|\^/| Maple 2016 (X86 64 LINUX)
._|\| |/|_. Copyright (c) Maplesoft, a division of Waterloo Maple Inc. 2016
\ MAPLE / All rights reserved. Maple is a trademark of
<____ ____> Waterloo Maple Inc.
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#BEGIN OUTFILE1
# before write maple top matter
# before write_ats library and user def block
#BEGIN ATS LIBRARY BLOCK
# Begin Function number 2
> omniout_str := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s\n",str);
> fi;# end if 1;
> end;
omniout_str := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s\n", str) end if
end proc
# End Function number 2
# Begin Function number 3
> omniout_str_noeol := proc(iolevel,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> printf("%s",str);
> fi;# end if 1;
> end;
omniout_str_noeol := proc(iolevel, str)
global glob_iolevel;
if iolevel <= glob_iolevel then printf("%s", str) end if
end proc
# End Function number 3
# Begin Function number 4
> omniout_labstr := proc(iolevel,label,str)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> print(label,str);
> fi;# end if 1;
> end;
omniout_labstr := proc(iolevel, label, str)
global glob_iolevel;
if iolevel <= glob_iolevel then print(label, str) end if
end proc
# End Function number 4
# Begin Function number 5
> omniout_float := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 1
> if vallen = 4 then
> printf("%-30s = %-42.4g %s \n",prelabel,value, postlabel);
> else
> printf("%-30s = %-42.32g %s \n",prelabel,value, postlabel);
> fi;# end if 1;
> fi;# end if 0;
> end;
omniout_float := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then
printf("%-30s = %-42.4g %s \n", prelabel, value, postlabel)
else printf("%-30s = %-42.32g %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 5
# Begin Function number 6
> omniout_complex := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number 0
> if vallen = 4 then
> printf("%-30s = %-20.4g %-20g %s \n",prelabel,Re(value), Im(value), postlabel);
> else
> printf("%-30s = %-20.12g %-20.12g %s \n",prelabel,Re(value),Im(value), postlabel);
> fi;# end if 0;
> fi;# end if -1;
> end;
omniout_complex := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 4 then printf("%-30s = %-20.4g %-20g %s \n", prelabel,
Re(value), Im(value), postlabel)
else printf("%-30s = %-20.12g %-20.12g %s \n", prelabel, Re(value),
Im(value), postlabel)
end if
end if
end proc
# End Function number 6
# Begin Function number 7
> omniout_int := proc(iolevel,prelabel,prelen,value,vallen,postlabel)
> global glob_iolevel;
> if (glob_iolevel >= iolevel) then # if number -1
> if vallen = 5 then # if number 0
> printf("%-30s = %-32d %s\n",prelabel,value, postlabel);
> else
> printf("%-30s = %-32d %s \n",prelabel,value, postlabel);
> fi;# end if 0;
> fi;# end if -1;
> end;
omniout_int := proc(iolevel, prelabel, prelen, value, vallen, postlabel)
global glob_iolevel;
if iolevel <= glob_iolevel then
if vallen = 5 then
printf("%-30s = %-32d %s\n", prelabel, value, postlabel)
else printf("%-30s = %-32d %s \n", prelabel, value, postlabel)
end if
end if
end proc
# End Function number 7
# Begin Function number 8
> logitem_time := proc(fd,secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> fprintf(fd,"
");
> if (secs_in >= 0) then # if number -1
> years_int := int_trunc(secs_in / glob_sec_in_year);
> sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
> days_int := int_trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := sec_temp mod int_trunc(glob_sec_in_day) ;
> hours_int := int_trunc(sec_temp / glob_sec_in_hour);
> sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
> minutes_int := int_trunc(sec_temp / glob_sec_in_minute);
> sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
> if (years_int > 0) then # if number 0
> fprintf(fd,"%d Years %d Days %d Hours %d Minutes %d Seconds",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 1
> fprintf(fd,"%d Days %d Hours %d Minutes %d Seconds",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 2
> fprintf(fd,"%d Hours %d Minutes %d Seconds",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 3
> fprintf(fd,"%d Minutes %d Seconds",minutes_int,sec_int);
> else
> fprintf(fd,"%d Seconds",sec_int);
> fi;# end if 3
> else
> fprintf(fd," 0.0 Seconds");
> fi;# end if 2
> fprintf(fd," | \n");
> end;
logitem_time := proc(fd, secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
fprintf(fd, "");
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then fprintf(fd,
"%d Years %d Days %d Hours %d Minutes %d Seconds", years_int,
days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then fprintf(fd,
"%d Days %d Hours %d Minutes %d Seconds", days_int, hours_int,
minutes_int, sec_int)
elif 0 < hours_int then fprintf(fd,
"%d Hours %d Minutes %d Seconds", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
fprintf(fd, "%d Minutes %d Seconds", minutes_int, sec_int)
else fprintf(fd, "%d Seconds", sec_int)
end if
else fprintf(fd, " 0.0 Seconds")
end if;
fprintf(fd, " | \n")
end proc
# End Function number 8
# Begin Function number 9
> omniout_timestr := proc(secs_in)
> global glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
> local days_int, hours_int,minutes_int, sec_int, sec_temp, years_int;
> if (secs_in >= 0) then # if number 2
> years_int := int_trunc(secs_in / glob_sec_in_year);
> sec_temp := (int_trunc(secs_in) mod int_trunc(glob_sec_in_year));
> days_int := int_trunc(sec_temp / glob_sec_in_day) ;
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_day)) ;
> hours_int := int_trunc(sec_temp / glob_sec_in_hour);
> sec_temp := (sec_temp mod int_trunc(glob_sec_in_hour));
> minutes_int := int_trunc(sec_temp / glob_sec_in_minute);
> sec_int := (sec_temp mod int_trunc(glob_sec_in_minute));
> if (years_int > 0) then # if number 3
> printf(" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",years_int,days_int,hours_int,minutes_int,sec_int);
> elif
> (days_int > 0) then # if number 4
> printf(" = %d Days %d Hours %d Minutes %d Seconds\n",days_int,hours_int,minutes_int,sec_int);
> elif
> (hours_int > 0) then # if number 5
> printf(" = %d Hours %d Minutes %d Seconds\n",hours_int,minutes_int,sec_int);
> elif
> (minutes_int > 0) then # if number 6
> printf(" = %d Minutes %d Seconds\n",minutes_int,sec_int);
> else
> printf(" = %d Seconds\n",sec_int);
> fi;# end if 6
> else
> printf(" 0.0 Seconds\n");
> fi;# end if 5
> end;
omniout_timestr := proc(secs_in)
local days_int, hours_int, minutes_int, sec_int, sec_temp, years_int;
global
glob_sec_in_day, glob_sec_in_hour, glob_sec_in_minute, glob_sec_in_year;
if 0 <= secs_in then
years_int := int_trunc(secs_in/glob_sec_in_year);
sec_temp := int_trunc(secs_in) mod int_trunc(glob_sec_in_year);
days_int := int_trunc(sec_temp/glob_sec_in_day);
sec_temp := sec_temp mod int_trunc(glob_sec_in_day);
hours_int := int_trunc(sec_temp/glob_sec_in_hour);
sec_temp := sec_temp mod int_trunc(glob_sec_in_hour);
minutes_int := int_trunc(sec_temp/glob_sec_in_minute);
sec_int := sec_temp mod int_trunc(glob_sec_in_minute);
if 0 < years_int then printf(
" = %d Years %d Days %d Hours %d Minutes %d Seconds\n",
years_int, days_int, hours_int, minutes_int, sec_int)
elif 0 < days_int then printf(
" = %d Days %d Hours %d Minutes %d Seconds\n", days_int,
hours_int, minutes_int, sec_int)
elif 0 < hours_int then printf(
" = %d Hours %d Minutes %d Seconds\n", hours_int, minutes_int,
sec_int)
elif 0 < minutes_int then
printf(" = %d Minutes %d Seconds\n", minutes_int, sec_int)
else printf(" = %d Seconds\n", sec_int)
end if
else printf(" 0.0 Seconds\n")
end if
end proc
# End Function number 9
# Begin Function number 10
> zero_ats_ar := proc(arr_a)
> global ATS_MAX_TERMS;
> local iii;
> iii := 1;
> while (iii <= ATS_MAX_TERMS) do # do number 1
> arr_a [iii] := glob__0;
> iii := iii + 1;
> od;# end do number 1
> end;
zero_ats_ar := proc(arr_a)
local iii;
global ATS_MAX_TERMS;
iii := 1;
while iii <= ATS_MAX_TERMS do arr_a[iii] := glob__0; iii := iii + 1
end do
end proc
# End Function number 10
# Begin Function number 11
> ats := proc(mmm_ats,arr_a,arr_b,jjj_ats)
> global ATS_MAX_TERMS;
> local iii_ats, lll_ats,ma_ats, ret_ats;
> ret_ats := glob__0;
> if (jjj_ats <= mmm_ats) then # if number 5
> ma_ats := mmm_ats + 1;
> iii_ats := jjj_ats;
> while (iii_ats <= mmm_ats) do # do number 1
> lll_ats := ma_ats - iii_ats;
> if ((lll_ats <= ATS_MAX_TERMS and (iii_ats <= ATS_MAX_TERMS) )) then # if number 6
> ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats]);
> fi;# end if 6;
> iii_ats := iii_ats + 1;
> od;# end do number 1
> fi;# end if 5;
> ret_ats;
> end;
ats := proc(mmm_ats, arr_a, arr_b, jjj_ats)
local iii_ats, lll_ats, ma_ats, ret_ats;
global ATS_MAX_TERMS;
ret_ats := glob__0;
if jjj_ats <= mmm_ats then
ma_ats := mmm_ats + 1;
iii_ats := jjj_ats;
while iii_ats <= mmm_ats do
lll_ats := ma_ats - iii_ats;
if lll_ats <= ATS_MAX_TERMS and iii_ats <= ATS_MAX_TERMS then
ret_ats := ret_ats + c(arr_a[iii_ats])*c(arr_b[lll_ats])
end if;
iii_ats := iii_ats + 1
end do
end if;
ret_ats
end proc
# End Function number 11
# Begin Function number 12
> att := proc(mmm_att,arr_aa,arr_bb,jjj_att)
> global ATS_MAX_TERMS;
> local al_att, iii_att,lll_att, ma_att, ret_att;
> ret_att := glob__0;
> if (jjj_att < mmm_att) then # if number 5
> ma_att := mmm_att + 2;
> iii_att := jjj_att;
> while ((iii_att < mmm_att) and (iii_att <= ATS_MAX_TERMS) ) do # do number 1
> lll_att := ma_att - iii_att;
> al_att := (lll_att - 1);
> if ((lll_att <= ATS_MAX_TERMS and (iii_att <= ATS_MAX_TERMS) )) then # if number 6
> ret_att := ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])* c(al_att);
> fi;# end if 6;
> iii_att := iii_att + 1;
> od;# end do number 1;
> ret_att := ret_att / c(mmm_att) ;
> fi;# end if 5;
> ret_att;
> end;
att := proc(mmm_att, arr_aa, arr_bb, jjj_att)
local al_att, iii_att, lll_att, ma_att, ret_att;
global ATS_MAX_TERMS;
ret_att := glob__0;
if jjj_att < mmm_att then
ma_att := mmm_att + 2;
iii_att := jjj_att;
while iii_att < mmm_att and iii_att <= ATS_MAX_TERMS do
lll_att := ma_att - iii_att;
al_att := lll_att - 1;
if lll_att <= ATS_MAX_TERMS and iii_att <= ATS_MAX_TERMS then
ret_att :=
ret_att + c(arr_aa[iii_att])*c(arr_bb[lll_att])*c(al_att)
end if;
iii_att := iii_att + 1
end do;
ret_att := ret_att/c(mmm_att)
end if;
ret_att
end proc
# End Function number 12
# Begin Function number 13
> logditto := proc(file)
> fprintf(file,"");
> fprintf(file,"ditto");
> fprintf(file," | ");
> end;
logditto := proc(file)
fprintf(file, ""); fprintf(file, "ditto"); fprintf(file, " | ")
end proc
# End Function number 13
# Begin Function number 14
> logitem_integer := proc(file,n)
> fprintf(file,"");
> fprintf(file,"%d",n);
> fprintf(file," | ");
> end;
logitem_integer := proc(file, n)
fprintf(file, ""); fprintf(file, "%d", n); fprintf(file, " | ")
end proc
# End Function number 14
# Begin Function number 15
> logitem_str := proc(file,str)
> fprintf(file,"");
> fprintf(file,str);
> fprintf(file," | ");
> end;
logitem_str := proc(file, str)
fprintf(file, ""); fprintf(file, str); fprintf(file, " | ")
end proc
# End Function number 15
# Begin Function number 16
> logitem_good_digits := proc(file,rel_error)
> global glob_small_float,glob_prec;
> local good_digits;
> fprintf(file,"");
> fprintf(file,"%d",glob_min_good_digits);
> fprintf(file," | ");
> end;
logitem_good_digits := proc(file, rel_error)
local good_digits;
global glob_small_float, glob_prec;
fprintf(file, "");
fprintf(file, "%d", glob_min_good_digits);
fprintf(file, " | ")
end proc
# End Function number 16
# Begin Function number 17
> log_revs := proc(file,revs)
> fprintf(file,revs);
> end;
log_revs := proc(file, revs) fprintf(file, revs) end proc
# End Function number 17
# Begin Function number 18
> logitem_float := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g",x);
> fprintf(file," | ");
> end;
logitem_float := proc(file, x)
fprintf(file, ""); fprintf(file, "%g", x); fprintf(file, " | ")
end proc
# End Function number 18
# Begin Function number 19
> logitem_complex := proc(file,x)
> fprintf(file,"");
> fprintf(file,"%g + %g I",Re(x),Im(x));
> fprintf(file," | ");
> end;
logitem_complex := proc(file, x)
fprintf(file, "");
fprintf(file, "%g + %g I", Re(x), Im(x));
fprintf(file, " | ")
end proc
# End Function number 19
# Begin Function number 20
> logitem_h_reason := proc(file)
> global glob_h_reason;
> fprintf(file,"");
> if (glob_h_reason = 1) then # if number 5
> fprintf(file,"Max H");
> elif
> (glob_h_reason = 2) then # if number 6
> fprintf(file,"Display Interval");
> elif
> (glob_h_reason = 3) then # if number 7
> fprintf(file,"Optimal");
> elif
> (glob_h_reason = 4) then # if number 8
> fprintf(file,"Pole Accuracy");
> elif
> (glob_h_reason = 5) then # if number 9
> fprintf(file,"Min H (Pole)");
> elif
> (glob_h_reason = 6) then # if number 10
> fprintf(file,"Pole");
> elif
> (glob_h_reason = 7) then # if number 11
> fprintf(file,"Opt Iter");
> else
> fprintf(file,"Impossible");
> fi;# end if 11
> fprintf(file," | ");
> end;
logitem_h_reason := proc(file)
global glob_h_reason;
fprintf(file, "");
if glob_h_reason = 1 then fprintf(file, "Max H")
elif glob_h_reason = 2 then fprintf(file, "Display Interval")
elif glob_h_reason = 3 then fprintf(file, "Optimal")
elif glob_h_reason = 4 then fprintf(file, "Pole Accuracy")
elif glob_h_reason = 5 then fprintf(file, "Min H (Pole)")
elif glob_h_reason = 6 then fprintf(file, "Pole")
elif glob_h_reason = 7 then fprintf(file, "Opt Iter")
else fprintf(file, "Impossible")
end if;
fprintf(file, " | ")
end proc
# End Function number 20
# Begin Function number 21
> logstart := proc(file)
> fprintf(file,"");
> end;
logstart := proc(file) fprintf(file, "
") end proc
# End Function number 21
# Begin Function number 22
> logend := proc(file)
> fprintf(file,"
\n");
> end;
logend := proc(file) fprintf(file, "\n") end proc
# End Function number 22
# Begin Function number 23
> chk_data := proc()
> global glob_max_iter,ALWAYS, ATS_MAX_TERMS;
> local errflag;
> errflag := false;
> if (glob_max_iter < 2) then # if number 11
> omniout_str(ALWAYS,"Illegal max_iter");
> errflag := true;
> fi;# end if 11;
> if (errflag) then # if number 11
> quit;
> fi;# end if 11
> end;
chk_data := proc()
local errflag;
global glob_max_iter, ALWAYS, ATS_MAX_TERMS;
errflag := false;
if glob_max_iter < 2 then
omniout_str(ALWAYS, "Illegal max_iter"); errflag := true
end if;
if errflag then quit end if
end proc
# End Function number 23
# Begin Function number 24
> comp_expect_sec := proc(t_end2,t_start2,t2,clock_sec2)
> global glob_small_float;
> local ms2, rrr, sec_left, sub1, sub2;
> ;
> ms2 := c(clock_sec2);
> sub1 := c(t_end2-t_start2);
> sub2 := c(t2-t_start2);
> if (sub1 = glob__0) then # if number 11
> sec_left := glob__0;
> else
> if (sub2 > glob__0) then # if number 12
> rrr := (sub1/sub2);
> sec_left := rrr * c(ms2) - c(ms2);
> else
> sec_left := glob__0;
> fi;# end if 12
> fi;# end if 11;
> sec_left;
> end;
comp_expect_sec := proc(t_end2, t_start2, t2, clock_sec2)
local ms2, rrr, sec_left, sub1, sub2;
global glob_small_float;
ms2 := c(clock_sec2);
sub1 := c(t_end2 - t_start2);
sub2 := c(t2 - t_start2);
if sub1 = glob__0 then sec_left := glob__0
else
if glob__0 < sub2 then
rrr := sub1/sub2; sec_left := rrr*c(ms2) - c(ms2)
else sec_left := glob__0
end if
end if;
sec_left
end proc
# End Function number 24
# Begin Function number 25
> comp_percent := proc(t_end2,t_start2, t2)
> global glob_small_float;
> local rrr, sub1, sub2;
> sub1 := (t_end2-t_start2);
> sub2 := (t2-t_start2);
> if (sub2 > glob_small_float) then # if number 11
> rrr := (glob__100*sub2)/sub1;
> else
> rrr := 0.0;
> fi;# end if 11;
> rrr;
> end;
comp_percent := proc(t_end2, t_start2, t2)
local rrr, sub1, sub2;
global glob_small_float;
sub1 := t_end2 - t_start2;
sub2 := t2 - t_start2;
if glob_small_float < sub2 then rrr := glob__100*sub2/sub1
else rrr := 0.
end if;
rrr
end proc
# End Function number 25
# Begin Function number 26
> comp_rad_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 11
> ret := float_abs(term1 * glob_h / term2);
> else
> ret := glob_larger_float;
> fi;# end if 11;
> ret;
> #BOTTOM TWO TERM RADIUS ANALYSIS
> end;
comp_rad_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := float_abs(term1*glob_h/term2)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 26
# Begin Function number 27
> comp_ord_from_ratio := proc(term1,term2,last_no)
> #TOP TWO TERM ORDER ANALYSIS
> global glob_h,glob_larger_float;
> local ret;
> if (float_abs(term2) > glob__0) then # if number 11
> ret := glob__1 + float_abs(term2) * c(last_no) * ln(float_abs(term1 * glob_h / term2))/ln(c(last_no));
> else
> ret := glob_larger_float;
> fi;# end if 11;
> ret;
> #BOTTOM TWO TERM ORDER ANALYSIS
> end;
comp_ord_from_ratio := proc(term1, term2, last_no)
local ret;
global glob_h, glob_larger_float;
if glob__0 < float_abs(term2) then ret := glob__1 + float_abs(term2)*
c(last_no)*ln(float_abs(term1*glob_h/term2))/ln(c(last_no))
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 27
# Begin Function number 28
> c := proc(in_val)
> #To Force Conversion when needed
> local ret;
> ret := evalc(in_val);
> ret;
> #End Conversion
> end;
c := proc(in_val) local ret; ret := evalc(in_val); ret end proc
# End Function number 28
# Begin Function number 29
> comp_rad_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float;
> local ret,temp;
> temp := float_abs(term2*term2*c(last_no)+glob__m2*term2*term2-term1*term3*c(last_no)+term1*term3);
> if (float_abs(temp) > glob__0) then # if number 11
> ret := float_abs((term2*glob_h*term1)/(temp));
> else
> ret := glob_larger_float;
> fi;# end if 11;
> ret;
> #BOTTOM THREE TERM RADIUS ANALYSIS
> end;
comp_rad_from_three_terms := proc(term1, term2, term3, last_no)
local ret, temp;
global glob_h, glob_larger_float;
temp := float_abs(term2*term2*c(last_no) + glob__m2*term2*term2
- term1*term3*c(last_no) + term1*term3);
if glob__0 < float_abs(temp) then
ret := float_abs(term2*glob_h*term1/temp)
else ret := glob_larger_float
end if;
ret
end proc
# End Function number 29
# Begin Function number 30
> comp_ord_from_three_terms := proc(term1,term2,term3,last_no)
> #TOP THREE TERM ORDER ANALYSIS
> local ret;
> ret := float_abs((glob__4*term1*term3*c(last_no)-glob__3*term1*term3-glob__4*term2*term2*c(last_no)+glob__4*term2*term2+term2*term2*c(last_no*last_no)-term1*term3*c(last_no*last_no))/(term2*term2*c(last_no)-glob__2*term2*term2-term1*term3*c(last_no)+term1*term3));
> ret;
> #TOP THREE TERM ORDER ANALYSIS
> end;
comp_ord_from_three_terms := proc(term1, term2, term3, last_no)
local ret;
ret := float_abs((glob__4*term1*term3*c(last_no) - glob__3*term1*term3
- glob__4*term2*term2*c(last_no) + glob__4*term2*term2
+ term2*term2*c(last_no*last_no) - term1*term3*c(last_no*last_no))
/(term2*term2*c(last_no) - glob__2*term2*term2
- term1*term3*c(last_no) + term1*term3));
ret
end proc
# End Function number 30
# Begin Function number 31
> comp_rad_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> #TOP SIX TERM RADIUS ANALYSIS
> global glob_h,glob_larger_float,glob_six_term_ord_save;
> local ret,rm0,rm1,rm2,rm3,rm4,nr1,nr2,dr1,dr2,ds2,rad_c,ord_no,ds1,rcs;
> if ((term5 <> glob__0) and (term4 <> glob__0) and (term3 <> glob__0) and (term2 <> glob__0) and (term1 <> glob__0)) then # if number 11
> rm0 := term6/term5;
> rm1 := term5/term4;
> rm2 := term4/term3;
> rm3 := term3/term2;
> rm4 := term2/term1;
> nr1 := c(last_no-1)*rm0 - glob__2*c(last_no-2)*rm1 + c(last_no-3)*rm2;
> nr2 := c(last_no-2)*rm1 - glob__2*c(last_no-3)*rm2 + c(last_no-4)*rm3;
> dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
> dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
> ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
> ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
> if ((float_abs(nr1 * dr2 - nr2 * dr1) = glob__0) or (float_abs(dr1) = glob__0)) then # if number 12
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> else
> if (float_abs(nr1*dr2 - nr2 * dr1) > glob__0) then # if number 13
> rcs := ((ds1*dr2 - ds2*dr1 +dr1*dr2)/(nr1*dr2 - nr2 * dr1));
> #(Manuels) rcs := (ds1*dr2 - ds2*dr1)/(nr1*dr2 - nr2 * dr1)
> ord_no := (rcs*nr1 - ds1)/(glob__2*dr1) -c(last_no)/glob__2;
> if (float_abs(rcs) <> glob__0) then # if number 14
> if (rcs > glob__0) then # if number 15
> rad_c := float_abs( sqrt(rcs) * float_abs(glob_h));
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 15
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 14
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 13
> fi;# end if 12
> else
> rad_c := glob_larger_float;
> ord_no := glob_larger_float;
> fi;# end if 11;
> glob_six_term_ord_save := ord_no;
> rad_c;
> #BOTTOM SIX TERM RADIUS ANALYSIS
> end;
comp_rad_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
local ret, rm0, rm1, rm2, rm3, rm4, nr1, nr2, dr1, dr2, ds2, rad_c, ord_no,
ds1, rcs;
global glob_h, glob_larger_float, glob_six_term_ord_save;
if term5 <> glob__0 and term4 <> glob__0 and term3 <> glob__0 and
term2 <> glob__0 and term1 <> glob__0 then
rm0 := term6/term5;
rm1 := term5/term4;
rm2 := term4/term3;
rm3 := term3/term2;
rm4 := term2/term1;
nr1 := c(last_no - 1)*rm0 - glob__2*c(last_no - 2)*rm1
+ c(last_no - 3)*rm2;
nr2 := c(last_no - 2)*rm1 - glob__2*c(last_no - 3)*rm2
+ c(last_no - 4)*rm3;
dr1 := glob__m1/rm1 + glob__2/rm2 - glob__1/rm3;
dr2 := glob__m1/rm2 + glob__2/rm3 - glob__1/rm4;
ds1 := glob__3/rm1 - glob__8/rm2 + glob__5/rm3;
ds2 := glob__3/rm2 - glob__8/rm3 + glob__5/rm4;
if
float_abs(nr1*dr2 - nr2*dr1) = glob__0 or float_abs(dr1) = glob__0
then rad_c := glob_larger_float; ord_no := glob_larger_float
else
if glob__0 < float_abs(nr1*dr2 - nr2*dr1) then
rcs := (ds1*dr2 - ds2*dr1 + dr1*dr2)/(nr1*dr2 - nr2*dr1);
ord_no :=
(rcs*nr1 - ds1)/(glob__2*dr1) - c(last_no)/glob__2;
if float_abs(rcs) <> glob__0 then
if glob__0 < rcs then
rad_c := float_abs(sqrt(rcs)*float_abs(glob_h))
else
rad_c := glob_larger_float;
ord_no := glob_larger_float
end if
else
rad_c := glob_larger_float; ord_no := glob_larger_float
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if
end if
else rad_c := glob_larger_float; ord_no := glob_larger_float
end if;
glob_six_term_ord_save := ord_no;
rad_c
end proc
# End Function number 31
# Begin Function number 32
> comp_ord_from_six_terms := proc(term1,term2,term3,term4,term5,term6,last_no)
> global glob_six_term_ord_save;
> #TOP SIX TERM ORDER ANALYSIS
> #TOP SAVED FROM SIX TERM RADIUS ANALYSIS
> glob_six_term_ord_save;
> #BOTTOM SIX TERM ORDER ANALYSIS
> end;
comp_ord_from_six_terms := proc(
term1, term2, term3, term4, term5, term6, last_no)
global glob_six_term_ord_save;
glob_six_term_ord_save
end proc
# End Function number 32
# Begin Function number 33
> factorial_2 := proc(nnn)
> ret := nnn!;
> ret;;
> end;
Warning, `ret` is implicitly declared local to procedure `factorial_2`
factorial_2 := proc(nnn) local ret; ret := nnn!; ret end proc
# End Function number 33
# Begin Function number 34
> factorial_1 := proc(nnn)
> global ATS_MAX_TERMS,array_fact_1;
> local ret;
> if (nnn <= ATS_MAX_TERMS) then # if number 11
> if (array_fact_1[nnn] = 0) then # if number 12
> ret := factorial_2(nnn);
> array_fact_1[nnn] := ret;
> else
> ret := array_fact_1[nnn];
> fi;# end if 12;
> else
> ret := factorial_2(nnn);
> fi;# end if 11;
> ret;
> end;
factorial_1 := proc(nnn)
local ret;
global ATS_MAX_TERMS, array_fact_1;
if nnn <= ATS_MAX_TERMS then
if array_fact_1[nnn] = 0 then
ret := factorial_2(nnn); array_fact_1[nnn] := ret
else ret := array_fact_1[nnn]
end if
else ret := factorial_2(nnn)
end if;
ret
end proc
# End Function number 34
# Begin Function number 35
> factorial_3 := proc(mmm,nnn)
> global ATS_MAX_TERMS,array_fact_2;
> local ret;
> if ((nnn <= ATS_MAX_TERMS) and (mmm <= ATS_MAX_TERMS)) then # if number 11
> if (array_fact_2[mmm,nnn] = 0) then # if number 12
> ret := factorial_1(mmm)/factorial_1(nnn);
> array_fact_2[mmm,nnn] := ret;
> else
> ret := array_fact_2[mmm,nnn];
> fi;# end if 12;
> else
> ret := factorial_2(mmm)/factorial_2(nnn);
> fi;# end if 11;
> ret;
> end;
factorial_3 := proc(mmm, nnn)
local ret;
global ATS_MAX_TERMS, array_fact_2;
if nnn <= ATS_MAX_TERMS and mmm <= ATS_MAX_TERMS then
if array_fact_2[mmm, nnn] = 0 then
ret := factorial_1(mmm)/factorial_1(nnn);
array_fact_2[mmm, nnn] := ret
else ret := array_fact_2[mmm, nnn]
end if
else ret := factorial_2(mmm)/factorial_2(nnn)
end if;
ret
end proc
# End Function number 35
# Begin Function number 36
> convfloat := proc(mmm)
> (mmm);
> end;
convfloat := proc(mmm) mmm end proc
# End Function number 36
# Begin Function number 37
> elapsed_time_seconds := proc()
> time();
> end;
elapsed_time_seconds := proc() time() end proc
# End Function number 37
# Begin Function number 38
> float_abs := proc(x)
> abs(x);
> end;
float_abs := proc(x) abs(x) end proc
# End Function number 38
# Begin Function number 39
> expt := proc(x,y)
> x^y;
> end;
expt := proc(x, y) x^y end proc
# End Function number 39
# Begin Function number 40
> neg := proc(x)
> -x;
> end;
neg := proc(x) -x end proc
# End Function number 40
# Begin Function number 41
> int_trunc := proc(x)
> trunc(x);
> end;
int_trunc := proc(x) trunc(x) end proc
# End Function number 41
# Begin Function number 42
> estimated_needed_step_error := proc(x_start,x_end,estimated_h,estimated_answer)
> local desired_abs_gbl_error,range,estimated_steps,step_error;
> global glob_desired_digits_correct,ALWAYS,ATS_MAX_TERMS;
> omniout_float(ALWAYS,"glob_desired_digits_correct",32,glob_desired_digits_correct,32,"");
> desired_abs_gbl_error := expt(glob__10,c( -glob_desired_digits_correct)) * c(float_abs(c(estimated_answer)));
> omniout_float(ALWAYS,"estimated_h",32,estimated_h,32,"");
> omniout_float(ALWAYS,"estimated_answer",32,estimated_answer,32,"");
> omniout_float(ALWAYS,"desired_abs_gbl_error",32,desired_abs_gbl_error,32,"");
> range := (x_end - x_start);
> omniout_float(ALWAYS,"range",32,range,32,"");
> estimated_steps := range / estimated_h;
> omniout_float(ALWAYS,"estimated_steps",32,estimated_steps,32,"");
> step_error := (c(float_abs(desired_abs_gbl_error) /sqrt(c( estimated_steps))/c(ATS_MAX_TERMS)));
> omniout_float(ALWAYS,"step_error",32,step_error,32,"");
> (step_error);;
> end;
estimated_needed_step_error := proc(
x_start, x_end, estimated_h, estimated_answer)
local desired_abs_gbl_error, range, estimated_steps, step_error;
global glob_desired_digits_correct, ALWAYS, ATS_MAX_TERMS;
omniout_float(ALWAYS, "glob_desired_digits_correct", 32,
glob_desired_digits_correct, 32, "");
desired_abs_gbl_error :=
expt(glob__10, c(-glob_desired_digits_correct))*
c(float_abs(c(estimated_answer)));
omniout_float(ALWAYS, "estimated_h", 32, estimated_h, 32, "");
omniout_float(ALWAYS, "estimated_answer", 32, estimated_answer, 32, "")
;
omniout_float(ALWAYS, "desired_abs_gbl_error", 32,
desired_abs_gbl_error, 32, "");
range := x_end - x_start;
omniout_float(ALWAYS, "range", 32, range, 32, "");
estimated_steps := range/estimated_h;
omniout_float(ALWAYS, "estimated_steps", 32, estimated_steps, 32, "");
step_error := c(float_abs(desired_abs_gbl_error)/(
sqrt(c(estimated_steps))*c(ATS_MAX_TERMS)));
omniout_float(ALWAYS, "step_error", 32, step_error, 32, "");
step_error
end proc
# End Function number 42
#END ATS LIBRARY BLOCK
#BEGIN USER FUNCTION BLOCK
#BEGIN BLOCK 3
#BEGIN USER DEF BLOCK
> exact_soln_y := proc(x)
> return(c(5.0) * ln(c(0.1) * c(x) + c(0.2)) * ( c(0.1) * c(x) + c(0.2)) - c(0.5) * c(x) - c(1.0));
> end;
exact_soln_y := proc(x)
return c(5.0)*ln(c(0.1)*c(x) + c(0.2))*(c(0.1)*c(x) + c(0.2))
- c(0.5)*c(x) - c(1.0)
end proc
> next_delta := proc()
> global glob_nxt, x_delta;
> x_delta := [ 0.001 + 0.00004 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.0001 + 0.004 * I,
> 0.003 + 0.006 * I,
> 0.0001 + 0.005 * I,
> 0.0001 + 0.003 * I,
> 0.001 + 0.001 * I,
> 0.001 + 0.003 * I,
> 0.000 + 0.000 * I ];
> glob_nxt := glob_nxt + 1;
> it := x_delta[glob_nxt];
> return it;
> end;
Warning, `it` is implicitly declared local to procedure `next_delta`
next_delta := proc()
local it;
global glob_nxt, x_delta;
x_delta := [0.001 + 0.00004*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.0001 + 0.004*I,
0.003 + 0.006*I, 0.0001 + 0.005*I, 0.0001 + 0.003*I,
0.001 + 0.001*I, 0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.001 + 0.003*I, 0.0001 + 0.004*I, 0.003 + 0.006*I,
0.0001 + 0.005*I, 0.0001 + 0.003*I, 0.001 + 0.001*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I,
0.0001 + 0.004*I, 0.003 + 0.006*I, 0.0001 + 0.005*I,
0.0001 + 0.003*I, 0.001 + 0.001*I, 0.001 + 0.003*I, 0. + 0.*I];
glob_nxt := glob_nxt + 1;
it := x_delta[glob_nxt];
return it
end proc
#END USER DEF BLOCK
#END BLOCK 3
#END USER FUNCTION BLOCK
# before write_aux functions
# Begin Function number 2
> display_poles := proc()
> local rad_given;
> global ALWAYS,glob_display_flag,glob_larger_float, glob_large_float, glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm, glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord, glob_guess_error_rc, glob_type_given_pole,array_given_rad_poles,array_given_ord_poles,array_rad_test_poles,array_ord_test_poles,glob_least_3_sing,glob_least_6_sing,glob_least_given_sing,glob_least_ratio_sing,array_x ;
> if ((glob_type_given_pole = 1) or (glob_type_given_pole = 2)) then # if number 1
> rad_given := float_abs(array_x[1] - (array_given_rad_poles[1,1] + array_given_rad_poles[1,2] * I ));
> omniout_float(ALWAYS,"Radius of convergence (given) for eq 1 ",4,rad_given,4," ");
> omniout_complex(ALWAYS,"Order of pole (given) ",4,array_given_ord_poles[1,1],4," ");
> if ((float_abs(rad_given) < float_abs(glob_least_given_sing)) and
> (float_abs(rad_given) > 0.0)) then # if number 2
> glob_least_given_sing := rad_given;
> fi;# end if 2;
> elif
> (glob_type_given_pole = 3) then # if number 2
> omniout_str(ALWAYS,"NO POLE (given) for Equation 1");
> elif
> (glob_type_given_pole = 5) then # if number 3
> omniout_str(ALWAYS,"SOME POLE (given) for Equation 1");
> else
> omniout_str(ALWAYS,"NO INFO (given) for Equation 1");
> fi;# end if 3;
> if (array_rad_test_poles[1,1] < glob_large_float) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (ratio test) for eq 1 ",4,array_rad_test_poles[1,1],4," ");
> if ((float_abs(array_rad_test_poles[1,1]) < glob_least_ratio_sing)) then # if number 4
> glob_least_ratio_sing := array_rad_test_poles[1,1];
> fi;# end if 4;
> omniout_complex(ALWAYS,"Order of pole (ratio test) ",4, array_ord_test_poles[1,1],4," ");
> else
> omniout_str(ALWAYS,"NO POLE (ratio test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,2] > glob__small) and (array_rad_test_poles[1,2] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (three term test) for eq 1 ",4,array_rad_test_poles[1,2],4," ");
> if ((float_abs(array_rad_test_poles[1,2]) < glob_least_3_sing)) then # if number 4
> glob_least_3_sing := array_rad_test_poles[1,2];
> fi;# end if 4;
> omniout_complex(ALWAYS,"Order of pole (three term test) ",4, array_ord_test_poles[1,2],4," ");
> else
> omniout_str(ALWAYS,"NO REAL POLE (three term test) for Equation 1");
> fi;# end if 3;
> if ((array_rad_test_poles[1,3] > glob__small) and (array_rad_test_poles[1,3] < glob_large_float)) then # if number 3
> omniout_float(ALWAYS,"Radius of convergence (six term test) for eq 1 ",4,array_rad_test_poles[1,3],4," ");
> if ((float_abs(array_rad_test_poles[1,3]) < glob_least_6_sing)) then # if number 4
> glob_least_6_sing := array_rad_test_poles[1,3];
> fi;# end if 4;
> omniout_complex(ALWAYS,"Order of pole (six term test) ",4, array_ord_test_poles[1,3],4," ");
> else
> omniout_str(ALWAYS,"NO COMPLEX POLE (six term test) for Equation 1");
> fi;# end if 3
> ;
> end;
display_poles := proc()
local rad_given;
global ALWAYS, glob_display_flag, glob_larger_float, glob_large_float,
glob_diff_ord_fm, glob_diff_ord_fmm1, glob_diff_ord_fmm2, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_guess_error_ord,
glob_guess_error_rc, glob_type_given_pole, array_given_rad_poles,
array_given_ord_poles, array_rad_test_poles, array_ord_test_poles,
glob_least_3_sing, glob_least_6_sing, glob_least_given_sing,
glob_least_ratio_sing, array_x;
if glob_type_given_pole = 1 or glob_type_given_pole = 2 then
rad_given := float_abs(array_x[1] - array_given_rad_poles[1, 1]
- array_given_rad_poles[1, 2]*I);
omniout_float(ALWAYS,
"Radius of convergence (given) for eq 1 ", 4,
rad_given, 4, " ");
omniout_complex(ALWAYS,
"Order of pole (given) ", 4,
array_given_ord_poles[1, 1], 4, " ");
if float_abs(rad_given) < float_abs(glob_least_given_sing) and
0. < float_abs(rad_given) then glob_least_given_sing := rad_given
end if
elif glob_type_given_pole = 3 then
omniout_str(ALWAYS, "NO POLE (given) for Equation 1")
elif glob_type_given_pole = 5 then
omniout_str(ALWAYS, "SOME POLE (given) for Equation 1")
else omniout_str(ALWAYS, "NO INFO (given) for Equation 1")
end if;
if array_rad_test_poles[1, 1] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (ratio test) for eq 1 ", 4,
array_rad_test_poles[1, 1], 4, " ");
if float_abs(array_rad_test_poles[1, 1]) < glob_least_ratio_sing
then glob_least_ratio_sing := array_rad_test_poles[1, 1]
end if;
omniout_complex(ALWAYS,
"Order of pole (ratio test) ", 4,
array_ord_test_poles[1, 1], 4, " ")
else omniout_str(ALWAYS, "NO POLE (ratio test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 2] and
array_rad_test_poles[1, 2] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (three term test) for eq 1 ", 4,
array_rad_test_poles[1, 2], 4, " ");
if float_abs(array_rad_test_poles[1, 2]) < glob_least_3_sing then
glob_least_3_sing := array_rad_test_poles[1, 2]
end if;
omniout_complex(ALWAYS,
"Order of pole (three term test) ", 4,
array_ord_test_poles[1, 2], 4, " ")
else omniout_str(ALWAYS,
"NO REAL POLE (three term test) for Equation 1")
end if;
if glob__small < array_rad_test_poles[1, 3] and
array_rad_test_poles[1, 3] < glob_large_float then
omniout_float(ALWAYS,
"Radius of convergence (six term test) for eq 1 ", 4,
array_rad_test_poles[1, 3], 4, " ");
if float_abs(array_rad_test_poles[1, 3]) < glob_least_6_sing then
glob_least_6_sing := array_rad_test_poles[1, 3]
end if;
omniout_complex(ALWAYS,
"Order of pole (six term test) ", 4,
array_ord_test_poles[1, 3], 4, " ")
else omniout_str(ALWAYS,
"NO COMPLEX POLE (six term test) for Equation 1")
end if
end proc
# End Function number 2
# Begin Function number 3
> my_check_sign := proc( x0 ,xf)
> local ret;
> if (xf > x0) then # if number 3
> ret := glob__1;
> else
> ret := glob__m1;
> fi;# end if 3;
> ret;;
> end;
my_check_sign := proc(x0, xf)
local ret;
if x0 < xf then ret := glob__1 else ret := glob__m1 end if; ret
end proc
# End Function number 3
# Begin Function number 4
> est_size_answer := proc()
> global
> ALWAYS,
> INFO,
> DEBUGL,
> DEBUGMASSIVE,
> glob_iolevel,
> glob_yes_pole,
> glob_no_pole,
> glob_not_given,
> glob_no_sing_tests,
> glob_ratio_test,
> glob_three_term_test,
> glob_six_term_test,
> glob_log_10,
#Top Generate Globals Decl
> MAX_UNCHANGED,
> glob__small,
> glob_small_float,
> glob_smallish_float,
> glob_large_float,
> glob_larger_float,
> glob__m2,
> glob__m1,
> glob__0,
> glob__1,
> glob__2,
> glob__3,
> glob__4,
> glob__5,
> glob__8,
> glob__10,
> glob__100,
> glob__pi,
> glob__0_5,
> glob__0_8,
> glob__m0_8,
> glob__0_25,
> glob__0_125,
> glob_h,
> glob_nxt,
> glob_prec,
> glob_check_sign,
> glob_desired_digits_correct,
> glob_max_estimated_step_error,
> glob_ratio_of_radius,
> glob_percent_done,
> glob_total_exp_sec,
> glob_optimal_expect_sec,
> glob_estimated_size_answer,
> glob_almost_1,
> glob_clock_sec,
> glob_clock_start_sec,
> glob_disp_incr,
> glob_diff_rc_fm,
> glob_diff_rc_fmm1,
> glob_diff_rc_fmm2,
> glob_diff_ord_fm,
> glob_diff_ord_fmm1,
> glob_diff_ord_fmm2,
> glob_six_term_ord_save,
> glob_guess_error_rc,
> glob_guess_error_ord,
> glob_least_given_sing,
> glob_least_ratio_sing,
> glob_least_3_sing,
> glob_least_6_sing,
> glob_last_good_h,
> glob_max_h,
> glob_min_h,
> glob_display_interval,
> glob_abserr,
> glob_relerr,
> glob_min_pole_est,
> glob_max_rel_trunc_err,
> glob_max_trunc_err,
> glob_max_hours,
> glob_optimal_clock_start_sec,
> glob_optimal_start,
> glob_upper_ratio_limit,
> glob_lower_ratio_limit,
> glob_max_sec,
> glob_orig_start_sec,
> glob_normmax,
> glob_max_minutes,
> glob_next_display,
> glob_est_digits,
> glob_subiter_method,
> glob_html_log,
> glob_min_good_digits,
> glob_good_digits,
> glob_min_apfp_est_good_digits,
> glob_apfp_est_good_digits,
> glob_max_opt_iter,
> glob_dump,
> glob_djd_debug,
> glob_display_flag,
> glob_djd_debug2,
> glob_h_reason,
> glob_sec_in_minute,
> glob_min_in_hour,
> glob_hours_in_day,
> glob_days_in_year,
> glob_sec_in_hour,
> glob_sec_in_day,
> glob_sec_in_year,
> glob_not_yet_finished,
> glob_initial_pass,
> glob_not_yet_start_msg,
> glob_reached_optimal_h,
> glob_optimal_done,
> glob_type_given_pole,
> glob_optimize,
> glob_look_poles,
> glob_dump_closed_form,
> glob_max_iter,
> glob_no_eqs,
> glob_unchanged_h_cnt,
> glob_warned,
> glob_warned2,
> glob_start,
> glob_iter,
#Bottom Generate Globals Decl
#BEGIN CONST
> array_const_1,
> array_const_0D0,
> array_const_0D1,
> array_const_0D2,
#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 ln 1 FULL $eq_no = 1
> array_tmp4[1] := ln(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 ln 2 FULL $eq_no = 1
> array_tmp4[2] := array_tmp3[2] / 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 ln ID_FULL iii = 3 $eq_no = 1
> #emit pre ln 3 $eq_no = 1
> array_tmp4[3] := ( array_tmp3[3] - att(2,array_tmp3,array_tmp4,2) ) / 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 ln ID_FULL iii = 4 $eq_no = 1
> #emit pre ln 4 $eq_no = 1
> array_tmp4[4] := ( array_tmp3[4] - att(3,array_tmp3,array_tmp4,2) ) / 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 ln ID_FULL iii = 5 $eq_no = 1
> #emit pre ln 5 $eq_no = 1
> array_tmp4[5] := ( array_tmp3[5] - att(4,array_tmp3,array_tmp4,2) ) / 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 ln FULL $eq_no = 1
> array_tmp4[kkk] := (array_tmp3[kkk] - att(kkk-1,array_tmp3,array_tmp4,2))/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] := ln(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] := array_tmp3[2]/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] :=
(array_tmp3[3] - att(2, array_tmp3, array_tmp4, 2))/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] :=
(array_tmp3[4] - att(3, array_tmp3, array_tmp4, 2))/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] :=
(array_tmp3[5] - att(4, array_tmp3, array_tmp4, 2))/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] := (
array_tmp3[kkk] - att(kkk - 1, array_tmp3, array_tmp4, 2))/
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:=32;
> max_terms:=40;
> #END BLOCK 1
> #END FIRST INPUT BLOCK
> #START OF INITS AFTER INPUT BLOCK
> glob_html_log := true;
> #END OF INITS AFTER INPUT BLOCK
> # before generate arrays
> array_y_init:= Array(0..(40),[]);
> array_norms:= Array(0..(40),[]);
> array_fact_1:= Array(0..(40),[]);
> array_1st_rel_error:= Array(0..(2),[]);
> array_last_rel_error:= Array(0..(2),[]);
> array_est_rel_error:= Array(0..(2),[]);
> array_max_est_error:= Array(0..(2),[]);
> array_type_pole:= Array(0..(2),[]);
> array_type_real_pole:= Array(0..(2),[]);
> array_type_complex_pole:= Array(0..(2),[]);
> array_est_digits:= Array(0..(2),[]);
> array_y:= Array(0..(40),[]);
> array_x:= Array(0..(40),[]);
> array_tmp0:= Array(0..(40),[]);
> array_tmp1:= Array(0..(40),[]);
> array_tmp2:= Array(0..(40),[]);
> array_tmp3:= Array(0..(40),[]);
> array_tmp4:= 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/ln_sqrtpostcpx.cpx#################");
> omniout_str(ALWAYS,"diff ( y , x , 1 ) = ln ( sqrt ( 0.1 * x + 0.2 ) ) ; ");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#BEGIN FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"Digits:=32;");
> omniout_str(ALWAYS,"max_terms:=40;");
> omniout_str(ALWAYS,"!");
> omniout_str(ALWAYS,"#END FIRST INPUT BLOCK");
> omniout_str(ALWAYS,"#BEGIN SECOND INPUT BLOCK");
> omniout_str(ALWAYS,"x_start := 10.1 + 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,"glob_min_h := 0.001;");
> 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,"");
> omniout_str(ALWAYS,"return(c(5.0) * ln(c(0.1) * c(x) + c(0.2)) * ( c(0.1) * c(x) + c(0.2)) - c(0.5) * c(x) - c(1.0));");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"next_delta := proc()");
> omniout_str(ALWAYS,"global glob_nxt, x_delta;");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"x_delta := [ 0.001 + 0.00004 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.004 * I,");
> omniout_str(ALWAYS,"0.003 + 0.006 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.005 * I,");
> omniout_str(ALWAYS,"0.0001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.001 + 0.001 * I,");
> omniout_str(ALWAYS,"0.001 + 0.003 * I,");
> omniout_str(ALWAYS,"0.000 + 0.000 * I ];");
> omniout_str(ALWAYS,"");
> omniout_str(ALWAYS,"glob_nxt := glob_nxt + 1;");
> omniout_str(ALWAYS,"it := x_delta[glob_nxt];");
> omniout_str(ALWAYS,"return it;");
> omniout_str(ALWAYS,"end;");
> omniout_str(ALWAYS,"#END USER DEF BLOCK");
> omniout_str(ALWAYS,"#######END OF ECHO OF PROBLEM#################");
> glob_unchanged_h_cnt := 0;
> glob_warned := false;
> glob_warned2 := false;
> glob_small_float := glob__0;
> glob_smallish_float := glob__0;
> glob_large_float := c(1.0e100);
> glob_larger_float := c( 1.1e100);
> glob_almost_1 := c( 0.99);
> # before second block
> #TOP SECOND INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> #BEGIN BLOCK 2
> #END FIRST INPUT BLOCK
> #BEGIN SECOND INPUT BLOCK
> x_start := 10.1 + 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_min_h := 0.001;
> 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 ) = ln ( 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,"2017-11-26T15:05:08-06:00")
> ;
> logitem_str(html_log_file,"Maple")
> ;
> logitem_str(html_log_file,"ln_sqrt")
> ;
> logitem_str(html_log_file,"diff ( y , x , 1 ) = ln ( 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,"ln_sqrt diffeq.mxt")
> ;
> logitem_str(html_log_file,"ln_sqrt maple results")
> ;
> logitem_str(html_log_file,"OK")
> ;
> logend(html_log_file)
> ;
> ;
> fi;# end if 15;
> if (glob_html_log) then # if number 15
> fclose(html_log_file);
> fi;# end if 15
> ;
> ;;
> end;
> # End Function number 12
> #END OUTFILEMAIN
> end;
Warning, `h_new` is implicitly declared local to procedure `main`
Warning, `ratio` is implicitly declared local to procedure `main`
main := proc()
local d1, d2, d3, d4, est_err_2, niii, done_once, max_terms, display_max,
term, ord, order_diff, term_no, html_log_file, iiif, jjjf, rows, r_order,
sub_iter, calc_term, iii, temp_sum, current_iter, x_start, x_end, it,
last_min_pole_est, opt_iter, tmp, subiter, est_needed_step_err,
estimated_step_error, min_value, est_answer, found_h, repeat_it, h_new,
ratio;
global ALWAYS, INFO, DEBUGL, DEBUGMASSIVE, glob_iolevel, glob_yes_pole,
glob_no_pole, glob_not_given, glob_no_sing_tests, glob_ratio_test,
glob_three_term_test, glob_six_term_test, glob_log_10, MAX_UNCHANGED,
glob__small, glob_small_float, glob_smallish_float, glob_large_float,
glob_larger_float, glob__m2, glob__m1, glob__0, glob__1, glob__2, glob__3,
glob__4, glob__5, glob__8, glob__10, glob__100, glob__pi, glob__0_5,
glob__0_8, glob__m0_8, glob__0_25, glob__0_125, glob_h, glob_nxt, glob_prec,
glob_check_sign, glob_desired_digits_correct, glob_max_estimated_step_error,
glob_ratio_of_radius, glob_percent_done, glob_total_exp_sec,
glob_optimal_expect_sec, glob_estimated_size_answer, glob_almost_1,
glob_clock_sec, glob_clock_start_sec, glob_disp_incr, glob_diff_rc_fm,
glob_diff_rc_fmm1, glob_diff_rc_fmm2, glob_diff_ord_fm, glob_diff_ord_fmm1,
glob_diff_ord_fmm2, glob_six_term_ord_save, glob_guess_error_rc,
glob_guess_error_ord, glob_least_given_sing, glob_least_ratio_sing,
glob_least_3_sing, glob_least_6_sing, glob_last_good_h, glob_max_h,
glob_min_h, glob_display_interval, glob_abserr, glob_relerr,
glob_min_pole_est, glob_max_rel_trunc_err, glob_max_trunc_err,
glob_max_hours, glob_optimal_clock_start_sec, glob_optimal_start,
glob_upper_ratio_limit, glob_lower_ratio_limit, glob_max_sec,
glob_orig_start_sec, glob_normmax, glob_max_minutes, glob_next_display,
glob_est_digits, glob_subiter_method, glob_html_log, glob_min_good_digits,
glob_good_digits, glob_min_apfp_est_good_digits, glob_apfp_est_good_digits,
glob_max_opt_iter, glob_dump, glob_djd_debug, glob_display_flag,
glob_djd_debug2, glob_h_reason, glob_sec_in_minute, glob_min_in_hour,
glob_hours_in_day, glob_days_in_year, glob_sec_in_hour, glob_sec_in_day,
glob_sec_in_year, glob_not_yet_finished, glob_initial_pass,
glob_not_yet_start_msg, glob_reached_optimal_h, glob_optimal_done,
glob_type_given_pole, glob_optimize, glob_look_poles, glob_dump_closed_form,
glob_max_iter, glob_no_eqs, glob_unchanged_h_cnt, glob_warned, glob_warned2,
glob_start, glob_iter, array_const_1, array_const_0D0, array_const_0D1,
array_const_0D2, array_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 := 32;
max_terms := 40;
glob_html_log := true;
array_y_init := Array(0 .. 40, []);
array_norms := Array(0 .. 40, []);
array_fact_1 := Array(0 .. 40, []);
array_1st_rel_error := Array(0 .. 2, []);
array_last_rel_error := Array(0 .. 2, []);
array_est_rel_error := Array(0 .. 2, []);
array_max_est_error := Array(0 .. 2, []);
array_type_pole := Array(0 .. 2, []);
array_type_real_pole := Array(0 .. 2, []);
array_type_complex_pole := Array(0 .. 2, []);
array_est_digits := Array(0 .. 2, []);
array_y := Array(0 .. 40, []);
array_x := Array(0 .. 40, []);
array_tmp0 := Array(0 .. 40, []);
array_tmp1 := Array(0 .. 40, []);
array_tmp2 := Array(0 .. 40, []);
array_tmp3 := Array(0 .. 40, []);
array_tmp4 := 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/ln_sqrtpostcpx.cpx#################");
omniout_str(ALWAYS, "diff ( y , x , 1 ) = ln ( sqrt ( 0.1 \
* x + 0.2 ) ) ; ");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#BEGIN FIRST INPUT BLOCK");
omniout_str(ALWAYS, "Digits:=32;");
omniout_str(ALWAYS, "max_terms:=40;");
omniout_str(ALWAYS, "!");
omniout_str(ALWAYS, "#END FIRST INPUT BLOCK");
omniout_str(ALWAYS, "#BEGIN SECOND INPUT BLOCK");
omniout_str(ALWAYS, "x_start := 10.1 + 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, "glob_min_h := 0.001;");
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, "");
omniout_str(ALWAYS, "return(c(5.0) * ln(c(0.1) * c(x) + c(0.2)) * ( c\
(0.1) * c(x) + c(0.2)) - c(0.5) * c(x) - c(1.0));");
omniout_str(ALWAYS, "end;");
omniout_str(ALWAYS, "next_delta := proc()");
omniout_str(ALWAYS, "global glob_nxt, x_delta;");
omniout_str(ALWAYS, "");
omniout_str(ALWAYS, "x_delta := [ 0.001 + 0.00004 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
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omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 0.005 * I,");
omniout_str(ALWAYS, "0.0001 + 0.003 * I,");
omniout_str(ALWAYS, "0.001 + 0.001 * I,");
omniout_str(ALWAYS, "0.001 + 0.003 * I,");
omniout_str(ALWAYS, "0.0001 + 0.004 * I,");
omniout_str(ALWAYS, "0.003 + 0.006 * I,");
omniout_str(ALWAYS, "0.0001 + 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 := 10.1 + 0.1*I;
x_end := 99.0 + 99.0*I;
array_y_init[1] := exact_soln_y(x_start);
glob_look_poles := true;
glob_min_h := 0.001;
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 ) = ln ( 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, "2017-11-26T15:05:08-06:00");
logitem_str(html_log_file, "Maple");
logitem_str(html_log_file,
"ln_sqrt");
logitem_str(html_log_file, "diff ( y , x , 1 ) = ln\
( 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,
"ln_sqrt diffeq.mxt")
;
logitem_str(html_log_file, "ln_sqrt maple results");
logitem_str(html_log_file, "OK");
logend(html_log_file)
end if;
if glob_html_log then fclose(html_log_file) end if
end if
end proc
# End Function number 12
> main();
memory used=3.9MB, alloc=40.3MB, time=0.08
##############ECHO OF PROBLEM#################
##############temp/ln_sqrtpostcpx.cpx#################
diff ( y , x , 1 ) = ln ( sqrt ( 0.1 * x + 0.2 ) ) ;
!
#BEGIN FIRST INPUT BLOCK
Digits:=32;
max_terms:=40;
!
#END FIRST INPUT BLOCK
#BEGIN SECOND INPUT BLOCK
x_start := 10.1 + 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_min_h := 0.001;
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(5.0) * ln(c(0.1) * c(x) + c(0.2)) * ( c(0.1) * c(x) + c(0.2)) - c(0.5) * c(x) - c(1.0));
end;
next_delta := proc()
global glob_nxt, x_delta;
x_delta := [ 0.001 + 0.00004 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.0001 + 0.004 * I,
0.003 + 0.006 * I,
0.0001 + 0.005 * I,
0.0001 + 0.003 * I,
0.001 + 0.001 * I,
0.001 + 0.003 * I,
0.000 + 0.000 * I ];
glob_nxt := glob_nxt + 1;
it := x_delta[glob_nxt];
return it;
end;
#END USER DEF BLOCK
#######END OF ECHO OF PROBLEM#################
START of Soultion
x[1] = 10.1 0.1
h = 0.0001 0.005
y[1] (numeric) = -4.89695343359 0.00953158714665
y[1] (closed_form) = -4.89695343359 0.00953158714665
absolute error = 0
relative error = 0 %
Correct digits = 30
Radius of convergence (given) for eq 1 = 12.1
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=29.0MB, alloc=40.3MB, time=0.38
x[1] = 10.1001 0.105
h = 0.0001 0.003
y[1] (numeric) = -4.89696497438 0.0100086586628
y[1] (closed_form) = -4.89696507766 0.0100086616307
absolute error = 1.033e-07
relative error = 2.110e-06 %
Correct digits = 8
Radius of convergence (given) for eq 1 = 12.1
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.1002 0.108
h = 0.001 0.001
y[1] (numeric) = -4.8969687667 0.0102951111784
y[1] (closed_form) = -4.89696874606 0.0102951089328
absolute error = 2.076e-08
relative error = 4.240e-07 %
Correct digits = 8
Radius of convergence (given) for eq 1 = 12.1
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.1012 0.109
h = 0.001 0.003
y[1] (numeric) = -4.8968779503 0.010394976736
y[1] (closed_form) = -4.89687786995 0.0103949512271
absolute error = 8.430e-08
relative error = 1.722e-06 %
Correct digits = 8
Radius of convergence (given) for eq 1 = 12.1
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.1022 0.112
h = 0.0001 0.004
y[1] (numeric) = -4.89679612151 0.0106857034405
y[1] (closed_form) = -4.89679616472 0.0106857203735
absolute error = 4.641e-08
relative error = 9.477e-07 %
Correct digits = 8
Radius of convergence (given) for eq 1 = 12.1
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.1023 0.116
h = 0.003 0.006
y[1] (numeric) = -4.89680533274 0.0110679472208
y[1] (closed_form) = -4.8968054611 0.0110678926684
absolute error = 1.395e-07
relative error = 2.848e-06 %
Correct digits = 8
Radius of convergence (given) for eq 1 = 12.1
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=74.5MB, alloc=52.3MB, time=0.96
x[1] = 10.1053 0.122
h = 0.0001 0.005
y[1] (numeric) = -4.89654828921 0.0116551582618
y[1] (closed_form) = -4.89654848095 0.0116555876986
absolute error = 4.703e-07
relative error = 9.605e-06 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.11
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] = 10.1054 0.127
h = 0.0001 0.003
y[1] (numeric) = -4.89656453848 0.0121337631714
y[1] (closed_form) = -4.89656463604 0.0121338901724
absolute error = 1.601e-07
relative error = 3.271e-06 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.11
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] = 10.1055 0.13
h = 0.001 0.001
y[1] (numeric) = -4.89657102797 0.0124209898556
y[1] (closed_form) = -4.89657100168 0.0124211114208
absolute error = 1.244e-07
relative error = 2.540e-06 %
Correct digits = 8
Radius of convergence (given) for eq 1 = 12.11
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] = 10.1065 0.131
h = 0.001 0.003
y[1] (numeric) = -4.89648089018 0.0125219899982
y[1] (closed_form) = -4.89648080425 0.0125220882025
absolute error = 1.305e-07
relative error = 2.665e-06 %
Correct digits = 8
Radius of convergence (given) for eq 1 = 12.11
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=120.0MB, alloc=52.3MB, time=1.51
x[1] = 10.1075 0.134
h = 0.0001 0.004
y[1] (numeric) = -4.89640155293 0.0128143070583
y[1] (closed_form) = -4.89640159042 0.0128144479089
absolute error = 1.458e-07
relative error = 2.977e-06 %
Correct digits = 8
Radius of convergence (given) for eq 1 = 12.11
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] = 10.1076 0.138
h = 0.003 0.006
y[1] (numeric) = -4.8964143667 0.0131975544037
y[1] (closed_form) = -4.89641448944 0.013197623956
absolute error = 1.411e-07
relative error = 2.881e-06 %
Correct digits = 8
Radius of convergence (given) for eq 1 = 12.11
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] = 10.1106 0.144
h = 0.0001 0.005
y[1] (numeric) = -4.89616207512 0.0137888557365
y[1] (closed_form) = -4.89616226033 0.0137894091708
absolute error = 5.836e-07
relative error = 1.192e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.11
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] = 10.1107 0.149
h = 0.0001 0.003
y[1] (numeric) = -4.89618283054 0.0142686962782
y[1] (closed_form) = -4.89618292216 0.014268947245
absolute error = 2.672e-07
relative error = 5.457e-06 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.11
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] = 10.1108 0.152
h = 0.001 0.001
y[1] (numeric) = -4.89619201455 0.0145567016621
y[1] (closed_form) = -4.89619198239 0.0145569469714
absolute error = 2.474e-07
relative error = 5.053e-06 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.11
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=165.5MB, alloc=52.3MB, time=2.06
x[1] = 10.1118 0.153
h = 0.001 0.003
y[1] (numeric) = -4.89610255302 0.0146588370983
y[1] (closed_form) = -4.89610246129 0.0146590589495
absolute error = 2.401e-07
relative error = 4.903e-06 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.11
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] = 10.1128 0.156
h = 0.0001 0.004
y[1] (numeric) = -4.89602570327 0.014952748297
y[1] (closed_form) = -4.89602573483 0.0149530129983
absolute error = 2.666e-07
relative error = 5.445e-06 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.11
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] = 10.1129 0.16
h = 0.003 0.006
y[1] (numeric) = -4.89604211611 0.0153370052708
y[1] (closed_form) = -4.89604223301 0.0153371988609
absolute error = 2.261e-07
relative error = 4.619e-06 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.11
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] = 10.1159 0.166
h = 0.0001 0.005
y[1] (numeric) = -4.89579456688 0.0159324036181
y[1] (closed_form) = -4.89579474535 0.0159330809796
absolute error = 7.005e-07
relative error = 1.431e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.12
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=211.0MB, alloc=52.3MB, time=2.61
x[1] = 10.116 0.171
h = 0.0001 0.003
y[1] (numeric) = -4.89581982413 0.0164134873781
y[1] (closed_form) = -4.8958199096 0.0164138622428
absolute error = 3.845e-07
relative error = 7.853e-06 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.12
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] = 10.1161 0.174
h = 0.001 0.001
y[1] (numeric) = -4.89583170002 0.0167022759792
y[1] (closed_form) = -4.89583166177 0.016702644965
absolute error = 3.710e-07
relative error = 7.577e-06 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.12
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] = 10.1171 0.175
h = 0.001 0.003
y[1] (numeric) = -4.89574291238 0.0168055474083
y[1] (closed_form) = -4.89574281463 0.016805892839
absolute error = 3.590e-07
relative error = 7.333e-06 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.12
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] = 10.1181 0.178
h = 0.0001 0.004
y[1] (numeric) = -4.8956685461 0.0171010565106
y[1] (closed_form) = -4.89566857151 0.0171014449946
absolute error = 3.893e-07
relative error = 7.952e-06 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.12
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=256.4MB, alloc=52.3MB, time=3.16
x[1] = 10.1182 0.182
h = 0.003 0.006
y[1] (numeric) = -4.89568855452 0.0174863291576
y[1] (closed_form) = -4.89568866535 0.0174866467177
absolute error = 3.363e-07
relative error = 6.870e-06 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.12
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] = 10.1212 0.188
h = 0.0001 0.005
y[1] (numeric) = -4.89544573804 0.0180858312014
y[1] (closed_form) = -4.89544590953 0.0180866324193
absolute error = 8.194e-07
relative error = 1.674e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.12
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] = 10.1213 0.193
h = 0.0001 0.003
y[1] (numeric) = -4.89547549278 0.0185681657433
y[1] (closed_form) = -4.89547557187 0.018568664437
absolute error = 5.049e-07
relative error = 1.031e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.12
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] = 10.1214 0.196
h = 0.001 0.001
y[1] (numeric) = -4.89549005787 0.0188577420651
y[1] (closed_form) = -4.89549001331 0.0188582346591
absolute error = 4.946e-07
relative error = 1.010e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.12
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] = 10.1224 0.197
h = 0.0001 0.004
y[1] (numeric) = -4.89540194175 0.0189621501772
y[1] (closed_form) = -4.89540183775 0.0189626191196
absolute error = 4.803e-07
relative error = 9.812e-06 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.12
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=301.8MB, alloc=52.3MB, time=3.71
x[1] = 10.1225 0.201
h = 0.003 0.006
y[1] (numeric) = -4.89542488964 0.0193482523223
y[1] (closed_form) = -4.89542503602 0.0193486573139
absolute error = 4.306e-07
relative error = 8.797e-06 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.12
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] = 10.1255 0.207
h = 0.0001 0.005
y[1] (numeric) = -4.89518618823 0.0199512357904
y[1] (closed_form) = -4.89518639449 0.0199521243501
absolute error = 9.122e-07
relative error = 1.863e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.13
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] = 10.1256 0.212
h = 0.0001 0.003
y[1] (numeric) = -4.8952198258 0.0204345994997
y[1] (closed_form) = -4.89521994016 0.0204351855064
absolute error = 5.971e-07
relative error = 1.220e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.13
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] = 10.1257 0.215
h = 0.001 0.001
y[1] (numeric) = -4.89523671297 0.0207248254708
y[1] (closed_form) = -4.89523670374 0.0207254051872
absolute error = 5.798e-07
relative error = 1.184e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.13
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
memory used=347.4MB, alloc=52.3MB, time=4.27
x[1] = 10.1267 0.216
h = 0.001 0.003
y[1] (numeric) = -4.89514918653 0.0208302045866
y[1] (closed_form) = -4.89514911793 0.0208307605677
absolute error = 5.602e-07
relative error = 1.144e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.13
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] = 10.1277 0.219
h = 0.0001 0.004
y[1] (numeric) = -4.89507944978 0.0211286675041
y[1] (closed_form) = -4.89507950409 0.0211292669163
absolute error = 6.019e-07
relative error = 1.230e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.13
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] = 10.1278 0.223
h = 0.003 0.006
y[1] (numeric) = -4.89510615164 0.0215158033769
y[1] (closed_form) = -4.89510629154 0.0215163322131
absolute error = 5.470e-07
relative error = 1.117e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.13
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] = 10.1308 0.229
h = 0.0001 0.005
y[1] (numeric) = -4.89487216514 0.0221229029807
y[1] (closed_form) = -4.89487236402 0.0221239152655
absolute error = 1.032e-06
relative error = 2.108e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.13
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] = 10.1309 0.234
h = 0.0001 0.003
y[1] (numeric) = -4.89491029215 0.0226075315375
y[1] (closed_form) = -4.89491039973 0.0226082412461
absolute error = 7.178e-07
relative error = 1.466e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.13
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
memory used=392.9MB, alloc=52.3MB, time=4.82
x[1] = 10.131 0.237
h = 0.001 0.001
y[1] (numeric) = -4.89492986359 0.0228985536049
y[1] (closed_form) = -4.89492984763 0.022899256803
absolute error = 7.034e-07
relative error = 1.437e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.13
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] = 10.132 0.238
h = 0.001 0.003
y[1] (numeric) = -4.89484300426 0.0230050706914
y[1] (closed_form) = -4.89484292901 0.0230057500585
absolute error = 6.835e-07
relative error = 1.396e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.13
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] = 10.133 0.241
h = 0.0001 0.004
y[1] (numeric) = -4.89477573943 0.0233051422318
y[1] (closed_form) = -4.89477578696 0.0233058652311
absolute error = 7.246e-07
relative error = 1.480e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.14
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] = 10.1331 0.245
h = 0.003 0.006
y[1] (numeric) = -4.89480602686 0.0236933110122
y[1] (closed_form) = -4.89480616005 0.0236939636233
absolute error = 6.661e-07
relative error = 1.361e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.14
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=438.4MB, alloc=52.3MB, time=5.37
x[1] = 10.1361 0.251
h = 0.0001 0.005
y[1] (numeric) = -4.8945767456 0.0243045333165
y[1] (closed_form) = -4.89457693688 0.0243056692536
absolute error = 1.152e-06
relative error = 2.353e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.14
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] = 10.1362 0.256
h = 0.0001 0.003
y[1] (numeric) = -4.89461935767 0.0247904342195
y[1] (closed_form) = -4.89461945823 0.0247912675591
absolute error = 8.394e-07
relative error = 1.715e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.14
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] = 10.1363 0.259
h = 0.001 0.001
y[1] (numeric) = -4.89464161065 0.025082256847
y[1] (closed_form) = -4.89464158775 0.0250830834566
absolute error = 8.269e-07
relative error = 1.689e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.14
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] = 10.1373 0.26
h = 0.001 0.003
y[1] (numeric) = -4.89455541607 0.0251899125682
y[1] (closed_form) = -4.89455533395 0.0251907152511
absolute error = 8.069e-07
relative error = 1.648e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.14
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] = 10.1383 0.263
h = 0.0001 0.004
y[1] (numeric) = -4.8944906191 0.0254915964264
y[1] (closed_form) = -4.89449065961 0.0254924429421
absolute error = 8.475e-07
relative error = 1.731e-05 %
Correct digits = 7
memory used=484.0MB, alloc=52.3MB, time=5.92
Radius of convergence (given) for eq 1 = 12.14
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] = 10.1384 0.267
h = 0.003 0.006
y[1] (numeric) = -4.89452448851 0.0258808040888
y[1] (closed_form) = -4.89452461479 0.0258815804041
absolute error = 7.865e-07
relative error = 1.607e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.14
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] = 10.1414 0.273
h = 0.0001 0.005
y[1] (numeric) = -4.89429990284 0.0264961556174
y[1] (closed_form) = -4.8943000863 0.0264974151329
absolute error = 1.273e-06
relative error = 2.601e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.14
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] = 10.1415 0.278
h = 0.0001 0.003
y[1] (numeric) = -4.89434699553 0.026983336342
y[1] (closed_form) = -4.89434708885 0.026984293241
absolute error = 9.614e-07
relative error = 1.964e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.14
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] = 10.1416 0.281
h = 0.001 0.001
y[1] (numeric) = -4.89437192734 0.0272759639796
y[1] (closed_form) = -4.89437189728 0.0272769139295
absolute error = 9.504e-07
relative error = 1.942e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.14
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=529.6MB, alloc=52.3MB, time=6.48
x[1] = 10.1426 0.282
h = 0.001 0.003
y[1] (numeric) = -4.89428639515 0.0273847589901
y[1] (closed_form) = -4.89428630594 0.0273856849182
absolute error = 9.302e-07
relative error = 1.901e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.15
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] = 10.1436 0.285
h = 0.0001 0.004
y[1] (numeric) = -4.89422406194 0.0276880588431
y[1] (closed_form) = -4.89422409523 0.0276890288038
absolute error = 9.705e-07
relative error = 1.983e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.15
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] = 10.1437 0.289
h = 0.003 0.006
y[1] (numeric) = -4.89426150977 0.0280783113431
y[1] (closed_form) = -4.8942616289 0.0280792112915
absolute error = 9.078e-07
relative error = 1.855e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.15
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] = 10.1467 0.295
h = 0.0001 0.005
y[1] (numeric) = -4.89404161 0.0286977985788
y[1] (closed_form) = -4.89404178542 0.0286991815983
absolute error = 1.394e-06
relative error = 2.849e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.15
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=575.1MB, alloc=52.3MB, time=7.03
x[1] = 10.1468 0.3
h = 0.0001 0.003
y[1] (numeric) = -4.89409317885 0.0291862665773
y[1] (closed_form) = -4.89409326473 0.0291873469636
absolute error = 1.084e-06
relative error = 2.214e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.15
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] = 10.1469 0.303
h = 0.001 0.001
y[1] (numeric) = -4.89412078676 0.029479703661
y[1] (closed_form) = -4.89412074932 0.0294807768795
absolute error = 1.074e-06
relative error = 2.194e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.15
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] = 10.1479 0.304
h = 0.0001 0.004
y[1] (numeric) = -4.89403591459 0.0295896386063
y[1] (closed_form) = -4.89403581807 0.029590687708
absolute error = 1.054e-06
relative error = 2.153e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.15
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] = 10.148 0.308
h = 0.003 0.006
y[1] (numeric) = -4.89407628783 0.0299807444157
y[1] (closed_form) = -4.89407644166 0.0299817319055
absolute error = 9.994e-07
relative error = 2.042e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.15
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] = 10.151 0.314
h = 0.0001 0.005
y[1] (numeric) = -4.89386046313 0.0306037410287
y[1] (closed_form) = -4.89386067248 0.0306052114869
absolute error = 1.485e-06
relative error = 3.035e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.16
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=620.7MB, alloc=52.3MB, time=7.58
x[1] = 10.1511 0.319
h = 0.0001 0.003
y[1] (numeric) = -4.8939158968 0.0310932697723
y[1] (closed_form) = -4.89391601711 0.0310944375774
absolute error = 1.174e-06
relative error = 2.399e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.16
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.1512 0.322
h = 0.001 0.001
y[1] (numeric) = -4.89394581571 0.0313873753086
y[1] (closed_form) = -4.89394581277 0.0313885357572
absolute error = 1.160e-06
relative error = 2.371e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.16
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.1522 0.323
h = 0.001 0.003
y[1] (numeric) = -4.89386152335 0.031498284158
y[1] (closed_form) = -4.89386146139 0.0314994204076
absolute error = 1.138e-06
relative error = 2.325e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.16
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.1532 0.326
h = 0.0001 0.004
y[1] (numeric) = -4.8938037831 0.0318045714909
y[1] (closed_form) = -4.89380384337 0.0318057521448
absolute error = 1.182e-06
relative error = 2.416e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.16
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=666.3MB, alloc=52.3MB, time=8.13
x[1] = 10.1533 0.33
h = 0.003 0.006
y[1] (numeric) = -4.89384789254 0.0321967414532
y[1] (closed_form) = -4.89384803882 0.0321978524439
absolute error = 1.121e-06
relative error = 2.290e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.16
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.1563 0.336
h = 0.0001 0.005
y[1] (numeric) = -4.89363673577 0.0328238858423
y[1] (closed_form) = -4.89363693667 0.0328254796668
absolute error = 1.606e-06
relative error = 3.283e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.16
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.1564 0.341
h = 0.0001 0.003
y[1] (numeric) = -4.89369663735 0.033314715719
y[1] (closed_form) = -4.8936967498 0.0333160068775
absolute error = 1.296e-06
relative error = 2.648e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.16
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.1565 0.344
h = 0.001 0.001
y[1] (numeric) = -4.89372922729 0.0336096389509
y[1] (closed_form) = -4.89372921656 0.0336109225351
absolute error = 1.284e-06
relative error = 2.623e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.16
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.1575 0.345
h = 0.001 0.003
y[1] (numeric) = -4.89364559055 0.0337216889401
y[1] (closed_form) = -4.89364552087 0.0337229482311
absolute error = 1.261e-06
relative error = 2.577e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.16
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=711.9MB, alloc=52.3MB, time=8.69
x[1] = 10.1585 0.348
h = 0.0001 0.004
y[1] (numeric) = -4.89359030238 0.0340296027348
y[1] (closed_form) = -4.8935903548 0.034030906628
absolute error = 1.305e-06
relative error = 2.667e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.16
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.1586 0.352
h = 0.003 0.006
y[1] (numeric) = -4.89363797996 0.0344228345131
y[1] (closed_form) = -4.89363811848 0.0344240689314
absolute error = 1.242e-06
relative error = 2.538e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.16
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.1616 0.358
h = 0.0001 0.005
y[1] (numeric) = -4.89343148139 0.0350541330437
y[1] (closed_form) = -4.89343167363 0.035055850158
absolute error = 1.728e-06
relative error = 3.531e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.17
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] = 10.1617 0.363
h = 0.0001 0.003
y[1] (numeric) = -4.89349584638 0.0355462714395
y[1] (closed_form) = -4.89349595076 0.035547685877
absolute error = 1.418e-06
relative error = 2.898e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.17
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=757.5MB, alloc=52.3MB, time=9.24
x[1] = 10.1618 0.366
h = 0.001 0.001
y[1] (numeric) = -4.89353110458 0.0358420167626
y[1] (closed_form) = -4.89353108584 0.0358434234085
absolute error = 1.407e-06
relative error = 2.875e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.17
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] = 10.1628 0.367
h = 0.001 0.003
y[1] (numeric) = -4.89344812108 0.035955208511
y[1] (closed_form) = -4.89344804347 0.0359565907698
absolute error = 1.384e-06
relative error = 2.829e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.17
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] = 10.1638 0.37
h = 0.0001 0.004
y[1] (numeric) = -4.89339528088 0.0362647523741
y[1] (closed_form) = -4.89339532523 0.0362661794323
absolute error = 1.428e-06
relative error = 2.918e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.17
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] = 10.1639 0.374
h = 0.003 0.006
y[1] (numeric) = -4.89344652295 0.0366590518521
y[1] (closed_form) = -4.89344665348 0.0366604096239
absolute error = 1.364e-06
relative error = 2.787e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.17
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] = 10.1669 0.38
h = 0.0001 0.005
y[1] (numeric) = -4.89324467285 0.0372945108484
y[1] (closed_form) = -4.89324485621 0.0372963511753
absolute error = 1.849e-06
relative error = 3.779e-05 %
Correct digits = 6
memory used=803.1MB, alloc=52.3MB, time=9.79
Radius of convergence (given) for eq 1 = 12.17
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] = 10.167 0.385
h = 0.0001 0.003
y[1] (numeric) = -4.89331349671 0.0377879651259
y[1] (closed_form) = -4.89331359279 0.0377895027674
absolute error = 1.541e-06
relative error = 3.148e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.17
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] = 10.1671 0.388
h = 0.001 0.001
y[1] (numeric) = -4.89335142037 0.0380845369215
y[1] (closed_form) = -4.89335139342 0.0380860665546
absolute error = 1.530e-06
relative error = 3.126e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.17
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] = 10.1681 0.389
h = 0.001 0.003
y[1] (numeric) = -4.89326908775 0.0381988710393
y[1] (closed_form) = -4.893269002 0.0382003761918
absolute error = 1.508e-06
relative error = 3.081e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.17
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] = 10.1691 0.392
h = 0.0001 0.004
y[1] (numeric) = -4.89321869139 0.0385100485591
y[1] (closed_form) = -4.89321872746 0.0385115987074
absolute error = 1.551e-06
relative error = 3.169e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.18
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=848.7MB, alloc=52.3MB, time=10.34
x[1] = 10.1692 0.396
h = 0.003 0.006
y[1] (numeric) = -4.89327349429 0.0389054216015
y[1] (closed_form) = -4.89327361661 0.0389069026521
absolute error = 1.486e-06
relative error = 3.037e-05 %
Correct digits = 7
Radius of convergence (given) for eq 1 = 12.18
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] = 10.1722 0.402
h = 0.0001 0.005
y[1] (numeric) = -4.89307628291 0.0395450473465
y[1] (closed_form) = -4.89307645717 0.0395470108083
absolute error = 1.971e-06
relative error = 4.028e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.18
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] = 10.1723 0.407
h = 0.0001 0.003
y[1] (numeric) = -4.89314956108 0.040039824845
y[1] (closed_form) = -4.89314964865 0.0400414856148
absolute error = 1.663e-06
relative error = 3.399e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.18
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] = 10.1724 0.41
h = 0.001 0.001
y[1] (numeric) = -4.89319014741 0.0403372274801
y[1] (closed_form) = -4.89319011202 0.0403388800251
absolute error = 1.653e-06
relative error = 3.378e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.18
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=894.3MB, alloc=52.3MB, time=10.90
x[1] = 10.1734 0.411
h = 0.0001 0.004
y[1] (numeric) = -4.8931084633 0.0404527045685
y[1] (closed_form) = -4.89310836918 0.0404543325397
absolute error = 1.631e-06
relative error = 3.333e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.18
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] = 10.1735 0.415
h = 0.003 0.006
y[1] (numeric) = -4.89316617721 0.0408489543731
y[1] (closed_form) = -4.89316633338 0.0408505230597
absolute error = 1.576e-06
relative error = 3.222e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.18
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] = 10.1765 0.421
h = 0.0001 0.005
y[1] (numeric) = -4.8929730006 0.0414921166183
y[1] (closed_form) = -4.89297320795 0.0414941676004
absolute error = 2.061e-06
relative error = 4.213e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.18
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] = 10.1766 0.426
h = 0.0001 0.003
y[1] (numeric) = -4.89305012511 0.0419879859749
y[1] (closed_form) = -4.89305024626 0.041989734254
absolute error = 1.752e-06
relative error = 3.581e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.18
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] = 10.1767 0.429
h = 0.001 0.001
y[1] (numeric) = -4.89309301109 0.0422860755829
y[1] (closed_form) = -4.89309300936 0.0422878154505
absolute error = 1.740e-06
relative error = 3.556e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.18
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=939.9MB, alloc=52.3MB, time=11.45
x[1] = 10.1777 0.43
h = 0.001 0.003
y[1] (numeric) = -4.89301189693 0.0424025292901
y[1] (closed_form) = -4.89301183652 0.0424042445032
absolute error = 1.716e-06
relative error = 3.507e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.19
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] = 10.1787 0.433
h = 0.0001 0.004
y[1] (numeric) = -4.89296605654 0.0427167271566
y[1] (closed_form) = -4.89296611769 0.042718487731
absolute error = 1.762e-06
relative error = 3.600e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.19
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] = 10.1788 0.437
h = 0.003 0.006
y[1] (numeric) = -4.89302748843 0.0431140710842
y[1] (closed_form) = -4.89302763599 0.043115762911
absolute error = 1.698e-06
relative error = 3.471e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.19
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] = 10.1818 0.443
h = 0.0001 0.005
y[1] (numeric) = -4.89283893245 0.0437614117764
y[1] (closed_form) = -4.89283913029 0.0437635857491
absolute error = 2.183e-06
relative error = 4.461e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.19
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
memory used=985.7MB, alloc=52.3MB, time=12.01
x[1] = 10.1819 0.448
h = 0.0001 0.003
y[1] (numeric) = -4.89292050281 0.0442586180023
y[1] (closed_form) = -4.89292061505 0.0442604892695
absolute error = 1.875e-06
relative error = 3.831e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.19
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] = 10.182 0.451
h = 0.001 0.001
y[1] (numeric) = -4.89296604628 0.0445575465712
y[1] (closed_form) = -4.89296603571 0.0445594092114
absolute error = 1.863e-06
relative error = 3.807e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.19
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] = 10.183 0.452
h = 0.001 0.003
y[1] (numeric) = -4.89288557623 0.0446751443718
y[1] (closed_form) = -4.89288550706 0.0446769822649
absolute error = 1.839e-06
relative error = 3.759e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.19
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] = 10.184 0.455
h = 0.0001 0.004
y[1] (numeric) = -4.89284216787 0.0449909861083
y[1] (closed_form) = -4.89284222012 0.0449928695571
absolute error = 1.884e-06
relative error = 3.851e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.19
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] = 10.1841 0.459
h = 0.003 0.006
y[1] (numeric) = -4.89290715006 0.0453894203178
y[1] (closed_form) = -4.89290728879 0.045391235208
absolute error = 1.820e-06
relative error = 3.720e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.19
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
memory used=1031.2MB, alloc=52.3MB, time=12.56
x[1] = 10.1871 0.465
h = 0.0001 0.005
y[1] (numeric) = -4.89272320492 0.0460409456224
y[1] (closed_form) = -4.89272339305 0.0460432425059
absolute error = 2.305e-06
relative error = 4.710e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.2
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] = 10.1872 0.47
h = 0.0001 0.003
y[1] (numeric) = -4.89280921652 0.0465394959895
y[1] (closed_form) = -4.89280931963 0.0465414901669
absolute error = 1.997e-06
relative error = 4.081e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.2
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] = 10.1873 0.473
h = 0.001 0.001
y[1] (numeric) = -4.89285741464 0.0468392678452
y[1] (closed_form) = -4.89285739501 0.0468412531806
absolute error = 1.985e-06
relative error = 4.058e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.2
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] = 10.1883 0.474
h = 0.001 0.003
y[1] (numeric) = -4.89277758633 0.0469580103144
y[1] (closed_form) = -4.89277750818 0.0469599708106
absolute error = 1.962e-06
relative error = 4.010e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.2
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=1076.9MB, alloc=52.3MB, time=13.11
x[1] = 10.1893 0.477
h = 0.0001 0.004
y[1] (numeric) = -4.89273660584 0.0472754994383
y[1] (closed_form) = -4.89273664897 0.047277505684
absolute error = 2.007e-06
relative error = 4.101e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.2
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] = 10.1894 0.481
h = 0.003 0.006
y[1] (numeric) = -4.8928051346 0.0476750297213
y[1] (closed_form) = -4.89280526429 0.0476769675974
absolute error = 1.942e-06
relative error = 3.969e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.2
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] = 10.1924 0.487
h = 0.0001 0.005
y[1] (numeric) = -4.8926257905 0.0483307457627
y[1] (closed_form) = -4.89262596871 0.0483331654765
absolute error = 2.426e-06
relative error = 4.959e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.2
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] = 10.1925 0.492
h = 0.0001 0.003
y[1] (numeric) = -4.8927162387 0.0488306475187
y[1] (closed_form) = -4.89271633247 0.0488327645279
absolute error = 2.119e-06
relative error = 4.331e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.2
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] = 10.1926 0.495
h = 0.001 0.001
y[1] (numeric) = -4.89276708862 0.0491312669727
y[1] (closed_form) = -4.89276705972 0.0491333749254
absolute error = 2.108e-06
relative error = 4.308e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.2
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=1122.5MB, alloc=52.3MB, time=13.66
x[1] = 10.1936 0.496
h = 0.001 0.003
y[1] (numeric) = -4.89268789968 0.0492511546767
y[1] (closed_form) = -4.89268781234 0.0492532376984
absolute error = 2.085e-06
relative error = 4.261e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.2
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] = 10.1946 0.499
h = 0.0001 0.004
y[1] (numeric) = -4.8926493429 0.0495702946871
y[1] (closed_form) = -4.8926493767 0.0495724236514
absolute error = 2.129e-06
relative error = 4.352e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.2
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] = 10.1947 0.503
h = 0.003 0.006
y[1] (numeric) = -4.89272141449 0.049970926816
y[1] (closed_form) = -4.89272153492 0.0499729875997
absolute error = 2.064e-06
relative error = 4.219e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.21
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] = 10.1977 0.509
h = 0.0001 0.005
y[1] (numeric) = -4.89254666162 0.0506308396774
y[1] (closed_form) = -4.89254682968 0.0506333821401
absolute error = 2.548e-06
relative error = 5.208e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.21
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1168.0MB, alloc=52.3MB, time=14.21
x[1] = 10.1978 0.514
h = 0.0001 0.003
y[1] (numeric) = -4.89264154175 0.0511321000462
y[1] (closed_form) = -4.89264162596 0.0511343398079
absolute error = 2.241e-06
relative error = 4.581e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.21
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] = 10.1979 0.517
h = 0.001 0.001
y[1] (numeric) = -4.89269504061 0.0514335713954
y[1] (closed_form) = -4.89269500224 0.0514358018868
absolute error = 2.231e-06
relative error = 4.559e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.21
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] = 10.1989 0.518
h = 0.0001 0.004
y[1] (numeric) = -4.89261648868 0.0515546048914
y[1] (closed_form) = -4.89261639193 0.0515568103603
absolute error = 2.208e-06
relative error = 4.512e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.21
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] = 10.199 0.522
h = 0.003 0.006
y[1] (numeric) = -4.89269145653 0.0519561368703
y[1] (closed_form) = -4.89269160997 0.0519582853695
absolute error = 2.154e-06
relative error = 4.402e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.21
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1213.6MB, alloc=52.3MB, time=14.78
x[1] = 10.202 0.528
h = 0.0001 0.005
y[1] (numeric) = -4.89252069787 0.0526196125228
y[1] (closed_form) = -4.89252089818 0.0526222425727
absolute error = 2.638e-06
relative error = 5.391e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.21
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] = 10.2021 0.533
h = 0.0001 0.003
y[1] (numeric) = -4.89261940542 0.0531219953895
y[1] (closed_form) = -4.89261952237 0.0531243227362
absolute error = 2.330e-06
relative error = 4.763e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.21
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] = 10.2022 0.536
h = 0.001 0.001
y[1] (numeric) = -4.89267519231 0.053424171944
y[1] (closed_form) = -4.89267518675 0.0534264898355
absolute error = 2.318e-06
relative error = 4.737e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.21
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] = 10.2032 0.537
h = 0.001 0.003
y[1] (numeric) = -4.89259720046 0.0535461845892
y[1] (closed_form) = -4.89259713659 0.053548477379
absolute error = 2.294e-06
relative error = 4.688e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.22
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] = 10.2042 0.54
h = 0.0001 0.004
y[1] (numeric) = -4.89256316228 0.0538683770104
y[1] (closed_form) = -4.89256321927 0.0538707161019
absolute error = 2.340e-06
relative error = 4.782e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.22
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
memory used=1259.2MB, alloc=52.3MB, time=15.32
x[1] = 10.2043 0.544
h = 0.003 0.006
y[1] (numeric) = -4.89264182946 0.0542710326189
y[1] (closed_form) = -4.89264197324 0.054273303881
absolute error = 2.276e-06
relative error = 4.651e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.22
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] = 10.2073 0.55
h = 0.0001 0.005
y[1] (numeric) = -4.89247564382 0.0549387164184
y[1] (closed_form) = -4.89247583359 0.0549414690669
absolute error = 2.759e-06
relative error = 5.639e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.22
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] = 10.2074 0.555
h = 0.0001 0.003
y[1] (numeric) = -4.89257877466 0.0554424713322
y[1] (closed_form) = -4.89257888165 0.055444921285
absolute error = 2.452e-06
relative error = 5.012e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.22
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] = 10.2075 0.558
h = 0.001 0.001
y[1] (numeric) = -4.89263720519 0.055745507773
y[1] (closed_form) = -4.89263718975 0.0557479480576
absolute error = 2.440e-06
relative error = 4.987e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.22
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
memory used=1304.9MB, alloc=52.3MB, time=15.88
x[1] = 10.2085 0.559
h = 0.001 0.003
y[1] (numeric) = -4.89255984596 0.0558686672513
y[1] (closed_form) = -4.89255977228 0.0558710823433
absolute error = 2.416e-06
relative error = 4.938e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.22
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] = 10.2095 0.562
h = 0.0001 0.004
y[1] (numeric) = -4.89252821955 0.0561925205172
y[1] (closed_form) = -4.89252826659 0.056194982102
absolute error = 2.462e-06
relative error = 5.032e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.22
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] = 10.2096 0.566
h = 0.003 0.006
y[1] (numeric) = -4.8926104188 0.0565962944238
y[1] (closed_form) = -4.89261055271 0.0565986883684
absolute error = 2.398e-06
relative error = 4.900e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.22
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] = 10.2126 0.572
h = 0.0001 0.005
y[1] (numeric) = -4.89244879634 0.0572681923357
y[1] (closed_form) = -4.89244897535 0.0572710674997
absolute error = 2.881e-06
relative error = 5.888e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.23
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] = 10.2127 0.577
h = 0.0001 0.003
y[1] (numeric) = -4.89255634574 0.0577733264519
y[1] (closed_form) = -4.89255644257 0.0577758989297
absolute error = 2.574e-06
relative error = 5.261e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.23
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=1350.4MB, alloc=52.3MB, time=16.43
x[1] = 10.2128 0.58
h = 0.001 0.001
y[1] (numeric) = -4.89261741702 0.0580772270343
y[1] (closed_form) = -4.89261739149 0.0580797896313
absolute error = 2.563e-06
relative error = 5.238e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.23
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] = 10.2138 0.581
h = 0.001 0.003
y[1] (numeric) = -4.89254068803 0.0582015338772
y[1] (closed_form) = -4.89254060433 0.0582040711913
absolute error = 2.539e-06
relative error = 5.189e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.23
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] = 10.2148 0.584
h = 0.0001 0.004
y[1] (numeric) = -4.8925114692 0.0585270514157
y[1] (closed_form) = -4.89251150609 0.0585296354129
absolute error = 2.584e-06
relative error = 5.282e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.23
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] = 10.2149 0.588
h = 0.003 0.006
y[1] (numeric) = -4.8925971967 0.0589319493183
y[1] (closed_form) = -4.89259732052 0.0589344658647
absolute error = 2.520e-06
relative error = 5.149e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.23
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=1396.1MB, alloc=52.3MB, time=16.98
x[1] = 10.2179 0.594
h = 0.0001 0.005
y[1] (numeric) = -4.89244012756 0.059608067267
y[1] (closed_form) = -4.89244029562 0.0596110648627
absolute error = 3.002e-06
relative error = 6.136e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.23
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] = 10.218 0.599
h = 0.0001 0.003
y[1] (numeric) = -4.89255209079 0.0601145877169
y[1] (closed_form) = -4.89255217723 0.0601172826379
absolute error = 2.696e-06
relative error = 5.511e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.23
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] = 10.2181 0.602
h = 0.001 0.001
y[1] (numeric) = -4.89261579991 0.0604193566814
y[1] (closed_form) = -4.89261576407 0.0604220415096
absolute error = 2.685e-06
relative error = 5.488e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.23
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] = 10.2191 0.603
h = 0.001 0.003
y[1] (numeric) = -4.89253969879 0.0605448114113
y[1] (closed_form) = -4.89253960487 0.0605474708666
absolute error = 2.661e-06
relative error = 5.439e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.23
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] = 10.2201 0.606
h = 0.0001 0.004
y[1] (numeric) = -4.89251288334 0.0608719966321
y[1] (closed_form) = -4.89251290985 0.06087470296
absolute error = 2.706e-06
relative error = 5.531e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.24
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1441.8MB, alloc=52.3MB, time=17.54
x[1] = 10.2202 0.61
h = 0.003 0.006
y[1] (numeric) = -4.89260213526 0.061278024209
y[1] (closed_form) = -4.89260224878 0.0612806632756
absolute error = 2.642e-06
relative error = 5.399e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.24
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] = 10.2232 0.616
h = 0.0001 0.005
y[1] (numeric) = -4.89244960958 0.0619583680778
y[1] (closed_form) = -4.89244976646 0.0619614880207
absolute error = 3.124e-06
relative error = 6.385e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.24
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] = 10.2233 0.621
h = 0.0001 0.003
y[1] (numeric) = -4.89256598188 0.0624662819682
y[1] (closed_form) = -4.89256605772 0.06246909925
absolute error = 2.818e-06
relative error = 5.760e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.24
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] = 10.2234 0.624
h = 0.001 0.001
y[1] (numeric) = -4.8926323259 0.0627719235405
y[1] (closed_form) = -4.89263227955 0.062774730518
absolute error = 2.807e-06
relative error = 5.737e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.24
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1487.5MB, alloc=52.3MB, time=18.09
x[1] = 10.2244 0.625
h = 0.0001 0.004
y[1] (numeric) = -4.89255685031 0.0628985266712
y[1] (closed_form) = -4.89255674595 0.062901308186
absolute error = 2.783e-06
relative error = 5.689e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.24
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] = 10.2245 0.629
h = 0.003 0.006
y[1] (numeric) = -4.89264898342 0.0633054768153
y[1] (closed_form) = -4.89264912911 0.0633082036618
absolute error = 2.731e-06
relative error = 5.581e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.24
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] = 10.2275 0.635
h = 0.0001 0.005
y[1] (numeric) = -4.89250041114 0.0639894089334
y[1] (closed_form) = -4.89250059942 0.0639926165153
absolute error = 3.213e-06
relative error = 6.567e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.24
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] = 10.2276 0.64
h = 0.0001 0.003
y[1] (numeric) = -4.89262059149 0.0644984754802
y[1] (closed_form) = -4.89262069924 0.0645013804076
absolute error = 2.907e-06
relative error = 5.941e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.24
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1533.1MB, alloc=52.3MB, time=18.64
x[1] = 10.2277 0.643
h = 0.001 0.001
y[1] (numeric) = -4.89268921168 0.0648048401975
y[1] (closed_form) = -4.89268919731 0.0648077346378
absolute error = 2.894e-06
relative error = 5.915e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.24
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] = 10.2287 0.644
h = 0.001 0.003
y[1] (numeric) = -4.89261428631 0.0649324248248
y[1] (closed_form) = -4.89261421398 0.0649352937247
absolute error = 2.870e-06
relative error = 5.865e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.25
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.2297 0.647
h = 0.0001 0.004
y[1] (numeric) = -4.89259195171 0.0652626937138
y[1] (closed_form) = -4.89259199955 0.0652656098391
absolute error = 2.917e-06
relative error = 5.961e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.25
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.2298 0.651
h = 0.003 0.006
y[1] (numeric) = -4.8926877651 0.0656707965233
y[1] (closed_form) = -4.89268790009 0.0656736457391
absolute error = 2.852e-06
relative error = 5.829e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.25
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.2328 0.657
h = 0.0001 0.005
y[1] (numeric) = -4.89254371797 0.0663589655172
y[1] (closed_form) = -4.89254389468 0.0663622952898
absolute error = 3.334e-06
relative error = 6.815e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.25
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1578.7MB, alloc=52.3MB, time=19.20
x[1] = 10.2329 0.662
h = 0.0001 0.003
y[1] (numeric) = -4.89266829855 0.0668694387212
y[1] (closed_form) = -4.89266839531 0.0668724658567
absolute error = 3.029e-06
relative error = 6.190e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.25
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.233 0.665
h = 0.001 0.001
y[1] (numeric) = -4.89273954824 0.0671766839052
y[1] (closed_form) = -4.89273952296 0.0671797003431
absolute error = 3.017e-06
relative error = 6.165e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.25
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.234 0.666
h = 0.001 0.003
y[1] (numeric) = -4.89266524399 0.0673054178934
y[1] (closed_form) = -4.89266516084 0.0673084087018
absolute error = 2.992e-06
relative error = 6.115e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.25
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.235 0.669
h = 0.0001 0.004
y[1] (numeric) = -4.89264530073 0.0676373641666
y[1] (closed_form) = -4.89264533759 0.067640402388
absolute error = 3.038e-06
relative error = 6.210e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.25
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1624.4MB, alloc=52.3MB, time=19.75
x[1] = 10.2351 0.673
h = 0.003 0.006
y[1] (numeric) = -4.89274462755 0.0680466128333
y[1] (closed_form) = -4.89274475164 0.0680495843348
absolute error = 2.974e-06
relative error = 6.078e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.25
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.2381 0.679
h = 0.0001 0.005
y[1] (numeric) = -4.89260509568 0.0687390244685
y[1] (closed_form) = -4.89260526062 0.0687424763456
absolute error = 3.456e-06
relative error = 7.063e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.26
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] = 10.2382 0.684
h = 0.0001 0.003
y[1] (numeric) = -4.89273407167 0.069250911367
y[1] (closed_form) = -4.89273415723 0.0692540606263
absolute error = 3.150e-06
relative error = 6.438e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.26
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] = 10.2383 0.687
h = 0.001 0.001
y[1] (numeric) = -4.89280794791 0.0695590412014
y[1] (closed_form) = -4.89280791151 0.069562179553
absolute error = 3.139e-06
relative error = 6.414e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.26
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] = 10.2393 0.688
h = 0.001 0.003
y[1] (numeric) = -4.89273426242 0.0696889250384
y[1] (closed_form) = -4.89273416823 0.0696920376719
absolute error = 3.114e-06
relative error = 6.364e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.26
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=1670.0MB, alloc=52.3MB, time=20.30
x[1] = 10.2403 0.691
h = 0.0001 0.004
y[1] (numeric) = -4.89271670626 0.070022552034
y[1] (closed_form) = -4.89271673193 0.0700257122673
absolute error = 3.160e-06
relative error = 6.459e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.26
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] = 10.2404 0.695
h = 0.003 0.006
y[1] (numeric) = -4.89281954263 0.0704329521608
y[1] (closed_form) = -4.89281965559 0.0704360458639
absolute error = 3.096e-06
relative error = 6.327e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.26
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] = 10.2434 0.701
h = 0.0001 0.005
y[1] (numeric) = -4.8926845161 0.0711296121619
y[1] (closed_form) = -4.89268466905 0.0711331860564
absolute error = 3.577e-06
relative error = 7.310e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.26
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] = 10.2435 0.706
h = 0.0001 0.003
y[1] (numeric) = -4.89281788266 0.0716429197677
y[1] (closed_form) = -4.89281795681 0.0716461910658
absolute error = 3.272e-06
relative error = 6.687e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.26
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=1715.6MB, alloc=52.3MB, time=20.86
x[1] = 10.2436 0.709
h = 0.001 0.001
y[1] (numeric) = -4.89289438249 0.071951938421
y[1] (closed_form) = -4.89289433476 0.0719551986019
absolute error = 3.261e-06
relative error = 6.663e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.26
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] = 10.2446 0.71
h = 0.001 0.003
y[1] (numeric) = -4.8928213134 0.0720829725862
y[1] (closed_form) = -4.89282120795 0.0720862069607
absolute error = 3.236e-06
relative error = 6.613e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.27
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] = 10.2456 0.713
h = 0.0001 0.004
y[1] (numeric) = -4.8928061401 0.0724182836237
y[1] (closed_form) = -4.89280615437 0.0724215657842
absolute error = 3.282e-06
relative error = 6.707e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.27
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] = 10.2457 0.717
h = 0.003 0.006
y[1] (numeric) = -4.89291248209 0.0728298407938
y[1] (closed_form) = -4.89291258373 0.0728330566138
absolute error = 3.217e-06
relative error = 6.575e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.27
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] = 10.2487 0.723
h = 0.0001 0.005
y[1] (numeric) = -4.89278195101 0.0735307548443
y[1] (closed_form) = -4.89278209176 0.0735344506684
absolute error = 3.699e-06
relative error = 7.558e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.27
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=1761.1MB, alloc=52.3MB, time=21.41
x[1] = 10.2488 0.728
h = 0.0001 0.003
y[1] (numeric) = -4.89291970327 0.0740454901455
y[1] (closed_form) = -4.8929197658 0.0740488833968
absolute error = 3.394e-06
relative error = 6.935e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.27
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] = 10.2489 0.731
h = 0.001 0.001
y[1] (numeric) = -4.89299882371 0.0743554017714
y[1] (closed_form) = -4.89299876445 0.0743587836964
absolute error = 3.382e-06
relative error = 6.912e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.27
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] = 10.2499 0.732
h = 0.0001 0.004
y[1] (numeric) = -4.89292636866 0.0744875867351
y[1] (closed_form) = -4.89292625176 0.0744909427658
absolute error = 3.358e-06
relative error = 6.862e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.27
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] = 10.25 0.736
h = 0.003 0.006
y[1] (numeric) = -4.89303557648 0.0749000888133
y[1] (closed_form) = -4.89303570944 0.0749033924627
absolute error = 3.306e-06
relative error = 6.756e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.27
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=1806.6MB, alloc=52.3MB, time=21.96
x[1] = 10.253 0.742
h = 0.0001 0.005
y[1] (numeric) = -4.89290895774 0.0756046157387
y[1] (closed_form) = -4.89290912907 0.0756083992392
absolute error = 3.787e-06
relative error = 7.740e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.28
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] = 10.2531 0.747
h = 0.0001 0.003
y[1] (numeric) = -4.89305049829 0.0761205333664
y[1] (closed_form) = -4.89305059189 0.076124014309
absolute error = 3.482e-06
relative error = 7.116e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.28
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] = 10.2532 0.75
h = 0.001 0.001
y[1] (numeric) = -4.89313188278 0.0764311857798
y[1] (closed_form) = -4.89313185466 0.0764346552157
absolute error = 3.470e-06
relative error = 7.090e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.28
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] = 10.2542 0.751
h = 0.001 0.003
y[1] (numeric) = -4.89305996809 0.0765643544064
y[1] (closed_form) = -4.8930598824 0.0765677978716
absolute error = 3.445e-06
relative error = 7.039e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.28
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
memory used=1852.4MB, alloc=52.3MB, time=22.51
x[1] = 10.2552 0.754
h = 0.0001 0.004
y[1] (numeric) = -4.89304923757 0.0769027795599
y[1] (closed_form) = -4.89304927131 0.0769062711573
absolute error = 3.492e-06
relative error = 7.135e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.28
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] = 10.2553 0.758
h = 0.0001 0.004
y[1] (numeric) = -4.8931621062 0.0773164628612
y[1] (closed_form) = -4.89316222745 0.0773198884705
absolute error = 3.428e-06
relative error = 7.004e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.28
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] = 10.2554 0.762
h = 0.003 0.006
y[1] (numeric) = -4.89327571021 0.0777301528675
y[1] (closed_form) = -4.89327583145 0.0777335784941
absolute error = 3.428e-06
relative error = 7.004e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.28
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] = 10.2584 0.768
h = 0.0001 0.005
y[1] (numeric) = -4.89315449987 0.0784395163947
y[1] (closed_form) = -4.89315465845 0.0784434216785
absolute error = 3.909e-06
relative error = 7.987e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.28
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] = 10.2585 0.773
h = 0.0001 0.003
y[1] (numeric) = -4.89330122689 0.0789569622122
y[1] (closed_form) = -4.89330130842 0.0789605649489
absolute error = 3.604e-06
relative error = 7.364e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.28
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
memory used=1898.1MB, alloc=52.3MB, time=23.07
x[1] = 10.2586 0.776
h = 0.001 0.001
y[1] (numeric) = -4.89338571178 0.0792685744977
y[1] (closed_form) = -4.89338567168 0.0792721654804
absolute error = 3.591e-06
relative error = 7.338e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.28
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] = 10.2596 0.777
h = 0.001 0.003
y[1] (numeric) = -4.89331455465 0.0794030713887
y[1] (closed_form) = -4.89331445706 0.0794066362956
absolute error = 3.566e-06
relative error = 7.287e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.28
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] = 10.2606 0.78
h = 0.0001 0.004
y[1] (numeric) = -4.89330666717 0.0797433952726
y[1] (closed_form) = -4.89330668886 0.0797470085331
absolute error = 3.613e-06
relative error = 7.383e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.29
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] = 10.2607 0.784
h = 0.003 0.006
y[1] (numeric) = -4.89342367761 0.0801583253077
y[1] (closed_form) = -4.89342378688 0.0801618728002
absolute error = 3.549e-06
relative error = 7.252e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.29
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1943.8MB, alloc=52.3MB, time=23.62
x[1] = 10.2637 0.79
h = 0.0001 0.005
y[1] (numeric) = -4.89330693285 0.080871960362
y[1] (closed_form) = -4.8933070786 0.0808759873158
absolute error = 4.030e-06
relative error = 8.234e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.29
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] = 10.2638 0.795
h = 0.0001 0.003
y[1] (numeric) = -4.89345803106 0.081390855165
y[1] (closed_form) = -4.89345810033 0.0813945796012
absolute error = 3.725e-06
relative error = 7.611e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.29
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] = 10.2639 0.798
h = 0.001 0.001
y[1] (numeric) = -4.89354512766 0.0817033730799
y[1] (closed_form) = -4.89354507539 0.0817070855548
absolute error = 3.713e-06
relative error = 7.586e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.29
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] = 10.2649 0.799
h = 0.001 0.003
y[1] (numeric) = -4.89347457743 0.0818390222581
y[1] (closed_form) = -4.89347446775 0.0818427085703
absolute error = 3.688e-06
relative error = 7.535e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.29
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] = 10.2659 0.802
h = 0.0001 0.004
y[1] (numeric) = -4.89346905578 0.0821810435954
y[1] (closed_form) = -4.89346906523 0.0821847784444
absolute error = 3.735e-06
relative error = 7.631e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.29
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=1989.5MB, alloc=52.3MB, time=24.18
x[1] = 10.266 0.806
h = 0.003 0.006
y[1] (numeric) = -4.8935895562 0.0825971531878
y[1] (closed_form) = -4.8935896533 0.0826008224588
absolute error = 3.671e-06
relative error = 7.500e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.29
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] = 10.269 0.812
h = 0.0001 0.005
y[1] (numeric) = -4.89347726707 0.0833150652875
y[1] (closed_form) = -4.89347739978 0.0833192138211
absolute error = 4.151e-06
relative error = 8.481e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.3
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] = 10.2691 0.817
h = 0.0001 0.003
y[1] (numeric) = -4.89363273153 0.0838354159651
y[1] (closed_form) = -4.89363278833 0.0838392620127
absolute error = 3.846e-06
relative error = 7.859e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.3
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] = 10.2692 0.82
h = 0.001 0.001
y[1] (numeric) = -4.89372243681 0.0841488436031
y[1] (closed_form) = -4.89372237217 0.0841526774824
absolute error = 3.834e-06
relative error = 7.834e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.3
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
memory used=2035.2MB, alloc=52.3MB, time=24.73
x[1] = 10.2702 0.821
h = 0.001 0.003
y[1] (numeric) = -4.89365249113 0.0842856455033
y[1] (closed_form) = -4.89365236916 0.0842894531335
absolute error = 3.810e-06
relative error = 7.784e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.3
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] = 10.2712 0.824
h = 0.0001 0.004
y[1] (numeric) = -4.89364933103 0.0846293675204
y[1] (closed_form) = -4.89364932803 0.08463322387
absolute error = 3.856e-06
relative error = 7.879e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.3
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] = 10.2713 0.828
h = 0.003 0.006
y[1] (numeric) = -4.89377331744 0.085046662154
y[1] (closed_form) = -4.89377340215 0.0850504531154
absolute error = 3.792e-06
relative error = 7.747e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.3
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] = 10.2743 0.834
h = 0.0001 0.005
y[1] (numeric) = -4.89366547398 0.0857688567762
y[1] (closed_form) = -4.89366559345 0.0857731267988
absolute error = 4.272e-06
relative error = 8.728e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.3
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] = 10.2744 0.839
h = 0.0001 0.003
y[1] (numeric) = -4.89382529972 0.0862906701928
y[1] (closed_form) = -4.89382534386 0.0862946377629
absolute error = 3.968e-06
relative error = 8.107e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.3
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
memory used=2080.9MB, alloc=52.3MB, time=25.28
x[1] = 10.2745 0.842
h = 0.001 0.001
y[1] (numeric) = -4.89391761067 0.0866050116324
y[1] (closed_form) = -4.89391753344 0.0866089668278
absolute error = 3.956e-06
relative error = 8.082e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.3
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] = 10.2755 0.843
h = 0.001 0.003
y[1] (numeric) = -4.89384826718 0.0867429666806
y[1] (closed_form) = -4.89384813269 0.0867468955408
absolute error = 3.931e-06
relative error = 8.032e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.3
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] = 10.2765 0.846
h = 0.0001 0.004
y[1] (numeric) = -4.89384746434 0.0870883925856
y[1] (closed_form) = -4.89384744868 0.0870923703469
absolute error = 3.978e-06
relative error = 8.127e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.31
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.2766 0.85
h = 0.003 0.006
y[1] (numeric) = -4.89397493273 0.087506877724
y[1] (closed_form) = -4.89397500486 0.0875107902872
absolute error = 3.913e-06
relative error = 7.995e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.31
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=2126.5MB, alloc=52.3MB, time=25.84
x[1] = 10.2796 0.856
h = 0.0001 0.005
y[1] (numeric) = -4.89387152498 0.088233360305
y[1] (closed_form) = -4.893871631 0.0882377517251
absolute error = 4.393e-06
relative error = 8.974e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.31
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.2797 0.861
h = 0.0001 0.003
y[1] (numeric) = -4.89403570704 0.0887566433
y[1] (closed_form) = -4.89403573829 0.088760732303
absolute error = 4.089e-06
relative error = 8.354e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.31
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.2798 0.864
h = 0.001 0.001
y[1] (numeric) = -4.89413062059 0.0890719026044
y[1] (closed_form) = -4.89413053058 0.0890759790268
absolute error = 4.077e-06
relative error = 8.330e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.31
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.2808 0.865
h = 0.0001 0.004
y[1] (numeric) = -4.89406187693 0.089211011218
y[1] (closed_form) = -4.89406172974 0.0892150612196
absolute error = 4.053e-06
relative error = 8.279e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.31
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.2809 0.869
h = 0.003 0.006
y[1] (numeric) = -4.8941921918 0.0896304685776
y[1] (closed_form) = -4.89419229421 0.0896344690172
absolute error = 4.002e-06
relative error = 8.175e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.31
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=2172.2MB, alloc=52.3MB, time=26.39
x[1] = 10.2839 0.875
h = 0.0001 0.005
y[1] (numeric) = -4.89409264532 0.0903605937363
y[1] (closed_form) = -4.89409278089 0.0903650728649
absolute error = 4.481e-06
relative error = 9.155e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.32
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] = 10.284 0.88
h = 0.0001 0.003
y[1] (numeric) = -4.89426059077 0.0908850953416
y[1] (closed_form) = -4.89426065207 0.0908892720784
absolute error = 4.177e-06
relative error = 8.533e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.32
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] = 10.2841 0.883
h = 0.001 0.001
y[1] (numeric) = -4.89435775312 0.0912011170029
y[1] (closed_form) = -4.89435769322 0.0912052809815
absolute error = 4.164e-06
relative error = 8.507e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.32
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] = 10.2851 0.884
h = 0.001 0.003
y[1] (numeric) = -4.89428953764 0.0913412117878
y[1] (closed_form) = -4.89428942063 0.091345349271
absolute error = 4.139e-06
relative error = 8.456e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.32
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
memory used=2217.7MB, alloc=52.3MB, time=26.94
x[1] = 10.2861 0.887
h = 0.0001 0.004
y[1] (numeric) = -4.89429313008 0.0916897887462
y[1] (closed_form) = -4.8942931316 0.0916939754686
absolute error = 4.187e-06
relative error = 8.553e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.32
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] = 10.2862 0.891
h = 0.003 0.006
y[1] (numeric) = -4.89442708127 0.0921104622453
y[1] (closed_form) = -4.8944271707 0.0921145841223
absolute error = 4.123e-06
relative error = 8.422e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.32
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] = 10.2892 0.897
h = 0.0001 0.005
y[1] (numeric) = -4.89433195199 0.0928448854882
y[1] (closed_form) = -4.89433207373 0.0928494858448
absolute error = 4.602e-06
relative error = 9.401e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.32
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] = 10.2893 0.902
h = 0.0001 0.003
y[1] (numeric) = -4.89450424453 0.0933708693913
y[1] (closed_form) = -4.89450429256 0.0933751673953
absolute error = 4.298e-06
relative error = 8.780e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.32
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
memory used=2263.4MB, alloc=52.3MB, time=27.50
x[1] = 10.2894 0.905
h = 0.001 0.001
y[1] (numeric) = -4.89460400384 0.0936878164746
y[1] (closed_form) = -4.89460393077 0.0936921015155
absolute error = 4.286e-06
relative error = 8.754e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.32
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] = 10.2904 0.906
h = 0.001 0.003
y[1] (numeric) = -4.89453638382 0.0938290656063
y[1] (closed_form) = -4.89453625371 0.0938333240668
absolute error = 4.260e-06
relative error = 8.703e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.32
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] = 10.2914 0.909
h = 0.0001 0.004
y[1] (numeric) = -4.89454232126 0.0941793555784
y[1] (closed_form) = -4.89454230954 0.0941836634578
absolute error = 4.308e-06
relative error = 8.800e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.32
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] = 10.2915 0.913
h = 0.003 0.006
y[1] (numeric) = -4.89467974298 0.0946012351501
y[1] (closed_form) = -4.89467981923 0.0946054783741
absolute error = 4.244e-06
relative error = 8.669e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.33
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] = 10.2945 0.919
h = 0.0001 0.005
y[1] (numeric) = -4.89458902091 0.0953399617964
y[1] (closed_form) = -4.89458912861 0.0953446832877
absolute error = 4.723e-06
relative error = 9.647e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.33
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
memory used=2309.0MB, alloc=52.3MB, time=28.05
x[1] = 10.2946 0.924
h = 0.0001 0.003
y[1] (numeric) = -4.8947656555 0.0958674347651
y[1] (closed_form) = -4.89476569007 0.095871853945
absolute error = 4.419e-06
relative error = 9.027e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.33
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] = 10.2947 0.927
h = 0.001 0.001
y[1] (numeric) = -4.8948680087 0.0961853112902
y[1] (closed_form) = -4.89486792226 0.0961897173026
absolute error = 4.407e-06
relative error = 9.001e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.33
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] = 10.2957 0.928
h = 0.001 0.003
y[1] (numeric) = -4.89480098179 0.0963277151612
y[1] (closed_form) = -4.89480083839 0.0963320945086
absolute error = 4.382e-06
relative error = 8.950e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.33
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] = 10.2967 0.931
h = 0.0001 0.004
y[1] (numeric) = -4.89480925992 0.0966797212834
y[1] (closed_form) = -4.89480923476 0.0966841502287
absolute error = 4.429e-06
relative error = 9.047e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.33
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
memory used=2354.7MB, alloc=52.3MB, time=28.60
x[1] = 10.2968 0.935
h = 0.003 0.006
y[1] (numeric) = -4.8949501481 0.0971028123137
y[1] (closed_form) = -4.89495021097 0.0971071767936
absolute error = 4.365e-06
relative error = 8.915e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.33
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] = 10.2998 0.941
h = 0.0001 0.005
y[1] (numeric) = -4.89486382324 0.0978458476417
y[1] (closed_form) = -4.8948639167 0.0978506901739
absolute error = 4.843e-06
relative error = 9.893e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.34
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.2999 0.946
h = 0.0001 0.003
y[1] (numeric) = -4.89504479485 0.0983748164187
y[1] (closed_form) = -4.89504481575 0.0983793566825
absolute error = 4.540e-06
relative error = 9.273e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.34
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.3 0.949
h = 0.001 0.001
y[1] (numeric) = -4.89514973886 0.0986936263902
y[1] (closed_form) = -4.89514963883 0.0986981532828
absolute error = 4.528e-06
relative error = 9.248e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.34
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.301 0.95
h = 0.001 0.003
y[1] (numeric) = -4.8950833027 0.0988371853843
y[1] (closed_form) = -4.89508314579 0.0988416855276
absolute error = 4.503e-06
relative error = 9.197e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.34
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2400.4MB, alloc=52.3MB, time=29.16
x[1] = 10.302 0.953
h = 0.0001 0.004
y[1] (numeric) = -4.89509391721 0.0991909107743
y[1] (closed_form) = -4.89509387839 0.0991954606936
absolute error = 4.550e-06
relative error = 9.293e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.34
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.3021 0.957
h = 0.003 0.006
y[1] (numeric) = -4.89523826778 0.099615218629
y[1] (closed_form) = -4.89523831706 0.0996197042731
absolute error = 4.486e-06
relative error = 9.162e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.34
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.3051 0.963
h = 0.0001 0.005
y[1] (numeric) = -4.89515633012 0.100362567876
y[1] (closed_form) = -4.89515640914 0.100367531355
absolute error = 4.964e-06
relative error = 0.0001014 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.34
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.3052 0.968
h = 0.0001 0.003
y[1] (numeric) = -4.89534163368 0.100893039179
y[1] (closed_form) = -4.8953416407 0.100897700434
absolute error = 4.661e-06
relative error = 9.520e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.34
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2446.1MB, alloc=52.3MB, time=29.71
x[1] = 10.3053 0.971
h = 0.001 0.001
y[1] (numeric) = -4.89544916539 0.101212786586
y[1] (closed_form) = -4.89544905158 0.101217434267
absolute error = 4.649e-06
relative error = 9.495e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.34
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.3063 0.972
h = 0.0001 0.004
y[1] (numeric) = -4.89538331764 0.101357501078
y[1] (closed_form) = -4.89538314703 0.101362121926
absolute error = 4.624e-06
relative error = 9.444e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.34
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.3064 0.976
h = 0.003 0.006
y[1] (numeric) = -4.89553049865 0.101782802636
y[1] (closed_form) = -4.89553057738 0.101787376174
absolute error = 4.574e-06
relative error = 9.342e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.35
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] = 10.3094 0.982
h = 0.0001 0.005
y[1] (numeric) = -4.89545238081 0.102533817226
y[1] (closed_form) = -4.89545248855 0.102538868419
absolute error = 5.052e-06
relative error = 0.0001032 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.35
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] = 10.3095 0.987
h = 0.0001 0.003
y[1] (numeric) = -4.8956414271 0.103065535693
y[1] (closed_form) = -4.89564146333 0.103070284696
absolute error = 4.749e-06
relative error = 9.699e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.35
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
memory used=2491.8MB, alloc=52.3MB, time=30.26
x[1] = 10.3096 0.99
h = 0.001 0.001
y[1] (numeric) = -4.89575119497 0.103386062422
y[1] (closed_form) = -4.89575111044 0.103390797675
absolute error = 4.736e-06
relative error = 9.672e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.35
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] = 10.3106 0.991
h = 0.001 0.003
y[1] (numeric) = -4.89568586559 0.103531764852
y[1] (closed_form) = -4.89568572433 0.103536473198
absolute error = 4.710e-06
relative error = 9.620e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.35
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] = 10.3116 0.994
h = 0.0001 0.004
y[1] (numeric) = -4.8957008366 0.103888669923
y[1] (closed_form) = -4.89570081315 0.103893428377
absolute error = 4.759e-06
relative error = 9.718e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.35
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] = 10.3117 0.998
h = 0.003 0.006
y[1] (numeric) = -4.89585163364 0.104315215087
y[1] (closed_form) = -4.8958516984 0.104319909619
absolute error = 4.695e-06
relative error = 9.588e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.35
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
memory used=2537.4MB, alloc=52.3MB, time=30.82
x[1] = 10.3147 1.004
h = 0.0001 0.005
y[1] (numeric) = -4.89577788442 0.105070553352
y[1] (closed_form) = -4.89577797734 0.105075725317
absolute error = 5.173e-06
relative error = 0.0001056 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.36
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] = 10.3148 1.009
h = 0.0001 0.003
y[1] (numeric) = -4.89597125327 0.105603786838
y[1] (closed_form) = -4.89597127525 0.10560865666
absolute error = 4.870e-06
relative error = 9.944e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.36
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] = 10.3149 1.012
h = 0.001 0.001
y[1] (numeric) = -4.89608360311 0.105925258422
y[1] (closed_form) = -4.89608350442 0.105930114293
absolute error = 4.857e-06
relative error = 9.918e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.36
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] = 10.3159 1.013
h = 0.001 0.003
y[1] (numeric) = -4.89601885777 0.106072117053
y[1] (closed_form) = -4.89601870243 0.106076945935
absolute error = 4.831e-06
relative error = 9.866e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.36
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] = 10.3169 1.016
h = 0.0001 0.004
y[1] (numeric) = -4.89603615282 0.10643075026
memory used=2583.1MB, alloc=52.3MB, time=31.37
y[1] (closed_form) = -4.89603611513 0.106435629425
absolute error = 4.879e-06
relative error = 9.963e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.36
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] = 10.317 1.02
h = 0.003 0.006
y[1] (numeric) = -4.89619040058 0.106858527537
y[1] (closed_form) = -4.89619045117 0.106863342969
absolute error = 4.816e-06
relative error = 9.833e-05 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.36
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] = 10.32 1.026
h = 0.0001 0.005
y[1] (numeric) = -4.89612100997 0.107618194598
y[1] (closed_form) = -4.89612108787 0.107623487237
absolute error = 5.293e-06
relative error = 0.0001081 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.36
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] = 10.3201 1.031
h = 0.0001 0.003
y[1] (numeric) = -4.89631869626 0.108152949747
y[1] (closed_form) = -4.89631870378 0.108157940295
absolute error = 4.991e-06
relative error = 0.0001019 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.36
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] = 10.3202 1.034
h = 0.001 0.001
y[1] (numeric) = -4.89643362493 0.108475370133
y[1] (closed_form) = -4.89643351189 0.108480346527
absolute error = 4.978e-06
relative error = 0.0001016 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.36
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
memory used=2628.8MB, alloc=52.3MB, time=31.92
x[1] = 10.3212 1.035
h = 0.001 0.003
y[1] (numeric) = -4.89636946129 0.108623385315
y[1] (closed_form) = -4.89636929168 0.108628334638
absolute error = 4.952e-06
relative error = 0.0001011 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.36
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] = 10.3222 1.038
h = 0.0001 0.004
y[1] (numeric) = -4.89638907603 0.108983749704
y[1] (closed_form) = -4.89638902391 0.108988749486
absolute error = 5.000e-06
relative error = 0.0001021 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.37
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.3223 1.042
h = 0.003 0.006
y[1] (numeric) = -4.8965467704 0.10941276438
y[1] (closed_form) = -4.89654680661 0.109417700619
absolute error = 4.936e-06
relative error = 0.0001008 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.37
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.3253 1.048
h = 0.0001 0.005
y[1] (numeric) = -4.89648172836 0.110176765317
y[1] (closed_form) = -4.89648179104 0.110182178535
absolute error = 5.414e-06
relative error = 0.0001105 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.37
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2674.4MB, alloc=52.3MB, time=32.48
x[1] = 10.3254 1.053
h = 0.0001 0.003
y[1] (numeric) = -4.89668372696 0.11071304875
y[1] (closed_form) = -4.89668371983 0.110718159929
absolute error = 5.111e-06
relative error = 0.0001044 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.37
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.3255 1.056
h = 0.001 0.001
y[1] (numeric) = -4.89680123134 0.111036421866
y[1] (closed_form) = -4.89680110373 0.111041518691
absolute error = 5.098e-06
relative error = 0.0001041 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.37
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.3265 1.057
h = 0.001 0.003
y[1] (numeric) = -4.89673764705 0.111185593943
y[1] (closed_form) = -4.89673746295 0.111190663613
absolute error = 5.073e-06
relative error = 0.0001036 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.37
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.3275 1.06
h = 0.0001 0.004
y[1] (numeric) = -4.89675957714 0.111547692541
y[1] (closed_form) = -4.89675951037 0.111552812845
absolute error = 5.121e-06
relative error = 0.0001045 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.37
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.3276 1.064
h = 0.003 0.006
y[1] (numeric) = -4.89692071397 0.111977949883
y[1] (closed_form) = -4.8969207356 0.111983006834
absolute error = 5.057e-06
relative error = 0.0001032 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.37
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2719.9MB, alloc=52.3MB, time=33.03
x[1] = 10.3306 1.07
h = 0.0001 0.005
y[1] (numeric) = -4.89686001047 0.112746289736
y[1] (closed_form) = -4.89686005772 0.112751823436
absolute error = 5.534e-06
relative error = 0.000113 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.38
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.3307 1.075
h = 0.0001 0.003
y[1] (numeric) = -4.89706631623 0.113284108046
y[1] (closed_form) = -4.89706629424 0.113289339761
absolute error = 5.232e-06
relative error = 0.0001068 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.38
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.3308 1.078
h = 0.001 0.001
y[1] (numeric) = -4.89718639316 0.113608437808
y[1] (closed_form) = -4.8971862508 0.113613654968
absolute error = 5.219e-06
relative error = 0.0001065 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.38
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.3318 1.079
h = 0.0001 0.004
y[1] (numeric) = -4.89712338589 0.113758767113
y[1] (closed_form) = -4.89712318711 0.113763957036
absolute error = 5.194e-06
relative error = 0.000106 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.38
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2765.6MB, alloc=52.3MB, time=33.58
x[1] = 10.3319 1.083
h = 0.003 0.006
y[1] (numeric) = -4.89728733685 0.114190039249
y[1] (closed_form) = -4.89728738711 0.114195184097
absolute error = 5.145e-06
relative error = 0.000105 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.38
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.3349 1.089
h = 0.0001 0.005
y[1] (numeric) = -4.89723041153 0.114962066383
y[1] (closed_form) = -4.89723048669 0.114967687788
absolute error = 5.622e-06
relative error = 0.0001148 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.38
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.335 1.094
h = 0.0001 0.003
y[1] (numeric) = -4.89744043902 0.115501159902
y[1] (closed_form) = -4.89744044541 0.115506479364
absolute error = 5.319e-06
relative error = 0.0001086 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.38
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.3351 1.097
h = 0.001 0.001
y[1] (numeric) = -4.89756273925 0.115826285643
y[1] (closed_form) = -4.89756262535 0.115831590377
absolute error = 5.306e-06
relative error = 0.0001083 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.38
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.3361 1.098
h = 0.001 0.003
y[1] (numeric) = -4.89750024056 0.115977604476
y[1] (closed_form) = -4.89750007031 0.115982881901
absolute error = 5.280e-06
relative error = 0.0001078 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.38
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2811.2MB, alloc=52.3MB, time=34.14
x[1] = 10.3371 1.101
h = 0.0001 0.004
y[1] (numeric) = -4.89752648813 0.116342910568
y[1] (closed_form) = -4.89752643493 0.116348238952
absolute error = 5.329e-06
relative error = 0.0001088 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.39
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.3372 1.105
h = 0.003 0.006
y[1] (numeric) = -4.89769403447 0.116775453281
y[1] (closed_form) = -4.89769406977 0.116780718666
absolute error = 5.266e-06
relative error = 0.0001075 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.39
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.3402 1.111
h = 0.0001 0.005
y[1] (numeric) = -4.89764142905 0.117551828719
y[1] (closed_form) = -4.89764148842 0.117557570425
absolute error = 5.742e-06
relative error = 0.0001172 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.39
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.3403 1.116
h = 0.0001 0.003
y[1] (numeric) = -4.89785575415 0.11809246938
y[1] (closed_form) = -4.89785574532 0.118097909201
absolute error = 5.440e-06
relative error = 0.000111 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.39
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2856.9MB, alloc=52.3MB, time=34.70
x[1] = 10.3404 1.119
h = 0.001 0.001
y[1] (numeric) = -4.89798062111 0.118418559048
y[1] (closed_form) = -4.89798049207 0.11842398394
absolute error = 5.426e-06
relative error = 0.0001108 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.39
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.3414 1.12
h = 0.001 0.003
y[1] (numeric) = -4.89791869508 0.118571035733
y[1] (closed_form) = -4.89791850978 0.118576433236
absolute error = 5.401e-06
relative error = 0.0001102 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.39
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.3424 1.123
h = 0.0001 0.004
y[1] (numeric) = -4.89794724557 0.118938084645
y[1] (closed_form) = -4.89794717715 0.118943533279
absolute error = 5.449e-06
relative error = 0.0001112 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.39
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.3425 1.127
h = 0.003 0.006
y[1] (numeric) = -4.89811822252 0.119371885029
y[1] (closed_form) = -4.89811824267 0.119377270854
absolute error = 5.386e-06
relative error = 0.0001099 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.39
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.3455 1.133
h = 0.0001 0.005
y[1] (numeric) = -4.89806992695 0.120152613694
y[1] (closed_form) = -4.89806997032 0.120158475602
absolute error = 5.862e-06
relative error = 0.0001196 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.4
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2902.5MB, alloc=52.3MB, time=35.25
x[1] = 10.3456 1.138
h = 0.0001 0.003
y[1] (numeric) = -4.89828854447 0.120694808018
y[1] (closed_form) = -4.8982885202 0.1207003681
absolute error = 5.560e-06
relative error = 0.0001135 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.4
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.3457 1.141
h = 0.001 0.001
y[1] (numeric) = -4.89841597497 0.121021865483
y[1] (closed_form) = -4.8984158306 0.121027410438
absolute error = 5.547e-06
relative error = 0.0001132 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.4
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.3467 1.142
h = 0.001 0.003
y[1] (numeric) = -4.89835461926 0.121175500331
y[1] (closed_form) = -4.89835441871 0.121181017816
absolute error = 5.521e-06
relative error = 0.0001127 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.4
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.3477 1.145
h = 0.0001 0.004
y[1] (numeric) = -4.89838546831 0.121544295018
y[1] (closed_form) = -4.89838538449 0.121549863805
absolute error = 5.569e-06
relative error = 0.0001137 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.4
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2948.1MB, alloc=52.3MB, time=35.80
x[1] = 10.3478 1.149
h = 0.003 0.006
y[1] (numeric) = -4.89855987168 0.121979358261
y[1] (closed_form) = -4.89855987647 0.121984864429
absolute error = 5.506e-06
relative error = 0.0001124 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.4
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.3508 1.155
h = 0.0001 0.005
y[1] (numeric) = -4.8985158759 0.122764445036
y[1] (closed_form) = -4.89851590308 0.122770427046
absolute error = 5.982e-06
relative error = 0.0001221 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.4
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.3509 1.16
h = 0.0001 0.003
y[1] (numeric) = -4.89873878062 0.123308199518
y[1] (closed_form) = -4.89873874073 0.123313879765
absolute error = 5.680e-06
relative error = 0.0001159 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.41
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.351 1.163
h = 0.001 0.001
y[1] (numeric) = -4.89886877149 0.123636228635
y[1] (closed_form) = -4.89886861159 0.123641893556
absolute error = 5.667e-06
relative error = 0.0001156 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.41
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=2993.7MB, alloc=52.3MB, time=36.36
x[1] = 10.352 1.164
h = 0.001 0.003
y[1] (numeric) = -4.89880798377 0.123791021947
y[1] (closed_form) = -4.89880776776 0.123796659316
absolute error = 5.642e-06
relative error = 0.0001151 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.41
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.353 1.167
h = 0.0001 0.004
y[1] (numeric) = -4.898841127 0.124161565346
y[1] (closed_form) = -4.89884102757 0.124167254189
absolute error = 5.690e-06
relative error = 0.0001161 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.41
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.3531 1.171
h = 0.003 0.006
y[1] (numeric) = -4.89901895258 0.124597896615
y[1] (closed_form) = -4.89901894182 0.124603523029
absolute error = 5.626e-06
relative error = 0.0001148 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.41
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.3561 1.177
h = 0.0001 0.005
y[1] (numeric) = -4.89897924653 0.125387346342
y[1] (closed_form) = -4.89897925732 0.125393448355
absolute error = 6.102e-06
relative error = 0.0001245 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.41
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.3562 1.182
h = 0.0001 0.003
y[1] (numeric) = -4.89920643323 0.125932667454
y[1] (closed_form) = -4.8992063775 0.125938467766
absolute error = 5.801e-06
relative error = 0.0001184 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.41
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3039.2MB, alloc=52.3MB, time=36.92
x[1] = 10.3563 1.185
h = 0.001 0.001
y[1] (numeric) = -4.89933898126 0.126261672062
y[1] (closed_form) = -4.89933880563 0.126267456851
absolute error = 5.787e-06
relative error = 0.0001181 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.41
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.3573 1.186
h = 0.0001 0.004
y[1] (numeric) = -4.89927875919 0.126417624129
y[1] (closed_form) = -4.89927852754 0.126423381286
absolute error = 5.762e-06
relative error = 0.0001176 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.41
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.3574 1.19
h = 0.003 0.006
y[1] (numeric) = -4.89945938233 0.126854990889
y[1] (closed_form) = -4.89945939938 0.126860705189
absolute error = 5.714e-06
relative error = 0.0001166 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.41
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.3604 1.196
h = 0.0001 0.005
y[1] (numeric) = -4.89942341272 0.127648149011
y[1] (closed_form) = -4.8994234506 0.127654338707
absolute error = 6.190e-06
relative error = 0.0001263 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.42
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=3084.8MB, alloc=52.3MB, time=37.47
x[1] = 10.3605 1.201
h = 0.0001 0.003
y[1] (numeric) = -4.89965429977 0.128194772864
y[1] (closed_form) = -4.89965427161 0.128200660908
absolute error = 5.888e-06
relative error = 0.0001201 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.42
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] = 10.3606 1.204
h = 0.001 0.001
y[1] (numeric) = -4.89978905805 0.128524589796
y[1] (closed_form) = -4.89978891007 0.128530462147
absolute error = 5.874e-06
relative error = 0.0001198 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.42
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] = 10.3616 1.205
h = 0.001 0.003
y[1] (numeric) = -4.89972933481 0.128681532809
y[1] (closed_form) = -4.89972913087 0.128687377458
absolute error = 5.848e-06
relative error = 0.0001193 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.42
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] = 10.3626 1.208
h = 0.0001 0.004
y[1] (numeric) = -4.89976675625 0.129055310702
y[1] (closed_form) = -4.8997666686 0.129061207144
absolute error = 5.897e-06
relative error = 0.0001203 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.42
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] = 10.3627 1.212
h = 0.003 0.006
y[1] (numeric) = -4.89995095379 0.129493974509
y[1] (closed_form) = -4.89995095491 0.129499808873
absolute error = 5.834e-06
relative error = 0.000119 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.42
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=3130.4MB, alloc=52.3MB, time=38.02
x[1] = 10.3657 1.218
h = 0.0001 0.005
y[1] (numeric) = -4.89991925522 0.130291504605
y[1] (closed_form) = -4.89991927634 0.130297814118
absolute error = 6.310e-06
relative error = 0.0001287 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.43
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] = 10.3658 1.223
h = 0.0001 0.003
y[1] (numeric) = -4.90015441454 0.13083970712
y[1] (closed_form) = -4.9001543702 0.130845715048
absolute error = 6.008e-06
relative error = 0.0001226 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.43
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] = 10.3659 1.226
h = 0.001 0.001
y[1] (numeric) = -4.90029172407 0.131170506685
y[1] (closed_form) = -4.90029155999 0.131176498723
absolute error = 5.994e-06
relative error = 0.0001223 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.43
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] = 10.3669 1.227
h = 0.001 0.003
y[1] (numeric) = -4.90023256215 0.131328609002
y[1] (closed_form) = -4.9002323422 0.131334573259
absolute error = 5.968e-06
relative error = 0.0001218 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.43
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3176.0MB, alloc=52.3MB, time=38.58
x[1] = 10.3679 1.23
h = 0.0001 0.004
y[1] (numeric) = -4.90027226528 0.131704143961
y[1] (closed_form) = -4.90027216145 0.131710160178
absolute error = 6.017e-06
relative error = 0.0001227 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.43
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] = 10.368 1.234
h = 0.003 0.006
y[1] (numeric) = -4.900459873 0.132144090513
y[1] (closed_form) = -4.900459858 0.132150044843
absolute error = 5.954e-06
relative error = 0.0001215 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.43
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] = 10.371 1.24
h = 0.0001 0.005
y[1] (numeric) = -4.90043243539 0.13294599731
y[1] (closed_form) = -4.90043243957 0.132952426538
absolute error = 6.429e-06
relative error = 0.0001311 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.43
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] = 10.3711 1.245
h = 0.0001 0.003
y[1] (numeric) = -4.90067186172 0.133495784884
y[1] (closed_form) = -4.90067180098 0.133501912596
absolute error = 6.128e-06
relative error = 0.000125 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.43
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] = 10.3712 1.248
h = 0.001 0.001
y[1] (numeric) = -4.90081171928 0.133827570877
y[1] (closed_form) = -4.90081153891 0.133833682502
absolute error = 6.114e-06
relative error = 0.0001247 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.43
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3221.6MB, alloc=52.3MB, time=39.13
x[1] = 10.3722 1.249
h = 0.001 0.003
y[1] (numeric) = -4.90075311634 0.133986832767
y[1] (closed_form) = -4.90075288018 0.133992916533
absolute error = 6.088e-06
relative error = 0.0001242 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.44
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] = 10.3732 1.252
h = 0.0001 0.004
y[1] (numeric) = -4.90079509677 0.134364127656
y[1] (closed_form) = -4.90079497657 0.134370263551
absolute error = 6.137e-06
relative error = 0.0001252 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.44
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] = 10.3733 1.256
h = 0.003 0.006
y[1] (numeric) = -4.90098611041 0.134805362042
y[1] (closed_form) = -4.9009860791 0.134811436239
absolute error = 6.074e-06
relative error = 0.0001239 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.44
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] = 10.3763 1.262
h = 0.0001 0.005
y[1] (numeric) = -4.90096292369 0.135611650227
y[1] (closed_form) = -4.90096291072 0.135618199068
absolute error = 6.549e-06
relative error = 0.0001336 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.44
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3267.1MB, alloc=52.3MB, time=39.69
x[1] = 10.3764 1.267
h = 0.0001 0.003
y[1] (numeric) = -4.90120661173 0.13616302923
y[1] (closed_form) = -4.9012065344 0.136169276626
absolute error = 6.248e-06
relative error = 0.0001274 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.44
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] = 10.3765 1.27
h = 0.001 0.001
y[1] (numeric) = -4.90134901409 0.136495805429
y[1] (closed_form) = -4.90134881723 0.136502036543
absolute error = 6.234e-06
relative error = 0.0001271 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.44
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] = 10.3775 1.271
h = 0.001 0.003
y[1] (numeric) = -4.90129096781 0.136656227153
y[1] (closed_form) = -4.90129071524 0.136662430328
absolute error = 6.208e-06
relative error = 0.0001266 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.44
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] = 10.3785 1.274
h = 0.0001 0.004
y[1] (numeric) = -4.90133522114 0.13703528482
y[1] (closed_form) = -4.90133508438 0.137041540291
absolute error = 6.257e-06
relative error = 0.0001276 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.44
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3312.7MB, alloc=52.3MB, time=40.24
x[1] = 10.3786 1.278
h = 0.003 0.006
y[1] (numeric) = -4.90152963645 0.137477812106
y[1] (closed_form) = -4.90152958862 0.137484006069
absolute error = 6.194e-06
relative error = 0.0001263 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.44
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] = 10.3816 1.284
h = 0.0001 0.005
y[1] (numeric) = -4.90151069052 0.138288486325
y[1] (closed_form) = -4.90151066021 0.138295154675
absolute error = 6.668e-06
relative error = 0.000136 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.45
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] = 10.3817 1.289
h = 0.0001 0.003
y[1] (numeric) = -4.90175863497 0.138841463102
y[1] (closed_form) = -4.90175854086 0.13884783008
absolute error = 6.368e-06
relative error = 0.0001299 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.45
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] = 10.3818 1.292
h = 0.001 0.001
y[1] (numeric) = -4.90190357888 0.139175233271
y[1] (closed_form) = -4.90190336534 0.139181583772
absolute error = 6.354e-06
relative error = 0.0001296 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.45
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] = 10.3828 1.293
h = 0.0001 0.004
y[1] (numeric) = -4.90184608694 0.139336815081
y[1] (closed_form) = -4.90184581776 0.139343137564
absolute error = 6.328e-06
relative error = 0.000129 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.45
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
memory used=3358.3MB, alloc=52.3MB, time=40.80
x[1] = 10.3829 1.297
h = 0.003 0.006
y[1] (numeric) = -4.90204328298 0.139780398158
y[1] (closed_form) = -4.90204326214 0.139786679981
absolute error = 6.282e-06
relative error = 0.0001281 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.45
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] = 10.3859 1.303
h = 0.0001 0.005
y[1] (numeric) = -4.90202803163 0.140594801065
y[1] (closed_form) = -4.90202802761 0.140601557064
absolute error = 6.756e-06
relative error = 0.0001378 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.45
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] = 10.386 1.308
h = 0.0001 0.003
y[1] (numeric) = -4.90227965473 0.141149107598
y[1] (closed_form) = -4.90227958737 0.141155562281
absolute error = 6.455e-06
relative error = 0.0001316 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.45
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] = 10.3861 1.311
h = 0.001 0.001
y[1] (numeric) = -4.90242679563 0.141483706124
y[1] (closed_form) = -4.90242660893 0.141490144162
absolute error = 6.441e-06
relative error = 0.0001313 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.46
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3403.8MB, alloc=52.3MB, time=41.35
x[1] = 10.3871 1.312
h = 0.001 0.003
y[1] (numeric) = -4.9023697928 0.141646280126
y[1] (closed_form) = -4.90236955054 0.141652690077
absolute error = 6.415e-06
relative error = 0.0001308 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.46
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.3881 1.315
h = 0.0001 0.004
y[1] (numeric) = -4.90241828485 0.142028598474
y[1] (closed_form) = -4.9024181581 0.142035061033
absolute error = 6.464e-06
relative error = 0.0001318 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.46
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.3882 1.319
h = 0.003 0.006
y[1] (numeric) = -4.902619034 0.14247350456
y[1] (closed_form) = -4.90261899628 0.142479905964
absolute error = 6.402e-06
relative error = 0.0001305 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.46
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.3912 1.325
h = 0.0001 0.005
y[1] (numeric) = -4.90260800473 0.14329230216
y[1] (closed_form) = -4.902607983 0.143299177478
absolute error = 6.875e-06
relative error = 0.0001402 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.46
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.3913 1.33
h = 0.0001 0.003
y[1] (numeric) = -4.90286387439 0.143848218268
y[1] (closed_form) = -4.90286378989 0.143854792347
absolute error = 6.575e-06
relative error = 0.000134 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.46
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3449.3MB, alloc=52.3MB, time=41.90
x[1] = 10.3914 1.333
h = 0.001 0.001
y[1] (numeric) = -4.90301355085 0.144183817765
y[1] (closed_form) = -4.9030133471 0.144190375004
absolute error = 6.560e-06
relative error = 0.0001337 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.46
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.3924 1.334
h = 0.001 0.003
y[1] (numeric) = -4.90295709803 0.144347552326
y[1] (closed_form) = -4.9029568388 0.144354081401
absolute error = 6.534e-06
relative error = 0.0001332 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.46
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.3934 1.337
h = 0.0001 0.004
y[1] (numeric) = -4.90300785043 0.144731641547
y[1] (closed_form) = -4.90300770655 0.144738223395
absolute error = 6.583e-06
relative error = 0.0001342 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.47
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.3935 1.341
h = 0.003 0.006
y[1] (numeric) = -4.90321198902 0.145177854966
y[1] (closed_form) = -4.90321193423 0.145184375849
absolute error = 6.521e-06
relative error = 0.0001329 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.47
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=3494.9MB, alloc=52.3MB, time=42.46
x[1] = 10.3965 1.347
h = 0.0001 0.005
y[1] (numeric) = -4.90320517173 0.146001051789
y[1] (closed_form) = -4.90320513211 0.146008046323
absolute error = 6.995e-06
relative error = 0.0001426 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.47
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.3966 1.352
h = 0.0001 0.003
y[1] (numeric) = -4.90346528261 0.146558583744
y[1] (closed_form) = -4.90346518077 0.146565277115
absolute error = 6.694e-06
relative error = 0.0001365 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.47
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.3967 1.355
h = 0.001 0.001
y[1] (numeric) = -4.90361749136 0.14689518793
y[1] (closed_form) = -4.90361727037 0.146901864269
absolute error = 6.680e-06
relative error = 0.0001362 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.47
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.3977 1.356
h = 0.001 0.003
y[1] (numeric) = -4.90356158623 0.147060083279
y[1] (closed_form) = -4.90356130985 0.147066731376
absolute error = 6.654e-06
relative error = 0.0001356 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.47
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.3987 1.359
h = 0.0001 0.004
y[1] (numeric) = -4.90361459456 0.147445946148
y[1] (closed_form) = -4.90361443337 0.147452647183
absolute error = 6.703e-06
relative error = 0.0001366 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.47
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=3540.5MB, alloc=52.3MB, time=43.00
x[1] = 10.3988 1.363
h = 0.003 0.006
y[1] (numeric) = -4.90382211829 0.147893471887
y[1] (closed_form) = -4.90382204623 0.147900112145
absolute error = 6.641e-06
relative error = 0.0001354 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.47
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.4018 1.369
h = 0.0001 0.005
y[1] (numeric) = -4.90381950289 0.148721072425
y[1] (closed_form) = -4.90381944518 0.148728186069
absolute error = 7.114e-06
relative error = 0.000145 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.48
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] = 10.4019 1.374
h = 0.0001 0.003
y[1] (numeric) = -4.90408384962 0.14928022647
y[1] (closed_form) = -4.90408373024 0.149287039031
absolute error = 6.814e-06
relative error = 0.0001389 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.48
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] = 10.402 1.377
h = 0.001 0.001
y[1] (numeric) = -4.90423858738 0.149617839049
y[1] (closed_form) = -4.90423834896 0.149624634385
absolute error = 6.800e-06
relative error = 0.0001386 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.48
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
memory used=3586.0MB, alloc=52.3MB, time=43.56
x[1] = 10.403 1.378
h = 0.001 0.003
y[1] (numeric) = -4.90418322763 0.149783895405
y[1] (closed_form) = -4.9041829339 0.149790662423
absolute error = 6.773e-06
relative error = 0.0001381 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.48
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] = 10.404 1.381
h = 0.0001 0.004
y[1] (numeric) = -4.90423848748 0.150171534681
y[1] (closed_form) = -4.90423830878 0.150178354799
absolute error = 6.822e-06
relative error = 0.000139 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.48
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] = 10.4041 1.385
h = 0.003 0.006
y[1] (numeric) = -4.90444939203 0.150620377705
y[1] (closed_form) = -4.9044493025 0.150627137236
absolute error = 6.760e-06
relative error = 0.0001378 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.48
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] = 10.4071 1.391
h = 0.0001 0.005
y[1] (numeric) = -4.9044509684 0.151452386408
y[1] (closed_form) = -4.90445089241 0.151459619058
absolute error = 7.233e-06
relative error = 0.0001474 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.48
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
memory used=3631.7MB, alloc=52.3MB, time=44.12
x[1] = 10.4072 1.396
h = 0.0001 0.003
y[1] (numeric) = -4.90471954561 0.152013168764
y[1] (closed_form) = -4.9047194085 0.152020100411
absolute error = 6.933e-06
relative error = 0.0001413 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.49
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] = 10.4073 1.399
h = 0.001 0.001
y[1] (numeric) = -4.9048768091 0.152351793423
y[1] (closed_form) = -4.90487655306 0.152358707653
absolute error = 6.919e-06
relative error = 0.000141 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.49
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] = 10.4083 1.4
h = 0.003 0.006
y[1] (numeric) = -4.90482199241 0.152519010999
y[1] (closed_form) = -4.90482168114 0.152525896833
absolute error = 6.893e-06
relative error = 0.0001405 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.49
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] = 10.4113 1.406
h = 0.0001 0.005
y[1] (numeric) = -4.90482593149 0.153354041768
y[1] (closed_form) = -4.90482603693 0.153361518622
absolute error = 7.478e-06
relative error = 0.0001524 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.49
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] = 10.4114 1.411
h = 0.0001 0.003
y[1] (numeric) = -4.90509737445 0.153916054219
y[1] (closed_form) = -4.90509741915 0.153923230142
absolute error = 7.176e-06
relative error = 0.0001462 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.49
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
memory used=3677.2MB, alloc=52.3MB, time=44.67
x[1] = 10.4115 1.414
h = 0.001 0.001
y[1] (numeric) = -4.90525634786 0.154255440734
y[1] (closed_form) = -4.90525627369 0.15426259911
absolute error = 7.159e-06
relative error = 0.0001459 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.49
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] = 10.4125 1.415
h = 0.001 0.003
y[1] (numeric) = -4.90520187413 0.154423470826
y[1] (closed_form) = -4.90520174479 0.154430600757
absolute error = 7.131e-06
relative error = 0.0001453 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.49
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] = 10.4135 1.418
h = 0.0001 0.004
y[1] (numeric) = -4.90526087937 0.154814171151
y[1] (closed_form) = -4.90526086478 0.154821354453
absolute error = 7.183e-06
relative error = 0.0001464 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.49
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] = 10.4136 1.422
h = 0.003 0.006
y[1] (numeric) = -4.90547744705 0.155265333735
y[1] (closed_form) = -4.90547752171 0.155272456771
absolute error = 7.123e-06
relative error = 0.0001451 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.49
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
memory used=3722.8MB, alloc=52.3MB, time=45.23
x[1] = 10.4166 1.428
h = 0.0001 0.005
y[1] (numeric) = -4.90548596446 0.156104897946
y[1] (closed_form) = -4.9054860513 0.156112493622
absolute error = 7.596e-06
relative error = 0.0001548 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.5
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] = 10.4167 1.433
h = 0.0001 0.003
y[1] (numeric) = -4.90576162863 0.156668549009
y[1] (closed_form) = -4.90576165527 0.156675843838
absolute error = 7.295e-06
relative error = 0.0001486 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.5
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] = 10.4168 1.436
h = 0.001 0.001
y[1] (numeric) = -4.90592312212 0.157008953709
y[1] (closed_form) = -4.90592303001 0.157016230799
absolute error = 7.278e-06
relative error = 0.0001483 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.5
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] = 10.4178 1.437
h = 0.001 0.003
y[1] (numeric) = -4.90586918754 0.157178145302
y[1] (closed_form) = -4.90586904034 0.15718539387
absolute error = 7.250e-06
relative error = 0.0001477 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.5
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] = 10.4188 1.44
h = 0.0001 0.004
y[1] (numeric) = -4.90593043235 0.15757062924
y[1] (closed_form) = -4.90593039973 0.157577931343
absolute error = 7.302e-06
relative error = 0.0001488 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.5
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
memory used=3768.3MB, alloc=52.3MB, time=45.78
x[1] = 10.4189 1.444
h = 0.003 0.006
y[1] (numeric) = -4.90615036904 0.158023122244
y[1] (closed_form) = -4.90615042572 0.15803036427
absolute error = 7.242e-06
relative error = 0.0001475 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.5
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] = 10.4219 1.45
h = 0.0001 0.005
y[1] (numeric) = -4.90616305096 0.158867106134
y[1] (closed_form) = -4.90616311901 0.158874820524
absolute error = 7.715e-06
relative error = 0.0001572 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.51
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.422 1.455
h = 0.0001 0.003
y[1] (numeric) = -4.90644293091 0.159432401957
y[1] (closed_form) = -4.90644293932 0.159439815586
absolute error = 7.414e-06
relative error = 0.000151 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.51
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.4221 1.458
h = 0.001 0.001
y[1] (numeric) = -4.90660694118 0.159773828487
y[1] (closed_form) = -4.90660683094 0.159781224187
absolute error = 7.397e-06
relative error = 0.0001507 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.51
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=3813.9MB, alloc=52.3MB, time=46.33
x[1] = 10.4231 1.459
h = 0.001 0.003
y[1] (numeric) = -4.90655354344 0.159944181769
y[1] (closed_form) = -4.90655337819 0.159951548872
absolute error = 7.369e-06
relative error = 0.0001501 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.51
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.4241 1.462
h = 0.0001 0.004
y[1] (numeric) = -4.90661702339 0.160338452012
y[1] (closed_form) = -4.90661697256 0.160345872809
absolute error = 7.421e-06
relative error = 0.0001512 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.51
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.4242 1.466
h = 0.003 0.006
y[1] (numeric) = -4.90684032472 0.160792280325
y[1] (closed_form) = -4.90684036324 0.160799641234
absolute error = 7.361e-06
relative error = 0.0001499 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.51
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.4272 1.472
h = 0.0001 0.005
y[1] (numeric) = -4.90685716104 0.161640688196
y[1] (closed_form) = -4.90685721012 0.161648521193
absolute error = 7.833e-06
relative error = 0.0001596 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.51
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.4273 1.477
h = 0.0001 0.003
y[1] (numeric) = -4.90714125135 0.162207634902
y[1] (closed_form) = -4.90714124133 0.162215167225
absolute error = 7.532e-06
relative error = 0.0001534 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.51
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=3859.4MB, alloc=52.3MB, time=46.88
x[1] = 10.4274 1.48
h = 0.001 0.001
y[1] (numeric) = -4.9073077751 0.162550086891
y[1] (closed_form) = -4.90730764652 0.162557601096
absolute error = 7.515e-06
relative error = 0.0001531 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.52
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.4284 1.481
h = 0.0001 0.004
y[1] (numeric) = -4.90725491189 0.162721602045
y[1] (closed_form) = -4.90725472839 0.162729087578
absolute error = 7.488e-06
relative error = 0.0001525 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.52
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.4285 1.485
h = 0.003 0.006
y[1] (numeric) = -4.90748096369 0.163176520756
y[1] (closed_form) = -4.90748102777 0.163183969445
absolute error = 7.449e-06
relative error = 0.0001517 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.52
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.4315 1.491
h = 0.0001 0.005
y[1] (numeric) = -4.90750142064 0.164028690737
y[1] (closed_form) = -4.90750149458 0.164036611282
absolute error = 7.921e-06
relative error = 0.0001613 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.52
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3905.0MB, alloc=52.3MB, time=47.44
x[1] = 10.4316 1.496
h = 0.0001 0.003
y[1] (numeric) = -4.90778915049 0.164597013285
y[1] (closed_form) = -4.90778916581 0.164604633227
absolute error = 7.620e-06
relative error = 0.0001552 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.52
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.4317 1.499
h = 0.001 0.001
y[1] (numeric) = -4.90795784736 0.164940320963
y[1] (closed_form) = -4.90795774422 0.164947922622
absolute error = 7.602e-06
relative error = 0.0001548 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.52
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.4327 1.5
h = 0.001 0.003
y[1] (numeric) = -4.90790545626 0.165112830028
y[1] (closed_form) = -4.90790529827 0.165120402949
absolute error = 7.575e-06
relative error = 0.0001542 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.52
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.4337 1.503
h = 0.0001 0.004
y[1] (numeric) = -4.90797310483 0.165510404759
y[1] (closed_form) = -4.90797306096 0.165518031673
absolute error = 7.627e-06
relative error = 0.0001553 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.52
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=3950.5MB, alloc=52.3MB, time=47.99
x[1] = 10.4338 1.507
h = 0.003 0.006
y[1] (numeric) = -4.90820267137 0.165966690753
y[1] (closed_form) = -4.90820271693 0.165974258131
absolute error = 7.568e-06
relative error = 0.0001541 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.52
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.4368 1.513
h = 0.0001 0.005
y[1] (numeric) = -4.90822726396 0.16682329274
y[1] (closed_form) = -4.90822731857 0.166831331693
absolute error = 8.039e-06
relative error = 0.0001637 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.53
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] = 10.4369 1.518
h = 0.0001 0.003
y[1] (numeric) = -4.90851919409 0.167393277559
y[1] (closed_form) = -4.90851919063 0.167401016
absolute error = 7.738e-06
relative error = 0.0001576 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.53
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] = 10.437 1.521
h = 0.001 0.001
y[1] (numeric) = -4.90869039829 0.167737617446
y[1] (closed_form) = -4.90869027647 0.167745337415
absolute error = 7.721e-06
relative error = 0.0001572 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.53
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] = 10.438 1.522
h = 0.001 0.003
y[1] (numeric) = -4.90863853743 0.167911288727
y[1] (closed_form) = -4.90863836085 0.167918979884
absolute error = 7.693e-06
relative error = 0.0001566 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.53
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
memory used=3995.9MB, alloc=52.3MB, time=48.54
x[1] = 10.439 1.525
h = 0.0001 0.004
y[1] (numeric) = -4.90870840849 0.168310657406
y[1] (closed_form) = -4.90870834586 0.168318402716
absolute error = 7.746e-06
relative error = 0.0001577 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.53
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] = 10.4391 1.529
h = 0.003 0.006
y[1] (numeric) = -4.90894132718 0.168768292631
y[1] (closed_form) = -4.90894135403 0.168775978593
absolute error = 7.686e-06
relative error = 0.0001565 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.53
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] = 10.4421 1.535
h = 0.0001 0.005
y[1] (numeric) = -4.90897004528 0.169629330815
y[1] (closed_form) = -4.90897008038 0.169637488068
absolute error = 8.157e-06
relative error = 0.0001661 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.54
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] = 10.4422 1.54
h = 0.0001 0.003
y[1] (numeric) = -4.90926617023 0.170200983953
y[1] (closed_form) = -4.90926614779 0.170208840786
absolute error = 7.857e-06
relative error = 0.0001599 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.54
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
memory used=4041.5MB, alloc=52.3MB, time=49.09
x[1] = 10.4423 1.543
h = 0.001 0.001
y[1] (numeric) = -4.90943987842 0.170546359633
y[1] (closed_form) = -4.90943973774 0.170554197807
absolute error = 7.839e-06
relative error = 0.0001596 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.54
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] = 10.4433 1.544
h = 0.001 0.003
y[1] (numeric) = -4.90938854551 0.17072119329
y[1] (closed_form) = -4.90938835014 0.170729002577
absolute error = 7.812e-06
relative error = 0.000159 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.54
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] = 10.4443 1.547
h = 0.0001 0.004
y[1] (numeric) = -4.90946063461 0.171122358536
y[1] (closed_form) = -4.90946055303 0.171130222133
absolute error = 7.864e-06
relative error = 0.0001601 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.54
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] = 10.4444 1.551
h = 0.003 0.006
y[1] (numeric) = -4.90969690105 0.171581347799
y[1] (closed_form) = -4.90969690899 0.171589152238
absolute error = 7.804e-06
relative error = 0.0001589 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.54
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] = 10.4474 1.557
h = 0.0001 0.005
y[1] (numeric) = -4.90972973455 0.172446826331
y[1] (closed_form) = -4.90972974994 0.172455101776
absolute error = 8.275e-06
relative error = 0.0001684 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.54
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
memory used=4087.1MB, alloc=52.3MB, time=49.64
x[1] = 10.4475 1.562
h = 0.0001 0.003
y[1] (numeric) = -4.91003004883 0.173020153809
y[1] (closed_form) = -4.91003000723 0.173028128928
absolute error = 7.975e-06
relative error = 0.0001623 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.55
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] = 10.4476 1.565
h = 0.001 0.001
y[1] (numeric) = -4.91020625767 0.173366568852
y[1] (closed_form) = -4.91020609793 0.173374525123
absolute error = 7.958e-06
relative error = 0.000162 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.55
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] = 10.4486 1.566
h = 0.001 0.003
y[1] (numeric) = -4.91015545041 0.173542565035
y[1] (closed_form) = -4.91015523607 0.173550492346
absolute error = 7.930e-06
relative error = 0.0001614 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.55
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] = 10.4496 1.569
h = 0.0001 0.004
y[1] (numeric) = -4.91022975309 0.173945529448
y[1] (closed_form) = -4.91022965238 0.173953511226
absolute error = 7.982e-06
relative error = 0.0001625 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.55
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4132.6MB, alloc=52.3MB, time=50.20
x[1] = 10.4497 1.573
h = 0.003 0.006
y[1] (numeric) = -4.91046936286 0.174405877536
y[1] (closed_form) = -4.91046935172 0.174413800344
absolute error = 7.923e-06
relative error = 0.0001612 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.55
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] = 10.4527 1.579
h = 0.0001 0.005
y[1] (numeric) = -4.91050630165 0.175275800529
y[1] (closed_form) = -4.91050629715 0.175284194054
absolute error = 8.394e-06
relative error = 0.0001708 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.55
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] = 10.4528 1.584
h = 0.0001 0.003
y[1] (numeric) = -4.91081079975 0.175850808343
y[1] (closed_form) = -4.91081073881 0.175858901638
absolute error = 8.094e-06
relative error = 0.0001647 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.55
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] = 10.4529 1.587
h = 0.001 0.001
y[1] (numeric) = -4.91098950589 0.176198266299
y[1] (closed_form) = -4.91098932692 0.17620634056
absolute error = 8.076e-06
relative error = 0.0001643 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.55
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] = 10.4539 1.588
h = 0.0001 0.004
y[1] (numeric) = -4.91093922199 0.176375425152
y[1] (closed_form) = -4.91093898849 0.176383470379
absolute error = 8.049e-06
relative error = 0.0001638 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.55
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4178.3MB, alloc=52.3MB, time=50.75
x[1] = 10.454 1.592
h = 0.003 0.006
y[1] (numeric) = -4.91118156479 0.176836882828
y[1] (closed_form) = -4.91118157841 0.176844893354
absolute error = 8.011e-06
relative error = 0.000163 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.56
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] = 10.457 1.598
h = 0.0001 0.005
y[1] (numeric) = -4.91122208217 0.177710585989
y[1] (closed_form) = -4.91122210174 0.177719066991
absolute error = 8.481e-06
relative error = 0.0001726 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.56
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] = 10.4571 1.603
h = 0.0001 0.003
y[1] (numeric) = -4.91153019728 0.178286995213
y[1] (closed_form) = -4.91153016088 0.178295176062
absolute error = 8.181e-06
relative error = 0.0001665 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.56
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] = 10.4572 1.606
h = 0.001 0.001
y[1] (numeric) = -4.9117110628 0.178635324014
y[1] (closed_form) = -4.91171090846 0.178643485667
absolute error = 8.163e-06
relative error = 0.0001661 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.56
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
memory used=4223.9MB, alloc=52.3MB, time=51.30
x[1] = 10.4582 1.607
h = 0.001 0.003
y[1] (numeric) = -4.91166124139 0.178813477566
y[1] (closed_form) = -4.9116610326 0.178821610121
absolute error = 8.135e-06
relative error = 0.0001655 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.56
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] = 10.4592 1.61
h = 0.0001 0.004
y[1] (numeric) = -4.91173967273 0.179219770421
y[1] (closed_form) = -4.91173957726 0.179227957737
absolute error = 8.188e-06
relative error = 0.0001666 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.56
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] = 10.4593 1.614
h = 0.003 0.006
y[1] (numeric) = -4.91198550817 0.179682619934
y[1] (closed_form) = -4.91198550235 0.17969074863
absolute error = 8.129e-06
relative error = 0.0001654 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.56
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] = 10.4623 1.62
h = 0.0001 0.005
y[1] (numeric) = -4.91203011205 0.180560775222
y[1] (closed_form) = -4.9120301114 0.180569374102
absolute error = 8.599e-06
relative error = 0.0001749 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.57
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
memory used=4269.4MB, alloc=52.3MB, time=51.86
x[1] = 10.4624 1.625
h = 0.0001 0.003
y[1] (numeric) = -4.9123424008 0.181138875934
y[1] (closed_form) = -4.9123423447 0.181147174761
absolute error = 8.299e-06
relative error = 0.0001688 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.57
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] = 10.4625 1.628
h = 0.001 0.001
y[1] (numeric) = -4.91252575741 0.181488254258
y[1] (closed_form) = -4.91252558348 0.181496533702
absolute error = 8.281e-06
relative error = 0.0001685 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.57
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] = 10.4635 1.629
h = 0.001 0.003
y[1] (numeric) = -4.91247645509 0.181667570751
y[1] (closed_form) = -4.9124762268 0.181675821025
absolute error = 8.253e-06
relative error = 0.0001679 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.57
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] = 10.4645 1.632
h = 0.0001 0.004
y[1] (numeric) = -4.91255708732 0.182075670164
y[1] (closed_form) = -4.91255697218 0.182083975353
absolute error = 8.306e-06
relative error = 0.000169 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.57
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] = 10.4646 1.636
h = 0.003 0.006
y[1] (numeric) = -4.91280625345 0.182539892132
y[1] (closed_form) = -4.912806228 0.18254813889
absolute error = 8.247e-06
relative error = 0.0001677 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.57
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
memory used=4315.0MB, alloc=52.3MB, time=52.41
x[1] = 10.4676 1.642
h = 0.0001 0.005
y[1] (numeric) = -4.91285493371 0.183422503547
y[1] (closed_form) = -4.91285491264 0.183431220193
absolute error = 8.717e-06
relative error = 0.0001773 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.58
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.4677 1.647
h = 0.0001 0.003
y[1] (numeric) = -4.91317139056 0.184002301669
y[1] (closed_form) = -4.91317131458 0.184010718363
absolute error = 8.417e-06
relative error = 0.0001712 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.58
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.4678 1.65
h = 0.001 0.001
y[1] (numeric) = -4.91335723489 0.184352733022
y[1] (closed_form) = -4.91335704118 0.184361130148
absolute error = 8.399e-06
relative error = 0.0001708 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.58
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.4688 1.651
h = 0.001 0.003
y[1] (numeric) = -4.91330844937 0.184533212577
y[1] (closed_form) = -4.91330820139 0.18454158046
absolute error = 8.372e-06
relative error = 0.0001703 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.58
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4360.6MB, alloc=52.3MB, time=52.96
x[1] = 10.4698 1.654
h = 0.0001 0.004
y[1] (numeric) = -4.91339127803 0.184943121075
y[1] (closed_form) = -4.91339114304 0.184951544029
absolute error = 8.424e-06
relative error = 0.0001713 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.58
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.4699 1.658
h = 0.003 0.006
y[1] (numeric) = -4.91364377039 0.185408720206
y[1] (closed_form) = -4.91364372512 0.185417084917
absolute error = 8.365e-06
relative error = 0.0001701 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.58
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.4729 1.664
h = 0.0001 0.005
y[1] (numeric) = -4.91369651691 0.186295791709
y[1] (closed_form) = -4.91369647523 0.18630462601
absolute error = 8.834e-06
relative error = 0.0001797 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.58
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.473 1.669
h = 0.0001 0.003
y[1] (numeric) = -4.91401713632 0.186877293133
y[1] (closed_form) = -4.91401704027 0.186885827585
absolute error = 8.535e-06
relative error = 0.0001736 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.58
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.4731 1.672
h = 0.001 0.001
y[1] (numeric) = -4.91420546498 0.187228781006
y[1] (closed_form) = -4.91420525132 0.187237295705
absolute error = 8.517e-06
relative error = 0.0001732 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.58
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4406.1MB, alloc=52.3MB, time=53.52
x[1] = 10.4741 1.673
h = 0.001 0.003
y[1] (numeric) = -4.91415719397 0.187410423737
y[1] (closed_form) = -4.91415692611 0.187418909121
absolute error = 8.490e-06
relative error = 0.0001726 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.59
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.4751 1.676
h = 0.0001 0.004
y[1] (numeric) = -4.9142422146 0.187822143832
y[1] (closed_form) = -4.91424205958 0.18783068444
absolute error = 8.542e-06
relative error = 0.0001737 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.59
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.4752 1.68
h = 0.003 0.006
y[1] (numeric) = -4.91449802872 0.188289124809
y[1] (closed_form) = -4.91449796346 0.188297607363
absolute error = 8.483e-06
relative error = 0.0001725 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.59
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.4782 1.686
h = 0.0001 0.005
y[1] (numeric) = -4.91455483139 0.189180660321
y[1] (closed_form) = -4.91455476892 0.189189612165
absolute error = 8.952e-06
relative error = 0.000182 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.59
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4451.7MB, alloc=52.3MB, time=54.08
x[1] = 10.4783 1.691
h = 0.0001 0.003
y[1] (numeric) = -4.91487960779 0.189763870917
y[1] (closed_form) = -4.91487949149 0.189772523016
absolute error = 8.653e-06
relative error = 0.0001759 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.59
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.4784 1.694
h = 0.001 0.001
y[1] (numeric) = -4.91507041739 0.190116418786
y[1] (closed_form) = -4.91507018359 0.190125050948
absolute error = 8.635e-06
relative error = 0.0001756 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.59
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.4794 1.695
h = 0.0001 0.004
y[1] (numeric) = -4.91502265861 0.190299224796
y[1] (closed_form) = -4.9150223707 0.190307827571
absolute error = 8.608e-06
relative error = 0.000175 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.59
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.4795 1.699
h = 0.003 0.006
y[1] (numeric) = -4.91528118812 0.190767334145
y[1] (closed_form) = -4.91528114683 0.190775904342
absolute error = 8.570e-06
relative error = 0.0001742 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.59
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.4825 1.705
h = 0.0001 0.005
y[1] (numeric) = -4.91534152732 0.191662667084
y[1] (closed_form) = -4.91534148814 0.191671706321
absolute error = 9.039e-06
relative error = 0.0001838 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.6
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4497.2MB, alloc=52.3MB, time=54.63
x[1] = 10.4826 1.71
h = 0.0001 0.003
y[1] (numeric) = -4.91566989791 0.19224730413
y[1] (closed_form) = -4.91566980536 0.192256043707
absolute error = 8.740e-06
relative error = 0.0001777 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.6
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] = 10.4827 1.713
h = 0.001 0.001
y[1] (numeric) = -4.915862853 0.19260073768
y[1] (closed_form) = -4.91586264304 0.192609457161
absolute error = 8.722e-06
relative error = 0.0001773 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.6
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] = 10.4837 1.714
h = 0.001 0.003
y[1] (numeric) = -4.91581554715 0.192784539016
y[1] (closed_form) = -4.91581528316 0.192793229048
absolute error = 8.694e-06
relative error = 0.0001767 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.6
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] = 10.4847 1.717
h = 0.0001 0.004
y[1] (numeric) = -4.91590465632 0.193199610708
y[1] (closed_form) = -4.91590450484 0.193208356249
absolute error = 8.747e-06
relative error = 0.0001778 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.6
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4542.7MB, alloc=52.3MB, time=55.18
x[1] = 10.4848 1.721
h = 0.003 0.006
y[1] (numeric) = -4.91616665612 0.193669135932
y[1] (closed_form) = -4.91616659449 0.193677823769
absolute error = 8.688e-06
relative error = 0.0001766 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.6
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] = 10.4878 1.727
h = 0.0001 0.005
y[1] (numeric) = -4.91623103268 0.194568940193
y[1] (closed_form) = -4.91623097236 0.194578096766
absolute error = 9.157e-06
relative error = 0.0001861 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.61
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] = 10.4879 1.732
h = 0.0001 0.003
y[1] (numeric) = -4.91656354994 0.195155297327
y[1] (closed_form) = -4.91656343681 0.195164154346
absolute error = 8.858e-06
relative error = 0.00018 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.61
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] = 10.488 1.735
h = 0.001 0.001
y[1] (numeric) = -4.9167589797 0.195509797338
y[1] (closed_form) = -4.91675874926 0.195518634078
absolute error = 8.840e-06
relative error = 0.0001796 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.61
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
memory used=4588.3MB, alloc=52.3MB, time=55.74
x[1] = 10.489 1.736
h = 0.001 0.003
y[1] (numeric) = -4.91671218185 0.195694762154
y[1] (closed_form) = -4.91671189745 0.195703569375
absolute error = 8.812e-06
relative error = 0.0001791 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.61
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] = 10.49 1.739
h = 0.0001 0.004
y[1] (numeric) = -4.91680347024 0.19611165258
y[1] (closed_form) = -4.9168032982 0.196120515462
absolute error = 8.865e-06
relative error = 0.0001801 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.61
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] = 10.4901 1.743
h = 0.003 0.006
y[1] (numeric) = -4.91706877903 0.19658257299
y[1] (closed_form) = -4.91706869686 0.196591378355
absolute error = 8.806e-06
relative error = 0.0001789 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.61
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] = 10.4931 1.749
h = 0.0001 0.005
y[1] (numeric) = -4.91713718282 0.197486852383
y[1] (closed_form) = -4.91713710119 0.197496126178
absolute error = 9.274e-06
relative error = 0.0001885 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.61
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] = 10.4932 1.754
h = 0.0001 0.003
y[1] (numeric) = -4.91747384117 0.198074935398
y[1] (closed_form) = -4.91747370725 0.198083909748
absolute error = 8.975e-06
relative error = 0.0001824 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.62
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4633.8MB, alloc=52.3MB, time=56.28
x[1] = 10.4933 1.757
h = 0.001 0.001
y[1] (numeric) = -4.91767174218 0.198430505299
y[1] (closed_form) = -4.91767149108 0.198439459188
absolute error = 8.957e-06
relative error = 0.000182 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.62
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.4943 1.758
h = 0.001 0.003
y[1] (numeric) = -4.91762545004 0.198616633679
y[1] (closed_form) = -4.91762514506 0.198625557978
absolute error = 8.930e-06
relative error = 0.0001814 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.62
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.4953 1.761
h = 0.0001 0.004
y[1] (numeric) = -4.9177189132 0.19903534528
y[1] (closed_form) = -4.91771872042 0.199044325391
absolute error = 8.982e-06
relative error = 0.0001825 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.62
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.4954 1.765
h = 0.003 0.006
y[1] (numeric) = -4.91798752646 0.199507665479
y[1] (closed_form) = -4.91798742358 0.199516588261
absolute error = 8.923e-06
relative error = 0.0001813 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.62
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4679.4MB, alloc=52.3MB, time=56.84
x[1] = 10.4984 1.771
h = 0.0001 0.005
y[1] (numeric) = -4.91805994736 0.200416423775
y[1] (closed_form) = -4.91805984425 0.200425814678
absolute error = 9.391e-06
relative error = 0.0001908 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.62
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.4985 1.776
h = 0.0001 0.003
y[1] (numeric) = -4.9184007412 0.201006238438
y[1] (closed_form) = -4.91840058632 0.201015330007
absolute error = 9.093e-06
relative error = 0.0001847 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.62
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.4986 1.779
h = 0.001 0.001
y[1] (numeric) = -4.91860111005 0.201362881643
y[1] (closed_form) = -4.9186008381 0.20137195257
absolute error = 9.075e-06
relative error = 0.0001843 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.62
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.4996 1.78
h = 0.001 0.003
y[1] (numeric) = -4.91855532135 0.201550173662
y[1] (closed_form) = -4.91855499561 0.201559214928
absolute error = 9.047e-06
relative error = 0.0001838 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.63
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] = 10.5006 1.783
h = 0.0001 0.004
y[1] (numeric) = -4.9186509548 0.201970708861
y[1] (closed_form) = -4.91865074109 0.201979806089
absolute error = 9.100e-06
relative error = 0.0001848 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.63
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4724.9MB, alloc=52.3MB, time=57.39
x[1] = 10.5007 1.787
h = 0.003 0.006
y[1] (numeric) = -4.91892286802 0.202444433431
y[1] (closed_form) = -4.91892274425 0.202453473518
absolute error = 9.041e-06
relative error = 0.0001836 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.63
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] = 10.5037 1.793
h = 0.0001 0.005
y[1] (numeric) = -4.91899929592 0.203357674362
y[1] (closed_form) = -4.91899917113 0.20336718226
absolute error = 9.509e-06
relative error = 0.0001931 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.63
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] = 10.5038 1.798
h = 0.0001 0.003
y[1] (numeric) = -4.91934421961 0.203949226413
y[1] (closed_form) = -4.9193440436 0.203958435089
absolute error = 9.210e-06
relative error = 0.0001871 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.63
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] = 10.5039 1.801
h = 0.001 0.001
y[1] (numeric) = -4.91954705289 0.204306946322
y[1] (closed_form) = -4.91954675991 0.204316134174
absolute error = 9.193e-06
relative error = 0.0001867 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.63
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4770.5MB, alloc=52.3MB, time=57.94
x[1] = 10.5049 1.802
h = 0.0001 0.004
y[1] (numeric) = -4.91950176535 0.204495402046
y[1] (closed_form) = -4.91950141867 0.204504560167
absolute error = 9.165e-06
relative error = 0.0001861 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.63
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] = 10.505 1.806
h = 0.003 0.006
y[1] (numeric) = -4.91977637612 0.204970273368
y[1] (closed_form) = -4.91977627553 0.204979401011
absolute error = 9.128e-06
relative error = 0.0001854 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.63
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] = 10.508 1.812
h = 0.0001 0.005
y[1] (numeric) = -4.91985629847 0.205887328193
y[1] (closed_form) = -4.91985619619 0.205896923388
absolute error = 9.596e-06
relative error = 0.0001949 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.64
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.5081 1.817
h = 0.0001 0.003
y[1] (numeric) = -4.92020479328 0.206480331204
y[1] (closed_form) = -4.92020464023 0.206489627268
absolute error = 9.297e-06
relative error = 0.0001888 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.64
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.5082 1.82
h = 0.001 0.001
y[1] (numeric) = -4.92040975799 0.206838951311
y[1] (closed_form) = -4.92040948807 0.206848226394
absolute error = 9.279e-06
relative error = 0.0001884 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.64
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4816.2MB, alloc=52.3MB, time=58.49
x[1] = 10.5092 1.821
h = 0.001 0.003
y[1] (numeric) = -4.92036491388 0.207028402829
y[1] (closed_form) = -4.92036459033 0.207037648122
absolute error = 9.251e-06
relative error = 0.0001878 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.64
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.5102 1.824
h = 0.0001 0.004
y[1] (numeric) = -4.92046459563 0.207452311979
y[1] (closed_form) = -4.9204643838 0.207461613512
absolute error = 9.304e-06
relative error = 0.0001889 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.64
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.5103 1.828
h = 0.003 0.006
y[1] (numeric) = -4.9207426541 0.207928622698
y[1] (closed_form) = -4.92074253228 0.207937867438
absolute error = 9.246e-06
relative error = 0.0001877 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.64
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.5133 1.834
h = 0.0001 0.005
y[1] (numeric) = -4.92082656467 0.208850167122
y[1] (closed_form) = -4.92082644038 0.2088598791
absolute error = 9.713e-06
relative error = 0.0001972 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.65
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4861.7MB, alloc=52.3MB, time=59.04
x[1] = 10.5134 1.839
h = 0.0001 0.003
y[1] (numeric) = -4.92117917892 0.2094449182
y[1] (closed_form) = -4.92117900439 0.209454331162
absolute error = 9.415e-06
relative error = 0.0001911 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.65
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.5135 1.842
h = 0.001 0.001
y[1] (numeric) = -4.9213866017 0.209804621331
y[1] (closed_form) = -4.92138631042 0.209814013133
absolute error = 9.396e-06
relative error = 0.0001908 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.65
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.5145 1.843
h = 0.001 0.003
y[1] (numeric) = -4.92134225454 0.209995236687
y[1] (closed_form) = -4.92134190972 0.210004598628
absolute error = 9.368e-06
relative error = 0.0001902 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.65
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.5155 1.846
h = 0.0001 0.004
y[1] (numeric) = -4.92144409381 0.21042097632
y[1] (closed_form) = -4.92144386053 0.21043039465
absolute error = 9.421e-06
relative error = 0.0001913 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.65
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4907.3MB, alloc=52.3MB, time=59.60
x[1] = 10.5156 1.85
h = 0.003 0.006
y[1] (numeric) = -4.92172543932 0.210898704457
y[1] (closed_form) = -4.92172529609 0.210908066181
absolute error = 9.363e-06
relative error = 0.0001901 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.65
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.5186 1.856
h = 0.0001 0.005
y[1] (numeric) = -4.92181332799 0.211824742101
y[1] (closed_form) = -4.92181318151 0.211834570746
absolute error = 9.830e-06
relative error = 0.0001995 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.66
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.5187 1.861
h = 0.0001 0.003
y[1] (numeric) = -4.92217005603 0.212421246912
y[1] (closed_form) = -4.92216985984 0.212430776658
absolute error = 9.532e-06
relative error = 0.0001935 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.66
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.5188 1.864
h = 0.001 0.001
y[1] (numeric) = -4.92237993345 0.21278203642
y[1] (closed_form) = -4.92237962062 0.212791544826
absolute error = 9.514e-06
relative error = 0.0001931 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.66
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.5198 1.865
h = 0.001 0.003
y[1] (numeric) = -4.92233608097 0.212973815659
y[1] (closed_form) = -4.92233571469 0.212983294136
absolute error = 9.486e-06
relative error = 0.0001925 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.66
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4952.8MB, alloc=52.3MB, time=60.15
x[1] = 10.5208 1.868
h = 0.0001 0.004
y[1] (numeric) = -4.92244007328 0.213401388128
y[1] (closed_form) = -4.92243981837 0.213410923141
absolute error = 9.538e-06
relative error = 0.0001936 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.66
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.5209 1.872
h = 0.003 0.006
y[1] (numeric) = -4.92272470129 0.213880538184
y[1] (closed_form) = -4.92272453646 0.213890016778
absolute error = 9.480e-06
relative error = 0.0001924 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.66
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.5239 1.878
h = 0.0001 0.005
y[1] (numeric) = -4.92281655794 0.214811072632
y[1] (closed_form) = -4.9228163891 0.214821017827
absolute error = 9.947e-06
relative error = 0.0002019 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.66
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.524 1.883
h = 0.0001 0.003
y[1] (numeric) = -4.9231773941 0.215409336814
y[1] (closed_form) = -4.92317717608 0.21541898323
absolute error = 9.649e-06
relative error = 0.0001958 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.66
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=4998.4MB, alloc=52.3MB, time=60.71
x[1] = 10.5241 1.886
h = 0.001 0.001
y[1] (numeric) = -4.92338972271 0.215771216037
y[1] (closed_form) = -4.92338938815 0.215780840934
absolute error = 9.631e-06
relative error = 0.0001954 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.67
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.5251 1.887
h = 0.001 0.003
y[1] (numeric) = -4.92334636266 0.215964159196
y[1] (closed_form) = -4.92334597474 0.215973754096
absolute error = 9.603e-06
relative error = 0.0001949 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.67
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.5261 1.89
h = 0.0001 0.004
y[1] (numeric) = -4.92345250353 0.216393566837
y[1] (closed_form) = -4.92345222681 0.216403218418
absolute error = 9.656e-06
relative error = 0.0001959 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.67
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.5262 1.894
h = 0.003 0.006
y[1] (numeric) = -4.92374040946 0.216874143291
y[1] (closed_form) = -4.92374022286 0.21688373864
absolute error = 9.597e-06
relative error = 0.0001947 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.67
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.5292 1.9
h = 0.0001 0.005
y[1] (numeric) = -4.92383622399 0.217809178088
y[1] (closed_form) = -4.92383603261 0.217819239718
absolute error = 1.006e-05
relative error = 0.0002042 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.67
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5044.0MB, alloc=52.3MB, time=61.26
x[1] = 10.5293 1.905
h = 0.0001 0.003
y[1] (numeric) = -4.92420116259 0.218409207255
y[1] (closed_form) = -4.92420092256 0.218418970225
absolute error = 9.766e-06
relative error = 0.0001981 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.67
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.5294 1.908
h = 0.001 0.001
y[1] (numeric) = -4.92441593894 0.218772179513
y[1] (closed_form) = -4.92441558249 0.218781920787
absolute error = 9.748e-06
relative error = 0.0001978 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.67
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.5304 1.909
h = 0.0001 0.004
y[1] (numeric) = -4.92437306906 0.218966286623
y[1] (closed_form) = -4.92437265932 0.218975997831
absolute error = 9.720e-06
relative error = 0.0001972 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.67
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.5305 1.913
h = 0.003 0.006
y[1] (numeric) = -4.92466365454 0.2194480278
y[1] (closed_form) = -4.92466349034 0.219457710608
absolute error = 9.684e-06
relative error = 0.0001965 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.68
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5089.6MB, alloc=52.3MB, time=61.82
x[1] = 10.5335 1.919
h = 0.0001 0.005
y[1] (numeric) = -4.92476292145 0.220386892176
y[1] (closed_form) = -4.9247627518 0.220397040996
absolute error = 1.015e-05
relative error = 0.0002059 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.68
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] = 10.5336 1.924
h = 0.0001 0.003
y[1] (numeric) = -4.92513140786 0.220988396281
y[1] (closed_form) = -4.92513119001 0.22099824654
absolute error = 9.853e-06
relative error = 0.0001998 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.68
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] = 10.5337 1.927
h = 0.001 0.001
y[1] (numeric) = -4.92534830144 0.221352282934
y[1] (closed_form) = -4.92534796727 0.221362111341
absolute error = 9.834e-06
relative error = 0.0001995 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.68
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] = 10.5347 1.928
h = 0.001 0.003
y[1] (numeric) = -4.92530586554 0.22154738615
y[1] (closed_form) = -4.92530547816 0.221557184432
absolute error = 9.806e-06
relative error = 0.0001989 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.68
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] = 10.5357 1.931
h = 0.0001 0.004
y[1] (numeric) = -4.92541601437 0.221980189303
y[1] (closed_form) = -4.92541573788 0.22199004454
absolute error = 9.859e-06
relative error = 0.0002 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.68
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5135.1MB, alloc=52.3MB, time=62.37
x[1] = 10.5358 1.935
h = 0.003 0.006
y[1] (numeric) = -4.92571002472 0.222463392884
y[1] (closed_form) = -4.92570983841 0.222473192236
absolute error = 9.801e-06
relative error = 0.0001988 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.68
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] = 10.5388 1.941
h = 0.0001 0.005
y[1] (numeric) = -4.92581323073 0.223406764225
y[1] (closed_form) = -4.92581303821 0.223417029264
absolute error = 1.027e-05
relative error = 0.0002082 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.69
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] = 10.5389 1.946
h = 0.0001 0.003
y[1] (numeric) = -4.92618580906 0.224010043757
y[1] (closed_form) = -4.92618556887 0.224020010357
absolute error = 9.969e-06
relative error = 0.0002022 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.69
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] = 10.539 1.949
h = 0.001 0.001
y[1] (numeric) = -4.92640514398 0.224375029623
y[1] (closed_form) = -4.92640478757 0.224384974195
absolute error = 9.951e-06
relative error = 0.0002018 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.69
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5180.7MB, alloc=52.3MB, time=62.92
x[1] = 10.54 1.95
h = 0.001 0.003
y[1] (numeric) = -4.92636319405 0.224571296853
y[1] (closed_form) = -4.92636278452 0.224581211233
absolute error = 9.923e-06
relative error = 0.0002012 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.69
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] = 10.541 1.953
h = 0.0001 0.004
y[1] (numeric) = -4.92647547864 0.225005941813
y[1] (closed_form) = -4.92647517984 0.225015913291
absolute error = 9.976e-06
relative error = 0.0002023 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.69
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] = 10.5411 1.957
h = 0.003 0.006
y[1] (numeric) = -4.92677275388 0.225490584546
y[1] (closed_form) = -4.92677254528 0.225500500326
absolute error = 9.918e-06
relative error = 0.0002011 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.69
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] = 10.5441 1.963
h = 0.0001 0.005
y[1] (numeric) = -4.92687988889 0.226438466288
y[1] (closed_form) = -4.92687967332 0.226448847428
absolute error = 1.038e-05
relative error = 0.0002105 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.7
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
memory used=5226.2MB, alloc=52.3MB, time=63.48
x[1] = 10.5442 1.968
h = 0.0001 0.003
y[1] (numeric) = -4.92725655344 0.227043526784
y[1] (closed_form) = -4.92725629072 0.22705360961
absolute error = 1.009e-05
relative error = 0.0002045 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.7
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] = 10.5443 1.971
h = 0.001 0.001
y[1] (numeric) = -4.92747832621 0.227409615139
y[1] (closed_form) = -4.9274779474 0.22741967576
absolute error = 1.007e-05
relative error = 0.0002041 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.7
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] = 10.5453 1.972
h = 0.001 0.003
y[1] (numeric) = -4.92743686002 0.227607046393
y[1] (closed_form) = -4.92743642817 0.227617076755
absolute error = 1.004e-05
relative error = 0.0002035 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.7
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] = 10.5463 1.975
h = 0.0001 0.004
y[1] (numeric) = -4.92755127588 0.228043535425
y[1] (closed_form) = -4.92755095458 0.228053623029
absolute error = 1.009e-05
relative error = 0.0002046 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.7
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] = 10.5464 1.979
h = 0.003 0.006
y[1] (numeric) = -4.92785181142 0.228529621708
y[1] (closed_form) = -4.92785158036 0.228539653801
absolute error = 1.003e-05
relative error = 0.0002034 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.7
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
memory used=5271.8MB, alloc=52.3MB, time=64.03
x[1] = 10.5494 1.985
h = 0.0001 0.005
y[1] (numeric) = -4.92796286532 0.229482017249
y[1] (closed_form) = -4.92796262652 0.229492514373
absolute error = 1.050e-05
relative error = 0.0002128 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.71
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.5495 1.99
h = 0.0001 0.003
y[1] (numeric) = -4.92834361037 0.23008886422
y[1] (closed_form) = -4.92834332495 0.230099063156
absolute error = 1.020e-05
relative error = 0.0002068 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.71
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.5496 1.993
h = 0.001 0.001
y[1] (numeric) = -4.92856781753 0.230456058324
y[1] (closed_form) = -4.92856741613 0.23046623488
absolute error = 1.018e-05
relative error = 0.0002064 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.71
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.5506 1.994
h = 0.001 0.003
y[1] (numeric) = -4.92852683281 0.230654653603
y[1] (closed_form) = -4.92852637846 0.230664799833
absolute error = 1.016e-05
relative error = 0.0002058 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.71
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5317.3MB, alloc=52.3MB, time=64.58
x[1] = 10.5516 1.997
h = 0.0001 0.004
y[1] (numeric) = -4.92864337545 0.231092988956
y[1] (closed_form) = -4.92864303149 0.23110319257
absolute error = 1.021e-05
relative error = 0.0002069 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.71
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.5517 2.001
h = 0.003 0.006
y[1] (numeric) = -4.92894716669 0.231580523166
y[1] (closed_form) = -4.928946913 0.231590671455
absolute error = 1.015e-05
relative error = 0.0002057 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.71
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.5547 2.007
h = 0.0001 0.005
y[1] (numeric) = -4.92906212939 0.232537435868
y[1] (closed_form) = -4.92906186719 0.232548048856
absolute error = 1.062e-05
relative error = 0.0002151 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.71
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.5548 2.012
h = 0.0001 0.003
y[1] (numeric) = -4.92944694921 0.233146074799
y[1] (closed_form) = -4.92944664091 0.233156389727
absolute error = 1.032e-05
relative error = 0.0002091 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.71
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.5549 2.015
h = 0.001 0.001
y[1] (numeric) = -4.92967358726 0.233514377896
y[1] (closed_form) = -4.92967316311 0.233524670268
absolute error = 1.030e-05
relative error = 0.0002087 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.72
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5362.8MB, alloc=52.3MB, time=65.13
x[1] = 10.5559 2.016
h = 0.0001 0.004
y[1] (numeric) = -4.92963308179 0.233714137193
y[1] (closed_form) = -4.92963260477 0.233724399174
absolute error = 1.027e-05
relative error = 0.0002082 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.72
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] = 10.556 2.02
h = 0.003 0.006
y[1] (numeric) = -4.9299395344 0.234202853691
y[1] (closed_form) = -4.92993930233 0.234213089328
absolute error = 1.024e-05
relative error = 0.0002074 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.72
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] = 10.559 2.026
h = 0.0001 0.005
y[1] (numeric) = -4.93005790743 0.235163610878
y[1] (closed_form) = -4.9300576662 0.235174310937
absolute error = 1.070e-05
relative error = 0.0002168 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.72
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] = 10.5591 2.031
h = 0.0001 0.003
y[1] (numeric) = -4.93044625152 0.235773748195
y[1] (closed_form) = -4.93044596464 0.235784150298
absolute error = 1.041e-05
relative error = 0.0002108 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.72
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5408.4MB, alloc=52.3MB, time=65.69
x[1] = 10.5592 2.034
h = 0.001 0.001
y[1] (numeric) = -4.93067499248 0.236142979561
y[1] (closed_form) = -4.93067458984 0.236153358957
absolute error = 1.039e-05
relative error = 0.0002104 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.72
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] = 10.5602 2.035
h = 0.001 0.003
y[1] (numeric) = -4.93063491159 0.236343735124
y[1] (closed_form) = -4.93063445616 0.236354084071
absolute error = 1.036e-05
relative error = 0.0002099 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.72
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] = 10.5612 2.038
h = 0.0001 0.004
y[1] (numeric) = -4.93075542178 0.236785486763
y[1] (closed_form) = -4.93075507642 0.23679589336
absolute error = 1.041e-05
relative error = 0.0002109 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.73
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] = 10.5613 2.042
h = 0.003 0.006
y[1] (numeric) = -4.93106527622 0.237275688155
y[1] (closed_form) = -4.93106502118 0.237286039772
absolute error = 1.035e-05
relative error = 0.0002097 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.73
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] = 10.5643 2.048
h = 0.0001 0.005
y[1] (numeric) = -4.93118753929 0.238240968774
y[1] (closed_form) = -4.93118727434 0.238251784479
absolute error = 1.082e-05
relative error = 0.0002191 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.73
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
memory used=5454.1MB, alloc=52.3MB, time=66.24
x[1] = 10.5644 2.053
h = 0.0001 0.003
y[1] (numeric) = -4.93157994753 0.238852908255
y[1] (closed_form) = -4.93157963745 0.238863426135
absolute error = 1.052e-05
relative error = 0.0002131 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.73
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] = 10.5645 2.056
h = 0.001 0.001
y[1] (numeric) = -4.93181111293 0.23922325465
y[1] (closed_form) = -4.93181068721 0.239233749648
absolute error = 1.050e-05
relative error = 0.0002127 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.73
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] = 10.5655 2.057
h = 0.001 0.003
y[1] (numeric) = -4.93177150712 0.239425174227
y[1] (closed_form) = -4.93177102868 0.23943563871
absolute error = 1.048e-05
relative error = 0.0002122 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.73
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] = 10.5665 2.06
h = 0.0001 0.004
y[1] (numeric) = -4.93189413127 0.239868778574
y[1] (closed_form) = -4.93189376274 0.239879300848
absolute error = 1.053e-05
relative error = 0.0002132 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.73
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
memory used=5499.7MB, alloc=52.3MB, time=66.79
x[1] = 10.5666 2.064
h = 0.003 0.006
y[1] (numeric) = -4.93220722825 0.240360440353
y[1] (closed_form) = -4.93220695007 0.240370907834
absolute error = 1.047e-05
relative error = 0.0002121 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.73
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] = 10.5696 2.07
h = 0.0001 0.005
y[1] (numeric) = -4.93233337127 0.241330247658
y[1] (closed_form) = -4.93233308242 0.241341178889
absolute error = 1.094e-05
relative error = 0.0002214 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.74
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.5697 2.075
h = 0.0001 0.003
y[1] (numeric) = -4.93272983791 0.241943994714
y[1] (closed_form) = -4.93272950445 0.241954628251
absolute error = 1.064e-05
relative error = 0.0002154 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.74
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.5698 2.078
h = 0.001 0.001
y[1] (numeric) = -4.93296342425 0.242315459334
y[1] (closed_form) = -4.93296297526 0.242326069817
absolute error = 1.062e-05
relative error = 0.000215 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.74
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5545.3MB, alloc=52.3MB, time=67.35
x[1] = 10.5708 2.079
h = 0.001 0.003
y[1] (numeric) = -4.93292429128 0.242518542899
y[1] (closed_form) = -4.93292378967 0.242529122802
absolute error = 1.059e-05
relative error = 0.0002145 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.74
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.5718 2.082
h = 0.0001 0.004
y[1] (numeric) = -4.9330490249 0.242964002134
y[1] (closed_form) = -4.93304863302 0.242974639967
absolute error = 1.065e-05
relative error = 0.0002155 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.74
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.5719 2.086
h = 0.003 0.006
y[1] (numeric) = -4.93336535979 0.243457128597
y[1] (closed_form) = -4.93336505829 0.243467711822
absolute error = 1.059e-05
relative error = 0.0002143 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.74
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.5749 2.092
h = 0.0001 0.005
y[1] (numeric) = -4.93349537266 0.244431465802
y[1] (closed_form) = -4.93349505975 0.244442512438
absolute error = 1.105e-05
relative error = 0.0002237 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.75
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] = 10.575 2.097
h = 0.0001 0.003
y[1] (numeric) = -4.93389589194 0.245047025815
y[1] (closed_form) = -4.93389553493 0.245057774892
absolute error = 1.076e-05
relative error = 0.0002177 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.75
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
memory used=5590.8MB, alloc=52.3MB, time=67.90
x[1] = 10.5751 2.1
h = 0.001 0.001
y[1] (numeric) = -4.93413189571 0.245419611844
y[1] (closed_form) = -4.93413142329 0.245430337694
absolute error = 1.074e-05
relative error = 0.0002173 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.75
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] = 10.5761 2.101
h = 0.001 0.003
y[1] (numeric) = -4.93409323335 0.245623859363
y[1] (closed_form) = -4.9340927084 0.245634554568
absolute error = 1.071e-05
relative error = 0.0002168 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.75
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] = 10.5771 2.104
h = 0.0001 0.004
y[1] (numeric) = -4.93422007194 0.246071175646
y[1] (closed_form) = -4.93421965655 0.24608192892
absolute error = 1.076e-05
relative error = 0.0002178 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.75
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] = 10.5772 2.108
h = 0.003 0.006
y[1] (numeric) = -4.93453964011 0.246565771068
y[1] (closed_form) = -4.93453931512 0.24657646992
absolute error = 1.070e-05
relative error = 0.0002166 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.75
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
memory used=5636.4MB, alloc=52.3MB, time=68.46
x[1] = 10.5802 2.114
h = 0.0001 0.005
y[1] (numeric) = -4.93467351275 0.247544641351
y[1] (closed_form) = -4.93467317561 0.247555803273
absolute error = 1.117e-05
relative error = 0.000226 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.76
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] = 10.5803 2.119
h = 0.0001 0.003
y[1] (numeric) = -4.93507807889 0.248162019678
y[1] (closed_form) = -4.93507769816 0.248172884176
absolute error = 1.087e-05
relative error = 0.00022 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.76
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] = 10.5804 2.122
h = 0.001 0.001
y[1] (numeric) = -4.93531649658 0.248535730283
y[1] (closed_form) = -4.93531600056 0.248546571381
absolute error = 1.085e-05
relative error = 0.0002196 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.76
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] = 10.5814 2.123
h = 0.0001 0.004
y[1] (numeric) = -4.9352783026 0.248741141714
y[1] (closed_form) = -4.93527775413 0.248751952104
absolute error = 1.082e-05
relative error = 0.000219 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.76
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] = 10.5815 2.127
h = 0.003 0.006
y[1] (numeric) = -4.93560051381 0.249236936583
y[1] (closed_form) = -4.93560020967 0.249247722661
absolute error = 1.079e-05
relative error = 0.0002183 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.76
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
memory used=5681.9MB, alloc=52.3MB, time=69.01
x[1] = 10.5845 2.133
h = 0.0001 0.005
y[1] (numeric) = -4.93573775478 0.25021966549
y[1] (closed_form) = -4.93573743785 0.250230914352
absolute error = 1.125e-05
relative error = 0.0002277 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.76
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] = 10.5846 2.138
h = 0.0001 0.003
y[1] (numeric) = -4.93614582143 0.25083856512
y[1] (closed_form) = -4.93614546136 0.250849516668
absolute error = 1.096e-05
relative error = 0.0002217 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.76
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] = 10.5847 2.141
h = 0.001 0.001
y[1] (numeric) = -4.93638632758 0.251213217548
y[1] (closed_form) = -4.93638585231 0.251224145548
absolute error = 1.094e-05
relative error = 0.0002213 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.77
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.5857 2.142
h = 0.001 0.003
y[1] (numeric) = -4.93634854885 0.251419625254
y[1] (closed_form) = -4.93634802121 0.251430522489
absolute error = 1.091e-05
relative error = 0.0002207 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.77
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5727.6MB, alloc=52.3MB, time=69.56
x[1] = 10.5867 2.145
h = 0.0001 0.004
y[1] (numeric) = -4.93647931453 0.251870377817
y[1] (closed_form) = -4.93647889613 0.251881333379
absolute error = 1.096e-05
relative error = 0.0002218 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.77
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.5868 2.149
h = 0.003 0.006
y[1] (numeric) = -4.93680490431 0.252367679549
y[1] (closed_form) = -4.93680457637 0.252378581034
absolute error = 1.091e-05
relative error = 0.0002206 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.77
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.5898 2.155
h = 0.0001 0.005
y[1] (numeric) = -4.93694598634 0.253354947467
y[1] (closed_form) = -4.93694564484 0.253366311392
absolute error = 1.137e-05
relative error = 0.00023 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.77
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.5899 2.16
h = 0.0001 0.003
y[1] (numeric) = -4.93735808914 0.253975675379
y[1] (closed_form) = -4.93735770502 0.253986742128
absolute error = 1.107e-05
relative error = 0.000224 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.77
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.59 2.163
h = 0.001 0.001
y[1] (numeric) = -4.93760100269 0.254351458274
y[1] (closed_form) = -4.9376005035 0.254362501304
absolute error = 1.105e-05
relative error = 0.0002236 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.77
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5773.1MB, alloc=52.3MB, time=70.11
x[1] = 10.591 2.164
h = 0.001 0.003
y[1] (numeric) = -4.93756368821 0.254559029823
y[1] (closed_form) = -4.93756313674 0.254570042024
absolute error = 1.103e-05
relative error = 0.000223 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.78
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] = 10.592 2.167
h = 0.0001 0.004
y[1] (numeric) = -4.93769654603 0.255011645576
y[1] (closed_form) = -4.93769610362 0.255022716241
absolute error = 1.108e-05
relative error = 0.0002241 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.78
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] = 10.5921 2.171
h = 0.003 0.006
y[1] (numeric) = -4.93802535582 0.255510428435
y[1] (closed_form) = -4.93802500389 0.255521445208
absolute error = 1.102e-05
relative error = 0.0002229 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.78
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] = 10.5951 2.177
h = 0.0001 0.005
y[1] (numeric) = -4.93817026882 0.256502238435
y[1] (closed_form) = -4.9381699026 0.2565137173
absolute error = 1.148e-05
relative error = 0.0002323 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.78
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5818.6MB, alloc=52.3MB, time=70.66
x[1] = 10.5952 2.182
h = 0.0001 0.003
y[1] (numeric) = -4.93858640197 0.25712479991
y[1] (closed_form) = -4.93858599364 0.25713598174
absolute error = 1.119e-05
relative error = 0.0002263 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.78
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] = 10.5953 2.185
h = 0.001 0.001
y[1] (numeric) = -4.93883171941 0.257501716395
y[1] (closed_form) = -4.93883119612 0.257512874335
absolute error = 1.117e-05
relative error = 0.0002259 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.78
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] = 10.5963 2.186
h = 0.001 0.003
y[1] (numeric) = -4.93879486696 0.257710451725
y[1] (closed_form) = -4.93879429147 0.257721578772
absolute error = 1.114e-05
relative error = 0.0002253 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.78
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] = 10.5973 2.189
h = 0.0001 0.004
y[1] (numeric) = -4.93892981241 0.25816493276
y[1] (closed_form) = -4.93892934583 0.258176118408
absolute error = 1.120e-05
relative error = 0.0002264 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.79
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5864.2MB, alloc=52.3MB, time=71.22
x[1] = 10.5974 2.193
h = 0.003 0.006
y[1] (numeric) = -4.93926183755 0.25866520094
y[1] (closed_form) = -4.93926146147 0.25867633288
absolute error = 1.114e-05
relative error = 0.0002252 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.79
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6004 2.199
h = 0.0001 0.005
y[1] (numeric) = -4.93941057145 0.259661556056
y[1] (closed_form) = -4.93941018033 0.25967314974
absolute error = 1.160e-05
relative error = 0.0002345 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.79
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6005 2.204
h = 0.0001 0.003
y[1] (numeric) = -4.93983072913 0.26028595635
y[1] (closed_form) = -4.93983029642 0.26029725314
absolute error = 1.131e-05
relative error = 0.0002285 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.79
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6006 2.207
h = 0.001 0.001
y[1] (numeric) = -4.94007844692 0.26066400953
y[1] (closed_form) = -4.94007789937 0.260675282259
absolute error = 1.129e-05
relative error = 0.0002281 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.79
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6016 2.208
h = 0.001 0.003
y[1] (numeric) = -4.94004205429 0.260873908571
y[1] (closed_form) = -4.94004145463 0.260885150346
absolute error = 1.126e-05
relative error = 0.0002276 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.79
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5909.8MB, alloc=52.3MB, time=71.77
x[1] = 10.6026 2.211
h = 0.0001 0.004
y[1] (numeric) = -4.94017908289 0.261330256966
y[1] (closed_form) = -4.94017859195 0.261341557476
absolute error = 1.131e-05
relative error = 0.0002286 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.8
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] = 10.6027 2.215
h = 0.003 0.006
y[1] (numeric) = -4.94051431869 0.261832014638
y[1] (closed_form) = -4.94051391829 0.261843261625
absolute error = 1.125e-05
relative error = 0.0002275 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.8
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] = 10.6057 2.221
h = 0.0001 0.005
y[1] (numeric) = -4.94066686342 0.262832917867
y[1] (closed_form) = -4.94066644725 0.262844626248
absolute error = 1.172e-05
relative error = 0.0002368 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.8
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] = 10.6058 2.226
h = 0.0001 0.003
y[1] (numeric) = -4.94109103982 0.26345916221
y[1] (closed_form) = -4.94109058256 0.263470573839
absolute error = 1.142e-05
relative error = 0.0002308 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.8
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=5955.3MB, alloc=52.3MB, time=72.32
x[1] = 10.6059 2.229
h = 0.001 0.001
y[1] (numeric) = -4.94134115443 0.263838355174
y[1] (closed_form) = -4.94134058245 0.263849742574
absolute error = 1.140e-05
relative error = 0.0002304 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.8
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] = 10.6069 2.23
h = 0.0001 0.004
y[1] (numeric) = -4.94130521939 0.26404941785
y[1] (closed_form) = -4.94130459539 0.264060774233
absolute error = 1.137e-05
relative error = 0.0002298 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.8
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] = 10.607 2.234
h = 0.003 0.006
y[1] (numeric) = -4.94164307976 0.264552391722
y[1] (closed_form) = -4.94164269944 0.264563725802
absolute error = 1.134e-05
relative error = 0.0002292 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.8
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] = 10.61 2.24
h = 0.0001 0.005
y[1] (numeric) = -4.94179895089 0.265557166954
y[1] (closed_form) = -4.94179855416 0.265568962134
absolute error = 1.180e-05
relative error = 0.0002385 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.81
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6101 2.245
h = 0.0001 0.003
y[1] (numeric) = -4.94222660385 0.266184954985
y[1] (closed_form) = -4.94222616648 0.26619645353
absolute error = 1.151e-05
relative error = 0.0002325 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.81
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6000.8MB, alloc=52.3MB, time=72.87
x[1] = 10.6102 2.248
h = 0.001 0.001
y[1] (numeric) = -4.94247879234 0.266565103006
y[1] (closed_form) = -4.94247824036 0.266576577175
absolute error = 1.149e-05
relative error = 0.0002321 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.81
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6112 2.249
h = 0.001 0.003
y[1] (numeric) = -4.94244326329 0.266777161819
y[1] (closed_form) = -4.94244265936 0.266788604916
absolute error = 1.146e-05
relative error = 0.0002315 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.81
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6122 2.252
h = 0.0001 0.004
y[1] (numeric) = -4.94258417847 0.267236965712
y[1] (closed_form) = -4.94258368294 0.267248467797
absolute error = 1.151e-05
relative error = 0.0002326 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.81
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6123 2.256
h = 0.003 0.006
y[1] (numeric) = -4.94292539398 0.267741467902
y[1] (closed_form) = -4.94292498902 0.267752916807
absolute error = 1.146e-05
relative error = 0.0002314 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.81
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6046.3MB, alloc=52.3MB, time=73.43
x[1] = 10.6153 2.262
h = 0.0001 0.005
y[1] (numeric) = -4.94308505725 0.268750796846
y[1] (closed_form) = -4.94308463515 0.268762706496
absolute error = 1.192e-05
relative error = 0.0002407 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.82
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6154 2.267
h = 0.0001 0.003
y[1] (numeric) = -4.94351671814 0.269380438657
y[1] (closed_form) = -4.9435162559 0.269392051816
absolute error = 1.162e-05
relative error = 0.0002348 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.82
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6155 2.27
h = 0.001 0.001
y[1] (numeric) = -4.94377129688 0.26976173221
y[1] (closed_form) = -4.94377072016 0.269773320827
absolute error = 1.160e-05
relative error = 0.0002343 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.82
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6165 2.271
h = 0.001 0.003
y[1] (numeric) = -4.94373622133 0.269974954525
y[1] (closed_form) = -4.94373559274 0.269986512008
absolute error = 1.157e-05
relative error = 0.0002338 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.82
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6175 2.274
h = 0.0001 0.004
y[1] (numeric) = -4.94387920681 0.270436631674
y[1] (closed_form) = -4.94387868645 0.270448248278
absolute error = 1.163e-05
relative error = 0.0002349 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.82
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6091.9MB, alloc=52.3MB, time=73.98
x[1] = 10.6176 2.278
h = 0.003 0.006
y[1] (numeric) = -4.94422361962 0.270942635233
y[1] (closed_form) = -4.94422318986 0.27095419884
absolute error = 1.157e-05
relative error = 0.0002337 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.82
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6206 2.284
h = 0.0001 0.005
y[1] (numeric) = -4.94438706499 0.271956520779
y[1] (closed_form) = -4.94438661735 0.271968544777
absolute error = 1.203e-05
relative error = 0.000243 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.83
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6207 2.289
h = 0.0001 0.003
y[1] (numeric) = -4.94482272796 0.272588021524
y[1] (closed_form) = -4.94482224068 0.272599749177
absolute error = 1.174e-05
relative error = 0.000237 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.83
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6208 2.292
h = 0.001 0.001
y[1] (numeric) = -4.94507969341 0.272970463655
y[1] (closed_form) = -4.94507909177 0.272982166598
absolute error = 1.172e-05
relative error = 0.0002366 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.83
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6137.4MB, alloc=52.3MB, time=74.53
x[1] = 10.6218 2.293
h = 0.001 0.003
y[1] (numeric) = -4.94504506915 0.273184849375
y[1] (closed_form) = -4.94504441573 0.273196521123
absolute error = 1.169e-05
relative error = 0.000236 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.83
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6228 2.296
h = 0.0001 0.004
y[1] (numeric) = -4.94519012043 0.273648401789
y[1] (closed_form) = -4.94518957508 0.27366013279
absolute error = 1.174e-05
relative error = 0.0002371 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.83
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6229 2.3
h = 0.003 0.006
y[1] (numeric) = -4.94553772585 0.274155910807
y[1] (closed_form) = -4.9455372711 0.274167588996
absolute error = 1.169e-05
relative error = 0.000236 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.83
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6259 2.306
h = 0.0001 0.005
y[1] (numeric) = -4.94570494326 0.275174355812
y[1] (closed_form) = -4.94570446991 0.275186494033
absolute error = 1.215e-05
relative error = 0.0002452 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.83
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6183.0MB, alloc=52.3MB, time=75.08
x[1] = 10.626 2.311
h = 0.0001 0.003
y[1] (numeric) = -4.94614460245 0.275807720619
y[1] (closed_form) = -4.94614408998 0.275819562643
absolute error = 1.185e-05
relative error = 0.0002393 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.84
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6261 2.314
h = 0.001 0.001
y[1] (numeric) = -4.94640395105 0.276191314356
y[1] (closed_form) = -4.94640332433 0.276203131504
absolute error = 1.183e-05
relative error = 0.0002389 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.84
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6271 2.315
h = 0.001 0.003
y[1] (numeric) = -4.94636977589 0.276406863378
y[1] (closed_form) = -4.94636909748 0.276418649269
absolute error = 1.181e-05
relative error = 0.0002383 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.84
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6281 2.318
h = 0.0001 0.004
y[1] (numeric) = -4.94651688847 0.276872293048
y[1] (closed_form) = -4.94651631795 0.276884138324
absolute error = 1.186e-05
relative error = 0.0002394 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.84
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6282 2.322
h = 0.003 0.006
y[1] (numeric) = -4.94686768179 0.277381311597
y[1] (closed_form) = -4.9468672019 0.277393104244
absolute error = 1.180e-05
relative error = 0.0002382 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.84
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6228.7MB, alloc=52.3MB, time=75.64
x[1] = 10.6312 2.328
h = 0.0001 0.005
y[1] (numeric) = -4.9470386612 0.278404318878
y[1] (closed_form) = -4.94703816197 0.278416571198
absolute error = 1.226e-05
relative error = 0.0002475 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.84
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6313 2.333
h = 0.0001 0.003
y[1] (numeric) = -4.94748231076 0.279039552849
y[1] (closed_form) = -4.94748177291 0.279051509122
absolute error = 1.197e-05
relative error = 0.0002415 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.84
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6314 2.336
h = 0.001 0.001
y[1] (numeric) = -4.94774403894 0.279424301206
y[1] (closed_form) = -4.94774338697 0.279436232436
absolute error = 1.195e-05
relative error = 0.0002411 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.85
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6324 2.337
h = 0.0001 0.004
y[1] (numeric) = -4.94771031068 0.279641013419
y[1] (closed_form) = -4.94770960711 0.279652913332
absolute error = 1.192e-05
relative error = 0.0002405 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.85
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6274.2MB, alloc=52.3MB, time=76.19
x[1] = 10.6325 2.341
h = 0.003 0.006
y[1] (numeric) = -4.94806370994 0.280151264513
y[1] (closed_form) = -4.94806324938 0.280163144109
absolute error = 1.189e-05
relative error = 0.0002399 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.85
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6355 2.347
h = 0.0001 0.005
y[1] (numeric) = -4.94823797389 0.281178156429
y[1] (closed_form) = -4.94823749338 0.281190495395
absolute error = 1.235e-05
relative error = 0.0002491 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.85
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6356 2.352
h = 0.0001 0.003
y[1] (numeric) = -4.94868507588 0.281814955942
y[1] (closed_form) = -4.94868455718 0.281826998984
absolute error = 1.205e-05
relative error = 0.0002432 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.85
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6357 2.355
h = 0.001 0.001
y[1] (numeric) = -4.94894886328 0.28220067227
y[1] (closed_form) = -4.94894823056 0.282212690126
absolute error = 1.203e-05
relative error = 0.0002428 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.85
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6367 2.356
h = 0.001 0.003
y[1] (numeric) = -4.9489155318 0.282418380338
y[1] (closed_form) = -4.94891484755 0.282430366824
absolute error = 1.201e-05
relative error = 0.0002422 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.85
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6319.8MB, alloc=52.3MB, time=76.75
x[1] = 10.6377 2.359
h = 0.0001 0.004
y[1] (numeric) = -4.94906649043 0.282887283957
y[1] (closed_form) = -4.94906591375 0.282899330073
absolute error = 1.206e-05
relative error = 0.0002433 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.86
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] = 10.6378 2.363
h = 0.003 0.006
y[1] (numeric) = -4.94942322123 0.283399084309
y[1] (closed_form) = -4.94942273522 0.283411078137
absolute error = 1.200e-05
relative error = 0.0002421 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.86
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] = 10.6408 2.369
h = 0.0001 0.005
y[1] (numeric) = -4.94960122854 0.284430543769
y[1] (closed_form) = -4.94960072184 0.284442996605
absolute error = 1.246e-05
relative error = 0.0002514 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.86
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] = 10.6409 2.374
h = 0.0001 0.003
y[1] (numeric) = -4.95005231002 0.28506922194
y[1] (closed_form) = -4.95005176564 0.285081379005
absolute error = 1.217e-05
relative error = 0.0002454 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.86
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6365.4MB, alloc=52.3MB, time=77.31
x[1] = 10.641 2.377
h = 0.001 0.001
y[1] (numeric) = -4.9503184704 0.285456098494
y[1] (closed_form) = -4.95031781213 0.285468230207
absolute error = 1.215e-05
relative error = 0.000245 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.86
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] = 10.642 2.378
h = 0.001 0.003
y[1] (numeric) = -4.95028558175 0.285674969557
y[1] (closed_form) = -4.95028487203 0.285687069839
absolute error = 1.212e-05
relative error = 0.0002444 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.86
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] = 10.643 2.381
h = 0.0001 0.004
y[1] (numeric) = -4.95043858884 0.286145756087
y[1] (closed_form) = -4.95043798652 0.286157916129
absolute error = 1.217e-05
relative error = 0.0002455 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.87
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6431 2.385
h = 0.003 0.006
y[1] (numeric) = -4.95079849408 0.286659077554
y[1] (closed_form) = -4.95079798245 0.286671185492
absolute error = 1.212e-05
relative error = 0.0002444 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.87
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6461 2.391
h = 0.0001 0.005
y[1] (numeric) = -4.95098023471 0.287695107272
y[1] (closed_form) = -4.95097970168 0.287707673853
absolute error = 1.258e-05
relative error = 0.0002536 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.87
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6410.9MB, alloc=52.3MB, time=77.87
x[1] = 10.6462 2.396
h = 0.0001 0.003
y[1] (numeric) = -4.95143528981 0.28833566913
y[1] (closed_form) = -4.95143471959 0.288347940092
absolute error = 1.228e-05
relative error = 0.0002477 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.87
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6463 2.399
h = 0.001 0.001
y[1] (numeric) = -4.95170381961 0.288723708878
y[1] (closed_form) = -4.95170313561 0.288735954324
absolute error = 1.226e-05
relative error = 0.0002473 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.87
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6473 2.4
h = 0.001 0.003
y[1] (numeric) = -4.95167137159 0.288943742805
y[1] (closed_form) = -4.95167063624 0.288955956761
absolute error = 1.224e-05
relative error = 0.0002467 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.87
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6483 2.403
h = 0.0001 0.004
y[1] (numeric) = -4.95182642265 0.289416414171
y[1] (closed_form) = -4.95182579452 0.289428688016
absolute error = 1.229e-05
relative error = 0.0002478 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.87
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6456.4MB, alloc=52.3MB, time=78.42
x[1] = 10.6484 2.407
h = 0.003 0.006
y[1] (numeric) = -4.9521894976 0.289931260742
y[1] (closed_form) = -4.95218896018 0.289943482666
absolute error = 1.223e-05
relative error = 0.0002466 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.88
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] = 10.6514 2.413
h = 0.0001 0.005
y[1] (numeric) = -4.95237496153 0.290971863398
y[1] (closed_form) = -4.95237440199 0.290984543598
absolute error = 1.269e-05
relative error = 0.0002559 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.88
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] = 10.6515 2.418
h = 0.0001 0.003
y[1] (numeric) = -4.95283398435 0.291614313943
y[1] (closed_form) = -4.95283338813 0.291626698679
absolute error = 1.240e-05
relative error = 0.0002499 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.88
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] = 10.6516 2.421
h = 0.001 0.001
y[1] (numeric) = -4.95310487998 0.292003519836
y[1] (closed_form) = -4.9531041701 0.292015878893
absolute error = 1.238e-05
relative error = 0.0002495 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.88
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6502.0MB, alloc=52.3MB, time=78.98
x[1] = 10.6526 2.422
h = 0.001 0.003
y[1] (numeric) = -4.95307287042 0.292224716491
y[1] (closed_form) = -4.95307210928 0.292237043998
absolute error = 1.235e-05
relative error = 0.0002489 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.88
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] = 10.6536 2.425
h = 0.0001 0.004
y[1] (numeric) = -4.95322996094 0.292699274601
y[1] (closed_form) = -4.95322930685 0.292711662125
absolute error = 1.240e-05
relative error = 0.00025 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.88
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] = 10.6537 2.429
h = 0.003 0.006
y[1] (numeric) = -4.95359620087 0.293215650245
y[1] (closed_form) = -4.95359563749 0.29322798603
absolute error = 1.235e-05
relative error = 0.0002489 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.88
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] = 10.6567 2.435
h = 0.0001 0.005
y[1] (numeric) = -4.95378537808 0.29426082848
y[1] (closed_form) = -4.95378479187 0.294273622175
absolute error = 1.281e-05
relative error = 0.0002581 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.89
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6568 2.44
h = 0.0001 0.003
y[1] (numeric) = -4.95424836272 0.294905172687
y[1] (closed_form) = -4.95424774033 0.294917671073
absolute error = 1.251e-05
relative error = 0.0002521 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.89
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6547.6MB, alloc=52.3MB, time=79.53
x[1] = 10.6569 2.443
h = 0.001 0.001
y[1] (numeric) = -4.9545216206 0.295295547664
y[1] (closed_form) = -4.95452088468 0.295308020207
absolute error = 1.249e-05
relative error = 0.0002517 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.89
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6579 2.444
h = 0.0001 0.004
y[1] (numeric) = -4.95449004733 0.295517906903
y[1] (closed_form) = -4.95448926023 0.295530347838
absolute error = 1.247e-05
relative error = 0.0002512 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.89
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.658 2.448
h = 0.003 0.006
y[1] (numeric) = -4.95485887446 0.296035531034
y[1] (closed_form) = -4.95485832968 0.296047953612
absolute error = 1.243e-05
relative error = 0.0002505 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.89
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.661 2.454
h = 0.0001 0.005
y[1] (numeric) = -4.95505129446 0.297084605795
y[1] (closed_form) = -4.95505072623 0.297097485972
absolute error = 1.289e-05
relative error = 0.0002597 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.9
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6593.1MB, alloc=52.3MB, time=80.09
x[1] = 10.6611 2.459
h = 0.0001 0.003
y[1] (numeric) = -4.95551770723 0.29773053687
y[1] (closed_form) = -4.95551710324 0.297743121868
absolute error = 1.260e-05
relative error = 0.0002538 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.9
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] = 10.6612 2.462
h = 0.001 0.001
y[1] (numeric) = -4.95579300955 0.298121892412
y[1] (closed_form) = -4.95579229213 0.298134451426
absolute error = 1.258e-05
relative error = 0.0002534 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.9
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] = 10.6622 2.463
h = 0.001 0.003
y[1] (numeric) = -4.95576182392 0.298345247083
y[1] (closed_form) = -4.9557610554 0.298357774438
absolute error = 1.255e-05
relative error = 0.0002528 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.9
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] = 10.6632 2.466
h = 0.0001 0.004
y[1] (numeric) = -4.95592271996 0.298823296833
y[1] (closed_form) = -4.95592205817 0.298835884443
absolute error = 1.260e-05
relative error = 0.0002539 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.9
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] = 10.6633 2.47
h = 0.003 0.006
y[1] (numeric) = -4.95629485486 0.299342490647
y[1] (closed_form) = -4.95629428383 0.299355026857
absolute error = 1.255e-05
relative error = 0.0002527 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.9
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6638.7MB, alloc=52.3MB, time=80.64
x[1] = 10.6663 2.476
h = 0.0001 0.005
y[1] (numeric) = -4.95649096956 0.30039614593
y[1] (closed_form) = -4.95649037435 0.300409139368
absolute error = 1.301e-05
relative error = 0.0002619 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.91
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6664 2.481
h = 0.0001 0.003
y[1] (numeric) = -4.95696133321 0.301043979926
y[1] (closed_form) = -4.95696070274 0.301056678343
absolute error = 1.271e-05
relative error = 0.000256 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.91
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6665 2.484
h = 0.001 0.001
y[1] (numeric) = -4.95723899114 0.301436510014
y[1] (closed_form) = -4.95723824737 0.301449182287
absolute error = 1.269e-05
relative error = 0.0002556 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.91
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6675 2.485
h = 0.001 0.003
y[1] (numeric) = -4.95720823775 0.30166102701
y[1] (closed_form) = -4.95720744297 0.301673667565
absolute error = 1.267e-05
relative error = 0.000255 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.91
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6684.3MB, alloc=52.3MB, time=81.20
x[1] = 10.6685 2.488
h = 0.0001 0.004
y[1] (numeric) = -4.95737116041 0.30214096892
y[1] (closed_form) = -4.95737047218 0.302153669855
absolute error = 1.272e-05
relative error = 0.0002561 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.91
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6686 2.492
h = 0.003 0.006
y[1] (numeric) = -4.95774644674 0.302661703101
y[1] (closed_form) = -4.95774584929 0.302674352819
absolute error = 1.266e-05
relative error = 0.000255 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.91
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6716 2.498
h = 0.0001 0.005
y[1] (numeric) = -4.95794624613 0.303719941446
y[1] (closed_form) = -4.95794562379 0.303733048018
absolute error = 1.312e-05
relative error = 0.0002642 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.92
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6717 2.503
h = 0.0001 0.003
y[1] (numeric) = -4.95842055475 0.304369683263
y[1] (closed_form) = -4.95841989765 0.304382494975
absolute error = 1.283e-05
relative error = 0.0002582 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.92
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6718 2.506
h = 0.001 0.001
y[1] (numeric) = -4.95870056469 0.30476339079
y[1] (closed_form) = -4.95869979441 0.304776176196
absolute error = 1.281e-05
relative error = 0.0002578 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.92
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6728 2.507
h = 0.001 0.003
y[1] (numeric) = -4.95867024137 0.304989069949
y[1] (closed_form) = -4.95866942017 0.305001823578
absolute error = 1.278e-05
relative error = 0.0002572 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.92
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6738 2.51
h = 0.0001 0.004
y[1] (numeric) = -4.95883518615 0.305470905859
y[1] (closed_form) = -4.95883447133 0.305483719995
absolute error = 1.283e-05
relative error = 0.0002583 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.92
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6739 2.514
h = 0.003 0.006
y[1] (numeric) = -4.95921361917 0.305993184295
y[1] (closed_form) = -4.95921299513 0.306005947395
absolute error = 1.278e-05
relative error = 0.0002572 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.92
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6769 2.52
h = 0.0001 0.005
y[1] (numeric) = -4.95941709325 0.307056008206
y[1] (closed_form) = -4.95941644362 0.307069227786
absolute error = 1.324e-05
relative error = 0.0002664 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.92
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=6772.2MB, alloc=84.3MB, time=82.34
x[1] = 10.677 2.525
h = 0.0001 0.003
y[1] (numeric) = -4.95989534091 0.30770766272
y[1] (closed_form) = -4.95989465701 0.307720587601
absolute error = 1.294e-05
relative error = 0.0002605 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.93
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] = 10.6771 2.528
h = 0.001 0.001
y[1] (numeric) = -4.96017769926 0.308102550562
y[1] (closed_form) = -4.96017690232 0.308115448975
absolute error = 1.292e-05
relative error = 0.00026 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.93
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] = 10.6781 2.529
h = 0.001 0.003
y[1] (numeric) = -4.96014780385 0.308329391714
y[1] (closed_form) = -4.96014695607 0.308342258293
absolute error = 1.289e-05
relative error = 0.0002595 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.93
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] = 10.6791 2.532
h = 0.0001 0.004
y[1] (numeric) = -4.96031476626 0.308813123449
y[1] (closed_form) = -4.96031402468 0.30882605066
absolute error = 1.295e-05
relative error = 0.0002605 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.93
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] = 10.6792 2.536
h = 0.003 0.006
y[1] (numeric) = -4.96069634119 0.309336950007
y[1] (closed_form) = -4.96069569041 0.309349826364
absolute error = 1.289e-05
relative error = 0.0002594 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.93
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] = 10.6822 2.542
h = 0.0001 0.005
y[1] (numeric) = -4.96090347998 0.310404361954
y[1] (closed_form) = -4.9609028029 0.310417694414
absolute error = 1.335e-05
relative error = 0.0002686 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.93
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] = 10.6823 2.547
h = 0.0001 0.003
y[1] (numeric) = -4.96138566074 0.311057934013
y[1] (closed_form) = -4.96138494989 0.311070971936
absolute error = 1.306e-05
relative error = 0.0002627 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.94
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] = 10.6824 2.55
h = 0.001 0.001
y[1] (numeric) = -4.96167036391 0.311454005029
y[1] (closed_form) = -4.96166954013 0.311467016325
absolute error = 1.304e-05
relative error = 0.0002622 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.94
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
memory used=6860.3MB, alloc=84.3MB, time=83.46
x[1] = 10.6834 2.551
h = 0.0001 0.004
y[1] (numeric) = -4.96164089425 0.311682007998
y[1] (closed_form) = -4.96164001972 0.311694987403
absolute error = 1.301e-05
relative error = 0.0002617 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.94
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] = 10.6835 2.555
h = 0.003 0.006
y[1] (numeric) = -4.96202503752 0.312207098582
y[1] (closed_form) = -4.9620244046 0.312220061566
absolute error = 1.298e-05
relative error = 0.000261 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.94
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] = 10.6865 2.561
h = 0.0001 0.005
y[1] (numeric) = -4.96223537747 0.313278418216
y[1] (closed_form) = -4.96223471764 0.313291836986
absolute error = 1.343e-05
relative error = 0.0002702 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.94
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] = 10.6866 2.566
h = 0.0001 0.003
y[1] (numeric) = -4.96272096189 0.313933597942
y[1] (closed_form) = -4.96272026871 0.31394672231
absolute error = 1.314e-05
relative error = 0.0002643 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.94
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] = 10.6867 2.569
h = 0.001 0.001
y[1] (numeric) = -4.96300769464 0.3143306618
y[1] (closed_form) = -4.96300688864 0.314343759403
absolute error = 1.312e-05
relative error = 0.0002639 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.94
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] = 10.6877 2.57
h = 0.001 0.003
y[1] (numeric) = -4.96297860356 0.314559659641
y[1] (closed_form) = -4.96297774688 0.314572725302
absolute error = 1.309e-05
relative error = 0.0002633 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.95
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6887 2.573
h = 0.0001 0.004
y[1] (numeric) = -4.96314933098 0.315046899956
y[1] (closed_form) = -4.96314858019 0.31506002648
absolute error = 1.315e-05
relative error = 0.0002644 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.95
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6888 2.577
h = 0.003 0.006
y[1] (numeric) = -4.96353675812 0.315573580136
y[1] (closed_form) = -4.96353609815 0.315586656144
absolute error = 1.309e-05
relative error = 0.0002632 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.95
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6918 2.583
h = 0.0001 0.005
y[1] (numeric) = -4.96375074424 0.316649492425
y[1] (closed_form) = -4.96375005666 0.316663023839
absolute error = 1.355e-05
relative error = 0.0002724 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.95
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=6948.2MB, alloc=84.3MB, time=84.59
x[1] = 10.6919 2.588
h = 0.0001 0.003
y[1] (numeric) = -4.96424025076 0.31730659872
y[1] (closed_form) = -4.96423953033 0.317319835897
absolute error = 1.326e-05
relative error = 0.0002665 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.95
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.692 2.591
h = 0.001 0.001
y[1] (numeric) = -4.96452932165 0.317704851076
y[1] (closed_form) = -4.96452848852 0.317718061329
absolute error = 1.324e-05
relative error = 0.0002661 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.95
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.693 2.592
h = 0.001 0.003
y[1] (numeric) = -4.9645006523 0.317935010414
y[1] (closed_form) = -4.96449976859 0.31794818867
absolute error = 1.321e-05
relative error = 0.0002655 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.95
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.694 2.595
h = 0.0001 0.004
y[1] (numeric) = -4.96467338452 0.318424151735
y[1] (closed_form) = -4.96467260651 0.318437390976
absolute error = 1.326e-05
relative error = 0.0002666 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.96
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6941 2.599
h = 0.003 0.006
y[1] (numeric) = -4.96506393996 0.318952391041
y[1] (closed_form) = -4.96506325279 0.318965579947
absolute error = 1.321e-05
relative error = 0.0002654 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.96
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6971 2.605
h = 0.0001 0.005
y[1] (numeric) = -4.96528156228 0.320032898355
y[1] (closed_form) = -4.9652808468 0.320046542285
absolute error = 1.366e-05
relative error = 0.0002746 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.96
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6972 2.61
h = 0.0001 0.003
y[1] (numeric) = -4.96577498496 0.320691935993
y[1] (closed_form) = -4.96577423711 0.320705285853
absolute error = 1.337e-05
relative error = 0.0002687 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.96
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6973 2.613
h = 0.001 0.001
y[1] (numeric) = -4.96606639036 0.321091379663
y[1] (closed_form) = -4.96606552995 0.32110470244
absolute error = 1.335e-05
relative error = 0.0002683 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.96
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7036.1MB, alloc=84.3MB, time=85.73
x[1] = 10.6983 2.614
h = 0.001 0.003
y[1] (numeric) = -4.96603814061 0.321322700304
y[1] (closed_form) = -4.96603722969 0.321335991028
absolute error = 1.332e-05
relative error = 0.0002677 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.96
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6993 2.617
h = 0.0001 0.004
y[1] (numeric) = -4.96621287313 0.321813744388
y[1] (closed_form) = -4.96621206775 0.321827096219
absolute error = 1.338e-05
relative error = 0.0002688 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.97
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.6994 2.621
h = 0.003 0.006
y[1] (numeric) = -4.96660655207 0.322343546608
y[1] (closed_form) = -4.96660583755 0.322356848284
absolute error = 1.332e-05
relative error = 0.0002676 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.97
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.7024 2.627
h = 0.0001 0.005
y[1] (numeric) = -4.96682780064 0.32342865128
y[1] (closed_form) = -4.96682705711 0.323442407598
absolute error = 1.378e-05
relative error = 0.0002768 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.97
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.7025 2.632
h = 0.0001 0.003
y[1] (numeric) = -4.96732513351 0.32408962501
y[1] (closed_form) = -4.9673243581 0.324103087425
absolute error = 1.348e-05
relative error = 0.0002709 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.97
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.7026 2.635
h = 0.001 0.001
y[1] (numeric) = -4.96761886982 0.324490262793
y[1] (closed_form) = -4.96761798197 0.324503697968
absolute error = 1.346e-05
relative error = 0.0002705 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.97
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.7036 2.636
h = 0.001 0.003
y[1] (numeric) = -4.96759103751 0.324722744536
y[1] (closed_form) = -4.96759009924 0.324736147602
absolute error = 1.344e-05
relative error = 0.0002699 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.97
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.7046 2.639
h = 0.0001 0.004
y[1] (numeric) = -4.96776776584 0.325215693127
y[1] (closed_form) = -4.96776693293 0.325229157421
absolute error = 1.349e-05
relative error = 0.000271 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.98
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.7047 2.643
h = 0.003 0.006
y[1] (numeric) = -4.96816456351 0.325747062027
y[1] (closed_form) = -4.96816382147 0.325760476347
absolute error = 1.343e-05
relative error = 0.0002698 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.98
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7124.0MB, alloc=84.3MB, time=86.85
x[1] = 10.7077 2.649
h = 0.0001 0.005
y[1] (numeric) = -4.96838942837 0.326836766355
y[1] (closed_form) = -4.96838865663 0.326850634932
absolute error = 1.389e-05
relative error = 0.000279 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.98
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.7078 2.654
h = 0.0001 0.003
y[1] (numeric) = -4.96889066548 0.3274996809
y[1] (closed_form) = -4.96888986234 0.327513255743
absolute error = 1.360e-05
relative error = 0.0002731 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.98
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.7079 2.657
h = 0.001 0.001
y[1] (numeric) = -4.96918672907 0.32790151558
y[1] (closed_form) = -4.96918581362 0.327915063026
absolute error = 1.358e-05
relative error = 0.0002727 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.98
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.7089 2.658
h = 0.0001 0.004
y[1] (numeric) = -4.96915931206 0.328135158217
y[1] (closed_form) = -4.96915834628 0.328148673499
absolute error = 1.355e-05
relative error = 0.0002721 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.98
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.709 2.662
h = 0.003 0.006
y[1] (numeric) = -4.96955865913 0.328667806282
y[1] (closed_form) = -4.9695579342 0.328681307053
absolute error = 1.352e-05
relative error = 0.0002715 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.98
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.712 2.668
h = 0.0001 0.005
y[1] (numeric) = -4.96978668363 0.329761428739
y[1] (closed_form) = -4.96978592841 0.329775383442
absolute error = 1.398e-05
relative error = 0.0002806 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.99
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.7121 2.673
h = 0.0001 0.003
y[1] (numeric) = -4.97029129978 0.330425971224
y[1] (closed_form) = -4.97029051358 0.330439632335
absolute error = 1.368e-05
relative error = 0.0002747 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.99
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.7122 2.676
h = 0.001 0.001
y[1] (numeric) = -4.97058937803 0.330828810708
y[1] (closed_form) = -4.97058847962 0.330842444286
absolute error = 1.366e-05
relative error = 0.0002743 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.99
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7211.9MB, alloc=84.3MB, time=87.98
x[1] = 10.7132 2.677
h = 0.001 0.003
y[1] (numeric) = -4.9705623306 0.33106344752
y[1] (closed_form) = -4.97056138195 0.331077048885
absolute error = 1.363e-05
relative error = 0.0002737 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.99
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.7142 2.68
h = 0.0001 0.004
y[1] (numeric) = -4.97074278347 0.331559920887
y[1] (closed_form) = -4.97074193984 0.331573583704
absolute error = 1.369e-05
relative error = 0.0002748 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.99
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.7143 2.684
h = 0.003 0.006
y[1] (numeric) = -4.97114539035 0.332094177949
y[1] (closed_form) = -4.97114463762 0.332107791128
absolute error = 1.363e-05
relative error = 0.0002737 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 12.99
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.7173 2.69
h = 0.0001 0.005
y[1] (numeric) = -4.97137701268 0.333192404365
y[1] (closed_form) = -4.97137622895 0.33320647109
absolute error = 1.409e-05
relative error = 0.0002828 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 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] = 10.7174 2.695
h = 0.0001 0.003
y[1] (numeric) = -4.971885522 0.333858896456
y[1] (closed_form) = -4.97188470778 0.333872669758
absolute error = 1.380e-05
relative error = 0.0002769 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 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] = 10.7175 2.698
h = 0.001 0.001
y[1] (numeric) = -4.97218592082 0.33426293802
y[1] (closed_form) = -4.97218499452 0.334276683634
absolute error = 1.378e-05
relative error = 0.0002765 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 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] = 10.7185 2.699
h = 0.001 0.003
y[1] (numeric) = -4.97215928472 0.334498735348
y[1] (closed_form) = -4.97215830826 0.334512448694
absolute error = 1.375e-05
relative error = 0.0002759 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 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] = 10.7195 2.702
h = 0.0001 0.004
y[1] (numeric) = -4.97234172057 0.334997118167
y[1] (closed_form) = -4.97234084898 0.335010893085
absolute error = 1.380e-05
relative error = 0.000277 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 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] = 10.7196 2.706
h = 0.003 0.006
y[1] (numeric) = -4.9727474325 0.335532952626
y[1] (closed_form) = -4.9727466518 0.335546678085
absolute error = 1.375e-05
relative error = 0.0002758 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 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
memory used=7300.0MB, alloc=84.3MB, time=89.10
x[1] = 10.7226 2.712
h = 0.0001 0.005
y[1] (numeric) = -4.97298264272 0.336635785202
y[1] (closed_form) = -4.97298183033 0.336649963816
absolute error = 1.420e-05
relative error = 0.0002849 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 13.01
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] = 10.7227 2.717
h = 0.0001 0.003
y[1] (numeric) = -4.97349503923 0.337304231547
y[1] (closed_form) = -4.97349419684 0.337318116912
absolute error = 1.391e-05
relative error = 0.0002791 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 13.01
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] = 10.7228 2.72
h = 0.001 0.001
y[1] (numeric) = -4.97379775499 0.337709477931
y[1] (closed_form) = -4.97379680064 0.337723335453
absolute error = 1.389e-05
relative error = 0.0002786 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 13.01
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] = 10.7238 2.721
h = 0.001 0.003
y[1] (numeric) = -4.97377152808 0.337946435549
y[1] (closed_form) = -4.97377052367 0.337960260748
absolute error = 1.386e-05
relative error = 0.0002781 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 13.01
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] = 10.7248 2.724
h = 0.0001 0.004
y[1] (numeric) = -4.97395594245 0.338446729498
y[1] (closed_form) = -4.97395504271 0.338460616388
absolute error = 1.392e-05
relative error = 0.0002791 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 13.01
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] = 10.7249 2.728
h = 0.003 0.006
y[1] (numeric) = -4.9743647546 0.33898414504
y[1] (closed_form) = -4.97436394577 0.338997982651
absolute error = 1.386e-05
relative error = 0.000278 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 13.01
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] = 10.7279 2.734
h = 0.0001 0.005
y[1] (numeric) = -4.97460354278 0.340091585939
y[1] (closed_form) = -4.97460270159 0.340105876314
absolute error = 1.432e-05
relative error = 0.0002871 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 13.02
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] = 10.728 2.739
h = 0.0001 0.003
y[1] (numeric) = -4.9751198205 0.340761991162
y[1] (closed_form) = -4.97511894978 0.340775988462
absolute error = 1.402e-05
relative error = 0.0002812 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 13.02
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] = 10.7281 2.742
h = 0.001 0.001
y[1] (numeric) = -4.97542484957 0.34116844509
y[1] (closed_form) = -4.97542386702 0.341182414392
absolute error = 1.400e-05
relative error = 0.0002808 %
Correct digits = 6
memory used=7387.3MB, alloc=340.3MB, time=90.25
Radius of convergence (given) for eq 1 = 13.02
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] = 10.7291 2.743
h = 0.001 0.003
y[1] (numeric) = -4.97539902973 0.341406562765
y[1] (closed_form) = -4.97539799721 0.341420499691
absolute error = 1.398e-05
relative error = 0.0002802 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 13.02
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] = 10.7301 2.746
h = 0.0001 0.004
y[1] (numeric) = -4.97558541812 0.341908769507
y[1] (closed_form) = -4.9755844901 0.341922768241
absolute error = 1.403e-05
relative error = 0.0002813 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 13.02
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] = 10.7302 2.75
h = 0.003 0.006
y[1] (numeric) = -4.97599732569 0.342447769798
y[1] (closed_form) = -4.97599648859 0.342461719431
absolute error = 1.397e-05
relative error = 0.0002802 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 13.02
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] = 10.7332 2.756
h = 0.0001 0.005
y[1] (numeric) = -4.97623968193 0.34355982115
y[1] (closed_form) = -4.97623881177 0.343574223157
absolute error = 1.443e-05
relative error = 0.0002893 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 13.03
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.7333 2.761
h = 0.0001 0.003
y[1] (numeric) = -4.97675983485 0.344232189849
y[1] (closed_form) = -4.97675893565 0.344246298954
absolute error = 1.414e-05
relative error = 0.0002834 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 13.03
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.7334 2.764
h = 0.001 0.001
y[1] (numeric) = -4.97706717359 0.34463985403
y[1] (closed_form) = -4.9770661627 0.344653934984
absolute error = 1.412e-05
relative error = 0.000283 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 13.03
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.7344 2.765
h = 0.0001 0.004
y[1] (numeric) = -4.97704175871 0.344879131524
y[1] (closed_form) = -4.97704069791 0.344893180048
absolute error = 1.409e-05
relative error = 0.0002824 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 13.03
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.7345 2.769
h = 0.003 0.006
y[1] (numeric) = -4.97745619663 0.345419425718
y[1] (closed_form) = -4.97745537592 0.345433461617
absolute error = 1.406e-05
relative error = 0.0002818 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 13.03
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7475.2MB, alloc=340.3MB, time=91.36
x[1] = 10.7375 2.775
h = 0.0001 0.005
y[1] (numeric) = -4.97770167115 0.346535404934
y[1] (closed_form) = -4.9777008168 0.346549892875
absolute error = 1.451e-05
relative error = 0.0002909 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 13.04
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.7376 2.78
h = 0.0001 0.003
y[1] (numeric) = -4.97822517838 0.347209421324
y[1] (closed_form) = -4.9782242954 0.34722361651
absolute error = 1.422e-05
relative error = 0.000285 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 13.04
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.7377 2.783
h = 0.001 0.001
y[1] (numeric) = -4.97853451676 0.347618101955
y[1] (closed_form) = -4.9785335222 0.347632268856
absolute error = 1.420e-05
relative error = 0.0002846 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 13.04
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.7387 2.784
h = 0.001 0.003
y[1] (numeric) = -4.97850946255 0.347858372796
y[1] (closed_form) = -4.97850841817 0.347872507221
absolute error = 1.417e-05
relative error = 0.000284 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 13.04
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.7397 2.787
h = 0.0001 0.004
y[1] (numeric) = -4.97869953504 0.348364119775
y[1] (closed_form) = -4.97869859483 0.348378316225
absolute error = 1.423e-05
relative error = 0.0002851 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 13.04
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.7398 2.791
h = 0.003 0.006
y[1] (numeric) = -4.97911720862 0.348906041862
y[1] (closed_form) = -4.97911635934 0.348920189546
absolute error = 1.417e-05
relative error = 0.000284 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 13.04
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.7428 2.797
h = 0.0001 0.005
y[1] (numeric) = -4.97936623279 0.350026635523
y[1] (closed_form) = -4.97936534919 0.350041234853
absolute error = 1.463e-05
relative error = 0.000293 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 13.05
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.7429 2.802
h = 0.0001 0.003
y[1] (numeric) = -4.97989360412 0.350702623946
y[1] (closed_form) = -4.97989269237 0.350716930699
absolute error = 1.434e-05
relative error = 0.0002872 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 13.05
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.743 2.805
h = 0.001 0.001
y[1] (numeric) = -4.98020524544 0.351112519873
y[1] (closed_form) = -4.98020422223 0.351126798189
absolute error = 1.431e-05
relative error = 0.0002867 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 13.05
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7563.2MB, alloc=340.3MB, time=92.47
x[1] = 10.744 2.806
h = 0.001 0.003
y[1] (numeric) = -4.98018059223 0.351353950098
y[1] (closed_form) = -4.98017951929 0.351368195884
absolute error = 1.429e-05
relative error = 0.0002861 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 13.05
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.745 2.809
h = 0.0001 0.004
y[1] (numeric) = -4.98037262594 0.351861614584
y[1] (closed_form) = -4.980371657 0.351875922511
absolute error = 1.434e-05
relative error = 0.0002872 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 13.05
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.7451 2.813
h = 0.003 0.006
y[1] (numeric) = -4.98079338119 0.35240513185
y[1] (closed_form) = -4.9807925032 0.352419391189
absolute error = 1.429e-05
relative error = 0.0002861 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 13.05
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.7481 2.819
h = 0.0001 0.005
y[1] (numeric) = -4.98104594512 0.353530341989
y[1] (closed_form) = -4.98104503213 0.353545052577
absolute error = 1.474e-05
relative error = 0.0002952 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 13.06
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] = 10.7482 2.824
h = 0.0001 0.003
y[1] (numeric) = -4.98157717455 0.35420830697
y[1] (closed_form) = -4.98157623388 0.35422272516
absolute error = 1.445e-05
relative error = 0.0002893 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 13.06
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] = 10.7483 2.827
h = 0.001 0.001
y[1] (numeric) = -4.98189111515 0.354619420858
y[1] (closed_form) = -4.98189006315 0.354633810459
absolute error = 1.443e-05
relative error = 0.0002889 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 13.06
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] = 10.7493 2.828
h = 0.001 0.003
y[1] (numeric) = -4.98186686084 0.354862010209
y[1] (closed_form) = -4.9818657592 0.354876367227
absolute error = 1.440e-05
relative error = 0.0002883 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 13.06
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] = 10.7503 2.831
h = 0.0001 0.004
y[1] (numeric) = -4.98206085129 0.3553715938
y[1] (closed_form) = -4.98205985348 0.355386013074
absolute error = 1.445e-05
relative error = 0.0002894 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 13.06
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7651.2MB, alloc=340.3MB, time=93.60
x[1] = 10.7504 2.835
h = 0.003 0.006
y[1] (numeric) = -4.98248468339 0.355916709832
y[1] (closed_form) = -4.98248377652 0.355931080697
absolute error = 1.440e-05
relative error = 0.0002883 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 13.06
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] = 10.7534 2.841
h = 0.0001 0.005
y[1] (numeric) = -4.98274077719 0.357046538447
y[1] (closed_form) = -4.98273983465 0.357061360163
absolute error = 1.485e-05
relative error = 0.0002973 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 13.07
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.7535 2.846
h = 0.0001 0.003
y[1] (numeric) = -4.9832758587 0.357726484485
y[1] (closed_form) = -4.98327488896 0.357741013982
absolute error = 1.456e-05
relative error = 0.0002915 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 13.07
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.7536 2.849
h = 0.001 0.001
y[1] (numeric) = -4.98359209494 0.358138818983
y[1] (closed_form) = -4.983591014 0.35815331974
absolute error = 1.454e-05
relative error = 0.000291 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 13.07
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.7546 2.85
h = 0.001 0.003
y[1] (numeric) = -4.98356823742 0.358382567197
y[1] (closed_form) = -4.98356710692 0.358397035319
absolute error = 1.451e-05
relative error = 0.0002905 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 13.07
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.7556 2.853
h = 0.0001 0.004
y[1] (numeric) = -4.98376418014 0.358894071475
y[1] (closed_form) = -4.98376315329 0.358908601966
absolute error = 1.457e-05
relative error = 0.0002915 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 13.07
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.7557 2.857
h = 0.003 0.006
y[1] (numeric) = -4.98419108425 0.359440789839
y[1] (closed_form) = -4.98419014836 0.359455272099
absolute error = 1.451e-05
relative error = 0.0002904 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 13.07
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.7587 2.863
h = 0.0001 0.005
y[1] (numeric) = -4.98445069806 0.360575238896
y[1] (closed_form) = -4.98444972582 0.360590171608
absolute error = 1.496e-05
relative error = 0.0002994 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 13.08
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.7588 2.868
h = 0.0001 0.003
y[1] (numeric) = -4.98498962562 0.361257170463
y[1] (closed_form) = -4.98498862666 0.361271811137
absolute error = 1.467e-05
relative error = 0.0002936 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 13.08
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
memory used=7739.1MB, alloc=340.3MB, time=94.72
x[1] = 10.7589 2.871
h = 0.001 0.001
y[1] (numeric) = -4.98530815387 0.361670728205
y[1] (closed_form) = -4.98530704383 0.361685339988
absolute error = 1.465e-05
relative error = 0.0002932 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 13.08
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
x[1] = 10.7599 2.872
h = 0.001 0.003
y[1] (numeric) = -4.98528469102 0.361915635015
y[1] (closed_form) = -4.98528353152 0.36193021411
absolute error = 1.463e-05
relative error = 0.0002926 %
Correct digits = 6
Radius of convergence (given) for eq 1 = 13.08
Order of pole (given) = 0.5 0
NO POLE (ratio test) for Equation 1
NO REAL POLE (three term test) for Equation 1
NO COMPLEX POLE (six term test) for Equation 1
Finished!
diff ( y , x , 1 ) = ln ( sqrt ( 0.1 * x + 0.2 ) ) ;
Iterations = 754
Total Elapsed Time = 1 Minutes 34 Seconds
Expected Time Remaining = 0 Seconds
Optimized Time Remaining = 0 Seconds
Expected Total Time = 1 Minutes 34 Seconds
> quit
memory used=7768.5MB, alloc=340.3MB, time=95.06