13.4486169229 1.14700923765
absolute error = 0.000163
relative error = 0.001208 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.26
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] = 2.2181 0.602
h = 0.001 0.001
y[1] (numeric) = -13.4485473683 1.15268572968
y[1] (closed_form) = -13.4486905607 1.15276491045
absolute error = 0.0001636
relative error = 0.001212 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.261
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2191 0.603
h = 0.001 0.003
y[1] (numeric) = -13.4467203643 1.15468997314
y[1] (closed_form) = -13.4468635531 1.15476930073
absolute error = 0.0001637
relative error = 0.001213 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.262
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2201 0.606
h = 0.0001 0.004
y[1] (numeric) = -13.445070879 1.1605260586
y[1] (closed_form) = -13.4452146442 1.16060584123
absolute error = 0.0001644
relative error = 0.001218 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.263
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
x[1] = 2.2202 0.61
h = 0.003 0.006
y[1] (numeric) = -13.4452360849 1.16819870629
y[1] (closed_form) = -13.4453810227 1.16827857674
absolute error = 0.0001655
relative error = 0.001226 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.264
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=1332.6MB, alloc=52.3MB, time=17.31
x[1] = 2.2232 0.616
h = 0.0001 0.005
y[1] (numeric) = -13.4400269216 1.17996383396
y[1] (closed_form) = -13.4401737754 1.18004639635
absolute error = 0.0001685
relative error = 0.001249 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.268
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
x[1] = 2.2233 0.621
h = 0.0001 0.003
y[1] (numeric) = -13.4402885614 1.18955501832
y[1] (closed_form) = -13.4404372481 1.18963770008
absolute error = 0.0001701
relative error = 0.001261 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.269
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2234 0.624
h = 0.001 0.001
y[1] (numeric) = -13.440371086 1.19531352823
y[1] (closed_form) = -13.4405204314 1.19539627057
absolute error = 0.0001707
relative error = 0.001265 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.269
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2244 0.625
h = 0.0001 0.004
y[1] (numeric) = -13.4385464333 1.1973218411
y[1] (closed_form) = -13.438695775 1.19740473019
absolute error = 0.0001708
relative error = 0.001266 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.27
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
x[1] = 2.2245 0.629
h = 0.003 0.006
y[1] (numeric) = -13.4387226624 1.20499757152
y[1] (closed_form) = -13.438873176 1.2050805493
absolute error = 0.0001719
relative error = 0.001274 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.271
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1379.2MB, alloc=52.3MB, time=17.92
x[1] = 2.2275 0.635
h = 0.0001 0.005
y[1] (numeric) = -13.4335280321 1.21677522897
y[1] (closed_form) = -13.4336804591 1.216860899
absolute error = 0.0001749
relative error = 0.001296 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.275
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2276 0.64
h = 0.0001 0.003
y[1] (numeric) = -13.4338034637 1.22637020158
y[1] (closed_form) = -13.4339577227 1.22645599222
absolute error = 0.0001765
relative error = 0.001308 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.276
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2277 0.643
h = 0.001 0.001
y[1] (numeric) = -13.4338942342 1.23213109681
y[1] (closed_form) = -13.4340491517 1.23221694847
absolute error = 0.0001771
relative error = 0.001313 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.276
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2287 0.644
h = 0.001 0.003
y[1] (numeric) = -13.4320716504 1.23414288457
y[1] (closed_form) = -13.432226564 1.23422888292
absolute error = 0.0001772
relative error = 0.001314 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.277
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] = 2.2297 0.647
h = 0.0001 0.004
y[1] (numeric) = -13.4304385486 1.23998963836
y[1] (closed_form) = -13.4305940375 1.24007609223
absolute error = 0.0001779
relative error = 0.001319 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.279
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1425.7MB, alloc=52.3MB, time=18.54
x[1] = 2.2298 0.651
h = 0.003 0.006
y[1] (numeric) = -13.4306275235 1.24766913485
y[1] (closed_form) = -13.4307841838 1.24775567823
absolute error = 0.000179
relative error = 0.001327 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.28
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] = 2.2328 0.657
h = 0.0001 0.005
y[1] (numeric) = -13.425449554 1.2594615859
y[1] (closed_form) = -13.4256081247 1.25955082181
absolute error = 0.000182
relative error = 0.001349 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.283
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] = 2.2329 0.662
h = 0.0001 0.003
y[1] (numeric) = -13.4257409339 1.26906119038
y[1] (closed_form) = -13.4259013356 1.26915054831
absolute error = 0.0001836
relative error = 0.001362 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.284
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.233 0.665
h = 0.001 0.001
y[1] (numeric) = -13.4258412378 1.27482499468
y[1] (closed_form) = -13.4260022976 1.27491441413
absolute error = 0.0001842
relative error = 0.001366 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.285
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
x[1] = 2.234 0.666
h = 0.001 0.003
y[1] (numeric) = -13.4240209972 1.2768408519
y[1] (closed_form) = -13.424182053 1.27693041796
absolute error = 0.0001843
relative error = 0.001367 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.286
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1472.3MB, alloc=52.3MB, time=19.13
x[1] = 2.235 0.669
h = 0.0001 0.004
y[1] (numeric) = -13.4223966505 1.28269340138
y[1] (closed_form) = -13.422558281 1.28278342321
absolute error = 0.000185
relative error = 0.001372 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.288
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2351 0.673
h = 0.003 0.006
y[1] (numeric) = -13.4225983622 1.2903766723
y[1] (closed_form) = -13.4227611635 1.29046678454
absolute error = 0.0001861
relative error = 0.00138 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.288
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2381 0.679
h = 0.0001 0.005
y[1] (numeric) = -13.417437034 1.30218392332
y[1] (closed_form) = -13.4176017425 1.30227672832
absolute error = 0.0001891
relative error = 0.001402 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.292
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2382 0.684
h = 0.0001 0.003
y[1] (numeric) = -13.4177443509 1.3117881702
y[1] (closed_form) = -13.4179108896 1.31188109862
absolute error = 0.0001907
relative error = 0.001415 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.293
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
x[1] = 2.2383 0.687
h = 0.001 0.001
y[1] (numeric) = -13.4178541813 1.31755488979
y[1] (closed_form) = -13.4180213777 1.31764788022
absolute error = 0.0001913
relative error = 0.001419 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.294
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=1518.8MB, alloc=52.3MB, time=19.73
x[1] = 2.2393 0.688
h = 0.001 0.003
y[1] (numeric) = -13.4160362795 1.31957481639
y[1] (closed_form) = -13.4162034718 1.31966795338
absolute error = 0.0001914
relative error = 0.00142 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.295
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2403 0.691
h = 0.0001 0.004
y[1] (numeric) = -13.4144206793 1.32543316578
y[1] (closed_form) = -13.4145884456 1.32552675876
absolute error = 0.0001921
relative error = 0.001425 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.296
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2404 0.695
h = 0.003 0.006
y[1] (numeric) = -13.4146351187 1.33312021945
y[1] (closed_form) = -13.4148040552 1.33321390372
absolute error = 0.0001932
relative error = 0.001433 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.297
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] = 2.2434 0.701
h = 0.0001 0.005
y[1] (numeric) = -13.409490412 1.34494227657
y[1] (closed_form) = -13.4096612527 1.34503865381
absolute error = 0.0001962
relative error = 0.001455 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.301
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2435 0.706
h = 0.0001 0.003
y[1] (numeric) = -13.4098136547 1.35455117623
y[1] (closed_form) = -13.4099863246 1.35464767828
absolute error = 0.0001978
relative error = 0.001468 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.302
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=1565.4MB, alloc=52.3MB, time=20.32
x[1] = 2.2436 0.709
h = 0.001 0.001
y[1] (numeric) = -13.4099330048 1.36032081723
y[1] (closed_form) = -13.4101063319 1.36041738178
absolute error = 0.0001984
relative error = 0.001472 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.302
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
x[1] = 2.2446 0.71
h = 0.001 0.003
y[1] (numeric) = -13.4081174374 1.36234481311
y[1] (closed_form) = -13.4082907604 1.36244152414
absolute error = 0.0001985
relative error = 0.001473 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.304
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] = 2.2456 0.713
h = 0.0001 0.004
y[1] (numeric) = -13.4065105748 1.3682089665
y[1] (closed_form) = -13.4066844712 1.36830613375
absolute error = 0.0001992
relative error = 0.001478 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.305
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2457 0.717
h = 0.003 0.006
y[1] (numeric) = -13.4067377329 1.37589981112
y[1] (closed_form) = -13.4069127987 1.37599707053
absolute error = 0.0002003
relative error = 0.001486 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.306
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2487 0.723
h = 0.0001 0.005
y[1] (numeric) = -13.4016096279 1.38773668024
y[1] (closed_form) = -13.401786595 1.38783663281
absolute error = 0.0002032
relative error = 0.001508 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.31
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1611.9MB, alloc=52.3MB, time=20.92
x[1] = 2.2488 0.728
h = 0.0001 0.003
y[1] (numeric) = -13.4019487851 1.39735024291
y[1] (closed_form) = -13.4021275804 1.39745032166
absolute error = 0.0002049
relative error = 0.001521 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.311
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2489 0.731
h = 0.001 0.001
y[1] (numeric) = -13.4020776478 1.40312281136
y[1] (closed_form) = -13.4022571001 1.40322295308
absolute error = 0.0002055
relative error = 0.001525 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.311
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2499 0.732
h = 0.0001 0.004
y[1] (numeric) = -13.4002644106 1.40515087635
y[1] (closed_form) = -13.4004438586 1.40525116448
absolute error = 0.0002056
relative error = 0.001526 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.312
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
x[1] = 2.25 0.736
h = 0.003 0.006
y[1] (numeric) = -13.4005025545 1.41284483913
y[1] (closed_form) = -13.4006831713 1.41294522024
absolute error = 0.0002066
relative error = 0.001533 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.313
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] = 2.253 0.742
h = 0.0001 0.005
y[1] (numeric) = -13.3953889006 1.42469426505
y[1] (closed_form) = -13.395571416 1.42479733948
absolute error = 0.0002096
relative error = 0.001556 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.317
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=1658.6MB, alloc=52.3MB, time=21.52
x[1] = 2.2531 0.747
h = 0.0001 0.003
y[1] (numeric) = -13.395741803 1.43431166017
y[1] (closed_form) = -13.3959261457 1.43441486196
absolute error = 0.0002113
relative error = 0.001568 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.318
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2532 0.75
h = 0.001 0.001
y[1] (numeric) = -13.3958788833 1.44008664002
y[1] (closed_form) = -13.3960638827 1.4401899052
absolute error = 0.0002119
relative error = 0.001573 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.319
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] = 2.2542 0.751
h = 0.001 0.003
y[1] (numeric) = -13.3940676968 1.44211817972
y[1] (closed_form) = -13.3942526918 1.44222159124
absolute error = 0.0002119
relative error = 0.001573 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.32
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2552 0.754
h = 0.0001 0.004
y[1] (numeric) = -13.3924771387 1.44799303973
y[1] (closed_form) = -13.392662706 1.44809690789
absolute error = 0.0002127
relative error = 0.001579 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.321
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2553 0.758
h = 0.0001 0.004
y[1] (numeric) = -13.3927279842 1.45569080856
y[1] (closed_form) = -13.3929147196 1.45579477049
absolute error = 0.0002137
relative error = 0.001586 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.322
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1705.2MB, alloc=52.3MB, time=22.12
x[1] = 2.2554 0.762
h = 0.003 0.006
y[1] (numeric) = -13.3929811659 1.46338876523
y[1] (closed_form) = -13.3931690696 1.46349282099
absolute error = 0.0002148
relative error = 0.001594 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.323
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] = 2.2584 0.768
h = 0.0001 0.005
y[1] (numeric) = -13.3878874893 1.47525496272
y[1] (closed_form) = -13.388077288 1.47536171206
absolute error = 0.0002178
relative error = 0.001617 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.327
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
x[1] = 2.2585 0.773
h = 0.0001 0.003
y[1] (numeric) = -13.3882592052 1.4848772606
y[1] (closed_form) = -13.3884508301 1.4849841389
absolute error = 0.0002194
relative error = 0.001629 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.328
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
x[1] = 2.2586 0.776
h = 0.001 0.001
y[1] (numeric) = -13.3884075361 1.49065533524
y[1] (closed_form) = -13.3885998172 1.4907622775
absolute error = 0.00022
relative error = 0.001633 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.329
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2596 0.777
h = 0.001 0.003
y[1] (numeric) = -13.3865992238 1.49269156102
y[1] (closed_form) = -13.3867915004 1.49279864953
absolute error = 0.0002201
relative error = 0.001634 %
Correct digits = 5
memory used=1751.9MB, alloc=52.3MB, time=22.72
Radius of convergence (given) for eq 1 = 4.33
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] = 2.2606 0.78
h = 0.0001 0.004
y[1] (numeric) = -13.3850190993 1.49857291897
y[1] (closed_form) = -13.3852119474 1.49868046438
absolute error = 0.0002208
relative error = 0.001639 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.331
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2607 0.784
h = 0.003 0.006
y[1] (numeric) = -13.3852849721 1.50627469105
y[1] (closed_form) = -13.3854789877 1.50638233124
absolute error = 0.0002219
relative error = 0.001647 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.332
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2637 0.79
h = 0.0001 0.005
y[1] (numeric) = -13.3802078378 1.51815571806
y[1] (closed_form) = -13.3804037455 1.51826605191
absolute error = 0.0002248
relative error = 0.00167 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.336
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
x[1] = 2.2638 0.795
h = 0.0001 0.003
y[1] (numeric) = -13.3805954338 1.52778270961
y[1] (closed_form) = -13.3807931666 1.52789317374
absolute error = 0.0002265
relative error = 0.001682 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.337
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=1798.5MB, alloc=52.3MB, time=23.31
x[1] = 2.2639 0.798
h = 0.001 0.001
y[1] (numeric) = -13.3807532564 1.53356372976
y[1] (closed_form) = -13.3809516451 1.53367425832
absolute error = 0.0002271
relative error = 0.001686 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.338
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2649 0.799
h = 0.001 0.003
y[1] (numeric) = -13.3789472612 1.53560402411
y[1] (closed_form) = -13.3791456453 1.53571469884
absolute error = 0.0002272
relative error = 0.001687 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.339
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2659 0.802
h = 0.0001 0.004
y[1] (numeric) = -13.377375839 1.54149120197
y[1] (closed_form) = -13.3775747939 1.54160233381
absolute error = 0.0002279
relative error = 0.001692 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.341
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] = 2.266 0.806
h = 0.003 0.006
y[1] (numeric) = -13.3776543935 1.54919679726
y[1] (closed_form) = -13.3778545152 1.54930802472
absolute error = 0.000229
relative error = 0.0017 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.341
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] = 2.269 0.812
h = 0.0001 0.005
y[1] (numeric) = -13.372593782 1.5610926588
y[1] (closed_form) = -13.3727957927 1.56120657996
absolute error = 0.0002319
relative error = 0.001723 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.346
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
memory used=1845.0MB, alloc=52.3MB, time=23.91
x[1] = 2.2691 0.817
h = 0.0001 0.003
y[1] (numeric) = -13.3729972463 1.57072435363
y[1] (closed_form) = -13.3732010812 1.57083840639
absolute error = 0.0002336
relative error = 0.001735 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.347
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2692 0.82
h = 0.001 0.001
y[1] (numeric) = -13.3731645536 1.57650832495
y[1] (closed_form) = -13.3733690439 1.57662244259
absolute error = 0.0002342
relative error = 0.001739 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.347
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2702 0.821
h = 0.001 0.003
y[1] (numeric) = -13.3713608713 1.57855268753
y[1] (closed_form) = -13.3715653569 1.57866695127
absolute error = 0.0002342
relative error = 0.00174 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.348
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] = 2.2712 0.824
h = 0.0001 0.004
y[1] (numeric) = -13.3697981425 1.58444568888
y[1] (closed_form) = -13.3700031983 1.58456040991
absolute error = 0.000235
relative error = 0.001745 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.35
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2713 0.828
h = 0.003 0.006
y[1] (numeric) = -13.3700893693 1.59215511497
y[1] (closed_form) = -13.3702955913 1.59226993245
absolute error = 0.000236
relative error = 0.001753 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.351
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=1891.5MB, alloc=52.3MB, time=24.50
x[1] = 2.2743 0.834
h = 0.0001 0.005
y[1] (numeric) = -13.3650452608 1.60406581582
y[1] (closed_form) = -13.3652533689 1.60418332701
absolute error = 0.000239
relative error = 0.001775 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.355
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2744 0.839
h = 0.0001 0.003
y[1] (numeric) = -13.3654645818 1.61370222338
y[1] (closed_form) = -13.3656745129 1.61381986747
absolute error = 0.0002406
relative error = 0.001788 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.356
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2745 0.842
h = 0.001 0.001
y[1] (numeric) = -13.3656413667 1.61948915143
y[1] (closed_form) = -13.3658519529 1.61960686086
absolute error = 0.0002413
relative error = 0.001792 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.357
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2755 0.843
h = 0.001 0.003
y[1] (numeric) = -13.363839993 1.62153758187
y[1] (closed_form) = -13.3640505744 1.62165543731
absolute error = 0.0002413
relative error = 0.001793 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.358
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
x[1] = 2.2765 0.846
h = 0.0001 0.004
y[1] (numeric) = -13.3622859488 1.62743641018
y[1] (closed_form) = -13.3624970997 1.6275547231
absolute error = 0.000242
relative error = 0.001798 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.359
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1938.1MB, alloc=52.3MB, time=25.10
x[1] = 2.2766 0.85
h = 0.003 0.006
y[1] (numeric) = -13.3625898384 1.63514967452
y[1] (closed_form) = -13.3628021549 1.6352680847
absolute error = 0.0002431
relative error = 0.001806 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.36
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] = 2.2796 0.856
h = 0.0001 0.005
y[1] (numeric) = -13.3575622134 1.64707521924
y[1] (closed_form) = -13.357776413 1.64719632313
absolute error = 0.0002461
relative error = 0.001828 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.364
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2797 0.861
h = 0.0001 0.003
y[1] (numeric) = -13.3579973793 1.65671634885
y[1] (closed_form) = -13.3582134009 1.65683758691
absolute error = 0.0002477
relative error = 0.00184 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.365
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
x[1] = 2.2798 0.864
h = 0.001 0.001
y[1] (numeric) = -13.3581836346 1.66250623911
y[1] (closed_form) = -13.3584003109 1.66262754295
absolute error = 0.0002483
relative error = 0.001845 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.366
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] = 2.2808 0.865
h = 0.0001 0.004
y[1] (numeric) = -13.3563845654 1.66455873698
y[1] (closed_form) = -13.3566012367 1.66468018676
absolute error = 0.0002484
relative error = 0.001845 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.367
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
memory used=1984.8MB, alloc=52.3MB, time=25.71
x[1] = 2.2809 0.869
h = 0.003 0.006
y[1] (numeric) = -13.3566993931 1.67227516027
y[1] (closed_form) = -13.3569172294 1.67239670808
absolute error = 0.0002495
relative error = 0.001853 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.368
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2839 0.875
h = 0.0001 0.005
y[1] (numeric) = -13.3516861178 1.68421328956
y[1] (closed_form) = -13.3519058345 1.68433753108
absolute error = 0.0002524
relative error = 0.001876 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.372
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.284 0.88
h = 0.0001 0.003
y[1] (numeric) = -13.3521349693 1.69385830254
y[1] (closed_form) = -13.3523565072 1.69398267932
absolute error = 0.0002541
relative error = 0.001888 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.373
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2841 0.883
h = 0.001 0.001
y[1] (numeric) = -13.3523294061 1.69965063418
y[1] (closed_form) = -13.3525515983 1.69977507714
absolute error = 0.0002547
relative error = 0.001892 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.374
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2851 0.884
h = 0.001 0.003
y[1] (numeric) = -13.3505323655 1.7017066054
y[1] (closed_form) = -13.3507545527 1.70183119423
absolute error = 0.0002547
relative error = 0.001893 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.375
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2031.4MB, alloc=52.3MB, time=26.31
x[1] = 2.2861 0.887
h = 0.0001 0.004
y[1] (numeric) = -13.3489945271 1.707616182
y[1] (closed_form) = -13.3492172827 1.70774122865
absolute error = 0.0002555
relative error = 0.001898 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.377
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2862 0.891
h = 0.003 0.006
y[1] (numeric) = -13.3493220002 1.71533645728
y[1] (closed_form) = -13.34954592 1.71546160268
absolute error = 0.0002565
relative error = 0.001906 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.378
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] = 2.2892 0.897
h = 0.0001 0.005
y[1] (numeric) = -13.3443251719 1.7272894386
y[1] (closed_form) = -13.3445509693 1.72741727764
absolute error = 0.0002595
relative error = 0.001928 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.382
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2893 0.902
h = 0.0001 0.003
y[1] (numeric) = -13.3447898464 1.73693919067
y[1] (closed_form) = -13.3450174638 1.73706716622
absolute error = 0.0002611
relative error = 0.00194 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.383
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] = 2.2894 0.905
h = 0.001 0.001
y[1] (numeric) = -13.3449937403 1.74273449453
y[1] (closed_form) = -13.3452220117 1.7428625367
absolute error = 0.0002617
relative error = 0.001945 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.384
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=2078.0MB, alloc=52.3MB, time=26.91
x[1] = 2.2904 0.906
h = 0.001 0.003
y[1] (numeric) = -13.3431989963 1.74479453235
y[1] (closed_form) = -13.3434272626 1.7449227203
absolute error = 0.0002618
relative error = 0.001945 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.385
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2914 0.909
h = 0.0001 0.004
y[1] (numeric) = -13.3416698172 1.75070994537
y[1] (closed_form) = -13.3418986512 1.75083859131
absolute error = 0.0002625
relative error = 0.001951 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.387
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] = 2.2915 0.913
h = 0.003 0.006
y[1] (numeric) = -13.342009926 1.75843407967
y[1] (closed_form) = -13.3422399236 1.75856282515
absolute error = 0.0002636
relative error = 0.001959 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.388
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2945 0.919
h = 0.0001 0.005
y[1] (numeric) = -13.3370295252 1.77040191695
y[1] (closed_form) = -13.3372613974 1.77053335597
absolute error = 0.0002665
relative error = 0.001981 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.392
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2946 0.924
h = 0.0001 0.003
y[1] (numeric) = -13.3375100108 1.78005641698
y[1] (closed_form) = -13.337743702 1.78018799376
absolute error = 0.0002682
relative error = 0.001993 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.393
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
memory used=2124.6MB, alloc=52.3MB, time=27.50
x[1] = 2.2947 0.927
h = 0.001 0.001
y[1] (numeric) = -13.3377233546 1.78585469829
y[1] (closed_form) = -13.3379576993 1.7859863421
absolute error = 0.0002688
relative error = 0.001997 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.394
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] = 2.2957 0.928
h = 0.001 0.003
y[1] (numeric) = -13.3359309031 1.78791880215
y[1] (closed_form) = -13.3361652425 1.78805059167
absolute error = 0.0002689
relative error = 0.001998 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.395
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2967 0.931
h = 0.0001 0.004
y[1] (numeric) = -13.3344103744 1.79384005467
y[1] (closed_form) = -13.334645281 1.79397230233
absolute error = 0.0002696
relative error = 0.002004 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.396
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
x[1] = 2.2968 0.935
h = 0.003 0.006
y[1] (numeric) = -13.3347631094 1.80156805497
y[1] (closed_form) = -13.3349991788 1.80170040295
absolute error = 0.0002706
relative error = 0.002011 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.397
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.2998 0.941
h = 0.0001 0.005
y[1] (numeric) = -13.3297991166 1.81355075196
y[1] (closed_form) = -13.3300370577 1.81368579334
absolute error = 0.0002736
relative error = 0.002034 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.402
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=2171.2MB, alloc=52.3MB, time=28.10
x[1] = 2.2999 0.946
h = 0.0001 0.003
y[1] (numeric) = -13.3302954013 1.82321000867
y[1] (closed_form) = -13.3305351602 1.82334518903
absolute error = 0.0002752
relative error = 0.002046 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.403
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3 0.949
h = 0.001 0.001
y[1] (numeric) = -13.3305181877 1.82901127252
y[1] (closed_form) = -13.3307585998 1.82914652036
absolute error = 0.0002758
relative error = 0.00205 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.403
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.301 0.95
h = 0.001 0.003
y[1] (numeric) = -13.3287280245 1.83107944185
y[1] (closed_form) = -13.3289684313 1.8312148353
absolute error = 0.0002759
relative error = 0.002051 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.405
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] = 2.302 0.953
h = 0.0001 0.004
y[1] (numeric) = -13.3272161373 1.83700653685
y[1] (closed_form) = -13.3274571106 1.83714238859
absolute error = 0.0002766
relative error = 0.002056 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.406
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3021 0.957
h = 0.003 0.006
y[1] (numeric) = -13.3275814888 1.84473841
y[1] (closed_form) = -13.3278236242 1.84487436283
absolute error = 0.0002777
relative error = 0.002064 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.407
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
memory used=2217.8MB, alloc=52.3MB, time=28.70
x[1] = 2.3051 0.963
h = 0.0001 0.005
y[1] (numeric) = -13.3226338845 1.85673597022
y[1] (closed_form) = -13.3228778887 1.8568746163
absolute error = 0.0002806
relative error = 0.002086 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.411
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
x[1] = 2.3052 0.968
h = 0.0001 0.003
y[1] (numeric) = -13.3231459563 1.86639999217
y[1] (closed_form) = -13.3233917772 1.86653877843
absolute error = 0.0002823
relative error = 0.002098 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.413
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3053 0.971
h = 0.001 0.001
y[1] (numeric) = -13.3233781781 1.8722042436
y[1] (closed_form) = -13.3236246517 1.87234309776
absolute error = 0.0002829
relative error = 0.002103 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.413
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3063 0.972
h = 0.0001 0.004
y[1] (numeric) = -13.321590299 1.87427647777
y[1] (closed_form) = -13.3218367673 1.87441547746
absolute error = 0.000283
relative error = 0.002103 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.415
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] = 2.3064 0.976
h = 0.003 0.006
y[1] (numeric) = -13.321966549 1.88201153975
y[1] (closed_form) = -13.3222141787 1.88215064126
absolute error = 0.000284
relative error = 0.002111 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.416
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2264.4MB, alloc=52.3MB, time=29.30
x[1] = 2.3094 0.982
h = 0.0001 0.005
y[1] (numeric) = -13.3170332129 1.8940217015
y[1] (closed_form) = -13.3172827089 1.89416349613
absolute error = 0.000287
relative error = 0.002133 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.42
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3095 0.987
h = 0.0001 0.003
y[1] (numeric) = -13.317558921 1.90368964409
y[1] (closed_form) = -13.3178102328 1.90383157994
absolute error = 0.0002886
relative error = 0.002145 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.421
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3096 0.99
h = 0.001 0.001
y[1] (numeric) = -13.3177992941 1.90949635881
y[1] (closed_form) = -13.3180512583 1.90963836292
absolute error = 0.0002892
relative error = 0.00215 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.422
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3106 0.991
h = 0.001 0.003
y[1] (numeric) = -13.3160134264 1.91157206419
y[1] (closed_form) = -13.3162653851 1.91171421376
absolute error = 0.0002893
relative error = 0.00215 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.423
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] = 2.3116 0.994
h = 0.0001 0.004
y[1] (numeric) = -13.3145176652 1.91750993556
y[1] (closed_form) = -13.3147701892 1.91765254369
absolute error = 0.00029
relative error = 0.002156 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.425
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2311.0MB, alloc=52.3MB, time=29.90
x[1] = 2.3117 0.998
h = 0.003 0.006
y[1] (numeric) = -13.3149065138 1.92524888303
y[1] (closed_form) = -13.3151601986 1.92539159366
absolute error = 0.0002911
relative error = 0.002164 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.426
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
x[1] = 2.3147 1.004
h = 0.0001 0.005
y[1] (numeric) = -13.30998953 1.93727391422
y[1] (closed_form) = -13.3102450781 1.93741931776
absolute error = 0.000294
relative error = 0.002186 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.43
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
x[1] = 2.3148 1.009
h = 0.0001 0.003
y[1] (numeric) = -13.3105310028 1.94694663774
y[1] (closed_form) = -13.3107883656 1.94709218367
absolute error = 0.0002957
relative error = 0.002198 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.431
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3149 1.012
h = 0.001 0.001
y[1] (numeric) = -13.3107807977 1.95275634923
y[1] (closed_form) = -13.3110388126 1.95290196383
absolute error = 0.0002963
relative error = 0.002202 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.432
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] = 2.3159 1.013
h = 0.001 0.003
y[1] (numeric) = -13.3089972066 1.95483611824
y[1] (closed_form) = -13.3092552158 1.95498187822
absolute error = 0.0002963
relative error = 0.002203 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.433
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
memory used=2357.6MB, alloc=52.3MB, time=30.49
x[1] = 2.3169 1.016
h = 0.0001 0.004
y[1] (numeric) = -13.3075100616 1.96077984015
y[1] (closed_form) = -13.3077686355 1.96092605881
absolute error = 0.0002971
relative error = 0.002208 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.435
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.317 1.02
h = 0.003 0.006
y[1] (numeric) = -13.3079114991 1.96852267955
y[1] (closed_form) = -13.308171233 1.96866900146
absolute error = 0.0002981
relative error = 0.002216 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.436
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.32 1.026
h = 0.0001 0.005
y[1] (numeric) = -13.3030108482 1.98056258312
y[1] (closed_form) = -13.3032724426 1.98071159769
absolute error = 0.0003011
relative error = 0.002238 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.44
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
x[1] = 2.3201 1.031
h = 0.0001 0.003
y[1] (numeric) = -13.3035680736 1.99024009568
y[1] (closed_form) = -13.3038314816 1.99038925381
absolute error = 0.0003027
relative error = 0.00225 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.441
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3202 1.034
h = 0.001 0.001
y[1] (numeric) = -13.303827283 1.99605280871
y[1] (closed_form) = -13.3040913426 1.99620203592
absolute error = 0.0003033
relative error = 0.002255 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.442
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2404.3MB, alloc=52.3MB, time=31.09
x[1] = 2.3212 1.035
h = 0.001 0.003
y[1] (numeric) = -13.3020459643 1.99813664062
y[1] (closed_form) = -13.3023100182 1.99828601311
absolute error = 0.0003034
relative error = 0.002255 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.443
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3222 1.038
h = 0.0001 0.004
y[1] (numeric) = -13.3005674267 2.00408621565
y[1] (closed_form) = -13.3008320447 2.00423604696
absolute error = 0.0003041
relative error = 0.002261 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.445
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3223 1.042
h = 0.003 0.006
y[1] (numeric) = -13.3009814433 2.01183295339
y[1] (closed_form) = -13.3012472206 2.01198288866
absolute error = 0.0003052
relative error = 0.002268 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.446
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] = 2.3253 1.048
h = 0.0001 0.005
y[1] (numeric) = -13.296097106 2.02388773204
y[1] (closed_form) = -13.2963647408 2.02404035972
absolute error = 0.0003081
relative error = 0.002291 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.45
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3254 1.053
h = 0.0001 0.003
y[1] (numeric) = -13.2966700718 2.03357004164
y[1] (closed_form) = -13.2969395192 2.03372281401
absolute error = 0.0003097
relative error = 0.002303 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.452
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2450.9MB, alloc=52.3MB, time=31.70
x[1] = 2.3255 1.056
h = 0.001 0.001
y[1] (numeric) = -13.2969386882 2.03938576088
y[1] (closed_form) = -13.2972087867 2.03953860273
absolute error = 0.0003103
relative error = 0.002307 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.453
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
x[1] = 2.3265 1.057
h = 0.001 0.003
y[1] (numeric) = -13.2951596381 2.04147365491
y[1] (closed_form) = -13.2954297308 2.04162664196
absolute error = 0.0003104
relative error = 0.002308 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.454
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] = 2.3275 1.06
h = 0.0001 0.004
y[1] (numeric) = -13.293689699 2.04742908556
y[1] (closed_form) = -13.2939603551 2.04758253155
absolute error = 0.0003111
relative error = 0.002313 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.455
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3276 1.064
h = 0.003 0.006
y[1] (numeric) = -13.2941162849 2.0551797279
y[1] (closed_form) = -13.2943880996 2.05533327856
absolute error = 0.0003122
relative error = 0.002321 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.456
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3306 1.07
h = 0.0001 0.005
y[1] (numeric) = -13.2892482418 2.06724938416
y[1] (closed_form) = -13.2895219113 2.06740562693
absolute error = 0.0003151
relative error = 0.002343 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.461
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=2497.5MB, alloc=52.3MB, time=32.29
x[1] = 2.3307 1.075
h = 0.0001 0.003
y[1] (numeric) = -13.2898369359 2.07693649861
y[1] (closed_form) = -13.2901124167 2.07709288721
absolute error = 0.0003168
relative error = 0.002355 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.462
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3308 1.078
h = 0.001 0.001
y[1] (numeric) = -13.290114952 2.08275522865
y[1] (closed_form) = -13.2903910835 2.08291168711
absolute error = 0.0003174
relative error = 0.002359 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.463
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3318 1.079
h = 0.0001 0.004
y[1] (numeric) = -13.2883381663 2.08484718399
y[1] (closed_form) = -13.2886142919 2.08500378758
absolute error = 0.0003174
relative error = 0.00236 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.464
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3319 1.083
h = 0.003 0.006
y[1] (numeric) = -13.2887756103 2.09260104256
y[1] (closed_form) = -13.2890528939 2.09275775152
absolute error = 0.0003185
relative error = 0.002368 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.465
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] = 2.3349 1.089
h = 0.0001 0.005
y[1] (numeric) = -13.2839217546 2.10468331305
y[1] (closed_form) = -13.2842008904 2.10484271387
absolute error = 0.0003214
relative error = 0.00239 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.47
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2544.2MB, alloc=52.3MB, time=32.89
x[1] = 2.335 1.094
h = 0.0001 0.003
y[1] (numeric) = -13.2845240346 2.11437438236
y[1] (closed_form) = -13.2848049807 2.11453392998
absolute error = 0.0003231
relative error = 0.002402 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.471
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
x[1] = 2.3351 1.097
h = 0.001 0.001
y[1] (numeric) = -13.2848101715 2.12019559574
y[1] (closed_form) = -13.2850917681 2.12035521357
absolute error = 0.0003237
relative error = 0.002406 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.472
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] = 2.3361 1.098
h = 0.001 0.003
y[1] (numeric) = -13.2830353802 2.12229101934
y[1] (closed_form) = -13.2833169708 2.12245078222
absolute error = 0.0003238
relative error = 0.002407 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.473
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] = 2.3371 1.101
h = 0.0001 0.004
y[1] (numeric) = -13.2815814872 2.12825725007
y[1] (closed_form) = -13.28186364 2.12841747208
absolute error = 0.0003245
relative error = 0.002412 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.475
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
x[1] = 2.3372 1.105
h = 0.003 0.006
y[1] (numeric) = -13.2820314823 2.13601502478
y[1] (closed_form) = -13.2823147923 2.13617535279
absolute error = 0.0003255
relative error = 0.00242 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.476
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2590.8MB, alloc=52.3MB, time=33.49
x[1] = 2.3402 1.111
h = 0.0001 0.005
y[1] (numeric) = -13.277193885 2.14811217724
y[1] (closed_form) = -13.2774790444 2.14827519677
absolute error = 0.0003285
relative error = 0.002442 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.48
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3403 1.116
h = 0.0001 0.003
y[1] (numeric) = -13.2778118705 2.15780806573
y[1] (closed_form) = -13.2780988392 2.15797123316
absolute error = 0.0003301
relative error = 0.002454 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.481
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3404 1.119
h = 0.001 0.001
y[1] (numeric) = -13.2781073934 2.16363229828
y[1] (closed_form) = -13.278395012 2.16379553631
absolute error = 0.0003307
relative error = 0.002458 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.482
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3414 1.12
h = 0.001 0.003
y[1] (numeric) = -13.276334859 2.16573178164
y[1] (closed_form) = -13.2766224716 2.16589516462
absolute error = 0.0003308
relative error = 0.002459 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.484
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3424 1.123
h = 0.0001 0.004
y[1] (numeric) = -13.2748895393 2.17170387468
y[1] (closed_form) = -13.2751777135 2.1718677169
absolute error = 0.0003315
relative error = 0.002464 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.485
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
memory used=2637.4MB, alloc=52.3MB, time=34.08
x[1] = 2.3425 1.127
h = 0.003 0.006
y[1] (numeric) = -13.2753520757 2.17946557139
y[1] (closed_form) = -13.2756414064 2.1796295203
absolute error = 0.0003326
relative error = 0.002472 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.486
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] = 2.3455 1.133
h = 0.0001 0.005
y[1] (numeric) = -13.2705307176 2.19157760776
y[1] (closed_form) = -13.2708218949 2.19174424781
absolute error = 0.0003355
relative error = 0.002494 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.491
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
x[1] = 2.3456 1.138
h = 0.0001 0.003
y[1] (numeric) = -13.2711643963 2.20127832283
y[1] (closed_form) = -13.2714573817 2.20144511187
absolute error = 0.0003371
relative error = 0.002506 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.492
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3457 1.141
h = 0.001 0.001
y[1] (numeric) = -13.2714692976 2.20710557888
y[1] (closed_form) = -13.2717629325 2.20727243889
absolute error = 0.0003377
relative error = 0.00251 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.493
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
x[1] = 2.3467 1.142
h = 0.001 0.003
y[1] (numeric) = -13.2696990163 2.20920912108
y[1] (closed_form) = -13.2699926451 2.20937612596
absolute error = 0.0003378
relative error = 0.002511 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.494
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=2684.1MB, alloc=52.3MB, time=34.70
x[1] = 2.3477 1.145
h = 0.0001 0.004
y[1] (numeric) = -13.2682622611 2.21518707856
y[1] (closed_form) = -13.2685564508 2.21535454277
absolute error = 0.0003385
relative error = 0.002516 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.496
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3478 1.149
h = 0.003 0.006
y[1] (numeric) = -13.2687373288 2.22295270307
y[1] (closed_form) = -13.2690326743 2.22312027465
absolute error = 0.0003396
relative error = 0.002524 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.497
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3508 1.155
h = 0.0001 0.005
y[1] (numeric) = -13.2639321908 2.2350796251
y[1] (closed_form) = -13.2642293801 2.23524988742
absolute error = 0.0003425
relative error = 0.002546 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.501
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3509 1.16
h = 0.0001 0.003
y[1] (numeric) = -13.2645815504 2.24478517401
y[1] (closed_form) = -13.2648805466 2.24495558638
absolute error = 0.0003441
relative error = 0.002558 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.503
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] = 2.351 1.163
h = 0.001 0.001
y[1] (numeric) = -13.2648958227 2.25061545779
y[1] (closed_form) = -13.265195468 2.25078594151
absolute error = 0.0003447
relative error = 0.002562 %
Correct digits = 5
memory used=2730.8MB, alloc=52.3MB, time=35.30
Radius of convergence (given) for eq 1 = 4.504
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.352 1.164
h = 0.001 0.003
y[1] (numeric) = -13.2631277906 2.25272305788
y[1] (closed_form) = -13.2634274296 2.25289368638
absolute error = 0.0003448
relative error = 0.002563 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.505
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.353 1.167
h = 0.0001 0.004
y[1] (numeric) = -13.261699591 2.25870688182
y[1] (closed_form) = -13.2619997903 2.25887796974
absolute error = 0.0003455
relative error = 0.002568 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.507
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] = 2.3531 1.171
h = 0.003 0.006
y[1] (numeric) = -13.2621871802 2.26647643984
y[1] (closed_form) = -13.2624885345 2.26664763579
absolute error = 0.0003466
relative error = 0.002576 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.508
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3561 1.177
h = 0.0001 0.005
y[1] (numeric) = -13.2573982432 2.27861824907
y[1] (closed_form) = -13.2577014385 2.27879213533
absolute error = 0.0003495
relative error = 0.002598 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.512
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2777.5MB, alloc=52.3MB, time=35.90
x[1] = 2.3562 1.182
h = 0.0001 0.003
y[1] (numeric) = -13.2580632713 2.28832863891
y[1] (closed_form) = -13.2583682724 2.28850267629
absolute error = 0.0003512
relative error = 0.00261 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.514
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3563 1.185
h = 0.001 0.001
y[1] (numeric) = -13.2583869071 2.29416195458
y[1] (closed_form) = -13.2586925568 2.29433606367
absolute error = 0.0003518
relative error = 0.002614 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.515
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3573 1.186
h = 0.0001 0.004
y[1] (numeric) = -13.2566211202 2.29627361158
y[1] (closed_form) = -13.2569267636 2.29644786536
absolute error = 0.0003518
relative error = 0.002615 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.516
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3574 1.19
h = 0.003 0.006
y[1] (numeric) = -13.2571195265 2.30404641082
y[1] (closed_form) = -13.2574263242 2.30422077329
absolute error = 0.0003529
relative error = 0.002622 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.517
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3604 1.196
h = 0.0001 0.005
y[1] (numeric) = -13.2523446969 2.31620084287
y[1] (closed_form) = -13.2526533331 2.31637789529
absolute error = 0.0003558
relative error = 0.002645 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.521
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2824.0MB, alloc=52.3MB, time=36.49
x[1] = 2.3605 1.201
h = 0.0001 0.003
y[1] (numeric) = -13.2530232598 2.32591521878
y[1] (closed_form) = -13.2533337008 2.32609242322
absolute error = 0.0003575
relative error = 0.002657 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.523
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3606 1.204
h = 0.001 0.001
y[1] (numeric) = -13.2533549856 2.33175103602
y[1] (closed_form) = -13.2536660748 2.33192831249
absolute error = 0.0003581
relative error = 0.002661 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.524
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] = 2.3616 1.205
h = 0.001 0.003
y[1] (numeric) = -13.2515911765 2.33386615757
y[1] (closed_form) = -13.2519022594 2.33404357865
absolute error = 0.0003581
relative error = 0.002661 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.525
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
x[1] = 2.3626 1.208
h = 0.0001 0.004
y[1] (numeric) = -13.2501789435 2.33986080102
y[1] (closed_form) = -13.2504905855 2.34003868167
absolute error = 0.0003588
relative error = 0.002667 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.527
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3627 1.212
h = 0.003 0.006
y[1] (numeric) = -13.2506898528 2.34763754423
y[1] (closed_form) = -13.2510026484 2.34781553415
absolute error = 0.0003599
relative error = 0.002674 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.528
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2870.7MB, alloc=52.3MB, time=37.10
x[1] = 2.3657 1.218
h = 0.0001 0.005
y[1] (numeric) = -13.2459311887 2.35980686607
y[1] (closed_form) = -13.2462458202 2.35998754547
absolute error = 0.0003628
relative error = 0.002697 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.532
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3658 1.223
h = 0.0001 0.003
y[1] (numeric) = -13.2466253972 2.3695260959
y[1] (closed_form) = -13.2469418323 2.36970692834
absolute error = 0.0003645
relative error = 0.002708 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.534
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3659 1.226
h = 0.001 0.001
y[1] (numeric) = -13.2469664726 2.37536495259
y[1] (closed_form) = -13.2472835554 2.37554585743
absolute error = 0.0003651
relative error = 0.002712 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.535
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3669 1.227
h = 0.001 0.003
y[1] (numeric) = -13.2452049015 2.37748412917
y[1] (closed_form) = -13.2455219779 2.37766517852
absolute error = 0.0003651
relative error = 0.002713 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.536
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
x[1] = 2.3679 1.23
h = 0.0001 0.004
y[1] (numeric) = -13.243801199 2.38348464446
y[1] (closed_form) = -13.2441188339 2.38366615344
absolute error = 0.0003658
relative error = 0.002719 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.538
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=2917.2MB, alloc=52.3MB, time=37.69
x[1] = 2.368 1.234
h = 0.003 0.006
y[1] (numeric) = -13.2443246013 2.39126533691
y[1] (closed_form) = -13.2446433891 2.39144695581
absolute error = 0.0003669
relative error = 0.002726 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.539
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.371 1.24
h = 0.0001 0.005
y[1] (numeric) = -13.239582084 2.40344954954
y[1] (closed_form) = -13.2399027048 2.40363385742
absolute error = 0.0003698
relative error = 0.002748 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.543
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] = 2.3711 1.245
h = 0.0001 0.003
y[1] (numeric) = -13.2402919256 2.41317363998
y[1] (closed_form) = -13.2406143488 2.41335810192
absolute error = 0.0003715
relative error = 0.00276 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.545
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
x[1] = 2.3712 1.248
h = 0.001 0.001
y[1] (numeric) = -13.240642343 2.41901554002
y[1] (closed_form) = -13.2409654136 2.4192000747
absolute error = 0.0003721
relative error = 0.002764 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.546
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3722 1.249
h = 0.001 0.003
y[1] (numeric) = -13.2388830061 2.42113877053
y[1] (closed_form) = -13.2392060701 2.42132344964
absolute error = 0.0003721
relative error = 0.002765 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.547
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=2963.8MB, alloc=52.3MB, time=38.30
x[1] = 2.3732 1.252
h = 0.0001 0.004
y[1] (numeric) = -13.2374878254 2.42714515933
y[1] (closed_form) = -13.2378114474 2.42733029813
absolute error = 0.0003728
relative error = 0.00277 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.549
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3733 1.256
h = 0.003 0.006
y[1] (numeric) = -13.2380237108 2.43492980627
y[1] (closed_form) = -13.2383484849 2.43511505562
absolute error = 0.0003739
relative error = 0.002778 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.55
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] = 2.3763 1.262
h = 0.0001 0.005
y[1] (numeric) = -13.2332973213 2.44712891049
y[1] (closed_form) = -13.2336239256 2.44731684829
absolute error = 0.0003768
relative error = 0.0028 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.555
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3764 1.267
h = 0.0001 0.003
y[1] (numeric) = -13.2340227835 2.45685786808
y[1] (closed_form) = -13.2343511891 2.45704596093
absolute error = 0.0003785
relative error = 0.002812 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.556
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3765 1.27
h = 0.001 0.001
y[1] (numeric) = -13.2343825354 2.46270281528
y[1] (closed_form) = -13.2347115879 2.46289098122
absolute error = 0.0003791
relative error = 0.002816 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.557
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=3010.3MB, alloc=52.3MB, time=38.89
x[1] = 2.3775 1.271
h = 0.001 0.003
y[1] (numeric) = -13.2326254289 2.46483009862
y[1] (closed_form) = -13.2329544748 2.46501840889
absolute error = 0.0003791
relative error = 0.002817 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.558
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] = 2.3785 1.274
h = 0.0001 0.004
y[1] (numeric) = -13.2312387612 2.47084236249
y[1] (closed_form) = -13.2315683644 2.47103113251
absolute error = 0.0003798
relative error = 0.002822 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.56
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] = 2.3786 1.278
h = 0.003 0.006
y[1] (numeric) = -13.2317871197 2.47863096904
y[1] (closed_form) = -13.2321178742 2.47881985023
absolute error = 0.0003809
relative error = 0.002829 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.561
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3816 1.284
h = 0.0001 0.005
y[1] (numeric) = -13.2270768391 2.49084496547
y[1] (closed_form) = -13.2274094212 2.49103653456
absolute error = 0.0003838
relative error = 0.002851 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.566
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3817 1.289
h = 0.0001 0.003
y[1] (numeric) = -13.2278179096 2.50057879661
y[1] (closed_form) = -13.2281522917 2.50077052174
absolute error = 0.0003854
relative error = 0.002863 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.567
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=3056.9MB, alloc=52.3MB, time=39.49
x[1] = 2.3818 1.292
h = 0.001 0.001
y[1] (numeric) = -13.2281869885 2.50642679469
y[1] (closed_form) = -13.2285220171 2.50661859325
absolute error = 0.000386
relative error = 0.002867 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.568
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3828 1.293
h = 0.0001 0.004
y[1] (numeric) = -13.2264321085 2.50855812969
y[1] (closed_form) = -13.2267671304 2.50875007249
absolute error = 0.0003861
relative error = 0.002868 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.57
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3829 1.297
h = 0.003 0.006
y[1] (numeric) = -13.2269912428 2.51635000008
y[1] (closed_form) = -13.2273274152 2.51654205465
absolute error = 0.0003872
relative error = 0.002875 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.571
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] = 2.3859 1.303
h = 0.0001 0.005
y[1] (numeric) = -13.2222949906 2.528576624
y[1] (closed_form) = -13.2226329883 2.52877136601
absolute error = 0.0003901
relative error = 0.002898 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.575
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.386 1.308
h = 0.0001 0.003
y[1] (numeric) = -13.2230495443 2.53831446942
y[1] (closed_form) = -13.2233893409 2.53850936831
absolute error = 0.0003917
relative error = 0.002909 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.577
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3103.4MB, alloc=52.3MB, time=40.09
x[1] = 2.3861 1.311
h = 0.001 0.001
y[1] (numeric) = -13.2234266819 2.54416498553
y[1] (closed_form) = -13.2237671246 2.54435995814
absolute error = 0.0003923
relative error = 0.002913 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.578
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3871 1.312
h = 0.001 0.003
y[1] (numeric) = -13.2216737637 2.54629978066
y[1] (closed_form) = -13.2220141996 2.54649489744
absolute error = 0.0003924
relative error = 0.002914 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.579
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
x[1] = 2.3881 1.315
h = 0.0001 0.004
y[1] (numeric) = -13.2203029835 2.5523228794
y[1] (closed_form) = -13.2206439757 2.55251845601
absolute error = 0.0003931
relative error = 0.002919 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.581
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3882 1.319
h = 0.003 0.006
y[1] (numeric) = -13.2208745722 2.5601187188
y[1] (closed_form) = -13.2212167142 2.56031440773
absolute error = 0.0003942
relative error = 0.002927 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.582
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3912 1.325
h = 0.0001 0.005
y[1] (numeric) = -13.2161943942 2.57236023582
y[1] (closed_form) = -13.2165383587 2.57255861159
absolute error = 0.0003971
relative error = 0.002949 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.587
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3150.0MB, alloc=52.3MB, time=40.69
x[1] = 2.3913 1.33
h = 0.0001 0.003
y[1] (numeric) = -13.2169645328 2.58210296646
y[1] (closed_form) = -13.2173102951 2.58230150006
absolute error = 0.0003987
relative error = 0.002961 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.588
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3914 1.333
h = 0.001 0.001
y[1] (numeric) = -13.2173509834 2.58795654024
y[1] (closed_form) = -13.2176973914 2.58815514789
absolute error = 0.0003993
relative error = 0.002965 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.589
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3924 1.334
h = 0.001 0.003
y[1] (numeric) = -13.2156002848 2.59009538485
y[1] (closed_form) = -13.2159466859 2.59029413658
absolute error = 0.0003994
relative error = 0.002965 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.591
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3934 1.337
h = 0.0001 0.004
y[1] (numeric) = -13.2142379928 2.59612436277
y[1] (closed_form) = -13.2145849494 2.59632357436
absolute error = 0.0004001
relative error = 0.002971 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.592
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] = 2.3935 1.341
h = 0.003 0.006
y[1] (numeric) = -13.2148220259 2.60392417591
y[1] (closed_form) = -13.2151701316 2.60412350042
absolute error = 0.0004011
relative error = 0.002978 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.594
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=3196.6MB, alloc=52.3MB, time=41.29
x[1] = 2.3965 1.347
h = 0.0001 0.005
y[1] (numeric) = -13.2101579034 2.61618058613
y[1] (closed_form) = -13.2105078289 2.61638259686
absolute error = 0.000404
relative error = 0.003 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.598
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
x[1] = 2.3966 1.352
h = 0.0001 0.003
y[1] (numeric) = -13.2109436145 2.62592820798
y[1] (closed_form) = -13.2112953366 2.62613037748
absolute error = 0.0004057
relative error = 0.003012 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.6
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
x[1] = 2.3967 1.355
h = 0.001 0.001
y[1] (numeric) = -13.2113393705 2.63178484289
y[1] (closed_form) = -13.2116917378 2.63198708677
absolute error = 0.0004063
relative error = 0.003016 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.601
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3977 1.356
h = 0.001 0.003
y[1] (numeric) = -13.2095908877 2.63392773574
y[1] (closed_form) = -13.2099432481 2.6341301236
absolute error = 0.0004063
relative error = 0.003017 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.602
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.3987 1.359
h = 0.0001 0.004
y[1] (numeric) = -13.2082370751 2.63996259407
y[1] (closed_form) = -13.2085899905 2.64016544182
absolute error = 0.0004071
relative error = 0.003022 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.604
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3243.1MB, alloc=52.3MB, time=41.88
x[1] = 2.3988 1.363
h = 0.003 0.006
y[1] (numeric) = -13.2088335427 2.64776638564
y[1] (closed_form) = -13.2091876063 2.6479693469
absolute error = 0.0004081
relative error = 0.003029 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.605
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4018 1.369
h = 0.0001 0.005
y[1] (numeric) = -13.204185457 2.66003768897
y[1] (closed_form) = -13.2045413379 2.6602433358
absolute error = 0.000411
relative error = 0.003051 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.61
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4019 1.374
h = 0.0001 0.003
y[1] (numeric) = -13.2049867281 2.66979020787
y[1] (closed_form) = -13.2053444043 2.66999601439
absolute error = 0.0004127
relative error = 0.003063 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.611
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] = 2.402 1.377
h = 0.001 0.001
y[1] (numeric) = -13.2053917819 2.67564990731
y[1] (closed_form) = -13.2057501029 2.67585578853
absolute error = 0.0004133
relative error = 0.003067 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.612
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.403 1.378
h = 0.001 0.003
y[1] (numeric) = -13.2036455113 2.67779684713
y[1] (closed_form) = -13.2040038253 2.67800287223
absolute error = 0.0004133
relative error = 0.003068 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.614
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=3289.8MB, alloc=52.3MB, time=42.50
x[1] = 2.404 1.381
h = 0.0001 0.004
y[1] (numeric) = -13.2023001695 2.683837587
y[1] (closed_form) = -13.2026590378 2.68404407203
absolute error = 0.000414
relative error = 0.003073 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.615
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] = 2.4041 1.385
h = 0.003 0.006
y[1] (numeric) = -13.2029090614 2.69164536157
y[1] (closed_form) = -13.2032690772 2.69185196067
absolute error = 0.0004151
relative error = 0.00308 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.617
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] = 2.4071 1.391
h = 0.0001 0.005
y[1] (numeric) = -13.1982769942 2.70393155774
y[1] (closed_form) = -13.1986388245 2.70414084175
absolute error = 0.000418
relative error = 0.003103 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.621
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4072 1.396
h = 0.0001 0.003
y[1] (numeric) = -13.1990938127 2.71368897939
y[1] (closed_form) = -13.1994574371 2.71389842401
absolute error = 0.0004196
relative error = 0.003114 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.623
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4073 1.399
h = 0.001 0.001
y[1] (numeric) = -13.1995081567 2.71955174667
y[1] (closed_form) = -13.1998724256 2.7197612663
absolute error = 0.0004202
relative error = 0.003118 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.624
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
memory used=3336.3MB, alloc=52.3MB, time=43.09
x[1] = 2.4083 1.4
h = 0.003 0.006
y[1] (numeric) = -13.1977640946 2.72170273214
y[1] (closed_form) = -13.1981283563 2.72191239556
absolute error = 0.0004203
relative error = 0.003119 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.625
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4113 1.406
h = 0.0001 0.005
y[1] (numeric) = -13.1931426606 2.73399957543
y[1] (closed_form) = -13.1935087348 2.73421192341
absolute error = 0.0004232
relative error = 0.003141 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.63
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
x[1] = 2.4114 1.411
h = 0.0001 0.003
y[1] (numeric) = -13.193970043 2.74376076414
y[1] (closed_form) = -13.1943379105 2.74397327331
absolute error = 0.0004248
relative error = 0.003152 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.632
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4115 1.414
h = 0.001 0.001
y[1] (numeric) = -13.1943906959 2.74962587742
y[1] (closed_form) = -13.1947592074 2.7498384618
absolute error = 0.0004254
relative error = 0.003156 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.633
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
x[1] = 2.4125 1.415
h = 0.001 0.003
y[1] (numeric) = -13.192648049 2.75177970059
y[1] (closed_form) = -13.1930165534 2.7519924287
absolute error = 0.0004255
relative error = 0.003157 %
Correct digits = 5
Radius of convergence (given) for eq 1 = 4.634
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=3382.9MB, alloc=52.3MB, time=43.69
x[1] = 2.4135 1.418
h = 0.0001 0.004
y[1] (numeric) = -13.1913168371 2.7578305831
y[1] (closed_form) = -13.1916858948 2.75804377115
absolute error = 0.0004262
relative error = 0.003162 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.636
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] = 2.4136 1.422
h = 0.003 0.006
y[1] (numeric) = -13.1919465765 2.76564540298
y[1] (closed_form) = -13.1923167804 2.76585870603
absolute error = 0.0004273
relative error = 0.00317 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.637
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] = 2.4166 1.428
h = 0.0001 0.005
y[1] (numeric) = -13.1873411296 2.77795713801
y[1] (closed_form) = -13.1877131435 2.77817312472
absolute error = 0.0004302
relative error = 0.003192 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.642
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4167 1.433
h = 0.0001 0.003
y[1] (numeric) = -13.1881840382 2.78772323847
y[1] (closed_form) = -13.1885578441 2.78793938726
absolute error = 0.0004318
relative error = 0.003203 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.643
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4168 1.436
h = 0.001 0.001
y[1] (numeric) = -13.1886139685 2.79359142478
y[1] (closed_form) = -13.188988418 2.79380764908
absolute error = 0.0004324
relative error = 0.003207 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.644
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3429.5MB, alloc=52.3MB, time=44.29
x[1] = 2.4178 1.437
h = 0.001 0.003
y[1] (numeric) = -13.1868735239 2.79574929125
y[1] (closed_form) = -13.1872479662 2.79596565918
absolute error = 0.0004325
relative error = 0.003208 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.646
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4188 1.44
h = 0.0001 0.004
y[1] (numeric) = -13.1855507596 2.80180605773
y[1] (closed_form) = -13.1859257546 2.8020228856
absolute error = 0.0004332
relative error = 0.003213 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.648
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4189 1.444
h = 0.003 0.006
y[1] (numeric) = -13.1861928962 2.80962487206
y[1] (closed_form) = -13.1865690366 2.80984181549
absolute error = 0.0004342
relative error = 0.003221 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.649
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4219 1.45
h = 0.0001 0.005
y[1] (numeric) = -13.1816034183 2.8219514979
y[1] (closed_form) = -13.1819813662 2.82217112426
absolute error = 0.0004371
relative error = 0.003243 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.654
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
x[1] = 2.422 1.455
h = 0.0001 0.003
y[1] (numeric) = -13.1824618404 2.83172251544
y[1] (closed_form) = -13.182841579 2.83194230475
absolute error = 0.0004388
relative error = 0.003254 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.655
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
memory used=3476.1MB, alloc=52.3MB, time=44.88
x[1] = 2.4221 1.458
h = 0.001 0.001
y[1] (numeric) = -13.1829010405 2.83759377786
y[1] (closed_form) = -13.1832814223 2.83781364298
absolute error = 0.0004394
relative error = 0.003258 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.656
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4231 1.459
h = 0.001 0.003
y[1] (numeric) = -13.1811627947 2.83975568624
y[1] (closed_form) = -13.1815431692 2.83997569489
absolute error = 0.0004394
relative error = 0.003259 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.658
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
x[1] = 2.4241 1.462
h = 0.0001 0.004
y[1] (numeric) = -13.1798484694 2.8458183375
y[1] (closed_form) = -13.180229396 2.8460388061
absolute error = 0.0004401
relative error = 0.003264 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.659
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4242 1.466
h = 0.003 0.006
y[1] (numeric) = -13.1805029931 2.85364115044
y[1] (closed_form) = -13.1808850643 2.85386173514
absolute error = 0.0004412
relative error = 0.003271 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.661
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4272 1.472
h = 0.0001 0.005
y[1] (numeric) = -13.175929466 2.86598266619
y[1] (closed_form) = -13.1763133421 2.86620593307
absolute error = 0.0004441
relative error = 0.003293 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.665
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3522.8MB, alloc=52.3MB, time=45.48
x[1] = 2.4273 1.477
h = 0.0001 0.003
y[1] (numeric) = -13.1768033891 2.87575860601
y[1] (closed_form) = -13.1771890547 2.87598203668
absolute error = 0.0004457
relative error = 0.003305 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.667
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4274 1.48
h = 0.001 0.001
y[1] (numeric) = -13.1772518514 2.88163294754
y[1] (closed_form) = -13.1776381597 2.88185645432
absolute error = 0.0004463
relative error = 0.003309 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.668
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] = 2.4284 1.481
h = 0.0001 0.004
y[1] (numeric) = -13.1755158008 2.88379889641
y[1] (closed_form) = -13.1759021018 2.88402254662
absolute error = 0.0004464
relative error = 0.003309 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.669
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4285 1.485
h = 0.003 0.006
y[1] (numeric) = -13.1761810267 2.89162500701
y[1] (closed_form) = -13.1765684714 2.89184877386
absolute error = 0.0004474
relative error = 0.003317 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.671
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4315 1.491
h = 0.0001 0.005
y[1] (numeric) = -13.1716213922 2.90397914894
y[1] (closed_form) = -13.1720106396 2.90420559733
absolute error = 0.0004503
relative error = 0.003339 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.676
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3569.6MB, alloc=52.3MB, time=46.08
x[1] = 2.4316 1.496
h = 0.0001 0.003
y[1] (numeric) = -13.1725087067 2.91375914529
y[1] (closed_form) = -13.1728997426 2.91398575821
absolute error = 0.000452
relative error = 0.00335 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.677
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] = 2.4317 1.499
h = 0.001 0.001
y[1] (numeric) = -13.1729651722 2.91963602934
y[1] (closed_form) = -13.1733568504 2.91986271863
absolute error = 0.0004525
relative error = 0.003354 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.678
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4327 1.5
h = 0.001 0.003
y[1] (numeric) = -13.1712310565 2.92180542888
y[1] (closed_form) = -13.1716227273 2.92203226152
absolute error = 0.0004526
relative error = 0.003355 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.68
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
x[1] = 2.4337 1.503
h = 0.0001 0.004
y[1] (numeric) = -13.1699324816 2.92787893197
y[1] (closed_form) = -13.1703247034 2.92810622456
absolute error = 0.0004533
relative error = 0.00336 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.682
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4338 1.507
h = 0.003 0.006
y[1] (numeric) = -13.1706100757 2.9357090488
y[1] (closed_form) = -13.1710034406 2.93593645848
absolute error = 0.0004544
relative error = 0.003367 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.683
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
memory used=3616.2MB, alloc=52.3MB, time=46.72
x[1] = 2.4368 1.513
h = 0.0001 0.005
y[1] (numeric) = -13.1660663583 2.94807807873
y[1] (closed_form) = -13.1664615233 2.94830816916
absolute error = 0.0004573
relative error = 0.003389 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.688
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4369 1.518
h = 0.0001 0.003
y[1] (numeric) = -13.1669691504 2.95786300679
y[1] (closed_form) = -13.1673661026 2.95809326258
absolute error = 0.0004589
relative error = 0.0034 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.689
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.437 1.521
h = 0.001 0.001
y[1] (numeric) = -13.1674348641 2.9637429754
y[1] (closed_form) = -13.1678324581 2.96397330784
absolute error = 0.0004595
relative error = 0.003404 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.69
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] = 2.438 1.522
h = 0.001 0.003
y[1] (numeric) = -13.165702937 2.96591641277
y[1] (closed_form) = -13.1661005236 2.96614688847
absolute error = 0.0004596
relative error = 0.003405 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.692
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.439 1.525
h = 0.0001 0.004
y[1] (numeric) = -13.1644127767 2.97199580264
y[1] (closed_form) = -13.1648109137 2.97222673827
absolute error = 0.0004603
relative error = 0.00341 %
Correct digits = 4
memory used=3662.9MB, alloc=52.3MB, time=47.32
Radius of convergence (given) for eq 1 = 4.694
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4391 1.529
h = 0.003 0.006
y[1] (numeric) = -13.1651027292 2.97982992948
y[1] (closed_form) = -13.1655020084 2.98006098271
absolute error = 0.0004613
relative error = 0.003417 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.695
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4421 1.535
h = 0.0001 0.005
y[1] (numeric) = -13.1605749107 2.99221384602
y[1] (closed_form) = -13.1609759875 2.9924475792
absolute error = 0.0004642
relative error = 0.003439 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.7
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4422 1.54
h = 0.0001 0.003
y[1] (numeric) = -13.1614931679 3.0020037106
y[1] (closed_form) = -13.1618960307 3.00223760995
absolute error = 0.0004658
relative error = 0.003451 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.702
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4423 1.543
h = 0.001 0.001
y[1] (numeric) = -13.1619681221 3.00788676653
y[1] (closed_form) = -13.1623716263 3.00812074281
absolute error = 0.0004664
relative error = 0.003455 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.703
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3709.5MB, alloc=52.3MB, time=47.91
x[1] = 2.4433 1.544
h = 0.001 0.003
y[1] (numeric) = -13.1602383801 3.01006424023
y[1] (closed_form) = -13.1606418768 3.01029835966
absolute error = 0.0004665
relative error = 0.003455 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.704
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4443 1.547
h = 0.0001 0.004
y[1] (numeric) = -13.1589566259 3.01614951737
y[1] (closed_form) = -13.1593606724 3.01638409673
absolute error = 0.0004672
relative error = 0.003461 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.706
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] = 2.4444 1.551
h = 0.003 0.006
y[1] (numeric) = -13.1596589267 3.02398765795
y[1] (closed_form) = -13.1600641146 3.02422235542
absolute error = 0.0004683
relative error = 0.003468 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.707
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4474 1.557
h = 0.0001 0.005
y[1] (numeric) = -13.1551469892 3.03638645957
y[1] (closed_form) = -13.1555539722 3.03662383614
absolute error = 0.0004712
relative error = 0.00349 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.712
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4475 1.562
h = 0.0001 0.003
y[1] (numeric) = -13.1560806989 3.04618126533
y[1] (closed_form) = -13.1564894666 3.04641880887
absolute error = 0.0004728
relative error = 0.003501 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.714
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3756.1MB, alloc=52.3MB, time=48.51
x[1] = 2.4476 1.565
h = 0.001 0.001
y[1] (numeric) = -13.1565648861 3.05206741126
y[1] (closed_form) = -13.1569742947 3.052305032
absolute error = 0.0004734
relative error = 0.003505 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.715
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4486 1.566
h = 0.001 0.003
y[1] (numeric) = -13.1548373258 3.05424891977
y[1] (closed_form) = -13.1552467268 3.05448668357
absolute error = 0.0004734
relative error = 0.003506 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.716
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] = 2.4496 1.569
h = 0.0001 0.004
y[1] (numeric) = -13.1535639692 3.06034008462
y[1] (closed_form) = -13.1539739195 3.06057830831
absolute error = 0.0004741
relative error = 0.003511 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.718
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
x[1] = 2.4497 1.573
h = 0.003 0.006
y[1] (numeric) = -13.1542786081 3.06818224256
y[1] (closed_form) = -13.154689699 3.06842058486
absolute error = 0.0004752
relative error = 0.003518 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.72
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
x[1] = 2.4527 1.579
h = 0.0001 0.005
y[1] (numeric) = -13.1497825338 3.08059592754
y[1] (closed_form) = -13.1501954172 3.0808369481
absolute error = 0.0004781
relative error = 0.00354 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.724
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3802.6MB, alloc=52.3MB, time=49.11
x[1] = 2.4528 1.584
h = 0.0001 0.003
y[1] (numeric) = -13.1507316834 3.09039567902
y[1] (closed_form) = -13.1511463504 3.09063686732
absolute error = 0.0004797
relative error = 0.003551 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.726
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
x[1] = 2.4529 1.587
h = 0.001 0.001
y[1] (numeric) = -13.151225096 3.09628491756
y[1] (closed_form) = -13.1516404034 3.09652618333
absolute error = 0.0004803
relative error = 0.003555 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.727
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4539 1.588
h = 0.0001 0.004
y[1] (numeric) = -13.1494997139 3.09847045931
y[1] (closed_form) = -13.1499150136 3.09871186805
absolute error = 0.0004804
relative error = 0.003556 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.729
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
x[1] = 2.454 1.592
h = 0.003 0.006
y[1] (numeric) = -13.150225013 3.10631593123
y[1] (closed_form) = -13.1506414526 3.10655745906
absolute error = 0.0004814
relative error = 0.003563 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.73
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.457 1.598
h = 0.0001 0.005
y[1] (numeric) = -13.1457427562 3.11874223716
y[1] (closed_form) = -13.1461609861 3.11898644253
absolute error = 0.0004843
relative error = 0.003585 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.735
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=3849.3MB, alloc=52.3MB, time=49.71
x[1] = 2.4571 1.603
h = 0.0001 0.003
y[1] (numeric) = -13.1467052449 3.12854606555
y[1] (closed_form) = -13.1471252573 3.12879043934
absolute error = 0.0004859
relative error = 0.003596 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.737
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
x[1] = 2.4572 1.606
h = 0.001 0.001
y[1] (numeric) = -13.1472066291 3.13443785835
y[1] (closed_form) = -13.1476272816 3.13468230984
absolute error = 0.0004865
relative error = 0.0036 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.738
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] = 2.4582 1.607
h = 0.001 0.003
y[1] (numeric) = -13.1454831673 3.13662684465
y[1] (closed_form) = -13.145903812 3.13687143902
absolute error = 0.0004866
relative error = 0.0036 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.739
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4592 1.61
h = 0.0001 0.004
y[1] (numeric) = -13.1442254845 3.14272886619
y[1] (closed_form) = -13.1446466774 3.1429739204
absolute error = 0.0004873
relative error = 0.003606 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.741
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] = 2.4593 1.614
h = 0.003 0.006
y[1] (numeric) = -13.144963103 3.1505783621
y[1] (closed_form) = -13.145385435 3.15082353583
absolute error = 0.0004883
relative error = 0.003613 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.742
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3896.0MB, alloc=52.3MB, time=50.30
x[1] = 2.4623 1.62
h = 0.0001 0.005
y[1] (numeric) = -13.1404966762 3.16301954801
y[1] (closed_form) = -13.1409207961 3.16326739838
absolute error = 0.0004912
relative error = 0.003634 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.747
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4624 1.625
h = 0.0001 0.003
y[1] (numeric) = -13.1414745816 3.17282833034
y[1] (closed_form) = -13.1419004826 3.17307634989
absolute error = 0.0004929
relative error = 0.003645 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.749
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
x[1] = 2.4625 1.628
h = 0.001 0.001
y[1] (numeric) = -13.1419851771 3.17872322047
y[1] (closed_form) = -13.1424117178 3.17897131798
absolute error = 0.0004934
relative error = 0.003649 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.75
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4635 1.629
h = 0.001 0.003
y[1] (numeric) = -13.1402638871 3.18091623711
y[1] (closed_form) = -13.14069042 3.18116447741
absolute error = 0.0004935
relative error = 0.00365 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.751
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] = 2.4645 1.632
h = 0.0001 0.004
y[1] (numeric) = -13.139014578 3.18702414721
y[1] (closed_form) = -13.1394416584 3.18727284731
absolute error = 0.0004942
relative error = 0.003655 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.753
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3942.7MB, alloc=52.3MB, time=50.90
x[1] = 2.4646 1.636
h = 0.003 0.006
y[1] (numeric) = -13.1397645058 3.19487767039
y[1] (closed_form) = -13.1401927246 3.19512649047
absolute error = 0.0004953
relative error = 0.003662 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.755
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] = 2.4676 1.642
h = 0.0001 0.005
y[1] (numeric) = -13.1353138915 3.20733373412
y[1] (closed_form) = -13.1357438957 3.20758522994
absolute error = 0.0004982
relative error = 0.003684 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.76
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] = 2.4677 1.647
h = 0.0001 0.003
y[1] (numeric) = -13.1363072009 3.21714747455
y[1] (closed_form) = -13.136738985 3.21739914029
absolute error = 0.0004998
relative error = 0.003695 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.762
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
x[1] = 2.4678 1.65
h = 0.001 0.001
y[1] (numeric) = -13.1368270002 3.22304546438
y[1] (closed_form) = -13.1372594234 3.22329720833
absolute error = 0.0005004
relative error = 0.003699 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.763
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
x[1] = 2.4688 1.651
h = 0.001 0.003
y[1] (numeric) = -13.1351078786 3.22524250974
y[1] (closed_form) = -13.135540294 3.22549439637
absolute error = 0.0005004
relative error = 0.0037 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.764
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3989.3MB, alloc=52.3MB, time=51.50
x[1] = 2.4698 1.654
h = 0.0001 0.004
y[1] (numeric) = -13.1338669347 3.23135630852
y[1] (closed_form) = -13.1342998971 3.23160865491
absolute error = 0.0005011
relative error = 0.003705 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.766
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
x[1] = 2.4699 1.658
h = 0.003 0.006
y[1] (numeric) = -13.1346291619 3.23921386218
y[1] (closed_form) = -13.1350632618 3.23946632902
absolute error = 0.0005022
relative error = 0.003712 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.767
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4729 1.664
h = 0.0001 0.005
y[1] (numeric) = -13.1301943425 3.25168480142
y[1] (closed_form) = -13.1306302254 3.25193994306
absolute error = 0.0005051
relative error = 0.003734 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.772
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.473 1.669
h = 0.0001 0.003
y[1] (numeric) = -13.1312030434 3.26150350397
y[1] (closed_form) = -13.1316407049 3.26175881625
absolute error = 0.0005067
relative error = 0.003745 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.774
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4731 1.672
h = 0.001 0.001
y[1] (numeric) = -13.1317320388 3.26740459579
y[1] (closed_form) = -13.132170339 3.26765998654
absolute error = 0.0005073
relative error = 0.003749 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.775
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
memory used=4035.9MB, alloc=52.3MB, time=52.10
x[1] = 2.4741 1.673
h = 0.001 0.003
y[1] (numeric) = -13.1300150824 3.26960566822
y[1] (closed_form) = -13.1304533747 3.26986120155
absolute error = 0.0005073
relative error = 0.003749 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.777
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4751 1.676
h = 0.0001 0.004
y[1] (numeric) = -13.1287824954 3.27572535572
y[1] (closed_form) = -13.1292213341 3.27598134876
absolute error = 0.000508
relative error = 0.003754 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.779
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4752 1.68
h = 0.003 0.006
y[1] (numeric) = -13.1295570119 3.28358694298
y[1] (closed_form) = -13.1299969873 3.28384305692
absolute error = 0.0005091
relative error = 0.003761 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.78
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4782 1.686
h = 0.0001 0.005
y[1] (numeric) = -13.1251379699 3.29607275526
y[1] (closed_form) = -13.1255797258 3.29633154305
absolute error = 0.000512
relative error = 0.003783 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.785
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4783 1.691
h = 0.0001 0.003
y[1] (numeric) = -13.1261620497 3.30589642382
y[1] (closed_form) = -13.126605583 3.30615538297
absolute error = 0.0005136
relative error = 0.003794 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.787
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4082.6MB, alloc=52.3MB, time=52.70
x[1] = 2.4784 1.694
h = 0.001 0.001
y[1] (numeric) = -13.1267002337 3.31180061986
y[1] (closed_form) = -13.1271444053 3.31205965771
absolute error = 0.0005142
relative error = 0.003798 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.788
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4794 1.695
h = 0.0001 0.004
y[1] (numeric) = -13.1249854392 3.31400571768
y[1] (closed_form) = -13.1254296027 3.31426489803
absolute error = 0.0005143
relative error = 0.003799 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.789
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4795 1.699
h = 0.003 0.006
y[1] (numeric) = -13.125770574 3.32187063306
y[1] (closed_form) = -13.1262158735 3.32212993474
absolute error = 0.0005153
relative error = 0.003806 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.791
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4825 1.705
h = 0.0001 0.005
y[1] (numeric) = -13.1213652758 3.3343690578
y[1] (closed_form) = -13.1218123538 3.33463103254
absolute error = 0.0005182
relative error = 0.003827 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.796
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4826 1.71
h = 0.0001 0.003
y[1] (numeric) = -13.1224026425 3.34419682097
y[1] (closed_form) = -13.1228514968 3.34445896768
absolute error = 0.0005198
relative error = 0.003838 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.798
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4129.4MB, alloc=52.3MB, time=53.30
x[1] = 2.4827 1.713
h = 0.001 0.001
y[1] (numeric) = -13.1229487667 3.3501035814
y[1] (closed_form) = -13.1233982588 3.35036580703
absolute error = 0.0005204
relative error = 0.003842 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.799
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4837 1.714
h = 0.001 0.003
y[1] (numeric) = -13.1212358783 3.35231211709
y[1] (closed_form) = -13.1216853623 3.35257448513
absolute error = 0.0005205
relative error = 0.003843 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.8
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4847 1.717
h = 0.0001 0.004
y[1] (numeric) = -13.1200188897 3.35844266266
y[1] (closed_form) = -13.120468919 3.3587054903
absolute error = 0.0005212
relative error = 0.003848 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.802
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
x[1] = 2.4848 1.721
h = 0.003 0.006
y[1] (numeric) = -13.120816295 3.36631161732
y[1] (closed_form) = -13.1212674596 3.36657456669
absolute error = 0.0005222
relative error = 0.003855 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.804
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4878 1.727
h = 0.0001 0.005
y[1] (numeric) = -13.1164267419 3.37882491032
y[1] (closed_form) = -13.1168796826 3.37909053175
absolute error = 0.0005251
relative error = 0.003877 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.809
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
memory used=4176.0MB, alloc=52.3MB, time=53.89
x[1] = 2.4879 1.732
h = 0.0001 0.003
y[1] (numeric) = -13.1174794643 3.38865764655
y[1] (closed_form) = -13.11793418 3.38892344065
absolute error = 0.0005267
relative error = 0.003887 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.811
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.488 1.735
h = 0.001 0.001
y[1] (numeric) = -13.1180347631 3.39456751522
y[1] (closed_form) = -13.1184901161 3.39483338847
absolute error = 0.0005273
relative error = 0.003891 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.812
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] = 2.489 1.736
h = 0.001 0.003
y[1] (numeric) = -13.1163240304 3.39678007317
y[1] (closed_form) = -13.1167793753 3.39704608872
absolute error = 0.0005274
relative error = 0.003892 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.813
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.49 1.739
h = 0.0001 0.004
y[1] (numeric) = -13.115115375 3.40291650724
y[1] (closed_form) = -13.1155712647 3.40318298233
absolute error = 0.0005281
relative error = 0.003897 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.815
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
x[1] = 2.4901 1.743
h = 0.003 0.006
y[1] (numeric) = -13.1159250409 3.41078950396
y[1] (closed_form) = -13.116382065 3.4110561012
absolute error = 0.0005291
relative error = 0.003904 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.817
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4222.7MB, alloc=52.3MB, time=54.49
x[1] = 2.4931 1.749
h = 0.0001 0.005
y[1] (numeric) = -13.1115512157 3.42331766232
y[1] (closed_form) = -13.1120100135 3.42358693062
absolute error = 0.000532
relative error = 0.003926 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.822
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] = 2.4932 1.754
h = 0.0001 0.003
y[1] (numeric) = -13.1126192812 3.43315537515
y[1] (closed_form) = -13.1130798528 3.43342481679
absolute error = 0.0005336
relative error = 0.003936 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.823
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] = 2.4933 1.757
h = 0.001 0.001
y[1] (numeric) = -13.113183747 3.43906835404
y[1] (closed_form) = -13.1136449554 3.43933787507
absolute error = 0.0005342
relative error = 0.00394 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.825
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4943 1.758
h = 0.001 0.003
y[1] (numeric) = -13.1114751668 3.4412849325
y[1] (closed_form) = -13.1119363671 3.44155459573
absolute error = 0.0005343
relative error = 0.003941 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.826
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4953 1.761
h = 0.0001 0.004
y[1] (numeric) = -13.1102748365 3.44742725483
y[1] (closed_form) = -13.110736581 3.44769737753
absolute error = 0.000535
relative error = 0.003946 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.828
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=4269.3MB, alloc=52.3MB, time=55.09
x[1] = 2.4954 1.765
h = 0.003 0.006
y[1] (numeric) = -13.1110967529 3.45530429633
y[1] (closed_form) = -13.111559631 3.45557454159
absolute error = 0.000536
relative error = 0.003953 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.829
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] = 2.4984 1.771
h = 0.0001 0.005
y[1] (numeric) = -13.1067386384 3.46784731701
y[1] (closed_form) = -13.1072032878 3.46812023232
absolute error = 0.0005389
relative error = 0.003974 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.834
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4985 1.776
h = 0.0001 0.003
y[1] (numeric) = -13.1078220347 3.47769000983
y[1] (closed_form) = -13.1082884565 3.47796309914
absolute error = 0.0005405
relative error = 0.003985 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.836
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4986 1.779
h = 0.001 0.001
y[1] (numeric) = -13.1083956599 3.48360610089
y[1] (closed_form) = -13.1088627182 3.4838792698
absolute error = 0.0005411
relative error = 0.003989 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.838
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.4996 1.78
h = 0.001 0.003
y[1] (numeric) = -13.106689229 3.4858266981
y[1] (closed_form) = -13.107156279 3.48610000911
absolute error = 0.0005411
relative error = 0.00399 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.839
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4315.9MB, alloc=52.3MB, time=55.68
x[1] = 2.5006 1.783
h = 0.0001 0.004
y[1] (numeric) = -13.1054972155 3.49197490836
y[1] (closed_form) = -13.1059648092 3.49224867877
absolute error = 0.0005418
relative error = 0.003995 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.841
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5007 1.787
h = 0.003 0.006
y[1] (numeric) = -13.1063313725 3.49985599724
y[1] (closed_form) = -13.106800099 3.50012989063
absolute error = 0.0005429
relative error = 0.004002 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.842
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] = 2.5037 1.793
h = 0.0001 0.005
y[1] (numeric) = -13.1019889517 3.51241387706
y[1] (closed_form) = -13.1024594471 3.51269043945
absolute error = 0.0005458
relative error = 0.004023 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.847
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5038 1.798
h = 0.0001 0.003
y[1] (numeric) = -13.1030876661 3.52226155317
y[1] (closed_form) = -13.1035599327 3.5225382902
absolute error = 0.0005474
relative error = 0.004034 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.849
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] = 2.5039 1.801
h = 0.001 0.001
y[1] (numeric) = -13.1036704433 3.52818075824
y[1] (closed_form) = -13.1041433459 3.52845757509
absolute error = 0.000548
relative error = 0.004038 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.851
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4362.5MB, alloc=52.3MB, time=56.28
x[1] = 2.5049 1.802
h = 0.0001 0.004
y[1] (numeric) = -13.1019661585 3.5304053724
y[1] (closed_form) = -13.1024390528 3.53068233126
absolute error = 0.000548
relative error = 0.004039 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.852
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.505 1.806
h = 0.003 0.006
y[1] (numeric) = -13.102810892 3.53828980147
y[1] (closed_form) = -13.1032849183 3.53856688371
absolute error = 0.0005491
relative error = 0.004045 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.854
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.508 1.812
h = 0.0001 0.005
y[1] (numeric) = -13.0984821431 3.55086028221
y[1] (closed_form) = -13.0989579364 3.55114003258
absolute error = 0.0005519
relative error = 0.004067 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.859
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5081 1.817
h = 0.0001 0.003
y[1] (numeric) = -13.0995940923 3.56071206802
y[1] (closed_form) = -13.1000716557 3.56099199359
absolute error = 0.0005536
relative error = 0.004078 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.86
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] = 2.5082 1.82
h = 0.001 0.001
y[1] (numeric) = -13.1001847783 3.56663384606
y[1] (closed_form) = -13.1006629773 3.56691385164
absolute error = 0.0005541
relative error = 0.004081 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.862
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=4409.2MB, alloc=52.3MB, time=56.88
x[1] = 2.5092 1.821
h = 0.001 0.003
y[1] (numeric) = -13.0984823861 3.56886189093
y[1] (closed_form) = -13.0989605767 3.56914203843
absolute error = 0.0005542
relative error = 0.004082 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.863
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
x[1] = 2.5102 1.824
h = 0.0001 0.004
y[1] (numeric) = -13.0973058969 3.5750209573
y[1] (closed_form) = -13.0977846301 3.57530156405
absolute error = 0.0005549
relative error = 0.004087 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.865
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5103 1.828
h = 0.003 0.006
y[1] (numeric) = -13.0981628522 3.58290943854
y[1] (closed_form) = -13.0986427168 3.58319016901
absolute error = 0.0005559
relative error = 0.004094 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.867
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] = 2.5133 1.834
h = 0.0001 0.005
y[1] (numeric) = -13.0938497655 3.59549477232
y[1] (closed_form) = -13.0943313946 3.59577816985
absolute error = 0.0005588
relative error = 0.004115 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.872
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5134 1.839
h = 0.0001 0.003
y[1] (numeric) = -13.0949770097 3.60535154733
y[1] (closed_form) = -13.0954604077 3.60563512068
absolute error = 0.0005604
relative error = 0.004126 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.874
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4455.7MB, alloc=52.3MB, time=57.48
x[1] = 2.5135 1.842
h = 0.001 0.001
y[1] (numeric) = -13.0955768337 3.61127644271
y[1] (closed_form) = -13.0960608669 3.61156009629
absolute error = 0.000561
relative error = 0.00413 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.875
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5145 1.843
h = 0.001 0.003
y[1] (numeric) = -13.0938765817 3.61350850119
y[1] (closed_form) = -13.0943606064 3.61379229658
absolute error = 0.0005611
relative error = 0.004131 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.876
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] = 2.5155 1.846
h = 0.0001 0.004
y[1] (numeric) = -13.0927083862 3.61967345426
y[1] (closed_form) = -13.0931929529 3.61995770883
absolute error = 0.0005618
relative error = 0.004136 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.878
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5156 1.85
h = 0.003 0.006
y[1] (numeric) = -13.0935775535 3.62756598996
y[1] (closed_form) = -13.0940632507 3.62785036862
absolute error = 0.0005628
relative error = 0.004142 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.88
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5186 1.856
h = 0.0001 0.005
y[1] (numeric) = -13.0892801121 3.6401661732
y[1] (closed_form) = -13.0897675717 3.64045321783
absolute error = 0.0005657
relative error = 0.004164 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.885
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=4502.4MB, alloc=52.3MB, time=58.08
x[1] = 2.5187 1.861
h = 0.0001 0.003
y[1] (numeric) = -13.0904226389 3.65002794033
y[1] (closed_form) = -13.090911866 3.65031516139
absolute error = 0.0005673
relative error = 0.004174 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.887
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5188 1.864
h = 0.001 0.001
y[1] (numeric) = -13.0910315934 3.65595595471
y[1] (closed_form) = -13.0915214552 3.65624325619
absolute error = 0.0005679
relative error = 0.004178 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.888
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5198 1.865
h = 0.001 0.003
y[1] (numeric) = -13.0893334786 3.65819202494
y[1] (closed_form) = -13.0898233319 3.65847946815
absolute error = 0.000568
relative error = 0.004179 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.889
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
x[1] = 2.5208 1.868
h = 0.0001 0.004
y[1] (numeric) = -13.0881735686 3.66436286412
y[1] (closed_form) = -13.0886639634 3.6646507664
absolute error = 0.0005687
relative error = 0.004184 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.892
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5209 1.872
h = 0.003 0.006
y[1] (numeric) = -13.089054938 3.67225945651
y[1] (closed_form) = -13.0895464624 3.67254748327
absolute error = 0.0005697
relative error = 0.00419 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.893
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=4549.2MB, alloc=52.3MB, time=58.68
x[1] = 2.5239 1.878
h = 0.0001 0.005
y[1] (numeric) = -13.0847731252 3.68487448548
y[1] (closed_form) = -13.0852664097 3.68516517711
absolute error = 0.0005726
relative error = 0.004212 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.898
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.524 1.883
h = 0.0001 0.003
y[1] (numeric) = -13.0859309221 3.69474124755
y[1] (closed_form) = -13.0864259729 3.69503211619
absolute error = 0.0005742
relative error = 0.004222 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.9
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
x[1] = 2.5241 1.886
h = 0.001 0.001
y[1] (numeric) = -13.0865489997 3.70067238248
y[1] (closed_form) = -13.0870446847 3.70096333176
absolute error = 0.0005748
relative error = 0.004226 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.901
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5251 1.887
h = 0.001 0.003
y[1] (numeric) = -13.0848530189 3.70291246261
y[1] (closed_form) = -13.0853486953 3.7032035535
absolute error = 0.0005748
relative error = 0.004227 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.903
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5261 1.89
h = 0.0001 0.004
y[1] (numeric) = -13.0837013865 3.70908918721
y[1] (closed_form) = -13.0841976039 3.70938073708
absolute error = 0.0005755
relative error = 0.004232 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.905
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4595.7MB, alloc=52.3MB, time=59.28
x[1] = 2.5262 1.894
h = 0.003 0.006
y[1] (numeric) = -13.084594948 3.71698983845
y[1] (closed_form) = -13.0850922941 3.71728151316
absolute error = 0.0005766
relative error = 0.004239 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.906
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5292 1.9
h = 0.0001 0.005
y[1] (numeric) = -13.0803287472 3.7296197093
y[1] (closed_form) = -13.0808278512 3.72991404775
absolute error = 0.0005794
relative error = 0.00426 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.912
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5293 1.905
h = 0.0001 0.003
y[1] (numeric) = -13.0815018018 3.73949146898
y[1] (closed_form) = -13.0820026708 3.73978598504
absolute error = 0.000581
relative error = 0.00427 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.914
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] = 2.5294 1.908
h = 0.001 0.001
y[1] (numeric) = -13.082128995 3.74542572597
y[1] (closed_form) = -13.0826304977 3.74572032285
absolute error = 0.0005816
relative error = 0.004274 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.915
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5304 1.909
h = 0.0001 0.004
y[1] (numeric) = -13.0804351452 3.74766981409
y[1] (closed_form) = -13.0809366393 3.74796455249
absolute error = 0.0005817
relative error = 0.004275 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.916
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=4642.5MB, alloc=52.3MB, time=59.87
x[1] = 2.5305 1.913
h = 0.003 0.006
y[1] (numeric) = -13.0813392416 3.75557381557
y[1] (closed_form) = -13.0818418639 3.75586867917
absolute error = 0.0005827
relative error = 0.004282 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.918
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] = 2.5335 1.919
h = 0.0001 0.005
y[1] (numeric) = -13.0770866427 3.76821627292
y[1] (closed_form) = -13.0775910207 3.76851379932
absolute error = 0.0005856
relative error = 0.004303 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.923
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] = 2.5336 1.924
h = 0.0001 0.003
y[1] (numeric) = -13.0782728803 3.7780921549
y[1] (closed_form) = -13.0787790223 3.7783898594
absolute error = 0.0005872
relative error = 0.004313 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.925
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
x[1] = 2.5337 1.927
h = 0.001 0.001
y[1] (numeric) = -13.0789079511 3.78402899193
y[1] (closed_form) = -13.0794147264 3.78432677743
absolute error = 0.0005878
relative error = 0.004317 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.926
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] = 2.5347 1.928
h = 0.001 0.003
y[1] (numeric) = -13.0772159808 3.78627650313
y[1] (closed_form) = -13.0777227476 3.78657443007
absolute error = 0.0005879
relative error = 0.004318 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.928
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
memory used=4689.2MB, alloc=52.3MB, time=60.47
x[1] = 2.5357 1.931
h = 0.0001 0.004
y[1] (numeric) = -13.0760798 3.79246407876
y[1] (closed_form) = -13.0765871066 3.79276246449
absolute error = 0.0005886
relative error = 0.004323 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.93
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5358 1.935
h = 0.003 0.006
y[1] (numeric) = -13.07699607 3.80037214298
y[1] (closed_form) = -13.0775045039 3.80067065421
absolute error = 0.0005896
relative error = 0.004329 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.931
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5388 1.941
h = 0.0001 0.005
y[1] (numeric) = -13.0727590523 3.81302943487
y[1] (closed_form) = -13.0732692399 3.81333060776
absolute error = 0.0005924
relative error = 0.00435 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.936
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] = 2.5389 1.946
h = 0.0001 0.003
y[1] (numeric) = -13.0739605247 3.8229103193
y[1] (closed_form) = -13.0744724749 3.82321167084
absolute error = 0.0005941
relative error = 0.004361 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.938
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
x[1] = 2.539 1.949
h = 0.001 0.001
y[1] (numeric) = -13.0746046972 3.82885028108
y[1] (closed_form) = -13.0751172803 3.8291517138
absolute error = 0.0005946
relative error = 0.004365 %
Correct digits = 4
memory used=4735.9MB, alloc=52.3MB, time=61.07
Radius of convergence (given) for eq 1 = 4.94
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] = 2.54 1.95
h = 0.001 0.003
y[1] (numeric) = -13.0729148523 3.83110179674
y[1] (closed_form) = -13.0734274268 3.8314033708
absolute error = 0.0005947
relative error = 0.004365 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.941
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.541 1.953
h = 0.0001 0.004
y[1] (numeric) = -13.0717869263 3.8372952556
y[1] (closed_form) = -13.0723000401 3.83759728834
absolute error = 0.0005954
relative error = 0.00437 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.943
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5411 1.957
h = 0.003 0.006
y[1] (numeric) = -13.0727153601 3.84520738438
y[1] (closed_form) = -13.0732296003 3.84550954297
absolute error = 0.0005964
relative error = 0.004377 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.945
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5441 1.963
h = 0.0001 0.005
y[1] (numeric) = -13.0684939074 3.85787950659
y[1] (closed_form) = -13.069009899 3.85818432566
absolute error = 0.0005993
relative error = 0.004398 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.95
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=4782.6MB, alloc=52.3MB, time=61.67
x[1] = 2.5442 1.968
h = 0.0001 0.003
y[1] (numeric) = -13.0697106021 3.86776539582
y[1] (closed_form) = -13.0702283551 3.86807039409
absolute error = 0.0006009
relative error = 0.004409 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.952
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5443 1.971
h = 0.001 0.001
y[1] (numeric) = -13.0703638689 3.87370848364
y[1] (closed_form) = -13.0708822543 3.87401356327
absolute error = 0.0006015
relative error = 0.004412 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.953
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5453 1.972
h = 0.001 0.003
y[1] (numeric) = -13.0686761464 3.87596400181
y[1] (closed_form) = -13.0691945232 3.87626922268
absolute error = 0.0006016
relative error = 0.004413 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.955
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5463 1.975
h = 0.0001 0.004
y[1] (numeric) = -13.0675564673 3.88216334297
y[1] (closed_form) = -13.0680753829 3.88246902241
absolute error = 0.0006023
relative error = 0.004418 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.957
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5464 1.979
h = 0.003 0.006
y[1] (numeric) = -13.0684970549 3.8900795381
y[1] (closed_form) = -13.0690170961 3.89038534372
absolute error = 0.0006033
relative error = 0.004424 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.958
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
memory used=4829.3MB, alloc=52.3MB, time=62.27
x[1] = 2.5494 1.985
h = 0.0001 0.005
y[1] (numeric) = -13.0642911509 3.90276648626
y[1] (closed_form) = -13.0648129413 3.90307495118
absolute error = 0.0006061
relative error = 0.004445 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.964
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5495 1.99
h = 0.0001 0.003
y[1] (numeric) = -13.0655230557 3.91265738253
y[1] (closed_form) = -13.0660466062 3.91296602718
absolute error = 0.0006078
relative error = 0.004456 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.966
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5496 1.993
h = 0.001 0.001
y[1] (numeric) = -13.0661854094 3.9186035976
y[1] (closed_form) = -13.0667095919 3.91891232379
absolute error = 0.0006083
relative error = 0.004459 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.967
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5506 1.994
h = 0.001 0.003
y[1] (numeric) = -13.0644998064 3.92086311632
y[1] (closed_form) = -13.0650239801 3.92117198364
absolute error = 0.0006084
relative error = 0.00446 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.968
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] = 2.5516 1.997
h = 0.0001 0.004
y[1] (numeric) = -13.0633883664 3.92706833879
y[1] (closed_form) = -13.0639130784 3.92737766456
absolute error = 0.0006091
relative error = 0.004465 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.97
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=4875.9MB, alloc=52.3MB, time=62.87
x[1] = 2.5517 2.001
h = 0.003 0.006
y[1] (numeric) = -13.064341098 3.93498860195
y[1] (closed_form) = -13.0648669348 3.93529805423
absolute error = 0.0006101
relative error = 0.004472 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.972
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5547 2.007
h = 0.0001 0.005
y[1] (numeric) = -13.0601507265 3.94769037158
y[1] (closed_form) = -13.0606783104 3.94800248197
absolute error = 0.000613
relative error = 0.004493 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.977
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5548 2.012
h = 0.0001 0.003
y[1] (numeric) = -13.0613978291 3.957586277
y[1] (closed_form) = -13.0619271717 3.95789856763
absolute error = 0.0006146
relative error = 0.004503 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.979
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] = 2.5549 2.015
h = 0.001 0.001
y[1] (numeric) = -13.0620692623 3.9635356205
y[1] (closed_form) = -13.0625992364 3.96384799284
absolute error = 0.0006152
relative error = 0.004507 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.981
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5559 2.016
h = 0.0001 0.004
y[1] (numeric) = -13.0603857758 3.96579913776
y[1] (closed_form) = -13.0609157411 3.96611165114
absolute error = 0.0006152
relative error = 0.004507 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.982
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=4922.5MB, alloc=52.3MB, time=63.46
x[1] = 2.556 2.02
h = 0.003 0.006
y[1] (numeric) = -13.0613490012 3.9737227593
y[1] (closed_form) = -13.0618800906 3.97403539951
absolute error = 0.0006163
relative error = 0.004514 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.984
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.559 2.026
h = 0.0001 0.005
y[1] (numeric) = -13.0571721632 3.9864370983
y[1] (closed_form) = -13.0577049978 3.9867523956
absolute error = 0.0006191
relative error = 0.004535 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.989
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
x[1] = 2.5591 2.031
h = 0.0001 0.003
y[1] (numeric) = -13.0584323974 3.9963371362
y[1] (closed_form) = -13.0589669897 3.9966526142
absolute error = 0.0006207
relative error = 0.004545 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.991
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
x[1] = 2.5592 2.034
h = 0.001 0.001
y[1] (numeric) = -13.0591116772 4.00228906538
y[1] (closed_form) = -13.0596469006 4.00260462524
absolute error = 0.0006213
relative error = 0.004549 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.992
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5602 2.035
h = 0.001 0.003
y[1] (numeric) = -13.0574300579 4.0045559977
y[1] (closed_form) = -13.0579652725 4.00487169851
absolute error = 0.0006214
relative error = 0.00455 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.994
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
memory used=4969.2MB, alloc=52.3MB, time=64.06
x[1] = 2.5612 2.038
h = 0.0001 0.004
y[1] (numeric) = -13.0563339982 4.01077206312
y[1] (closed_form) = -13.05686975 4.01108822216
absolute error = 0.0006221
relative error = 0.004554 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.996
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5613 2.042
h = 0.003 0.006
y[1] (numeric) = -13.0573093492 4.01869975575
y[1] (closed_form) = -13.0578462243 4.01901604188
absolute error = 0.0006231
relative error = 0.004561 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 4.998
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
x[1] = 2.5643 2.048
h = 0.0001 0.005
y[1] (numeric) = -13.0531480139 4.03142890773
y[1] (closed_form) = -13.0536866321 4.03174784973
absolute error = 0.000626
relative error = 0.004582 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.003
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] = 2.5644 2.053
h = 0.0001 0.003
y[1] (numeric) = -13.054423423 4.04133395857
y[1] (closed_form) = -13.0549637976 4.04165308176
absolute error = 0.0006276
relative error = 0.004592 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.005
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] = 2.5645 2.056
h = 0.001 0.001
y[1] (numeric) = -13.0551117686 4.04728901823
y[1] (closed_form) = -13.0556527739 4.04760822345
absolute error = 0.0006282
relative error = 0.004596 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.006
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=5015.9MB, alloc=52.3MB, time=64.67
x[1] = 2.5655 2.057
h = 0.001 0.003
y[1] (numeric) = -13.0534322605 4.0495599454
y[1] (closed_form) = -13.0539732569 4.04987929146
absolute error = 0.0006282
relative error = 0.004596 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.007
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] = 2.5665 2.06
h = 0.0001 0.004
y[1] (numeric) = -13.0523444176 4.05578188902
y[1] (closed_form) = -13.0528859507 4.05610169318
absolute error = 0.0006289
relative error = 0.004601 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.01
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5666 2.064
h = 0.003 0.006
y[1] (numeric) = -13.0533318845 4.06371365412
y[1] (closed_form) = -13.0538745401 4.06403358568
absolute error = 0.0006299
relative error = 0.004608 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.011
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5696 2.07
h = 0.0001 0.005
y[1] (numeric) = -13.049186036 4.07645761424
y[1] (closed_form) = -13.0497304325 4.07678020044
absolute error = 0.0006328
relative error = 0.004628 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.017
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5697 2.075
h = 0.0001 0.003
y[1] (numeric) = -13.0504766078 4.08636767982
y[1] (closed_form) = -13.0510227595 4.08669044768
absolute error = 0.0006344
relative error = 0.004639 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.019
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5062.5MB, alloc=52.3MB, time=65.27
x[1] = 2.5698 2.078
h = 0.001 0.001
y[1] (numeric) = -13.0511740119 4.09232587093
y[1] (closed_form) = -13.0517207937 4.09264872097
absolute error = 0.000635
relative error = 0.004642 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.02
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
x[1] = 2.5708 2.079
h = 0.001 0.003
y[1] (numeric) = -13.049496612 4.0946007909
y[1] (closed_form) = -13.050043385 4.09492378169
absolute error = 0.000635
relative error = 0.004643 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.021
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
x[1] = 2.5718 2.082
h = 0.0001 0.004
y[1] (numeric) = -13.0484169782 4.10082861148
y[1] (closed_form) = -13.0489642873 4.10115206024
absolute error = 0.0006357
relative error = 0.004648 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.024
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5719 2.086
h = 0.003 0.006
y[1] (numeric) = -13.0494165513 4.1087644504
y[1] (closed_form) = -13.0499649821 4.10908802685
absolute error = 0.0006368
relative error = 0.004654 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.025
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5749 2.092
h = 0.0001 0.005
y[1] (numeric) = -13.0452861738 4.12152321371
y[1] (closed_form) = -13.0458363433 4.12184944354
absolute error = 0.0006396
relative error = 0.004675 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.031
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=5109.1MB, alloc=52.3MB, time=65.87
x[1] = 2.575 2.097
h = 0.0001 0.003
y[1] (numeric) = -13.0465918961 4.13143829571
y[1] (closed_form) = -13.0471438196 4.13176470767
absolute error = 0.0006412
relative error = 0.004685 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.033
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] = 2.5751 2.1
h = 0.001 0.001
y[1] (numeric) = -13.0472983513 4.13739961916
y[1] (closed_form) = -13.0478509044 4.13772611346
absolute error = 0.0006418
relative error = 0.004689 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.034
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] = 2.5761 2.101
h = 0.001 0.003
y[1] (numeric) = -13.045623057 4.13967852988
y[1] (closed_form) = -13.0461756012 4.14000516483
absolute error = 0.0006419
relative error = 0.00469 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.035
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] = 2.5771 2.104
h = 0.0001 0.004
y[1] (numeric) = -13.0445516246 4.14591222612
y[1] (closed_form) = -13.0451047045 4.1462393189
absolute error = 0.0006426
relative error = 0.004694 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.038
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
x[1] = 2.5772 2.108
h = 0.003 0.006
y[1] (numeric) = -13.045563294 4.15385214011
y[1] (closed_form) = -13.0461174947 4.15417936086
absolute error = 0.0006436
relative error = 0.004701 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.039
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=5155.8MB, alloc=52.3MB, time=66.47
x[1] = 2.5802 2.114
h = 0.0001 0.005
y[1] (numeric) = -13.0414483718 4.16662570153
y[1] (closed_form) = -13.0420043092 4.1669555744
absolute error = 0.0006464
relative error = 0.004721 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.045
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5803 2.119
h = 0.0001 0.003
y[1] (numeric) = -13.0427692325 4.17654580152
y[1] (closed_form) = -13.0433269225 4.17687585697
absolute error = 0.000648
relative error = 0.004732 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.047
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] = 2.5804 2.122
h = 0.001 0.001
y[1] (numeric) = -13.0434847314 4.18251025815
y[1] (closed_form) = -13.0440430507 4.1828403961
absolute error = 0.0006486
relative error = 0.004735 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.048
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
x[1] = 2.5814 2.123
h = 0.0001 0.004
y[1] (numeric) = -13.0418115398 4.18479315755
y[1] (closed_form) = -13.0423698501 4.18512343605
absolute error = 0.0006487
relative error = 0.004736 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.049
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5815 2.127
h = 0.003 0.006
y[1] (numeric) = -13.0428336622 4.19273643618
y[1] (closed_form) = -13.0433930926 4.19306684294
absolute error = 0.0006497
relative error = 0.004742 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.051
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5202.4MB, alloc=52.3MB, time=67.06
x[1] = 2.5845 2.133
h = 0.0001 0.005
y[1] (numeric) = -13.0387322071 4.20552254731
y[1] (closed_form) = -13.0392933724 4.20585560513
absolute error = 0.0006526
relative error = 0.004763 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.056
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
x[1] = 2.5846 2.138
h = 0.0001 0.003
y[1] (numeric) = -13.0400661485 4.21544678767
y[1] (closed_form) = -13.0406290653 4.21578002846
absolute error = 0.0006542
relative error = 0.004773 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.059
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5847 2.141
h = 0.001 0.001
y[1] (numeric) = -13.0407894635 4.22141383425
y[1] (closed_form) = -13.0413530091 4.22174715766
absolute error = 0.0006547
relative error = 0.004776 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.06
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] = 2.5857 2.142
h = 0.001 0.003
y[1] (numeric) = -13.0391181271 4.2237001403
y[1] (closed_form) = -13.0396816638 4.22403360418
absolute error = 0.0006548
relative error = 0.004777 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.061
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5867 2.145
h = 0.0001 0.004
y[1] (numeric) = -13.0380620054 4.22994466861
y[1] (closed_form) = -13.0386260767 4.23027859005
absolute error = 0.0006555
relative error = 0.004782 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.063
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=5249.2MB, alloc=52.3MB, time=67.66
x[1] = 2.5868 2.149
h = 0.003 0.006
y[1] (numeric) = -13.039096206 4.23789202456
y[1] (closed_form) = -13.0396613966 4.2382260745
absolute error = 0.0006565
relative error = 0.004788 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.065
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
x[1] = 2.5898 2.155
h = 0.0001 0.005
y[1] (numeric) = -13.0350101772 4.25069292424
y[1] (closed_form) = -13.0355771007 4.25102962394
absolute error = 0.0006594
relative error = 0.004809 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.071
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
x[1] = 2.5899 2.16
h = 0.0001 0.003
y[1] (numeric) = -13.0363592343 4.26062218538
y[1] (closed_form) = -13.0369279081 4.26095906849
absolute error = 0.000661
relative error = 0.004819 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.073
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.59 2.163
h = 0.001 0.001
y[1] (numeric) = -13.0370915795 4.2665923666
y[1] (closed_form) = -13.0376608816 4.26692933247
absolute error = 0.0006616
relative error = 0.004822 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.074
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] = 2.591 2.164
h = 0.001 0.003
y[1] (numeric) = -13.0354223408 4.26888265746
y[1] (closed_form) = -13.0359916339 4.26921976369
absolute error = 0.0006616
relative error = 0.004823 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.075
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=5295.8MB, alloc=52.3MB, time=68.26
x[1] = 2.592 2.167
h = 0.0001 0.004
y[1] (numeric) = -13.0343743987 4.27513305747
y[1] (closed_form) = -13.034944226 4.27547062111
absolute error = 0.0006623
relative error = 0.004828 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.078
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] = 2.5921 2.171
h = 0.003 0.006
y[1] (numeric) = -13.0354206679 4.2830844917
y[1] (closed_form) = -13.0359916137 4.2834221841
absolute error = 0.0006633
relative error = 0.004834 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.079
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] = 2.5951 2.177
h = 0.0001 0.005
y[1] (numeric) = -13.03135005 4.29590017452
y[1] (closed_form) = -13.0319227266 4.29624051539
absolute error = 0.0006662
relative error = 0.004855 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.085
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] = 2.5952 2.182
h = 0.0001 0.003
y[1] (numeric) = -13.0327142108 4.3058344577
y[1] (closed_form) = -13.0332886364 4.3061749824
absolute error = 0.0006678
relative error = 0.004865 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.087
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5953 2.185
h = 0.001 0.001
y[1] (numeric) = -13.0334555789 4.31180777421
y[1] (closed_form) = -13.0340306324 4.31214838181
absolute error = 0.0006684
relative error = 0.004868 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.088
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=5342.5MB, alloc=52.3MB, time=68.86
x[1] = 2.5963 2.186
h = 0.001 0.003
y[1] (numeric) = -13.0317884352 4.31410204777
y[1] (closed_form) = -13.0323634795 4.31444279563
absolute error = 0.0006684
relative error = 0.004869 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.09
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5973 2.189
h = 0.0001 0.004
y[1] (numeric) = -13.0307486652 4.32035831793
y[1] (closed_form) = -13.0313242433 4.32069952305
absolute error = 0.0006691
relative error = 0.004874 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.092
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.5974 2.193
h = 0.003 0.006
y[1] (numeric) = -13.0318069933 4.32831383137
y[1] (closed_form) = -13.032383689 4.32865516549
absolute error = 0.0006701
relative error = 0.00488 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.094
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6004 2.199
h = 0.0001 0.005
y[1] (numeric) = -13.027751771 4.34114429182
y[1] (closed_form) = -13.0283301955 4.3414882731
absolute error = 0.000673
relative error = 0.004901 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.099
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] = 2.6005 2.204
h = 0.0001 0.003
y[1] (numeric) = -13.0291310235 4.35108359821
y[1] (closed_form) = -13.0297111957 4.35142776372
absolute error = 0.0006746
relative error = 0.004911 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.101
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5389.1MB, alloc=52.3MB, time=69.45
x[1] = 2.6006 2.207
h = 0.001 0.001
y[1] (numeric) = -13.0298814073 4.35706005059
y[1] (closed_form) = -13.030462207 4.35740429914
absolute error = 0.0006752
relative error = 0.004914 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.103
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] = 2.6016 2.208
h = 0.001 0.003
y[1] (numeric) = -13.0282163557 4.35935830471
y[1] (closed_form) = -13.0287971463 4.35970269342
absolute error = 0.0006752
relative error = 0.004915 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.104
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6026 2.211
h = 0.0001 0.004
y[1] (numeric) = -13.0271847505 4.36562044344
y[1] (closed_form) = -13.0277660742 4.36596528925
absolute error = 0.0006759
relative error = 0.004919 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.106
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6027 2.215
h = 0.003 0.006
y[1] (numeric) = -13.0282551278 4.37358003691
y[1] (closed_form) = -13.0288375684 4.37392501198
absolute error = 0.0006769
relative error = 0.004926 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.108
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
x[1] = 2.6057 2.221
h = 0.0001 0.005
y[1] (numeric) = -13.0242152859 4.38642526937
y[1] (closed_form) = -13.0247994533 4.38677289026
absolute error = 0.0006798
relative error = 0.004946 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.113
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=5435.8MB, alloc=52.3MB, time=70.06
x[1] = 2.6058 2.226
h = 0.0001 0.003
y[1] (numeric) = -13.025609618 4.39636960002
y[1] (closed_form) = -13.0261955318 4.39671740553
absolute error = 0.0006814
relative error = 0.004956 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.116
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] = 2.6059 2.229
h = 0.001 0.001
y[1] (numeric) = -13.0263690103 4.4023491888
y[1] (closed_form) = -13.026955551 4.40269707748
absolute error = 0.000682
relative error = 0.004959 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.117
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
x[1] = 2.6069 2.23
h = 0.0001 0.004
y[1] (numeric) = -13.0247060483 4.40465142134
y[1] (closed_form) = -13.0252925799 4.40499945008
absolute error = 0.000682
relative error = 0.00496 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.118
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.607 2.234
h = 0.003 0.006
y[1] (numeric) = -13.0257868382 4.41261438394
y[1] (closed_form) = -13.0263744859 4.41296254221
absolute error = 0.000683
relative error = 0.004966 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.12
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] = 2.61 2.24
h = 0.0001 0.005
y[1] (numeric) = -13.0217603989 4.42547214411
y[1] (closed_form) = -13.0223497717 4.42582294707
absolute error = 0.0006859
relative error = 0.004987 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.125
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=5482.4MB, alloc=52.3MB, time=70.65
x[1] = 2.6101 2.245
h = 0.0001 0.003
y[1] (numeric) = -13.0231677613 4.4354206208
y[1] (closed_form) = -13.0237588794 4.43577160873
absolute error = 0.0006875
relative error = 0.004997 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.128
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6102 2.248
h = 0.001 0.001
y[1] (numeric) = -13.0239349394 4.44140280247
y[1] (closed_form) = -13.0245266841 4.44175387368
absolute error = 0.000688
relative error = 0.005 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.129
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6112 2.249
h = 0.001 0.003
y[1] (numeric) = -13.0222738213 4.44370843291
y[1] (closed_form) = -13.0228655568 4.4440596441
absolute error = 0.0006881
relative error = 0.005001 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.13
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6122 2.252
h = 0.0001 0.004
y[1] (numeric) = -13.0212574586 4.4499813902
y[1] (closed_form) = -13.0218497264 4.45033305819
absolute error = 0.0006888
relative error = 0.005005 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.133
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] = 2.6123 2.256
h = 0.003 0.006
y[1] (numeric) = -13.0223502799 4.45794843433
y[1] (closed_form) = -13.022943663 4.45830023203
absolute error = 0.0006898
relative error = 0.005011 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.134
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
memory used=5529.0MB, alloc=52.3MB, time=71.25
x[1] = 2.6153 2.262
h = 0.0001 0.005
y[1] (numeric) = -13.0183391929 4.47082095593
y[1] (closed_form) = -13.0189342991 4.47117539698
absolute error = 0.0006927
relative error = 0.005032 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.14
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] = 2.6154 2.267
h = 0.0001 0.003
y[1] (numeric) = -13.0197616126 4.48077445872
y[1] (closed_form) = -13.0203584629 4.48112908511
absolute error = 0.0006943
relative error = 0.005042 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.142
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] = 2.6155 2.27
h = 0.001 0.001
y[1] (numeric) = -13.0205377858 4.48675977768
y[1] (closed_form) = -13.0211352621 4.48711448747
absolute error = 0.0006948
relative error = 0.005045 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.144
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6165 2.271
h = 0.001 0.003
y[1] (numeric) = -13.0188787523 4.48906938253
y[1] (closed_form) = -13.0194762195 4.48942423219
absolute error = 0.0006949
relative error = 0.005046 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.145
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6175 2.274
h = 0.0001 0.004
y[1] (numeric) = -13.0178705332 4.49534820361
y[1] (closed_form) = -13.0184685321 4.49570350991
absolute error = 0.0006956
relative error = 0.00505 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.147
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=5575.6MB, alloc=52.3MB, time=71.84
x[1] = 2.6176 2.278
h = 0.003 0.006
y[1] (numeric) = -13.0189753763 4.50331932981
y[1] (closed_form) = -13.0195744897 4.50367476605
absolute error = 0.0006966
relative error = 0.005057 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.149
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6206 2.284
h = 0.0001 0.005
y[1] (numeric) = -13.0149796265 4.51620660693
y[1] (closed_form) = -13.0155804612 4.51656468515
absolute error = 0.0006994
relative error = 0.005077 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.154
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] = 2.6207 2.289
h = 0.0001 0.003
y[1] (numeric) = -13.0164170917 4.52616513656
y[1] (closed_form) = -13.0170196691 4.52652340049
absolute error = 0.000701
relative error = 0.005087 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.157
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] = 2.6208 2.292
h = 0.001 0.001
y[1] (numeric) = -13.0172022527 4.53215359316
y[1] (closed_form) = -13.0178054558 4.53251194061
absolute error = 0.0007016
relative error = 0.00509 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.158
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
x[1] = 2.6218 2.293
h = 0.001 0.003
y[1] (numeric) = -13.0155453014 4.53446717023
y[1] (closed_form) = -13.0161484952 4.53482565745
absolute error = 0.0007017
relative error = 0.005091 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.159
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5622.3MB, alloc=52.3MB, time=72.44
x[1] = 2.6228 2.296
h = 0.0001 0.004
y[1] (numeric) = -13.0145452184 4.54075185329
y[1] (closed_form) = -13.0151489434 4.54111079698
absolute error = 0.0007024
relative error = 0.005095 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.162
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6229 2.3
h = 0.003 0.006
y[1] (numeric) = -13.0156620738 4.54872706209
y[1] (closed_form) = -13.0162669126 4.54908613593
absolute error = 0.0007034
relative error = 0.005101 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.163
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6259 2.306
h = 0.0001 0.005
y[1] (numeric) = -13.0116816465 4.56162908869
y[1] (closed_form) = -13.0122882045 4.56199080314
absolute error = 0.0007062
relative error = 0.005122 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.169
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] = 2.626 2.311
h = 0.0001 0.003
y[1] (numeric) = -13.0131341452 4.57159264583
y[1] (closed_form) = -13.0137424447 4.57195454634
absolute error = 0.0007078
relative error = 0.005132 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.171
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] = 2.6261 2.314
h = 0.001 0.001
y[1] (numeric) = -13.013928287 4.57758424036
y[1] (closed_form) = -13.0145372117 4.57794622449
absolute error = 0.0007084
relative error = 0.005135 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.173
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=5669.0MB, alloc=52.3MB, time=73.04
x[1] = 2.6271 2.315
h = 0.001 0.003
y[1] (numeric) = -13.0122734153 4.57990178744
y[1] (closed_form) = -13.0128823307 4.58026391125
absolute error = 0.0007085
relative error = 0.005135 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.174
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6281 2.318
h = 0.0001 0.004
y[1] (numeric) = -13.011281461 4.58619233063
y[1] (closed_form) = -13.0118909072 4.58655491073
absolute error = 0.0007091
relative error = 0.00514 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.176
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6282 2.322
h = 0.003 0.006
y[1] (numeric) = -13.0124103193 4.59417162245
y[1] (closed_form) = -13.0130208783 4.59453433292
absolute error = 0.0007102
relative error = 0.005146 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.178
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6312 2.328
h = 0.0001 0.005
y[1] (numeric) = -13.0084451997 4.6070883924
y[1] (closed_form) = -13.0090574761 4.6074537421
absolute error = 0.000713
relative error = 0.005166 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.183
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
x[1] = 2.6313 2.333
h = 0.0001 0.003
y[1] (numeric) = -13.00991272 4.61705697762
y[1] (closed_form) = -13.0105267366 4.6174225137
absolute error = 0.0007146
relative error = 0.005176 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.186
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=5715.7MB, alloc=52.3MB, time=73.64
x[1] = 2.6314 2.336
h = 0.001 0.001
y[1] (numeric) = -13.0107158355 4.62305171029
y[1] (closed_form) = -13.0113304768 4.62341733012
absolute error = 0.0007152
relative error = 0.005179 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.187
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
x[1] = 2.6324 2.337
h = 0.0001 0.004
y[1] (numeric) = -13.0090630408 4.62537322517
y[1] (closed_form) = -13.0096776728 4.62573898457
absolute error = 0.0007152
relative error = 0.00518 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.189
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] = 2.6325 2.341
h = 0.003 0.006
y[1] (numeric) = -13.0102022718 4.63335588896
y[1] (closed_form) = -13.0108180159 4.63372177895
absolute error = 0.0007163
relative error = 0.005186 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.19
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6355 2.347
h = 0.0001 0.005
y[1] (numeric) = -13.0062504924 4.6462851624
y[1] (closed_form) = -13.0068679523 4.64665369045
absolute error = 0.0007191
relative error = 0.005206 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.196
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
x[1] = 2.6356 2.352
h = 0.0001 0.003
y[1] (numeric) = -13.0077309932 4.65625789723
y[1] (closed_form) = -13.0083501923 4.65662661196
absolute error = 0.0007207
relative error = 0.005216 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.198
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5762.3MB, alloc=52.3MB, time=74.24
x[1] = 2.6357 2.355
h = 0.001 0.001
y[1] (numeric) = -13.0085418646 4.66225522448
y[1] (closed_form) = -13.009161688 4.66262402305
absolute error = 0.0007212
relative error = 0.005219 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.2
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] = 2.6367 2.356
h = 0.001 0.003
y[1] (numeric) = -13.006890903 4.66458012822
y[1] (closed_form) = -13.007510717 4.66494906628
absolute error = 0.0007213
relative error = 0.00522 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.201
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] = 2.6377 2.359
h = 0.0001 0.004
y[1] (numeric) = -13.0059141251 4.67088147397
y[1] (closed_form) = -13.0065344689 4.67125086799
absolute error = 0.000722
relative error = 0.005224 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.203
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
x[1] = 2.6378 2.363
h = 0.003 0.006
y[1] (numeric) = -13.0070653412 4.67886822154
y[1] (closed_form) = -13.0076867964 4.6792377463
absolute error = 0.000723
relative error = 0.00523 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.205
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5808.9MB, alloc=52.3MB, time=74.84
x[1] = 2.6408 2.369
h = 0.0001 0.005
y[1] (numeric) = -13.0031288424 4.69181222683
y[1] (closed_form) = -13.0037520114 4.69218438825
absolute error = 0.0007258
relative error = 0.00525 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.21
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
x[1] = 2.6409 2.374
h = 0.0001 0.003
y[1] (numeric) = -13.0046243428 4.70178999065
y[1] (closed_form) = -13.0052492497 4.70216233907
absolute error = 0.0007274
relative error = 0.00526 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.213
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.641 2.377
h = 0.001 0.001
y[1] (numeric) = -13.0054441747 4.70779045641
y[1] (closed_form) = -13.0060697055 4.70816288877
absolute error = 0.000728
relative error = 0.005263 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.214
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] = 2.642 2.378
h = 0.001 0.003
y[1] (numeric) = -13.0037952855 4.71011932381
y[1] (closed_form) = -13.0044208069 4.71049189556
absolute error = 0.0007281
relative error = 0.005264 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.216
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.643 2.381
h = 0.0001 0.004
y[1] (numeric) = -13.0028266157 4.71642652415
y[1] (closed_form) = -13.0034526664 4.71679955168
absolute error = 0.0007288
relative error = 0.005268 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.218
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=5855.6MB, alloc=52.3MB, time=75.43
x[1] = 2.6431 2.385
h = 0.003 0.006
y[1] (numeric) = -13.0039898075 4.72441735567
y[1] (closed_form) = -13.0046169689 4.72479051413
absolute error = 0.0007298
relative error = 0.005274 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.22
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6461 2.391
h = 0.0001 0.005
y[1] (numeric) = -13.0000685748 4.7373760864
y[1] (closed_form) = -13.0006974481 4.7377518801
absolute error = 0.0007326
relative error = 0.005294 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.225
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] = 2.6462 2.396
h = 0.0001 0.003
y[1] (numeric) = -13.0015790631 4.74735887949
y[1] (closed_form) = -13.002209673 4.7477348605
absolute error = 0.0007342
relative error = 0.005304 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.228
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] = 2.6463 2.399
h = 0.001 0.001
y[1] (numeric) = -13.0024078483 4.75336248381
y[1] (closed_form) = -13.0030390817 4.75373854885
absolute error = 0.0007348
relative error = 0.005307 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.229
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
x[1] = 2.6473 2.4
h = 0.001 0.003
y[1] (numeric) = -13.0007610291 4.75569531263
y[1] (closed_form) = -13.0013922531 4.75607151696
absolute error = 0.0007348
relative error = 0.005308 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.23
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
memory used=5902.2MB, alloc=52.3MB, time=76.03
x[1] = 2.6483 2.403
h = 0.0001 0.004
y[1] (numeric) = -12.9998004603 4.76200836549
y[1] (closed_form) = -13.0004322131 4.76238502541
absolute error = 0.0007355
relative error = 0.005312 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.233
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6484 2.407
h = 0.003 0.006
y[1] (numeric) = -13.0009756185 4.7700032811
y[1] (closed_form) = -13.0016084811 4.77038007213
absolute error = 0.0007365
relative error = 0.005318 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.235
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] = 2.6514 2.413
h = 0.0001 0.005
y[1] (numeric) = -12.9970696375 4.78297673076
y[1] (closed_form) = -12.9977042102 4.78335615561
absolute error = 0.0007394
relative error = 0.005338 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.24
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
x[1] = 2.6515 2.418
h = 0.0001 0.003
y[1] (numeric) = -12.998595102 4.7929645533
y[1] (closed_form) = -12.9992314101 4.79334416575
absolute error = 0.0007409
relative error = 0.005348 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.242
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] = 2.6516 2.421
h = 0.001 0.001
y[1] (numeric) = -12.9994328336 4.79897129618
y[1] (closed_form) = -13.0000697646 4.79935099276
absolute error = 0.0007415
relative error = 0.005351 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.244
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5948.8MB, alloc=52.3MB, time=76.63
x[1] = 2.6526 2.422
h = 0.001 0.003
y[1] (numeric) = -12.9977880819 4.80130808415
y[1] (closed_form) = -12.9984250035 4.80168791991
absolute error = 0.0007416
relative error = 0.005352 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.245
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] = 2.6536 2.425
h = 0.0001 0.004
y[1] (numeric) = -12.996835607 4.80762698743
y[1] (closed_form) = -12.997473057 4.80800727859
absolute error = 0.0007423
relative error = 0.005356 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.248
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6537 2.429
h = 0.003 0.006
y[1] (numeric) = -12.9980227222 4.81562598718
y[1] (closed_form) = -12.9986612811 4.81600640963
absolute error = 0.0007433
relative error = 0.005362 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.249
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6567 2.435
h = 0.0001 0.005
y[1] (numeric) = -12.9941319786 4.82861414916
y[1] (closed_form) = -12.9947722459 4.828997204
absolute error = 0.0007461
relative error = 0.005382 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.255
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6568 2.44
h = 0.0001 0.003
y[1] (numeric) = -12.9956724076 4.83860700124
y[1] (closed_form) = -12.9963144089 4.83899024396
absolute error = 0.0007477
relative error = 0.005391 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.257
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=5995.4MB, alloc=52.3MB, time=77.23
x[1] = 2.6569 2.443
h = 0.001 0.001
y[1] (numeric) = -12.9965190786 4.84461688264
y[1] (closed_form) = -12.9971617024 4.84500020957
absolute error = 0.0007483
relative error = 0.005395 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.259
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6579 2.444
h = 0.0001 0.004
y[1] (numeric) = -12.994876392 4.84695762747
y[1] (closed_form) = -12.9955190064 4.8473410935
absolute error = 0.0007483
relative error = 0.005395 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.26
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] = 2.658 2.448
h = 0.003 0.006
y[1] (numeric) = -12.9960738406 4.85496000038
y[1] (closed_form) = -12.9967175631 4.8553435979
absolute error = 0.0007494
relative error = 0.005401 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.262
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.661 2.454
h = 0.0001 0.005
y[1] (numeric) = -12.9921963768 4.86796063961
y[1] (closed_form) = -12.9928418061 4.86834686829
absolute error = 0.0007522
relative error = 0.005421 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.268
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
x[1] = 2.6611 2.459
h = 0.0001 0.003
y[1] (numeric) = -12.9937497373 4.87795764288
y[1] (closed_form) = -12.9943968996 4.87834405969
absolute error = 0.0007537
relative error = 0.00543 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.27
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=6042.1MB, alloc=52.3MB, time=77.83
x[1] = 2.6612 2.462
h = 0.001 0.001
y[1] (numeric) = -12.9946041347 4.88397011934
y[1] (closed_form) = -12.9952519191 4.88435662045
absolute error = 0.0007543
relative error = 0.005434 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.271
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6622 2.463
h = 0.001 0.003
y[1] (numeric) = -12.9929632709 4.88631424372
y[1] (closed_form) = -12.9936110459 4.88670088383
absolute error = 0.0007544
relative error = 0.005434 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.273
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6632 2.466
h = 0.0001 0.004
y[1] (numeric) = -12.9920259078 4.89264393124
y[1] (closed_form) = -12.9926742102 4.89303102638
absolute error = 0.0007551
relative error = 0.005439 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.275
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6633 2.47
h = 0.003 0.006
y[1] (numeric) = -12.9932352959 4.90065038836
y[1] (closed_form) = -12.9938847058 4.90103761511
absolute error = 0.0007561
relative error = 0.005444 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.277
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] = 2.6663 2.476
h = 0.0001 0.005
y[1] (numeric) = -12.9893730433 4.91366572754
y[1] (closed_form) = -12.9900241581 4.91405558401
absolute error = 0.0007589
relative error = 0.005464 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.283
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
memory used=6088.7MB, alloc=52.3MB, time=78.43
x[1] = 2.6664 2.481
h = 0.0001 0.003
y[1] (numeric) = -12.9909413466 4.9236677604
y[1] (closed_form) = -12.9915941932 4.92405780526
absolute error = 0.0007605
relative error = 0.005474 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.285
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
x[1] = 2.6665 2.484
h = 0.001 0.001
y[1] (numeric) = -12.9918046704 4.92968337521
y[1] (closed_form) = -12.9924581386 4.93007350445
absolute error = 0.0007611
relative error = 0.005477 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.286
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6675 2.485
h = 0.001 0.003
y[1] (numeric) = -12.9901658673 4.93203145222
y[1] (closed_form) = -12.9908193261 4.93242172036
absolute error = 0.0007611
relative error = 0.005477 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.288
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6685 2.488
h = 0.0001 0.004
y[1] (numeric) = -12.989236578 4.93836698391
y[1] (closed_form) = -12.9898905638 4.93875770689
absolute error = 0.0007618
relative error = 0.005482 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.29
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6686 2.492
h = 0.003 0.006
y[1] (numeric) = -12.9904578965 4.94637752503
y[1] (closed_form) = -12.9911129889 4.94676837977
absolute error = 0.0007628
relative error = 0.005488 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.292
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6135.5MB, alloc=52.3MB, time=79.03
x[1] = 2.6716 2.498
h = 0.0001 0.005
y[1] (numeric) = -12.9866108411 4.95940755732
y[1] (closed_form) = -12.9872676366 4.95980104031
absolute error = 0.0007656
relative error = 0.005507 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.298
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
x[1] = 2.6717 2.503
h = 0.0001 0.003
y[1] (numeric) = -12.9881940756 4.96941461959
y[1] (closed_form) = -12.9888526017 4.96980829123
absolute error = 0.0007672
relative error = 0.005517 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.3
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6718 2.506
h = 0.001 0.001
y[1] (numeric) = -12.9890663188 4.97543337253
y[1] (closed_form) = -12.9897254661 4.97582712862
absolute error = 0.0007678
relative error = 0.00552 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.301
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6728 2.507
h = 0.001 0.003
y[1] (numeric) = -12.9874295742 4.97778539986
y[1] (closed_form) = -12.9880887119 4.97817929475
absolute error = 0.0007679
relative error = 0.00552 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.303
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6738 2.51
h = 0.0001 0.004
y[1] (numeric) = -12.9865083517 4.98412677341
y[1] (closed_form) = -12.987168016 4.98452112294
absolute error = 0.0007685
relative error = 0.005525 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.305
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6182.0MB, alloc=52.3MB, time=79.63
x[1] = 2.6739 2.514
h = 0.003 0.006
y[1] (numeric) = -12.9877415913 4.99214139831
y[1] (closed_form) = -12.9884023614 4.99253587975
absolute error = 0.0007696
relative error = 0.005531 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.307
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6769 2.52
h = 0.0001 0.005
y[1] (numeric) = -12.9839097192 5.00518611674
y[1] (closed_form) = -12.9845721907 5.00558322496
absolute error = 0.0007724
relative error = 0.00555 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.313
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] = 2.677 2.525
h = 0.0001 0.003
y[1] (numeric) = -12.9855078735 5.01519820816
y[1] (closed_form) = -12.9861720743 5.01559550527
absolute error = 0.000774
relative error = 0.00556 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.315
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6771 2.528
h = 0.001 0.001
y[1] (numeric) = -12.9863890291 5.02122009897
y[1] (closed_form) = -12.9870538507 5.0216174806
absolute error = 0.0007745
relative error = 0.005563 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.317
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6781 2.529
h = 0.001 0.003
y[1] (numeric) = -12.9847543406 5.02357607429
y[1] (closed_form) = -12.9854191527 5.02397359463
absolute error = 0.0007746
relative error = 0.005563 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.318
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6228.7MB, alloc=52.3MB, time=80.22
x[1] = 2.6791 2.532
h = 0.0001 0.004
y[1] (numeric) = -12.9838411781 5.02992328736
y[1] (closed_form) = -12.9845065162 5.03032126213
absolute error = 0.0007753
relative error = 0.005568 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.32
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6792 2.536
h = 0.003 0.006
y[1] (numeric) = -12.9850863296 5.03794199573
y[1] (closed_form) = -12.9857527727 5.03834010255
absolute error = 0.0007763
relative error = 0.005573 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.322
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6822 2.542
h = 0.0001 0.005
y[1] (numeric) = -12.9812696271 5.05100139327
y[1] (closed_form) = -12.9819377699 5.05140212539
absolute error = 0.0007791
relative error = 0.005593 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.328
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
x[1] = 2.6823 2.547
h = 0.0001 0.003
y[1] (numeric) = -12.9828826896 5.06101851347
y[1] (closed_form) = -12.9835525604 5.06141943471
absolute error = 0.0007807
relative error = 0.005602 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.33
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] = 2.6824 2.55
h = 0.001 0.001
y[1] (numeric) = -12.9837727508 5.06704354183
y[1] (closed_form) = -12.9844432419 5.06744454766
absolute error = 0.0007813
relative error = 0.005605 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.332
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6275.3MB, alloc=52.3MB, time=80.82
x[1] = 2.6834 2.551
h = 0.0001 0.004
y[1] (numeric) = -12.9821401162 5.06940346281
y[1] (closed_form) = -12.9828105977 5.06980460725
absolute error = 0.0007813
relative error = 0.005606 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.333
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6835 2.555
h = 0.003 0.006
y[1] (numeric) = -12.9833955624 5.07742554402
y[1] (closed_form) = -12.9840671482 5.07782682068
absolute error = 0.0007823
relative error = 0.005611 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.335
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6865 2.561
h = 0.0001 0.005
y[1] (numeric) = -12.9795920811 5.09049739067
y[1] (closed_form) = -12.9802653651 5.09090129137
absolute error = 0.0007851
relative error = 0.005631 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.341
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] = 2.6866 2.566
h = 0.0001 0.003
y[1] (numeric) = -12.9812180268 5.10051866172
y[1] (closed_form) = -12.9818930377 5.10092275174
absolute error = 0.0007867
relative error = 0.00564 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.343
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6867 2.569
h = 0.001 0.001
y[1] (numeric) = -12.9821157856 5.10654628451
y[1] (closed_form) = -12.9827914164 5.10695045918
absolute error = 0.0007873
relative error = 0.005643 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.345
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=6322.0MB, alloc=52.3MB, time=81.42
x[1] = 2.6877 2.57
h = 0.001 0.003
y[1] (numeric) = -12.980484964 5.10890957548
y[1] (closed_form) = -12.9811605852 5.10931388868
absolute error = 0.0007874
relative error = 0.005644 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.346
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] = 2.6887 2.573
h = 0.0001 0.004
y[1] (numeric) = -12.9795868505 5.11526755229
y[1] (closed_form) = -12.9802629969 5.11567231953
absolute error = 0.000788
relative error = 0.005648 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.348
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] = 2.6888 2.577
h = 0.003 0.006
y[1] (numeric) = -12.9808541914 5.12329371637
y[1] (closed_form) = -12.9815314414 5.12369861592
absolute error = 0.0007891
relative error = 0.005654 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.35
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6918 2.583
h = 0.0001 0.005
y[1] (numeric) = -12.9770658543 5.13638022897
y[1] (closed_form) = -12.9777448008 5.13678775106
absolute error = 0.0007919
relative error = 0.005673 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.356
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6919 2.588
h = 0.0001 0.003
y[1] (numeric) = -12.9787066869 5.14640652803
y[1] (closed_form) = -12.9793873591 5.14681423966
absolute error = 0.0007934
relative error = 0.005683 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.358
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=6368.7MB, alloc=52.3MB, time=82.02
x[1] = 2.692 2.591
h = 0.001 0.001
y[1] (numeric) = -12.9796133385 5.15243728771
y[1] (closed_form) = -12.9802946301 5.15284508405
absolute error = 0.000794
relative error = 0.005685 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.36
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] = 2.693 2.592
h = 0.001 0.003
y[1] (numeric) = -12.9779845666 5.15480452
y[1] (closed_form) = -12.9786658486 5.15521245477
absolute error = 0.0007941
relative error = 0.005686 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.361
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.694 2.595
h = 0.0001 0.004
y[1] (numeric) = -12.9770944934 5.16116832942
y[1] (closed_form) = -12.9777763002 5.16157671802
absolute error = 0.0007948
relative error = 0.00569 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.364
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6941 2.599
h = 0.003 0.006
y[1] (numeric) = -12.9783737201 5.16919857584
y[1] (closed_form) = -12.9790566296 5.16960709687
absolute error = 0.0007958
relative error = 0.005696 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.366
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] = 2.6971 2.605
h = 0.0001 0.005
y[1] (numeric) = -12.9746005137 5.1822997471
y[1] (closed_form) = -12.975285118 5.18271088916
absolute error = 0.0007986
relative error = 0.005716 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.371
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6415.3MB, alloc=52.3MB, time=82.62
x[1] = 2.6972 2.61
h = 0.0001 0.003
y[1] (numeric) = -12.9762562218 5.19233107357
y[1] (closed_form) = -12.9769425506 5.19274240536
absolute error = 0.0008002
relative error = 0.005725 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.374
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6973 2.613
h = 0.001 0.001
y[1] (numeric) = -12.9771717594 5.19836496966
y[1] (closed_form) = -12.9778587072 5.19877638624
absolute error = 0.0008007
relative error = 0.005727 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.375
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6983 2.614
h = 0.001 0.003
y[1] (numeric) = -12.975545035 5.20073614092
y[1] (closed_form) = -12.9762319731 5.20114769582
absolute error = 0.0008008
relative error = 0.005728 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.377
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.6993 2.617
h = 0.0001 0.004
y[1] (numeric) = -12.9746629955 5.20710578043
y[1] (closed_form) = -12.9753504579 5.20751778894
absolute error = 0.0008015
relative error = 0.005732 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.379
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] = 2.6994 2.621
h = 0.003 0.006
y[1] (numeric) = -12.9759540987 5.21514010859
y[1] (closed_form) = -12.9766426631 5.21555224965
absolute error = 0.0008025
relative error = 0.005738 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.381
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=6462.0MB, alloc=52.3MB, time=83.22
x[1] = 2.7024 2.627
h = 0.0001 0.005
y[1] (numeric) = -12.9721960097 5.22825593116
y[1] (closed_form) = -12.9728862671 5.22867069174
absolute error = 0.0008053
relative error = 0.005757 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.386
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7025 2.632
h = 0.0001 0.003
y[1] (numeric) = -12.973866582 5.23829228433
y[1] (closed_form) = -12.9745585627 5.23870723483
absolute error = 0.0008069
relative error = 0.005766 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.389
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7026 2.635
h = 0.001 0.001
y[1] (numeric) = -12.9747909988 5.24432931632
y[1] (closed_form) = -12.9754835981 5.24474435166
absolute error = 0.0008074
relative error = 0.005769 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.391
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7036 2.636
h = 0.001 0.003
y[1] (numeric) = -12.9731663197 5.24670442417
y[1] (closed_form) = -12.9738589093 5.24711959774
absolute error = 0.0008075
relative error = 0.00577 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.392
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7046 2.639
h = 0.0001 0.004
y[1] (numeric) = -12.9722923072 5.25307989119
y[1] (closed_form) = -12.9729854207 5.25349551815
absolute error = 0.0008082
relative error = 0.005774 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.394
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
memory used=6508.7MB, alloc=52.3MB, time=83.82
x[1] = 2.7047 2.643
h = 0.003 0.006
y[1] (numeric) = -12.973595278 5.26111830047
y[1] (closed_form) = -12.9742894926 5.26153406008
absolute error = 0.0008092
relative error = 0.00578 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.396
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
x[1] = 2.7077 2.649
h = 0.0001 0.005
y[1] (numeric) = -12.969852293 5.2742487669
y[1] (closed_form) = -12.970548199 5.27466714452
absolute error = 0.000812
relative error = 0.005799 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.402
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7078 2.654
h = 0.0001 0.003
y[1] (numeric) = -12.9715377182 5.28429014599
y[1] (closed_form) = -12.9722353462 5.2847087137
absolute error = 0.0008136
relative error = 0.005808 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.404
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7079 2.657
h = 0.001 0.001
y[1] (numeric) = -12.9724710074 5.2903303133
y[1] (closed_form) = -12.9731692536 5.29074896591
absolute error = 0.0008141
relative error = 0.005811 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.406
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7089 2.658
h = 0.0001 0.004
y[1] (numeric) = -12.9708483715 5.29270935537
y[1] (closed_form) = -12.971546608 5.2931281461
absolute error = 0.0008142
relative error = 0.005812 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.407
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
memory used=6555.4MB, alloc=52.3MB, time=84.42
x[1] = 2.709 2.662
h = 0.003 0.006
y[1] (numeric) = -12.9721615989 5.30075113571
y[1] (closed_form) = -12.9728609358 5.30117005924
absolute error = 0.0008152
relative error = 0.005817 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.409
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.712 2.668
h = 0.0001 0.005
y[1] (numeric) = -12.9684317787 5.31389402137
y[1] (closed_form) = -12.9691328056 5.31431556161
absolute error = 0.000818
relative error = 0.005836 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.415
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] = 2.7121 2.673
h = 0.0001 0.003
y[1] (numeric) = -12.9701300397 5.32393954917
y[1] (closed_form) = -12.9708327875 5.32436127966
absolute error = 0.0008196
relative error = 0.005845 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.417
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7122 2.676
h = 0.001 0.001
y[1] (numeric) = -12.9710709979 5.32998230918
y[1] (closed_form) = -12.9717743635 5.33040412461
absolute error = 0.0008202
relative error = 0.005848 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.419
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7132 2.677
h = 0.001 0.003
y[1] (numeric) = -12.9694501659 5.33236471148
y[1] (closed_form) = -12.9701535217 5.33278666495
absolute error = 0.0008202
relative error = 0.005849 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.42
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=6602.0MB, alloc=52.3MB, time=85.02
x[1] = 2.7142 2.68
h = 0.0001 0.004
y[1] (numeric) = -12.9685911413 5.33875091971
y[1] (closed_form) = -12.9692950202 5.33917332616
absolute error = 0.0008209
relative error = 0.005853 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.423
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] = 2.7143 2.684
h = 0.003 0.006
y[1] (numeric) = -12.9699162194 5.34679677994
y[1] (closed_form) = -12.970621198 5.34721931923
absolute error = 0.0008219
relative error = 0.005858 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.425
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7173 2.69
h = 0.0001 0.005
y[1] (numeric) = -12.9662014788 5.35995429556
y[1] (closed_form) = -12.9669081457 5.36037945004
absolute error = 0.0008247
relative error = 0.005878 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.43
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
x[1] = 2.7174 2.695
h = 0.0001 0.003
y[1] (numeric) = -12.9679145717 5.37000484772
y[1] (closed_form) = -12.9686229583 5.37043019262
absolute error = 0.0008263
relative error = 0.005887 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.433
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] = 2.7175 2.698
h = 0.001 0.001
y[1] (numeric) = -12.9688643898 5.37605074194
y[1] (closed_form) = -12.9695733937 5.37647617182
absolute error = 0.0008268
relative error = 0.005889 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.435
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6648.7MB, alloc=52.3MB, time=85.63
x[1] = 2.7185 2.699
h = 0.001 0.003
y[1] (numeric) = -12.967245597 5.37843707403
y[1] (closed_form) = -12.9679545912 5.37886264185
absolute error = 0.0008269
relative error = 0.00589 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.436
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7195 2.702
h = 0.0001 0.004
y[1] (numeric) = -12.9663945804 5.38482910226
y[1] (closed_form) = -12.9671040972 5.38525512283
absolute error = 0.0008276
relative error = 0.005894 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.438
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7196 2.706
h = 0.003 0.006
y[1] (numeric) = -12.9677315004 5.39287904149
y[1] (closed_form) = -12.9684421161 5.393305195
absolute error = 0.0008286
relative error = 0.0059 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.44
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
x[1] = 2.7226 2.712
h = 0.0001 0.005
y[1] (numeric) = -12.9640318262 5.40605117943
y[1] (closed_form) = -12.9647441287 5.40647994657
absolute error = 0.0008314
relative error = 0.005919 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.446
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] = 2.7227 2.717
h = 0.0001 0.003
y[1] (numeric) = -12.96575974 5.41610675493
y[1] (closed_form) = -12.9664737608 5.41653571264
absolute error = 0.000833
relative error = 0.005928 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.448
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=6695.3MB, alloc=52.3MB, time=86.22
x[1] = 2.7228 2.72
h = 0.001 0.001
y[1] (numeric) = -12.9667184113 5.42215578264
y[1] (closed_form) = -12.967433049 5.42258482537
absolute error = 0.0008335
relative error = 0.00593 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.45
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7238 2.721
h = 0.001 0.003
y[1] (numeric) = -12.9651016556 5.42454604211
y[1] (closed_form) = -12.9658162836 5.42497522269
absolute error = 0.0008336
relative error = 0.005931 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.451
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] = 2.7248 2.724
h = 0.0001 0.004
y[1] (numeric) = -12.9642586405 5.43094388759
y[1] (closed_form) = -12.9649737906 5.4313735207
absolute error = 0.0008343
relative error = 0.005935 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.454
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] = 2.7249 2.728
h = 0.003 0.006
y[1] (numeric) = -12.9656073933 5.43899790493
y[1] (closed_form) = -12.9663236417 5.43942767106
absolute error = 0.0008353
relative error = 0.00594 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.456
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7279 2.734
h = 0.0001 0.005
y[1] (numeric) = -12.9619227729 5.45218465745
y[1] (closed_form) = -12.9626407063 5.45261703565
absolute error = 0.0008381
relative error = 0.00596 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.461
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=6742.0MB, alloc=52.3MB, time=86.82
x[1] = 2.728 2.739
h = 0.0001 0.003
y[1] (numeric) = -12.9636654963 5.46224525518
y[1] (closed_form) = -12.9643851469 5.4626778241
absolute error = 0.0008397
relative error = 0.005968 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.464
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7281 2.742
h = 0.001 0.001
y[1] (numeric) = -12.9646330141 5.46829741561
y[1] (closed_form) = -12.9653532812 5.4687300696
absolute error = 0.0008402
relative error = 0.005971 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.466
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] = 2.7291 2.743
h = 0.001 0.003
y[1] (numeric) = -12.9630182935 5.47069160006
y[1] (closed_form) = -12.9637385509 5.47112439179
absolute error = 0.0008403
relative error = 0.005972 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.467
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7301 2.746
h = 0.0001 0.004
y[1] (numeric) = -12.9621832734 5.47709526002
y[1] (closed_form) = -12.9629040524 5.47752850404
absolute error = 0.000841
relative error = 0.005976 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.469
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
x[1] = 2.7302 2.75
h = 0.003 0.006
y[1] (numeric) = -12.9635438502 5.48515335451
y[1] (closed_form) = -12.9642657267 5.48558673163
absolute error = 0.000842
relative error = 0.005981 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.471
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=6788.7MB, alloc=52.3MB, time=87.42
x[1] = 2.7332 2.756
h = 0.0001 0.005
y[1] (numeric) = -12.9598742707 5.49835471378
y[1] (closed_form) = -12.9605978307 5.49879070143
absolute error = 0.0008448
relative error = 0.006 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.477
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7333 2.761
h = 0.0001 0.003
y[1] (numeric) = -12.9616317926 5.50842033257
y[1] (closed_form) = -12.9623570686 5.50885651106
absolute error = 0.0008463
relative error = 0.006009 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.48
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7334 2.764
h = 0.001 0.001
y[1] (numeric) = -12.9626081504 5.51447562491
y[1] (closed_form) = -12.9633340423 5.51491188849
absolute error = 0.0008469
relative error = 0.006012 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.481
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7344 2.765
h = 0.0001 0.004
y[1] (numeric) = -12.9609954629 5.51687373191
y[1] (closed_form) = -12.9617213451 5.51731013315
absolute error = 0.000847
relative error = 0.006012 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.483
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7345 2.769
h = 0.003 0.006
y[1] (numeric) = -12.962366259 5.52493519431
y[1] (closed_form) = -12.9630932378 5.52537172875
absolute error = 0.000848
relative error = 0.006018 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.485
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
memory used=6835.4MB, alloc=52.3MB, time=88.02
x[1] = 2.7375 2.775
h = 0.0001 0.005
y[1] (numeric) = -12.9587097898 5.53814894133
y[1] (closed_form) = -12.9594384508 5.53858808497
absolute error = 0.0008508
relative error = 0.006037 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.49
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] = 2.7376 2.78
h = 0.0001 0.003
y[1] (numeric) = -12.9604801008 5.54821870496
y[1] (closed_form) = -12.9612104768 5.54865803956
absolute error = 0.0008523
relative error = 0.006045 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.493
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
x[1] = 2.7377 2.783
h = 0.001 0.001
y[1] (numeric) = -12.9614640996 5.55427658726
y[1] (closed_form) = -12.9621950912 5.55471600699
absolute error = 0.0008529
relative error = 0.006048 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.495
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7387 2.784
h = 0.001 0.003
y[1] (numeric) = -12.9598532073 5.55667804454
y[1] (closed_form) = -12.960584189 5.55711760185
absolute error = 0.000853
relative error = 0.006049 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.496
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7397 2.787
h = 0.0001 0.004
y[1] (numeric) = -12.9590331158 5.5630924213
y[1] (closed_form) = -12.9597646185 5.56353243046
absolute error = 0.0008536
relative error = 0.006053 %
Correct digits = 4
memory used=6882.0MB, alloc=52.3MB, time=88.62
Radius of convergence (given) for eq 1 = 5.498
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7398 2.791
h = 0.003 0.006
y[1] (numeric) = -12.9604157195 5.57115795901
y[1] (closed_form) = -12.9611483181 5.57159810141
absolute error = 0.0008546
relative error = 0.006058 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.5
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] = 2.7428 2.797
h = 0.0001 0.005
y[1] (numeric) = -12.9567742675 5.58438629822
y[1] (closed_form) = -12.9575085468 5.58482904824
absolute error = 0.0008574
relative error = 0.006077 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.506
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
x[1] = 2.7429 2.802
h = 0.0001 0.003
y[1] (numeric) = -12.9585593566 5.59446108061
y[1] (closed_form) = -12.9592953495 5.59490402171
absolute error = 0.000859
relative error = 0.006086 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.509
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.743 2.805
h = 0.001 0.001
y[1] (numeric) = -12.959552183 5.60052209327
y[1] (closed_form) = -12.9602887911 5.60096511952
absolute error = 0.0008596
relative error = 0.006088 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.51
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=6928.4MB, alloc=52.3MB, time=89.22
x[1] = 2.744 2.806
h = 0.001 0.003
y[1] (numeric) = -12.9579433199 5.6029274686
y[1] (closed_form) = -12.9586799183 5.60337063233
absolute error = 0.0008596
relative error = 0.006089 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.512
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] = 2.745 2.809
h = 0.0001 0.004
y[1] (numeric) = -12.9571312051 5.60934765175
y[1] (closed_form) = -12.9578683239 5.60979126709
absolute error = 0.0008603
relative error = 0.006093 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.514
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7451 2.813
h = 0.003 0.006
y[1] (numeric) = -12.9585256075 5.6174172636
y[1] (closed_form) = -12.9592638214 5.61786101223
absolute error = 0.0008613
relative error = 0.006098 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.516
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7481 2.819
h = 0.0001 0.005
y[1] (numeric) = -12.9548991603 5.63066018699
y[1] (closed_form) = -12.9556390534 5.63110654168
absolute error = 0.0008641
relative error = 0.006117 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.522
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7482 2.824
h = 0.0001 0.003
y[1] (numeric) = -12.9566990164 5.64073998673
y[1] (closed_form) = -12.957440622 5.64118653259
absolute error = 0.0008657
relative error = 0.006126 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.525
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=6975.1MB, alloc=52.3MB, time=89.82
x[1] = 2.7483 2.827
h = 0.001 0.001
y[1] (numeric) = -12.9577006638 5.64680412878
y[1] (closed_form) = -12.9584428841 5.64725075983
absolute error = 0.0008662
relative error = 0.006128 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.526
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7493 2.828
h = 0.001 0.003
y[1] (numeric) = -12.9560938282 5.64921341974
y[1] (closed_form) = -12.9568360387 5.64966018816
absolute error = 0.0008663
relative error = 0.006129 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.528
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7503 2.831
h = 0.0001 0.004
y[1] (numeric) = -12.9552896835 5.65563940634
y[1] (closed_form) = -12.9560324141 5.65608662613
absolute error = 0.000867
relative error = 0.006133 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.53
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7504 2.835
h = 0.003 0.006
y[1] (numeric) = -12.956695876 5.66371309111
y[1] (closed_form) = -12.9574397009 5.66416044425
absolute error = 0.000868
relative error = 0.006138 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.532
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7534 2.841
h = 0.0001 0.005
y[1] (numeric) = -12.9530844211 5.6769705906
y[1] (closed_form) = -12.9538299237 5.67742054821
absolute error = 0.0008708
relative error = 0.006157 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.538
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=7021.7MB, alloc=52.3MB, time=90.42
x[1] = 2.7535 2.846
h = 0.0001 0.003
y[1] (numeric) = -12.9548990334 5.68705540619
y[1] (closed_form) = -12.9556462472 5.68750555508
absolute error = 0.0008723
relative error = 0.006165 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.54
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7536 2.849
h = 0.001 0.001
y[1] (numeric) = -12.9559094953 5.69312267666
y[1] (closed_form) = -12.9566573234 5.69357291075
absolute error = 0.0008729
relative error = 0.006168 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.542
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7546 2.85
h = 0.001 0.003
y[1] (numeric) = -12.9543046852 5.69553588078
y[1] (closed_form) = -12.9550525035 5.69598625215
absolute error = 0.000873
relative error = 0.006169 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.543
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] = 2.7556 2.853
h = 0.0001 0.004
y[1] (numeric) = -12.9535085044 5.70196766787
y[1] (closed_form) = -12.9542568424 5.70241849036
absolute error = 0.0008736
relative error = 0.006172 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.546
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7557 2.857
h = 0.003 0.006
y[1] (numeric) = -12.9549264782 5.7100454243
y[1] (closed_form) = -12.9556759097 5.71049638019
absolute error = 0.0008746
relative error = 0.006178 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.548
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
memory used=7068.3MB, alloc=52.3MB, time=91.01
x[1] = 2.7587 2.863
h = 0.0001 0.005
y[1] (numeric) = -12.9513300034 5.72331749174
y[1] (closed_form) = -12.952081111 5.72377105051
absolute error = 0.0008774
relative error = 0.006196 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.554
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7588 2.868
h = 0.0001 0.003
y[1] (numeric) = -12.9531593609 5.73340732162
y[1] (closed_form) = -12.9539121786 5.73386107175
absolute error = 0.000879
relative error = 0.006205 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.556
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 2.7589 2.871
h = 0.001 0.001
y[1] (numeric) = -12.9541786308 5.73947771946
y[1] (closed_form) = -12.9549320623 5.73993155481
absolute error = 0.0008796
relative error = 0.006207 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.558
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] = 2.7599 2.872
h = 0.001 0.003
y[1] (numeric) = -12.9525758443 5.7418948343
y[1] (closed_form) = -12.953329266 5.74234880684
absolute error = 0.0008796
relative error = 0.006208 %
Correct digits = 4
Radius of convergence (given) for eq 1 = 5.559
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff ( y , x , 1 ) = exp ( sqrt ( 0.1 * x + 0.2 ) ) ;
Iterations = 754
Total Elapsed Time = 1 Minutes 31 Seconds
Expected Time Remaining = 0 Seconds
Optimized Time Remaining = 0 Seconds
Expected Total Time = 1 Minutes 31 Seconds
> quit
memory used=7108.4MB, alloc=52.3MB, time=91.50